Subgroups — #38735016

Order 24896.

58 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	#27159452	C₂	1	1	yes	maximal, characteristic, complemented
3	#27159407	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#13095555	—	2	1	no	—
5	#20261969	—	2	1	no	—
6	#20261967	—	2	1	no	—
7	#20261953	—	2	1	no	—
8	D₃₁₁₂	C₄	1	1	yes	characteristic, complemented
9	C₈×D₃₈₉	C₂²	1	1	yes	characteristic
10	Q₁₆×C₃₈₉	C₄	1	1	yes	characteristic, complemented
11	C₂×#13095555	—	4	1	no	—
12	D₁₅₅₆	—	2	1	no	—
13	D₁₅₅₆	—	4	1	no	—
14	C₄×D₃₈₉	—	4	1	no	—
15	C₄×D₃₈₉	D₄	1	1	yes	characteristic
16	#15691005	D₄	1	1	yes	characteristic
17	Q₈×C₃₈₉	—	2	1	no	—
18	C₈×C₃₈₉	C₂×C₄	1	1	yes	characteristic
19	C₂×D₃₈₉	—	4	1	no	—
20	C₂×D₃₈₉	D₈	1	1	yes	characteristic
21	#13095555	—	8	1	no	—
22	C₄×C₃₈₉	—	4	1	no	—
23	C₄×C₃₈₉	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₃₈₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₃₈₉	#102	1	1	yes	characteristic
26	D₃₈₉	—	2	1	no	—
27	D₃₈₉	—	8	1	no	—
28	C₃₈₉	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	389	1	no	maximal, Sylow
30	#135	—	389	1	no	—
31	M₃₂	—	389	1	no	—
32	#106	—	389	1	no	—
33	#41	—	778	1	no	—
34	Q₁₆	#13095555	1	1	yes	characteristic, complemented
35	SD₁₆	—	778	1	no	—
36	D₈	—	389	1	no	—
37	C₂×C₈	—	389	1	no	—
38	C₄⋊C₄	—	778	1	no	—
39	C₁₆	—	778	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	778	1	no	—
42	D₄	—	1556	1	no	—
43	C₂×C₄	—	1556	1	no	—
44	C₂×C₄	—	1556	1	no	—
45	C₂×C₄	—	389	1	no	—
46	C₈	—	389	1	no	—
47	C₈	C₂×#13095555	1	1	yes	characteristic
48	C₂²	—	1556	1	no	—
49	C₂²	—	389	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	3112	1	no	—
52	C₄	—	389	1	no	—
53	C₄	C₂²⋊#13095555	1	1	yes	characteristic
54	C₂	—	778	1	no	—
55	C₂	—	3112	1	no	—
56	C₂	#27159446	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27159446
commutator	C₈×C₃₈₉	C₂×C₄
Frattini	C₈	C₂×#13095555
Fitting	Q₁₆×C₃₈₉	C₄
socle	C₂×C₃₈₉	#102
prime radical	#27159407	C₂
cosocle	C₈×D₃₈₉	C₂²
hypercenter	Q₁₆	#13095555
hypocenter	C₃₈₉	#360
LCS	G ▷ C₈×C₃₈₉ ▷ C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #27159459	C₂	semidirect
2. #27159452	C₂	semidirect
8. D₃₁₁₂	C₄	semidirect
10. Q₁₆×C₃₈₉	C₄	semidirect
28. C₃₈₉	#360	semidirect
34. Q₁₆	#13095555	semidirect

Maximal subgroups

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

subgroup	index
#27159459	2
#27159452	2
#27159407	2
#360	389