Subgroups — #28392867

Order 14464.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299014	C₂	1	1	yes	maximal, characteristic
2	#20298432	C₂	1	1	yes	maximal, characteristic, complemented
3	#20298431	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₁₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₂×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#16813628	C₄	1	1	yes	characteristic
7	#16813562	C₄	1	1	yes	characteristic
8	#16813561	C₄	1	2	yes	—
9	C₁₆×D₁₁₃	C₂²	1	2	yes	—
10	#16813528	C₂²	1	2	yes	—
11	C₂×C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₃₂×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₃₂×C₁₁₃	C₂²	1	1	yes	characteristic
14	#14268647	C₈	1	1	yes	characteristic
15	#14268631	C₈	1	1	yes	characteristic
16	#14268630	C₈	1	2	yes	—
17	C₈×D₁₁₃	C₂×C₄	1	2	yes	—
18	#14268622	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
21	C₁₆×C₁₁₃	C₂³	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	1	yes	characteristic
28	C₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
29	#11744751	C₂×C₈	1	2	yes	—
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	2	no	—
44	C₂×C₃₂	D₁₁₃	1	1	yes	characteristic, complemented
45	#131	—	113	1	no	—
46	M₃₂	—	113	1	no	—
47	M₃₂	—	113	2	no	—
48	C₂×C₁₆	—	113	2	no	—
49	C₂×C₁₆	C₂×D₁₁₃	1	1	yes	characteristic
50	C₃₂	—	113	2	no	—
51	C₃₂	C₂×D₁₁₃	1	1	yes	characteristic
52	C₃₂	C₂×D₁₁₃	1	1	yes	characteristic
53	#41	—	113	1	no	—
54	M₁₆	—	113	1	no	—
55	M₁₆	—	113	2	no	—
56	C₂×C₈	—	113	2	no	—
57	C₂×C₈	C₄×D₁₁₃	1	1	yes	characteristic
58	C₁₆	—	113	2	no	—
59	C₁₆	C₄×D₁₁₃	1	1	yes	characteristic
60	C₁₆	C₂²×D₁₁₃	1	1	yes	characteristic
61	Q₈	—	113	1	no	—
62	D₄	—	113	2	no	—
63	D₄	—	113	1	no	—
64	C₂×C₄	—	113	2	no	—
65	C₂×C₄	C₈×D₁₁₃	1	1	yes	characteristic
66	C₈	—	113	2	no	—
67	C₈	C₈×D₁₁₃	1	1	yes	characteristic
68	C₈	C₂×C₄×D₁₁₃	1	1	yes	characteristic
69	C₂²	—	113	2	no	—
70	C₂²	C₁₆×D₁₁₃	1	1	yes	characteristic
71	C₄	—	113	2	no	—
72	C₄	C₁₆×D₁₁₃	1	1	yes	characteristic
73	C₄	C₂×C₈×D₁₁₃	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	226	2	no	—
76	C₂	C₂×C₁₆×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂×D₁₁₃
commutator, socle	C₂×C₁₁₃	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₁₃
Fitting	C₂×C₃₂×C₁₁₃	C₂
prime radical	#14268647	C₈
cosocle	C₁₆×C₁₁₃	C₂³
hypercenter	C₂×C₃₂	D₁₁₃
hypocenter	C₁₁₃	#2258
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #20298432	C₂	semidirect
3. #20298431	C₂	semidirect
4. C₃₂×D₁₁₃	C₂	semidirect
5. C₂×C₃₂×C₁₁₃	C₂	semidirect
39. C₁₁₃	#2258	semidirect
44. C₂×C₃₂	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299014	2
#20298432	2
#20298431	2
C₃₂×D₁₁₃	2
C₂×C₃₂×C₁₁₃	2
#2258	113