Finite Group Databasebeta

← C37×#18869 #22640122

Subgroups — C37×#18869 #22640122

Order 9472.

912 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3522C211yesmaximal, characteristic
2C37×#3233C211yesmaximal, characteristic, complemented
3C37×#3210C211yesmaximal, characteristic, complemented
4C37×#3104C211yesmaximal, characteristic, complemented
5C37×#1645C211yesmaximal, characteristic, complemented
6C37×#1644C211yesmaximal, characteristic, complemented
7C37×#1641C211yesmaximal, characteristic, complemented
8C37×#1640C211yesmaximal, characteristic, complemented
9C37×#1633C211yesmaximal, characteristic, complemented
10C37×#1632C211yesmaximal, characteristic, complemented
11C37×#1631C211yesmaximal, characteristic, complemented
12C37×#1630C211yesmaximal, characteristic, complemented
13C37×#1543C211yesmaximal, characteristic, complemented
14C37×#1482C211yesmaximal, characteristic, complemented
15C37×#1479C211yesmaximal, characteristic, complemented
16C37×#559—21no—
17C37×#559C2211yescharacteristic
18Q82×C37C2211yescharacteristic
19C37×#554—21no—
20C37×#554C2211yescharacteristic
21C37×#550C2211yescharacteristic
22C37×#548—21no—
23C37×#547—22no—
24C37×#547—21no—
25C37×#542—22no—
26C37×#542—21no—
27C37×#533C2211yescharacteristic
28C37×#532—21no—
29C37×#532C2211yescharacteristic
30C37×#529—21no—
31C37×#529C2211yescharacteristic
32C37×#520—21no—
33C2×C4×Q8×C37C2211yescharacteristic
34C37×#499—21no—
35C37×#494C2211yescharacteristic
36C37×#492C2211yescharacteristic
37C37×#488—21no—
38C37×#487C2211yescharacteristic
39C37×#486C2211yescharacteristic
40C37×#485—21no—
41C37×#484—21no—
42C37×#482—21no—
43C37×#477C2211yescharacteristic
44C37×#477C2211yescharacteristic
45C37×#477C2211yescharacteristic
46C37×#476C2211yescharacteristic
47C37×#475C2211yescharacteristic
48C37×#474C2211yescharacteristic
49C37×#464—22no—
50C37×#462C2211yescharacteristic
51C37×#462C2211yescharacteristic
52C37×#452—22no—
53C37×#451—21no—
54C4×Q16×C37—21no—
55C4×Q16×C37—21no—
56C37×#431C2211yescharacteristic
57C37×#431C2211yescharacteristic
58C37×#431C2211yescharacteristic
59C37×#333C2211yescharacteristic
60C37×#333C2211yescharacteristic
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—22no—
72C2×#41×C37—21no—
73C2×#41×C37D412yes—
74C22×Q8×C37D411yescharacteristic
75C2×Q16×C37—21no—
76C2×Q16×C37—21no—
77C2×Q16×C37—22no—
78C2×SD16×C37—22no—
79C4⋊Q8×C37—22no—
80C4⋊Q8×C37—21no—
81C4⋊Q8×C37—21no—
82C4⋊Q8×C37C2311yescharacteristic
83C4⋊Q8×C37C2311yescharacteristic
84C4⋊Q8×C37C2311yescharacteristic
85#127×C37—21no—
86#127×C37C2311yescharacteristic
87#126×C37—22no—
88#126×C37—21no—
89#125×C37—21no—
90#125×C37—21no—
91#125×C37D411yescharacteristic
92#124×C37—22no—
93#124×C37—22no—
94#124×C37—21no—
95#124×C37—21no—
96#124×C37D411yescharacteristic
97#124×C37D412yes—
98#123×C37—22no—
99#123×C37—22no—
100#123×C37—22no—
101#123×C37—22no—
102#123×C37—21no—
103C22⋊Q8×C37—22no—
104C22⋊Q8×C37—22no—
105C22⋊Q8×C37—22no—
106C22⋊Q8×C37—22no—
107C22⋊Q8×C37—21no—
108C22⋊Q8×C37—21no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37D411yescharacteristic
111#121×C37—22no—
112#121×C37—22no—
113#121×C37—21no—
114#121×C37—21no—
115#121×C37—21no—
116#121×C37D411yescharacteristic
117C4×Q8×C37—21no—
118C4×Q8×C37—21no—
119C4×Q8×C37—21no—
120C4×Q8×C37—21no—
121C4×Q8×C37—21no—
122C4×Q8×C37—21no—
123C4×Q8×C37D411yescharacteristic
124C4×Q8×C37D411yescharacteristic
125C4×Q8×C37C2311yescharacteristic
126C4×Q8×C37C2311yescharacteristic
127C4×Q8×C37C2311yescharacteristic
128C4×D4×C37—22no—
129C4×D4×C37—22no—
130C4×D4×C37—22no—
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×C37C2311yescharacteristic
139#117×C37—22no—
140#117×C37—21no—
141#117×C37—21no—
142C2×C4⋊C4×C37—22no—
143C2×C4⋊C4×C37—21no—
144C2×C4⋊C4×C37—21no—
145C2×C4⋊C4×C37D411yescharacteristic
146C2×C42×C37—21no—
147C2×C42×C37C2311yescharacteristic
148#107×C37—21no—
149#107×C37—21no—
150#107×C37—21no—
151#107×C37—21no—
152#106×C37—21no—
153#106×C37—21no—
154C4⋊C8×C37—21no—
155C4⋊C8×C37C2311yescharacteristic
156C4⋊C8×C37C2311yescharacteristic
157C4⋊C8×C37C2311yescharacteristic
158C4⋊C8×C37C2311yescharacteristic
159#103×C37—21no—
160#103×C37—21no—
161#103×C37—22no—
162#103×C37—21no—
163#103×C37—21no—
164#103×C37—21no—
165#103×C37—21no—
166#102×C37—22no—
167#102×C37—21no—
168#102×C37—21no—
169C22⋊C8×C37—21no—
170C22⋊C8×C37—21no—
171C22⋊C8×C37—21no—
172C4×C8×C37—21no—
173C4×C8×C37—21no—
174C4×C8×C37C2311yescharacteristic
175C4×C8×C37C2311yescharacteristic
176#41×C37—42no—
177#41×C37—42no—
178#41×C37—84no—
179#41×C37—82no—
180C2×Q8×C37—22no—
181C2×Q8×C37—21no—
182C2×Q8×C37—22no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—41no—
186C2×Q8×C37C2×D411yescharacteristic
187C2×Q8×C37C2×D411yescharacteristic
188C2×Q8×C37C2×D411yescharacteristic
189C2×Q8×C37C2×D412yes—
190C2×D4×C37—22no—
191C2×D4×C37—22no—
192C2×D4×C37—21no—
193C2×D4×C37—22no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37C2×D411yescharacteristic
197C2×D4×C37C2×D412yes—
198C22×C4×C37—22no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—22no—
202C22×C4×C37—22no—
203C22×C4×C37—21no—
204C22×C4×C37—22no—
205C22×C4×C37C2×D411yescharacteristic
206C22×C4×C37C2×D411yescharacteristic
207C22×C4×C37C2×D411yescharacteristic
208Q16×C37—42no—
209Q16×C37—42no—
210Q16×C37—82no—
211SD16×C37—82no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C4⋊C4×C37—22no—
219C4⋊C4×C37—22no—
220C4⋊C4×C37—22no—
221C4⋊C4×C37—22no—
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—21no—
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—41no—
238C4⋊C4×C37—41no—
239C4⋊C4×C37C2×D411yescharacteristic
240C4⋊C4×C37C2×D411yescharacteristic
241C4⋊C4×C37C2×D411yescharacteristic
242C4⋊C4×C37C2×D411yescharacteristic
243C22⋊C4×C37—22no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—22no—
248C22⋊C4×C37—21no—
249C22⋊C4×C37—22no—
250C22⋊C4×C37—21no—
251C22⋊C4×C37—21no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—21no—
254C22⋊C4×C37—21no—
255C22⋊C4×C37—41no—
256C42×C37—22no—
257C42×C37—21no—
258C42×C37—21no—
259C42×C37—21no—
260C42×C37—21no—
261C42×C37—21no—
262C42×C37—41no—
263C42×C37C2×D411yescharacteristic
264C42×C37C2×D411yescharacteristic
265C42×C37C2×D411yescharacteristic
266C42×C37C2411yescharacteristic
267C23×C37—21no—
268C23×C37—22no—
269C23×C37#12011yescharacteristic
270Q8×C37—21no—
271Q8×C37—21no—
272Q8×C37—21no—
273Q8×C37—21no—
274Q8×C37—21no—
275Q8×C37—42no—
276Q8×C37—42no—
277Q8×C37—42no—
278Q8×C37—41no—
279Q8×C37—41no—
280Q8×C37—82no—
281Q8×C37#13512yes—
282D4×C37—21no—
283D4×C37—21no—
284D4×C37—42no—
285D4×C37—44no—
286D4×C37—44no—
287D4×C37—42no—
288D4×C37—41no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—82no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—21no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—21no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—22no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—41no—
306C2×C4×C37—42no—
307C2×C4×C37—44no—
308C2×C4×C37—42no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—82no—
314C2×C4×C37—82no—
315C2×C4×C37—82no—
316C2×C4×C37#12011yescharacteristic
317C2×C4×C37#12011yescharacteristic
318C2×C4×C37#12011yescharacteristic
319C2×C4×C37C22×D411yescharacteristic
320C2×C4×C37C22×D411yescharacteristic
321C2×C4×C37C22×D411yescharacteristic
322C8×C37—41no—
323C8×C37—41no—
324C8×C37—41no—
325C8×C37—41no—
326C8×C37—41no—
327C8×C37—41no—
328#18869C3711yesmaximal, characteristic, direct product factor, Sylow
329C22×C37—21no—
330C22×C37—21no—
331C22×C37—21no—
332C22×C37—42no—
333C22×C37—41no—
334C22×C37—41no—
335C22×C37—42no—
336C22×C37—42no—
337C22×C37—41no—
338C22×C37C2×#12011yescharacteristic
339C4×C37—21no—
340C4×C37—22no—
341C4×C37—21no—
342C4×C37—21no—
343C4×C37—21no—
344C4×C37—41no—
345C4×C37—41no—
346C4×C37—41no—
347C4×C37—41no—
348C4×C37—41no—
349C4×C37—42no—
350C4×C37—41no—
351C4×C37—81no—
352C4×C37—81no—
353C4×C37C2×#13511yescharacteristic
354C4×C37#57511yescharacteristic
355C4×C37#57811yescharacteristic
356C4×C37#57811yescharacteristic
357#3522C2×C3711yescharacteristic
358#3233C2×C3711yescharacteristic, complemented
359#3210C2×C3711yescharacteristic, complemented
360#3104C2×C3711yescharacteristic, complemented
361#1645C2×C3711yescharacteristic, complemented
362#1644C2×C3711yescharacteristic, complemented
363#1641C2×C3711yescharacteristic, complemented
364#1640C2×C3711yescharacteristic, complemented
365#1633C2×C3711yescharacteristic, complemented
366#1632C2×C3711yescharacteristic, complemented
367#1631C2×C3711yescharacteristic, complemented
368#1630C2×C3711yescharacteristic, complemented
369#1543C2×C3711yescharacteristic, complemented
370#1482C2×C3711yescharacteristic, complemented
371#1479C2×C3711yescharacteristic, complemented
372C2×C37—41no—
373C2×C37—81no—
374C2×C37—82no—
375C2×C37#300211yescharacteristic
376C2×C37#301111yescharacteristic
377C2×C37#301911yescharacteristic
378#559—21no—
379#559C22×C3711yescharacteristic
380Q82C22×C3711yescharacteristic
381#554—21no—
382#554C22×C3711yescharacteristic
383#550C22×C3711yescharacteristic
384#548—21no—
385#547—22no—
386#547—21no—
387#542—22no—
388#542—21no—
389#533C22×C3711yescharacteristic
390#532—21no—
391#532C22×C3711yescharacteristic
392#529—21no—
393#529C22×C3711yescharacteristic
394#520—21no—
395C2×C4×Q8C22×C3711yescharacteristic
396#499—21no—
397#494C22×C3711yescharacteristic
398#492C22×C3711yescharacteristic
399#488—21no—
400#487C22×C3711yescharacteristic
401#486C22×C3711yescharacteristic
402#485—21no—
403#484—21no—
404#482—21no—
405#477C22×C3711yescharacteristic
406#477C22×C3711yescharacteristic
407#477C22×C3711yescharacteristic
408#476C22×C3711yescharacteristic
409#475C22×C3711yescharacteristic
410#474C22×C3711yescharacteristic
411#464—22no—
412#462C22×C3711yescharacteristic
413#462C22×C3711yescharacteristic
414#452—22no—
415#451—21no—
416C4×Q16—21no—
417C4×Q16—21no—
418#431C22×C3711yescharacteristic
419#431C22×C3711yescharacteristic
420#431C22×C3711yescharacteristic
421#333C22×C3711yescharacteristic
422#333C22×C3711yescharacteristic
423#331C22×C3711yescharacteristic
424#331C22×C3711yescharacteristic
425Q8⋊C8C22×C3711yescharacteristic
426Q8⋊C8C22×C3711yescharacteristic
427Q8⋊C8C22×C3711yescharacteristic
428Q8⋊C8C22×C3711yescharacteristic
429Q8⋊C8C22×C3711yescharacteristic
430Q8⋊C8C22×C3711yescharacteristic
431D4⋊C8C22×C3711yescharacteristic
432D4⋊C8C22×C3711yescharacteristic
433C37#1886911yescharacteristic, direct product factor, Sylow
434C2×#41—22no—
435C2×#41—21no—
436C2×#41D4×C3712yes—
437C22×Q8D4×C3711yescharacteristic
438C2×Q16—21no—
439C2×Q16—21no—
440C2×Q16—22no—
441C2×SD16—22no—
442C4⋊Q8—22no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8C23×C3711yescharacteristic
446C4⋊Q8C23×C3711yescharacteristic
447C4⋊Q8C23×C3711yescharacteristic
448#127—21no—
449#127C23×C3711yescharacteristic
450#126—22no—
451#126—21no—
452#125—21no—
453#125—21no—
454#125D4×C3711yescharacteristic
455#124—22no—
456#124—22no—
457#124—21no—
458#124—21no—
459#124D4×C3711yescharacteristic
460#124D4×C3712yes—
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—21no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8D4×C3711yescharacteristic
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121D4×C3711yescharacteristic
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8D4×C3711yescharacteristic
487C4×Q8D4×C3711yescharacteristic
488C4×Q8C23×C3711yescharacteristic
489C4×Q8C23×C3711yescharacteristic
490C4×Q8C23×C3711yescharacteristic
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4C23×C3711yescharacteristic
502#117—22no—
503#117—21no—
504#117—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4D4×C3711yescharacteristic
509C2×C42—21no—
510C2×C42C23×C3711yescharacteristic
511#107—21no—
512#107—21no—
513#107—21no—
514#107—21no—
515#106—21no—
516#106—21no—
517C4⋊C8—21no—
518C4⋊C8C23×C3711yescharacteristic
519C4⋊C8C23×C3711yescharacteristic
520C4⋊C8C23×C3711yescharacteristic
521C4⋊C8C23×C3711yescharacteristic
522#103—21no—
523#103—21no—
524#103—22no—
525#103—21no—
526#103—21no—
527#103—21no—
528#103—21no—
529#102—22no—
530#102—21no—
531#102—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C4×C8—21no—
536C4×C8—21no—
537C4×C8C23×C3711yescharacteristic
538C4×C8C23×C3711yescharacteristic
539#41—42no—
540#41—42no—
541#41—84no—
542#41—82no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—41no—
549C2×Q8C2×D4×C3711yescharacteristic
550C2×Q8C2×D4×C3711yescharacteristic
551C2×Q8C2×D4×C3711yescharacteristic
552C2×Q8C2×D4×C3712yes—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4C2×D4×C3711yescharacteristic
560C2×D4C2×D4×C3712yes—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4C2×D4×C3711yescharacteristic
569C22×C4C2×D4×C3711yescharacteristic
570C22×C4C2×D4×C3711yescharacteristic
571Q16—42no—
572Q16—42no—
573Q16—82no—
574SD16—82no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4C2×D4×C3711yescharacteristic
603C4⋊C4C2×D4×C3711yescharacteristic
604C4⋊C4C2×D4×C3711yescharacteristic
605C4⋊C4C2×D4×C3711yescharacteristic
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—41no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—41no—
626C42C2×D4×C3711yescharacteristic
627C42C2×D4×C3711yescharacteristic
628C42C2×D4×C3711yescharacteristic
629C42C24×C3711yescharacteristic
630C23—21no—
631C23—22no—
632C23#120×C3711yescharacteristic
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—21no—
637Q8—21no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—41no—
642Q8—41no—
643Q8—82no—
644Q8#135×C3712yes—
645D4—21no—
646D4—21no—
647D4—42no—
648D4—44no—
649D4—44no—
650D4—42no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—82no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4#120×C3711yescharacteristic
680C2×C4#120×C3711yescharacteristic
681C2×C4#120×C3711yescharacteristic
682C2×C4C22×D4×C3711yescharacteristic
683C2×C4C22×D4×C3711yescharacteristic
684C2×C4C22×D4×C3711yescharacteristic
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—41no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—42no—
695C22—41no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—41no—
700C22C2×#120×C3711yescharacteristic
701C4—21no—
702C4—22no—
703C4—21no—
704C4—21no—
705C4—21no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—42no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4C2×#135×C3711yescharacteristic
716C4C37×#57511yescharacteristic
717C4C37×#57811yescharacteristic
718C4C37×#57811yescharacteristic
719C2—41no—
720C2—81no—
721C2—82no—
722C2C37×#300211yescharacteristic
723C2C37×#301111yescharacteristic
724C2C37×#301911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3522C2
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×#3210C2semidirect
4. C37×#3104C2semidirect
5. C37×#1645C2semidirect
6. C37×#1644C2semidirect
7. C37×#1641C2semidirect
8. C37×#1640C2semidirect
9. C37×#1633C2semidirect
10. C37×#1632C2semidirect
11. C37×#1631C2semidirect
12. C37×#1630C2semidirect
13. C37×#1543C2semidirect
14. C37×#1482C2semidirect
15. C37×#1479C2semidirect
328. #18869C37direct (N × H)
358. #3233C2×C37semidirect
359. #3210C2×C37semidirect
360. #3104C2×C37semidirect
361. #1645C2×C37semidirect
362. #1644C2×C37semidirect
363. #1641C2×C37semidirect
364. #1640C2×C37semidirect
365. #1633C2×C37semidirect
366. #1632C2×C37semidirect
367. #1631C2×C37semidirect
368. #1630C2×C37semidirect
369. #1543C2×C37semidirect
370. #1482C2×C37semidirect
371. #1479C2×C37semidirect
433. C37#18869direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35222
C37×#32332
C37×#32102
C37×#31042
C37×#16452
C37×#16442
C37×#16412
C37×#16402
C37×#16332
C37×#16322
C37×#16312
C37×#16302
C37×#15432
C37×#14822
C37×#14792
#1886937