Subgroups — #37565652

Order 24256.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131330	C₂	1	1	yes	maximal, characteristic
2	#27131322	C₂	1	1	yes	maximal, characteristic
3	#27131264	C₂	1	1	yes	maximal, characteristic
4	#27131263	C₂	1	1	yes	maximal, characteristic
5	#27131262	C₂	1	1	yes	maximal, characteristic
6	#27131241	C₂	1	1	yes	maximal, characteristic
7	#107×C₃₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₇₅₈	—	2	1	no	—
9	C₂×C₃₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃₇₉	—	2	1	no	—
11	C₄⋊Dic₃₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃₇₉	C₂²	1	1	yes	characteristic
13	Dic₃₇₉⋊C₄	—	2	1	no	—
14	Dic₃₇₉⋊C₄	—	2	1	no	—
15	C₄×Dic₃₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₃₇₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₃₇₉	C₂²	1	1	yes	characteristic
19	Dic₇₅₈	—	4	2	no	—
20	C₂×Dic₃₇₉	—	2	1	no	—
21	C₂×Dic₃₇₉	—	2	1	no	—
22	C₂×Dic₃₇₉	D₄	1	1	yes	characteristic
23	C₂×Dic₃₇₉	D₄	1	1	yes	characteristic
24	C₃₇₉⋊C₈	Q₈	1	2	yes	complemented
25	C₂×C₄×C₃₇₉	—	2	1	no	—
26	C₂×C₄×C₃₇₉	—	2	1	no	—
27	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
28	C₈×C₃₇₉	Q₈	1	2	yes	complemented
29	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₃₇₉	—	4	1	no	—
31	C₄×C₃₇₉	—	4	1	no	—
32	C₄×C₃₇₉	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₃₇₉	C₂×Q₈	1	1	yes	characteristic
34	Dic₃₇₉	—	2	1	no	—
35	Dic₃₇₉	—	2	1	no	—
36	Dic₃₇₉	—	4	1	no	—
37	Dic₃₇₉	—	4	1	no	—
38	C₂×C₃₇₉	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₃₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₃₇₉	#137	1	1	yes	characteristic
41	C₃₇₉	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	379	1	no	maximal, Sylow
43	C₄⋊Q₈	—	379	1	no	—
44	#125	—	379	1	no	—
45	#107	—	379	1	no	—
46	#107	D₃₇₉	1	1	yes	characteristic
47	#106	—	379	1	no	—
48	#106	—	379	1	no	—
49	#97	—	379	1	no	—
50	C₂×Q₈	—	758	1	no	—
51	C₂×C₈	—	379	1	no	—
52	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
53	C₄⋊C₄	—	379	1	no	—
54	C₄⋊C₄	—	379	1	no	—
55	C₄⋊C₄	—	758	1	no	—
56	C₄⋊C₄	—	758	1	no	—
57	C₄⋊C₄	—	758	1	no	—
58	C₄⋊C₄	C₂×D₃₇₉	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₃₇₉	1	1	yes	characteristic
60	C₄²	—	379	1	no	—
61	Q₈	—	1516	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	379	1	no	—
65	C₂×C₄	—	379	1	no	—
66	C₂×C₄	—	758	1	no	—
67	C₂×C₄	—	758	1	no	—
68	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
69	C₈	—	379	2	no	—
70	C₈	Dic₇₅₈	1	2	yes	complemented
71	C₂²	D₄×D₃₇₉	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	1516	1	no	—
75	C₄	—	1516	1	no	—
76	C₄	—	758	1	no	—
77	C₄	—	758	1	no	—
78	C₄	Q₈×D₃₇₉	1	1	yes	characteristic
79	C₄	C₂×Dic₇₅₈	1	1	yes	characteristic
80	C₂	#27131330	1	1	yes	characteristic
81	C₂	#27131355	1	1	yes	characteristic
82	C₂	#27131363	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₇₉
commutator, cosocle	C₂×C₄×C₃₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting	#107×C₃₇₉	C₂
socle, prime radical	C₂²×C₃₇₉	C₂×D₄
hypercenter	#107	D₃₇₉
hypocenter	C₃₇₉	#501
LCS	G ▷ C₂×C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
24. C₃₇₉⋊C₈	Q₈	semidirect
28. C₈×C₃₇₉	Q₈	semidirect
41. C₃₇₉	#501	semidirect
70. C₈	Dic₇₅₈	semidirect

Maximal subgroups

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

subgroup	index
#27131330	2
#27131322	2
#27131264	2
#27131263	2
#27131262	2
#27131241	2
#107×C₃₇₉	2
#501	379