Subgroups — #28407807

Order 14464.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299706	C₂	1	3	yes	maximal, complemented
2	C₂×#16813712	C₂	1	3	yes	maximal, complemented
3	#20299656	C₂	1	1	yes	maximal, characteristic
4	#16813712	C₂²	1	1	yes	characteristic
5	#16813712	C₂²	1	3	yes	—
6	#16813696	C₄	1	3	yes	—
7	C₂×#14268650	C₂²	1	3	yes	—
8	#16813629	C₄	1	1	yes	characteristic
9	#14268650	C₂×C₄	1	3	yes	—
10	#14268650	C₂³	1	1	yes	characteristic
11	#14268631	C₈	1	3	yes	—
12	C₂×#11744751	C₂×C₄	1	3	yes	—
13	#41×C₁₁₃	C₈	1	1	yes	characteristic
14	Q₈×C₁₁₃	C₁₆	1	1	yes	characteristic
15	D₄×C₁₁₃	C₁₆	1	3	yes	—
16	C₂×C₄×C₁₁₃	C₂×C₈	1	3	yes	—
17	#11744751	C₂×C₈	1	3	yes	—
18	#11744751	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₁₁₃	C₂×C₁₆	1	3	yes	—
20	C₄×C₁₁₃	C₂×C₁₆	1	3	yes	—
21	C₄×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₁₃	—	2	3	no	—
23	C₂×C₁₁₃	C₂²×C₁₆	1	1	yes	characteristic
24	#2258	—	113	1	no	maximal, Sylow
25	C₁₁₃	#2258	1	1	yes	characteristic, complemented, Sylow
26	#504	—	113	1	no	—
27	M₆₄	—	113	3	no	—
28	C₂×C₃₂	—	113	3	no	—
29	#131	—	113	1	no	—
30	M₃₂	—	113	3	no	—
31	C₂×C₁₆	—	113	3	no	—
32	C₃₂	—	113	1	no	—
33	C₃₂	—	113	3	no	—
34	#41	#11744762	1	1	yes	characteristic
35	M₁₆	—	113	3	no	—
36	C₂×C₈	—	113	3	no	—
37	C₁₆	—	113	1	no	—
38	C₁₆	—	113	3	no	—
39	Q₈	#14268659	1	1	yes	characteristic
40	D₄	#14268659	1	3	yes	—
41	C₂×C₄	C₂×#11744762	1	3	yes	—
42	C₈	—	113	1	no	—
43	C₈	—	113	3	no	—
44	C₂²	C₂×#14268659	1	3	yes	—
45	C₄	C₂×#14268659	1	3	yes	—
46	C₄	C₂²×#11744762	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#14268659	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#11744762
commutator, socle	C₂×C₁₁₃	C₂²×C₁₆
Fitting, prime radical	#41×C₁₁₃	C₈
cosocle	#14268650	C₂³
hypercenter	#41	#11744762
hypocenter	C₁₁₃	#2258
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #20299706	C₂	semidirect
2. C₂×#16813712	C₂	semidirect
25. C₁₁₃	#2258	semidirect

Maximal subgroups

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

subgroup	index
#20299706	2
C₂×#16813712	2
#20299656	2
#2258	113