Subgroups — #37565641

Order 24256.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131330	C₂	1	2	yes	maximal
2	#27131263	C₂	1	1	yes	maximal, characteristic
3	#27131262	C₂	1	2	yes	maximal
4	C₈×Dic₃₇₉	C₂	1	1	yes	maximal, characteristic
5	#106×C₃₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₅₈	—	2	2	no	—
7	C₂×C₃₇₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₃₇₉	C₂²	1	2	yes	—
9	Dic₃₇₉⋊C₄	—	2	2	no	—
10	C₄×Dic₃₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇₉	C₂²	1	2	yes	—
13	Dic₇₅₈	—	4	4	no	—
14	C₂×Dic₃₇₉	—	2	2	no	—
15	C₂×Dic₃₇₉	D₄	1	2	yes	—
16	C₃₇₉⋊C₈	Q₈	1	2	yes	complemented
17	C₂×C₄×C₃₇₉	—	2	2	no	—
18	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
19	C₈×C₃₇₉	Q₈	1	2	yes	complemented
20	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₇₉	—	4	2	no	—
22	C₄×C₃₇₉	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₃₇₉	C₂×Q₈	1	1	yes	characteristic
24	Dic₃₇₉	—	4	2	no	—
25	Dic₃₇₉	SD₁₆	1	4	yes	—
26	C₂×C₃₇₉	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₃₇₉	C₂×SD₁₆	1	2	yes	—
28	C₃₇₉	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	379	1	no	maximal, Sylow
30	C₄⋊Q₈	—	379	2	no	—
31	#106	—	379	1	no	—
32	#106	—	379	2	no	—
33	#106	D₃₇₉	1	1	yes	characteristic
34	C₄×C₈	—	379	1	no	—
35	C₂×Q₈	—	758	2	no	—
36	C₂×C₈	—	379	1	no	—
37	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
38	C₄⋊C₄	—	379	2	no	—
39	C₄⋊C₄	—	758	2	no	—
40	C₄⋊C₄	C₂×D₃₇₉	1	2	yes	—
41	C₄²	—	379	1	no	—
42	Q₈	—	1516	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	379	2	no	—
45	C₂×C₄	—	758	2	no	—
46	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
47	C₈	—	379	2	no	—
48	C₈	Dic₇₅₈	1	2	yes	complemented
49	C₂²	D₄×D₃₇₉	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	379	4	no	—
52	C₄	—	1516	2	no	—
53	C₄	Q₈×D₃₇₉	1	1	yes	characteristic
54	C₄	C₂×Dic₇₅₈	1	1	yes	characteristic
55	C₂	#27131330	1	1	yes	characteristic
56	C₂	SD₁₆×D₃₇₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₃₇₉
commutator, cosocle	C₂×C₄×C₃₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting	#106×C₃₇₉	C₂
socle, prime radical	C₂²×C₃₇₉	C₂×D₄
hypercenter	#106	D₃₇₉
hypocenter	C₃₇₉	#498
LCS	G ▷ C₂×C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
16. C₃₇₉⋊C₈	Q₈	semidirect
19. C₈×C₃₇₉	Q₈	semidirect
28. C₃₇₉	#498	semidirect
48. 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
#27131263	2
#27131262	2
C₈×Dic₃₇₉	2
#106×C₃₇₉	2
#498	379