Finite Group Databasebeta

← C37×#61066 #22682319

Subgroups — C37×#61066 #22682319

Order 9472.

2912 conjugacy classes of subgroups.

The subgroup lattice has 1616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#575C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
3D4×#41×C37C211yesmaximal, characteristic, complemented
4C2×C37×#546C211yesmaximal, characteristic, complemented
5C37×#3282C212yesmaximal, complemented
6C37×#3280C212yesmaximal, complemented
7C37×#3275C212yesmaximal, complemented
8C37×#3273C212yesmaximal, complemented
9C37×#3268C212yesmaximal, complemented
10C37×#3267C212yesmaximal, complemented
11C37×#3266C212yesmaximal, complemented
12C37×#3264C212yesmaximal, complemented
13C37×#3153C211yesmaximal, characteristic, complemented
14C37×#3056C211yesmaximal, characteristic, complemented
15C37×#3055C211yesmaximal, characteristic, complemented
16C37×#3040C211yesmaximal, characteristic, complemented
17C37×#3036C211yesmaximal, characteristic, complemented
18C37×#3007C211yesmaximal, characteristic, complemented
19C37×#3006C211yesmaximal, characteristic, complemented
20C37×#3005C211yesmaximal, characteristic, complemented
21C37×#3003C211yesmaximal, characteristic, complemented
22C4×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
23D4×M16×C37C211yesmaximal, characteristic, complemented
24C22×#41×C37C2211yescharacteristic
25C22×#41×C37C2211yescharacteristic, complemented
26C22×#41×C37C2211yescharacteristic, complemented
27C23×D4×C37C2211yescharacteristic, complemented
28C37×#575—28no—
29C2×#137×C37C2211yescharacteristic, complemented
30C2×#137×C37C2211yescharacteristic, complemented
31C2×#137×C37C2211yescharacteristic, complemented
32C2×#137×C37C2212yescomplemented
33C2×AGL(1,ℤ/8)×C37—28no—
34C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
35C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
36C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
38C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
39C2×AGL(1,ℤ/8)×C37C2212yescomplemented
40C2×AGL(1,ℤ/8)×C37C2212yescomplemented
41C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
42C2×AGL(1,ℤ/8)×C37C2212yescomplemented
43C2×#135×C37C2212yescomplemented
44C2×#135×C37C2212yescomplemented
45C22×SD16×C37C2212yescomplemented
46C22×D8×C37C2212yescomplemented
47C22×M16×C37C2211yescharacteristic, complemented
48C22×M16×C37C2211yescharacteristic, complemented
49C37×#550C2211yescharacteristic, complemented
50D4×Q8×C37C2211yescharacteristic, complemented
51C37×#548C2211yescharacteristic, complemented
52C37×#548C2211yescharacteristic, complemented
53C37×#547—21no—
54C37×#547C2211yescharacteristic, complemented
55C37×#546—21no—
56C37×#546—21no—
57C37×#546—21no—
58C37×#546—21no—
59C37×#546—21no—
60C37×#546—21no—
61C37×#546C2212yes—
62C37×#546C2212yescomplemented
63C37×#546C2212yescomplemented
64C37×#546C2212yescomplemented
65C37×#546C2211yescharacteristic, complemented
66C37×#546C2211yescharacteristic, complemented
67D42×C37—21no—
68D42×C37C2211yescharacteristic, complemented
69C37×#532—21no—
70C37×#532C2211yescharacteristic, complemented
71C2×#124×C37C2211yescharacteristic, complemented
72C37×#525—21no—
73C37×#525—21no—
74C37×#525C2211yescharacteristic
75C37×#525C2211yescharacteristic, complemented
76C2×#123×C37—21no—
77C2×C22⋊Q8×C37C2211yescharacteristic, complemented
78C2×#121×C37—21no—
79C2×#121×C37C2211yescharacteristic, complemented
80C2×#120×C37—21no—
81C4×#41×C37C2211yescharacteristic, complemented
82C2×C4×D4×C37—21no—
83C2×C4×D4×C37C2211yescharacteristic
84C2×C4×D4×C37C2211yescharacteristic, complemented
85C22×C22⋊C4×C37—21no—
86C37×#497C2212yescomplemented
87C37×#496C2212yescomplemented
88C37×#495C2212yescomplemented
89C37×#495C2212yescomplemented
90C37×#470C2212yescomplemented
91C37×#469C2212yescomplemented
92C37×#468C2212yescomplemented
93C37×#468C2212yescomplemented
94C37×#467C2212yescomplemented
95C37×#466C2212yescomplemented
96C37×#465C2212yescomplemented
97C37×#465C2212yescomplemented
98C37×#464C2212yescomplemented
99C37×#464C2212yescomplemented
100C37×#463C2212yescomplemented
101C37×#463C2212yescomplemented
102C37×#463C2212yescomplemented
103C37×#463C2212yescomplemented
104C37×#461C2212yescomplemented
105C37×#459C2212yescomplemented
106C37×#452C2212yescomplemented
107C37×#452C2212yescomplemented
108C37×#452C2212yescomplemented
109C37×#452C2212yescomplemented
110C37×#451C2212yescomplemented
111C37×#450C2212yescomplemented
112C37×#450C2212yescomplemented
113C37×#450C2212yescomplemented
114C37×#449C2212yescomplemented
115C37×#449C2212yescomplemented
116C37×#449C2212yescomplemented
117C37×#449C2212yescomplemented
118C37×#448C2212yescomplemented
119C37×#447C2212yescomplemented
120C37×#447C2212yescomplemented
121C37×#447C2212yescomplemented
122C37×#442C2212yescomplemented
123C37×#440C2212yescomplemented
124C4×SD16×C37C2212yescomplemented
125C4×D8×C37C2212yescomplemented
126C37×#436C2212yescomplemented
127C37×#435C2212yescomplemented
128C37×#435C2212yescomplemented
129C8×D4×C37C2212yescomplemented
130C37×#428C2211yescharacteristic, complemented
131C37×#423C2211yescharacteristic, complemented
132C37×#419C2211yescharacteristic, complemented
133C37×#418C2211yescharacteristic, complemented
134C37×#418C2211yescharacteristic, complemented
135C37×#417C2211yescharacteristic, complemented
136C37×#417C2211yescharacteristic, complemented
137C37×#417C2211yescharacteristic, complemented
138C37×#407C2211yescharacteristic, complemented
139C37×#407C2211yescharacteristic, complemented
140C4×M16×C37C2211yescharacteristic, complemented
141C25×C37—21no—
142C2×#41×C37—21no—
143C2×#41×C37—21no—
144C2×#41×C37—21no—
145C2×#41×C37—21no—
146C2×#41×C37—21no—
147C2×#41×C37—21no—
148C2×#41×C37—24no—
149C2×#41×C37—24no—
150C2×#41×C37—24no—
151C2×#41×C37—42no—
152C2×#41×C37—42no—
153C2×#41×C37—42no—
154C2×#41×C37C2311yescharacteristic
155C2×#41×C37C2311yescharacteristic
156C2×#41×C37C2312yes—
157C2×#41×C37C2312yes—
158C2×#41×C37C2311yescharacteristic
159C2×#41×C37C2311yescharacteristic
160C2×#41×C37C2311yescharacteristic
161C2×#41×C37C2311yescharacteristic, complemented
162C2×#41×C37C2311yescharacteristic, complemented
163C22×Q8×C37C2311yescharacteristic
164C22×Q8×C37C2311yescharacteristic
165C22×Q8×C37C2311yescharacteristic, complemented
166C22×D4×C37—24no—
167C22×D4×C37—21no—
168C22×D4×C37—21no—
169C22×D4×C37—21no—
170C22×D4×C37—21no—
171C22×D4×C37—21no—
172C22×D4×C37—21no—
173C22×D4×C37—21no—
174C22×D4×C37—21no—
175C22×D4×C37—42no—
176C22×D4×C37D411yescharacteristic
177C22×D4×C37C2311yescharacteristic
178C22×D4×C37C2311yescharacteristic
179C22×D4×C37C2312yes—
180C22×D4×C37C2312yes—
181C22×D4×C37C2311yescharacteristic
182C22×D4×C37C2311yescharacteristic, complemented
183C23×C4×C37—21no—
184C23×C4×C37—21no—
185C23×C4×C37—21no—
186C23×C4×C37—21no—
187C23×C4×C37C2311yescharacteristic
188C23×C4×C37C2311yescharacteristic
189#137×C37—24no—
190#137×C37—28no—
191#137×C37—24no—
192#137×C37—42no—
193AGL(1,ℤ/8)×C37—24no—
194AGL(1,ℤ/8)×C37—24no—
195AGL(1,ℤ/8)×C37—24no—
196AGL(1,ℤ/8)×C37—28no—
197AGL(1,ℤ/8)×C37—28no—
198AGL(1,ℤ/8)×C37—28no—
199AGL(1,ℤ/8)×C37—24no—
200AGL(1,ℤ/8)×C37—42no—
201AGL(1,ℤ/8)×C37D418yescomplemented
202#135×C37—28no—
203#135×C37—28no—
204C2×Q16×C37C2312yescomplemented
205C2×Q16×C37C2312yescomplemented
206C2×Q16×C37C2312yescomplemented
207C2×SD16×C37—28no—
208C2×SD16×C37C2312yes—
209C2×SD16×C37C2312yes—
210C2×SD16×C37C2312yes—
211C2×SD16×C37C2312yes—
212C2×SD16×C37C2312yes—
213C2×SD16×C37C2312yes—
214C2×SD16×C37C2312yescomplemented
215C2×SD16×C37C2312yescomplemented
216C2×SD16×C37C2312yescomplemented
217C2×D8×C37—28no—
218C2×D8×C37C2312yes—
219C2×D8×C37C2312yes—
220C2×D8×C37C2312yes—
221C2×D8×C37C2312yes—
222C2×D8×C37C2312yes—
223C2×D8×C37C2312yes—
224C2×M16×C37—24no—
225C2×M16×C37—24no—
226C2×M16×C37C2311yescharacteristic
227C2×M16×C37C2312yes—
228C2×M16×C37C2311yescharacteristic
229C2×M16×C37C2311yescharacteristic
230C2×M16×C37C2311yescharacteristic
231C2×M16×C37C2312yescomplemented
232C22×C8×C37C2312yes—
233C22×C8×C37C2312yescomplemented
234C4⋊Q8×C37—21no—
235C4⋊Q8×C37C2311yescharacteristic, complemented
236#127×C37—21no—
237#127×C37C2311yescharacteristic, complemented
238#124×C37—21no—
239#124×C37—21no—
240#124×C37—21no—
241#124×C37—21no—
242#124×C37C2312yes—
243#124×C37C2312yes—
244#124×C37C2311yescharacteristic, complemented
245#124×C37C2311yescharacteristic, complemented
246#123×C37—21no—
247#123×C37—21no—
248#123×C37—22no—
249#123×C37—22no—
250#123×C37—22no—
251#123×C37—22no—
252#123×C37—21no—
253#123×C37—21no—
254#123×C37—21no—
255#123×C37—21no—
256C22⋊Q8×C37—21no—
257C22⋊Q8×C37—21no—
258C22⋊Q8×C37—21no—
259C22⋊Q8×C37—21no—
260C22⋊Q8×C37—21no—
261C22⋊Q8×C37—21no—
262C22⋊Q8×C37C2312yes—
263C22⋊Q8×C37C2312yes—
264C22⋊Q8×C37C2311yescharacteristic
265C22⋊Q8×C37C2311yescharacteristic
266C22⋊Q8×C37C2311yescharacteristic, complemented
267C22⋊Q8×C37C2311yescharacteristic, complemented
268#121×C37—21no—
269#121×C37—21no—
270#121×C37—21no—
271#121×C37—21no—
272#121×C37—21no—
273#121×C37—21no—
274#121×C37—21no—
275#121×C37—21no—
276#121×C37—22no—
277#121×C37—22no—
278#121×C37—22no—
279#121×C37—22no—
280#121×C37—21no—
281#121×C37—21no—
282#121×C37—21no—
283#121×C37—21no—
284#121×C37C2312yes—
285#121×C37C2312yes—
286#121×C37C2311yescharacteristic
287#121×C37C2311yescharacteristic
288#121×C37C2311yescharacteristic, complemented
289#121×C37C2311yescharacteristic, complemented
290#120×C37—21no—
291#120×C37—21no—
292#120×C37—22no—
293#120×C37—22no—
294#120×C37—22no—
295#120×C37—22no—
296#120×C37—21no—
297#120×C37—21no—
298#120×C37—21no—
299#120×C37—21no—
300C4×Q8×C37C2311yescharacteristic, complemented
301C4×Q8×C37C2311yescharacteristic, complemented
302C4×D4×C37—21no—
303C4×D4×C37—21no—
304C4×D4×C37—21no—
305C4×D4×C37—21no—
306C4×D4×C37—21no—
307C4×D4×C37—21no—
308C4×D4×C37—21no—
309C4×D4×C37—21no—
310C4×D4×C37—21no—
311C4×D4×C37—21no—
312C4×D4×C37—21no—
313C4×D4×C37—21no—
314C4×D4×C37—21no—
315C4×D4×C37—21no—
316C4×D4×C37D411yescharacteristic
317C4×D4×C37D411yescharacteristic
318C4×D4×C37D411yescharacteristic
319C4×D4×C37D411yescharacteristic
320C4×D4×C37C2312yes—
321C4×D4×C37C2312yes—
322C4×D4×C37C2311yescharacteristic
323C4×D4×C37C2311yescharacteristic
324C4×D4×C37C2311yescharacteristic
325C4×D4×C37C2311yescharacteristic
326C4×D4×C37C2311yescharacteristic, complemented
327C4×D4×C37C2311yescharacteristic, complemented
328#117×C37—21no—
329#117×C37C2311yescharacteristic
330C2×C4⋊C4×C37—21no—
331C2×C4⋊C4×C37—21no—
332C2×C4⋊C4×C37D411yescharacteristic
333C2×C4⋊C4×C37C2311yescharacteristic
334C2×C22⋊C4×C37—21no—
335C2×C22⋊C4×C37—21no—
336C2×C22⋊C4×C37—21no—
337C2×C22⋊C4×C37—21no—
338C2×C22⋊C4×C37—21no—
339C2×C22⋊C4×C37—22no—
340C2×C22⋊C4×C37—22no—
341C2×C22⋊C4×C37—22no—
342C2×C22⋊C4×C37—22no—
343C2×C22⋊C4×C37—21no—
344C2×C22⋊C4×C37—21no—
345C2×C22⋊C4×C37D411yescharacteristic
346C2×C22⋊C4×C37D411yescharacteristic
347C2×C42×C37—21no—
348C2×C42×C37C2311yescharacteristic
349#107×C37C2312yescomplemented
350#106×C37C2312yescomplemented
351C4⋊C8×C37C2312yescomplemented
352C4⋊C8×C37C2312yescomplemented
353#103×C37C2312yescomplemented
354#103×C37C2312yescomplemented
355#103×C37C2312yescomplemented
356#103×C37C2312yescomplemented
357#103×C37C2312yescomplemented
358#102×C37C2312yes—
359#102×C37C2312yes—
360#102×C37C2312yes—
361#102×C37C2312yes—
362#102×C37C2312yescomplemented
363#102×C37C2312yescomplemented
364#102×C37C2312yescomplemented
365C22⋊C8×C37C2312yes—
366C22⋊C8×C37C2312yes—
367C22⋊C8×C37C2312yescomplemented
368C22⋊C8×C37C2312yescomplemented
369#97×C37C2312yescomplemented
370C4×C8×C37C2312yescomplemented
371C24×C37—21no—
372C24×C37—21no—
373C24×C37—22no—
374C24×C37—22no—
375C24×C37—21no—
376C24×C37—21no—
377C24×C37—44no—
378C24×C37—44no—
379C24×C37—82no—
380C24×C37C2×D411yescharacteristic
381C24×C37C2×D411yescharacteristic
382#41×C37—22no—
383#41×C37—22no—
384#41×C37—22no—
385#41×C37—24no—
386#41×C37—22no—
387#41×C37—22no—
388#41×C37—24no—
389#41×C37—22no—
390#41×C37—22no—
391#41×C37—22no—
392#41×C37—22no—
393#41×C37—44no—
394#41×C37—44no—
395#41×C37—41no—
396#41×C37—41no—
397#41×C37—42no—
398#41×C37—42no—
399#41×C37—41no—
400#41×C37—41no—
401#41×C37—44no—
402#41×C37—44no—
403#41×C37—44no—
404#41×C37—44no—
405#41×C37C2×D414yes—
406C2×Q8×C37—21no—
407C2×Q8×C37—21no—
408C2×Q8×C37—21no—
409C2×Q8×C37—22no—
410C2×Q8×C37—22no—
411C2×Q8×C37—22no—
412C2×Q8×C37—22no—
413C2×Q8×C37—41no—
414C2×Q8×C37—41no—
415C2×Q8×C37C2412yes—
416C2×Q8×C37C2411yescharacteristic
417C2×Q8×C37C2411yescharacteristic
418C2×Q8×C37C2411yescharacteristic
419C2×D4×C37—21no—
420C2×D4×C37—22no—
421C2×D4×C37—24no—
422C2×D4×C37—24no—
423C2×D4×C37—22no—
424C2×D4×C37—21no—
425C2×D4×C37—21no—
426C2×D4×C37—22no—
427C2×D4×C37—22no—
428C2×D4×C37—21no—
429C2×D4×C37—21no—
430C2×D4×C37—21no—
431C2×D4×C37—21no—
432C2×D4×C37—21no—
433C2×D4×C37—21no—
434C2×D4×C37—21no—
435C2×D4×C37—21no—
436C2×D4×C37—22no—
437C2×D4×C37—22no—
438C2×D4×C37—21no—
439C2×D4×C37—22no—
440C2×D4×C37—21no—
441C2×D4×C37—21no—
442C2×D4×C37—21no—
443C2×D4×C37—22no—
444C2×D4×C37—22no—
445C2×D4×C37—21no—
446C2×D4×C37—21no—
447C2×D4×C37—22no—
448C2×D4×C37—22no—
449C2×D4×C37—42no—
450C2×D4×C37—42no—
451C2×D4×C37—41no—
452C2×D4×C37—41no—
453C2×D4×C37—44no—
454C2×D4×C37—44no—
455C2×D4×C37—44no—
456C2×D4×C37—42no—
457C2×D4×C37—44no—
458C2×D4×C37—44no—
459C2×D4×C37—44no—
460C2×D4×C37—44no—
461C2×D4×C37—82no—
462C2×D4×C37C2×D411yescharacteristic
463C2×D4×C37C2×D411yescharacteristic
464C2×D4×C37C2×D411yescharacteristic
465C2×D4×C37C2×D411yescharacteristic
466C2×D4×C37C2×D414yescomplemented
467C2×D4×C37C2412yes—
468C2×D4×C37C2411yescharacteristic
469C2×D4×C37C2411yescharacteristic
470C2×D4×C37C2412yes—
471C2×D4×C37C2411yescharacteristic
472C22×C4×C37—21no—
473C22×C4×C37—22no—
474C22×C4×C37—22no—
475C22×C4×C37—22no—
476C22×C4×C37—22no—
477C22×C4×C37—21no—
478C22×C4×C37—21no—
479C22×C4×C37—21no—
480C22×C4×C37—21no—
481C22×C4×C37—21no—
482C22×C4×C37—22no—
483C22×C4×C37—22no—
484C22×C4×C37—21no—
485C22×C4×C37—21no—
486C22×C4×C37—21no—
487C22×C4×C37—21no—
488C22×C4×C37—21no—
489C22×C4×C37—21no—
490C22×C4×C37—21no—
491C22×C4×C37—22no—
492C22×C4×C37—22no—
493C22×C4×C37—44no—
494C22×C4×C37—44no—
495C22×C4×C37—44no—
496C22×C4×C37—82no—
497C22×C4×C37C2×D411yescharacteristic
498C22×C4×C37C2×D411yescharacteristic
499C22×C4×C37C2×D411yescharacteristic
500C22×C4×C37C2×D411yescharacteristic
501C22×C4×C37C2×D411yescharacteristic
502C22×C4×C37C2×D411yescharacteristic
503C22×C4×C37C2×D411yescharacteristic
504C22×C4×C37C2×D411yescharacteristic
505C22×C4×C37C2411yescharacteristic
506C22×C4×C37C2411yescharacteristic
507C22×C4×C37C2411yescharacteristic
508C22×C4×C37C2411yescharacteristic
509C22×C4×C37C2411yescharacteristic
510Q16×C37—24no—
511Q16×C37—24no—
512Q16×C37—42no—
513SD16×C37—24no—
514SD16×C37—24no—
515SD16×C37—24no—
516SD16×C37—24no—
517SD16×C37—24no—
518SD16×C37—24no—
519SD16×C37—42no—
520SD16×C37—42no—
521SD16×C37C2×D418yescomplemented
522D8×C37—24no—
523D8×C37—24no—
524D8×C37—24no—
525D8×C37—24no—
526D8×C37—42no—
527D8×C37C2×D418yescomplemented
528M16×C37—22no—
529M16×C37—22no—
530M16×C37—22no—
531M16×C37—24no—
532M16×C37—24no—
533M16×C37C2×D414yescomplemented
534C2×C8×C37—24no—
535C2×C8×C37—24no—
536C2×C8×C37C2412yes—
537C2×C8×C37C2412yes—
538C2×C8×C37C2412yes—
539C2×C8×C37C2412yes—
540C4⋊C4×C37—21no—
541C4⋊C4×C37—21no—
542C4⋊C4×C37—21no—
543C4⋊C4×C37—22no—
544C4⋊C4×C37—22no—
545C4⋊C4×C37—21no—
546C4⋊C4×C37—21no—
547C4⋊C4×C37—21no—
548C4⋊C4×C37—21no—
549C4⋊C4×C37—21no—
550C4⋊C4×C37—21no—
551C4⋊C4×C37C2×D411yescharacteristic
552C4⋊C4×C37C2×D411yescharacteristic
553C4⋊C4×C37C2×D411yescharacteristic
554C4⋊C4×C37C2×D411yescharacteristic
555C4⋊C4×C37C2411yescharacteristic
556C4⋊C4×C37C2411yescharacteristic
557C4⋊C4×C37C2412yes—
558C22⋊C4×C37—22no—
559C22⋊C4×C37—22no—
560C22⋊C4×C37—21no—
561C22⋊C4×C37—21no—
562C22⋊C4×C37—21no—
563C22⋊C4×C37—21no—
564C22⋊C4×C37—21no—
565C22⋊C4×C37—22no—
566C22⋊C4×C37—22no—
567C22⋊C4×C37—22no—
568C22⋊C4×C37—22no—
569C22⋊C4×C37—21no—
570C22⋊C4×C37—21no—
571C22⋊C4×C37—21no—
572C22⋊C4×C37—21no—
573C22⋊C4×C37—22no—
574C22⋊C4×C37—22no—
575C22⋊C4×C37—22no—
576C22⋊C4×C37—22no—
577C22⋊C4×C37—21no—
578C22⋊C4×C37—21no—
579C22⋊C4×C37—21no—
580C22⋊C4×C37—21no—
581C22⋊C4×C37—21no—
582C22⋊C4×C37—21no—
583C22⋊C4×C37C2×D411yescharacteristic
584C22⋊C4×C37C2×D411yescharacteristic
585C22⋊C4×C37C2×D411yescharacteristic
586C22⋊C4×C37C2×D411yescharacteristic
587C22⋊C4×C37C2×D411yescharacteristic
588C22⋊C4×C37C2×D411yescharacteristic
589C22⋊C4×C37C2×D411yescharacteristic
590C22⋊C4×C37C2×D411yescharacteristic
591C42×C37—21no—
592C42×C37—21no—
593C42×C37—21no—
594C42×C37C2×D411yescharacteristic
595C42×C37C2×D411yescharacteristic
596C42×C37C2411yescharacteristic
597C42×C37C2411yescharacteristic
598C23×C37—22no—
599C23×C37—24no—
600C23×C37—22no—
601C23×C37—21no—
602C23×C37—22no—
603C23×C37—22no—
604C23×C37—22no—
605C23×C37—21no—
606C23×C37—21no—
607C23×C37—41no—
608C23×C37—41no—
609C23×C37—41no—
610C23×C37—42no—
611C23×C37—42no—
612C23×C37—44no—
613C23×C37—44no—
614C23×C37—42no—
615C23×C37—42no—
616C23×C37—42no—
617C23×C37—42no—
618C23×C37—42no—
619C23×C37—44no—
620C23×C37—42no—
621C23×C37—42no—
622C23×C37—44no—
623C23×C37—81no—
624C23×C37—81no—
625C23×C37—82no—
626C23×C37—82no—
627C23×C37—816no—
628C23×C37C22×D411yescharacteristic
629C23×C37C22×D411yescharacteristic
630C23×C37C22×D411yescharacteristic
631C23×C37C22×D411yescharacteristic
632C23×C37C22×D411yescharacteristic
633Q8×C37—21no—
634Q8×C37—21no—
635Q8×C37—21no—
636Q8×C37—22no—
637Q8×C37—21no—
638Q8×C37—22no—
639Q8×C37—21no—
640Q8×C37—42no—
641Q8×C37—42no—
642Q8×C37—42no—
643Q8×C37C22×D412yes—
644D4×C37—24no—
645D4×C37—22no—
646D4×C37—22no—
647D4×C37—24no—
648D4×C37—21no—
649D4×C37—22no—
650D4×C37—21no—
651D4×C37—22no—
652D4×C37—21no—
653D4×C37—21no—
654D4×C37—22no—
655D4×C37—21no—
656D4×C37—41no—
657D4×C37—41no—
658D4×C37—44no—
659D4×C37—44no—
660D4×C37—42no—
661D4×C37—42no—
662D4×C37—42no—
663D4×C37—42no—
664D4×C37—42no—
665D4×C37—44no—
666D4×C37—42no—
667D4×C37—44no—
668D4×C37—42no—
669D4×C37—42no—
670D4×C37—42no—
671D4×C37—42no—
672D4×C37—42no—
673D4×C37—42no—
674D4×C37—81no—
675D4×C37—81no—
676D4×C37—81no—
677D4×C37—82no—
678D4×C37—82no—
679D4×C37C22×D412yes—
680D4×C37C22×D414yes—
681C2×C4×C37—22no—
682C2×C4×C37—22no—
683C2×C4×C37—21no—
684C2×C4×C37—22no—
685C2×C4×C37—22no—
686C2×C4×C37—22no—
687C2×C4×C37—22no—
688C2×C4×C37—24no—
689C2×C4×C37—21no—
690C2×C4×C37—21no—
691C2×C4×C37—21no—
692C2×C4×C37—21no—
693C2×C4×C37—21no—
694C2×C4×C37—21no—
695C2×C4×C37—21no—
696C2×C4×C37—21no—
697C2×C4×C37—21no—
698C2×C4×C37—21no—
699C2×C4×C37—22no—
700C2×C4×C37—22no—
701C2×C4×C37—21no—
702C2×C4×C37—21no—
703C2×C4×C37—41no—
704C2×C4×C37—41no—
705C2×C4×C37—42no—
706C2×C4×C37—42no—
707C2×C4×C37—42no—
708C2×C4×C37—42no—
709C2×C4×C37—42no—
710C2×C4×C37—44no—
711C2×C4×C37—42no—
712C2×C4×C37—44no—
713C2×C4×C37—42no—
714C2×C4×C37—42no—
715C2×C4×C37—42no—
716C2×C4×C37—42no—
717C2×C4×C37—42no—
718C2×C4×C37—81no—
719C2×C4×C37—82no—
720C2×C4×C37—82no—
721C2×C4×C37C22×D411yescharacteristic
722C2×C4×C37C22×D411yescharacteristic
723C2×C4×C37C22×D411yescharacteristic
724C2×C4×C37C22×D411yescharacteristic
725C2×C4×C37C22×D411yescharacteristic
726C2×C4×C37C22×D411yescharacteristic
727C2×C4×C37C22×D411yescharacteristic
728C2×C4×C37C22×D411yescharacteristic
729C2×C4×C37C22×D411yescharacteristic
730C2×C4×C37C22×D412yes—
731C2×C4×C37H(5,𝔽2)12yes—
732C2×C4×C37C2511yescharacteristic
733C8×C37—22no—
734C8×C37—22no—
735C8×C37—22no—
736C8×C37C22×D414yes—
737#61066C3711yesmaximal, characteristic, direct product factor, Sylow
738C22×C37—21no—
739C22×C37—21no—
740C22×C37—21no—
741C22×C37—21no—
742C22×C37—21no—
743C22×C37—21no—
744C22×C37—21no—
745C22×C37—21no—
746C22×C37—21no—
747C22×C37—21no—
748C22×C37—22no—
749C22×C37—24no—
750C22×C37—21no—
751C22×C37—21no—
752C22×C37—21no—
753C22×C37—44no—
754C22×C37—48no—
755C22×C37—42no—
756C22×C37—41no—
757C22×C37—41no—
758C22×C37—42no—
759C22×C37—42no—
760C22×C37—41no—
761C22×C37—41no—
762C22×C37—41no—
763C22×C37—41no—
764C22×C37—42no—
765C22×C37—41no—
766C22×C37—41no—
767C22×C37—42no—
768C22×C37—82no—
769C22×C37—84no—
770C22×C37—88no—
771C22×C37—84no—
772C22×C37—84no—
773C22×C37—88no—
774C22×C37D4212yes—
775C22×C37#57512yescomplemented
776C22×C37C23×D411yescharacteristic
777C4×C37—21no—
778C4×C37—21no—
779C4×C37—21no—
780C4×C37—21no—
781C4×C37—21no—
782C4×C37—21no—
783C4×C37—22no—
784C4×C37—21no—
785C4×C37—21no—
786C4×C37—42no—
787C4×C37—41no—
788C4×C37—42no—
789C4×C37—41no—
790C4×C37—41no—
791C4×C37—41no—
792C4×C37D4212yes—
793C4×C37C23×D411yescharacteristic
794C4×C37C2×H(5,𝔽2)11yescharacteristic
795C2×#575C2×C3711yescharacteristic, complemented
796C22×AGL(1,ℤ/8)C2×C3711yescharacteristic, complemented
797D4×#41C2×C3711yescharacteristic, complemented
798C2×#546C2×C3711yescharacteristic, complemented
799#3282C2×C3712yescomplemented
800#3280C2×C3712yescomplemented
801#3275C2×C3712yescomplemented
802#3273C2×C3712yescomplemented
803#3268C2×C3712yescomplemented
804#3267C2×C3712yescomplemented
805#3266C2×C3712yescomplemented
806#3264C2×C3712yescomplemented
807#3153C2×C3711yescharacteristic, complemented
808#3056C2×C3711yescharacteristic, complemented
809#3055C2×C3711yescharacteristic, complemented
810#3040C2×C3711yescharacteristic, complemented
811#3036C2×C3711yescharacteristic, complemented
812#3007C2×C3711yescharacteristic, complemented
813#3006C2×C3711yescharacteristic, complemented
814#3005C2×C3711yescharacteristic, complemented
815#3003C2×C3711yescharacteristic, complemented
816C4×AGL(1,ℤ/8)C2×C3711yescharacteristic, complemented
817D4×M16C2×C3711yescharacteristic, complemented
818C2×C37—22no—
819C2×C37—22no—
820C2×C37—41no—
821C2×C37—41no—
822C2×C37—41no—
823C2×C37—44no—
824C2×C37—42no—
825C2×C37—81no—
826C2×C37—81no—
827C2×C37—82no—
828C2×C37C2×D4211yescharacteristic
829C2×C37C2×#57511yescharacteristic
830C2×C37#358511yescharacteristic
831C22×#41C22×C3711yescharacteristic
832C22×#41C22×C3711yescharacteristic, complemented
833C22×#41C22×C3711yescharacteristic, complemented
834C23×D4C22×C3711yescharacteristic, complemented
835#575—28no—
836C2×#137C22×C3711yescharacteristic, complemented
837C2×#137C22×C3711yescharacteristic, complemented
838C2×#137C22×C3711yescharacteristic, complemented
839C2×#137C22×C3712yescomplemented
840C2×AGL(1,ℤ/8)—28no—
841C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
842C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
843C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
844C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
845C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
846C2×AGL(1,ℤ/8)C22×C3712yescomplemented
847C2×AGL(1,ℤ/8)C22×C3712yescomplemented
848C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
849C2×AGL(1,ℤ/8)C22×C3712yescomplemented
850C2×#135C22×C3712yescomplemented
851C2×#135C22×C3712yescomplemented
852C22×SD16C22×C3712yescomplemented
853C22×D8C22×C3712yescomplemented
854C22×M16C22×C3711yescharacteristic, complemented
855C22×M16C22×C3711yescharacteristic, complemented
856#550C22×C3711yescharacteristic, complemented
857D4×Q8C22×C3711yescharacteristic, complemented
858#548C22×C3711yescharacteristic, complemented
859#548C22×C3711yescharacteristic, complemented
860#547—21no—
861#547C22×C3711yescharacteristic, complemented
862#546—21no—
863#546—21no—
864#546—21no—
865#546—21no—
866#546—21no—
867#546—21no—
868#546C22×C3712yes—
869#546C22×C3712yescomplemented
870#546C22×C3712yescomplemented
871#546C22×C3712yescomplemented
872#546C22×C3711yescharacteristic, complemented
873#546C22×C3711yescharacteristic, complemented
874D42—21no—
875D42C22×C3711yescharacteristic, complemented
876#532—21no—
877#532C22×C3711yescharacteristic, complemented
878C2×#124C22×C3711yescharacteristic, complemented
879#525—21no—
880#525—21no—
881#525C22×C3711yescharacteristic
882#525C22×C3711yescharacteristic, complemented
883C2×#123—21no—
884C2×C22⋊Q8C22×C3711yescharacteristic, complemented
885C2×#121—21no—
886C2×#121C22×C3711yescharacteristic, complemented
887C2×#120—21no—
888C4×#41C22×C3711yescharacteristic, complemented
889C2×C4×D4—21no—
890C2×C4×D4C22×C3711yescharacteristic
891C2×C4×D4C22×C3711yescharacteristic, complemented
892C22×C22⋊C4—21no—
893#497C22×C3712yescomplemented
894#496C22×C3712yescomplemented
895#495C22×C3712yescomplemented
896#495C22×C3712yescomplemented
897#470C22×C3712yescomplemented
898#469C22×C3712yescomplemented
899#468C22×C3712yescomplemented
900#468C22×C3712yescomplemented
901#467C22×C3712yescomplemented
902#466C22×C3712yescomplemented
903#465C22×C3712yescomplemented
904#465C22×C3712yescomplemented
905#464C22×C3712yescomplemented
906#464C22×C3712yescomplemented
907#463C22×C3712yescomplemented
908#463C22×C3712yescomplemented
909#463C22×C3712yescomplemented
910#463C22×C3712yescomplemented
911#461C22×C3712yescomplemented
912#459C22×C3712yescomplemented
913#452C22×C3712yescomplemented
914#452C22×C3712yescomplemented
915#452C22×C3712yescomplemented
916#452C22×C3712yescomplemented
917#451C22×C3712yescomplemented
918#450C22×C3712yescomplemented
919#450C22×C3712yescomplemented
920#450C22×C3712yescomplemented
921#449C22×C3712yescomplemented
922#449C22×C3712yescomplemented
923#449C22×C3712yescomplemented
924#449C22×C3712yescomplemented
925#448C22×C3712yescomplemented
926#447C22×C3712yescomplemented
927#447C22×C3712yescomplemented
928#447C22×C3712yescomplemented
929#442C22×C3712yescomplemented
930#440C22×C3712yescomplemented
931C4×SD16C22×C3712yescomplemented
932C4×D8C22×C3712yescomplemented
933#436C22×C3712yescomplemented
934#435C22×C3712yescomplemented
935#435C22×C3712yescomplemented
936C8×D4C22×C3712yescomplemented
937#428C22×C3711yescharacteristic, complemented
938#423C22×C3711yescharacteristic, complemented
939#419C22×C3711yescharacteristic, complemented
940#418C22×C3711yescharacteristic, complemented
941#418C22×C3711yescharacteristic, complemented
942#417C22×C3711yescharacteristic, complemented
943#417C22×C3711yescharacteristic, complemented
944#417C22×C3711yescharacteristic, complemented
945#407C22×C3711yescharacteristic, complemented
946#407C22×C3711yescharacteristic, complemented
947C4×M16C22×C3711yescharacteristic, complemented
948C37#6106611yescharacteristic, direct product factor, Sylow
949C25—21no—
950C2×#41—21no—
951C2×#41—21no—
952C2×#41—21no—
953C2×#41—21no—
954C2×#41—21no—
955C2×#41—21no—
956C2×#41—24no—
957C2×#41—24no—
958C2×#41—24no—
959C2×#41—42no—
960C2×#41—42no—
961C2×#41—42no—
962C2×#41C23×C3711yescharacteristic
963C2×#41C23×C3711yescharacteristic
964C2×#41C23×C3712yes—
965C2×#41C23×C3712yes—
966C2×#41C23×C3711yescharacteristic
967C2×#41C23×C3711yescharacteristic
968C2×#41C23×C3711yescharacteristic
969C2×#41C23×C3711yescharacteristic, complemented
970C2×#41C23×C3711yescharacteristic, complemented
971C22×Q8C23×C3711yescharacteristic
972C22×Q8C23×C3711yescharacteristic
973C22×Q8C23×C3711yescharacteristic, complemented
974C22×D4—24no—
975C22×D4—21no—
976C22×D4—21no—
977C22×D4—21no—
978C22×D4—21no—
979C22×D4—21no—
980C22×D4—21no—
981C22×D4—21no—
982C22×D4—21no—
983C22×D4—42no—
984C22×D4D4×C3711yescharacteristic
985C22×D4C23×C3711yescharacteristic
986C22×D4C23×C3711yescharacteristic
987C22×D4C23×C3712yes—
988C22×D4C23×C3712yes—
989C22×D4C23×C3711yescharacteristic
990C22×D4C23×C3711yescharacteristic, complemented
991C23×C4—21no—
992C23×C4—21no—
993C23×C4—21no—
994C23×C4—21no—
995C23×C4C23×C3711yescharacteristic
996C23×C4C23×C3711yescharacteristic
997#137—24no—
998#137—28no—
999#137—24no—
1000#137—42no—
1001AGL(1,ℤ/8)—24no—
1002AGL(1,ℤ/8)—24no—
1003AGL(1,ℤ/8)—24no—
1004AGL(1,ℤ/8)—28no—
1005AGL(1,ℤ/8)—28no—
1006AGL(1,ℤ/8)—28no—
1007AGL(1,ℤ/8)—24no—
1008AGL(1,ℤ/8)—42no—
1009AGL(1,ℤ/8)D4×C3718yescomplemented
1010#135—28no—
1011#135—28no—
1012C2×Q16C23×C3712yescomplemented
1013C2×Q16C23×C3712yescomplemented
1014C2×Q16C23×C3712yescomplemented
1015C2×SD16—28no—
1016C2×SD16C23×C3712yes—
1017C2×SD16C23×C3712yes—
1018C2×SD16C23×C3712yes—
1019C2×SD16C23×C3712yes—
1020C2×SD16C23×C3712yes—
1021C2×SD16C23×C3712yes—
1022C2×SD16C23×C3712yescomplemented
1023C2×SD16C23×C3712yescomplemented
1024C2×SD16C23×C3712yescomplemented
1025C2×D8—28no—
1026C2×D8C23×C3712yes—
1027C2×D8C23×C3712yes—
1028C2×D8C23×C3712yes—
1029C2×D8C23×C3712yes—
1030C2×D8C23×C3712yes—
1031C2×D8C23×C3712yes—
1032C2×M16—24no—
1033C2×M16—24no—
1034C2×M16C23×C3711yescharacteristic
1035C2×M16C23×C3712yes—
1036C2×M16C23×C3711yescharacteristic
1037C2×M16C23×C3711yescharacteristic
1038C2×M16C23×C3711yescharacteristic
1039C2×M16C23×C3712yescomplemented
1040C22×C8C23×C3712yes—
1041C22×C8C23×C3712yescomplemented
1042C4⋊Q8—21no—
1043C4⋊Q8C23×C3711yescharacteristic, complemented
1044#127—21no—
1045#127C23×C3711yescharacteristic, complemented
1046#124—21no—
1047#124—21no—
1048#124—21no—
1049#124—21no—
1050#124C23×C3712yes—
1051#124C23×C3712yes—
1052#124C23×C3711yescharacteristic, complemented
1053#124C23×C3711yescharacteristic, complemented
1054#123—21no—
1055#123—21no—
1056#123—22no—
1057#123—22no—
1058#123—22no—
1059#123—22no—
1060#123—21no—
1061#123—21no—
1062#123—21no—
1063#123—21no—
1064C22⋊Q8—21no—
1065C22⋊Q8—21no—
1066C22⋊Q8—21no—
1067C22⋊Q8—21no—
1068C22⋊Q8—21no—
1069C22⋊Q8—21no—
1070C22⋊Q8C23×C3712yes—
1071C22⋊Q8C23×C3712yes—
1072C22⋊Q8C23×C3711yescharacteristic
1073C22⋊Q8C23×C3711yescharacteristic
1074C22⋊Q8C23×C3711yescharacteristic, complemented
1075C22⋊Q8C23×C3711yescharacteristic, complemented
1076#121—21no—
1077#121—21no—
1078#121—21no—
1079#121—21no—
1080#121—21no—
1081#121—21no—
1082#121—21no—
1083#121—21no—
1084#121—22no—
1085#121—22no—
1086#121—22no—
1087#121—22no—
1088#121—21no—
1089#121—21no—
1090#121—21no—
1091#121—21no—
1092#121C23×C3712yes—
1093#121C23×C3712yes—
1094#121C23×C3711yescharacteristic
1095#121C23×C3711yescharacteristic
1096#121C23×C3711yescharacteristic, complemented
1097#121C23×C3711yescharacteristic, complemented
1098#120—21no—
1099#120—21no—
1100#120—22no—
1101#120—22no—
1102#120—22no—
1103#120—22no—
1104#120—21no—
1105#120—21no—
1106#120—21no—
1107#120—21no—
1108C4×Q8C23×C3711yescharacteristic, complemented
1109C4×Q8C23×C3711yescharacteristic, complemented
1110C4×D4—21no—
1111C4×D4—21no—
1112C4×D4—21no—
1113C4×D4—21no—
1114C4×D4—21no—
1115C4×D4—21no—
1116C4×D4—21no—
1117C4×D4—21no—
1118C4×D4—21no—
1119C4×D4—21no—
1120C4×D4—21no—
1121C4×D4—21no—
1122C4×D4—21no—
1123C4×D4—21no—
1124C4×D4D4×C3711yescharacteristic
1125C4×D4D4×C3711yescharacteristic
1126C4×D4D4×C3711yescharacteristic
1127C4×D4D4×C3711yescharacteristic
1128C4×D4C23×C3712yes—
1129C4×D4C23×C3712yes—
1130C4×D4C23×C3711yescharacteristic
1131C4×D4C23×C3711yescharacteristic
1132C4×D4C23×C3711yescharacteristic
1133C4×D4C23×C3711yescharacteristic
1134C4×D4C23×C3711yescharacteristic, complemented
1135C4×D4C23×C3711yescharacteristic, complemented
1136#117—21no—
1137#117C23×C3711yescharacteristic
1138C2×C4⋊C4—21no—
1139C2×C4⋊C4—21no—
1140C2×C4⋊C4D4×C3711yescharacteristic
1141C2×C4⋊C4C23×C3711yescharacteristic
1142C2×C22⋊C4—21no—
1143C2×C22⋊C4—21no—
1144C2×C22⋊C4—21no—
1145C2×C22⋊C4—21no—
1146C2×C22⋊C4—21no—
1147C2×C22⋊C4—22no—
1148C2×C22⋊C4—22no—
1149C2×C22⋊C4—22no—
1150C2×C22⋊C4—22no—
1151C2×C22⋊C4—21no—
1152C2×C22⋊C4—21no—
1153C2×C22⋊C4D4×C3711yescharacteristic
1154C2×C22⋊C4D4×C3711yescharacteristic
1155C2×C42—21no—
1156C2×C42C23×C3711yescharacteristic
1157#107C23×C3712yescomplemented
1158#106C23×C3712yescomplemented
1159C4⋊C8C23×C3712yescomplemented
1160C4⋊C8C23×C3712yescomplemented
1161#103C23×C3712yescomplemented
1162#103C23×C3712yescomplemented
1163#103C23×C3712yescomplemented
1164#103C23×C3712yescomplemented
1165#103C23×C3712yescomplemented
1166#102C23×C3712yes—
1167#102C23×C3712yes—
1168#102C23×C3712yes—
1169#102C23×C3712yes—
1170#102C23×C3712yescomplemented
1171#102C23×C3712yescomplemented
1172#102C23×C3712yescomplemented
1173C22⋊C8C23×C3712yes—
1174C22⋊C8C23×C3712yes—
1175C22⋊C8C23×C3712yescomplemented
1176C22⋊C8C23×C3712yescomplemented
1177#97C23×C3712yescomplemented
1178C4×C8C23×C3712yescomplemented
1179C24—21no—
1180C24—21no—
1181C24—22no—
1182C24—22no—
1183C24—21no—
1184C24—21no—
1185C24—44no—
1186C24—44no—
1187C24—82no—
1188C24C2×D4×C3711yescharacteristic
1189C24C2×D4×C3711yescharacteristic
1190#41—22no—
1191#41—22no—
1192#41—22no—
1193#41—24no—
1194#41—22no—
1195#41—22no—
1196#41—24no—
1197#41—22no—
1198#41—22no—
1199#41—22no—
1200#41—22no—
1201#41—44no—
1202#41—44no—
1203#41—41no—
1204#41—41no—
1205#41—42no—
1206#41—42no—
1207#41—41no—
1208#41—41no—
1209#41—44no—
1210#41—44no—
1211#41—44no—
1212#41—44no—
1213#41C2×D4×C3714yes—
1214C2×Q8—21no—
1215C2×Q8—21no—
1216C2×Q8—21no—
1217C2×Q8—22no—
1218C2×Q8—22no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—41no—
1222C2×Q8—41no—
1223C2×Q8C24×C3712yes—
1224C2×Q8C24×C3711yescharacteristic
1225C2×Q8C24×C3711yescharacteristic
1226C2×Q8C24×C3711yescharacteristic
1227C2×D4—21no—
1228C2×D4—22no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—22no—
1232C2×D4—21no—
1233C2×D4—21no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—21no—
1237C2×D4—21no—
1238C2×D4—21no—
1239C2×D4—21no—
1240C2×D4—21no—
1241C2×D4—21no—
1242C2×D4—21no—
1243C2×D4—21no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—21no—
1247C2×D4—22no—
1248C2×D4—21no—
1249C2×D4—21no—
1250C2×D4—21no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—21no—
1254C2×D4—21no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—42no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—82no—
1270C2×D4C2×D4×C3711yescharacteristic
1271C2×D4C2×D4×C3711yescharacteristic
1272C2×D4C2×D4×C3711yescharacteristic
1273C2×D4C2×D4×C3711yescharacteristic
1274C2×D4C2×D4×C3714yescomplemented
1275C2×D4C24×C3712yes—
1276C2×D4C24×C3711yescharacteristic
1277C2×D4C24×C3711yescharacteristic
1278C2×D4C24×C3712yes—
1279C2×D4C24×C3711yescharacteristic
1280C22×C4—21no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—21no—
1286C22×C4—21no—
1287C22×C4—21no—
1288C22×C4—21no—
1289C22×C4—21no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—21no—
1293C22×C4—21no—
1294C22×C4—21no—
1295C22×C4—21no—
1296C22×C4—21no—
1297C22×C4—21no—
1298C22×C4—21no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—82no—
1305C22×C4C2×D4×C3711yescharacteristic
1306C22×C4C2×D4×C3711yescharacteristic
1307C22×C4C2×D4×C3711yescharacteristic
1308C22×C4C2×D4×C3711yescharacteristic
1309C22×C4C2×D4×C3711yescharacteristic
1310C22×C4C2×D4×C3711yescharacteristic
1311C22×C4C2×D4×C3711yescharacteristic
1312C22×C4C2×D4×C3711yescharacteristic
1313C22×C4C24×C3711yescharacteristic
1314C22×C4C24×C3711yescharacteristic
1315C22×C4C24×C3711yescharacteristic
1316C22×C4C24×C3711yescharacteristic
1317C22×C4C24×C3711yescharacteristic
1318Q16—24no—
1319Q16—24no—
1320Q16—42no—
1321SD16—24no—
1322SD16—24no—
1323SD16—24no—
1324SD16—24no—
1325SD16—24no—
1326SD16—24no—
1327SD16—42no—
1328SD16—42no—
1329SD16C2×D4×C3718yescomplemented
1330D8—24no—
1331D8—24no—
1332D8—24no—
1333D8—24no—
1334D8—42no—
1335D8C2×D4×C3718yescomplemented
1336M16—22no—
1337M16—22no—
1338M16—22no—
1339M16—24no—
1340M16—24no—
1341M16C2×D4×C3714yescomplemented
1342C2×C8—24no—
1343C2×C8—24no—
1344C2×C8C24×C3712yes—
1345C2×C8C24×C3712yes—
1346C2×C8C24×C3712yes—
1347C2×C8C24×C3712yes—
1348C4⋊C4—21no—
1349C4⋊C4—21no—
1350C4⋊C4—21no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—21no—
1354C4⋊C4—21no—
1355C4⋊C4—21no—
1356C4⋊C4—21no—
1357C4⋊C4—21no—
1358C4⋊C4—21no—
1359C4⋊C4C2×D4×C3711yescharacteristic
1360C4⋊C4C2×D4×C3711yescharacteristic
1361C4⋊C4C2×D4×C3711yescharacteristic
1362C4⋊C4C2×D4×C3711yescharacteristic
1363C4⋊C4C24×C3711yescharacteristic
1364C4⋊C4C24×C3711yescharacteristic
1365C4⋊C4C24×C3712yes—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—21no—
1369C22⋊C4—21no—
1370C22⋊C4—21no—
1371C22⋊C4—21no—
1372C22⋊C4—21no—
1373C22⋊C4—22no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—22no—
1377C22⋊C4—21no—
1378C22⋊C4—21no—
1379C22⋊C4—21no—
1380C22⋊C4—21no—
1381C22⋊C4—22no—
1382C22⋊C4—22no—
1383C22⋊C4—22no—
1384C22⋊C4—22no—
1385C22⋊C4—21no—
1386C22⋊C4—21no—
1387C22⋊C4—21no—
1388C22⋊C4—21no—
1389C22⋊C4—21no—
1390C22⋊C4—21no—
1391C22⋊C4C2×D4×C3711yescharacteristic
1392C22⋊C4C2×D4×C3711yescharacteristic
1393C22⋊C4C2×D4×C3711yescharacteristic
1394C22⋊C4C2×D4×C3711yescharacteristic
1395C22⋊C4C2×D4×C3711yescharacteristic
1396C22⋊C4C2×D4×C3711yescharacteristic
1397C22⋊C4C2×D4×C3711yescharacteristic
1398C22⋊C4C2×D4×C3711yescharacteristic
1399C42—21no—
1400C42—21no—
1401C42—21no—
1402C42C2×D4×C3711yescharacteristic
1403C42C2×D4×C3711yescharacteristic
1404C42C24×C3711yescharacteristic
1405C42C24×C3711yescharacteristic
1406C23—22no—
1407C23—24no—
1408C23—22no—
1409C23—21no—
1410C23—22no—
1411C23—22no—
1412C23—22no—
1413C23—21no—
1414C23—21no—
1415C23—41no—
1416C23—41no—
1417C23—41no—
1418C23—42no—
1419C23—42no—
1420C23—44no—
1421C23—44no—
1422C23—42no—
1423C23—42no—
1424C23—42no—
1425C23—42no—
1426C23—42no—
1427C23—44no—
1428C23—42no—
1429C23—42no—
1430C23—44no—
1431C23—82no—
1432C23—82no—
1433C23—81no—
1434C23—81no—
1435C23—816no—
1436C23C22×D4×C3711yescharacteristic
1437C23C22×D4×C3711yescharacteristic
1438C23C22×D4×C3711yescharacteristic
1439C23C22×D4×C3711yescharacteristic
1440C23C22×D4×C3711yescharacteristic
1441Q8—21no—
1442Q8—21no—
1443Q8—21no—
1444Q8—22no—
1445Q8—21no—
1446Q8—22no—
1447Q8—21no—
1448Q8—42no—
1449Q8—42no—
1450Q8—42no—
1451Q8C22×D4×C3712yes—
1452D4—24no—
1453D4—22no—
1454D4—22no—
1455D4—24no—
1456D4—21no—
1457D4—22no—
1458D4—21no—
1459D4—22no—
1460D4—21no—
1461D4—21no—
1462D4—22no—
1463D4—21no—
1464D4—41no—
1465D4—41no—
1466D4—44no—
1467D4—44no—
1468D4—42no—
1469D4—42no—
1470D4—42no—
1471D4—42no—
1472D4—42no—
1473D4—44no—
1474D4—42no—
1475D4—44no—
1476D4—42no—
1477D4—42no—
1478D4—42no—
1479D4—42no—
1480D4—42no—
1481D4—42no—
1482D4—81no—
1483D4—82no—
1484D4—82no—
1485D4—81no—
1486D4—81no—
1487D4C22×D4×C3712yes—
1488D4C22×D4×C3714yes—
1489C2×C4—22no—
1490C2×C4—22no—
1491C2×C4—21no—
1492C2×C4—22no—
1493C2×C4—22no—
1494C2×C4—22no—
1495C2×C4—22no—
1496C2×C4—24no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—41no—
1512C2×C4—41no—
1513C2×C4—42no—
1514C2×C4—42no—
1515C2×C4—42no—
1516C2×C4—42no—
1517C2×C4—42no—
1518C2×C4—44no—
1519C2×C4—42no—
1520C2×C4—44no—
1521C2×C4—42no—
1522C2×C4—42no—
1523C2×C4—42no—
1524C2×C4—42no—
1525C2×C4—42no—
1526C2×C4—82no—
1527C2×C4—82no—
1528C2×C4—81no—
1529C2×C4C22×D4×C3711yescharacteristic
1530C2×C4C22×D4×C3711yescharacteristic
1531C2×C4C22×D4×C3711yescharacteristic
1532C2×C4C22×D4×C3711yescharacteristic
1533C2×C4C22×D4×C3711yescharacteristic
1534C2×C4C22×D4×C3711yescharacteristic
1535C2×C4C22×D4×C3711yescharacteristic
1536C2×C4C22×D4×C3711yescharacteristic
1537C2×C4C22×D4×C3711yescharacteristic
1538C2×C4C22×D4×C3712yes—
1539C2×C4H(5,𝔽2)×C3712yes—
1540C2×C4C25×C3711yescharacteristic
1541C8—22no—
1542C8—22no—
1543C8—22no—
1544C8C22×D4×C3714yes—
1545C22—21no—
1546C22—21no—
1547C22—21no—
1548C22—21no—
1549C22—21no—
1550C22—21no—
1551C22—21no—
1552C22—22no—
1553C22—24no—
1554C22—21no—
1555C22—21no—
1556C22—21no—
1557C22—21no—
1558C22—21no—
1559C22—21no—
1560C22—44no—
1561C22—48no—
1562C22—41no—
1563C22—42no—
1564C22—42no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—42no—
1569C22—41no—
1570C22—41no—
1571C22—42no—
1572C22—42no—
1573C22—41no—
1574C22—41no—
1575C22—82no—
1576C22—88no—
1577C22—84no—
1578C22—84no—
1579C22—88no—
1580C22—84no—
1581C22D42×C3712yes—
1582C22C37×#57512yescomplemented
1583C22C23×D4×C3711yescharacteristic
1584C4—21no—
1585C4—21no—
1586C4—21no—
1587C4—21no—
1588C4—22no—
1589C4—21no—
1590C4—21no—
1591C4—21no—
1592C4—21no—
1593C4—42no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—42no—
1598C4—41no—
1599C4D42×C3712yes—
1600C4C23×D4×C3711yescharacteristic
1601C4C2×H(5,𝔽2)×C3711yescharacteristic
1602C2—22no—
1603C2—22no—
1604C2—41no—
1605C2—41no—
1606C2—41no—
1607C2—44no—
1608C2—42no—
1609C2—82no—
1610C2—81no—
1611C2—81no—
1612C2C2×D42×C3711yescharacteristic
1613C2C2×C37×#57511yescharacteristic
1614C2C37×#358511yescharacteristic
subgroupG/H
center, socleC22×C37C23×D4
commutator, Frattini, cosocleC2×C4C25×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C37×#575C2semidirect
2. C22×AGL(1,ℤ/8)×C37C2semidirect
3. D4×#41×C37C2semidirect
4. C2×C37×#546C2semidirect
5. C37×#3282C2semidirect
6. C37×#3280C2semidirect
7. C37×#3275C2semidirect
8. C37×#3273C2semidirect
9. C37×#3268C2semidirect
10. C37×#3267C2semidirect
11. C37×#3266C2semidirect
12. C37×#3264C2semidirect
13. C37×#3153C2semidirect
14. C37×#3056C2semidirect
15. C37×#3055C2semidirect
16. C37×#3040C2semidirect
17. C37×#3036C2semidirect
18. C37×#3007C2semidirect
19. C37×#3006C2semidirect
20. C37×#3005C2semidirect
21. C37×#3003C2semidirect
22. C4×AGL(1,ℤ/8)×C37C2semidirect
23. D4×M16×C37C2semidirect
25. C22×#41×C37C22semidirect
26. C22×#41×C37C22semidirect
27. C23×D4×C37C22semidirect
29. C2×#137×C37C22semidirect
30. C2×#137×C37C22semidirect
31. C2×#137×C37C22semidirect
32. C2×#137×C37C22semidirect
36. C2×AGL(1,ℤ/8)×C37C22semidirect
37. C2×AGL(1,ℤ/8)×C37C22semidirect
38. C2×AGL(1,ℤ/8)×C37C22semidirect
39. C2×AGL(1,ℤ/8)×C37C22semidirect
40. C2×AGL(1,ℤ/8)×C37C22semidirect
41. C2×AGL(1,ℤ/8)×C37C22semidirect
42. C2×AGL(1,ℤ/8)×C37C22semidirect
43. C2×#135×C37C22semidirect
44. C2×#135×C37C22semidirect
45. C22×SD16×C37C22semidirect
46. C22×D8×C37C22semidirect
47. C22×M16×C37C22semidirect
48. C22×M16×C37C22semidirect
49. C37×#550C22semidirect
50. D4×Q8×C37C22semidirect
51. C37×#548C22semidirect
52. C37×#548C22semidirect
54. C37×#547C22semidirect
62. C37×#546C22semidirect
63. C37×#546C22semidirect
64. C37×#546C22semidirect
65. C37×#546C22semidirect
66. C37×#546C22semidirect
68. D42×C37C22semidirect
70. C37×#532C22semidirect
71. C2×#124×C37C22semidirect
75. C37×#525C22semidirect
77. C2×C22⋊Q8×C37C22semidirect
79. C2×#121×C37C22semidirect
81. C4×#41×C37C22semidirect
84. C2×C4×D4×C37C22semidirect
86. C37×#497C22semidirect
87. C37×#496C22semidirect
88. C37×#495C22semidirect
89. C37×#495C22semidirect
90. C37×#470C22semidirect
91. C37×#469C22semidirect
92. C37×#468C22semidirect
93. C37×#468C22semidirect
94. C37×#467C22semidirect
95. C37×#466C22semidirect
96. C37×#465C22semidirect
97. C37×#465C22semidirect
98. C37×#464C22semidirect
99. C37×#464C22semidirect
100. C37×#463C22semidirect
101. C37×#463C22semidirect
102. C37×#463C22semidirect
103. C37×#463C22semidirect
104. C37×#461C22semidirect
105. C37×#459C22semidirect
106. C37×#452C22semidirect
107. C37×#452C22semidirect
108. C37×#452C22semidirect
109. C37×#452C22semidirect
110. C37×#451C22semidirect
111. C37×#450C22semidirect
112. C37×#450C22semidirect
113. C37×#450C22semidirect
114. C37×#449C22semidirect
115. C37×#449C22semidirect
116. C37×#449C22semidirect
117. C37×#449C22semidirect
118. C37×#448C22semidirect
119. C37×#447C22semidirect
120. C37×#447C22semidirect
121. C37×#447C22semidirect
122. C37×#442C22semidirect
123. C37×#440C22semidirect
124. C4×SD16×C37C22semidirect
125. C4×D8×C37C22semidirect
126. C37×#436C22semidirect
127. C37×#435C22semidirect
128. C37×#435C22semidirect
129. C8×D4×C37C22semidirect
130. C37×#428C22semidirect
131. C37×#423C22semidirect
132. C37×#419C22semidirect
133. C37×#418C22semidirect
134. C37×#418C22semidirect
135. C37×#417C22semidirect
136. C37×#417C22semidirect
137. C37×#417C22semidirect
138. C37×#407C22semidirect
139. C37×#407C22semidirect
140. C4×M16×C37C22semidirect
161. C2×#41×C37C23semidirect
162. C2×#41×C37C23semidirect
165. C22×Q8×C37C23semidirect
182. C22×D4×C37C23semidirect
201. AGL(1,ℤ/8)×C37D4semidirect
204. C2×Q16×C37C23semidirect
205. C2×Q16×C37C23semidirect
206. C2×Q16×C37C23semidirect
214. C2×SD16×C37C23semidirect
215. C2×SD16×C37C23semidirect
216. C2×SD16×C37C23semidirect
231. C2×M16×C37C23semidirect
233. C22×C8×C37C23semidirect
235. C4⋊Q8×C37C23semidirect
237. #127×C37C23semidirect
244. #124×C37C23semidirect
245. #124×C37C23semidirect
266. C22⋊Q8×C37C23semidirect
267. C22⋊Q8×C37C23semidirect
288. #121×C37C23semidirect
289. #121×C37C23semidirect
300. C4×Q8×C37C23semidirect
301. C4×Q8×C37C23semidirect
326. C4×D4×C37C23semidirect
327. C4×D4×C37C23semidirect
349. #107×C37C23semidirect
350. #106×C37C23semidirect
351. C4⋊C8×C37C23semidirect
352. C4⋊C8×C37C23semidirect
353. #103×C37C23semidirect
354. #103×C37C23semidirect
355. #103×C37C23semidirect
356. #103×C37C23semidirect
357. #103×C37C23semidirect
362. #102×C37C23semidirect
363. #102×C37C23semidirect
364. #102×C37C23semidirect
367. C22⋊C8×C37C23semidirect
368. C22⋊C8×C37C23semidirect
369. #97×C37C23semidirect
370. C4×C8×C37C23semidirect
466. C2×D4×C37C2×D4semidirect
521. SD16×C37C2×D4semidirect
527. D8×C37C2×D4semidirect
533. M16×C37C2×D4semidirect
737. #61066C37direct (N × H)
775. C22×C37#575semidirect
795. C2×#575C2×C37semidirect
796. C22×AGL(1,ℤ/8)C2×C37semidirect
797. D4×#41C2×C37semidirect
798. C2×#546C2×C37semidirect
799. #3282C2×C37semidirect
800. #3280C2×C37semidirect
801. #3275C2×C37semidirect
802. #3273C2×C37semidirect
803. #3268C2×C37semidirect
804. #3267C2×C37semidirect
805. #3266C2×C37semidirect
806. #3264C2×C37semidirect
807. #3153C2×C37semidirect
808. #3056C2×C37semidirect
809. #3055C2×C37semidirect
810. #3040C2×C37semidirect
811. #3036C2×C37semidirect
812. #3007C2×C37semidirect
813. #3006C2×C37semidirect
814. #3005C2×C37semidirect
815. #3003C2×C37semidirect
816. C4×AGL(1,ℤ/8)C2×C37semidirect
817. D4×M16C2×C37semidirect
832. C22×#41C22×C37semidirect
833. C22×#41C22×C37semidirect
834. C23×D4C22×C37semidirect
836. C2×#137C22×C37semidirect
837. C2×#137C22×C37semidirect
838. C2×#137C22×C37semidirect
839. C2×#137C22×C37semidirect
843. C2×AGL(1,ℤ/8)C22×C37semidirect
844. C2×AGL(1,ℤ/8)C22×C37semidirect
845. C2×AGL(1,ℤ/8)C22×C37semidirect
846. C2×AGL(1,ℤ/8)C22×C37semidirect
847. C2×AGL(1,ℤ/8)C22×C37semidirect
848. C2×AGL(1,ℤ/8)C22×C37semidirect
849. C2×AGL(1,ℤ/8)C22×C37semidirect
850. C2×#135C22×C37semidirect
851. C2×#135C22×C37semidirect
852. C22×SD16C22×C37semidirect
853. C22×D8C22×C37semidirect
854. C22×M16C22×C37semidirect
855. C22×M16C22×C37semidirect
856. #550C22×C37semidirect
857. D4×Q8C22×C37semidirect
858. #548C22×C37semidirect
859. #548C22×C37semidirect
861. #547C22×C37semidirect
869. #546C22×C37semidirect
870. #546C22×C37semidirect
871. #546C22×C37semidirect
872. #546C22×C37semidirect
873. #546C22×C37semidirect
875. D42C22×C37semidirect
877. #532C22×C37semidirect
878. C2×#124C22×C37semidirect
882. #525C22×C37semidirect
884. C2×C22⋊Q8C22×C37semidirect
886. C2×#121C22×C37semidirect
888. C4×#41C22×C37semidirect
891. C2×C4×D4C22×C37semidirect
893. #497C22×C37semidirect
894. #496C22×C37semidirect
895. #495C22×C37semidirect
896. #495C22×C37semidirect
897. #470C22×C37semidirect
898. #469C22×C37semidirect
899. #468C22×C37semidirect
900. #468C22×C37semidirect
901. #467C22×C37semidirect
902. #466C22×C37semidirect
903. #465C22×C37semidirect
904. #465C22×C37semidirect
905. #464C22×C37semidirect
906. #464C22×C37semidirect
907. #463C22×C37semidirect
908. #463C22×C37semidirect
909. #463C22×C37semidirect
910. #463C22×C37semidirect
911. #461C22×C37semidirect
912. #459C22×C37semidirect
913. #452C22×C37semidirect
914. #452C22×C37semidirect
915. #452C22×C37semidirect
916. #452C22×C37semidirect
917. #451C22×C37semidirect
918. #450C22×C37semidirect
919. #450C22×C37semidirect
920. #450C22×C37semidirect
921. #449C22×C37semidirect
922. #449C22×C37semidirect
923. #449C22×C37semidirect
924. #449C22×C37semidirect
925. #448C22×C37semidirect
926. #447C22×C37semidirect
927. #447C22×C37semidirect
928. #447C22×C37semidirect
929. #442C22×C37semidirect
930. #440C22×C37semidirect
931. C4×SD16C22×C37semidirect
932. C4×D8C22×C37semidirect
933. #436C22×C37semidirect
934. #435C22×C37semidirect
935. #435C22×C37semidirect
936. C8×D4C22×C37semidirect
937. #428C22×C37semidirect
938. #423C22×C37semidirect
939. #419C22×C37semidirect
940. #418C22×C37semidirect
941. #418C22×C37semidirect
942. #417C22×C37semidirect
943. #417C22×C37semidirect
944. #417C22×C37semidirect
945. #407C22×C37semidirect
946. #407C22×C37semidirect
947. C4×M16C22×C37semidirect
948. C37#61066direct (N × H)
969. C2×#41C23×C37semidirect
970. C2×#41C23×C37semidirect
973. C22×Q8C23×C37semidirect
990. C22×D4C23×C37semidirect
1009. AGL(1,ℤ/8)D4×C37semidirect
1012. C2×Q16C23×C37semidirect
1013. C2×Q16C23×C37semidirect
1014. C2×Q16C23×C37semidirect
1022. C2×SD16C23×C37semidirect
1023. C2×SD16C23×C37semidirect
1024. C2×SD16C23×C37semidirect
1039. C2×M16C23×C37semidirect
1041. C22×C8C23×C37semidirect
1043. C4⋊Q8C23×C37semidirect
1045. #127C23×C37semidirect
1052. #124C23×C37semidirect
1053. #124C23×C37semidirect
1074. C22⋊Q8C23×C37semidirect
1075. C22⋊Q8C23×C37semidirect
1096. #121C23×C37semidirect
1097. #121C23×C37semidirect
1108. C4×Q8C23×C37semidirect
1109. C4×Q8C23×C37semidirect
1134. C4×D4C23×C37semidirect
1135. C4×D4C23×C37semidirect
1157. #107C23×C37semidirect
1158. #106C23×C37semidirect
1159. C4⋊C8C23×C37semidirect
1160. C4⋊C8C23×C37semidirect
1161. #103C23×C37semidirect
1162. #103C23×C37semidirect
1163. #103C23×C37semidirect
1164. #103C23×C37semidirect
1165. #103C23×C37semidirect
1170. #102C23×C37semidirect
1171. #102C23×C37semidirect
1172. #102C23×C37semidirect
1175. C22⋊C8C23×C37semidirect
1176. C22⋊C8C23×C37semidirect
1177. #97C23×C37semidirect
1178. C4×C8C23×C37semidirect
1274. C2×D4C2×D4×C37semidirect
1329. SD16C2×D4×C37semidirect
1335. D8C2×D4×C37semidirect
1341. M16C2×D4×C37semidirect
1582. C22C37×#575semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C37×#5752
C22×AGL(1,ℤ/8)×C372
D4×#41×C372
C2×C37×#5462
C37×#32822
C37×#32802
C37×#32752
C37×#32732
C37×#32682
C37×#32672
C37×#32662
C37×#32642
C37×#31532
C37×#30562
C37×#30552
C37×#30402
C37×#30362
C37×#30072
C37×#30062
C37×#30052
C37×#30032
C4×AGL(1,ℤ/8)×C372
D4×M16×C372
#6106637