Subgroups — #38735017

Order 24896.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27159459	C₂	1	1	yes	maximal, characteristic, complemented
2	#27159454	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₃₈₉	C₂	1	1	yes	maximal, characteristic
4	#20261976	—	2	1	no	—
5	#20261969	—	2	1	no	—
6	D₄×D₃₈₉	—	2	1	no	—
7	D₃₁₁₂	C₄	1	1	yes	characteristic
8	#20261951	—	2	1	no	—
9	C₈×D₃₈₉	C₂²	1	1	yes	characteristic
10	D₈×C₃₈₉	C₄	1	1	yes	characteristic
11	#15691012	—	4	1	no	—
12	C₂²×D₃₈₉	—	4	1	no	—
13	D₁₅₅₆	—	2	1	no	—
14	C₂²⋊D₃₈₉	—	4	1	no	—
15	C₄×D₃₈₉	D₄	1	1	yes	characteristic
16	#15691005	D₄	1	1	yes	characteristic
17	D₄×C₃₈₉	—	2	1	no	—
18	C₈×C₃₈₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₃₈₉	—	4	1	no	—
20	C₂×D₃₈₉	—	4	1	no	—
21	C₂×D₃₈₉	—	8	2	no	—
22	C₂×D₃₈₉	SD₁₆	1	1	yes	characteristic
23	C₄×C₃₈₉	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₃₈₉	D₈	1	1	yes	characteristic
25	C₂×C₃₈₉	—	8	1	no	—
26	C₂×C₃₈₉	#102	1	1	yes	characteristic
27	D₃₈₉	—	2	1	no	—
28	D₃₈₉	—	8	1	no	—
29	C₃₈₉	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	389	1	no	maximal, Sylow
31	C₂×D₈	—	389	1	no	—
32	M₃₂	—	389	1	no	—
33	#108	—	389	1	no	—
34	C₂×D₄	—	778	1	no	—
35	D₈	—	778	1	no	—
36	D₈	—	389	1	no	—
37	D₈	#13095555	1	1	yes	characteristic
38	M₁₆	—	778	1	no	—
39	C₂×C₈	—	389	1	no	—
40	C₁₆	—	778	1	no	—
41	C₂³	—	1556	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	778	1	no	—
44	D₄	—	1556	1	no	—
45	C₂×C₄	—	389	1	no	—
46	C₈	—	1556	1	no	—
47	C₈	—	389	1	no	—
48	C₈	C₂×#13095555	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	1556	1	no	—
51	C₂²	—	3112	2	no	—
52	C₂²	—	389	1	no	—
53	C₄	—	389	1	no	—
54	C₄	C₂²⋊#13095555	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	778	1	no	—
57	C₂	—	3112	1	no	—
58	C₂	#27159446	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27159446
commutator	C₈×C₃₈₉	C₂×C₄
Frattini	C₈	C₂×#13095555
Fitting	D₈×C₃₈₉	C₄
socle	C₂×C₃₈₉	#102
prime radical	D₈×D₃₈₉	C₂
cosocle	C₈×D₃₈₉	C₂²
hypercenter	D₈	#13095555
hypocenter	C₃₈₉	#361
LCS	G ▷ C₈×C₃₈₉ ▷ C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #27159459	C₂	semidirect
2. #27159454	C₂	semidirect
29. C₃₈₉	#361	semidirect

Maximal subgroups

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

subgroup	index
#27159459	2
#27159454	2
D₈×D₃₈₉	2
#361	389