Subgroups — #28405692

Order 14464.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299530	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16813672	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299016	C₂	1	1	yes	maximal, characteristic
4	#16813672	—	2	1	no	—
5	#16813672	—	2	1	no	—
6	#16813628	C₄	1	1	yes	characteristic
7	#16813561	—	2	1	no	—
8	C₂×#14268622	C₂²	1	1	yes	characteristic
9	C₁₆×D₁₁₃	—	2	1	no	—
10	M₃₂×C₁₁₃	C₄	1	1	yes	characteristic
11	#14268647	C₈	1	1	yes	characteristic
12	#14268631	C₈	1	1	yes	characteristic
13	#14268630	—	2	1	no	—
14	C₈×D₁₁₃	—	2	1	no	—
15	#14268622	D₄	1	1	yes	characteristic
16	#14268622	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₁₁₃	—	2	1	no	—
19	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₁₁₃	—	2	1	no	—
21	D₄₅₂	C₁₆	1	1	yes	characteristic
22	C₄×D₁₁₃	—	2	1	no	—
23	Dic₂₂₆	C₁₆	1	1	yes	characteristic
24	C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
26	#11744751	—	2	1	no	—
27	C₂²×C₁₁₃	M₃₂	1	1	yes	characteristic
28	C₂×D₁₁₃	—	2	1	no	—
29	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
31	Dic₁₁₃	—	2	1	no	—
32	C₂×C₁₁₃	—	2	1	no	—
33	C₂×C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
34	D₁₁₃	—	4	1	no	—
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	—	226	1	no	—
42	M₃₂	#90673	1	1	yes	characteristic
43	C₂×C₁₆	—	113	1	no	—
44	C₂×C₁₆	—	226	1	no	—
45	C₃₂	—	226	1	no	—
46	C₃₂	—	226	1	no	—
47	#41	—	113	1	no	—
48	M₁₆	—	113	1	no	—
49	M₁₆	—	226	1	no	—
50	C₂×C₈	—	226	1	no	—
51	C₂×C₈	C₂×#90673	1	1	yes	characteristic
52	C₁₆	—	2	1	no	—
53	C₁₆	—	113	1	no	—
54	C₁₆	—	113	1	no	—
55	Q₈	—	113	1	no	—
56	D₄	—	113	1	no	—
57	D₄	—	226	1	no	—
58	C₂×C₄	—	226	1	no	—
59	C₂×C₄	#14268655	1	1	yes	characteristic
60	C₈	—	226	1	no	—
61	C₈	C₂²⋊#90673	1	1	yes	characteristic
62	C₈	#14268657	1	1	yes	characteristic
63	C₂²	—	226	1	no	—
64	C₂²	#16813697	1	1	yes	characteristic
65	C₄	—	226	1	no	—
66	C₄	#16813679	1	1	yes	characteristic
67	C₄	#16813695	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	452	1	no	—
70	C₂	#20299493	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#90673
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#90673
Fitting	M₃₂×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₂²⋊C₁₆
prime radical	#14268647	C₈
cosocle	C₂×#14268622	C₂²
hypercenter	M₃₂	#90673
hypocenter	C₁₁₃	#1401
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. #20299530	C₂	semidirect
2. C₂×#16813672	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
#20299530	2
C₂×#16813672	2
#20299016	2
#1401	113