Finite Group Databasebeta

← C37×#18739 #22639992

Subgroups — C37×#18739 #22639992

Order 9472.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3546C211yesmaximal, characteristic
2C37×#3246C211yesmaximal, characteristic, complemented
3C37×#3233C211yesmaximal, characteristic, complemented
4C37×#3182C211yesmaximal, characteristic, complemented
5C37×#1650C211yesmaximal, characteristic, complemented
6C37×#1647C211yesmaximal, characteristic, complemented
7C37×#1642C211yesmaximal, characteristic, complemented
8C37×#1639C211yesmaximal, characteristic, complemented
9C37×#1638C211yesmaximal, characteristic, complemented
10C37×#1635C211yesmaximal, characteristic, complemented
11C37×#1631C211yesmaximal, characteristic, complemented
12C37×#1629C211yesmaximal, characteristic, complemented
13C37×#1540C211yesmaximal, characteristic, complemented
14C37×#1484C211yesmaximal, characteristic, complemented
15C37×#1483C211yesmaximal, characteristic, complemented
16C37×#560—22no—
17C37×#556C2211yescharacteristic
18C37×#553—21no—
19C37×#550—21no—
20C37×#550C2211yescharacteristic
21C37×#547C2211yescharacteristic
22C37×#546—21no—
23C37×#546—21no—
24D42×C37C2211yescharacteristic
25C37×#542—21no—
26C37×#538—22no—
27C37×#537—21no—
28C37×#535—21no—
29C37×#535—21no—
30C37×#533C2211yescharacteristic, complemented
31C37×#532C2211yescharacteristic
32C37×#532C2211yescharacteristic
33C37×#529C2211yescharacteristic
34C37×#500C2211yescharacteristic, complemented
35C37×#499—21no—
36C37×#492C2211yescharacteristic
37C37×#488—21no—
38C37×#487C2211yescharacteristic, complemented
39C37×#486C2211yescharacteristic
40C37×#485—21no—
41C37×#482—21no—
42C37×#477C2211yescharacteristic, complemented
43C37×#476C2211yescharacteristic
44C37×#476C2211yescharacteristic
45C37×#476C2211yescharacteristic, complemented
46C37×#475—21no—
47C37×#475C2211yescharacteristic, complemented
48C37×#474C2211yescharacteristic
49C37×#468—22no—
50C37×#465—21no—
51C37×#465—21no—
52C37×#461C2211yescharacteristic
53C37×#461C2211yescharacteristic, complemented
54C37×#460—21no—
55C37×#440—22no—
56C37×#431C2211yescharacteristic, complemented
57C2×C4⋊C8×C37C2211yescharacteristic, complemented
58C4×M16×C37C2211yescharacteristic, complemented
59C37×#332C2211yescharacteristic, complemented
60C37×#332C2211yescharacteristic, complemented
61C37×#331C2211yescharacteristic
62C37×#331C2211yescharacteristic
63C37×Q8⋊C8C2211yescharacteristic, complemented
64C37×Q8⋊C8C2211yescharacteristic, complemented
65C37×D4⋊C8C2211yescharacteristic
66C37×D4⋊C8C2211yescharacteristic
67C37×D4⋊C8C2211yescharacteristic
68C37×D4⋊C8C2211yescharacteristic
69C37×D4⋊C8C2211yescharacteristic, complemented
70C37×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C37—21no—
72C2×#41×C37—21no—
73C2×#41×C37—21no—
74C2×#41×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C2×SD16×C37—22no—
78C2×SD16×C37—21no—
79C2×SD16×C37—21no—
80C2×M16×C37—21no—
81C22×C8×C37—21no—
82C4⋊Q8×C37D411yescharacteristic
83C4⋊Q8×C37C2311yescharacteristic
84C4⋊Q8×C37C2311yescharacteristic
85C4⋊Q8×C37C2311yescharacteristic
86#127×C37—22no—
87#127×C37—21no—
88#127×C37D411yescharacteristic
89#127×C37C2311yescharacteristic
90#126×C37—22no—
91#126×C37—22no—
92#126×C37—21no—
93#125×C37—21no—
94#125×C37D411yescharacteristic
95#124×C37—22no—
96#124×C37—21no—
97#124×C37—21no—
98#124×C37—21no—
99#124×C37D411yescharacteristic
100#123×C37—22no—
101#123×C37—22no—
102#123×C37—21no—
103#123×C37—22no—
104C22⋊Q8×C37—22no—
105C22⋊Q8×C37—21no—
106C22⋊Q8×C37—21no—
107C22⋊Q8×C37—21no—
108C22⋊Q8×C37—21no—
109C22⋊Q8×C37D411yescharacteristic
110#121×C37—22no—
111#121×C37—22no—
112#121×C37—22no—
113#121×C37—22no—
114#121×C37—22no—
115#121×C37—21no—
116#121×C37—22no—
117#121×C37—21no—
118#121×C37—21no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37D411yescharacteristic
123#121×C37D411yescharacteristic
124#121×C37D411yescharacteristic
125#121×C37D412yes—
126#120×C37—22no—
127#120×C37—22no—
128#120×C37—22no—
129#120×C37—22no—
130C4×Q8×C37—21no—
131C4×Q8×C37—21no—
132C4×Q8×C37—21no—
133C4×Q8×C37C2311yescharacteristic
134C4×D4×C37—22no—
135C4×D4×C37—21no—
136C4×D4×C37—21no—
137C4×D4×C37—21no—
138C4×D4×C37—21no—
139C4×D4×C37D412yes—
140C4×D4×C37C2311yescharacteristic
141C4×D4×C37C2311yescharacteristic
142C4×D4×C37C2311yescharacteristic
143#117×C37—21no—
144#117×C37—21no—
145#117×C37—21no—
146C2×C4⋊C4×C37—21no—
147C2×C22⋊C4×C37—22no—
148C2×C42×C37C2311yescharacteristic
149#107×C37—22no—
150#107×C37—21no—
151#107×C37—21no—
152#106×C37—21no—
153#106×C37—21no—
154#106×C37—21no—
155#106×C37—21no—
156C4⋊C8×C37—21no—
157C4⋊C8×C37C2311yescharacteristic
158C4⋊C8×C37C2311yescharacteristic
159C4⋊C8×C37C2311yescharacteristic
160C4⋊C8×C37C2311yescharacteristic
161#103×C37—21no—
162#103×C37—21no—
163#103×C37—22no—
164#103×C37—21no—
165#103×C37—21no—
166#102×C37—22no—
167#102×C37—21no—
168#102×C37—21no—
169#102×C37—21no—
170#102×C37—21no—
171C22⋊C8×C37—21no—
172#97×C37—21no—
173C4×C8×C37—21no—
174C4×C8×C37C2311yescharacteristic
175C4×C8×C37C2311yescharacteristic
176C24×C37—22no—
177#41×C37—81no—
178#41×C37—81no—
179#41×C37—81no—
180#41×C37—81no—
181#41×C37—81no—
182#41×C37—81no—
183#41×C37—81no—
184#41×C37—81no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37—21no—
188C2×Q8×C37—21no—
189C2×Q8×C37C2×D411yescharacteristic
190C2×D4×C37—22no—
191C2×D4×C37—22no—
192C2×D4×C37—22no—
193C2×D4×C37—22no—
194C2×D4×C37—22no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—22no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—81no—
204C2×D4×C37—81no—
205C2×D4×C37—81no—
206C2×D4×C37—81no—
207C2×D4×C37C2×D411yescharacteristic
208C2×D4×C37C2×D411yescharacteristic
209C2×D4×C37C2×D411yescharacteristic
210C2×D4×C37C2×D412yes—
211C22×C4×C37—22no—
212C22×C4×C37—22no—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—22no—
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37C2×D411yescharacteristic
220SD16×C37—44no—
221SD16×C37—81no—
222SD16×C37—81no—
223M16×C37—42no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—21no—
227C2×C8×C37—21no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—81no—
231C4⋊C4×C37—22no—
232C4⋊C4×C37—22no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—21no—
243C4⋊C4×C37—41no—
244C4⋊C4×C37—41no—
245C4⋊C4×C37C2×D411yescharacteristic
246C4⋊C4×C37C2×D411yescharacteristic
247C4⋊C4×C37C2×D412yes—
248C4⋊C4×C37C2×D411yescharacteristic
249C4⋊C4×C37C2×D411yescharacteristic
250C22⋊C4×C37—22no—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—22no—
255C22⋊C4×C37—21no—
256C22⋊C4×C37—21no—
257C22⋊C4×C37—21no—
258C22⋊C4×C37—21no—
259C22⋊C4×C37—21no—
260C22⋊C4×C37—21no—
261C22⋊C4×C37—22no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—21no—
264C22⋊C4×C37—21no—
265C22⋊C4×C37—21no—
266C22⋊C4×C37—41no—
267C42×C37—22no—
268C42×C37—21no—
269C42×C37—41no—
270C42×C37C2×D411yescharacteristic
271C42×C37C2×D411yescharacteristic
272C42×C37C2×D411yescharacteristic
273C42×C37C2411yescharacteristic
274C23×C37—21no—
275C23×C37—21no—
276C23×C37—22no—
277C23×C37—21no—
278C23×C37—82no—
279C23×C37—82no—
280C23×C37—82no—
281C23×C37#12011yescharacteristic
282Q8×C37—21no—
283Q8×C37—21no—
284Q8×C37—42no—
285Q8×C37—41no—
286Q8×C37—41no—
287Q8×C37—41no—
288Q8×C37—41no—
289Q8×C37—81no—
290D4×C37—21no—
291D4×C37—21no—
292D4×C37—21no—
293D4×C37—21no—
294D4×C37—21no—
295D4×C37—21no—
296D4×C37—42no—
297D4×C37—41no—
298D4×C37—41no—
299D4×C37—41no—
300D4×C37—41no—
301D4×C37—81no—
302D4×C37—81no—
303D4×C37—81no—
304D4×C37—81no—
305D4×C37—81no—
306D4×C37—82no—
307D4×C37—82no—
308D4×C37—82no—
309D4×C37—82no—
310D4×C37—82no—
311D4×C37—82no—
312C2×C4×C37—21no—
313C2×C4×C37—21no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—21no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—22no—
320C2×C4×C37—21no—
321C2×C4×C37—21no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
331C2×C4×C37—82no—
332C2×C4×C37—82no—
333C2×C4×C37—82no—
334C2×C4×C37#12011yescharacteristic
335C2×C4×C37#12011yescharacteristic
336C2×C4×C37#12011yescharacteristic
337C2×C4×C37C22×D411yescharacteristic
338C2×C4×C37C22×D411yescharacteristic
339C2×C4×C37C22×D411yescharacteristic
340C8×C37—22no—
341C8×C37—41no—
342C8×C37—41no—
343C8×C37—41no—
344C8×C37—41no—
345C8×C37—41no—
346#18739C3711yesmaximal, characteristic, direct product factor, Sylow
347C22×C37—21no—
348C22×C37—21no—
349C22×C37—21no—
350C22×C37—41no—
351C22×C37—41no—
352C22×C37—42no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—42no—
357C22×C37—41no—
358C22×C37—42no—
359C22×C37—41no—
360C22×C37—41no—
361C22×C37—41no—
362C22×C37—164no—
363C22×C37C2×#12011yescharacteristic
364C4×C37—21no—
365C4×C37—21no—
366C4×C37—21no—
367C4×C37—21no—
368C4×C37—41no—
369C4×C37—41no—
370C4×C37—41no—
371C4×C37—41no—
372C4×C37—42no—
373C4×C37—41no—
374C4×C37—81no—
375C4×C37—81no—
376C4×C37#57611yescharacteristic
377C4×C37#57711yescharacteristic
378C4×C37#57711yescharacteristic
379C4×C37#57711yescharacteristic
380#3546C2×C3711yescharacteristic
381#3246C2×C3711yescharacteristic, complemented
382#3233C2×C3711yescharacteristic, complemented
383#3182C2×C3711yescharacteristic, complemented
384#1650C2×C3711yescharacteristic, complemented
385#1647C2×C3711yescharacteristic, complemented
386#1642C2×C3711yescharacteristic, complemented
387#1639C2×C3711yescharacteristic, complemented
388#1638C2×C3711yescharacteristic, complemented
389#1635C2×C3711yescharacteristic, complemented
390#1631C2×C3711yescharacteristic, complemented
391#1629C2×C3711yescharacteristic, complemented
392#1540C2×C3711yescharacteristic, complemented
393#1484C2×C3711yescharacteristic, complemented
394#1483C2×C3711yescharacteristic, complemented
395C2×C37—41no—
396C2×C37—81no—
397C2×C37—82no—
398C2×C37—81no—
399C2×C37—81no—
400C2×C37#300911yescharacteristic
401C2×C37#301211yescharacteristic
402C2×C37#301811yescharacteristic
403#560—22no—
404#556C22×C3711yescharacteristic
405#553—21no—
406#550—21no—
407#550C22×C3711yescharacteristic
408#547C22×C3711yescharacteristic
409#546—21no—
410#546—21no—
411D42C22×C3711yescharacteristic
412#542—21no—
413#538—22no—
414#537—21no—
415#535—21no—
416#535—21no—
417#533C22×C3711yescharacteristic, complemented
418#532C22×C3711yescharacteristic
419#532C22×C3711yescharacteristic
420#529C22×C3711yescharacteristic
421#500C22×C3711yescharacteristic, complemented
422#499—21no—
423#492C22×C3711yescharacteristic
424#488—21no—
425#487C22×C3711yescharacteristic, complemented
426#486C22×C3711yescharacteristic
427#485—21no—
428#482—21no—
429#477C22×C3711yescharacteristic, complemented
430#476C22×C3711yescharacteristic
431#476C22×C3711yescharacteristic
432#476C22×C3711yescharacteristic, complemented
433#475—21no—
434#475C22×C3711yescharacteristic, complemented
435#474C22×C3711yescharacteristic
436#468—22no—
437#465—21no—
438#465—21no—
439#461C22×C3711yescharacteristic
440#461C22×C3711yescharacteristic, complemented
441#460—21no—
442#440—22no—
443#431C22×C3711yescharacteristic, complemented
444C2×C4⋊C8C22×C3711yescharacteristic, complemented
445C4×M16C22×C3711yescharacteristic, complemented
446#332C22×C3711yescharacteristic, complemented
447#332C22×C3711yescharacteristic, complemented
448#331C22×C3711yescharacteristic
449#331C22×C3711yescharacteristic
450Q8⋊C8C22×C3711yescharacteristic, complemented
451Q8⋊C8C22×C3711yescharacteristic, complemented
452D4⋊C8C22×C3711yescharacteristic
453D4⋊C8C22×C3711yescharacteristic
454D4⋊C8C22×C3711yescharacteristic
455D4⋊C8C22×C3711yescharacteristic
456D4⋊C8C22×C3711yescharacteristic, complemented
457D4⋊C8C22×C3711yescharacteristic, complemented
458C37#1873911yescharacteristic, direct product factor, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C3711yescharacteristic
471C4⋊Q8C23×C3711yescharacteristic
472C4⋊Q8C23×C3711yescharacteristic
473C4⋊Q8C23×C3711yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C3711yescharacteristic
477#127C23×C3711yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C3711yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C3711yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C3711yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C3711yescharacteristic
511#121D4×C3711yescharacteristic
512#121D4×C3711yescharacteristic
513#121D4×C3712yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C3711yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C3712yes—
528C4×D4C23×C3711yescharacteristic
529C4×D4C23×C3711yescharacteristic
530C4×D4C23×C3711yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C3711yescharacteristic
537#107—22no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C3711yescharacteristic
546C4⋊C8C23×C3711yescharacteristic
547C4⋊C8C23×C3711yescharacteristic
548C4⋊C8C23×C3711yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#103—21no—
553#103—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C3711yescharacteristic
563C4×C8C23×C3711yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C3711yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C3711yescharacteristic
596C2×D4C2×D4×C3711yescharacteristic
597C2×D4C2×D4×C3711yescharacteristic
598C2×D4C2×D4×C3712yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C3711yescharacteristic
606C22×C4C2×D4×C3711yescharacteristic
607C22×C4C2×D4×C3711yescharacteristic
608SD16—44no—
609SD16—81no—
610SD16—81no—
611M16—42no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C3711yescharacteristic
634C4⋊C4C2×D4×C3711yescharacteristic
635C4⋊C4C2×D4×C3712yes—
636C4⋊C4C2×D4×C3711yescharacteristic
637C4⋊C4C2×D4×C3711yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C3711yescharacteristic
659C42C2×D4×C3711yescharacteristic
660C42C2×D4×C3711yescharacteristic
661C42C24×C3711yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C3711yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—82no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C3711yescharacteristic
723C2×C4#120×C3711yescharacteristic
724C2×C4#120×C3711yescharacteristic
725C2×C4C22×D4×C3711yescharacteristic
726C2×C4C22×D4×C3711yescharacteristic
727C2×C4C22×D4×C3711yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C3711yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4C37×#57611yescharacteristic
764C4C37×#57711yescharacteristic
765C4C37×#57711yescharacteristic
766C4C37×#57711yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C37×#300911yescharacteristic
773C2C37×#301211yescharacteristic
774C2C37×#301811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3246C2semidirect
3. C37×#3233C2semidirect
4. C37×#3182C2semidirect
5. C37×#1650C2semidirect
6. C37×#1647C2semidirect
7. C37×#1642C2semidirect
8. C37×#1639C2semidirect
9. C37×#1638C2semidirect
10. C37×#1635C2semidirect
11. C37×#1631C2semidirect
12. C37×#1629C2semidirect
13. C37×#1540C2semidirect
14. C37×#1484C2semidirect
15. C37×#1483C2semidirect
30. C37×#533C22semidirect
34. C37×#500C22semidirect
38. C37×#487C22semidirect
42. C37×#477C22semidirect
45. C37×#476C22semidirect
47. C37×#475C22semidirect
53. C37×#461C22semidirect
56. C37×#431C22semidirect
57. C2×C4⋊C8×C37C22semidirect
58. C4×M16×C37C22semidirect
59. C37×#332C22semidirect
60. C37×#332C22semidirect
63. C37×Q8⋊C8C22semidirect
64. C37×Q8⋊C8C22semidirect
69. C37×D4⋊C8C22semidirect
70. C37×D4⋊C8C22semidirect
346. #18739C37direct (N × H)
381. #3246C2×C37semidirect
382. #3233C2×C37semidirect
383. #3182C2×C37semidirect
384. #1650C2×C37semidirect
385. #1647C2×C37semidirect
386. #1642C2×C37semidirect
387. #1639C2×C37semidirect
388. #1638C2×C37semidirect
389. #1635C2×C37semidirect
390. #1631C2×C37semidirect
391. #1629C2×C37semidirect
392. #1540C2×C37semidirect
393. #1484C2×C37semidirect
394. #1483C2×C37semidirect
417. #533C22×C37semidirect
421. #500C22×C37semidirect
425. #487C22×C37semidirect
429. #477C22×C37semidirect
432. #476C22×C37semidirect
434. #475C22×C37semidirect
440. #461C22×C37semidirect
443. #431C22×C37semidirect
444. C2×C4⋊C8C22×C37semidirect
445. C4×M16C22×C37semidirect
446. #332C22×C37semidirect
447. #332C22×C37semidirect
450. Q8⋊C8C22×C37semidirect
451. Q8⋊C8C22×C37semidirect
456. D4⋊C8C22×C37semidirect
457. D4⋊C8C22×C37semidirect
458. C37#18739direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35462
C37×#32462
C37×#32332
C37×#31822
C37×#16502
C37×#16472
C37×#16422
C37×#16392
C37×#16382
C37×#16352
C37×#16312
C37×#16292
C37×#15402
C37×#14842
C37×#14832
#1873937