Subgroups — #38734997

Order 24896.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27159458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20261969	C₂	1	1	yes	maximal, characteristic, complemented
3	#27159391	C₂	1	1	yes	maximal, characteristic
4	#20261969	—	2	1	no	—
5	#20261969	—	2	1	no	—
6	#20261950	—	2	1	no	—
7	#20261950	C₄	1	1	yes	characteristic
8	C₂×#15691005	—	2	1	no	—
9	C₂×#15691005	C₂²	1	1	yes	characteristic
10	#41×C₃₈₉	C₄	1	1	yes	characteristic
11	#15691005	—	2	1	no	—
12	#15691005	D₄	1	1	yes	characteristic
13	#15691005	D₄	1	1	yes	characteristic
14	Q₈×C₃₈₉	C₈	1	1	yes	characteristic
15	D₄×C₃₈₉	—	2	1	no	—
16	D₄×C₃₈₉	C₈	1	1	yes	characteristic
17	C₂×C₄×C₃₈₉	—	2	1	no	—
18	C₂×C₄×C₃₈₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₃₈₉	—	2	1	no	—
20	C₂²×C₃₈₉	M₁₆	1	1	yes	characteristic
21	C₄×C₃₈₉	—	2	1	no	—
22	C₄×C₃₈₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₃₈₉	C₂×C₈	1	1	yes	characteristic
24	C₂×C₃₈₉	—	2	1	no	—
25	C₂×C₃₈₉	—	4	1	no	—
26	C₂×C₃₈₉	C₂²⋊C₈	1	1	yes	characteristic
27	C₃₈₉	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	389	1	no	maximal, Sylow
29	#131	—	389	1	no	—
30	M₃₂	—	389	1	no	—
31	C₂×C₁₆	—	389	1	no	—
32	#41	#13095555	1	1	yes	characteristic
33	M₁₆	—	778	1	no	—
34	M₁₆	—	389	1	no	—
35	C₂×C₈	—	778	1	no	—
36	C₂×C₈	—	389	1	no	—
37	C₁₆	—	778	1	no	—
38	C₁₆	—	778	1	no	—
39	Q₈	#15691012	1	1	yes	characteristic
40	D₄	—	2	1	no	—
41	D₄	#15691012	1	1	yes	characteristic
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	C₂×#13095555	1	1	yes	characteristic
44	C₈	—	778	1	no	—
45	C₈	—	389	1	no	—
46	C₈	—	389	1	no	—
47	C₂²	—	2	1	no	—
48	C₂²	#20261975	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	C₂²⋊#13095555	1	1	yes	characteristic
51	C₄	C₂×#15691012	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	4	1	no	—
54	C₂	C₂²⋊#15691012	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#13095555
commutator	C₄×C₃₈₉	C₂×C₈
Frattini	C₂×C₄	C₂×#13095555
Fitting, prime radical	#41×C₃₈₉	C₄
socle	C₂×C₃₈₉	C₂²⋊C₈
cosocle	C₂×#15691005	C₂²
hypercenter	#41	#13095555
hypocenter	C₃₈₉	#350
LCS	G ▷ C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #27159458	C₂	semidirect
2. C₂×#20261969	C₂	semidirect
27. C₃₈₉	#350	semidirect

Maximal subgroups

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

subgroup	index
#27159458	2
C₂×#20261969	2
#27159391	2
#350	389