Finite Group Databasebeta

← C37×#18974 #22640227

Subgroups — C37×#18974 #22640227

Order 9472.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3546C211yesmaximal, characteristic
2C37×#3254C211yesmaximal, characteristic, complemented
3C37×#3248C211yesmaximal, characteristic, complemented
4C37×#3228C211yesmaximal, characteristic, complemented
5C37×#1654C211yesmaximal, characteristic, complemented
6C37×#1652C211yesmaximal, characteristic, complemented
7C37×#1650C211yesmaximal, characteristic, complemented
8C37×#1647C211yesmaximal, characteristic, complemented
9C37×#1642C211yesmaximal, characteristic, complemented
10C37×#1641C211yesmaximal, characteristic, complemented
11C37×#1639C211yesmaximal, characteristic, complemented
12C37×#1639C211yesmaximal, characteristic, complemented
13C37×#1547C211yesmaximal, characteristic, complemented
14C37×#1495C211yesmaximal, characteristic, complemented
15C37×#1480C211yesmaximal, 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×#498C2211yescharacteristic, complemented
36C37×#486C2211yescharacteristic
37C37×#486C2211yescharacteristic
38C37×#482—22no—
39C37×#479—21no—
40C37×#478—22no—
41C37×#477—21no—
42C37×#475C2211yescharacteristic, complemented
43C37×#474C2211yescharacteristic
44C37×#474C2211yescharacteristic
45C37×#474C2211yescharacteristic, complemented
46C37×#468—21no—
47C37×#468—21no—
48C37×#467—21no—
49C37×#465—21no—
50C37×#464—21no—
51C37×#462C2211yescharacteristic, complemented
52C37×#461C2211yescharacteristic
53C37×#461C2211yescharacteristic
54C37×#461C2211yescharacteristic, complemented
55C37×#460—21no—
56C37×#431C2211yescharacteristic, complemented
57C37×#423C2211yescharacteristic, complemented
58C2×C4⋊C8×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×Q16×C37—21no—
78C2×SD16×C37—21no—
79C2×SD16×C37—21no—
80C2×SD16×C37—21no—
81C2×M16×C37—21no—
82C22×C8×C37—21no—
83C4⋊Q8×C37D411yescharacteristic
84C4⋊Q8×C37C2311yescharacteristic
85C4⋊Q8×C37C2311yescharacteristic
86C4⋊Q8×C37C2311yescharacteristic
87#127×C37—22no—
88#127×C37—21no—
89#127×C37D411yescharacteristic
90#127×C37C2311yescharacteristic
91#126×C37—22no—
92#126×C37—22no—
93#126×C37—21no—
94#125×C37—21no—
95#125×C37D411yescharacteristic
96#124×C37—22no—
97#124×C37—21no—
98#124×C37—21no—
99#124×C37—21no—
100#124×C37D411yescharacteristic
101#123×C37—22no—
102#123×C37—22no—
103#123×C37—21no—
104#123×C37—22no—
105C22⋊Q8×C37—22no—
106C22⋊Q8×C37—21no—
107C22⋊Q8×C37—21no—
108C22⋊Q8×C37—21no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37D411yescharacteristic
111#121×C37—22no—
112#121×C37—22no—
113#121×C37—22no—
114#121×C37—22no—
115#121×C37—22no—
116#121×C37—21no—
117#121×C37—22no—
118#121×C37—21no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37D411yescharacteristic
124#121×C37D411yescharacteristic
125#121×C37D411yescharacteristic
126#121×C37D412yes—
127#120×C37—22no—
128#120×C37—22no—
129#120×C37—22no—
130#120×C37—22no—
131C4×Q8×C37—21no—
132C4×Q8×C37—21no—
133C4×Q8×C37—21no—
134C4×Q8×C37C2311yescharacteristic
135C4×D4×C37—22no—
136C4×D4×C37—21no—
137C4×D4×C37—21no—
138C4×D4×C37—21no—
139C4×D4×C37—21no—
140C4×D4×C37D412yes—
141C4×D4×C37C2311yescharacteristic
142C4×D4×C37C2311yescharacteristic
143C4×D4×C37C2311yescharacteristic
144#117×C37—21no—
145#117×C37—21no—
146#117×C37—21no—
147C2×C4⋊C4×C37—21no—
148C2×C22⋊C4×C37—22no—
149C2×C42×C37C2311yescharacteristic
150#107×C37—21no—
151#107×C37—21no—
152#107×C37—21no—
153#107×C37—22no—
154#106×C37—21no—
155#106×C37—22no—
156C4⋊C8×C37—21no—
157C4⋊C8×C37—21no—
158C4⋊C8×C37—21no—
159C4⋊C8×C37C2311yescharacteristic
160C4⋊C8×C37C2311yescharacteristic
161C4⋊C8×C37C2311yescharacteristic
162C4⋊C8×C37C2311yescharacteristic
163#103×C37—21no—
164#103×C37—21no—
165#103×C37—21no—
166#103×C37—21no—
167#103×C37—21no—
168#102×C37—21no—
169#102×C37—21no—
170#102×C37—21no—
171#102×C37—22no—
172#102×C37—22no—
173C22⋊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
220Q16×C37—81no—
221SD16×C37—81no—
222SD16×C37—81no—
223SD16×C37—81no—
224M16×C37—81no—
225C2×C8×C37—21no—
226C2×C8×C37—21no—
227C2×C8×C37—21no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—21no—
231C2×C8×C37—81no—
232C4⋊C4×C37—22no—
233C4⋊C4×C37—22no—
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—21no—
244C4⋊C4×C37—41no—
245C4⋊C4×C37—41no—
246C4⋊C4×C37C2×D411yescharacteristic
247C4⋊C4×C37C2×D411yescharacteristic
248C4⋊C4×C37C2×D411yescharacteristic
249C4⋊C4×C37C2×D411yescharacteristic
250C4⋊C4×C37C2×D412yes—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—22no—
255C22⋊C4×C37—22no—
256C22⋊C4×C37—21no—
257C22⋊C4×C37—21no—
258C22⋊C4×C37—21no—
259C22⋊C4×C37—21no—
260C22⋊C4×C37—21no—
261C22⋊C4×C37—21no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—22no—
264C22⋊C4×C37—21no—
265C22⋊C4×C37—21no—
266C22⋊C4×C37—21no—
267C22⋊C4×C37—41no—
268C42×C37—22no—
269C42×C37—21no—
270C42×C37—41no—
271C42×C37C2×D411yescharacteristic
272C42×C37C2×D411yescharacteristic
273C42×C37C2×D411yescharacteristic
274C42×C37C2411yescharacteristic
275C23×C37—21no—
276C23×C37—21no—
277C23×C37—22no—
278C23×C37—21no—
279C23×C37—82no—
280C23×C37—82no—
281C23×C37—82no—
282C23×C37#12011yescharacteristic
283Q8×C37—21no—
284Q8×C37—21no—
285Q8×C37—41no—
286Q8×C37—41no—
287Q8×C37—41no—
288Q8×C37—41no—
289Q8×C37—41no—
290Q8×C37—41no—
291Q8×C37—81no—
292D4×C37—21no—
293D4×C37—21no—
294D4×C37—21no—
295D4×C37—21no—
296D4×C37—21no—
297D4×C37—21no—
298D4×C37—42no—
299D4×C37—41no—
300D4×C37—41no—
301D4×C37—41no—
302D4×C37—41no—
303D4×C37—81no—
304D4×C37—81no—
305D4×C37—81no—
306D4×C37—81no—
307D4×C37—81no—
308D4×C37—82no—
309D4×C37—82no—
310D4×C37—82no—
311D4×C37—82no—
312D4×C37—82no—
313D4×C37—82no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—21no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—21no—
320C2×C4×C37—21no—
321C2×C4×C37—22no—
322C2×C4×C37—21no—
323C2×C4×C37—21no—
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—41no—
332C2×C4×C37—41no—
333C2×C4×C37—82no—
334C2×C4×C37—82no—
335C2×C4×C37—82no—
336C2×C4×C37#12011yescharacteristic
337C2×C4×C37#12011yescharacteristic
338C2×C4×C37#12011yescharacteristic
339C2×C4×C37C22×D411yescharacteristic
340C2×C4×C37C22×D411yescharacteristic
341C2×C4×C37C22×D411yescharacteristic
342C8×C37—41no—
343C8×C37—41no—
344C8×C37—41no—
345C8×C37—41no—
346C8×C37—41no—
347C8×C37—41no—
348#18974C3711yesmaximal, characteristic, direct product factor, Sylow
349C22×C37—21no—
350C22×C37—21no—
351C22×C37—21no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—42no—
357C22×C37—42no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—42no—
361C22×C37—41no—
362C22×C37—41no—
363C22×C37—41no—
364C22×C37—164no—
365C22×C37C2×#12011yescharacteristic
366C4×C37—21no—
367C4×C37—21no—
368C4×C37—21no—
369C4×C37—21no—
370C4×C37—41no—
371C4×C37—41no—
372C4×C37—41no—
373C4×C37—41no—
374C4×C37—42no—
375C4×C37—41no—
376C4×C37—81no—
377C4×C37—81no—
378C4×C37#57611yescharacteristic
379C4×C37#57611yescharacteristic
380C4×C37#57711yescharacteristic
381C4×C37#57711yescharacteristic
382#3546C2×C3711yescharacteristic
383#3254C2×C3711yescharacteristic, complemented
384#3248C2×C3711yescharacteristic, complemented
385#3228C2×C3711yescharacteristic, complemented
386#1654C2×C3711yescharacteristic, complemented
387#1652C2×C3711yescharacteristic, complemented
388#1650C2×C3711yescharacteristic, complemented
389#1647C2×C3711yescharacteristic, complemented
390#1642C2×C3711yescharacteristic, complemented
391#1641C2×C3711yescharacteristic, complemented
392#1639C2×C3711yescharacteristic, complemented
393#1639C2×C3711yescharacteristic, complemented
394#1547C2×C3711yescharacteristic, complemented
395#1495C2×C3711yescharacteristic, complemented
396#1480C2×C3711yescharacteristic, complemented
397C2×C37—41no—
398C2×C37—81no—
399C2×C37—82no—
400C2×C37—81no—
401C2×C37—81no—
402C2×C37#301211yescharacteristic
403C2×C37#301211yescharacteristic
404C2×C37#302211yescharacteristic
405#560—22no—
406#556C22×C3711yescharacteristic
407#553—21no—
408#550—21no—
409#550C22×C3711yescharacteristic
410#547C22×C3711yescharacteristic
411#546—21no—
412#546—21no—
413D42C22×C3711yescharacteristic
414#542—21no—
415#538—22no—
416#537—21no—
417#535—21no—
418#535—21no—
419#533C22×C3711yescharacteristic, complemented
420#532C22×C3711yescharacteristic
421#532C22×C3711yescharacteristic
422#529C22×C3711yescharacteristic
423#500C22×C3711yescharacteristic, complemented
424#498C22×C3711yescharacteristic, complemented
425#486C22×C3711yescharacteristic
426#486C22×C3711yescharacteristic
427#482—22no—
428#479—21no—
429#478—22no—
430#477—21no—
431#475C22×C3711yescharacteristic, complemented
432#474C22×C3711yescharacteristic
433#474C22×C3711yescharacteristic
434#474C22×C3711yescharacteristic, complemented
435#468—21no—
436#468—21no—
437#467—21no—
438#465—21no—
439#464—21no—
440#462C22×C3711yescharacteristic, complemented
441#461C22×C3711yescharacteristic
442#461C22×C3711yescharacteristic
443#461C22×C3711yescharacteristic, complemented
444#460—21no—
445#431C22×C3711yescharacteristic, complemented
446#423C22×C3711yescharacteristic, complemented
447C2×C4⋊C8C22×C3711yescharacteristic, complemented
448#332C22×C3711yescharacteristic, complemented
449#332C22×C3711yescharacteristic, complemented
450#331C22×C3711yescharacteristic
451#331C22×C3711yescharacteristic
452Q8⋊C8C22×C3711yescharacteristic, complemented
453Q8⋊C8C22×C3711yescharacteristic, complemented
454D4⋊C8C22×C3711yescharacteristic
455D4⋊C8C22×C3711yescharacteristic
456D4⋊C8C22×C3711yescharacteristic
457D4⋊C8C22×C3711yescharacteristic
458D4⋊C8C22×C3711yescharacteristic, complemented
459D4⋊C8C22×C3711yescharacteristic, complemented
460C37#1897411yescharacteristic, direct product factor, Sylow
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C3711yescharacteristic
474C4⋊Q8C23×C3711yescharacteristic
475C4⋊Q8C23×C3711yescharacteristic
476C4⋊Q8C23×C3711yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C3711yescharacteristic
480#127C23×C3711yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C3711yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C3711yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C3711yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C3711yescharacteristic
514#121D4×C3711yescharacteristic
515#121D4×C3711yescharacteristic
516#121D4×C3712yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C3711yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C3712yes—
531C4×D4C23×C3711yescharacteristic
532C4×D4C23×C3711yescharacteristic
533C4×D4C23×C3711yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C3711yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C3711yescharacteristic
550C4⋊C8C23×C3711yescharacteristic
551C4⋊C8C23×C3711yescharacteristic
552C4⋊C8C23×C3711yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C3711yescharacteristic
565C4×C8C23×C3711yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C3711yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C3711yescharacteristic
598C2×D4C2×D4×C3711yescharacteristic
599C2×D4C2×D4×C3711yescharacteristic
600C2×D4C2×D4×C3712yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C3711yescharacteristic
608C22×C4C2×D4×C3711yescharacteristic
609C22×C4C2×D4×C3711yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C3711yescharacteristic
637C4⋊C4C2×D4×C3711yescharacteristic
638C4⋊C4C2×D4×C3711yescharacteristic
639C4⋊C4C2×D4×C3711yescharacteristic
640C4⋊C4C2×D4×C3712yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C3711yescharacteristic
662C42C2×D4×C3711yescharacteristic
663C42C2×D4×C3711yescharacteristic
664C42C24×C3711yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C3711yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C3711yescharacteristic
727C2×C4#120×C3711yescharacteristic
728C2×C4#120×C3711yescharacteristic
729C2×C4C22×D4×C3711yescharacteristic
730C2×C4C22×D4×C3711yescharacteristic
731C2×C4C22×D4×C3711yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C3711yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4C37×#57611yescharacteristic
768C4C37×#57611yescharacteristic
769C4C37×#57711yescharacteristic
770C4C37×#57711yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C37×#301211yescharacteristic
777C2C37×#301211yescharacteristic
778C2C37×#302211yescharacteristic
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×#3254C2semidirect
3. C37×#3248C2semidirect
4. C37×#3228C2semidirect
5. C37×#1654C2semidirect
6. C37×#1652C2semidirect
7. C37×#1650C2semidirect
8. C37×#1647C2semidirect
9. C37×#1642C2semidirect
10. C37×#1641C2semidirect
11. C37×#1639C2semidirect
12. C37×#1639C2semidirect
13. C37×#1547C2semidirect
14. C37×#1495C2semidirect
15. C37×#1480C2semidirect
30. C37×#533C22semidirect
34. C37×#500C22semidirect
35. C37×#498C22semidirect
42. C37×#475C22semidirect
45. C37×#474C22semidirect
51. C37×#462C22semidirect
54. C37×#461C22semidirect
56. C37×#431C22semidirect
57. C37×#423C22semidirect
58. C2×C4⋊C8×C37C22semidirect
59. C37×#332C22semidirect
60. C37×#332C22semidirect
63. C37×Q8⋊C8C22semidirect
64. C37×Q8⋊C8C22semidirect
69. C37×D4⋊C8C22semidirect
70. C37×D4⋊C8C22semidirect
348. #18974C37direct (N × H)
383. #3254C2×C37semidirect
384. #3248C2×C37semidirect
385. #3228C2×C37semidirect
386. #1654C2×C37semidirect
387. #1652C2×C37semidirect
388. #1650C2×C37semidirect
389. #1647C2×C37semidirect
390. #1642C2×C37semidirect
391. #1641C2×C37semidirect
392. #1639C2×C37semidirect
393. #1639C2×C37semidirect
394. #1547C2×C37semidirect
395. #1495C2×C37semidirect
396. #1480C2×C37semidirect
419. #533C22×C37semidirect
423. #500C22×C37semidirect
424. #498C22×C37semidirect
431. #475C22×C37semidirect
434. #474C22×C37semidirect
440. #462C22×C37semidirect
443. #461C22×C37semidirect
445. #431C22×C37semidirect
446. #423C22×C37semidirect
447. C2×C4⋊C8C22×C37semidirect
448. #332C22×C37semidirect
449. #332C22×C37semidirect
452. Q8⋊C8C22×C37semidirect
453. Q8⋊C8C22×C37semidirect
458. D4⋊C8C22×C37semidirect
459. D4⋊C8C22×C37semidirect
460. C37#18974direct (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×#32542
C37×#32482
C37×#32282
C37×#16542
C37×#16522
C37×#16502
C37×#16472
C37×#16422
C37×#16412
C37×#16392
C37×#15472
C37×#14952
C37×#14802
#1897437