Finite Group Databasebeta

← C37×#18754 #22640007

Subgroups — C37×#18754 #22640007

Order 9472.

1042 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3481C211yesmaximal, characteristic, complemented
2C37×#3207C211yesmaximal, characteristic, complemented
3C37×#3115C211yesmaximal, characteristic, complemented
4C37×#3035C211yesmaximal, characteristic, complemented
5C37×#1644C211yesmaximal, characteristic, complemented
6C37×#1643C211yesmaximal, characteristic, complemented
7C37×#1640C211yesmaximal, characteristic, complemented
8C37×#1639C211yesmaximal, characteristic, complemented
9C37×#1622C211yesmaximal, characteristic, complemented
10C37×#1622C211yesmaximal, characteristic, complemented
11C37×#1620C211yesmaximal, characteristic, complemented
12C37×#1619C211yesmaximal, characteristic, complemented
13C37×#1551C211yesmaximal, characteristic, complemented
14C37×#1488C211yesmaximal, characteristic, complemented
15C37×#1477C211yesmaximal, characteristic, complemented
16C2×#135×C37—21no—
17C37×#559C2211yescharacteristic
18C37×#554C2211yescharacteristic
19C37×#554C2211yescharacteristic
20C37×#553—21no—
21C37×#553—21no—
22C37×#551—22no—
23C37×#546—21no—
24C37×#546—21no—
25D42×C37C2211yescharacteristic
26C37×#532C2211yescharacteristic
27C37×#532C2211yescharacteristic, complemented
28C37×#529—21no—
29C37×#529—21no—
30C37×#525—22no—
31C4×#41×C37C2211yescharacteristic
32C4×#41×C37C2211yescharacteristic
33C2×C4×D4×C37—21no—
34C2×C4×D4×C37—21no—
35C37×#493C2211yescharacteristic
36C37×#492C2211yescharacteristic, complemented
37C37×#487C2211yescharacteristic, complemented
38C37×#486C2211yescharacteristic
39C37×#482—21no—
40C37×#475C2211yescharacteristic, complemented
41C37×#474C2211yescharacteristic
42C37×#464—21no—
43C37×#463—22no—
44C37×#463—21no—
45C37×#462C2211yescharacteristic, complemented
46C37×#461C2211yescharacteristic
47C37×#460C2211yescharacteristic, complemented
48C37×#460C2211yescharacteristic, complemented
49C37×#459C2211yescharacteristic
50C37×#459C2211yescharacteristic
51C37×#449—22no—
52C37×#449—21no—
53C37×#442—21no—
54C37×#440—21no—
55C37×#432C2211yescharacteristic, complemented
56C37×#431C2211yescharacteristic, complemented
57C2×C4⋊C8×C37C2211yescharacteristic, complemented
58C37×#416—21no—
59C37×#333C2211yescharacteristic, complemented
60C37×#333C2211yescharacteristic, complemented
61C37×#331C2211yescharacteristic
62C37×#331C2211yescharacteristic
63C37×Q8⋊C8C2211yescharacteristic, complemented
64C37×Q8⋊C8C2211yescharacteristic, complemented
65C37×Q8⋊C8C2211yescharacteristic, complemented
66C37×Q8⋊C8C2211yescharacteristic, complemented
67C37×D4⋊C8C2211yescharacteristic
68C37×D4⋊C8C2211yescharacteristic
69C37×D4⋊C8C2211yescharacteristic
70C37×D4⋊C8C2211yescharacteristic
71C2×#41×C37—21no—
72C2×#41×C37D411yescharacteristic
73C2×#41×C37D411yescharacteristic
74C2×#41×C37D412yes—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C23×C4×C37—22no—
78#135×C37—44no—
79C2×Q16×C37—21no—
80C2×SD16×C37—21no—
81C2×SD16×C37—21no—
82C2×SD16×C37—21no—
83C2×SD16×C37—22no—
84C2×D8×C37—21no—
85C2×D8×C37—21no—
86C2×D8×C37—22no—
87C22×C8×C37—21no—
88C4⋊Q8×C37C2311yescharacteristic
89C4⋊Q8×C37C2311yescharacteristic
90#127×C37C2311yescharacteristic
91#127×C37C2311yescharacteristic
92#126×C37—22no—
93#126×C37—22no—
94#125×C37—21no—
95#125×C37—21no—
96#124×C37—21no—
97#124×C37—21no—
98#124×C37—21no—
99#124×C37D412yes—
100#123×C37—22no—
101#123×C37—22no—
102#123×C37—22no—
103#123×C37—22no—
104C22⋊Q8×C37—22no—
105C22⋊Q8×C37—22no—
106C22⋊Q8×C37—21no—
107C22⋊Q8×C37—21no—
108#121×C37—22no—
109#121×C37—22no—
110#121×C37—21no—
111#121×C37—21no—
112#121×C37—21no—
113#121×C37—21no—
114#121×C37—21no—
115#121×C37—21no—
116#120×C37—22no—
117#120×C37—22no—
118C4×Q8×C37D411yescharacteristic
119C4×Q8×C37D411yescharacteristic
120C4×Q8×C37C2311yescharacteristic
121C4×Q8×C37C2311yescharacteristic
122C4×D4×C37—22no—
123C4×D4×C37—22no—
124C4×D4×C37—22no—
125C4×D4×C37—22no—
126C4×D4×C37—21no—
127C4×D4×C37—21no—
128C4×D4×C37—21no—
129C4×D4×C37—21no—
130C4×D4×C37—21no—
131C4×D4×C37—21no—
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×C37D411yescharacteristic
139C4×D4×C37D411yescharacteristic
140C4×D4×C37C2311yescharacteristic
141C4×D4×C37C2311yescharacteristic
142#117×C37—22no—
143#117×C37—21no—
144#117×C37—21no—
145#117×C37D411yescharacteristic
146#117×C37D411yescharacteristic
147C2×C4⋊C4×C37—21no—
148C2×C4⋊C4×C37—21no—
149C2×C22⋊C4×C37—22no—
150C2×C22⋊C4×C37—22no—
151C2×C42×C37—21no—
152C2×C42×C37—21no—
153C2×C42×C37C2311yescharacteristic
154#107×C37—21no—
155#106×C37—21no—
156C4⋊C8×C37—21no—
157C4⋊C8×C37—21no—
158C4⋊C8×C37C2311yescharacteristic
159C4⋊C8×C37C2311yescharacteristic
160C4⋊C8×C37C2311yescharacteristic
161C4⋊C8×C37C2311yescharacteristic
162#103×C37—21no—
163#103×C37—22no—
164#103×C37—21no—
165#103×C37—21no—
166#102×C37—21no—
167#102×C37—22no—
168#102×C37—21no—
169#102×C37—21no—
170#102×C37—21no—
171#102×C37—21no—
172C22⋊C8×C37—21no—
173C22⋊C8×C37—21no—
174#97×C37—21no—
175C4×C8×C37C2311yescharacteristic
176C4×C8×C37C2311yescharacteristic
177C24×C37—22no—
178#41×C37—22no—
179#41×C37—22no—
180#41×C37—41no—
181#41×C37—41no—
182#41×C37—42no—
183#41×C37—42no—
184#41×C37—82no—
185C2×Q8×C37—21no—
186C2×Q8×C37C2×D411yescharacteristic
187C2×Q8×C37C2×D411yescharacteristic
188C2×Q8×C37C2×D412yes—
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—21no—
192C2×D4×C37—21no—
193C2×D4×C37—22no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—42no—
200C2×D4×C37—42no—
201C2×D4×C37—42no—
202C2×D4×C37—42no—
203C2×D4×C37—41no—
204C2×D4×C37C2×D411yescharacteristic
205C2×D4×C37C2×D411yescharacteristic
206C2×D4×C37C2×D412yes—
207C22×C4×C37—22no—
208C22×C4×C37—22no—
209C22×C4×C37—22no—
210C22×C4×C37—21no—
211C22×C4×C37—21no—
212C22×C4×C37—21no—
213C22×C4×C37—21no—
214C22×C4×C37—22no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—41no—
218C22×C4×C37—84no—
219C22×C4×C37C2×D411yescharacteristic
220C22×C4×C37C2×D411yescharacteristic
221C22×C4×C37C2×D411yescharacteristic
222Q16×C37—42no—
223SD16×C37—42no—
224SD16×C37—42no—
225SD16×C37—42no—
226SD16×C37—82no—
227D8×C37—42no—
228D8×C37—42no—
229D8×C37—82no—
230C2×C8×C37—21no—
231C2×C8×C37—21no—
232C2×C8×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—21no—
235C2×C8×C37—21no—
236C2×C8×C37—42no—
237C4⋊C4×C37—22no—
238C4⋊C4×C37—22no—
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×D411yescharacteristic
250C4⋊C4×C37C2×D411yescharacteristic
251C4⋊C4×C37C2×D411yescharacteristic
252C4⋊C4×C37C2×D411yescharacteristic
253C22⋊C4×C37—22no—
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—22no—
264C22⋊C4×C37—22no—
265C22⋊C4×C37—21no—
266C22⋊C4×C37—21no—
267C22⋊C4×C37—41no—
268C22⋊C4×C37—41no—
269C42×C37—21no—
270C42×C37—21no—
271C42×C37—21no—
272C42×C37—21no—
273C42×C37—21no—
274C42×C37—21no—
275C42×C37C2×D411yescharacteristic
276C42×C37C2×D411yescharacteristic
277C42×C37C2×D411yescharacteristic
278C42×C37C2411yescharacteristic
279C23×C37—21no—
280C23×C37—21no—
281C23×C37—22no—
282C23×C37—44no—
283C23×C37—44no—
284C23×C37—41no—
285C23×C37—82no—
286C23×C37#12011yescharacteristic
287Q8×C37—21no—
288Q8×C37—21no—
289Q8×C37—21no—
290Q8×C37—21no—
291Q8×C37—42no—
292Q8×C37—41no—
293Q8×C37—41no—
294D4×C37—21no—
295D4×C37—21no—
296D4×C37—42no—
297D4×C37—42no—
298D4×C37—42no—
299D4×C37—42no—
300D4×C37—44no—
301D4×C37—44no—
302D4×C37—41no—
303D4×C37—41no—
304D4×C37—41no—
305D4×C37—41no—
306D4×C37—41no—
307D4×C37—41no—
308D4×C37—41no—
309D4×C37—41no—
310D4×C37—82no—
311D4×C37—82no—
312D4×C37#13512yescomplemented
313D4×C37AGL(1,ℤ/8)12yes—
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—21no—
322C2×C4×C37—21no—
323C2×C4×C37—21no—
324C2×C4×C37—22no—
325C2×C4×C37—41no—
326C2×C4×C37—42no—
327C2×C4×C37—42no—
328C2×C4×C37—42no—
329C2×C4×C37—42no—
330C2×C4×C37—44no—
331C2×C4×C37—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—82no—
337C2×C4×C37—82no—
338C2×C4×C37—82no—
339C2×C4×C37—82no—
340C2×C4×C37#12011yescharacteristic
341C2×C4×C37#12011yescharacteristic
342C2×C4×C37#12011yescharacteristic
343C2×C4×C37C22×D411yescharacteristic
344C2×C4×C37C22×D411yescharacteristic
345C2×C4×C37C22×D411yescharacteristic
346C8×C37—41no—
347C8×C37—41no—
348C8×C37—41no—
349C8×C37—41no—
350C8×C37—41no—
351C8×C37—41no—
352#18754C3711yesmaximal, characteristic, direct product factor, Sylow
353C22×C37—21no—
354C22×C37—22no—
355C22×C37—21no—
356C22×C37—22no—
357C22×C37—21no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—41no—
361C22×C37—41no—
362C22×C37—42no—
363C22×C37—42no—
364C22×C37—42no—
365C22×C37—88no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37—81no—
369C22×C37C2×#12011yescharacteristic
370C4×C37—21no—
371C4×C37—21no—
372C4×C37—21no—
373C4×C37—21no—
374C4×C37—41no—
375C4×C37—41no—
376C4×C37—41no—
377C4×C37—41no—
378C4×C37—41no—
379C4×C37—41no—
380C4×C37—42no—
381C4×C37—81no—
382C4×C37C2×#13511yescharacteristic
383C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
384C4×C37#57511yescharacteristic
385C4×C37#57511yescharacteristic
386#3481C2×C3711yescharacteristic, complemented
387#3207C2×C3711yescharacteristic, complemented
388#3115C2×C3711yescharacteristic, complemented
389#3035C2×C3711yescharacteristic, complemented
390#1644C2×C3711yescharacteristic, complemented
391#1643C2×C3711yescharacteristic, complemented
392#1640C2×C3711yescharacteristic, complemented
393#1639C2×C3711yescharacteristic, complemented
394#1622C2×C3711yescharacteristic, complemented
395#1622C2×C3711yescharacteristic, complemented
396#1620C2×C3711yescharacteristic, complemented
397#1619C2×C3711yescharacteristic, complemented
398#1551C2×C3711yescharacteristic, complemented
399#1488C2×C3711yescharacteristic, complemented
400#1477C2×C3711yescharacteristic, complemented
401C2×C37—41no—
402C2×C37—42no—
403C2×C37—42no—
404C2×C37—82no—
405C2×C37—161no—
406C2×C37#300211yescharacteristic
407C2×C37#300611yescharacteristic
408C2×C37#301911yescharacteristic
409C2×#135—21no—
410#559C22×C3711yescharacteristic
411#554C22×C3711yescharacteristic
412#554C22×C3711yescharacteristic
413#553—21no—
414#553—21no—
415#551—22no—
416#546—21no—
417#546—21no—
418D42C22×C3711yescharacteristic
419#532C22×C3711yescharacteristic
420#532C22×C3711yescharacteristic, complemented
421#529—21no—
422#529—21no—
423#525—22no—
424C4×#41C22×C3711yescharacteristic
425C4×#41C22×C3711yescharacteristic
426C2×C4×D4—21no—
427C2×C4×D4—21no—
428#493C22×C3711yescharacteristic
429#492C22×C3711yescharacteristic, complemented
430#487C22×C3711yescharacteristic, complemented
431#486C22×C3711yescharacteristic
432#482—21no—
433#475C22×C3711yescharacteristic, complemented
434#474C22×C3711yescharacteristic
435#464—21no—
436#463—22no—
437#463—21no—
438#462C22×C3711yescharacteristic, complemented
439#461C22×C3711yescharacteristic
440#460C22×C3711yescharacteristic, complemented
441#460C22×C3711yescharacteristic, complemented
442#459C22×C3711yescharacteristic
443#459C22×C3711yescharacteristic
444#449—21no—
445#449—22no—
446#442—21no—
447#440—21no—
448#432C22×C3711yescharacteristic, complemented
449#431C22×C3711yescharacteristic, complemented
450C2×C4⋊C8C22×C3711yescharacteristic, complemented
451#416—21no—
452#333C22×C3711yescharacteristic, complemented
453#333C22×C3711yescharacteristic, complemented
454#331C22×C3711yescharacteristic
455#331C22×C3711yescharacteristic
456Q8⋊C8C22×C3711yescharacteristic, complemented
457Q8⋊C8C22×C3711yescharacteristic, complemented
458Q8⋊C8C22×C3711yescharacteristic, complemented
459Q8⋊C8C22×C3711yescharacteristic, complemented
460D4⋊C8C22×C3711yescharacteristic
461D4⋊C8C22×C3711yescharacteristic
462D4⋊C8C22×C3711yescharacteristic
463D4⋊C8C22×C3711yescharacteristic
464C37#1875411yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41D4×C3711yescharacteristic
467C2×#41D4×C3711yescharacteristic
468C2×#41D4×C3712yes—
469C22×D4—21no—
470C22×D4—21no—
471C23×C4—22no—
472#135—44no—
473C2×Q16—21no—
474C2×SD16—21no—
475C2×SD16—21no—
476C2×SD16—21no—
477C2×SD16—22no—
478C2×D8—21no—
479C2×D8—21no—
480C2×D8—22no—
481C22×C8—21no—
482C4⋊Q8C23×C3711yescharacteristic
483C4⋊Q8C23×C3711yescharacteristic
484#127C23×C3711yescharacteristic
485#127C23×C3711yescharacteristic
486#126—22no—
487#126—22no—
488#125—21no—
489#125—21no—
490#124—21no—
491#124—21no—
492#124—21no—
493#124D4×C3712yes—
494#123—22no—
495#123—22no—
496#123—22no—
497#123—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#120—22no—
511#120—22no—
512C4×Q8D4×C3711yescharacteristic
513C4×Q8D4×C3711yescharacteristic
514C4×Q8C23×C3711yescharacteristic
515C4×Q8C23×C3711yescharacteristic
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4D4×C3711yescharacteristic
533C4×D4D4×C3711yescharacteristic
534C4×D4C23×C3711yescharacteristic
535C4×D4C23×C3711yescharacteristic
536#117—22no—
537#117—21no—
538#117—21no—
539#117D4×C3711yescharacteristic
540#117D4×C3711yescharacteristic
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C42—21no—
546C2×C42—21no—
547C2×C42C23×C3711yescharacteristic
548#107—21no—
549#106—21no—
550C4⋊C8—21no—
551C4⋊C8—21no—
552C4⋊C8C23×C3711yescharacteristic
553C4⋊C8C23×C3711yescharacteristic
554C4⋊C8C23×C3711yescharacteristic
555C4⋊C8C23×C3711yescharacteristic
556#103—21no—
557#103—22no—
558#103—21no—
559#103—21no—
560#102—21no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566C22⋊C8—21no—
567C22⋊C8—21no—
568#97—21no—
569C4×C8C23×C3711yescharacteristic
570C4×C8C23×C3711yescharacteristic
571C24—22no—
572#41—22no—
573#41—22no—
574#41—41no—
575#41—41no—
576#41—42no—
577#41—42no—
578#41—82no—
579C2×Q8—21no—
580C2×Q8C2×D4×C3711yescharacteristic
581C2×Q8C2×D4×C3711yescharacteristic
582C2×Q8C2×D4×C3712yes—
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—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—41no—
598C2×D4C2×D4×C3711yescharacteristic
599C2×D4C2×D4×C3711yescharacteristic
600C2×D4C2×D4×C3712yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—41no—
612C22×C4—84no—
613C22×C4C2×D4×C3711yescharacteristic
614C22×C4C2×D4×C3711yescharacteristic
615C22×C4C2×D4×C3711yescharacteristic
616Q16—42no—
617SD16—42no—
618SD16—42no—
619SD16—42no—
620SD16—82no—
621D8—42no—
622D8—42no—
623D8—82no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—42no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4C2×D4×C3711yescharacteristic
644C4⋊C4C2×D4×C3711yescharacteristic
645C4⋊C4C2×D4×C3711yescharacteristic
646C4⋊C4C2×D4×C3711yescharacteristic
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42C2×D4×C3711yescharacteristic
670C42C2×D4×C3711yescharacteristic
671C42C2×D4×C3711yescharacteristic
672C42C24×C3711yescharacteristic
673C23—21no—
674C23—21no—
675C23—22no—
676C23—44no—
677C23—44no—
678C23—41no—
679C23—82no—
680C23#120×C3711yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4#135×C3712yescomplemented
707D4AGL(1,ℤ/8)×C3712yes—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4#120×C3711yescharacteristic
735C2×C4#120×C3711yescharacteristic
736C2×C4#120×C3711yescharacteristic
737C2×C4C22×D4×C3711yescharacteristic
738C2×C4C22×D4×C3711yescharacteristic
739C2×C4C22×D4×C3711yescharacteristic
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—22no—
748C22—21no—
749C22—22no—
750C22—21no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—88no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C2×#120×C3711yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4C2×#135×C3711yescharacteristic
776C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
777C4C37×#57511yescharacteristic
778C4C37×#57511yescharacteristic
779C2—41no—
780C2—42no—
781C2—42no—
782C2—82no—
783C2—161no—
784C2C37×#300211yescharacteristic
785C2C37×#300611yescharacteristic
786C2C37×#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×#3481C2semidirect
2. C37×#3207C2semidirect
3. C37×#3115C2semidirect
4. C37×#3035C2semidirect
5. C37×#1644C2semidirect
6. C37×#1643C2semidirect
7. C37×#1640C2semidirect
8. C37×#1639C2semidirect
9. C37×#1622C2semidirect
10. C37×#1622C2semidirect
11. C37×#1620C2semidirect
12. C37×#1619C2semidirect
13. C37×#1551C2semidirect
14. C37×#1488C2semidirect
15. C37×#1477C2semidirect
27. C37×#532C22semidirect
36. C37×#492C22semidirect
37. C37×#487C22semidirect
40. C37×#475C22semidirect
45. C37×#462C22semidirect
47. C37×#460C22semidirect
48. C37×#460C22semidirect
55. C37×#432C22semidirect
56. C37×#431C22semidirect
57. C2×C4⋊C8×C37C22semidirect
59. C37×#333C22semidirect
60. C37×#333C22semidirect
63. C37×Q8⋊C8C22semidirect
64. C37×Q8⋊C8C22semidirect
65. C37×Q8⋊C8C22semidirect
66. C37×Q8⋊C8C22semidirect
312. D4×C37#135semidirect
352. #18754C37direct (N × H)
386. #3481C2×C37semidirect
387. #3207C2×C37semidirect
388. #3115C2×C37semidirect
389. #3035C2×C37semidirect
390. #1644C2×C37semidirect
391. #1643C2×C37semidirect
392. #1640C2×C37semidirect
393. #1639C2×C37semidirect
394. #1622C2×C37semidirect
395. #1622C2×C37semidirect
396. #1620C2×C37semidirect
397. #1619C2×C37semidirect
398. #1551C2×C37semidirect
399. #1488C2×C37semidirect
400. #1477C2×C37semidirect
420. #532C22×C37semidirect
429. #492C22×C37semidirect
430. #487C22×C37semidirect
433. #475C22×C37semidirect
438. #462C22×C37semidirect
440. #460C22×C37semidirect
441. #460C22×C37semidirect
448. #432C22×C37semidirect
449. #431C22×C37semidirect
450. C2×C4⋊C8C22×C37semidirect
452. #333C22×C37semidirect
453. #333C22×C37semidirect
456. Q8⋊C8C22×C37semidirect
457. Q8⋊C8C22×C37semidirect
458. Q8⋊C8C22×C37semidirect
459. Q8⋊C8C22×C37semidirect
464. C37#18754direct (N × H)
706. D4#135×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34812
C37×#32072
C37×#31152
C37×#30352
C37×#16442
C37×#16432
C37×#16402
C37×#16392
C37×#16222
C37×#16202
C37×#16192
C37×#15512
C37×#14882
C37×#14772
#1875437