Finite Group Databasebeta

← C37×#18742 #22639995

Subgroups — C37×#18742 #22639995

Order 9472.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3554C211yesmaximal, characteristic, complemented
2C37×#3246C211yesmaximal, characteristic, complemented
3C37×#3212C211yesmaximal, characteristic, complemented
4C37×#3184C211yesmaximal, characteristic, complemented
5C37×#1653C211yesmaximal, characteristic, complemented
6C37×#1651C211yesmaximal, characteristic, complemented
7C37×#1642C211yesmaximal, characteristic, complemented
8C37×#1640C211yesmaximal, characteristic, complemented
9C37×#1627C211yesmaximal, characteristic, complemented
10C37×#1626C211yesmaximal, characteristic, complemented
11C37×#1621C211yesmaximal, characteristic, complemented
12C37×#1620C211yesmaximal, characteristic, complemented
13C37×#1540C211yesmaximal, characteristic, complemented
14C37×#1485C211yesmaximal, characteristic, complemented
15C37×#1483C211yesmaximal, characteristic, complemented
16C37×#562—22no—
17C37×#559—21no—
18C37×#559C2211yescharacteristic
19C37×#557C2211yescharacteristic
20C37×#554—21no—
21C37×#550C2211yescharacteristic
22D4×Q8×C37C2211yescharacteristic
23C37×#548—21no—
24C37×#547—21no—
25C37×#542—21no—
26C37×#542—21no—
27C37×#540—21no—
28C37×#539—22no—
29C37×#536—21no—
30C37×#533C2211yescharacteristic
31C37×#532C2211yescharacteristic
32C37×#532C2211yescharacteristic
33C37×#529C2211yescharacteristic
34C37×#498C2211yescharacteristic
35C37×#495—21no—
36C37×#493C2211yescharacteristic
37C37×#488—21no—
38C37×#486C2211yescharacteristic
39C37×#486C2211yescharacteristic
40C37×#476—21no—
41C37×#475C2211yescharacteristic
42C37×#475C2211yescharacteristic
43C37×#469—22no—
44C37×#465—21no—
45C37×#465—21no—
46C37×#462C2211yescharacteristic
47C37×#461—21no—
48C37×#461C2211yescharacteristic
49C37×#460C2211yescharacteristic
50C37×#460C2211yescharacteristic
51C37×#460C2211yescharacteristic
52C37×#459C2211yescharacteristic
53C37×#452—21no—
54C37×#449—21no—
55C37×#442—22no—
56C37×#431C2211yescharacteristic
57C2×C4⋊C8×C37C2211yescharacteristic
58C4×M16×C37C2211yescharacteristic
59C37×#332C2211yescharacteristic
60C37×#332C2211yescharacteristic
61C37×#331C2211yescharacteristic
62C37×#331C2211yescharacteristic
63C37×Q8⋊C8C2211yescharacteristic
64C37×Q8⋊C8C2211yescharacteristic
65C37×Q8⋊C8C2211yescharacteristic
66C37×Q8⋊C8C2211yescharacteristic
67C37×Q8⋊C8C2211yescharacteristic
68C37×Q8⋊C8C2211yescharacteristic
69C37×D4⋊C8C2211yescharacteristic
70C37×D4⋊C8C2211yescharacteristic
71C2×#41×C37—21no—
72C2×#41×C37—21no—
73C2×#41×C37—21no—
74C22×Q8×C37—21no—
75C2×Q16×C37—21no—
76C2×SD16×C37—21no—
77C2×SD16×C37—21no—
78C2×SD16×C37—21no—
79C2×SD16×C37—21no—
80C2×D8×C37—22no—
81C2×D8×C37—21no—
82C2×M16×C37—21no—
83C22×C8×C37—21no—
84C4⋊Q8×C37—21no—
85C4⋊Q8×C37—21no—
86C4⋊Q8×C37D411yescharacteristic
87C4⋊Q8×C37D411yescharacteristic
88C4⋊Q8×C37C2311yescharacteristic
89C4⋊Q8×C37C2311yescharacteristic
90#127×C37—21no—
91#127×C37C2311yescharacteristic
92#127×C37C2311yescharacteristic
93#126×C37—22no—
94#126×C37—21no—
95#125×C37—22no—
96#125×C37—21no—
97#125×C37—21no—
98#125×C37D411yescharacteristic
99#124×C37—22no—
100#124×C37—22no—
101#124×C37—21no—
102#124×C37—21no—
103#124×C37—21no—
104#124×C37—21no—
105#124×C37D411yescharacteristic
106#123×C37—22no—
107#123×C37—22no—
108#123×C37—22no—
109#123×C37—22no—
110#123×C37—22no—
111#123×C37—22no—
112#123×C37—21no—
113C22⋊Q8×C37—22no—
114C22⋊Q8×C37—22no—
115C22⋊Q8×C37—22no—
116C22⋊Q8×C37—22no—
117C22⋊Q8×C37—21no—
118C22⋊Q8×C37—22no—
119C22⋊Q8×C37—21no—
120C22⋊Q8×C37D411yescharacteristic
121C22⋊Q8×C37D411yescharacteristic
122C22⋊Q8×C37D411yescharacteristic
123#121×C37—22no—
124#121×C37—22no—
125#121×C37—22no—
126#121×C37—21no—
127#121×C37—21no—
128#121×C37—21no—
129#121×C37—21no—
130#121×C37D411yescharacteristic
131#121×C37D412yes—
132C4×Q8×C37—21no—
133C4×Q8×C37—21no—
134C4×Q8×C37—21no—
135C4×Q8×C37C2311yescharacteristic
136C4×Q8×C37C2311yescharacteristic
137C4×Q8×C37C2311yescharacteristic
138C4×D4×C37—22no—
139C4×D4×C37—21no—
140C4×D4×C37—21no—
141C4×D4×C37—21no—
142C4×D4×C37—21no—
143C4×D4×C37—21no—
144C4×D4×C37—21no—
145C4×D4×C37—21no—
146C4×D4×C37—21no—
147C4×D4×C37D412yes—
148C4×D4×C37C2311yescharacteristic
149#117×C37—21no—
150#117×C37—21no—
151C2×C4⋊C4×C37—22no—
152C2×C42×C37C2311yescharacteristic
153#106×C37—22no—
154#106×C37—21no—
155#106×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#102×C37—22no—
166#102×C37—22no—
167#102×C37—21no—
168#102×C37—21no—
169#102×C37—21no—
170#102×C37—21no—
171C22⋊C8×C37—21no—
172#97×C37—21no—
173C4×C8×C37—21no—
174C4×C8×C37C2311yescharacteristic
175C4×C8×C37C2311yescharacteristic
176#41×C37—81no—
177#41×C37—81no—
178#41×C37—81no—
179#41×C37—81no—
180#41×C37—81no—
181#41×C37—81no—
182C2×Q8×C37—22no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—81no—
187C2×Q8×C37—81no—
188C2×Q8×C37C2×D411yescharacteristic
189C2×Q8×C37C2×D411yescharacteristic
190C2×Q8×C37C2×D411yescharacteristic
191C2×D4×C37—22no—
192C2×D4×C37—22no—
193C2×D4×C37—21no—
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—41no—
201C2×D4×C37C2×D411yescharacteristic
202C2×D4×C37C2×D412yes—
203C22×C4×C37—22no—
204C22×C4×C37—22no—
205C22×C4×C37—22no—
206C22×C4×C37—21no—
207C22×C4×C37—22no—
208C22×C4×C37—41no—
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D411yescharacteristic
211C22×C4×C37C2×D411yescharacteristic
212Q16×C37—81no—
213SD16×C37—81no—
214SD16×C37—81no—
215SD16×C37—81no—
216SD16×C37—81no—
217D8×C37—44no—
218D8×C37—81no—
219M16×C37—42no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—81no—
227C4⋊C4×C37—22no—
228C4⋊C4×C37—22no—
229C4⋊C4×C37—22no—
230C4⋊C4×C37—22no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×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×C37C2×D411yescharacteristic
246C4⋊C4×C37C2×D411yescharacteristic
247C4⋊C4×C37C2×D411yescharacteristic
248C4⋊C4×C37C2×D412yes—
249C4⋊C4×C37C2×D411yescharacteristic
250C22⋊C4×C37—22no—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—22no—
255C22⋊C4×C37—21no—
256C22⋊C4×C37—21no—
257C22⋊C4×C37—21no—
258C22⋊C4×C37—21no—
259C22⋊C4×C37—21no—
260C22⋊C4×C37—21no—
261C22⋊C4×C37—22no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—21no—
264C22⋊C4×C37—41no—
265C22⋊C4×C37—41no—
266C42×C37—22no—
267C42×C37—21no—
268C42×C37—21no—
269C42×C37—21no—
270C42×C37C2×D411yescharacteristic
271C42×C37C2×D411yescharacteristic
272C42×C37C2×D411yescharacteristic
273C42×C37C2411yescharacteristic
274C23×C37—21no—
275C23×C37—22no—
276C23×C37—41no—
277C23×C37#12011yescharacteristic
278Q8×C37—21no—
279Q8×C37—21no—
280Q8×C37—21no—
281Q8×C37—21no—
282Q8×C37—21no—
283Q8×C37—21no—
284Q8×C37—41no—
285Q8×C37—41no—
286Q8×C37—41no—
287Q8×C37—41no—
288Q8×C37—81no—
289Q8×C37—82no—
290D4×C37—21no—
291D4×C37—21no—
292D4×C37—42no—
293D4×C37—42no—
294D4×C37—41no—
295D4×C37—41no—
296D4×C37—41no—
297D4×C37—41no—
298D4×C37—41no—
299D4×C37—41no—
300D4×C37—41no—
301D4×C37—41no—
302D4×C37—81no—
303D4×C37—82no—
304D4×C37—82no—
305D4×C37—82no—
306D4×C37—82no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—21no—
310C2×C4×C37—21no—
311C2×C4×C37—21no—
312C2×C4×C37—21no—
313C2×C4×C37—21no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—22no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—82no—
324C2×C4×C37—82no—
325C2×C4×C37—82no—
326C2×C4×C37—82no—
327C2×C4×C37—82no—
328C2×C4×C37#12011yescharacteristic
329C2×C4×C37#12011yescharacteristic
330C2×C4×C37#12011yescharacteristic
331C2×C4×C37C22×D411yescharacteristic
332C2×C4×C37C22×D411yescharacteristic
333C2×C4×C37C22×D411yescharacteristic
334C8×C37—22no—
335C8×C37—41no—
336C8×C37—41no—
337C8×C37—41no—
338C8×C37—41no—
339C8×C37—41no—
340#18742C3711yesmaximal, characteristic, direct product factor, Sylow
341C22×C37—21no—
342C22×C37—21no—
343C22×C37—21no—
344C22×C37—41no—
345C22×C37—42no—
346C22×C37—41no—
347C22×C37—42no—
348C22×C37—42no—
349C22×C37—41no—
350C22×C37—81no—
351C22×C37—81no—
352C22×C37—81no—
353C22×C37C2×#12011yescharacteristic
354C4×C37—21no—
355C4×C37—21no—
356C4×C37—21no—
357C4×C37—21no—
358C4×C37—41no—
359C4×C37—41no—
360C4×C37—41no—
361C4×C37—42no—
362C4×C37—41no—
363C4×C37—41no—
364C4×C37—41no—
365C4×C37—41no—
366C4×C37—81no—
367C4×C37#57611yescharacteristic
368C4×C37#57711yescharacteristic
369C4×C37#57711yescharacteristic
370C4×C37#57711yescharacteristic
371#3554C2×C3711yescharacteristic, complemented
372#3246C2×C3711yescharacteristic, complemented
373#3212C2×C3711yescharacteristic, complemented
374#3184C2×C3711yescharacteristic, complemented
375#1653C2×C3711yescharacteristic, complemented
376#1651C2×C3711yescharacteristic, complemented
377#1642C2×C3711yescharacteristic, complemented
378#1640C2×C3711yescharacteristic, complemented
379#1627C2×C3711yescharacteristic, complemented
380#1626C2×C3711yescharacteristic, complemented
381#1621C2×C3711yescharacteristic, complemented
382#1620C2×C3711yescharacteristic, complemented
383#1540C2×C3711yescharacteristic, complemented
384#1485C2×C3711yescharacteristic, complemented
385#1483C2×C3711yescharacteristic, complemented
386C2×C37—41no—
387C2×C37—81no—
388C2×C37—82no—
389C2×C37—161no—
390C2×C37#301011yescharacteristic
391C2×C37#301211yescharacteristic
392C2×C37#301811yescharacteristic
393#562—22no—
394#559—21no—
395#559C22×C3711yescharacteristic
396#557C22×C3711yescharacteristic
397#554—21no—
398#550C22×C3711yescharacteristic
399D4×Q8C22×C3711yescharacteristic
400#548—21no—
401#547—21no—
402#542—21no—
403#542—21no—
404#540—21no—
405#539—22no—
406#536—21no—
407#533C22×C3711yescharacteristic
408#532C22×C3711yescharacteristic
409#532C22×C3711yescharacteristic
410#529C22×C3711yescharacteristic
411#498C22×C3711yescharacteristic
412#495—21no—
413#493C22×C3711yescharacteristic
414#488—21no—
415#486C22×C3711yescharacteristic
416#486C22×C3711yescharacteristic
417#476—21no—
418#475C22×C3711yescharacteristic
419#475C22×C3711yescharacteristic
420#469—22no—
421#465—21no—
422#465—21no—
423#462C22×C3711yescharacteristic
424#461—21no—
425#461C22×C3711yescharacteristic
426#460C22×C3711yescharacteristic
427#460C22×C3711yescharacteristic
428#460C22×C3711yescharacteristic
429#459C22×C3711yescharacteristic
430#452—21no—
431#449—21no—
432#442—22no—
433#431C22×C3711yescharacteristic
434C2×C4⋊C8C22×C3711yescharacteristic
435C4×M16C22×C3711yescharacteristic
436#332C22×C3711yescharacteristic
437#332C22×C3711yescharacteristic
438#331C22×C3711yescharacteristic
439#331C22×C3711yescharacteristic
440Q8⋊C8C22×C3711yescharacteristic
441Q8⋊C8C22×C3711yescharacteristic
442Q8⋊C8C22×C3711yescharacteristic
443Q8⋊C8C22×C3711yescharacteristic
444Q8⋊C8C22×C3711yescharacteristic
445Q8⋊C8C22×C3711yescharacteristic
446D4⋊C8C22×C3711yescharacteristic
447D4⋊C8C22×C3711yescharacteristic
448C37#1874211yescharacteristic, direct product factor, Sylow
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×SD16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C3711yescharacteristic
465C4⋊Q8D4×C3711yescharacteristic
466C4⋊Q8C23×C3711yescharacteristic
467C4⋊Q8C23×C3711yescharacteristic
468#127—21no—
469#127C23×C3711yescharacteristic
470#127C23×C3711yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C3711yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C3711yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C3711yescharacteristic
499C22⋊Q8D4×C3711yescharacteristic
500C22⋊Q8D4×C3711yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C3711yescharacteristic
509#121D4×C3712yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C3711yescharacteristic
514C4×Q8C23×C3711yescharacteristic
515C4×Q8C23×C3711yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C3712yes—
526C4×D4C23×C3711yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C3711yescharacteristic
531#106—22no—
532#106—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C3711yescharacteristic
536C4⋊C8C23×C3711yescharacteristic
537C4⋊C8C23×C3711yescharacteristic
538C4⋊C8C23×C3711yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#103—21no—
543#102—22no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C3711yescharacteristic
553C4×C8C23×C3711yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C3711yescharacteristic
567C2×Q8C2×D4×C3711yescharacteristic
568C2×Q8C2×D4×C3711yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C3711yescharacteristic
580C2×D4C2×D4×C3712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C3711yescharacteristic
588C22×C4C2×D4×C3711yescharacteristic
589C22×C4C2×D4×C3711yescharacteristic
590Q16—81no—
591SD16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—42no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—81no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C3711yescharacteristic
624C4⋊C4C2×D4×C3711yescharacteristic
625C4⋊C4C2×D4×C3711yescharacteristic
626C4⋊C4C2×D4×C3712yes—
627C4⋊C4C2×D4×C3711yescharacteristic
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C3711yescharacteristic
649C42C2×D4×C3711yescharacteristic
650C42C2×D4×C3711yescharacteristic
651C42C24×C3711yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C3711yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C3711yescharacteristic
707C2×C4#120×C3711yescharacteristic
708C2×C4#120×C3711yescharacteristic
709C2×C4C22×D4×C3711yescharacteristic
710C2×C4C22×D4×C3711yescharacteristic
711C2×C4C22×D4×C3711yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C3711yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4C37×#57611yescharacteristic
745C4C37×#57711yescharacteristic
746C4C37×#57711yescharacteristic
747C4C37×#57711yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C37×#301011yescharacteristic
753C2C37×#301211yescharacteristic
754C2C37×#301811yescharacteristic
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×#3554C2semidirect
2. C37×#3246C2semidirect
3. C37×#3212C2semidirect
4. C37×#3184C2semidirect
5. C37×#1653C2semidirect
6. C37×#1651C2semidirect
7. C37×#1642C2semidirect
8. C37×#1640C2semidirect
9. C37×#1627C2semidirect
10. C37×#1626C2semidirect
11. C37×#1621C2semidirect
12. C37×#1620C2semidirect
13. C37×#1540C2semidirect
14. C37×#1485C2semidirect
15. C37×#1483C2semidirect
340. #18742C37direct (N × H)
371. #3554C2×C37semidirect
372. #3246C2×C37semidirect
373. #3212C2×C37semidirect
374. #3184C2×C37semidirect
375. #1653C2×C37semidirect
376. #1651C2×C37semidirect
377. #1642C2×C37semidirect
378. #1640C2×C37semidirect
379. #1627C2×C37semidirect
380. #1626C2×C37semidirect
381. #1621C2×C37semidirect
382. #1620C2×C37semidirect
383. #1540C2×C37semidirect
384. #1485C2×C37semidirect
385. #1483C2×C37semidirect
448. C37#18742direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35542
C37×#32462
C37×#32122
C37×#31842
C37×#16532
C37×#16512
C37×#16422
C37×#16402
C37×#16272
C37×#16262
C37×#16212
C37×#16202
C37×#15402
C37×#14852
C37×#14832
#1874237