Finite Group Databasebeta

← C37×#19588 #22640841

Subgroups — C37×#19588 #22640841

Order 9472.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3248C211yesmaximal, characteristic
2C37×#3238C211yesmaximal, characteristic
3C37×#3229C211yesmaximal, characteristic, complemented
4C37×#2994C211yesmaximal, characteristic
5C37×#1704C211yesmaximal, characteristic, complemented
6C37×#1703C211yesmaximal, characteristic, complemented
7C37×#1692C211yesmaximal, characteristic, complemented
8C37×#1691C211yesmaximal, characteristic, complemented
9C37×#1684C211yesmaximal, characteristic, complemented
10C37×#1683C211yesmaximal, characteristic, complemented
11C37×#1672C211yesmaximal, characteristic, complemented
12C37×#1671C211yesmaximal, characteristic, complemented
13C37×#1573C211yesmaximal, characteristic, complemented
14C37×#1552C211yesmaximal, characteristic, complemented
15C2×C37×#333C211yesmaximal, characteristic, complemented
16C37×#533C2211yescharacteristic
17C2×C4⋊Q8×C37C2211yescharacteristic
18C37×#529C2211yescharacteristic
19C37×#501—21no—
20C37×#498C2211yescharacteristic
21C37×#498C2211yescharacteristic
22C37×#489—21no—
23C37×#487C2211yescharacteristic
24C37×#487C2211yescharacteristic
25C37×#483—21no—
26C37×#483—21no—
27C37×#483—21no—
28C37×#480—21no—
29C37×#479—21no—
30C37×#477C2211yescharacteristic
31C37×#477C2211yescharacteristic
32C37×#476C2211yescharacteristic
33C37×#476C2211yescharacteristic
34C37×#475—21no—
35C37×#475—21no—
36C37×#475C2211yescharacteristic
37C37×#474C2211yescharacteristic
38C37×#467—21no—
39C37×#465—21no—
40C37×#464—21no—
41C37×#462C2211yescharacteristic
42C37×#461C2211yescharacteristic
43C37×#446C2211yescharacteristic
44C8×Q8×C37C2211yescharacteristic
45C37×#436C2211yescharacteristic
46C37×#435—21no—
47C8×D4×C37—21no—
48C8×D4×C37C2211yescharacteristic
49C37×#433—21no—
50C37×#432C2211yescharacteristic
51C37×#431C2211yescharacteristic
52C37×#424—21no—
53C2×C4⋊C8×C37C2211yescharacteristic
54C2×C4⋊C8×C37C2211yescharacteristic
55C37×#335C2211yescharacteristic
56C37×#335C2211yescharacteristic
57C37×#334C2211yescharacteristic
58C37×#334C2211yescharacteristic
59C37×#333C2211yescharacteristic
60C37×#333C2211yescharacteristic
61C37×#333C2211yescharacteristic
62C37×#333C2211yescharacteristic
63C37×#332C2211yescharacteristic
64C37×#332C2211yescharacteristic
65C37×#332C2211yescharacteristic
66C37×#332C2211yescharacteristic
67C22×Q8×C37—21no—
68C2×Q16×C37—21no—
69C2×SD16×C37—21no—
70C2×M16×C37—21no—
71C22×C8×C37—21no—
72C22×C8×C37—21no—
73C22×C8×C37—21no—
74C4⋊Q8×C37—21no—
75C4⋊Q8×C37—21no—
76C4⋊Q8×C37—21no—
77C4⋊Q8×C37C2311yescharacteristic
78C4⋊Q8×C37C2311yescharacteristic
79C4⋊Q8×C37C2311yescharacteristic
80C4⋊Q8×C37C2311yescharacteristic
81#126×C37—21no—
82#125×C37—21no—
83#125×C37D411yescharacteristic
84#124×C37D411yescharacteristic
85#123×C37—21no—
86C22⋊Q8×C37—21no—
87C22⋊Q8×C37—21no—
88C22⋊Q8×C37D411yescharacteristic
89#121×C37D411yescharacteristic
90C4×Q8×C37—21no—
91C4×Q8×C37—21no—
92C4×Q8×C37C2311yescharacteristic
93C4×D4×C37—21no—
94C4×D4×C37C2311yescharacteristic
95#117×C37—21no—
96#117×C37—21no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C42×C37C2311yescharacteristic
100#107×C37—21no—
101#107×C37—21no—
102#107×C37—21no—
103#106×C37—21no—
104#106×C37—21no—
105#106×C37—21no—
106#106×C37—21no—
107#106×C37—21no—
108#106×C37—21no—
109#106×C37—21no—
110C4⋊C8×C37—21no—
111C4⋊C8×C37—21no—
112C4⋊C8×C37—21no—
113C4⋊C8×C37—21no—
114C4⋊C8×C37D411yescharacteristic
115C4⋊C8×C37D411yescharacteristic
116C4⋊C8×C37C2311yescharacteristic
117C4⋊C8×C37C2311yescharacteristic
118C4⋊C8×C37C2311yescharacteristic
119C4⋊C8×C37C2311yescharacteristic
120C4⋊C8×C37C2311yescharacteristic
121C4⋊C8×C37C2311yescharacteristic
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#103×C37—21no—
131#102×C37—21no—
132#102×C37—21no—
133#102×C37—21no—
134C22⋊C8×C37—21no—
135C22⋊C8×C37—21no—
136C22⋊C8×C37—21no—
137C22⋊C8×C37D411yescharacteristic
138C22⋊C8×C37D411yescharacteristic
139#97×C37—21no—
140#97×C37—21no—
141C4×C8×C37—21no—
142C4×C8×C37C2311yescharacteristic
143C4×C8×C37C2311yescharacteristic
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—41no—
149C2×Q8×C37—82no—
150C2×Q8×C37C2×D411yescharacteristic
151C2×D4×C37—21no—
152C2×D4×C37C2×D411yescharacteristic
153C22×C4×C37—21no—
154C22×C4×C37—41no—
155C22×C4×C37C2×D411yescharacteristic
156C22×C4×C37C2×D411yescharacteristic
157C22×C4×C37#4111yescharacteristic
158Q16×C37—81no—
159SD16×C37—81no—
160M16×C37—81no—
161C2×C8×C37—21no—
162C2×C8×C37—21no—
163C2×C8×C37—21no—
164C2×C8×C37—21no—
165C2×C8×C37—21no—
166C2×C8×C37—21no—
167C2×C8×C37—81no—
168C2×C8×C37—81no—
169C2×C8×C37—81no—
170C2×C8×C37C2×D411yescharacteristic
171C2×C8×C37C2×D411yescharacteristic
172C2×C8×C37C2×D411yescharacteristic
173C2×C8×C37C2×D411yescharacteristic
174C4⋊C4×C37—21no—
175C4⋊C4×C37—21no—
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—21no—
196C22⋊C4×C37—21no—
197C22⋊C4×C37—41no—
198C42×C37—21no—
199C42×C37—41no—
200C42×C37C2×D411yescharacteristic
201C42×C37C2×D411yescharacteristic
202C42×C37#4111yescharacteristic
203C42×C37C2411yescharacteristic
204C23×C37—21no—
205C23×C37#12111yescharacteristic
206Q8×C37—21no—
207Q8×C37—21no—
208Q8×C37—41no—
209Q8×C37—41no—
210Q8×C37—41no—
211Q8×C37—41no—
212Q8×C37—81no—
213Q8×C37—81no—
214Q8×C37—82no—
215D4×C37—21no—
216D4×C37—21no—
217D4×C37—42no—
218C2×C4×C37—22no—
219C2×C4×C37—21no—
220C2×C4×C37—21no—
221C2×C4×C37—21no—
222C2×C4×C37—21no—
223C2×C4×C37—21no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—41no—
227C2×C4×C37—41no—
228C2×C4×C37—41no—
229C2×C4×C37—41no—
230C2×C4×C37—41no—
231C2×C4×C37—41no—
232C2×C4×C37—82no—
233C2×C4×C37#12111yescharacteristic
234C2×C4×C37#12111yescharacteristic
235C2×C4×C37#12111yescharacteristic
236C2×C4×C37C22×D411yescharacteristic
237C2×C4×C37C22×D411yescharacteristic
238C2×C4×C37C2×#4111yescharacteristic
239C8×C37—21no—
240C8×C37—21no—
241C8×C37—21no—
242C8×C37—21no—
243C8×C37—41no—
244C8×C37—41no—
245C8×C37—41no—
246C8×C37—41no—
247C8×C37—41no—
248C8×C37—41no—
249#19588C3711yesmaximal, characteristic, direct product factor, Sylow
250C22×C37—21no—
251C22×C37—21no—
252C22×C37—41no—
253C22×C37—41no—
254C22×C37—41no—
255C22×C37#47112yes—
256C22×C37C2×#12111yescharacteristic
257C4×C37—21no—
258C4×C37—21no—
259C4×C37—21no—
260C4×C37—21no—
261C4×C37—41no—
262C4×C37—41no—
263C4×C37—41no—
264C4×C37—81no—
265C4×C37—81no—
266C4×C37—81no—
267C4×C37—81no—
268C4×C37#57711yescharacteristic
269C4×C37#57711yescharacteristic
270C4×C37#57811yescharacteristic
271C4×C37#57811yescharacteristic
272#3248C2×C3711yescharacteristic
273#3238C2×C3711yescharacteristic
274#3229C2×C3711yescharacteristic, complemented
275#2994C2×C3711yescharacteristic
276#1704C2×C3711yescharacteristic, complemented
277#1703C2×C3711yescharacteristic, complemented
278#1692C2×C3711yescharacteristic, complemented
279#1691C2×C3711yescharacteristic, complemented
280#1684C2×C3711yescharacteristic, complemented
281#1683C2×C3711yescharacteristic, complemented
282#1672C2×C3711yescharacteristic, complemented
283#1671C2×C3711yescharacteristic, complemented
284#1573C2×C3711yescharacteristic, complemented
285#1552C2×C3711yescharacteristic, complemented
286C2×#333C2×C3711yescharacteristic, complemented
287C2×C37—22no—
288C2×C37—81no—
289C2×C37#304611yescharacteristic
290C2×C37#306311yescharacteristic
291C2×C37C2×#47111yescharacteristic
292#533C22×C3711yescharacteristic
293C2×C4⋊Q8C22×C3711yescharacteristic
294#529C22×C3711yescharacteristic
295#501—21no—
296#498C22×C3711yescharacteristic
297#498C22×C3711yescharacteristic
298#489—21no—
299#487C22×C3711yescharacteristic
300#487C22×C3711yescharacteristic
301#483—21no—
302#483—21no—
303#483—21no—
304#480—21no—
305#479—21no—
306#477C22×C3711yescharacteristic
307#477C22×C3711yescharacteristic
308#476C22×C3711yescharacteristic
309#476C22×C3711yescharacteristic
310#475—21no—
311#475—21no—
312#475C22×C3711yescharacteristic
313#474C22×C3711yescharacteristic
314#467—21no—
315#465—21no—
316#464—21no—
317#462C22×C3711yescharacteristic
318#461C22×C3711yescharacteristic
319#446C22×C3711yescharacteristic
320C8×Q8C22×C3711yescharacteristic
321#436C22×C3711yescharacteristic
322#435—21no—
323C8×D4—21no—
324C8×D4C22×C3711yescharacteristic
325#433—21no—
326#432C22×C3711yescharacteristic
327#431C22×C3711yescharacteristic
328#424—21no—
329C2×C4⋊C8C22×C3711yescharacteristic
330C2×C4⋊C8C22×C3711yescharacteristic
331#335C22×C3711yescharacteristic
332#335C22×C3711yescharacteristic
333#334C22×C3711yescharacteristic
334#334C22×C3711yescharacteristic
335#333C22×C3711yescharacteristic
336#333C22×C3711yescharacteristic
337#333C22×C3711yescharacteristic
338#333C22×C3711yescharacteristic
339#332C22×C3711yescharacteristic
340#332C22×C3711yescharacteristic
341#332C22×C3711yescharacteristic
342#332C22×C3711yescharacteristic
343C37#1958811yescharacteristic, direct product factor, Sylow
344C22×Q8—21no—
345C2×Q16—21no—
346C2×SD16—21no—
347C2×M16—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C3711yescharacteristic
355C4⋊Q8C23×C3711yescharacteristic
356C4⋊Q8C23×C3711yescharacteristic
357C4⋊Q8C23×C3711yescharacteristic
358#126—21no—
359#125—21no—
360#125D4×C3711yescharacteristic
361#124D4×C3711yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8D4×C3711yescharacteristic
366#121D4×C3711yescharacteristic
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C3711yescharacteristic
370C4×D4—21no—
371C4×D4C23×C3711yescharacteristic
372#117—21no—
373#117—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C42C23×C3711yescharacteristic
377#107—21no—
378#107—21no—
379#107—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8D4×C3711yescharacteristic
392C4⋊C8D4×C3711yescharacteristic
393C4⋊C8C23×C3711yescharacteristic
394C4⋊C8C23×C3711yescharacteristic
395C4⋊C8C23×C3711yescharacteristic
396C4⋊C8C23×C3711yescharacteristic
397C4⋊C8C23×C3711yescharacteristic
398C4⋊C8C23×C3711yescharacteristic
399#103—21no—
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#102—21no—
409#102—21no—
410#102—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8D4×C3711yescharacteristic
415C22⋊C8D4×C3711yescharacteristic
416#97—21no—
417#97—21no—
418C4×C8—21no—
419C4×C8C23×C3711yescharacteristic
420C4×C8C23×C3711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8C2×D4×C3711yescharacteristic
428C2×D4—21no—
429C2×D4C2×D4×C3711yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4C2×D4×C3711yescharacteristic
433C22×C4C2×D4×C3711yescharacteristic
434C22×C4#41×C3711yescharacteristic
435Q16—81no—
436SD16—81no—
437M16—81no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8C2×D4×C3711yescharacteristic
448C2×C8C2×D4×C3711yescharacteristic
449C2×C8C2×D4×C3711yescharacteristic
450C2×C8C2×D4×C3711yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C3711yescharacteristic
468C4⋊C4C2×D4×C3711yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C42—21no—
476C42—41no—
477C42C2×D4×C3711yescharacteristic
478C42C2×D4×C3711yescharacteristic
479C42#41×C3711yescharacteristic
480C42C24×C3711yescharacteristic
481C23—21no—
482C23#121×C3711yescharacteristic
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—81no—
491Q8—82no—
492D4—21no—
493D4—21no—
494D4—42no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4#121×C3711yescharacteristic
511C2×C4#121×C3711yescharacteristic
512C2×C4#121×C3711yescharacteristic
513C2×C4C22×D4×C3711yescharacteristic
514C2×C4C22×D4×C3711yescharacteristic
515C2×C4C2×#41×C3711yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22C37×#47112yes—
532C22C2×#121×C3711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4C37×#57711yescharacteristic
545C4C37×#57711yescharacteristic
546C4C37×#57811yescharacteristic
547C4C37×#57811yescharacteristic
548C2—22no—
549C2—81no—
550C2C37×#304611yescharacteristic
551C2C37×#306311yescharacteristic
552C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radical#121×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
3. C37×#3229C2semidirect
5. C37×#1704C2semidirect
6. C37×#1703C2semidirect
7. C37×#1692C2semidirect
8. C37×#1691C2semidirect
9. C37×#1684C2semidirect
10. C37×#1683C2semidirect
11. C37×#1672C2semidirect
12. C37×#1671C2semidirect
13. C37×#1573C2semidirect
14. C37×#1552C2semidirect
15. C2×C37×#333C2semidirect
249. #19588C37direct (N × H)
274. #3229C2×C37semidirect
276. #1704C2×C37semidirect
277. #1703C2×C37semidirect
278. #1692C2×C37semidirect
279. #1691C2×C37semidirect
280. #1684C2×C37semidirect
281. #1683C2×C37semidirect
282. #1672C2×C37semidirect
283. #1671C2×C37semidirect
284. #1573C2×C37semidirect
285. #1552C2×C37semidirect
286. C2×#333C2×C37semidirect
343. C37#19588direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32482
C37×#32382
C37×#32292
C37×#29942
C37×#17042
C37×#17032
C37×#16922
C37×#16912
C37×#16842
C37×#16832
C37×#16722
C37×#16712
C37×#15732
C37×#15522
C2×C37×#3332
#1958837