Finite Group Databasebeta

← C2×C37×#3265 #22682276

Subgroups — C2×C37×#3265 #22682276

Order 9472.

3226 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
2C23×SD16×C37C211yesmaximal, characteristic, complemented
3C2×C37×#548C211yesmaximal, characteristic, complemented
4C2×D42×C37C211yesmaximal, characteristic, complemented
5C37×#3265C2116yesmaximal, direct product factor
6C2×C37×#496C211yesmaximal, characteristic, complemented
7C2×C37×#468C211yesmaximal, characteristic, complemented
8C2×C37×#466C211yesmaximal, characteristic, complemented
9C2×C37×#460C211yesmaximal, characteristic, complemented
10C2×C37×#463C211yesmaximal, characteristic, complemented
11C2×C37×#449C211yesmaximal, characteristic, complemented
12C2×C37×#448C211yesmaximal, characteristic, complemented
13C2×C37×#450C211yesmaximal, characteristic, complemented
14C2×C37×#447C211yesmaximal, characteristic, complemented
15C2×C37×#440C211yesmaximal, characteristic, complemented
16C2×C37×#435C211yesmaximal, characteristic, complemented
17C22×#41×C37C2211yescharacteristic, complemented
18C23×Q8×C37C2211yescharacteristic, complemented
19C23×D4×C37—21no—
20C23×D4×C37C2211yescharacteristic
21C23×D4×C37C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C37—28no—
23C2×AGL(1,ℤ/8)×C37C2218yescomplemented
24C22×SD16×C37—28no—
25C22×SD16×C37C2211yescharacteristic
26C22×SD16×C37C2211yescharacteristic
27C22×SD16×C37C2211yescharacteristic, complemented
28C22×SD16×C37C2211yescharacteristic, complemented
29C22×SD16×C37C2211yescharacteristic, complemented
30C22×SD16×C37C2211yescharacteristic, complemented
31C22×SD16×C37C2218yescomplemented
32C22×D8×C37C2211yescharacteristic
33C22×D8×C37C2211yescharacteristic, complemented
34C22×D8×C37C2211yescharacteristic, complemented
35C22×M16×C37C2211yescharacteristic, complemented
36C23×C8×C37C2211yescharacteristic, complemented
37C37×#548—24no—
38C37×#548C2218yescomplemented
39D42×C37—24no—
40D42×C37C2218yescomplemented
41C2×#127×C37C2211yescharacteristic
42C2×#124×C37—21no—
43C2×#124×C37C2211yescharacteristic, complemented
44C2×C22⋊Q8×C37—21no—
45C2×C22⋊Q8×C37C2211yescharacteristic, complemented
46C2×#121×C37—21no—
47C2×#121×C37—21no—
48C2×#121×C37C2211yescharacteristic
49C2×#121×C37C2211yescharacteristic
50C2×#121×C37C2211yescharacteristic, complemented
51C2×#120×C37—21no—
52C2×#120×C37—21no—
53C2×C4×Q8×C37C2211yescharacteristic, complemented
54C2×C4×D4×C37—21no—
55C2×C4×D4×C37C2211yescharacteristic
56C2×C4×D4×C37C2211yescharacteristic
57C37×#496C2218yescomplemented
58C37×#468C2218yescomplemented
59C37×#466C2218yescomplemented
60C37×#463C2218yescomplemented
61C37×#460C2218yescomplemented
62C37×#450C2218yescomplemented
63C37×#449C2218yescomplemented
64C37×#448C2218yescomplemented
65C37×#447C2218yescomplemented
66C37×#440C2218yescomplemented
67C37×#435C2218yescomplemented
68C2×#107×C37C2211yescharacteristic, complemented
69C2×C4⋊C8×C37C2211yescharacteristic, complemented
70C2×#103×C37C2211yescharacteristic, complemented
71C2×#103×C37C2211yescharacteristic, complemented
72C2×#102×C37C2211yescharacteristic
73C2×#102×C37C2211yescharacteristic, complemented
74C2×#102×C37C2211yescharacteristic, complemented
75C2×#102×C37C2211yescharacteristic, complemented
76C2×C22⋊C8×C37C2211yescharacteristic, complemented
77C2×C22⋊C8×C37C2211yescharacteristic, complemented
78C2×#97×C37C2211yescharacteristic, complemented
79C25×C37—21no—
80C25×C37—21no—
81C2×#41×C37—22no—
82C2×#41×C37—24no—
83C2×#41×C37—42no—
84C2×#41×C37C2314yescomplemented
85C22×Q8×C37—21no—
86C22×Q8×C37—22no—
87C22×Q8×C37—24no—
88C22×Q8×C37—42no—
89C22×Q8×C37C2311yescharacteristic
90C22×Q8×C37C2311yescharacteristic
91C22×Q8×C37C2314yescomplemented
92C22×D4×C37—24no—
93C22×D4×C37—24no—
94C22×D4×C37—21no—
95C22×D4×C37—21no—
96C22×D4×C37—21no—
97C22×D4×C37—21no—
98C22×D4×C37—28no—
99C22×D4×C37—21no—
100C22×D4×C37—21no—
101C22×D4×C37—21no—
102C22×D4×C37—22no—
103C22×D4×C37—22no—
104C22×D4×C37—21no—
105C22×D4×C37—42no—
106C22×D4×C37—42no—
107C22×D4×C37—48no—
108C22×D4×C37D411yescharacteristic
109C22×D4×C37C2311yescharacteristic
110C22×D4×C37C2311yescharacteristic
111C22×D4×C37C2311yescharacteristic
112C22×D4×C37C2314yes—
113C22×D4×C37C2314yes—
114C22×D4×C37C2311yescharacteristic
115C23×C4×C37—21no—
116C23×C4×C37—21no—
117C23×C4×C37—21no—
118C23×C4×C37C2311yescharacteristic
119C23×C4×C37C2311yescharacteristic
120AGL(1,ℤ/8)×C37—232no—
121C2×SD16×C37—24no—
122C2×SD16×C37—24no—
123C2×SD16×C37—24no—
124C2×SD16×C37—232no—
125C2×SD16×C37—24no—
126C2×SD16×C37—42no—
127C2×SD16×C37D418yescomplemented
128C2×SD16×C37C2314yes—
129C2×SD16×C37C2314yes—
130C2×SD16×C37C2314yescomplemented
131C2×SD16×C37C2314yescomplemented
132C2×SD16×C37C2314yescomplemented
133C2×SD16×C37C2314yescomplemented
134C2×D8×C37—24no—
135C2×D8×C37—24no—
136C2×D8×C37—42no—
137C2×D8×C37C2314yes—
138C2×D8×C37C2314yescomplemented
139C2×D8×C37C2314yescomplemented
140C2×M16×C37—24no—
141C2×M16×C37C2314yescomplemented
142C22×C8×C37—24no—
143C22×C8×C37C2311yescharacteristic
144C22×C8×C37C2311yescharacteristic
145C22×C8×C37C2311yescharacteristic
146C22×C8×C37C2311yescharacteristic
147C22×C8×C37C2314yescomplemented
148#127×C37—22no—
149#127×C37C2314yes—
150#124×C37—28no—
151#124×C37—22no—
152#124×C37C2314yescomplemented
153C22⋊Q8×C37—22no—
154C22⋊Q8×C37—28no—
155C22⋊Q8×C37C2314yescomplemented
156#121×C37—28no—
157#121×C37—22no—
158#121×C37—22no—
159#121×C37—22no—
160#121×C37—28no—
161#121×C37C2314yes—
162#121×C37C2314yes—
163#121×C37C2314yescomplemented
164#120×C37—28no—
165#120×C37—28no—
166C4×Q8×C37—22no—
167C4×Q8×C37C2314yescomplemented
168C4×D4×C37—28no—
169C4×D4×C37—22no—
170C4×D4×C37D414yes—
171C4×D4×C37C2314yes—
172C4×D4×C37C2314yes—
173C2×C4⋊C4×C37—21no—
174C2×C4⋊C4×C37—21no—
175C2×C4⋊C4×C37D411yescharacteristic
176C2×C4⋊C4×C37C2311yescharacteristic
177C2×C4⋊C4×C37C2311yescharacteristic
178C2×C22⋊C4×C37—21no—
179C2×C22⋊C4×C37—21no—
180C2×C22⋊C4×C37—21no—
181C2×C22⋊C4×C37—21no—
182C2×C22⋊C4×C37—21no—
183C2×C22⋊C4×C37—21no—
184C2×C22⋊C4×C37—21no—
185C2×C22⋊C4×C37D411yescharacteristic
186C2×C22⋊C4×C37D411yescharacteristic
187C2×C42×C37—21no—
188C2×C42×C37C2311yescharacteristic
189#107×C37C2314yescomplemented
190C4⋊C8×C37C2314yescomplemented
191#103×C37C2314yescomplemented
192#103×C37C2314yescomplemented
193#102×C37C2314yes—
194#102×C37C2314yescomplemented
195#102×C37C2314yescomplemented
196#102×C37C2314yescomplemented
197C22⋊C8×C37C2314yescomplemented
198C22⋊C8×C37C2314yescomplemented
199#97×C37C2314yescomplemented
200C24×C37—21no—
201C24×C37—21no—
202C24×C37—21no—
203C24×C37—21no—
204C24×C37—24no—
205C24×C37—24no—
206C24×C37—44no—
207C24×C37—44no—
208C24×C37—44no—
209C24×C37—44no—
210C24×C37—82no—
211C24×C37—82no—
212C24×C37C2×D411yescharacteristic
213C24×C37C2×D411yescharacteristic
214#41×C37—28no—
215#41×C37—44no—
216#41×C37—48no—
217C2×Q8×C37—21no—
218C2×Q8×C37—21no—
219C2×Q8×C37—24no—
220C2×Q8×C37—22no—
221C2×Q8×C37—28no—
222C2×Q8×C37—22no—
223C2×Q8×C37—22no—
224C2×Q8×C37—44no—
225C2×Q8×C37—44no—
226C2×Q8×C37—48no—
227C2×Q8×C37C2×D414yescomplemented
228C2×Q8×C37C2412yes—
229C2×Q8×C37C2412yes—
230C2×D4×C37—24no—
231C2×D4×C37—28no—
232C2×D4×C37—28no—
233C2×D4×C37—24no—
234C2×D4×C37—24no—
235C2×D4×C37—24no—
236C2×D4×C37—24no—
237C2×D4×C37—21no—
238C2×D4×C37—22no—
239C2×D4×C37—22no—
240C2×D4×C37—22no—
241C2×D4×C37—24no—
242C2×D4×C37—24no—
243C2×D4×C37—21no—
244C2×D4×C37—21no—
245C2×D4×C37—21no—
246C2×D4×C37—24no—
247C2×D4×C37—24no—
248C2×D4×C37—22no—
249C2×D4×C37—22no—
250C2×D4×C37—22no—
251C2×D4×C37—22no—
252C2×D4×C37—44no—
253C2×D4×C37—44no—
254C2×D4×C37—48no—
255C2×D4×C37—48no—
256C2×D4×C37—44no—
257C2×D4×C37—44no—
258C2×D4×C37—44no—
259C2×D4×C37—44no—
260C2×D4×C37—432no—
261C2×D4×C37—44no—
262C2×D4×C37—44no—
263C2×D4×C37—44no—
264C2×D4×C37—82no—
265C2×D4×C37C2×D414yes—
266C2×D4×C37C2×D414yes—
267C2×D4×C37C2412yes—
268C2×D4×C37C2412yes—
269C2×D4×C37C2412yes—
270C2×D4×C37C2412yes—
271C22×C4×C37—21no—
272C22×C4×C37—22no—
273C22×C4×C37—22no—
274C22×C4×C37—22no—
275C22×C4×C37—22no—
276C22×C4×C37—24no—
277C22×C4×C37—21no—
278C22×C4×C37—21no—
279C22×C4×C37—21no—
280C22×C4×C37—24no—
281C22×C4×C37—24no—
282C22×C4×C37—44no—
283C22×C4×C37—44no—
284C22×C4×C37—44no—
285C22×C4×C37C2×D412yes—
286C22×C4×C37C2×D412yes—
287C22×C4×C37C2×D411yescharacteristic
288C22×C4×C37C2×D411yescharacteristic
289C22×C4×C37C2×D411yescharacteristic
290C22×C4×C37C2×D411yescharacteristic
291C22×C4×C37C2412yes—
292C22×C4×C37C2412yes—
293C22×C4×C37C2411yescharacteristic
294SD16×C37—28no—
295SD16×C37—28no—
296SD16×C37—28no—
297SD16×C37—28no—
298SD16×C37—44no—
299SD16×C37C2×D4116yescomplemented
300D8×C37—28no—
301D8×C37—28no—
302D8×C37—44no—
303M16×C37—28no—
304C2×C8×C37—22no—
305C2×C8×C37—22no—
306C2×C8×C37—22no—
307C2×C8×C37—28no—
308C2×C8×C37C2×D414yescomplemented
309C2×C8×C37C2412yes—
310C2×C8×C37C2412yes—
311C2×C8×C37C2412yes—
312C2×C8×C37C2412yes—
313C4⋊C4×C37—24no—
314C4⋊C4×C37—24no—
315C4⋊C4×C37—21no—
316C4⋊C4×C37—21no—
317C4⋊C4×C37C2×D414yes—
318C4⋊C4×C37C2412yes—
319C4⋊C4×C37C2412yes—
320C22⋊C4×C37—24no—
321C22⋊C4×C37—24no—
322C22⋊C4×C37—24no—
323C22⋊C4×C37—24no—
324C22⋊C4×C37—24no—
325C22⋊C4×C37—24no—
326C22⋊C4×C37—24no—
327C22⋊C4×C37C2×D414yes—
328C22⋊C4×C37C2×D414yes—
329C42×C37—24no—
330C42×C37C2×D412yes—
331C42×C37C2412yes—
332C23×C37—22no—
333C23×C37—22no—
334C23×C37—22no—
335C23×C37—24no—
336C23×C37—22no—
337C23×C37—22no—
338C23×C37—22no—
339C23×C37—22no—
340C23×C37—22no—
341C23×C37—22no—
342C23×C37—48no—
343C23×C37—48no—
344C23×C37—48no—
345C23×C37—42no—
346C23×C37—42no—
347C23×C37—42no—
348C23×C37—42no—
349C23×C37—42no—
350C23×C37—42no—
351C23×C37—42no—
352C23×C37—42no—
353C23×C37—48no—
354C23×C37—42no—
355C23×C37—42no—
356C23×C37—42no—
357C23×C37—84no—
358C23×C37—84no—
359C23×C37—816no—
360C23×C37—816no—
361C23×C37AGL(1,ℤ/8)14yescomplemented
362C23×C37C22×D412yes—
363C23×C37C22×D412yes—
364C23×C37C22×D411yescharacteristic
365Q8×C37—24no—
366Q8×C37—22no—
367Q8×C37—22no—
368Q8×C37—22no—
369Q8×C37—48no—
370Q8×C37—42no—
371Q8×C37C22×D414yescomplemented
372D4×C37—28no—
373D4×C37—24no—
374D4×C37—22no—
375D4×C37—22no—
376D4×C37—22no—
377D4×C37—22no—
378D4×C37—22no—
379D4×C37—22no—
380D4×C37—22no—
381D4×C37—48no—
382D4×C37—48no—
383D4×C37—48no—
384D4×C37—48no—
385D4×C37—48no—
386D4×C37—48no—
387D4×C37—48no—
388D4×C37—42no—
389D4×C37—42no—
390D4×C37—42no—
391D4×C37—84no—
392D4×C37C22×D414yes—
393C2×C4×C37—22no—
394C2×C4×C37—22no—
395C2×C4×C37—24no—
396C2×C4×C37—22no—
397C2×C4×C37—22no—
398C2×C4×C37—22no—
399C2×C4×C37—24no—
400C2×C4×C37—24no—
401C2×C4×C37—22no—
402C2×C4×C37—22no—
403C2×C4×C37—22no—
404C2×C4×C37—22no—
405C2×C4×C37—22no—
406C2×C4×C37—22no—
407C2×C4×C37—22no—
408C2×C4×C37—48no—
409C2×C4×C37—48no—
410C2×C4×C37—48no—
411C2×C4×C37—42no—
412C2×C4×C37—42no—
413C2×C4×C37—42no—
414C2×C4×C37C22×D412yes—
415C2×C4×C37C22×D412yes—
416C2×C4×C37C22×D412yes—
417C2×C4×C37C22×D412yes—
418C2×C4×C37C22×D411yescharacteristic
419C2×C4×C37C22×D412yes—
420C2×C4×C37H(5,𝔽2)12yes—
421C2×C4×C37C2511yescharacteristic
422C8×C37—22no—
423C8×C37—22no—
424C8×C37—22no—
425C8×C37C22×D414yescomplemented
426C2×#3265C3711yesmaximal, characteristic, direct product factor, Sylow
427C22×C37—22no—
428C22×C37—28no—
429C22×C37—22no—
430C22×C37—22no—
431C22×C37—24no—
432C22×C37—22no—
433C22×C37—22no—
434C22×C37—44no—
435C22×C37—48no—
436C22×C37—42no—
437C22×C37—42no—
438C22×C37—42no—
439C22×C37—42no—
440C22×C37—42no—
441C22×C37—42no—
442C22×C37—42no—
443C22×C37—42no—
444C22×C37—42no—
445C22×C37—42no—
446C22×C37—42no—
447C22×C37—816no—
448C22×C37—816no—
449C22×C37—84no—
450C22×C37—84no—
451C22×C37—84no—
452C22×C37D4212yes—
453C22×C37C2×AGL(1,ℤ/8)12yes—
454C22×C37C2×AGL(1,ℤ/8)14yescomplemented
455C22×C37#57712yes—
456C22×C37C23×D411yescharacteristic
457C4×C37—22no—
458C4×C37—22no—
459C4×C37—24no—
460C4×C37—22no—
461C4×C37—22no—
462C4×C37—42no—
463C4×C37—42no—
464C4×C37—42no—
465C4×C37D4212yes—
466C4×C37C23×D411yescharacteristic
467C4×C37C2×H(5,𝔽2)11yescharacteristic
468C22×AGL(1,ℤ/8)C2×C3711yescharacteristic, complemented
469C23×SD16C2×C3711yescharacteristic, complemented
470C2×#548C2×C3711yescharacteristic, complemented
471C2×D42C2×C3711yescharacteristic, complemented
472#3265C2×C37116yesdirect product factor
473C2×#496C2×C3711yescharacteristic, complemented
474C2×#468C2×C3711yescharacteristic, complemented
475C2×#466C2×C3711yescharacteristic, complemented
476C2×#460C2×C3711yescharacteristic, complemented
477C2×#463C2×C3711yescharacteristic, complemented
478C2×#449C2×C3711yescharacteristic, complemented
479C2×#448C2×C3711yescharacteristic, complemented
480C2×#450C2×C3711yescharacteristic, complemented
481C2×#447C2×C3711yescharacteristic, complemented
482C2×#440C2×C3711yescharacteristic, complemented
483C2×#435C2×C3711yescharacteristic, complemented
484C2×C37—24no—
485C2×C37—42no—
486C2×C37—44no—
487C2×C37—82no—
488C2×C37—82no—
489C2×C37—82no—
490C2×C37#326514yesdirect product factor
491C2×C37C2×D4211yescharacteristic
492C2×C37C22×AGL(1,ℤ/8)11yescharacteristic
493C2×C37C2×#57711yescharacteristic
494C22×#41C22×C3711yescharacteristic, complemented
495C23×Q8C22×C3711yescharacteristic, complemented
496C23×D4—21no—
497C23×D4C22×C3711yescharacteristic
498C23×D4C22×C3711yescharacteristic
499C2×AGL(1,ℤ/8)—28no—
500C2×AGL(1,ℤ/8)C22×C3718yescomplemented
501C22×SD16—28no—
502C22×SD16C22×C3711yescharacteristic
503C22×SD16C22×C3711yescharacteristic
504C22×SD16C22×C3711yescharacteristic, complemented
505C22×SD16C22×C3711yescharacteristic, complemented
506C22×SD16C22×C3711yescharacteristic, complemented
507C22×SD16C22×C3711yescharacteristic, complemented
508C22×SD16C22×C3718yescomplemented
509C22×D8C22×C3711yescharacteristic
510C22×D8C22×C3711yescharacteristic, complemented
511C22×D8C22×C3711yescharacteristic, complemented
512C22×M16C22×C3711yescharacteristic, complemented
513C23×C8C22×C3711yescharacteristic, complemented
514#548—24no—
515#548C22×C3718yescomplemented
516D42—24no—
517D42C22×C3718yescomplemented
518C2×#127C22×C3711yescharacteristic
519C2×#124—21no—
520C2×#124C22×C3711yescharacteristic, complemented
521C2×C22⋊Q8—21no—
522C2×C22⋊Q8C22×C3711yescharacteristic, complemented
523C2×#121—21no—
524C2×#121—21no—
525C2×#121C22×C3711yescharacteristic
526C2×#121C22×C3711yescharacteristic
527C2×#121C22×C3711yescharacteristic, complemented
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×Q8C22×C3711yescharacteristic, complemented
531C2×C4×D4—21no—
532C2×C4×D4C22×C3711yescharacteristic
533C2×C4×D4C22×C3711yescharacteristic
534#496C22×C3718yescomplemented
535#468C22×C3718yescomplemented
536#466C22×C3718yescomplemented
537#463C22×C3718yescomplemented
538#460C22×C3718yescomplemented
539#450C22×C3718yescomplemented
540#449C22×C3718yescomplemented
541#448C22×C3718yescomplemented
542#447C22×C3718yescomplemented
543#440C22×C3718yescomplemented
544#435C22×C3718yescomplemented
545C2×#107C22×C3711yescharacteristic, complemented
546C2×C4⋊C8C22×C3711yescharacteristic, complemented
547C2×#103C22×C3711yescharacteristic, complemented
548C2×#103C22×C3711yescharacteristic, complemented
549C2×#102C22×C3711yescharacteristic
550C2×#102C22×C3711yescharacteristic, complemented
551C2×#102C22×C3711yescharacteristic, complemented
552C2×#102C22×C3711yescharacteristic, complemented
553C2×C22⋊C8C22×C3711yescharacteristic, complemented
554C2×C22⋊C8C22×C3711yescharacteristic, complemented
555C2×#97C22×C3711yescharacteristic, complemented
556C37C2×#326511yescharacteristic, direct product factor, Sylow
557C25—21no—
558C25—21no—
559C2×#41—22no—
560C2×#41—24no—
561C2×#41—42no—
562C2×#41C23×C3714yescomplemented
563C22×Q8—21no—
564C22×Q8—22no—
565C22×Q8—24no—
566C22×Q8—42no—
567C22×Q8C23×C3711yescharacteristic
568C22×Q8C23×C3711yescharacteristic
569C22×Q8C23×C3714yescomplemented
570C22×D4—24no—
571C22×D4—24no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—28no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—21no—
583C22×D4—42no—
584C22×D4—42no—
585C22×D4—48no—
586C22×D4D4×C3711yescharacteristic
587C22×D4C23×C3711yescharacteristic
588C22×D4C23×C3711yescharacteristic
589C22×D4C23×C3711yescharacteristic
590C22×D4C23×C3714yes—
591C22×D4C23×C3714yes—
592C22×D4C23×C3711yescharacteristic
593C23×C4—21no—
594C23×C4—21no—
595C23×C4—21no—
596C23×C4C23×C3711yescharacteristic
597C23×C4C23×C3711yescharacteristic
598AGL(1,ℤ/8)—232no—
599C2×SD16—24no—
600C2×SD16—24no—
601C2×SD16—24no—
602C2×SD16—232no—
603C2×SD16—24no—
604C2×SD16—42no—
605C2×SD16D4×C3718yescomplemented
606C2×SD16C23×C3714yes—
607C2×SD16C23×C3714yes—
608C2×SD16C23×C3714yescomplemented
609C2×SD16C23×C3714yescomplemented
610C2×SD16C23×C3714yescomplemented
611C2×SD16C23×C3714yescomplemented
612C2×D8—24no—
613C2×D8—24no—
614C2×D8—42no—
615C2×D8C23×C3714yes—
616C2×D8C23×C3714yescomplemented
617C2×D8C23×C3714yescomplemented
618C2×M16—24no—
619C2×M16C23×C3714yescomplemented
620C22×C8—24no—
621C22×C8C23×C3711yescharacteristic
622C22×C8C23×C3711yescharacteristic
623C22×C8C23×C3711yescharacteristic
624C22×C8C23×C3711yescharacteristic
625C22×C8C23×C3714yescomplemented
626#127—22no—
627#127C23×C3714yes—
628#124—28no—
629#124—22no—
630#124C23×C3714yescomplemented
631C22⋊Q8—22no—
632C22⋊Q8—28no—
633C22⋊Q8C23×C3714yescomplemented
634#121—28no—
635#121—22no—
636#121—22no—
637#121—22no—
638#121—28no—
639#121C23×C3714yes—
640#121C23×C3714yes—
641#121C23×C3714yescomplemented
642#120—28no—
643#120—28no—
644C4×Q8—22no—
645C4×Q8C23×C3714yescomplemented
646C4×D4—28no—
647C4×D4—22no—
648C4×D4D4×C3714yes—
649C4×D4C23×C3714yes—
650C4×D4C23×C3714yes—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C3711yescharacteristic
654C2×C4⋊C4C23×C3711yescharacteristic
655C2×C4⋊C4C23×C3711yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C3711yescharacteristic
664C2×C22⋊C4D4×C3711yescharacteristic
665C2×C42—21no—
666C2×C42C23×C3711yescharacteristic
667#107C23×C3714yescomplemented
668C4⋊C8C23×C3714yescomplemented
669#103C23×C3714yescomplemented
670#103C23×C3714yescomplemented
671#102C23×C3714yes—
672#102C23×C3714yescomplemented
673#102C23×C3714yescomplemented
674#102C23×C3714yescomplemented
675C22⋊C8C23×C3714yescomplemented
676C22⋊C8C23×C3714yescomplemented
677#97C23×C3714yescomplemented
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—24no—
683C24—24no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—44no—
688C24—82no—
689C24—82no—
690C24C2×D4×C3711yescharacteristic
691C24C2×D4×C3711yescharacteristic
692#41—28no—
693#41—44no—
694#41—48no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—24no—
698C2×Q8—22no—
699C2×Q8—28no—
700C2×Q8—22no—
701C2×Q8—22no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—48no—
705C2×Q8C2×D4×C3714yescomplemented
706C2×Q8C24×C3712yes—
707C2×Q8C24×C3712yes—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—21no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—22no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—432no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—82no—
743C2×D4C2×D4×C3714yes—
744C2×D4C2×D4×C3714yes—
745C2×D4C24×C3712yes—
746C2×D4C24×C3712yes—
747C2×D4C24×C3712yes—
748C2×D4C24×C3712yes—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4C2×D4×C3711yescharacteristic
764C22×C4C2×D4×C3711yescharacteristic
765C22×C4C2×D4×C3711yescharacteristic
766C22×C4C2×D4×C3711yescharacteristic
767C22×C4C2×D4×C3712yes—
768C22×C4C2×D4×C3712yes—
769C22×C4C24×C3712yes—
770C22×C4C24×C3712yes—
771C22×C4C24×C3711yescharacteristic
772SD16—28no—
773SD16—28no—
774SD16—28no—
775SD16—28no—
776SD16—44no—
777SD16C2×D4×C37116yescomplemented
778D8—28no—
779D8—28no—
780D8—44no—
781M16—28no—
782C2×C8—22no—
783C2×C8—22no—
784C2×C8—22no—
785C2×C8—28no—
786C2×C8C2×D4×C3714yescomplemented
787C2×C8C24×C3712yes—
788C2×C8C24×C3712yes—
789C2×C8C24×C3712yes—
790C2×C8C24×C3712yes—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4C2×D4×C3714yes—
796C4⋊C4C24×C3712yes—
797C4⋊C4C24×C3712yes—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—24no—
804C22⋊C4—24no—
805C22⋊C4C2×D4×C3714yes—
806C22⋊C4C2×D4×C3714yes—
807C42—24no—
808C42C2×D4×C3712yes—
809C42C24×C3712yes—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—24no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—48no—
821C23—48no—
822C23—48no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—48no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—84no—
836C23—84no—
837C23—816no—
838C23—816no—
839C23AGL(1,ℤ/8)×C3714yescomplemented
840C23C22×D4×C3712yes—
841C23C22×D4×C3712yes—
842C23C22×D4×C3711yescharacteristic
843Q8—24no—
844Q8—22no—
845Q8—22no—
846Q8—22no—
847Q8—48no—
848Q8—42no—
849Q8C22×D4×C3714yescomplemented
850D4—28no—
851D4—24no—
852D4—22no—
853D4—22no—
854D4—22no—
855D4—22no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—48no—
860D4—48no—
861D4—48no—
862D4—48no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—42no—
867D4—42no—
868D4—42no—
869D4—84no—
870D4C22×D4×C3714yes—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—48no—
887C2×C4—48no—
888C2×C4—48no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4C22×D4×C3712yes—
893C2×C4C22×D4×C3712yes—
894C2×C4C22×D4×C3712yes—
895C2×C4C22×D4×C3712yes—
896C2×C4C22×D4×C3711yescharacteristic
897C2×C4C22×D4×C3712yes—
898C2×C4H(5,𝔽2)×C3712yes—
899C2×C4C25×C3711yescharacteristic
900C8—22no—
901C8—22no—
902C8—22no—
903C8C22×D4×C3714yescomplemented
904C22—22no—
905C22—28no—
906C22—22no—
907C22—22no—
908C22—24no—
909C22—22no—
910C22—22no—
911C22—44no—
912C22—48no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—816no—
925C22—816no—
926C22—84no—
927C22—84no—
928C22—84no—
929C22D42×C3712yes—
930C22C2×AGL(1,ℤ/8)×C3712yes—
931C22C2×AGL(1,ℤ/8)×C3714yescomplemented
932C22C37×#57712yes—
933C22C23×D4×C3711yescharacteristic
934C4—22no—
935C4—22no—
936C4—24no—
937C4—22no—
938C4—22no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4D42×C3712yes—
943C4C23×D4×C3711yescharacteristic
944C4C2×H(5,𝔽2)×C3711yescharacteristic
945C2—24no—
946C2—42no—
947C2—44no—
948C2—82no—
949C2—82no—
950C2—82no—
951C2C37×#326514yesdirect product factor
952C2C2×D42×C3711yescharacteristic
953C2C22×AGL(1,ℤ/8)×C3711yescharacteristic
954C2C2×C37×#57711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC2×C4C25×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C37C2semidirect
2. C23×SD16×C37C2semidirect
3. C2×C37×#548C2semidirect
4. C2×D42×C37C2semidirect
5. C37×#3265C2direct (N × H)
6. C2×C37×#496C2semidirect
7. C2×C37×#468C2semidirect
8. C2×C37×#466C2semidirect
9. C2×C37×#460C2semidirect
10. C2×C37×#463C2semidirect
11. C2×C37×#449C2semidirect
12. C2×C37×#448C2semidirect
13. C2×C37×#450C2semidirect
14. C2×C37×#447C2semidirect
15. C2×C37×#440C2semidirect
16. C2×C37×#435C2semidirect
17. C22×#41×C37C22semidirect
18. C23×Q8×C37C22semidirect
23. C2×AGL(1,ℤ/8)×C37C22semidirect
27. C22×SD16×C37C22semidirect
28. C22×SD16×C37C22semidirect
29. C22×SD16×C37C22semidirect
30. C22×SD16×C37C22semidirect
31. C22×SD16×C37C22semidirect
33. C22×D8×C37C22semidirect
34. C22×D8×C37C22semidirect
35. C22×M16×C37C22semidirect
36. C23×C8×C37C22semidirect
38. C37×#548C22semidirect
40. D42×C37C22semidirect
43. C2×#124×C37C22semidirect
45. C2×C22⋊Q8×C37C22semidirect
50. C2×#121×C37C22semidirect
53. C2×C4×Q8×C37C22semidirect
57. C37×#496C22semidirect
58. C37×#468C22semidirect
59. C37×#466C22semidirect
60. C37×#463C22semidirect
61. C37×#460C22semidirect
62. C37×#450C22semidirect
63. C37×#449C22semidirect
64. C37×#448C22semidirect
65. C37×#447C22semidirect
66. C37×#440C22semidirect
67. C37×#435C22semidirect
68. C2×#107×C37C22semidirect
69. C2×C4⋊C8×C37C22semidirect
70. C2×#103×C37C22semidirect
71. C2×#103×C37C22semidirect
73. C2×#102×C37C22semidirect
74. C2×#102×C37C22semidirect
75. C2×#102×C37C22semidirect
76. C2×C22⋊C8×C37C22semidirect
77. C2×C22⋊C8×C37C22semidirect
78. C2×#97×C37C22semidirect
84. C2×#41×C37C23semidirect
91. C22×Q8×C37C23semidirect
127. C2×SD16×C37D4semidirect
130. C2×SD16×C37C23semidirect
131. C2×SD16×C37C23semidirect
132. C2×SD16×C37C23semidirect
133. C2×SD16×C37C23semidirect
138. C2×D8×C37C23semidirect
139. C2×D8×C37C23semidirect
141. C2×M16×C37C23semidirect
147. C22×C8×C37C23semidirect
152. #124×C37C23semidirect
155. C22⋊Q8×C37C23semidirect
163. #121×C37C23semidirect
167. C4×Q8×C37C23semidirect
189. #107×C37C23semidirect
190. C4⋊C8×C37C23semidirect
191. #103×C37C23semidirect
192. #103×C37C23semidirect
194. #102×C37C23semidirect
195. #102×C37C23semidirect
196. #102×C37C23semidirect
197. C22⋊C8×C37C23semidirect
198. C22⋊C8×C37C23semidirect
199. #97×C37C23semidirect
227. C2×Q8×C37C2×D4semidirect
299. SD16×C37C2×D4semidirect
308. C2×C8×C37C2×D4semidirect
361. C23×C37AGL(1,ℤ/8)semidirect
371. Q8×C37C22×D4semidirect
425. C8×C37C22×D4semidirect
426. C2×#3265C37direct (N × H)
454. C22×C37C2×AGL(1,ℤ/8)semidirect
468. C22×AGL(1,ℤ/8)C2×C37semidirect
469. C23×SD16C2×C37semidirect
470. C2×#548C2×C37semidirect
471. C2×D42C2×C37semidirect
472. #3265C2×C37direct (N × H)
473. C2×#496C2×C37semidirect
474. C2×#468C2×C37semidirect
475. C2×#466C2×C37semidirect
476. C2×#460C2×C37semidirect
477. C2×#463C2×C37semidirect
478. C2×#449C2×C37semidirect
479. C2×#448C2×C37semidirect
480. C2×#450C2×C37semidirect
481. C2×#447C2×C37semidirect
482. C2×#440C2×C37semidirect
483. C2×#435C2×C37semidirect
490. C2×C37#3265direct (N × H)
494. C22×#41C22×C37semidirect
495. C23×Q8C22×C37semidirect
500. C2×AGL(1,ℤ/8)C22×C37semidirect
504. C22×SD16C22×C37semidirect
505. C22×SD16C22×C37semidirect
506. C22×SD16C22×C37semidirect
507. C22×SD16C22×C37semidirect
508. C22×SD16C22×C37semidirect
510. C22×D8C22×C37semidirect
511. C22×D8C22×C37semidirect
512. C22×M16C22×C37semidirect
513. C23×C8C22×C37semidirect
515. #548C22×C37semidirect
517. D42C22×C37semidirect
520. C2×#124C22×C37semidirect
522. C2×C22⋊Q8C22×C37semidirect
527. C2×#121C22×C37semidirect
530. C2×C4×Q8C22×C37semidirect
534. #496C22×C37semidirect
535. #468C22×C37semidirect
536. #466C22×C37semidirect
537. #463C22×C37semidirect
538. #460C22×C37semidirect
539. #450C22×C37semidirect
540. #449C22×C37semidirect
541. #448C22×C37semidirect
542. #447C22×C37semidirect
543. #440C22×C37semidirect
544. #435C22×C37semidirect
545. C2×#107C22×C37semidirect
546. C2×C4⋊C8C22×C37semidirect
547. C2×#103C22×C37semidirect
548. C2×#103C22×C37semidirect
550. C2×#102C22×C37semidirect
551. C2×#102C22×C37semidirect
552. C2×#102C22×C37semidirect
553. C2×C22⋊C8C22×C37semidirect
554. C2×C22⋊C8C22×C37semidirect
555. C2×#97C22×C37semidirect
556. C37C2×#3265direct (N × H)
562. C2×#41C23×C37semidirect
569. C22×Q8C23×C37semidirect
605. C2×SD16D4×C37semidirect
608. C2×SD16C23×C37semidirect
609. C2×SD16C23×C37semidirect
610. C2×SD16C23×C37semidirect
611. C2×SD16C23×C37semidirect
616. C2×D8C23×C37semidirect
617. C2×D8C23×C37semidirect
619. C2×M16C23×C37semidirect
625. C22×C8C23×C37semidirect
630. #124C23×C37semidirect
633. C22⋊Q8C23×C37semidirect
641. #121C23×C37semidirect
645. C4×Q8C23×C37semidirect
667. #107C23×C37semidirect
668. C4⋊C8C23×C37semidirect
669. #103C23×C37semidirect
670. #103C23×C37semidirect
672. #102C23×C37semidirect
673. #102C23×C37semidirect
674. #102C23×C37semidirect
675. C22⋊C8C23×C37semidirect
676. C22⋊C8C23×C37semidirect
677. #97C23×C37semidirect
705. C2×Q8C2×D4×C37semidirect
777. SD16C2×D4×C37semidirect
786. C2×C8C2×D4×C37semidirect
839. C23AGL(1,ℤ/8)×C37semidirect
849. Q8C22×D4×C37semidirect
903. C8C22×D4×C37semidirect
931. C22C2×AGL(1,ℤ/8)×C37semidirect
951. C2C37×#3265direct (N × H)

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C372
C23×SD16×C372
C2×C37×#5482
C2×D42×C372
C37×#32652
C2×C37×#4962
C2×C37×#4682
C2×C37×#4662
C2×C37×#4602
C2×C37×#4632
C2×C37×#4492
C2×C37×#4482
C2×C37×#4502
C2×C37×#4472
C2×C37×#4402
C2×C37×#4352
C2×#326537