Finite Group Databasebeta

← C37×#18810 #22640063

Subgroups — C37×#18810 #22640063

Order 9472.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3519C211yesmaximal, characteristic, complemented
2C37×#3251C211yesmaximal, characteristic, complemented
3C37×#3207C211yesmaximal, characteristic, complemented
4C37×#3036C211yesmaximal, characteristic, complemented
5C37×#1646C211yesmaximal, characteristic, complemented
6C37×#1643C211yesmaximal, characteristic, complemented
7C37×#1642C211yesmaximal, characteristic, complemented
8C37×#1639C211yesmaximal, characteristic, complemented
9C37×#1624C211yesmaximal, characteristic, complemented
10C37×#1622C211yesmaximal, characteristic, complemented
11C37×#1621C211yesmaximal, characteristic, complemented
12C37×#1619C211yesmaximal, characteristic, complemented
13C37×#1560C211yesmaximal, characteristic, complemented
14C37×#1495C211yesmaximal, characteristic, complemented
15C37×#1486C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C37—21no—
17C37×#555C2211yescharacteristic
18C37×#554C2211yescharacteristic
19C37×#553—21no—
20C37×#553—21no—
21C37×#550C2211yescharacteristic
22C37×#546—22no—
23C37×#546—21no—
24D42×C37—21no—
25D42×C37C2211yescharacteristic
26C37×#540—21no—
27C37×#538—22no—
28C37×#532C2211yescharacteristic
29C37×#532C2211yescharacteristic, complemented
30C37×#529C2211yescharacteristic
31C37×#525—21no—
32C2×#121×C37—21no—
33C37×#518—21no—
34C2×C4×D4×C37C2211yescharacteristic
35C37×#493C2211yescharacteristic, complemented
36C37×#492C2211yescharacteristic, complemented
37C37×#487C2211yescharacteristic, complemented
38C37×#486C2211yescharacteristic, complemented
39C37×#478—21no—
40C37×#475C2211yescharacteristic, complemented
41C37×#474C2211yescharacteristic, complemented
42C37×#469—21no—
43C37×#468—21no—
44C37×#463—22no—
45C37×#463—21no—
46C37×#463—21no—
47C37×#463—21no—
48C37×#461C2211yescharacteristic
49C37×#461C2211yescharacteristic, complemented
50C37×#460C2211yescharacteristic, complemented
51C37×#459C2211yescharacteristic
52C37×#459C2211yescharacteristic, complemented
53C37×#459C2211yescharacteristic, complemented
54C37×#449—22no—
55C37×#431C2211yescharacteristic, complemented
56C37×#423C2211yescharacteristic, complemented
57C37×#423C2211yescharacteristic, complemented
58C37×#417—21no—
59C37×#333C2211yescharacteristic, complemented
60C37×#333C2211yescharacteristic, complemented
61C37×#331C2211yescharacteristic, complemented
62C37×#331C2211yescharacteristic, complemented
63C37×Q8⋊C8C2211yescharacteristic, complemented
64C37×Q8⋊C8C2211yescharacteristic, complemented
65C37×D4⋊C8C2211yescharacteristic
66C37×D4⋊C8C2211yescharacteristic
67C37×D4⋊C8C2211yescharacteristic, complemented
68C37×D4⋊C8C2211yescharacteristic, complemented
69C37×D4⋊C8C2211yescharacteristic, complemented
70C37×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C37—21no—
72C2×#41×C37—21no—
73C2×#41×C37D412yes—
74C22×D4×C37—22no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37D411yescharacteristic
78C23×C4×C37—21no—
79AGL(1,ℤ/8)×C37—44no—
80C2×SD16×C37—21no—
81C2×SD16×C37—21no—
82C2×SD16×C37—22no—
83C2×SD16×C37—21no—
84C2×D8×C37—21no—
85C2×D8×C37—21no—
86C2×D8×C37—22no—
87C2×D8×C37—21no—
88C2×M16×C37—21no—
89C2×M16×C37—21no—
90C4⋊Q8×C37C2311yescharacteristic
91C4⋊Q8×C37C2311yescharacteristic
92#127×C37—21no—
93#127×C37C2311yescharacteristic
94#127×C37C2311yescharacteristic
95#126×C37—22no—
96#126×C37—21no—
97#125×C37—21no—
98#125×C37D411yescharacteristic
99#124×C37—22no—
100#124×C37—21no—
101#124×C37D411yescharacteristic
102#124×C37D412yes—
103#123×C37—22no—
104#123×C37—22no—
105#123×C37—22no—
106#123×C37—21no—
107C22⋊Q8×C37—21no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37D411yescharacteristic
110#121×C37—22no—
111#121×C37—22no—
112#121×C37—22no—
113#121×C37—22no—
114#121×C37—21no—
115#121×C37—22no—
116#121×C37—21no—
117#121×C37—21no—
118#121×C37—21no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37D411yescharacteristic
125#120×C37—22no—
126#120×C37—22no—
127#120×C37—22no—
128C4×Q8×C37C2311yescharacteristic
129C4×D4×C37—22no—
130C4×D4×C37—22no—
131C4×D4×C37—22no—
132C4×D4×C37—21no—
133C4×D4×C37—21no—
134C4×D4×C37—21no—
135C4×D4×C37—21no—
136C4×D4×C37—21no—
137C4×D4×C37—21no—
138C4×D4×C37—21no—
139C4×D4×C37—21no—
140C4×D4×C37—21no—
141C4×D4×C37D411yescharacteristic
142C4×D4×C37D411yescharacteristic
143C4×D4×C37C2311yescharacteristic
144C4×D4×C37C2311yescharacteristic
145C4×D4×C37C2311yescharacteristic
146#117×C37—21no—
147#117×C37—21no—
148#117×C37—21no—
149C2×C4⋊C4×C37—21no—
150C2×C4⋊C4×C37D411yescharacteristic
151C2×C22⋊C4×C37—22no—
152C2×C22⋊C4×C37—22no—
153C2×C22⋊C4×C37—21no—
154C2×C42×C37C2311yescharacteristic
155#107×C37—21no—
156#106×C37—21no—
157C4⋊C8×C37—21no—
158C4⋊C8×C37—21no—
159C4⋊C8×C37—21no—
160C4⋊C8×C37C2311yescharacteristic
161C4⋊C8×C37C2311yescharacteristic
162C4⋊C8×C37C2311yescharacteristic
163C4⋊C8×C37C2311yescharacteristic
164#103×C37—22no—
165#103×C37—21no—
166#103×C37—21no—
167#103×C37—21no—
168#102×C37—22no—
169#102×C37—21no—
170#102×C37—21no—
171#102×C37—21no—
172#102×C37—21no—
173#102×C37—21no—
174C22⋊C8×C37—21no—
175C4×C8×C37C2311yescharacteristic
176C4×C8×C37C2311yescharacteristic
177C24×C37—22no—
178C24×C37—21no—
179#41×C37—42no—
180#41×C37—42no—
181#41×C37—81no—
182#41×C37—81no—
183#41×C37—82no—
184C2×Q8×C37—21no—
185C2×Q8×C37C2×D411yescharacteristic
186C2×Q8×C37C2×D412yes—
187C2×D4×C37—22no—
188C2×D4×C37—22no—
189C2×D4×C37—22no—
190C2×D4×C37—21no—
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—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—41no—
202C2×D4×C37—42no—
203C2×D4×C37—42no—
204C2×D4×C37—41no—
205C2×D4×C37—81no—
206C2×D4×C37—81no—
207C2×D4×C37—84no—
208C2×D4×C37C2×D411yescharacteristic
209C2×D4×C37C2×D411yescharacteristic
210C2×D4×C37C2×D411yescharacteristic
211C2×D4×C37C2×D412yes—
212C22×C4×C37—22no—
213C22×C4×C37—22no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—22no—
220C22×C4×C37—21no—
221C22×C4×C37—41no—
222C22×C4×C37—81no—
223C22×C4×C37—81no—
224C22×C4×C37C2×D411yescharacteristic
225C22×C4×C37C2×D411yescharacteristic
226C22×C4×C37C2×D411yescharacteristic
227SD16×C37—42no—
228SD16×C37—42no—
229SD16×C37—81no—
230SD16×C37—82no—
231D8×C37—42no—
232D8×C37—42no—
233D8×C37—81no—
234D8×C37—82no—
235M16×C37—42no—
236M16×C37—81no—
237C2×C8×C37—21no—
238C2×C8×C37—21no—
239C2×C8×C37—21no—
240C2×C8×C37—21no—
241C2×C8×C37—21no—
242C2×C8×C37—21no—
243C4⋊C4×C37—22no—
244C4⋊C4×C37—22no—
245C4⋊C4×C37—21no—
246C4⋊C4×C37—21no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—21no—
251C4⋊C4×C37—21no—
252C4⋊C4×C37—21no—
253C4⋊C4×C37—21no—
254C4⋊C4×C37C2×D411yescharacteristic
255C4⋊C4×C37C2×D411yescharacteristic
256C4⋊C4×C37C2×D411yescharacteristic
257C4⋊C4×C37C2×D411yescharacteristic
258C22⋊C4×C37—22no—
259C22⋊C4×C37—22no—
260C22⋊C4×C37—22no—
261C22⋊C4×C37—22no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—21no—
264C22⋊C4×C37—21no—
265C22⋊C4×C37—21no—
266C22⋊C4×C37—21no—
267C22⋊C4×C37—22no—
268C22⋊C4×C37—21no—
269C22⋊C4×C37—21no—
270C22⋊C4×C37—22no—
271C22⋊C4×C37—21no—
272C22⋊C4×C37—21no—
273C22⋊C4×C37—21no—
274C22⋊C4×C37—41no—
275C22⋊C4×C37—41no—
276C42×C37—22no—
277C42×C37—21no—
278C42×C37C2×D411yescharacteristic
279C42×C37C2×D411yescharacteristic
280C42×C37C2×D411yescharacteristic
281C42×C37C2411yescharacteristic
282C23×C37—21no—
283C23×C37—21no—
284C23×C37—21no—
285C23×C37—22no—
286C23×C37—42no—
287C23×C37—42no—
288C23×C37—44no—
289C23×C37—41no—
290C23×C37—81no—
291C23×C37—82no—
292C23×C37—82no—
293C23×C37#12011yescharacteristic
294Q8×C37—21no—
295Q8×C37—21no—
296Q8×C37—42no—
297Q8×C37—41no—
298Q8×C37—41no—
299D4×C37—21no—
300D4×C37—21no—
301D4×C37—21no—
302D4×C37—21no—
303D4×C37—21no—
304D4×C37—42no—
305D4×C37—42no—
306D4×C37—42no—
307D4×C37—44no—
308D4×C37—42no—
309D4×C37—44no—
310D4×C37—41no—
311D4×C37—41no—
312D4×C37—41no—
313D4×C37—41no—
314D4×C37—41no—
315D4×C37—41no—
316D4×C37—41no—
317D4×C37—41no—
318D4×C37—82no—
319D4×C37—82no—
320D4×C37—82no—
321D4×C37—82no—
322D4×C37—82no—
323D4×C37AGL(1,ℤ/8)12yes—
324C2×C4×C37—21no—
325C2×C4×C37—21no—
326C2×C4×C37—21no—
327C2×C4×C37—21no—
328C2×C4×C37—21no—
329C2×C4×C37—21no—
330C2×C4×C37—21no—
331C2×C4×C37—22no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—81no—
343C2×C4×C37—81no—
344C2×C4×C37—82no—
345C2×C4×C37—82no—
346C2×C4×C37—81no—
347C2×C4×C37—82no—
348C2×C4×C37—82no—
349C2×C4×C37#12011yescharacteristic
350C2×C4×C37#12011yescharacteristic
351C2×C4×C37#12011yescharacteristic
352C2×C4×C37C22×D411yescharacteristic
353C2×C4×C37C22×D411yescharacteristic
354C2×C4×C37C22×D411yescharacteristic
355C8×C37—41no—
356C8×C37—41no—
357C8×C37—41no—
358C8×C37—41no—
359C8×C37—41no—
360C8×C37—41no—
361#18810C3711yesmaximal, characteristic, direct product factor, Sylow
362C22×C37—21no—
363C22×C37—22no—
364C22×C37—21no—
365C22×C37—21no—
366C22×C37—41no—
367C22×C37—41no—
368C22×C37—41no—
369C22×C37—41no—
370C22×C37—42no—
371C22×C37—41no—
372C22×C37—42no—
373C22×C37—41no—
374C22×C37—42no—
375C22×C37—41no—
376C22×C37—41no—
377C22×C37—84no—
378C22×C37—81no—
379C22×C37—81no—
380C22×C37—81no—
381C22×C37—164no—
382C22×C37C2×#12011yescharacteristic
383C4×C37—21no—
384C4×C37—21no—
385C4×C37—21no—
386C4×C37—21no—
387C4×C37—41no—
388C4×C37—41no—
389C4×C37—41no—
390C4×C37—41no—
391C4×C37—41no—
392C4×C37—42no—
393C4×C37—81no—
394C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
395C4×C37#57511yescharacteristic
396C4×C37#57611yescharacteristic
397C4×C37#57711yescharacteristic
398#3519C2×C3711yescharacteristic, complemented
399#3251C2×C3711yescharacteristic, complemented
400#3207C2×C3711yescharacteristic, complemented
401#3036C2×C3711yescharacteristic, complemented
402#1646C2×C3711yescharacteristic, complemented
403#1643C2×C3711yescharacteristic, complemented
404#1642C2×C3711yescharacteristic, complemented
405#1639C2×C3711yescharacteristic, complemented
406#1624C2×C3711yescharacteristic, complemented
407#1622C2×C3711yescharacteristic, complemented
408#1621C2×C3711yescharacteristic, complemented
409#1619C2×C3711yescharacteristic, complemented
410#1560C2×C3711yescharacteristic, complemented
411#1495C2×C3711yescharacteristic, complemented
412#1486C2×C3711yescharacteristic, complemented
413C2×C37—41no—
414C2×C37—42no—
415C2×C37—81no—
416C2×C37—82no—
417C2×C37—81no—
418C2×C37—161no—
419C2×C37#300611yescharacteristic
420C2×C37#301211yescharacteristic
421C2×C37#301911yescharacteristic
422C2×AGL(1,ℤ/8)—21no—
423#555C22×C3711yescharacteristic
424#554C22×C3711yescharacteristic
425#553—21no—
426#553—21no—
427#550C22×C3711yescharacteristic
428#546—22no—
429#546—21no—
430D42—21no—
431D42C22×C3711yescharacteristic
432#540—21no—
433#538—22no—
434#532C22×C3711yescharacteristic
435#532C22×C3711yescharacteristic, complemented
436#529C22×C3711yescharacteristic
437#525—21no—
438C2×#121—21no—
439#518—21no—
440C2×C4×D4C22×C3711yescharacteristic
441#493C22×C3711yescharacteristic, complemented
442#492C22×C3711yescharacteristic, complemented
443#487C22×C3711yescharacteristic, complemented
444#486C22×C3711yescharacteristic, complemented
445#478—21no—
446#475C22×C3711yescharacteristic, complemented
447#474C22×C3711yescharacteristic, complemented
448#469—21no—
449#468—21no—
450#463—22no—
451#463—21no—
452#463—21no—
453#463—21no—
454#461C22×C3711yescharacteristic
455#461C22×C3711yescharacteristic, complemented
456#460C22×C3711yescharacteristic, complemented
457#459C22×C3711yescharacteristic
458#459C22×C3711yescharacteristic, complemented
459#459C22×C3711yescharacteristic, complemented
460#449—22no—
461#431C22×C3711yescharacteristic, complemented
462#423C22×C3711yescharacteristic, complemented
463#423C22×C3711yescharacteristic, complemented
464#417—21no—
465#333C22×C3711yescharacteristic, complemented
466#333C22×C3711yescharacteristic, complemented
467#331C22×C3711yescharacteristic, complemented
468#331C22×C3711yescharacteristic, complemented
469Q8⋊C8C22×C3711yescharacteristic, complemented
470Q8⋊C8C22×C3711yescharacteristic, complemented
471D4⋊C8C22×C3711yescharacteristic
472D4⋊C8C22×C3711yescharacteristic
473D4⋊C8C22×C3711yescharacteristic, complemented
474D4⋊C8C22×C3711yescharacteristic, complemented
475D4⋊C8C22×C3711yescharacteristic, complemented
476D4⋊C8C22×C3711yescharacteristic, complemented
477C37#1881011yescharacteristic, direct product factor, Sylow
478C2×#41—21no—
479C2×#41—21no—
480C2×#41D4×C3712yes—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C3711yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—44no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16—21no—
491C2×D8—21no—
492C2×D8—21no—
493C2×D8—22no—
494C2×D8—21no—
495C2×M16—21no—
496C2×M16—21no—
497C4⋊Q8C23×C3711yescharacteristic
498C4⋊Q8C23×C3711yescharacteristic
499#127—21no—
500#127C23×C3711yescharacteristic
501#127C23×C3711yescharacteristic
502#126—22no—
503#126—21no—
504#125—21no—
505#125D4×C3711yescharacteristic
506#124—22no—
507#124—21no—
508#124D4×C3711yescharacteristic
509#124D4×C3712yes—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—22no—
516C22⋊Q8D4×C3711yescharacteristic
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121D4×C3711yescharacteristic
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8C23×C3711yescharacteristic
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C3711yescharacteristic
549C4×D4D4×C3711yescharacteristic
550C4×D4C23×C3711yescharacteristic
551C4×D4C23×C3711yescharacteristic
552C4×D4C23×C3711yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C3711yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C42C23×C3711yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567C4⋊C8C23×C3711yescharacteristic
568C4⋊C8C23×C3711yescharacteristic
569C4⋊C8C23×C3711yescharacteristic
570C4⋊C8C23×C3711yescharacteristic
571#103—22no—
572#103—21no—
573#103—21no—
574#103—21no—
575#102—22no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581C22⋊C8—21no—
582C4×C8C23×C3711yescharacteristic
583C4×C8C23×C3711yescharacteristic
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C3711yescharacteristic
593C2×Q8C2×D4×C3712yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
615C2×D4C2×D4×C3711yescharacteristic
616C2×D4C2×D4×C3711yescharacteristic
617C2×D4C2×D4×C3711yescharacteristic
618C2×D4C2×D4×C3712yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C3711yescharacteristic
632C22×C4C2×D4×C3711yescharacteristic
633C22×C4C2×D4×C3711yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C2×D4×C3711yescharacteristic
662C4⋊C4C2×D4×C3711yescharacteristic
663C4⋊C4C2×D4×C3711yescharacteristic
664C4⋊C4C2×D4×C3711yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C3711yescharacteristic
686C42C2×D4×C3711yescharacteristic
687C42C2×D4×C3711yescharacteristic
688C42C24×C3711yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C3711yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4AGL(1,ℤ/8)×C3712yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4#120×C3711yescharacteristic
757C2×C4#120×C3711yescharacteristic
758C2×C4#120×C3711yescharacteristic
759C2×C4C22×D4×C3711yescharacteristic
760C2×C4C22×D4×C3711yescharacteristic
761C2×C4C22×D4×C3711yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×#120×C3711yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
801C4C37×#57511yescharacteristic
802C4C37×#57611yescharacteristic
803C4C37×#57711yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2C37×#300611yescharacteristic
811C2C37×#301211yescharacteristic
812C2C37×#301911yescharacteristic
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×#3519C2semidirect
2. C37×#3251C2semidirect
3. C37×#3207C2semidirect
4. C37×#3036C2semidirect
5. C37×#1646C2semidirect
6. C37×#1643C2semidirect
7. C37×#1642C2semidirect
8. C37×#1639C2semidirect
9. C37×#1624C2semidirect
10. C37×#1622C2semidirect
11. C37×#1621C2semidirect
12. C37×#1619C2semidirect
13. C37×#1560C2semidirect
14. C37×#1495C2semidirect
15. C37×#1486C2semidirect
29. C37×#532C22semidirect
35. C37×#493C22semidirect
36. C37×#492C22semidirect
37. C37×#487C22semidirect
38. C37×#486C22semidirect
40. C37×#475C22semidirect
41. C37×#474C22semidirect
49. C37×#461C22semidirect
50. C37×#460C22semidirect
52. C37×#459C22semidirect
53. C37×#459C22semidirect
55. C37×#431C22semidirect
56. C37×#423C22semidirect
57. C37×#423C22semidirect
59. C37×#333C22semidirect
60. C37×#333C22semidirect
61. C37×#331C22semidirect
62. C37×#331C22semidirect
63. C37×Q8⋊C8C22semidirect
64. C37×Q8⋊C8C22semidirect
67. C37×D4⋊C8C22semidirect
68. C37×D4⋊C8C22semidirect
69. C37×D4⋊C8C22semidirect
70. C37×D4⋊C8C22semidirect
361. #18810C37direct (N × H)
398. #3519C2×C37semidirect
399. #3251C2×C37semidirect
400. #3207C2×C37semidirect
401. #3036C2×C37semidirect
402. #1646C2×C37semidirect
403. #1643C2×C37semidirect
404. #1642C2×C37semidirect
405. #1639C2×C37semidirect
406. #1624C2×C37semidirect
407. #1622C2×C37semidirect
408. #1621C2×C37semidirect
409. #1619C2×C37semidirect
410. #1560C2×C37semidirect
411. #1495C2×C37semidirect
412. #1486C2×C37semidirect
435. #532C22×C37semidirect
441. #493C22×C37semidirect
442. #492C22×C37semidirect
443. #487C22×C37semidirect
444. #486C22×C37semidirect
446. #475C22×C37semidirect
447. #474C22×C37semidirect
455. #461C22×C37semidirect
456. #460C22×C37semidirect
458. #459C22×C37semidirect
459. #459C22×C37semidirect
461. #431C22×C37semidirect
462. #423C22×C37semidirect
463. #423C22×C37semidirect
465. #333C22×C37semidirect
466. #333C22×C37semidirect
467. #331C22×C37semidirect
468. #331C22×C37semidirect
469. Q8⋊C8C22×C37semidirect
470. Q8⋊C8C22×C37semidirect
473. D4⋊C8C22×C37semidirect
474. D4⋊C8C22×C37semidirect
475. D4⋊C8C22×C37semidirect
476. D4⋊C8C22×C37semidirect
477. C37#18810direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35192
C37×#32512
C37×#32072
C37×#30362
C37×#16462
C37×#16432
C37×#16422
C37×#16392
C37×#16242
C37×#16222
C37×#16212
C37×#16192
C37×#15602
C37×#14952
C37×#14862
#1881037