Finite Group Databasebeta

← C37×#23881 #22645134

Subgroups — C37×#23881 #22645134

Order 9472.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#575C211yesmaximal, characteristic, complemented
2C37×#3489C211yesmaximal, characteristic, complemented
3C2×C37×#456C211yesmaximal, characteristic, complemented
4C2×C37×#454C211yesmaximal, characteristic, complemented
5C37×#3005C211yesmaximal, characteristic, complemented
6C37×#2432C211yesmaximal, characteristic, complemented
7C37×#2007C211yesmaximal, characteristic, complemented
8C37×#2006C211yesmaximal, characteristic, complemented
9C37×#2005C211yesmaximal, characteristic, complemented
10C37×#2003C211yesmaximal, characteristic, complemented
11C37×#1901C211yesmaximal, characteristic, complemented
12C37×#1883C211yesmaximal, characteristic, complemented
13C37×#1882C211yesmaximal, characteristic, complemented
14C37×#1871C211yesmaximal, characteristic, complemented
15C37×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C22×#41×C37C2211yescharacteristic
19C37×#575—24no—
20C37×#575—24no—
21C2×#137×C37—21no—
22C2×#137×C37C2211yescharacteristic
23C2×#137×C37C2211yescharacteristic
24C2×#137×C37C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C37—21no—
26C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
29C2×#135×C37—21no—
30C2×#135×C37—21no—
31C22×M16×C37C2211yescharacteristic
32D4×Q8×C37—21no—
33C37×#548—21no—
34C37×#547—21no—
35C37×#547—22no—
36C37×#546—21no—
37C37×#546—22no—
38C37×#537—21no—
39C37×#537C2211yescharacteristic
40C37×#536—21no—
41C37×#536C2211yescharacteristic
42C2×C4⋊Q8×C37C2211yescharacteristic, complemented
43C2×#124×C37C2211yescharacteristic, complemented
44C37×#525—21no—
45C37×#525C2211yescharacteristic
46C2×C22⋊Q8×C37—21no—
47C2×C22⋊Q8×C37C2211yescharacteristic
48C37×#520C2211yescharacteristic
49C37×#456—24no—
50C37×#454—24no—
51C37×#452—21no—
52C37×#452—21no—
53C37×#449—21no—
54C37×#449—21no—
55C2×#104×C37C2211yescharacteristic
56C2×#104×C37C2211yescharacteristic
57C2×#104×C37C2211yescharacteristic
58C2×#104×C37C2211yescharacteristic
59C2×#104×C37C2211yescharacteristic, complemented
60C2×#104×C37C2211yescharacteristic, complemented
61C37×#419C2211yescharacteristic, complemented
62C37×#418C2211yescharacteristic, complemented
63C2×#101×C37C2211yescharacteristic, complemented
64C2×#101×C37C2211yescharacteristic, complemented
65C37×#407C2211yescharacteristic
66C37×#394—22no—
67C37×#391C2211yescharacteristic, complemented
68C37×#390C2211yescharacteristic, complemented
69C37×#385—22no—
70C4×C22⋊C4×C37C2211yescharacteristic
71C37×#343C2211yescharacteristic, complemented
72C37×#343C2211yescharacteristic, complemented
73C37×#339C2211yescharacteristic, complemented
74C37×#339C2211yescharacteristic, complemented
752−1+4×C37—22no—
762−1+4×C37—22no—
772−1+4×C37—41no—
782−1+4×C37—41no—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—21no—
82C2×#41×C37—22no—
83C2×#41×C37—21no—
84C2×#41×C37—22no—
85C2×#41×C37—22no—
86C2×#41×C37—22no—
87C2×#41×C37—22no—
88C2×#41×C37—21no—
89C2×#41×C37—21no—
90C2×#41×C37—21no—
91C2×#41×C37—21no—
92C2×#41×C37—41no—
93C2×#41×C37—41no—
94C2×#41×C37—41no—
95C2×#41×C37—41no—
96C2×#41×C37D411yescharacteristic
97C2×#41×C37D411yescharacteristic
98C2×#41×C37C2311yescharacteristic
99C2×#41×C37C2311yescharacteristic
100C2×#41×C37C2311yescharacteristic
101C22×Q8×C37—21no—
102C22×Q8×C37—21no—
103C22×Q8×C37D411yescharacteristic
104C22×Q8×C37C2311yescharacteristic
105C22×Q8×C37C2311yescharacteristic
106C22×D4×C37—21no—
107C22×D4×C37—21no—
108C22×D4×C37D411yescharacteristic
109C22×D4×C37C2311yescharacteristic
110C23×C4×C37—21no—
111C23×C4×C37—21no—
112C23×C4×C37C2311yescharacteristic
113#137×C37—28no—
114#137×C37—22no—
115#137×C37—22no—
116#137×C37—22no—
117#137×C37—22no—
118#137×C37—41no—
119#137×C37D414yescomplemented
120AGL(1,ℤ/8)×C37—28no—
121AGL(1,ℤ/8)×C37—22no—
122AGL(1,ℤ/8)×C37—22no—
123AGL(1,ℤ/8)×C37—22no—
124AGL(1,ℤ/8)×C37—22no—
125AGL(1,ℤ/8)×C37—41no—
126AGL(1,ℤ/8)×C37D414yescomplemented
127#135×C37—28no—
128#135×C37—28no—
129C2×Q16×C37—21no—
130C2×Q16×C37—21no—
131C2×Q16×C37—21no—
132C2×SD16×C37—21no—
133C2×SD16×C37—21no—
134C2×SD16×C37—21no—
135C2×SD16×C37—21no—
136C2×SD16×C37—21no—
137C2×SD16×C37—21no—
138C2×D8×C37—21no—
139C2×D8×C37—21no—
140C2×D8×C37—21no—
141C2×M16×C37—21no—
142C2×M16×C37—22no—
143C2×M16×C37—22no—
144C2×M16×C37C2311yescharacteristic
145C2×M16×C37C2311yescharacteristic
146C2×M16×C37C2311yescharacteristic
147C2×M16×C37C2311yescharacteristic
148C22×C8×C37—21no—
149C4⋊Q8×C37—22no—
150C4⋊Q8×C37—21no—
151C4⋊Q8×C37—22no—
152C4⋊Q8×C37—41no—
153#124×C37—22no—
154#124×C37—21no—
155#124×C37—22no—
156#124×C37—41no—
157#123×C37—22no—
158#123×C37—22no—
159#123×C37—22no—
160#123×C37—21no—
161#123×C37—22no—
162C22⋊Q8×C37—22no—
163C22⋊Q8×C37—22no—
164C22⋊Q8×C37—22no—
165C22⋊Q8×C37—21no—
166C22⋊Q8×C37—21no—
167C22⋊Q8×C37—21no—
168C22⋊Q8×C37—21no—
169C22⋊Q8×C37—21no—
170C22⋊Q8×C37—21no—
171C22⋊Q8×C37—21no—
172C22⋊Q8×C37—21no—
173C22⋊Q8×C37D411yescharacteristic
174C22⋊Q8×C37D411yescharacteristic
175#121×C37—22no—
176#121×C37—22no—
177#121×C37—22no—
178#121×C37—21no—
179#121×C37—21no—
180#121×C37—22no—
181#121×C37D411yescharacteristic
182#121×C37D411yescharacteristic
183#120×C37—22no—
184#120×C37—21no—
185C4×Q8×C37—21no—
186C4×D4×C37—22no—
187C4×D4×C37—22no—
188C4×D4×C37—21no—
189C4×D4×C37—22no—
190C4×D4×C37—21no—
191C4×D4×C37—21no—
192#117×C37—21no—
193#117×C37C2311yescharacteristic
194C2×C4⋊C4×C37—22no—
195C2×C4⋊C4×C37—21no—
196C2×C4⋊C4×C37—22no—
197C2×C4⋊C4×C37D412yes—
198C2×C4⋊C4×C37C2311yescharacteristic
199C2×C22⋊C4×C37—22no—
200C2×C22⋊C4×C37—21no—
201C2×C22⋊C4×C37—22no—
202C2×C22⋊C4×C37—22no—
203C2×C22⋊C4×C37D412yes—
204C2×C42×C37C2311yescharacteristic
205C2×C42×C37C2311yescharacteristic
206#104×C37—22no—
207#104×C37—22no—
208#104×C37—22no—
209#104×C37—22no—
210#104×C37—41no—
211#104×C37—41no—
212#103×C37—21no—
213#103×C37—21no—
214#102×C37—21no—
215#102×C37—21no—
216#101×C37—22no—
217#101×C37—22no—
218C22⋊C8×C37—21no—
219C22⋊C8×C37—21no—
220#95×C37—21no—
221#95×C37—22no—
222C24×C37—21no—
223C24×C37—21no—
224C24×C37C2×D411yescharacteristic
225#41×C37—21no—
226#41×C37—21no—
227#41×C37—24no—
228#41×C37—24no—
229#41×C37—22no—
230#41×C37—22no—
231#41×C37—21no—
232#41×C37—21no—
233#41×C37—21no—
234#41×C37—21no—
235#41×C37—21no—
236#41×C37—21no—
237#41×C37—21no—
238#41×C37—21no—
239#41×C37—42no—
240#41×C37—42no—
241#41×C37—41no—
242#41×C37—41no—
243#41×C37—42no—
244#41×C37—42no—
245#41×C37—42no—
246#41×C37—42no—
247#41×C37—42no—
248#41×C37—42no—
249#41×C37—44no—
250#41×C37—44no—
251#41×C37—42no—
252#41×C37—42no—
253#41×C37—42no—
254#41×C37—42no—
255#41×C37—42no—
256#41×C37—42no—
257#41×C37C2×D412yes—
258#41×C37C2×D412yes—
259C2×Q8×C37—22no—
260C2×Q8×C37—21no—
261C2×Q8×C37—21no—
262C2×Q8×C37—21no—
263C2×Q8×C37—21no—
264C2×Q8×C37—21no—
265C2×Q8×C37—21no—
266C2×Q8×C37—21no—
267C2×Q8×C37—21no—
268C2×Q8×C37—22no—
269C2×Q8×C37—21no—
270C2×Q8×C37—21no—
271C2×Q8×C37—21no—
272C2×Q8×C37—21no—
273C2×Q8×C37—41no—
274C2×Q8×C37—42no—
275C2×Q8×C37—42no—
276C2×Q8×C37—42no—
277C2×Q8×C37—42no—
278C2×Q8×C37C2×D411yescharacteristic
279C2×Q8×C37C2×D411yescharacteristic
280C2×Q8×C37C2×D412yes—
281C2×Q8×C37C2×D411yescharacteristic
282C2×D4×C37—21no—
283C2×D4×C37—22no—
284C2×D4×C37—22no—
285C2×D4×C37—21no—
286C2×D4×C37—21no—
287C2×D4×C37—21no—
288C2×D4×C37—21no—
289C2×D4×C37—21no—
290C2×D4×C37—22no—
291C2×D4×C37—21no—
292C2×D4×C37—21no—
293C2×D4×C37—21no—
294C2×D4×C37—21no—
295C2×D4×C37—21no—
296C2×D4×C37—21no—
297C2×D4×C37—21no—
298C2×D4×C37—41no—
299C2×D4×C37—42no—
300C2×D4×C37—42no—
301C2×D4×C37—42no—
302C2×D4×C37—42no—
303C2×D4×C37—41no—
304C2×D4×C37—41no—
305C2×D4×C37C2×D411yescharacteristic
306C2×D4×C37C2×D411yescharacteristic
307C2×D4×C37C2×D412yes—
308C2×D4×C37C2×D411yescharacteristic
309C22×C4×C37—21no—
310C22×C4×C37—21no—
311C22×C4×C37—21no—
312C22×C4×C37—21no—
313C22×C4×C37—21no—
314C22×C4×C37—22no—
315C22×C4×C37—22no—
316C22×C4×C37—21no—
317C22×C4×C37—21no—
318C22×C4×C37—21no—
319C22×C4×C37—22no—
320C22×C4×C37—21no—
321C22×C4×C37—21no—
322C22×C4×C37—21no—
323C22×C4×C37—21no—
324C22×C4×C37—21no—
325C22×C4×C37—42no—
326C22×C4×C37—42no—
327C22×C4×C37—42no—
328C22×C4×C37—42no—
329C22×C4×C37—41no—
330C22×C4×C37—41no—
331C22×C4×C37C2×D412yes—
332C22×C4×C37C2×D411yescharacteristic
333C22×C4×C37C2×D411yescharacteristic
334C22×C4×C37C2×D411yescharacteristic
335C22×C4×C37C2×D411yescharacteristic
336C22×C4×C37C2×D411yescharacteristic
337C22×C4×C37C2×D412yes—
338C22×C4×C37C2411yescharacteristic
339Q16×C37—24no—
340Q16×C37—24no—
341Q16×C37—42no—
342SD16×C37—24no—
343SD16×C37—24no—
344SD16×C37—24no—
345SD16×C37—24no—
346SD16×C37—42no—
347SD16×C37—42no—
348D8×C37—24no—
349D8×C37—24no—
350D8×C37—42no—
351M16×C37—24no—
352M16×C37—21no—
353M16×C37—21no—
354M16×C37—21no—
355M16×C37—21no—
356M16×C37—21no—
357M16×C37—21no—
358M16×C37C2×D412yes—
359M16×C37C2×D412yes—
360C2×C8×C37—24no—
361C2×C8×C37—21no—
362C2×C8×C37—21no—
363C2×C8×C37—21no—
364C2×C8×C37—21no—
365C4⋊C4×C37—22no—
366C4⋊C4×C37—22no—
367C4⋊C4×C37—22no—
368C4⋊C4×C37—22no—
369C4⋊C4×C37—21no—
370C4⋊C4×C37—22no—
371C4⋊C4×C37—22no—
372C4⋊C4×C37—21no—
373C4⋊C4×C37—21no—
374C4⋊C4×C37—21no—
375C4⋊C4×C37—44no—
376C4⋊C4×C37C2×D411yescharacteristic
377C4⋊C4×C37C2×D411yescharacteristic
378C22⋊C4×C37—22no—
379C22⋊C4×C37—22no—
380C22⋊C4×C37—22no—
381C22⋊C4×C37—22no—
382C22⋊C4×C37—22no—
383C22⋊C4×C37—21no—
384C22⋊C4×C37—22no—
385C22⋊C4×C37—22no—
386C22⋊C4×C37—21no—
387C22⋊C4×C37—21no—
388C22⋊C4×C37—21no—
389C22⋊C4×C37—21no—
390C22⋊C4×C37—44no—
391C22⋊C4×C37—44no—
392C22⋊C4×C37—42no—
393C42×C37—22no—
394C42×C37—21no—
395C42×C37—21no—
396C42×C37—21no—
397C42×C37—21no—
398C42×C37—21no—
399C23×C37—21no—
400C23×C37—21no—
401C23×C37—21no—
402C23×C37—21no—
403C23×C37—21no—
404C23×C37—22no—
405C23×C37—41no—
406C23×C37—41no—
407C23×C37—42no—
408C23×C37—42no—
409C23×C37—42no—
410C23×C37—42no—
411C23×C37—41no—
412C23×C37—41no—
413C23×C37—81no—
414C23×C37#12011yescharacteristic
415C23×C37#12011yescharacteristic
416C23×C37C22×D411yescharacteristic
417Q8×C37—21no—
418Q8×C37—21no—
419Q8×C37—22no—
420Q8×C37—21no—
421Q8×C37—21no—
422Q8×C37—22no—
423Q8×C37—21no—
424Q8×C37—42no—
425Q8×C37—44no—
426Q8×C37—41no—
427Q8×C37—41no—
428Q8×C37—41no—
429Q8×C37—41no—
430Q8×C37—41no—
431Q8×C37—41no—
432Q8×C37#12012yes—
433D4×C37—22no—
434D4×C37—22no—
435D4×C37—21no—
436D4×C37—22no—
437D4×C37—21no—
438D4×C37—21no—
439D4×C37—21no—
440D4×C37—22no—
441D4×C37—21no—
442D4×C37—42no—
443D4×C37—42no—
444D4×C37—42no—
445D4×C37—42no—
446D4×C37—44no—
447D4×C37—44no—
448D4×C37—44no—
449D4×C37—41no—
450D4×C37—41no—
451D4×C37—41no—
452D4×C37—41no—
453D4×C37—41no—
454D4×C37—41no—
455D4×C37—81no—
456D4×C37—82no—
457D4×C37#12012yes—
458C2×C4×C37—21no—
459C2×C4×C37—21no—
460C2×C4×C37—21no—
461C2×C4×C37—21no—
462C2×C4×C37—21no—
463C2×C4×C37—21no—
464C2×C4×C37—21no—
465C2×C4×C37—21no—
466C2×C4×C37—21no—
467C2×C4×C37—21no—
468C2×C4×C37—21no—
469C2×C4×C37—22no—
470C2×C4×C37—22no—
471C2×C4×C37—22no—
472C2×C4×C37—21no—
473C2×C4×C37—22no—
474C2×C4×C37—21no—
475C2×C4×C37—21no—
476C2×C4×C37—22no—
477C2×C4×C37—21no—
478C2×C4×C37—22no—
479C2×C4×C37—22no—
480C2×C4×C37—22no—
481C2×C4×C37—42no—
482C2×C4×C37—42no—
483C2×C4×C37—42no—
484C2×C4×C37—44no—
485C2×C4×C37—44no—
486C2×C4×C37—44no—
487C2×C4×C37—41no—
488C2×C4×C37—44no—
489C2×C4×C37—41no—
490C2×C4×C37—41no—
491C2×C4×C37—41no—
492C2×C4×C37—41no—
493C2×C4×C37—41no—
494C2×C4×C37—41no—
495C2×C4×C37—41no—
496C2×C4×C37—42no—
497C2×C4×C37—41no—
498C2×C4×C37—41no—
499C2×C4×C37—41no—
500C2×C4×C37—82no—
501C2×C4×C37#12011yescharacteristic
502C2×C4×C37#12011yescharacteristic
503C2×C4×C37C22×D411yescharacteristic
504C2×C4×C37C22×D411yescharacteristic
505C2×C4×C37C22×D411yescharacteristic
506C2×C4×C37C22×D411yescharacteristic
507C2×C4×C37H(5,𝔽2)11yescharacteristic
508C2×C4×C37H(5,𝔽2)11yescharacteristic
509C8×C37—22no—
510C8×C37—22no—
511C8×C37—41no—
512C8×C37—41no—
513#23881C3711yesmaximal, characteristic, direct product factor, Sylow
514C22×C37—21no—
515C22×C37—21no—
516C22×C37—21no—
517C22×C37—21no—
518C22×C37—22no—
519C22×C37—21no—
520C22×C37—21no—
521C22×C37—21no—
522C22×C37—21no—
523C22×C37—44no—
524C22×C37—41no—
525C22×C37—41no—
526C22×C37—41no—
527C22×C37—41no—
528C22×C37—42no—
529C22×C37—41no—
530C22×C37—41no—
531C22×C37—41no—
532C22×C37—41no—
533C22×C37—81no—
534C22×C37—81no—
535C22×C37—82no—
536C22×C37—84no—
537C22×C37—81no—
538C22×C37—81no—
539C22×C37C2×#12011yescharacteristic
540C22×C37D4211yescharacteristic
541C22×C37D4211yescharacteristic
542C4×C37—21no—
543C4×C37—21no—
544C4×C37—22no—
545C4×C37—42no—
546C4×C37—42no—
547C4×C37—41no—
548C4×C37—42no—
549C4×C37—41no—
550C4×C37—42no—
551C4×C37—41no—
552C4×C37—41no—
553C4×C37—81no—
554C4×C37C2×#12011yescharacteristic
555C4×C37#53411yescharacteristic
556C4×C37D4211yescharacteristic
557C4×C37D4211yescharacteristic
558C2×#575C2×C3711yescharacteristic, complemented
559#3489C2×C3711yescharacteristic, complemented
560C2×#456C2×C3711yescharacteristic, complemented
561C2×#454C2×C3711yescharacteristic, complemented
562#3005C2×C3711yescharacteristic, complemented
563#2432C2×C3711yescharacteristic, complemented
564#2007C2×C3711yescharacteristic, complemented
565#2006C2×C3711yescharacteristic, complemented
566#2005C2×C3711yescharacteristic, complemented
567#2003C2×C3711yescharacteristic, complemented
568#1901C2×C3711yescharacteristic, complemented
569#1883C2×C3711yescharacteristic, complemented
570#1882C2×C3711yescharacteristic, complemented
571#1871C2×C3711yescharacteristic, complemented
572#1789C2×C3711yescharacteristic, complemented
573C2×C37—21no—
574C2×C37—21no—
575C2×C37—41no—
576C2×C37—41no—
577C2×C37—42no—
578C2×C37—81no—
579C2×C37—82no—
580C2×C37—81no—
581C2×C37#240311yescharacteristic
582C2×C37#301811yescharacteristic
583C2×C37#302011yescharacteristic
584C2×2−1+4C22×C3711yescharacteristic
585C22×#41C22×C3711yescharacteristic
586C22×#41C22×C3711yescharacteristic
587#575—24no—
588#575—24no—
589C2×#137—21no—
590C2×#137C22×C3711yescharacteristic
591C2×#137C22×C3711yescharacteristic
592C2×#137C22×C3711yescharacteristic, complemented
593C2×AGL(1,ℤ/8)—21no—
594C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
595C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
596C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
597C2×#135—21no—
598C2×#135—21no—
599C22×M16C22×C3711yescharacteristic
600D4×Q8—21no—
601#548—21no—
602#547—21no—
603#547—22no—
604#546—21no—
605#546—22no—
606#537—21no—
607#537C22×C3711yescharacteristic
608#536—21no—
609#536C22×C3711yescharacteristic
610C2×C4⋊Q8C22×C3711yescharacteristic, complemented
611C2×#124C22×C3711yescharacteristic, complemented
612#525—21no—
613#525C22×C3711yescharacteristic
614C2×C22⋊Q8—21no—
615C2×C22⋊Q8C22×C3711yescharacteristic
616#520C22×C3711yescharacteristic
617#456—24no—
618#454—24no—
619#452—21no—
620#452—21no—
621#449—21no—
622#449—21no—
623C2×#104C22×C3711yescharacteristic
624C2×#104C22×C3711yescharacteristic
625C2×#104C22×C3711yescharacteristic
626C2×#104C22×C3711yescharacteristic
627C2×#104C22×C3711yescharacteristic, complemented
628C2×#104C22×C3711yescharacteristic, complemented
629#419C22×C3711yescharacteristic, complemented
630#418C22×C3711yescharacteristic, complemented
631C2×#101C22×C3711yescharacteristic, complemented
632C2×#101C22×C3711yescharacteristic, complemented
633#407C22×C3711yescharacteristic
634#394—22no—
635#391C22×C3711yescharacteristic, complemented
636#390C22×C3711yescharacteristic, complemented
637#385—22no—
638C4×C22⋊C4C22×C3711yescharacteristic
639#343C22×C3711yescharacteristic, complemented
640#343C22×C3711yescharacteristic, complemented
641#339C22×C3711yescharacteristic, complemented
642#339C22×C3711yescharacteristic, complemented
643C37#2388111yescharacteristic, direct product factor, Sylow
6442−1+4—22no—
6452−1+4—22no—
6462−1+4—41no—
6472−1+4—41no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—22no—
652C2×#41—21no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—22no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—21no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41—41no—
665C2×#41D4×C3711yescharacteristic
666C2×#41D4×C3711yescharacteristic
667C2×#41C23×C3711yescharacteristic
668C2×#41C23×C3711yescharacteristic
669C2×#41C23×C3711yescharacteristic
670C22×Q8—21no—
671C22×Q8—21no—
672C22×Q8D4×C3711yescharacteristic
673C22×Q8C23×C3711yescharacteristic
674C22×Q8C23×C3711yescharacteristic
675C22×D4—21no—
676C22×D4—21no—
677C22×D4D4×C3711yescharacteristic
678C22×D4C23×C3711yescharacteristic
679C23×C4—21no—
680C23×C4—21no—
681C23×C4C23×C3711yescharacteristic
682#137—28no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—22no—
687#137—41no—
688#137D4×C3714yescomplemented
689AGL(1,ℤ/8)—28no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—22no—
694AGL(1,ℤ/8)—41no—
695AGL(1,ℤ/8)D4×C3714yescomplemented
696#135—28no—
697#135—28no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×Q16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×SD16—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×D8—21no—
710C2×M16—21no—
711C2×M16—22no—
712C2×M16—22no—
713C2×M16C23×C3711yescharacteristic
714C2×M16C23×C3711yescharacteristic
715C2×M16C23×C3711yescharacteristic
716C2×M16C23×C3711yescharacteristic
717C22×C8—21no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—22no—
721C4⋊Q8—41no—
722#124—22no—
723#124—21no—
724#124—22no—
725#124—41no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8D4×C3711yescharacteristic
743C22⋊Q8D4×C3711yescharacteristic
744#121—22no—
745#121—22no—
746#121—22no—
747#121—21no—
748#121—21no—
749#121—22no—
750#121D4×C3711yescharacteristic
751#121D4×C3711yescharacteristic
752#120—22no—
753#120—21no—
754C4×Q8—21no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4—21no—
761#117—21no—
762#117C23×C3711yescharacteristic
763C2×C4⋊C4—22no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4D4×C3712yes—
767C2×C4⋊C4C23×C3711yescharacteristic
768C2×C22⋊C4—22no—
769C2×C22⋊C4—21no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4D4×C3712yes—
773C2×C42C23×C3711yescharacteristic
774C2×C42C23×C3711yescharacteristic
775#104—22no—
776#104—22no—
777#104—22no—
778#104—22no—
779#104—41no—
780#104—41no—
781#103—21no—
782#103—21no—
783#102—21no—
784#102—21no—
785#101—22no—
786#101—22no—
787C22⋊C8—21no—
788C22⋊C8—21no—
789#95—21no—
790#95—22no—
791C24—21no—
792C24—21no—
793C24C2×D4×C3711yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C3712yes—
827#41C2×D4×C3712yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C3711yescharacteristic
848C2×Q8C2×D4×C3711yescharacteristic
849C2×Q8C2×D4×C3712yes—
850C2×Q8C2×D4×C3711yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C3711yescharacteristic
875C2×D4C2×D4×C3711yescharacteristic
876C2×D4C2×D4×C3712yes—
877C2×D4C2×D4×C3711yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C3712yes—
901C22×C4C2×D4×C3711yescharacteristic
902C22×C4C2×D4×C3711yescharacteristic
903C22×C4C2×D4×C3711yescharacteristic
904C22×C4C2×D4×C3711yescharacteristic
905C22×C4C2×D4×C3711yescharacteristic
906C22×C4C2×D4×C3712yes—
907C22×C4C24×C3711yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C3712yes—
928M16C2×D4×C3712yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C3711yescharacteristic
946C4⋊C4C2×D4×C3711yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23#120×C3711yescharacteristic
984C23#120×C3711yescharacteristic
985C23C22×D4×C3711yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—22no—
989Q8—21no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8#120×C3712yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—22no—
1006D4—21no—
1007D4—21no—
1008D4—21no—
1009D4—22no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—44no—
1015D4—42no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4#120×C3712yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4#120×C3711yescharacteristic
1071C2×C4#120×C3711yescharacteristic
1072C2×C4C22×D4×C3711yescharacteristic
1073C2×C4C22×D4×C3711yescharacteristic
1074C2×C4C22×D4×C3711yescharacteristic
1075C2×C4C22×D4×C3711yescharacteristic
1076C2×C4H(5,𝔽2)×C3711yescharacteristic
1077C2×C4H(5,𝔽2)×C3711yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×#120×C3711yescharacteristic
1108C22D42×C3711yescharacteristic
1109C22D42×C3711yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×#120×C3711yescharacteristic
1123C4C37×#53411yescharacteristic
1124C4D42×C3711yescharacteristic
1125C4D42×C3711yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C37×#240311yescharacteristic
1135C2C37×#301811yescharacteristic
1136C2C37×#302011yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#575C2semidirect
2. C37×#3489C2semidirect
3. C2×C37×#456C2semidirect
4. C2×C37×#454C2semidirect
5. C37×#3005C2semidirect
6. C37×#2432C2semidirect
7. C37×#2007C2semidirect
8. C37×#2006C2semidirect
9. C37×#2005C2semidirect
10. C37×#2003C2semidirect
11. C37×#1901C2semidirect
12. C37×#1883C2semidirect
13. C37×#1882C2semidirect
14. C37×#1871C2semidirect
15. C37×#1789C2semidirect
24. C2×#137×C37C22semidirect
28. C2×AGL(1,ℤ/8)×C37C22semidirect
42. C2×C4⋊Q8×C37C22semidirect
43. C2×#124×C37C22semidirect
59. C2×#104×C37C22semidirect
60. C2×#104×C37C22semidirect
61. C37×#419C22semidirect
62. C37×#418C22semidirect
63. C2×#101×C37C22semidirect
64. C2×#101×C37C22semidirect
67. C37×#391C22semidirect
68. C37×#390C22semidirect
71. C37×#343C22semidirect
72. C37×#343C22semidirect
73. C37×#339C22semidirect
74. C37×#339C22semidirect
119. #137×C37D4semidirect
126. AGL(1,ℤ/8)×C37D4semidirect
513. #23881C37direct (N × H)
558. C2×#575C2×C37semidirect
559. #3489C2×C37semidirect
560. C2×#456C2×C37semidirect
561. C2×#454C2×C37semidirect
562. #3005C2×C37semidirect
563. #2432C2×C37semidirect
564. #2007C2×C37semidirect
565. #2006C2×C37semidirect
566. #2005C2×C37semidirect
567. #2003C2×C37semidirect
568. #1901C2×C37semidirect
569. #1883C2×C37semidirect
570. #1882C2×C37semidirect
571. #1871C2×C37semidirect
572. #1789C2×C37semidirect
592. C2×#137C22×C37semidirect
596. C2×AGL(1,ℤ/8)C22×C37semidirect
610. C2×C4⋊Q8C22×C37semidirect
611. C2×#124C22×C37semidirect
627. C2×#104C22×C37semidirect
628. C2×#104C22×C37semidirect
629. #419C22×C37semidirect
630. #418C22×C37semidirect
631. C2×#101C22×C37semidirect
632. C2×#101C22×C37semidirect
635. #391C22×C37semidirect
636. #390C22×C37semidirect
639. #343C22×C37semidirect
640. #343C22×C37semidirect
641. #339C22×C37semidirect
642. #339C22×C37semidirect
643. C37#23881direct (N × H)
688. #137D4×C37semidirect
695. AGL(1,ℤ/8)D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5752
C37×#34892
C2×C37×#4562
C2×C37×#4542
C37×#30052
C37×#24322
C37×#20072
C37×#20062
C37×#20052
C37×#20032
C37×#19012
C37×#18832
C37×#18822
C37×#18712
C37×#17892
#2388137