Subgroups — #28407670

Order 14464.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299706	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16813712	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299656	C₂	1	1	yes	maximal, characteristic
4	#16813712	—	2	1	no	—
5	#16813712	—	2	1	no	—
6	#16813696	—	2	1	no	—
7	#16813696	C₄	1	1	yes	characteristic
8	C₂×#14268650	—	2	1	no	—
9	C₂×#14268650	C₂²	1	1	yes	characteristic
10	#16813629	C₄	1	1	yes	characteristic
11	#14268650	—	2	1	no	—
12	#14268650	D₄	1	1	yes	characteristic
13	#14268650	D₄	1	1	yes	characteristic
14	#14268631	—	2	1	no	—
15	#14268631	C₈	1	1	yes	characteristic
16	C₂×#11744751	—	2	1	no	—
17	C₂×#11744751	C₂×C₄	1	1	yes	characteristic
18	#41×C₁₁₃	C₈	1	1	yes	characteristic
19	Q₈×C₁₁₃	C₁₆	1	1	yes	characteristic
20	D₄×C₁₁₃	—	2	1	no	—
21	D₄×C₁₁₃	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₁₃	—	2	1	no	—
23	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
24	#11744751	—	2	1	no	—
25	#11744751	C₂²⋊C₄	1	1	yes	characteristic
26	#11744751	M₁₆	1	1	yes	characteristic
27	C₂²×C₁₁₃	—	2	1	no	—
28	C₂²×C₁₁₃	M₃₂	1	1	yes	characteristic
29	C₄×C₁₁₃	—	2	1	no	—
30	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
32	C₂×C₁₁₃	—	2	1	no	—
33	C₂×C₁₁₃	—	4	1	no	—
34	C₂×C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	#1401	—	113	1	no	maximal, Sylow
36	C₁₁₃	#1401	1	1	yes	characteristic, complemented, Sylow
37	#504	—	113	1	no	—
38	M₆₄	—	113	1	no	—
39	C₂×C₃₂	—	113	1	no	—
40	#131	—	113	1	no	—
41	M₃₂	—	113	1	no	—
42	M₃₂	—	226	1	no	—
43	C₂×C₁₆	—	113	1	no	—
44	C₂×C₁₆	—	226	1	no	—
45	C₃₂	—	226	1	no	—
46	C₃₂	—	226	1	no	—
47	#41	#11744762	1	1	yes	characteristic
48	M₁₆	—	113	1	no	—
49	M₁₆	—	226	1	no	—
50	C₂×C₈	—	113	1	no	—
51	C₂×C₈	—	226	1	no	—
52	C₁₆	—	113	1	no	—
53	C₁₆	—	113	1	no	—
54	C₁₆	—	226	1	no	—
55	Q₈	#14268659	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	#14268659	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×#11744762	1	1	yes	characteristic
60	C₈	—	113	1	no	—
61	C₈	—	113	1	no	—
62	C₈	—	226	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	#16813718	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂²⋊#11744762	1	1	yes	characteristic
67	C₄	C₂×#14268659	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊#14268659	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#11744762
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₂×C₄	C₂×#11744762
Fitting, prime radical	#41×C₁₁₃	C₈
socle	C₂×C₁₁₃	C₂²⋊C₁₆
cosocle	C₂×#14268650	C₂²
hypercenter	#41	#11744762
hypocenter	C₁₁₃	#1401
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂×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
36. C₁₁₃	#1401	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
#1401	113