Subgroups — #28405642

Order 14464.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299608	C₂	1	2	yes	maximal
2	C₂×#16813561	C₂	1	1	yes	maximal, characteristic
3	#16813701	—	2	2	no	—
4	#16813691	—	2	2	no	—
5	#16813690	C₄	1	4	yes	complemented
6	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
7	#16813561	—	2	2	no	—
8	C₂×#14268622	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
10	C₄⋊#90673	—	2	4	no	—
11	C₂²⋊#90673	—	4	2	no	—
12	C₄×#90673	—	4	2	no	—
13	C₂×C₄×D₁₁₃	D₄	1	1	yes	characteristic
14	C₂×#11744751	Q₈	1	1	yes	characteristic
15	C₈×D₁₁₃	C₂×C₄	1	2	yes	—
16	C₈×D₁₁₃	D₄	1	2	yes	—
17	#14268622	—	2	1	no	—
18	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₁₃	—	2	1	no	—
20	C₂²×D₁₁₃	D₈	1	1	yes	characteristic
21	C₂×#90673	—	4	4	no	—
22	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
23	C₂×Dic₁₁₃	Q₁₆	1	1	yes	characteristic
24	C₄×D₁₁₃	C₂²⋊C₄	1	2	yes	—
25	C₄×D₁₁₃	SD₁₆	1	2	yes	—
26	C₈×C₁₁₃	C₄²	1	1	yes	characteristic
27	C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	#11744751	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₁₃	#107	1	1	yes	characteristic
30	C₂×D₁₁₃	—	4	1	no	—
31	C₂×D₁₁₃	#102	1	2	yes	—
32	#90673	—	8	4	no	—
33	C₄×C₁₁₃	#95	1	1	yes	characteristic
34	C₄×C₁₁₃	#106	1	1	yes	characteristic
35	Dic₁₁₃	#103	1	2	yes	—
36	C₂×C₁₁₃	—	2	1	no	—
37	C₂×C₁₁₃	#340	1	1	yes	characteristic
38	D₁₁₃	—	2	2	no	—
39	#1384	—	113	1	no	maximal, Sylow
40	C₁₁₃	#1384	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₃₂	—	113	1	no	—
42	#427	—	113	2	no	—
43	C₂²×C₈	—	113	1	no	—
44	#117	—	226	2	no	—
45	M₃₂	—	226	2	no	—
46	C₂×C₁₆	—	113	1	no	—
47	C₂×C₁₆	#90673	1	1	yes	characteristic, complemented
48	#107	—	226	2	no	—
49	#106	—	113	4	no	—
50	C₂²×C₄	—	113	1	no	—
51	C₂×C₈	—	113	1	no	—
52	C₂×C₈	—	113	2	no	—
53	C₂×C₈	—	113	2	no	—
54	C₂×C₈	C₂×#90673	1	1	yes	characteristic
55	C₄⋊C₄	—	226	4	no	—
56	C₂²⋊C₄	—	452	2	no	—
57	C₄²	—	452	2	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	226	1	no	—
60	C₂³	—	113	1	no	—
61	C₂×C₄	—	113	1	no	—
62	C₂×C₄	—	113	2	no	—
63	C₂×C₄	—	113	2	no	—
64	C₂×C₄	—	452	4	no	—
65	C₂×C₄	C₄⋊#90673	1	1	yes	characteristic
66	C₈	—	113	2	no	—
67	C₈	C₄×#90673	1	1	yes	characteristic
68	C₈	C₂²⋊#90673	1	1	yes	characteristic
69	C₂²	—	113	2	no	—
70	C₂²	—	452	1	no	—
71	C₂²	#16813691	1	1	yes	characteristic
72	C₄	—	113	2	no	—
73	C₄	—	904	4	no	—
74	C₄	(C₂×#90673)⋊C₄	1	1	yes	characteristic
75	C₄	#16813690	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	226	2	no	—
78	C₂	#20299472	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16813690
commutator	C₈×C₁₁₃	C₄²
Frattini	C₂×C₈	C₂×#90673
Fitting	C₂×C₁₆×C₁₁₃	C₄
socle	C₂×C₁₁₃	#340
prime radical	C₂²×D₁₁₃	D₈
cosocle	C₂×C₈×D₁₁₃	C₂²
hypercenter	C₂×C₁₆	#90673
hypocenter	C₁₁₃	#1384
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
5. #16813690	C₄	semidirect
8. C₂×#14268622	C₄	semidirect
9. C₂×C₁₆×C₁₁₃	C₄	semidirect
40. C₁₁₃	#1384	semidirect
47. C₂×C₁₆	#90673	semidirect

Maximal subgroups

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

subgroup	index
#20299608	2
C₂×#16813561	2
#1384	113