Subgroups — #37565154

Order 24256.

322 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₅₁₆	C₂	1	3	yes	maximal, complemented
2	C₂×(C₂×D₃₇₉)⋊C₄	C₂	1	3	yes	maximal, complemented
3	#95×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₃₇₉	C₂²	1	3	yes	—
5	C₂×D₁₅₁₆	—	2	12	no	—
6	C₂×D₁₅₁₆	—	2	6	no	—
7	C₂²×Dic₃₇₉	C₂²	1	1	yes	characteristic
8	(C₂×D₃₇₉)⋊C₄	—	2	6	no	—
9	C₂²×C₄×C₃₇₉	C₂²	1	3	yes	—
10	C₂²×D₃₇₉	—	2	3	no	—
11	C₂²×D₃₇₉	—	2	6	no	—
12	C₂²×D₃₇₉	—	2	6	no	—
13	C₂²×D₃₇₉	—	2	3	no	—
14	C₂²×D₃₇₉	D₄	1	6	yes	complemented
15	D₁₅₁₆	—	2	24	no	—
16	C₂×Dic₃₇₉	—	2	3	no	—
17	C₂³×C₃₇₉	C₂³	1	1	yes	characteristic
18	C₂×C₄×C₃₇₉	—	2	6	no	—
19	C₂×C₄×C₃₇₉	D₄	1	6	yes	complemented
20	C₂²×C₃₇₉	C₂×D₄	1	3	yes	—
21	C₂²×C₃₇₉	C₂×D₄	1	3	yes	—
22	C₂²×C₃₇₉	#41	1	1	yes	characteristic
23	C₂×D₃₇₉	—	2	12	no	—
24	C₂×D₃₇₉	—	2	6	no	—
25	C₂×D₃₇₉	—	4	3	no	—
26	C₂×D₃₇₉	—	4	6	no	—
27	C₂×D₃₇₉	—	4	3	no	—
28	C₄×C₃₇₉	—	2	6	no	—
29	Dic₃₇₉	—	4	1	no	—
30	C₂×C₃₇₉	#120	1	3	yes	—
31	C₂×C₃₇₉	#121	1	3	yes	—
32	C₂×C₃₇₉	#127	1	1	yes	characteristic
33	D₃₇₉	—	4	6	no	—
34	C₃₇₉	#392	1	1	yes	characteristic, complemented, Sylow
35	#392	—	379	1	no	maximal, Sylow
36	C₂²×D₄	—	379	3	no	—
37	C₂×C₂²⋊C₄	—	379	3	no	—
38	#95	D₃₇₉	1	1	yes	characteristic, complemented
39	C₂⁴	—	379	3	no	—
40	C₂×D₄	—	758	12	no	—
41	C₂×D₄	—	758	6	no	—
42	C₂²×C₄	—	379	1	no	—
43	C₂²×C₄	C₂×D₃₇₉	1	3	yes	—
44	C₂²⋊C₄	—	758	6	no	—
45	C₂³	—	379	6	no	—
46	C₂³	—	758	6	no	—
47	C₂³	—	758	3	no	—
48	C₂³	—	758	6	no	—
49	C₂³	—	758	3	no	—
50	C₂³	C₂²×D₃₇₉	1	1	yes	characteristic
51	D₄	—	758	24	no	—
52	C₂×C₄	—	2	6	no	—
53	C₂×C₄	—	758	3	no	—
54	C₂×C₄	D₁₅₁₆	1	6	yes	complemented
55	C₂²	—	1516	3	no	—
56	C₂²	—	1516	6	no	—
57	C₂²	—	1516	3	no	—
58	C₂²	—	758	12	no	—
59	C₂²	—	758	6	no	—
60	C₂²	D₄×D₃₇₉	1	3	yes	—
61	C₂²	C₂×D₁₅₁₆	1	3	yes	—
62	C₂²	#20258607	1	1	yes	characteristic
63	C₄	—	2	6	no	—
64	C₄	—	1516	1	no	—
65	C₂	—	1516	6	no	—
66	C₂	#27131301	1	3	yes	—
67	C₂	#27131306	1	3	yes	—
68	C₂	#27131328	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₇₉
commutator, socle, cosocle	C₂³×C₃₇₉	C₂³
Fitting	#95×C₃₇₉	C₂
hypercenter	#95	D₃₇₉
hypocenter	C₃₇₉	#392
LCS	G ▷ C₂³×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×D₁₅₁₆	C₂	semidirect
2. C₂×(C₂×D₃₇₉)⋊C₄	C₂	semidirect
3. #95×C₃₇₉	C₂	semidirect
14. C₂²×D₃₇₉	D₄	semidirect
19. C₂×C₄×C₃₇₉	D₄	semidirect
34. C₃₇₉	#392	semidirect
38. #95	D₃₇₉	semidirect
54. C₂×C₄	D₁₅₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₁₅₁₆	2
C₂×(C₂×D₃₇₉)⋊C₄	2
#95×C₃₇₉	2
#392	379