Finite Group Databasebeta

← C37×#18931 #22640184

Subgroups — C37×#18931 #22640184

Order 9472.

986 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×#3543C211yesmaximal, characteristic
2C37×#3252C211yesmaximal, characteristic, complemented
3C37×#3233C211yesmaximal, characteristic, complemented
4C37×#3208C211yesmaximal, characteristic, complemented
5C37×#1642C211yesmaximal, characteristic, complemented
6C37×#1641C211yesmaximal, characteristic, complemented
7C37×#1640C211yesmaximal, characteristic, complemented
8C37×#1639C211yesmaximal, characteristic, complemented
9C37×#1631C211yesmaximal, characteristic, complemented
10C37×#1631C211yesmaximal, characteristic, complemented
11C37×#1630C211yesmaximal, characteristic, complemented
12C37×#1629C211yesmaximal, characteristic, complemented
13C37×#1545C211yesmaximal, characteristic, complemented
14C37×#1495C211yesmaximal, characteristic, complemented
15C37×#1482C211yesmaximal, characteristic, complemented
16C37×#560—22no—
17C37×#559C2211yescharacteristic
18C37×#550C2211yescharacteristic
19C37×#550C2211yescharacteristic
20C37×#546—21no—
21C37×#546—21no—
22D42×C37—21no—
23D42×C37—21no—
24D42×C37C2211yescharacteristic
25C37×#540—21no—
26C37×#540—21no—
27C37×#535—21no—
28C37×#535—21no—
29C37×#534—22no—
30C37×#533C2211yescharacteristic, complemented
31C2×#127×C37C2211yescharacteristic
32C37×#529C2211yescharacteristic
33C37×#529C2211yescharacteristic
34C37×#499—21no—
35C37×#492C2211yescharacteristic
36C37×#492C2211yescharacteristic, complemented
37C37×#488—21no—
38C37×#486C2211yescharacteristic
39C37×#486C2211yescharacteristic, complemented
40C37×#485—21no—
41C37×#482—21no—
42C37×#479—21no—
43C37×#477C2211yescharacteristic, complemented
44C37×#477C2211yescharacteristic, complemented
45C37×#476C2211yescharacteristic, complemented
46C37×#476C2211yescharacteristic, complemented
47C37×#475C2211yescharacteristic, complemented
48C37×#474C2211yescharacteristic, complemented
49C37×#470—21no—
50C37×#468—21no—
51C37×#464—21no—
52C37×#462C2211yescharacteristic, complemented
53C37×#461C2211yescharacteristic, complemented
54C37×#460—22no—
55C37×#450—22no—
56C37×#431C2211yescharacteristic, complemented
57C37×#431C2211yescharacteristic, complemented
58C37×#423C2211yescharacteristic, complemented
59C37×#331C2211yescharacteristic
60C37×#331C2211yescharacteristic
61C37×#331C2211yescharacteristic, complemented
62C37×#331C2211yescharacteristic, complemented
63C37×Q8⋊C8C2211yescharacteristic, complemented
64C37×Q8⋊C8C2211yescharacteristic, complemented
65C37×Q8⋊C8C2211yescharacteristic, complemented
66C37×Q8⋊C8C2211yescharacteristic, complemented
67C37×D4⋊C8C2211yescharacteristic, complemented
68C37×D4⋊C8C2211yescharacteristic, complemented
69C37×D4⋊C8C2211yescharacteristic, complemented
70C37×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C37—21no—
72C2×#41×C37—21no—
73C22×D4×C37—22no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37D412yes—
79C2×Q16×C37—21no—
80C2×SD16×C37—22no—
81C2×SD16×C37—22no—
82C2×SD16×C37—21no—
83C2×M16×C37—21no—
84C4⋊Q8×C37C2311yescharacteristic
85C4⋊Q8×C37C2311yescharacteristic
86#127×C37—21no—
87#127×C37—21no—
88#127×C37—21no—
89#127×C37—21no—
90#127×C37D412yes—
91#127×C37C2311yescharacteristic
92#127×C37C2311yescharacteristic
93#126×C37—21no—
94#126×C37—21no—
95#125×C37—21no—
96#125×C37D411yescharacteristic
97#125×C37D411yescharacteristic
98#124×C37—21no—
99#124×C37—21no—
100#124×C37D411yescharacteristic
101#124×C37D411yescharacteristic
102#123×C37—22no—
103#123×C37—22no—
104#123×C37—22no—
105#123×C37—22no—
106#123×C37—21no—
107#123×C37—21no—
108C22⋊Q8×C37—21no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37D411yescharacteristic
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—22no—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37D411yescharacteristic
125#121×C37D411yescharacteristic
126#120×C37—22no—
127#120×C37—22no—
128#120×C37—22no—
129#120×C37—22no—
130#120×C37—22no—
131#120×C37—22no—
132C4×Q8×C37—21no—
133C4×Q8×C37—21no—
134C4×Q8×C37C2311yescharacteristic
135C4×Q8×C37C2311yescharacteristic
136C4×D4×C37—21no—
137C4×D4×C37—21no—
138C4×D4×C37—21no—
139C4×D4×C37—21no—
140C4×D4×C37—21no—
141C4×D4×C37—21no—
142C4×D4×C37C2311yescharacteristic
143C4×D4×C37C2311yescharacteristic
144#117×C37—21no—
145#117×C37—21no—
146#117×C37—21no—
147C2×C22⋊C4×C37—22no—
148C2×C42×C37C2311yescharacteristic
149#107×C37—21no—
150#107×C37—21no—
151#107×C37—21no—
152#106×C37—21no—
153#106×C37—21no—
154#106×C37—21no—
155C4⋊C8×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—21no—
164#103×C37—21no—
165#103×C37—21no—
166#102×C37—22no—
167#102×C37—22no—
168#102×C37—21no—
169#102×C37—21no—
170#102×C37—21no—
171C22⋊C8×C37—21no—
172C22⋊C8×C37—21no—
173C4×C8×C37—21no—
174C4×C8×C37C2311yescharacteristic
175C4×C8×C37C2311yescharacteristic
176C24×C37—22no—
177C24×C37—22no—
178#41×C37—81no—
179#41×C37—81no—
180#41×C37—81no—
181#41×C37—81no—
182C2×Q8×C37—21no—
183C2×Q8×C37—21no—
184C2×Q8×C37C2×D411yescharacteristic
185C2×Q8×C37C2×D411yescharacteristic
186C2×D4×C37—21no—
187C2×D4×C37—21no—
188C2×D4×C37—22no—
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—22no—
192C2×D4×C37—22no—
193C2×D4×C37—22no—
194C2×D4×C37—22no—
195C2×D4×C37—22no—
196C2×D4×C37—22no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—81no—
202C2×D4×C37—81no—
203C2×D4×C37—81no—
204C2×D4×C37—81no—
205C2×D4×C37—81no—
206C2×D4×C37—81no—
207C2×D4×C37—81no—
208C2×D4×C37—81no—
209C2×D4×C37—82no—
210C2×D4×C37—84no—
211C2×D4×C37C2×D411yescharacteristic
212C2×D4×C37C2×D411yescharacteristic
213C2×D4×C37C2×D412yes—
214C2×D4×C37C2×D412yes—
215C22×C4×C37—22no—
216C22×C4×C37—22no—
217C22×C4×C37—22no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37C2×D411yescharacteristic
221C22×C4×C37C2×D411yescharacteristic
222C22×C4×C37C2×D411yescharacteristic
223Q16×C37—81no—
224SD16×C37—81no—
225SD16×C37—82no—
226SD16×C37—82no—
227M16×C37—81no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—21no—
231C2×C8×C37—21no—
232C2×C8×C37—21no—
233C2×C8×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—21no—
244C4⋊C4×C37—21no—
245C4⋊C4×C37—21no—
246C4⋊C4×C37—41no—
247C4⋊C4×C37—41no—
248C4⋊C4×C37C2×D411yescharacteristic
249C4⋊C4×C37C2×D411yescharacteristic
250C4⋊C4×C37C2×D411yescharacteristic
251C4⋊C4×C37C2×D411yescharacteristic
252C22⋊C4×C37—22no—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—22no—
255C22⋊C4×C37—22no—
256C22⋊C4×C37—22no—
257C22⋊C4×C37—22no—
258C22⋊C4×C37—21no—
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—21no—
266C22⋊C4×C37—21no—
267C22⋊C4×C37—21no—
268C22⋊C4×C37—41no—
269C42×C37—21no—
270C42×C37—21no—
271C42×C37—41no—
272C42×C37C2×D411yescharacteristic
273C42×C37C2×D411yescharacteristic
274C42×C37C2×D411yescharacteristic
275C42×C37C2411yescharacteristic
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—22no—
279C23×C37—22no—
280C23×C37—44no—
281C23×C37—82no—
282C23×C37—82no—
283C23×C37—82no—
284C23×C37—82no—
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—21no—
297D4×C37—21no—
298D4×C37—42no—
299D4×C37—42no—
300D4×C37—42no—
301D4×C37—42no—
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—82no—
313D4×C37—82no—
314D4×C37—82no—
315D4×C37—82no—
316D4×C37—82no—
317D4×C37—82no—
318D4×C37—82no—
319C2×C4×C37—21no—
320C2×C4×C37—21no—
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—21no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
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#12011yescharacteristic
340C2×C4×C37#12011yescharacteristic
341C2×C4×C37#12011yescharacteristic
342C2×C4×C37C22×D411yescharacteristic
343C2×C4×C37C22×D411yescharacteristic
344C2×C4×C37C22×D411yescharacteristic
345C8×C37—41no—
346C8×C37—41no—
347C8×C37—41no—
348C8×C37—41no—
349C8×C37—41no—
350C8×C37—41no—
351#18931C3711yesmaximal, characteristic, direct product factor, Sylow
352C22×C37—21no—
353C22×C37—21no—
354C22×C37—21no—
355C22×C37—41no—
356C22×C37—42no—
357C22×C37—41no—
358C22×C37—42no—
359C22×C37—41no—
360C22×C37—42no—
361C22×C37—41no—
362C22×C37—42no—
363C22×C37—42no—
364C22×C37—41no—
365C22×C37—41no—
366C22×C37—42no—
367C22×C37—164no—
368C22×C37—164no—
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—81no—
381C4×C37—81no—
382C4×C37#57611yescharacteristic
383C4×C37#57711yescharacteristic
384C4×C37#57711yescharacteristic
385C4×C37#57711yescharacteristic
386#3543C2×C3711yescharacteristic
387#3252C2×C3711yescharacteristic, complemented
388#3233C2×C3711yescharacteristic, complemented
389#3208C2×C3711yescharacteristic, complemented
390#1642C2×C3711yescharacteristic, complemented
391#1641C2×C3711yescharacteristic, complemented
392#1640C2×C3711yescharacteristic, complemented
393#1639C2×C3711yescharacteristic, complemented
394#1631C2×C3711yescharacteristic, complemented
395#1631C2×C3711yescharacteristic, complemented
396#1630C2×C3711yescharacteristic, complemented
397#1629C2×C3711yescharacteristic, complemented
398#1545C2×C3711yescharacteristic, complemented
399#1495C2×C3711yescharacteristic, complemented
400#1482C2×C3711yescharacteristic, complemented
401C2×C37—41no—
402C2×C37—82no—
403C2×C37—81no—
404C2×C37—81no—
405C2×C37—82no—
406C2×C37#300911yescharacteristic
407C2×C37#301211yescharacteristic
408C2×C37#301911yescharacteristic
409#560—22no—
410#559C22×C3711yescharacteristic
411#550C22×C3711yescharacteristic
412#550C22×C3711yescharacteristic
413#546—21no—
414#546—21no—
415D42—21no—
416D42—21no—
417D42C22×C3711yescharacteristic
418#540—21no—
419#540—21no—
420#535—21no—
421#535—21no—
422#534—22no—
423#533C22×C3711yescharacteristic, complemented
424C2×#127C22×C3711yescharacteristic
425#529C22×C3711yescharacteristic
426#529C22×C3711yescharacteristic
427#499—21no—
428#492C22×C3711yescharacteristic
429#492C22×C3711yescharacteristic, complemented
430#488—21no—
431#486C22×C3711yescharacteristic
432#486C22×C3711yescharacteristic, complemented
433#485—21no—
434#482—21no—
435#479—21no—
436#477C22×C3711yescharacteristic, complemented
437#477C22×C3711yescharacteristic, complemented
438#476C22×C3711yescharacteristic, complemented
439#476C22×C3711yescharacteristic, complemented
440#475C22×C3711yescharacteristic, complemented
441#474C22×C3711yescharacteristic, complemented
442#470—21no—
443#468—21no—
444#464—21no—
445#462C22×C3711yescharacteristic, complemented
446#461C22×C3711yescharacteristic, complemented
447#460—22no—
448#450—22no—
449#431C22×C3711yescharacteristic, complemented
450#431C22×C3711yescharacteristic, complemented
451#423C22×C3711yescharacteristic, complemented
452#331C22×C3711yescharacteristic
453#331C22×C3711yescharacteristic
454#331C22×C3711yescharacteristic, complemented
455#331C22×C3711yescharacteristic, complemented
456Q8⋊C8C22×C3711yescharacteristic, complemented
457Q8⋊C8C22×C3711yescharacteristic, complemented
458Q8⋊C8C22×C3711yescharacteristic, complemented
459Q8⋊C8C22×C3711yescharacteristic, complemented
460D4⋊C8C22×C3711yescharacteristic, complemented
461D4⋊C8C22×C3711yescharacteristic, complemented
462D4⋊C8C22×C3711yescharacteristic, complemented
463D4⋊C8C22×C3711yescharacteristic, complemented
464C37#1893111yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C3712yes—
473C2×Q16—21no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—21no—
477C2×M16—21no—
478C4⋊Q8C23×C3711yescharacteristic
479C4⋊Q8C23×C3711yescharacteristic
480#127—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127D4×C3712yes—
485#127C23×C3711yescharacteristic
486#127C23×C3711yescharacteristic
487#126—21no—
488#126—21no—
489#125—21no—
490#125D4×C3711yescharacteristic
491#125D4×C3711yescharacteristic
492#124—21no—
493#124—21no—
494#124D4×C3711yescharacteristic
495#124D4×C3711yescharacteristic
496#123—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C3711yescharacteristic
505C22⋊Q8D4×C3711yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121D4×C3711yescharacteristic
519#121D4×C3711yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8C23×C3711yescharacteristic
529C4×Q8C23×C3711yescharacteristic
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4C23×C3711yescharacteristic
537C4×D4C23×C3711yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541C2×C22⋊C4—22no—
542C2×C42C23×C3711yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C3711yescharacteristic
552C4⋊C8C23×C3711yescharacteristic
553C4⋊C8C23×C3711yescharacteristic
554C4⋊C8C23×C3711yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C4×C8—21no—
568C4×C8C23×C3711yescharacteristic
569C4×C8C23×C3711yescharacteristic
570C24—22no—
571C24—22no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C3711yescharacteristic
579C2×Q8C2×D4×C3711yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—82no—
604C2×D4—84no—
605C2×D4C2×D4×C3711yescharacteristic
606C2×D4C2×D4×C3711yescharacteristic
607C2×D4C2×D4×C3712yes—
608C2×D4C2×D4×C3712yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4C2×D4×C3711yescharacteristic
615C22×C4C2×D4×C3711yescharacteristic
616C22×C4C2×D4×C3711yescharacteristic
617Q16—81no—
618SD16—81no—
619SD16—82no—
620SD16—82no—
621M16—81no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C3711yescharacteristic
643C4⋊C4C2×D4×C3711yescharacteristic
644C4⋊C4C2×D4×C3711yescharacteristic
645C4⋊C4C2×D4×C3711yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42C2×D4×C3711yescharacteristic
667C42C2×D4×C3711yescharacteristic
668C42C2×D4×C3711yescharacteristic
669C42C24×C3711yescharacteristic
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23#120×C3711yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709D4—82no—
710D4—82no—
711D4—82no—
712D4—82no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
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#120×C3711yescharacteristic
734C2×C4#120×C3711yescharacteristic
735C2×C4#120×C3711yescharacteristic
736C2×C4C22×D4×C3711yescharacteristic
737C2×C4C22×D4×C3711yescharacteristic
738C2×C4C22×D4×C3711yescharacteristic
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—164no—
761C22—164no—
762C22C2×#120×C3711yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4C37×#57611yescharacteristic
776C4C37×#57711yescharacteristic
777C4C37×#57711yescharacteristic
778C4C37×#57711yescharacteristic
779C2—41no—
780C2—81no—
781C2—81no—
782C2—82no—
783C2—82no—
784C2C37×#300911yescharacteristic
785C2C37×#301211yescharacteristic
786C2C37×#301911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3543C2
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×#3252C2semidirect
3. C37×#3233C2semidirect
4. C37×#3208C2semidirect
5. C37×#1642C2semidirect
6. C37×#1641C2semidirect
7. C37×#1640C2semidirect
8. C37×#1639C2semidirect
9. C37×#1631C2semidirect
10. C37×#1631C2semidirect
11. C37×#1630C2semidirect
12. C37×#1629C2semidirect
13. C37×#1545C2semidirect
14. C37×#1495C2semidirect
15. C37×#1482C2semidirect
30. C37×#533C22semidirect
36. C37×#492C22semidirect
39. C37×#486C22semidirect
43. C37×#477C22semidirect
44. C37×#477C22semidirect
45. C37×#476C22semidirect
46. C37×#476C22semidirect
47. C37×#475C22semidirect
48. C37×#474C22semidirect
52. C37×#462C22semidirect
53. C37×#461C22semidirect
56. C37×#431C22semidirect
57. C37×#431C22semidirect
58. C37×#423C22semidirect
61. C37×#331C22semidirect
62. C37×#331C22semidirect
63. C37×Q8⋊C8C22semidirect
64. C37×Q8⋊C8C22semidirect
65. C37×Q8⋊C8C22semidirect
66. C37×Q8⋊C8C22semidirect
67. C37×D4⋊C8C22semidirect
68. C37×D4⋊C8C22semidirect
69. C37×D4⋊C8C22semidirect
70. C37×D4⋊C8C22semidirect
351. #18931C37direct (N × H)
387. #3252C2×C37semidirect
388. #3233C2×C37semidirect
389. #3208C2×C37semidirect
390. #1642C2×C37semidirect
391. #1641C2×C37semidirect
392. #1640C2×C37semidirect
393. #1639C2×C37semidirect
394. #1631C2×C37semidirect
395. #1631C2×C37semidirect
396. #1630C2×C37semidirect
397. #1629C2×C37semidirect
398. #1545C2×C37semidirect
399. #1495C2×C37semidirect
400. #1482C2×C37semidirect
423. #533C22×C37semidirect
429. #492C22×C37semidirect
432. #486C22×C37semidirect
436. #477C22×C37semidirect
437. #477C22×C37semidirect
438. #476C22×C37semidirect
439. #476C22×C37semidirect
440. #475C22×C37semidirect
441. #474C22×C37semidirect
445. #462C22×C37semidirect
446. #461C22×C37semidirect
449. #431C22×C37semidirect
450. #431C22×C37semidirect
451. #423C22×C37semidirect
454. #331C22×C37semidirect
455. #331C22×C37semidirect
456. Q8⋊C8C22×C37semidirect
457. Q8⋊C8C22×C37semidirect
458. Q8⋊C8C22×C37semidirect
459. Q8⋊C8C22×C37semidirect
460. D4⋊C8C22×C37semidirect
461. D4⋊C8C22×C37semidirect
462. D4⋊C8C22×C37semidirect
463. D4⋊C8C22×C37semidirect
464. C37#18931direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35432
C37×#32522
C37×#32332
C37×#32082
C37×#16422
C37×#16412
C37×#16402
C37×#16392
C37×#16312
C37×#16302
C37×#16292
C37×#15452
C37×#14952
C37×#14822
#1893137