Finite Group Databasebeta

← C37×#18673 #22639926

Subgroups — C37×#18673 #22639926

Order 9472.

872 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3518C211yesmaximal, characteristic
2C37×#3233C211yesmaximal, characteristic, complemented
3C37×#3170C211yesmaximal, characteristic, complemented
4C37×#3116C211yesmaximal, characteristic, complemented
5C37×#1650C211yesmaximal, characteristic, complemented
6C37×#1649C211yesmaximal, characteristic, complemented
7C37×#1646C211yesmaximal, characteristic, complemented
8C37×#1645C211yesmaximal, characteristic, complemented
9C37×#1638C211yesmaximal, characteristic, complemented
10C37×#1637C211yesmaximal, characteristic, complemented
11C37×#1634C211yesmaximal, characteristic, complemented
12C37×#1633C211yesmaximal, characteristic, complemented
13C37×#1554C211yesmaximal, characteristic, complemented
14C37×#1494C211yesmaximal, characteristic, complemented
15C37×#1476C211yesmaximal, characteristic, complemented
16Q82×C37C2211yescharacteristic
17C37×#556—21no—
18C37×#556—22no—
19C37×#556—21no—
20C37×#556C2211yescharacteristic
21C37×#555—21no—
22C37×#555C2211yescharacteristic
23D4×Q8×C37C2211yescharacteristic
24C37×#548—21no—
25C37×#542—22no—
26C37×#542—21no—
27C37×#533—21no—
28C37×#533C2211yescharacteristic
29C37×#533C2211yescharacteristic
30C37×#529—21no—
31C37×#529C2211yescharacteristic
32C37×#519—21no—
33C4×#41×C37C2211yescharacteristic
34C37×#500C2211yescharacteristic
35C37×#499—21no—
36C37×#494C2211yescharacteristic
37C37×#488—21no—
38C37×#487C2211yescharacteristic
39C37×#487C2211yescharacteristic
40C37×#485—21no—
41C37×#485—21no—
42C37×#482—21no—
43C37×#477C2211yescharacteristic
44C37×#477C2211yescharacteristic
45C37×#476C2211yescharacteristic
46C37×#476C2211yescharacteristic
47C37×#475C2211yescharacteristic
48C37×#474C2211yescharacteristic
49C37×#467—22no—
50C37×#462C2211yescharacteristic
51C37×#461C2211yescharacteristic
52C37×#452—21no—
53C37×#441—21no—
54C37×#440—21no—
55C4×Q16×C37—22no—
56C37×#432C2211yescharacteristic
57C37×#431C2211yescharacteristic
58C2×C4×C8×C37C2211yescharacteristic
59C37×#333C2211yescharacteristic
60C37×#333C2211yescharacteristic
61C37×#332C2211yescharacteristic
62C37×#332C2211yescharacteristic
63C37×Q8⋊C8C2211yescharacteristic
64C37×Q8⋊C8C2211yescharacteristic
65C37×Q8⋊C8C2211yescharacteristic
66C37×Q8⋊C8C2211yescharacteristic
67C37×D4⋊C8C2211yescharacteristic
68C37×D4⋊C8C2211yescharacteristic
69C37×D4⋊C8C2211yescharacteristic
70C37×D4⋊C8C2211yescharacteristic
71C2×#41×C37D411yescharacteristic
72C22×Q8×C37—21no—
73C2×Q16×C37—22no—
74C2×Q16×C37—21no—
75C2×SD16×C37—21no—
76C22×C8×C37—21no—
77C4⋊Q8×C37—22no—
78C4⋊Q8×C37—21no—
79C4⋊Q8×C37—21no—
80C4⋊Q8×C37—21no—
81C4⋊Q8×C37C2311yescharacteristic
82C4⋊Q8×C37C2311yescharacteristic
83C4⋊Q8×C37C2311yescharacteristic
84C4⋊Q8×C37C2311yescharacteristic
85#126×C37—22no—
86#126×C37—22no—
87#126×C37—22no—
88#126×C37—22no—
89#126×C37—21no—
90#125×C37—21no—
91#125×C37—21no—
92#125×C37D411yescharacteristic
93#124×C37—22no—
94#124×C37—22no—
95#124×C37—22no—
96#124×C37—22no—
97#124×C37—21no—
98#124×C37D411yescharacteristic
99#123×C37—22no—
100#123×C37—21no—
101C22⋊Q8×C37—22no—
102C22⋊Q8×C37—22no—
103C22⋊Q8×C37—21no—
104C22⋊Q8×C37—21no—
105C22⋊Q8×C37—21no—
106C22⋊Q8×C37—22no—
107C22⋊Q8×C37—21no—
108C22⋊Q8×C37—21no—
109C22⋊Q8×C37D411yescharacteristic
110C22⋊Q8×C37D412yes—
111#121×C37—22no—
112#121×C37—21no—
113#121×C37—21no—
114#121×C37D411yescharacteristic
115C4×Q8×C37—22no—
116C4×Q8×C37—22no—
117C4×Q8×C37—22no—
118C4×Q8×C37—21no—
119C4×Q8×C37—21no—
120C4×Q8×C37—21no—
121C4×Q8×C37—21no—
122C4×Q8×C37—21no—
123C4×Q8×C37—21no—
124C4×Q8×C37D411yescharacteristic
125C4×Q8×C37D412yes—
126C4×Q8×C37C2311yescharacteristic
127C4×Q8×C37C2311yescharacteristic
128C4×D4×C37—22no—
129C4×D4×C37—21no—
130C4×D4×C37—21no—
131C4×D4×C37—21no—
132C4×D4×C37—21no—
133C4×D4×C37D411yescharacteristic
134C4×D4×C37C2311yescharacteristic
135C4×D4×C37C2311yescharacteristic
136#117×C37—22no—
137#117×C37—22no—
138#117×C37—21no—
139#117×C37—21no—
140#117×C37—21no—
141#117×C37—21no—
142#117×C37—21no—
143#117×C37—21no—
144#117×C37—21no—
145#117×C37D411yescharacteristic
146C2×C42×C37—21no—
147C2×C42×C37C2311yescharacteristic
148#107×C37—22no—
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×C37C2311yescharacteristic
156C4⋊C8×C37C2311yescharacteristic
157C4⋊C8×C37C2311yescharacteristic
158C4⋊C8×C37C2311yescharacteristic
159#103×C37—22no—
160#103×C37—21no—
161#103×C37—21no—
162#103×C37—21no—
163#103×C37—22no—
164#103×C37—21no—
165#103×C37—21no—
166#102×C37—21no—
167#102×C37—21no—
168#102×C37—21no—
169C22⋊C8×C37—21no—
170C22⋊C8×C37—21no—
171#97×C37—21no—
172C4×C8×C37—21no—
173C4×C8×C37—21no—
174C4×C8×C37C2311yescharacteristic
175C4×C8×C37C2311yescharacteristic
176#41×C37—22no—
177#41×C37—41no—
178C2×Q8×C37—22no—
179C2×Q8×C37—22no—
180C2×Q8×C37—21no—
181C2×Q8×C37—21no—
182C2×Q8×C37—21no—
183C2×Q8×C37—42no—
184C2×Q8×C37—42no—
185C2×Q8×C37C2×D411yescharacteristic
186C2×Q8×C37C2×D411yescharacteristic
187C2×Q8×C37C2×D412yes—
188C2×D4×C37—21no—
189C2×D4×C37—22no—
190C2×D4×C37—21no—
191C2×D4×C37C2×D411yescharacteristic
192C2×D4×C37C2×D411yescharacteristic
193C22×C4×C37—22no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37C2×D411yescharacteristic
199C22×C4×C37C2×D411yescharacteristic
200C22×C4×C37C2×D411yescharacteristic
201Q16×C37—44no—
202Q16×C37—42no—
203SD16×C37—42no—
204C2×C8×C37—21no—
205C2×C8×C37—21no—
206C2×C8×C37—21no—
207C2×C8×C37—21no—
208C2×C8×C37—21no—
209C2×C8×C37—21no—
210C2×C8×C37—42no—
211C4⋊C4×C37—22no—
212C4⋊C4×C37—22no—
213C4⋊C4×C37—22no—
214C4⋊C4×C37—22no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—22no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—22no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—21no—
225C4⋊C4×C37—21no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—41no—
231C4⋊C4×C37—41no—
232C4⋊C4×C37C2×D411yescharacteristic
233C4⋊C4×C37C2×D411yescharacteristic
234C4⋊C4×C37C2×D412yes—
235C4⋊C4×C37C2×D411yescharacteristic
236C4⋊C4×C37C2×D411yescharacteristic
237C22⋊C4×C37—22no—
238C22⋊C4×C37—22no—
239C22⋊C4×C37—22no—
240C22⋊C4×C37—22no—
241C22⋊C4×C37—22no—
242C22⋊C4×C37—22no—
243C22⋊C4×C37—21no—
244C22⋊C4×C37—21no—
245C22⋊C4×C37—21no—
246C22⋊C4×C37—21no—
247C22⋊C4×C37—21no—
248C22⋊C4×C37—21no—
249C22⋊C4×C37—21no—
250C22⋊C4×C37—21no—
251C22⋊C4×C37—41no—
252C42×C37—22no—
253C42×C37—22no—
254C42×C37—22no—
255C42×C37—21no—
256C42×C37—21no—
257C42×C37—22no—
258C42×C37—21no—
259C42×C37—21no—
260C42×C37—41no—
261C42×C37C2×D411yescharacteristic
262C42×C37C2×D411yescharacteristic
263C42×C37C2×D411yescharacteristic
264C42×C37C2411yescharacteristic
265C23×C37—21no—
266C23×C37—21no—
267C23×C37#12011yescharacteristic
268Q8×C37—21no—
269Q8×C37—21no—
270Q8×C37—21no—
271Q8×C37—42no—
272Q8×C37—44no—
273Q8×C37—42no—
274Q8×C37—41no—
275Q8×C37—41no—
276Q8×C37—41no—
277Q8×C37—41no—
278Q8×C37—82no—
279Q8×C37#13512yes—
280D4×C37—21no—
281D4×C37—21no—
282D4×C37—21no—
283D4×C37—21no—
284D4×C37—42no—
285D4×C37—81no—
286D4×C37—82no—
287C2×C4×C37—21no—
288C2×C4×C37—21no—
289C2×C4×C37—21no—
290C2×C4×C37—21no—
291C2×C4×C37—21no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—22no—
295C2×C4×C37—21no—
296C2×C4×C37—21no—
297C2×C4×C37—22no—
298C2×C4×C37—21no—
299C2×C4×C37—41no—
300C2×C4×C37—42no—
301C2×C4×C37—44no—
302C2×C4×C37—41no—
303C2×C4×C37—41no—
304C2×C4×C37—41no—
305C2×C4×C37—41no—
306C2×C4×C37—41no—
307C2×C4×C37—41no—
308C2×C4×C37—81no—
309C2×C4×C37#12011yescharacteristic
310C2×C4×C37#12011yescharacteristic
311C2×C4×C37#12011yescharacteristic
312C2×C4×C37C22×D411yescharacteristic
313C2×C4×C37C22×D411yescharacteristic
314C2×C4×C37C22×D411yescharacteristic
315C8×C37—22no—
316C8×C37—41no—
317C8×C37—41no—
318C8×C37—41no—
319C8×C37—41no—
320C8×C37—41no—
321#18673C3711yesmaximal, characteristic, direct product factor, Sylow
322C22×C37—21no—
323C22×C37—21no—
324C22×C37—21no—
325C22×C37—41no—
326C22×C37—41no—
327C22×C37—41no—
328C22×C37—41no—
329C22×C37—41no—
330C22×C37—41no—
331C22×C37C2×#12011yescharacteristic
332C4×C37—21no—
333C4×C37—22no—
334C4×C37—21no—
335C4×C37—21no—
336C4×C37—21no—
337C4×C37—42no—
338C4×C37—41no—
339C4×C37—41no—
340C4×C37—41no—
341C4×C37—41no—
342C4×C37—42no—
343C4×C37—41no—
344C4×C37—81no—
345C4×C37—81no—
346C4×C37C2×#13511yescharacteristic
347C4×C37#57511yescharacteristic
348C4×C37#57811yescharacteristic
349C4×C37#57811yescharacteristic
350#3518C2×C3711yescharacteristic
351#3233C2×C3711yescharacteristic, complemented
352#3170C2×C3711yescharacteristic, complemented
353#3116C2×C3711yescharacteristic, complemented
354#1650C2×C3711yescharacteristic, complemented
355#1649C2×C3711yescharacteristic, complemented
356#1646C2×C3711yescharacteristic, complemented
357#1645C2×C3711yescharacteristic, complemented
358#1638C2×C3711yescharacteristic, complemented
359#1637C2×C3711yescharacteristic, complemented
360#1634C2×C3711yescharacteristic, complemented
361#1633C2×C3711yescharacteristic, complemented
362#1554C2×C3711yescharacteristic, complemented
363#1494C2×C3711yescharacteristic, complemented
364#1476C2×C3711yescharacteristic, complemented
365C2×C37—41no—
366C2×C37—81no—
367C2×C37—81no—
368C2×C37#300211yescharacteristic
369C2×C37#301111yescharacteristic
370C2×C37#301811yescharacteristic
371Q82C22×C3711yescharacteristic
372#556—21no—
373#556—22no—
374#556—21no—
375#556C22×C3711yescharacteristic
376#555—21no—
377#555C22×C3711yescharacteristic
378D4×Q8C22×C3711yescharacteristic
379#548—21no—
380#542—22no—
381#542—21no—
382#533—21no—
383#533C22×C3711yescharacteristic
384#533C22×C3711yescharacteristic
385#529—21no—
386#529C22×C3711yescharacteristic
387#519—21no—
388C4×#41C22×C3711yescharacteristic
389#500C22×C3711yescharacteristic
390#499—21no—
391#494C22×C3711yescharacteristic
392#488—21no—
393#487C22×C3711yescharacteristic
394#487C22×C3711yescharacteristic
395#485—21no—
396#485—21no—
397#482—21no—
398#477C22×C3711yescharacteristic
399#477C22×C3711yescharacteristic
400#476C22×C3711yescharacteristic
401#476C22×C3711yescharacteristic
402#475C22×C3711yescharacteristic
403#474C22×C3711yescharacteristic
404#467—22no—
405#462C22×C3711yescharacteristic
406#461C22×C3711yescharacteristic
407#452—21no—
408#441—21no—
409#440—21no—
410C4×Q16—22no—
411#432C22×C3711yescharacteristic
412#431C22×C3711yescharacteristic
413C2×C4×C8C22×C3711yescharacteristic
414#333C22×C3711yescharacteristic
415#333C22×C3711yescharacteristic
416#332C22×C3711yescharacteristic
417#332C22×C3711yescharacteristic
418Q8⋊C8C22×C3711yescharacteristic
419Q8⋊C8C22×C3711yescharacteristic
420Q8⋊C8C22×C3711yescharacteristic
421Q8⋊C8C22×C3711yescharacteristic
422D4⋊C8C22×C3711yescharacteristic
423D4⋊C8C22×C3711yescharacteristic
424D4⋊C8C22×C3711yescharacteristic
425D4⋊C8C22×C3711yescharacteristic
426C37#1867311yescharacteristic, direct product factor, Sylow
427C2×#41D4×C3711yescharacteristic
428C22×Q8—21no—
429C2×Q16—22no—
430C2×Q16—21no—
431C2×SD16—21no—
432C22×C8—21no—
433C4⋊Q8—22no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436C4⋊Q8—21no—
437C4⋊Q8C23×C3711yescharacteristic
438C4⋊Q8C23×C3711yescharacteristic
439C4⋊Q8C23×C3711yescharacteristic
440C4⋊Q8C23×C3711yescharacteristic
441#126—22no—
442#126—22no—
443#126—22no—
444#126—22no—
445#126—21no—
446#125—21no—
447#125—21no—
448#125D4×C3711yescharacteristic
449#124—22no—
450#124—22no—
451#124—22no—
452#124—22no—
453#124—21no—
454#124D4×C3711yescharacteristic
455#123—22no—
456#123—21no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—21no—
462C22⋊Q8—22no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8D4×C3711yescharacteristic
466C22⋊Q8D4×C3712yes—
467#121—22no—
468#121—21no—
469#121—21no—
470#121D4×C3711yescharacteristic
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8D4×C3711yescharacteristic
481C4×Q8D4×C3712yes—
482C4×Q8C23×C3711yescharacteristic
483C4×Q8C23×C3711yescharacteristic
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4D4×C3711yescharacteristic
490C4×D4C23×C3711yescharacteristic
491C4×D4C23×C3711yescharacteristic
492#117—22no—
493#117—22no—
494#117—21no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—21no—
500#117—21no—
501#117D4×C3711yescharacteristic
502C2×C42—21no—
503C2×C42C23×C3711yescharacteristic
504#107—22no—
505#107—21no—
506#107—21no—
507#107—21no—
508#106—21no—
509#106—21no—
510#106—21no—
511C4⋊C8C23×C3711yescharacteristic
512C4⋊C8C23×C3711yescharacteristic
513C4⋊C8C23×C3711yescharacteristic
514C4⋊C8C23×C3711yescharacteristic
515#103—22no—
516#103—21no—
517#103—21no—
518#103—21no—
519#103—22no—
520#103—21no—
521#103—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527#97—21no—
528C4×C8—21no—
529C4×C8—21no—
530C4×C8C23×C3711yescharacteristic
531C4×C8C23×C3711yescharacteristic
532#41—22no—
533#41—41no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—42no—
540C2×Q8—42no—
541C2×Q8C2×D4×C3711yescharacteristic
542C2×Q8C2×D4×C3711yescharacteristic
543C2×Q8C2×D4×C3712yes—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4C2×D4×C3711yescharacteristic
548C2×D4C2×D4×C3711yescharacteristic
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4C2×D4×C3711yescharacteristic
555C22×C4C2×D4×C3711yescharacteristic
556C22×C4C2×D4×C3711yescharacteristic
557Q16—44no—
558Q16—42no—
559SD16—42no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—42no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4C2×D4×C3711yescharacteristic
589C4⋊C4C2×D4×C3711yescharacteristic
590C4⋊C4C2×D4×C3712yes—
591C4⋊C4C2×D4×C3711yescharacteristic
592C4⋊C4C2×D4×C3711yescharacteristic
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—41no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—21no—
612C42—21no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—41no—
617C42C2×D4×C3711yescharacteristic
618C42C2×D4×C3711yescharacteristic
619C42C2×D4×C3711yescharacteristic
620C42C24×C3711yescharacteristic
621C23—21no—
622C23—21no—
623C23#120×C3711yescharacteristic
624Q8—21no—
625Q8—21no—
626Q8—21no—
627Q8—42no—
628Q8—44no—
629Q8—42no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—82no—
635Q8#135×C3712yes—
636D4—21no—
637D4—21no—
638D4—21no—
639D4—21no—
640D4—42no—
641D4—81no—
642D4—82no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—44no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—81no—
665C2×C4#120×C3711yescharacteristic
666C2×C4#120×C3711yescharacteristic
667C2×C4#120×C3711yescharacteristic
668C2×C4C22×D4×C3711yescharacteristic
669C2×C4C22×D4×C3711yescharacteristic
670C2×C4C22×D4×C3711yescharacteristic
671C8—22no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22C2×#120×C3711yescharacteristic
687C4—21no—
688C4—22no—
689C4—21no—
690C4—21no—
691C4—21no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4C2×#135×C3711yescharacteristic
702C4C37×#57511yescharacteristic
703C4C37×#57811yescharacteristic
704C4C37×#57811yescharacteristic
705C2—41no—
706C2—81no—
707C2—81no—
708C2C37×#300211yescharacteristic
709C2C37×#301111yescharacteristic
710C2C37×#301811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3518C2
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×#3233C2semidirect
3. C37×#3170C2semidirect
4. C37×#3116C2semidirect
5. C37×#1650C2semidirect
6. C37×#1649C2semidirect
7. C37×#1646C2semidirect
8. C37×#1645C2semidirect
9. C37×#1638C2semidirect
10. C37×#1637C2semidirect
11. C37×#1634C2semidirect
12. C37×#1633C2semidirect
13. C37×#1554C2semidirect
14. C37×#1494C2semidirect
15. C37×#1476C2semidirect
321. #18673C37direct (N × H)
351. #3233C2×C37semidirect
352. #3170C2×C37semidirect
353. #3116C2×C37semidirect
354. #1650C2×C37semidirect
355. #1649C2×C37semidirect
356. #1646C2×C37semidirect
357. #1645C2×C37semidirect
358. #1638C2×C37semidirect
359. #1637C2×C37semidirect
360. #1634C2×C37semidirect
361. #1633C2×C37semidirect
362. #1554C2×C37semidirect
363. #1494C2×C37semidirect
364. #1476C2×C37semidirect
426. C37#18673direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35182
C37×#32332
C37×#31702
C37×#31162
C37×#16502
C37×#16492
C37×#16462
C37×#16452
C37×#16382
C37×#16372
C37×#16342
C37×#16332
C37×#15542
C37×#14942
C37×#14762
#1867337