Subgroups — #28390190

Order 14464.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299001	C₂	1	4	yes	maximal
2	#20298978	C₂	1	1	yes	maximal, characteristic
3	C₈×#11744751	C₂	1	1	yes	maximal, characteristic
4	#494×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₄₅₂	—	2	2	no	—
6	#16813622	C₂²	1	2	yes	—
7	#16813555	—	2	8	no	—
8	C₄×#11744751	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₁₁₃	—	2	2	no	—
10	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
11	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₂₂₆	—	2	2	no	—
13	Dic₄₅₂	—	4	4	no	—
14	C₂×#11744751	D₄	1	4	yes	—
15	C₄⋊Dic₁₁₃	—	2	4	no	—
16	C₂×Q₈×C₁₁₃	—	2	2	no	—
17	Q₁₆×C₁₁₃	—	4	4	no	—
18	C₂×C₈×C₁₁₃	D₄	1	2	yes	—
19	C₄⋊C₄×C₁₁₃	—	2	4	no	—
20	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
21	Q₈×C₁₁₃	—	4	4	no	—
22	C₂×C₄×C₁₁₃	—	4	2	no	—
23	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
24	C₂×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₁₁₃	—	4	2	no	—
26	Dic₂₂₆	—	4	4	no	—
27	C₈×C₁₁₃	D₈	1	4	yes	—
28	#11744751	Q₁₆	1	8	yes	complemented
29	C₂²×C₁₁₃	#127	1	1	yes	characteristic
30	C₄×C₁₁₃	—	8	2	no	—
31	C₄×C₁₁₃	C₂×D₈	1	2	yes	—
32	C₄×C₁₁₃	C₂×Q₁₆	1	4	yes	—
33	Dic₁₁₃	—	8	2	no	—
34	C₂×C₁₁₃	#493	1	1	yes	characteristic
35	C₂×C₁₁₃	#494	1	2	yes	—
36	#1713	—	113	1	no	maximal, Sylow
37	C₁₁₃	#1713	1	1	yes	characteristic, complemented, Sylow
38	#500	—	113	4	no	—
39	#494	—	113	1	no	—
40	#494	D₁₁₃	1	1	yes	characteristic
41	C₈²	—	113	1	no	—
42	C₂×Q₁₆	—	2	2	no	—
43	C₂×Q₁₆	—	226	2	no	—
44	C₄⋊Q₈	—	113	2	no	—
45	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	—
46	#107	—	226	8	no	—
47	C₄×C₈	—	113	2	no	—
48	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
49	C₂×Q₈	—	2	2	no	—
50	C₂×Q₈	—	226	2	no	—
51	Q₁₆	—	4	4	no	—
52	Q₁₆	—	452	4	no	—
53	C₂×C₈	—	113	4	no	—
54	C₂×C₈	C₂²⋊D₁₁₃	1	2	yes	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	—	226	4	no	—
57	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
58	Q₈	—	4	4	no	—
59	Q₈	—	452	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	452	2	no	—
62	C₂×C₄	D₄×D₁₁₃	1	2	yes	—
63	C₂×C₄	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
64	C₈	—	113	8	no	—
65	C₈	#14268632	1	4	yes	—
66	C₂²	#16813618	1	1	yes	characteristic
67	C₄	—	8	2	no	—
68	C₄	—	904	2	no	—
69	C₄	C₂×#14268632	1	2	yes	—
70	C₄	Q₁₆×D₁₁₃	1	4	yes	—
71	C₂	#20298974	1	1	yes	characteristic
72	C₂	#20298976	1	2	yes	—

	subgroup	G/H
center	C₂²	#16813618
commutator, cosocle	C₄²×C₁₁₃	C₂³
Frattini	C₄²	C₂²×D₁₁₃
Fitting	#494×C₁₁₃	C₂
socle, prime radical	C₂²×C₁₁₃	#127
hypercenter	#494	D₁₁₃
hypocenter	C₁₁₃	#1713
LCS	G ▷ C₄²×C₁₁₃ ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
28. #11744751	Q₁₆	semidirect
37. C₁₁₃	#1713	semidirect

Maximal subgroups

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

subgroup	index
#20299001	2
#20298978	2
C₈×#11744751	2
#494×C₁₁₃	2
#1713	113