Subgroups — #28407808

Order 14464.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299707	C₂	1	2	yes	maximal, complemented
2	#20299706	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299705	C₂	1	2	yes	maximal, complemented
4	C₂×#16813712	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299657	C₂	1	1	yes	maximal, characteristic
6	#16813712	C₂²	1	1	yes	characteristic
7	#16813712	C₂²	1	1	yes	characteristic
8	#16813712	C₂²	1	2	yes	—
9	#16813697	C₄	1	2	yes	—
10	#16813696	C₄	1	1	yes	characteristic
11	#16813695	C₂²	1	2	yes	—
12	C₂×#14268650	C₂²	1	1	yes	characteristic
13	#16813630	C₄	1	1	yes	characteristic
14	#14268650	C₂×C₄	1	1	yes	characteristic
15	#14268650	C₂×C₄	1	2	yes	—
16	#14268650	C₂³	1	1	yes	characteristic
17	#14268647	C₈	1	1	yes	characteristic
18	#14268630	C₈	1	2	yes	—
19	C₂×#11744751	C₂×C₄	1	1	yes	characteristic
20	C₈×D₁₁₃	C₂×C₄	1	2	yes	—
21	M₁₆×C₁₁₃	C₈	1	1	yes	characteristic
22	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₁₁₃	C₁₆	1	2	yes	—
24	D₄₅₂	C₁₆	1	1	yes	characteristic
25	C₄×D₁₁₃	C₂×C₈	1	2	yes	—
26	Dic₂₂₆	C₁₆	1	1	yes	characteristic
27	C₈×C₁₁₃	C₂×C₈	1	2	yes	—
28	#11744751	C₂×C₈	1	1	yes	characteristic
29	#11744751	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₁₁₃	C₂×C₁₆	1	2	yes	—
32	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
34	Dic₁₁₃	C₂×C₁₆	1	2	yes	—
35	C₂×C₁₁₃	—	2	1	no	—
36	C₂×C₁₁₃	C₂²×C₁₆	1	1	yes	characteristic
37	D₁₁₃	—	2	2	no	—
38	#2258	—	113	1	no	maximal, Sylow
39	C₁₁₃	#2258	1	1	yes	characteristic, complemented, Sylow
40	#504	—	113	1	no	—
41	M₆₄	—	113	1	no	—
42	M₆₄	—	113	2	no	—
43	C₂×C₃₂	—	113	1	no	—
44	C₂×C₃₂	—	113	2	no	—
45	#131	—	113	1	no	—
46	M₃₂	—	113	1	no	—
47	M₃₂	—	113	2	no	—
48	C₂×C₁₆	—	113	1	no	—
49	C₂×C₁₆	—	113	2	no	—
50	C₃₂	—	113	1	no	—
51	C₃₂	—	113	1	no	—
52	C₃₂	—	113	2	no	—
53	#41	—	113	1	no	—
54	M₁₆	—	113	2	no	—
55	M₁₆	#11744762	1	1	yes	characteristic
56	C₂×C₈	—	113	1	no	—
57	C₂×C₈	—	113	2	no	—
58	C₁₆	—	113	1	no	—
59	C₁₆	—	113	1	no	—
60	C₁₆	—	113	2	no	—
61	Q₈	—	113	1	no	—
62	D₄	—	113	2	no	—
63	D₄	—	113	1	no	—
64	C₂×C₄	—	113	2	no	—
65	C₂×C₄	C₂×#11744762	1	1	yes	characteristic
66	C₈	—	113	1	no	—
67	C₈	—	113	1	no	—
68	C₈	C₂×#11744762	1	2	yes	—
69	C₂²	—	113	2	no	—
70	C₂²	#16813717	1	1	yes	characteristic
71	C₄	—	113	2	no	—
72	C₄	#16813717	1	1	yes	characteristic
73	C₄	C₂²×#11744762	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	226	2	no	—
76	C₂	C₂×#16813717	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#11744762
commutator, socle	C₂×C₁₁₃	C₂²×C₁₆
Fitting	M₁₆×C₁₁₃	C₈
prime radical	#14268647	C₈
cosocle	#14268650	C₂³
hypercenter	M₁₆	#11744762
hypocenter	C₁₁₃	#2258
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #20299707	C₂	semidirect
2. #20299706	C₂	semidirect
3. #20299705	C₂	semidirect
4. C₂×#16813712	C₂	semidirect
39. C₁₁₃	#2258	semidirect

Maximal subgroups

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

subgroup	index
#20299707	2
#20299706	2
#20299705	2
C₂×#16813712	2
#20299657	2
#2258	113