Finite Group Databasebeta

← C37×#19418 #22640671

Subgroups — C37×#19418 #22640671

Order 9472.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3231C211yesmaximal, characteristic, complemented
2C37×#3116C211yesmaximal, characteristic
3C37×#3107C211yesmaximal, characteristic
4C37×#2988C211yesmaximal, characteristic
5C37×#1684C211yesmaximal, characteristic, complemented
6C37×#1683C211yesmaximal, characteristic, complemented
7C37×#1680C211yesmaximal, characteristic, complemented
8C37×#1679C211yesmaximal, characteristic, complemented
9C37×#1674C211yesmaximal, characteristic, complemented
10C37×#1673C211yesmaximal, characteristic, complemented
11C37×#1672C211yesmaximal, characteristic, complemented
12C37×#1671C211yesmaximal, characteristic, complemented
13C37×#1572C211yesmaximal, characteristic, complemented
14C37×#1552C211yesmaximal, characteristic, complemented
15C37×#1542C211yesmaximal, characteristic, complemented
16C37×#533C2211yescharacteristic
17C37×#533C2211yescharacteristic
18C4×#41×C37C2211yescharacteristic
19C37×#500C2211yescharacteristic
20C37×#498C2211yescharacteristic
21C37×#487C2211yescharacteristic
22C37×#487C2211yescharacteristic
23C37×#485—21no—
24C37×#485—21no—
25C37×#485—21no—
26C37×#485—21no—
27C37×#479—21no—
28C37×#479—21no—
29C37×#477C2211yescharacteristic
30C37×#476C2211yescharacteristic
31C37×#475C2211yescharacteristic
32C37×#474C2211yescharacteristic
33C37×#462C2211yescharacteristic
34C37×#462C2211yescharacteristic
35C37×#461C2211yescharacteristic
36C37×#461C2211yescharacteristic
37C37×#452—21no—
38C37×#452—21no—
39C8×Q8×C37C2211yescharacteristic
40C8×Q8×C37C2211yescharacteristic
41C37×#441—21no—
42C37×#440—21no—
43C4×Q16×C37—21no—
44C4×SD16×C37—21no—
45C8×D4×C37—21no—
46C8×D4×C37—21no—
47C8×D4×C37C2211yescharacteristic
48C8×D4×C37C2211yescharacteristic
49C37×#432C2211yescharacteristic
50C37×#431—21no—
51C37×#431C2211yescharacteristic
52C37×#431C2211yescharacteristic
53C2×C4⋊C8×C37—21no—
54C2×C4⋊C8×C37C2211yescharacteristic
55C37×#335C2211yescharacteristic
56C37×#335C2211yescharacteristic
57C37×#334C2211yescharacteristic
58C37×#334C2211yescharacteristic
59C37×#333C2211yescharacteristic
60C37×#333C2211yescharacteristic
61C37×#332C2211yescharacteristic
62C37×#332C2211yescharacteristic
63C37×#332C2211yescharacteristic
64C37×#332C2211yescharacteristic
65C37×#332C2211yescharacteristic
66C37×#332C2211yescharacteristic
67C2×#41×C37D411yescharacteristic
68C2×Q16×C37—21no—
69C2×Q16×C37—21no—
70C2×SD16×C37—21no—
71C2×SD16×C37—21no—
72C22×C8×C37—21no—
73C22×C8×C37—21no—
74C22×C8×C37—21no—
75C4⋊Q8×C37C2311yescharacteristic
76C4⋊Q8×C37C2311yescharacteristic
77C4⋊Q8×C37C2311yescharacteristic
78C4⋊Q8×C37C2311yescharacteristic
79#125×C37—21no—
80#125×C37—21no—
81C22⋊Q8×C37—21no—
82C22⋊Q8×C37—21no—
83C22⋊Q8×C37—21no—
84C22⋊Q8×C37—21no—
85C4×Q8×C37—21no—
86C4×Q8×C37—21no—
87C4×Q8×C37—21no—
88C4×Q8×C37—21no—
89C4×Q8×C37D411yescharacteristic
90C4×Q8×C37C2311yescharacteristic
91C4×D4×C37—21no—
92C4×D4×C37—21no—
93C4×D4×C37D411yescharacteristic
94C4×D4×C37C2311yescharacteristic
95#117×C37—21no—
96#117×C37—21no—
97#117×C37—21no—
98#117×C37D411yescharacteristic
99C2×C42×C37—21no—
100C2×C42×C37C2311yescharacteristic
101#107×C37—21no—
102#107×C37—21no—
103#107×C37—21no—
104#107×C37—21no—
105#106×C37—21no—
106#106×C37—21no—
107#106×C37—21no—
108#106×C37—21no—
109C4⋊C8×C37—21no—
110C4⋊C8×C37—21no—
111C4⋊C8×C37—21no—
112C4⋊C8×C37D411yescharacteristic
113C4⋊C8×C37D411yescharacteristic
114C4⋊C8×C37C2311yescharacteristic
115C4⋊C8×C37C2311yescharacteristic
116C4⋊C8×C37C2311yescharacteristic
117C4⋊C8×C37C2311yescharacteristic
118C4⋊C8×C37C2311yescharacteristic
119C4⋊C8×C37C2311yescharacteristic
120#103×C37—21no—
121#103×C37—21no—
122#103×C37—21no—
123#103×C37—21no—
124#103×C37—21no—
125#103×C37—21no—
126#103×C37—21no—
127#103×C37—21no—
128#103×C37—21no—
129#103×C37—21no—
130#102×C37—21no—
131#102×C37—21no—
132C22⋊C8×C37—21no—
133C22⋊C8×C37—21no—
134C22⋊C8×C37—21no—
135C22⋊C8×C37—21no—
136C22⋊C8×C37D411yescharacteristic
137C22⋊C8×C37D411yescharacteristic
138#97×C37—21no—
139C4×C8×C37—21no—
140C4×C8×C37—21no—
141C4×C8×C37—21no—
142C4×C8×C37C2311yescharacteristic
143C4×C8×C37C2311yescharacteristic
144#41×C37—22no—
145#41×C37—22no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37C2×D411yescharacteristic
151C2×D4×C37—21no—
152C2×D4×C37C2×D411yescharacteristic
153C22×C4×C37—21no—
154C22×C4×C37—21no—
155C22×C4×C37—21no—
156C22×C4×C37C2×D411yescharacteristic
157C22×C4×C37C2×D411yescharacteristic
158C22×C4×C37#4111yescharacteristic
159Q16×C37—42no—
160Q16×C37—42no—
161SD16×C37—42no—
162SD16×C37—42no—
163C2×C8×C37—21no—
164C2×C8×C37—21no—
165C2×C8×C37—21no—
166C2×C8×C37—21no—
167C2×C8×C37—21no—
168C2×C8×C37—21no—
169C2×C8×C37—81no—
170C2×C8×C37—81no—
171C2×C8×C37—81no—
172C2×C8×C37C2×D411yescharacteristic
173C2×C8×C37C2×D411yescharacteristic
174C2×C8×C37C2×D411yescharacteristic
175C2×C8×C37C2×D411yescharacteristic
176C4⋊C4×C37—21no—
177C4⋊C4×C37—21no—
178C4⋊C4×C37—21no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—21no—
181C4⋊C4×C37—21no—
182C4⋊C4×C37—21no—
183C4⋊C4×C37—21no—
184C4⋊C4×C37—21no—
185C4⋊C4×C37—21no—
186C4⋊C4×C37—41no—
187C4⋊C4×C37—41no—
188C4⋊C4×C37—41no—
189C4⋊C4×C37—41no—
190C4⋊C4×C37C2×D411yescharacteristic
191C4⋊C4×C37C2×D411yescharacteristic
192C22⋊C4×C37—21no—
193C22⋊C4×C37—21no—
194C22⋊C4×C37—21no—
195C22⋊C4×C37—41no—
196C22⋊C4×C37—41no—
197C42×C37—21no—
198C42×C37—21no—
199C42×C37—21no—
200C42×C37—41no—
201C42×C37—41no—
202C42×C37C2×D411yescharacteristic
203C42×C37C2×D411yescharacteristic
204C42×C37#4111yescharacteristic
205C42×C37C2411yescharacteristic
206C23×C37—21no—
207C23×C37#12111yescharacteristic
208Q8×C37—21no—
209Q8×C37—41no—
210Q8×C37—41no—
211Q8×C37—41no—
212Q8×C37—41no—
213Q8×C37—41no—
214Q8×C37—41no—
215Q8×C37—81no—
216Q8×C37#13512yes—
217D4×C37—24no—
218D4×C37—21no—
219D4×C37#13512yes—
220C2×C4×C37—24no—
221C2×C4×C37—21no—
222C2×C4×C37—21no—
223C2×C4×C37—21no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—21no—
227C2×C4×C37—21no—
228C2×C4×C37—41no—
229C2×C4×C37—41no—
230C2×C4×C37—41no—
231C2×C4×C37—41no—
232C2×C4×C37—41no—
233C2×C4×C37—41no—
234C2×C4×C37—41no—
235C2×C4×C37—81no—
236C2×C4×C37#12111yescharacteristic
237C2×C4×C37#12111yescharacteristic
238C2×C4×C37#12111yescharacteristic
239C2×C4×C37C22×D411yescharacteristic
240C2×C4×C37C22×D411yescharacteristic
241C2×C4×C37C2×#4111yescharacteristic
242C8×C37—21no—
243C8×C37—21no—
244C8×C37—21no—
245C8×C37—21no—
246C8×C37—41no—
247C8×C37—41no—
248C8×C37—41no—
249C8×C37—41no—
250C8×C37—41no—
251C8×C37—41no—
252#19418C3711yesmaximal, characteristic, direct product factor, Sylow
253C22×C37—21no—
254C22×C37—21no—
255C22×C37—22no—
256C22×C37—21no—
257C22×C37—41no—
258C22×C37—41no—
259C22×C37C2×#12111yescharacteristic
260C4×C37—21no—
261C4×C37—21no—
262C4×C37—22no—
263C4×C37—21no—
264C4×C37—21no—
265C4×C37—41no—
266C4×C37—41no—
267C4×C37—81no—
268C4×C37—81no—
269C4×C37—81no—
270C4×C37—81no—
271C4×C37C2×#13511yescharacteristic
272C4×C37C2×#13511yescharacteristic
273C4×C37#57711yescharacteristic
274C4×C37#57811yescharacteristic
275#3231C2×C3711yescharacteristic, complemented
276#3116C2×C3711yescharacteristic
277#3107C2×C3711yescharacteristic
278#2988C2×C3711yescharacteristic
279#1684C2×C3711yescharacteristic, complemented
280#1683C2×C3711yescharacteristic, complemented
281#1680C2×C3711yescharacteristic, complemented
282#1679C2×C3711yescharacteristic, complemented
283#1674C2×C3711yescharacteristic, complemented
284#1673C2×C3711yescharacteristic, complemented
285#1672C2×C3711yescharacteristic, complemented
286#1671C2×C3711yescharacteristic, complemented
287#1572C2×C3711yescharacteristic, complemented
288#1552C2×C3711yescharacteristic, complemented
289#1542C2×C3711yescharacteristic, complemented
290C2×C37—41no—
291C2×C37—42no—
292C2×C37#304611yescharacteristic
293C2×C37#305011yescharacteristic
294C2×C37#306911yescharacteristic
295#533C22×C3711yescharacteristic
296#533C22×C3711yescharacteristic
297C4×#41C22×C3711yescharacteristic
298#500C22×C3711yescharacteristic
299#498C22×C3711yescharacteristic
300#487C22×C3711yescharacteristic
301#487C22×C3711yescharacteristic
302#485—21no—
303#485—21no—
304#485—21no—
305#485—21no—
306#479—21no—
307#479—21no—
308#477C22×C3711yescharacteristic
309#476C22×C3711yescharacteristic
310#475C22×C3711yescharacteristic
311#474C22×C3711yescharacteristic
312#462C22×C3711yescharacteristic
313#462C22×C3711yescharacteristic
314#461C22×C3711yescharacteristic
315#461C22×C3711yescharacteristic
316#452—21no—
317#452—21no—
318C8×Q8C22×C3711yescharacteristic
319C8×Q8C22×C3711yescharacteristic
320#441—21no—
321#440—21no—
322C4×Q16—21no—
323C4×SD16—21no—
324C8×D4—21no—
325C8×D4—21no—
326C8×D4C22×C3711yescharacteristic
327C8×D4C22×C3711yescharacteristic
328#432C22×C3711yescharacteristic
329#431—21no—
330#431C22×C3711yescharacteristic
331#431C22×C3711yescharacteristic
332C2×C4⋊C8—21no—
333C2×C4⋊C8C22×C3711yescharacteristic
334#335C22×C3711yescharacteristic
335#335C22×C3711yescharacteristic
336#334C22×C3711yescharacteristic
337#334C22×C3711yescharacteristic
338#333C22×C3711yescharacteristic
339#333C22×C3711yescharacteristic
340#332C22×C3711yescharacteristic
341#332C22×C3711yescharacteristic
342#332C22×C3711yescharacteristic
343#332C22×C3711yescharacteristic
344#332C22×C3711yescharacteristic
345#332C22×C3711yescharacteristic
346C37#1941811yescharacteristic, direct product factor, Sylow
347C2×#41D4×C3711yescharacteristic
348C2×Q16—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8C23×C3711yescharacteristic
356C4⋊Q8C23×C3711yescharacteristic
357C4⋊Q8C23×C3711yescharacteristic
358C4⋊Q8C23×C3711yescharacteristic
359#125—21no—
360#125—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8D4×C3711yescharacteristic
370C4×Q8C23×C3711yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4D4×C3711yescharacteristic
374C4×D4C23×C3711yescharacteristic
375#117—21no—
376#117—21no—
377#117—21no—
378#117D4×C3711yescharacteristic
379C2×C42—21no—
380C2×C42C23×C3711yescharacteristic
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8D4×C3711yescharacteristic
393C4⋊C8D4×C3711yescharacteristic
394C4⋊C8C23×C3711yescharacteristic
395C4⋊C8C23×C3711yescharacteristic
396C4⋊C8C23×C3711yescharacteristic
397C4⋊C8C23×C3711yescharacteristic
398C4⋊C8C23×C3711yescharacteristic
399C4⋊C8C23×C3711yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#102—21no—
411#102—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8D4×C3711yescharacteristic
417C22⋊C8D4×C3711yescharacteristic
418#97—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C3711yescharacteristic
423C4×C8C23×C3711yescharacteristic
424#41—22no—
425#41—22no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8C2×D4×C3711yescharacteristic
431C2×D4—21no—
432C2×D4C2×D4×C3711yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×D4×C3711yescharacteristic
437C22×C4C2×D4×C3711yescharacteristic
438C22×C4#41×C3711yescharacteristic
439Q16—42no—
440Q16—42no—
441SD16—42no—
442SD16—42no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—81no—
450C2×C8—81no—
451C2×C8—81no—
452C2×C8C2×D4×C3711yescharacteristic
453C2×C8C2×D4×C3711yescharacteristic
454C2×C8C2×D4×C3711yescharacteristic
455C2×C8C2×D4×C3711yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4C2×D4×C3711yescharacteristic
471C4⋊C4C2×D4×C3711yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—41no—
482C42C2×D4×C3711yescharacteristic
483C42C2×D4×C3711yescharacteristic
484C42#41×C3711yescharacteristic
485C42C24×C3711yescharacteristic
486C23—21no—
487C23#121×C3711yescharacteristic
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—81no—
496Q8#135×C3712yes—
497D4—24no—
498D4—21no—
499D4#135×C3712yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4#121×C3711yescharacteristic
517C2×C4#121×C3711yescharacteristic
518C2×C4#121×C3711yescharacteristic
519C2×C4C22×D4×C3711yescharacteristic
520C2×C4C22×D4×C3711yescharacteristic
521C2×C4C2×#41×C3711yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—21no—
536C22—41no—
537C22—41no—
538C22C2×#121×C3711yescharacteristic
539C4—21no—
540C4—21no—
541C4—22no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C2×#135×C3711yescharacteristic
551C4C2×#135×C3711yescharacteristic
552C4C37×#57711yescharacteristic
553C4C37×#57811yescharacteristic
554C2—41no—
555C2—42no—
556C2C37×#304611yescharacteristic
557C2C37×#305011yescharacteristic
558C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC2×#41×C37D4
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×#3231C2semidirect
5. C37×#1684C2semidirect
6. C37×#1683C2semidirect
7. C37×#1680C2semidirect
8. C37×#1679C2semidirect
9. C37×#1674C2semidirect
10. C37×#1673C2semidirect
11. C37×#1672C2semidirect
12. C37×#1671C2semidirect
13. C37×#1572C2semidirect
14. C37×#1552C2semidirect
15. C37×#1542C2semidirect
252. #19418C37direct (N × H)
275. #3231C2×C37semidirect
279. #1684C2×C37semidirect
280. #1683C2×C37semidirect
281. #1680C2×C37semidirect
282. #1679C2×C37semidirect
283. #1674C2×C37semidirect
284. #1673C2×C37semidirect
285. #1672C2×C37semidirect
286. #1671C2×C37semidirect
287. #1572C2×C37semidirect
288. #1552C2×C37semidirect
289. #1542C2×C37semidirect
346. C37#19418direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32312
C37×#31162
C37×#31072
C37×#29882
C37×#16842
C37×#16832
C37×#16802
C37×#16792
C37×#16742
C37×#16732
C37×#16722
C37×#16712
C37×#15722
C37×#15522
C37×#15422
#1941837