Finite Group Databasebeta

← C37×#18962 #22640215

Subgroups — C37×#18962 #22640215

Order 9472.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3546C211yesmaximal, characteristic, complemented
2C37×#3253C211yesmaximal, characteristic, complemented
3C37×#3247C211yesmaximal, characteristic, complemented
4C37×#3207C211yesmaximal, characteristic, complemented
5C37×#1638C211yesmaximal, characteristic, complemented
6C37×#1635C211yesmaximal, characteristic, complemented
7C37×#1631C211yesmaximal, characteristic, complemented
8C37×#1629C211yesmaximal, characteristic, complemented
9C37×#1628C211yesmaximal, characteristic, complemented
10C37×#1625C211yesmaximal, characteristic, complemented
11C37×#1621C211yesmaximal, characteristic, complemented
12C37×#1619C211yesmaximal, 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×#532C2211yescharacteristic
31C37×#532C2211yescharacteristic
32C37×#532C2211yescharacteristic, complemented
33C37×#529C2211yescharacteristic
34C37×#493C2211yescharacteristic
35C37×#492C2211yescharacteristic
36C37×#487C2211yescharacteristic, complemented
37C37×#486C2211yescharacteristic, complemented
38C37×#478—21no—
39C37×#477C2211yescharacteristic, complemented
40C37×#476—21no—
41C37×#476C2211yescharacteristic
42C37×#476C2211yescharacteristic
43C37×#476C2211yescharacteristic, complemented
44C37×#469—21no—
45C37×#469—21no—
46C37×#466—21no—
47C37×#465—21no—
48C37×#463—21no—
49C37×#463—22no—
50C37×#460C2211yescharacteristic, complemented
51C37×#459—21no—
52C37×#459C2211yescharacteristic
53C37×#459C2211yescharacteristic
54C37×#459C2211yescharacteristic, complemented
55C37×#449—22no—
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—
75C2×#41×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C2×SD16×C37—21no—
79C2×SD16×C37—22no—
80C2×D8×C37—22no—
81C2×D8×C37—21no—
82C2×D8×C37—21no—
83C2×D8×C37—21no—
84C2×M16×C37—21no—
85C22×C8×C37—21no—
86C4⋊Q8×C37D411yescharacteristic
87C4⋊Q8×C37C2311yescharacteristic
88C4⋊Q8×C37C2311yescharacteristic
89#127×C37—22no—
90#127×C37—21no—
91#127×C37D411yescharacteristic
92#127×C37C2311yescharacteristic
93#127×C37C2311yescharacteristic
94#126×C37—22no—
95#126×C37—22no—
96#126×C37—21no—
97#125×C37D411yescharacteristic
98#124×C37—22no—
99#124×C37—21no—
100#124×C37—21no—
101#124×C37—21no—
102#124×C37—21no—
103#124×C37D411yescharacteristic
104#123×C37—22no—
105#123×C37—22no—
106#123×C37—21no—
107#123×C37—22no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37—21no—
111C22⋊Q8×C37D411yescharacteristic
112#121×C37—22no—
113#121×C37—22no—
114#121×C37—22no—
115#121×C37—22no—
116#121×C37—22no—
117#121×C37—21no—
118#121×C37—22no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37—21no—
125#121×C37—21no—
126#121×C37D411yescharacteristic
127#121×C37D411yescharacteristic
128#121×C37D411yescharacteristic
129#121×C37D412yes—
130#120×C37—22no—
131#120×C37—22no—
132#120×C37—22no—
133#120×C37—22no—
134C4×Q8×C37—21no—
135C4×Q8×C37C2311yescharacteristic
136C4×D4×C37—22no—
137C4×D4×C37—21no—
138C4×D4×C37—21no—
139C4×D4×C37—21no—
140C4×D4×C37—21no—
141C4×D4×C37—21no—
142C4×D4×C37—21no—
143C4×D4×C37D412yes—
144C4×D4×C37C2311yescharacteristic
145C4×D4×C37C2311yescharacteristic
146C4×D4×C37C2311yescharacteristic
147#117×C37—21no—
148#117×C37—21no—
149C2×C4⋊C4×C37—21no—
150C2×C22⋊C4×C37—22no—
151C2×C42×C37C2311yescharacteristic
152#107×C37—21no—
153#106×C37—21no—
154#106×C37—21no—
155#106×C37—21no—
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—22no—
165#102×C37—21no—
166#102×C37—21no—
167#102×C37—21no—
168#102×C37—22no—
169#102×C37—21no—
170#102×C37—21no—
171#102×C37—21no—
172#102×C37—21no—
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—
185#41×C37—82no—
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—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—41no—
207C2×D4×C37—81no—
208C2×D4×C37—81no—
209C2×D4×C37—81no—
210C2×D4×C37—81no—
211C2×D4×C37C2×D411yescharacteristic
212C2×D4×C37C2×D411yescharacteristic
213C2×D4×C37C2×D411yescharacteristic
214C2×D4×C37C2×D412yes—
215C22×C4×C37—22no—
216C22×C4×C37—22no—
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—22no—
221C22×C4×C37—41no—
222C22×C4×C37C2×D411yescharacteristic
223C22×C4×C37C2×D411yescharacteristic
224C22×C4×C37C2×D411yescharacteristic
225SD16×C37—81no—
226SD16×C37—82no—
227D8×C37—81no—
228D8×C37—81no—
229D8×C37—81no—
230D8×C37—82no—
231M16×C37—81no—
232C2×C8×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—21no—
235C2×C8×C37—21no—
236C2×C8×C37—21no—
237C2×C8×C37—21no—
238C2×C8×C37—81no—
239C4⋊C4×C37—22no—
240C4⋊C4×C37—22no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—21no—
243C4⋊C4×C37—21no—
244C4⋊C4×C37—21no—
245C4⋊C4×C37—21no—
246C4⋊C4×C37—21no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37C2×D412yes—
250C4⋊C4×C37C2×D411yescharacteristic
251C4⋊C4×C37C2×D411yescharacteristic
252C4⋊C4×C37C2×D411yescharacteristic
253C4⋊C4×C37C2×D411yescharacteristic
254C22⋊C4×C37—22no—
255C22⋊C4×C37—22no—
256C22⋊C4×C37—22no—
257C22⋊C4×C37—22no—
258C22⋊C4×C37—22no—
259C22⋊C4×C37—21no—
260C22⋊C4×C37—21no—
261C22⋊C4×C37—21no—
262C22⋊C4×C37—21no—
263C22⋊C4×C37—21no—
264C22⋊C4×C37—21no—
265C22⋊C4×C37—22no—
266C22⋊C4×C37—22no—
267C22⋊C4×C37—21no—
268C22⋊C4×C37—21no—
269C22⋊C4×C37—21no—
270C22⋊C4×C37—41no—
271C22⋊C4×C37—41no—
272C42×C37—22no—
273C42×C37—21no—
274C42×C37C2×D411yescharacteristic
275C42×C37C2×D411yescharacteristic
276C42×C37C2×D411yescharacteristic
277C42×C37C2411yescharacteristic
278C23×C37—21no—
279C23×C37—21no—
280C23×C37—22no—
281C23×C37—21no—
282C23×C37—41no—
283C23×C37—82no—
284C23×C37—82no—
285C23×C37—82no—
286C23×C37#12011yescharacteristic
287Q8×C37—21no—
288Q8×C37—21no—
289Q8×C37—42no—
290Q8×C37—41no—
291Q8×C37—41no—
292Q8×C37—81no—
293D4×C37—21no—
294D4×C37—21no—
295D4×C37—21no—
296D4×C37—21no—
297D4×C37—21no—
298D4×C37—21no—
299D4×C37—42no—
300D4×C37—42no—
301D4×C37—41no—
302D4×C37—41no—
303D4×C37—41no—
304D4×C37—41no—
305D4×C37—41no—
306D4×C37—41no—
307D4×C37—41no—
308D4×C37—41no—
309D4×C37—81no—
310D4×C37—81no—
311D4×C37—81no—
312D4×C37—81no—
313D4×C37—81no—
314D4×C37—82no—
315D4×C37—82no—
316D4×C37—82no—
317D4×C37—82no—
318D4×C37—82no—
319D4×C37—82no—
320D4×C37—82no—
321C2×C4×C37—21no—
322C2×C4×C37—21no—
323C2×C4×C37—21no—
324C2×C4×C37—21no—
325C2×C4×C37—21no—
326C2×C4×C37—21no—
327C2×C4×C37—21no—
328C2×C4×C37—22no—
329C2×C4×C37—21no—
330C2×C4×C37—21no—
331C2×C4×C37—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—82no—
340C2×C4×C37—82no—
341C2×C4×C37—82no—
342C2×C4×C37—82no—
343C2×C4×C37#12011yescharacteristic
344C2×C4×C37#12011yescharacteristic
345C2×C4×C37#12011yescharacteristic
346C2×C4×C37C22×D411yescharacteristic
347C2×C4×C37C22×D411yescharacteristic
348C2×C4×C37C22×D411yescharacteristic
349C8×C37—41no—
350C8×C37—41no—
351C8×C37—41no—
352C8×C37—41no—
353C8×C37—41no—
354C8×C37—41no—
355#18962C3711yesmaximal, characteristic, direct product factor, Sylow
356C22×C37—21no—
357C22×C37—21no—
358C22×C37—21no—
359C22×C37—41no—
360C22×C37—41no—
361C22×C37—41no—
362C22×C37—41no—
363C22×C37—42no—
364C22×C37—42no—
365C22×C37—41no—
366C22×C37—41no—
367C22×C37—42no—
368C22×C37—41no—
369C22×C37—41no—
370C22×C37—41no—
371C22×C37—81no—
372C22×C37—81no—
373C22×C37—81no—
374C22×C37—164no—
375C22×C37C2×#12011yescharacteristic
376C4×C37—21no—
377C4×C37—21no—
378C4×C37—21no—
379C4×C37—21no—
380C4×C37—41no—
381C4×C37—41no—
382C4×C37—41no—
383C4×C37—41no—
384C4×C37—42no—
385C4×C37—41no—
386C4×C37—81no—
387C4×C37#57611yescharacteristic
388C4×C37#57611yescharacteristic
389C4×C37#57711yescharacteristic
390C4×C37#57711yescharacteristic
391#3546C2×C3711yescharacteristic, complemented
392#3253C2×C3711yescharacteristic, complemented
393#3247C2×C3711yescharacteristic, complemented
394#3207C2×C3711yescharacteristic, complemented
395#1638C2×C3711yescharacteristic, complemented
396#1635C2×C3711yescharacteristic, complemented
397#1631C2×C3711yescharacteristic, complemented
398#1629C2×C3711yescharacteristic, complemented
399#1628C2×C3711yescharacteristic, complemented
400#1625C2×C3711yescharacteristic, complemented
401#1621C2×C3711yescharacteristic, complemented
402#1619C2×C3711yescharacteristic, complemented
403#1547C2×C3711yescharacteristic, complemented
404#1495C2×C3711yescharacteristic, complemented
405#1480C2×C3711yescharacteristic, complemented
406C2×C37—41no—
407C2×C37—81no—
408C2×C37—82no—
409C2×C37—81no—
410C2×C37—81no—
411C2×C37—161no—
412C2×C37#301211yescharacteristic
413C2×C37#301211yescharacteristic
414C2×C37#302111yescharacteristic
415#560—22no—
416#556C22×C3711yescharacteristic
417#553—21no—
418#550—21no—
419#550C22×C3711yescharacteristic
420#547C22×C3711yescharacteristic
421#546—21no—
422#546—21no—
423D42C22×C3711yescharacteristic
424#542—21no—
425#538—22no—
426#537—21no—
427#535—21no—
428#535—21no—
429#532C22×C3711yescharacteristic
430#532C22×C3711yescharacteristic
431#532C22×C3711yescharacteristic, complemented
432#529C22×C3711yescharacteristic
433#493C22×C3711yescharacteristic
434#492C22×C3711yescharacteristic
435#487C22×C3711yescharacteristic, complemented
436#486C22×C3711yescharacteristic, complemented
437#478—21no—
438#477C22×C3711yescharacteristic, complemented
439#476—21no—
440#476C22×C3711yescharacteristic
441#476C22×C3711yescharacteristic
442#476C22×C3711yescharacteristic, complemented
443#469—21no—
444#469—21no—
445#466—21no—
446#465—21no—
447#463—21no—
448#463—22no—
449#460C22×C3711yescharacteristic, complemented
450#459—21no—
451#459C22×C3711yescharacteristic
452#459C22×C3711yescharacteristic
453#459C22×C3711yescharacteristic, complemented
454#449—22no—
455#431C22×C3711yescharacteristic, complemented
456#423C22×C3711yescharacteristic, complemented
457C2×C4⋊C8C22×C3711yescharacteristic, complemented
458#332C22×C3711yescharacteristic, complemented
459#332C22×C3711yescharacteristic, complemented
460#331C22×C3711yescharacteristic
461#331C22×C3711yescharacteristic
462Q8⋊C8C22×C3711yescharacteristic, complemented
463Q8⋊C8C22×C3711yescharacteristic, complemented
464D4⋊C8C22×C3711yescharacteristic
465D4⋊C8C22×C3711yescharacteristic
466D4⋊C8C22×C3711yescharacteristic
467D4⋊C8C22×C3711yescharacteristic
468D4⋊C8C22×C3711yescharacteristic, complemented
469D4⋊C8C22×C3711yescharacteristic, complemented
470C37#1896211yescharacteristic, direct product factor, Sylow
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C3711yescharacteristic
487C4⋊Q8C23×C3711yescharacteristic
488C4⋊Q8C23×C3711yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C3711yescharacteristic
492#127C23×C3711yescharacteristic
493#127C23×C3711yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C3711yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C3711yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C3711yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C3711yescharacteristic
527#121D4×C3711yescharacteristic
528#121D4×C3711yescharacteristic
529#121D4×C3712yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C3711yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C3712yes—
544C4×D4C23×C3711yescharacteristic
545C4×D4C23×C3711yescharacteristic
546C4×D4C23×C3711yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C3711yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C3711yescharacteristic
560C4⋊C8C23×C3711yescharacteristic
561C4⋊C8C23×C3711yescharacteristic
562C4⋊C8C23×C3711yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C3711yescharacteristic
575C4×C8C23×C3711yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C3711yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C3711yescharacteristic
612C2×D4C2×D4×C3711yescharacteristic
613C2×D4C2×D4×C3711yescharacteristic
614C2×D4C2×D4×C3712yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C3711yescharacteristic
623C22×C4C2×D4×C3711yescharacteristic
624C22×C4C2×D4×C3711yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C3712yes—
650C4⋊C4C2×D4×C3711yescharacteristic
651C4⋊C4C2×D4×C3711yescharacteristic
652C4⋊C4C2×D4×C3711yescharacteristic
653C4⋊C4C2×D4×C3711yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C3711yescharacteristic
675C42C2×D4×C3711yescharacteristic
676C42C2×D4×C3711yescharacteristic
677C42C24×C3711yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C3711yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C3711yescharacteristic
744C2×C4#120×C3711yescharacteristic
745C2×C4#120×C3711yescharacteristic
746C2×C4C22×D4×C3711yescharacteristic
747C2×C4C22×D4×C3711yescharacteristic
748C2×C4C22×D4×C3711yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C3711yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4C37×#57611yescharacteristic
787C4C37×#57611yescharacteristic
788C4C37×#57711yescharacteristic
789C4C37×#57711yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C37×#301211yescharacteristic
797C2C37×#301211yescharacteristic
798C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
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
1. C37×#3546C2semidirect
2. C37×#3253C2semidirect
3. C37×#3247C2semidirect
4. C37×#3207C2semidirect
5. C37×#1638C2semidirect
6. C37×#1635C2semidirect
7. C37×#1631C2semidirect
8. C37×#1629C2semidirect
9. C37×#1628C2semidirect
10. C37×#1625C2semidirect
11. C37×#1621C2semidirect
12. C37×#1619C2semidirect
13. C37×#1547C2semidirect
14. C37×#1495C2semidirect
15. C37×#1480C2semidirect
32. C37×#532C22semidirect
36. C37×#487C22semidirect
37. C37×#486C22semidirect
39. C37×#477C22semidirect
43. C37×#476C22semidirect
50. C37×#460C22semidirect
54. C37×#459C22semidirect
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
355. #18962C37direct (N × H)
391. #3546C2×C37semidirect
392. #3253C2×C37semidirect
393. #3247C2×C37semidirect
394. #3207C2×C37semidirect
395. #1638C2×C37semidirect
396. #1635C2×C37semidirect
397. #1631C2×C37semidirect
398. #1629C2×C37semidirect
399. #1628C2×C37semidirect
400. #1625C2×C37semidirect
401. #1621C2×C37semidirect
402. #1619C2×C37semidirect
403. #1547C2×C37semidirect
404. #1495C2×C37semidirect
405. #1480C2×C37semidirect
431. #532C22×C37semidirect
435. #487C22×C37semidirect
436. #486C22×C37semidirect
438. #477C22×C37semidirect
442. #476C22×C37semidirect
449. #460C22×C37semidirect
453. #459C22×C37semidirect
455. #431C22×C37semidirect
456. #423C22×C37semidirect
457. C2×C4⋊C8C22×C37semidirect
458. #332C22×C37semidirect
459. #332C22×C37semidirect
462. Q8⋊C8C22×C37semidirect
463. Q8⋊C8C22×C37semidirect
468. D4⋊C8C22×C37semidirect
469. D4⋊C8C22×C37semidirect
470. C37#18962direct (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×#32532
C37×#32472
C37×#32072
C37×#16382
C37×#16352
C37×#16312
C37×#16292
C37×#16282
C37×#16252
C37×#16212
C37×#16192
C37×#15472
C37×#14952
C37×#14802
#1896237