Subgroups — #28405583

Order 14464.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299521	C₂	1	2	yes	maximal
2	#20298977	C₂	1	1	yes	maximal, characteristic
3	#16813696	—	2	2	no	—
4	C₂×#14268637	—	2	2	no	—
5	#16813622	C₄	1	1	yes	characteristic
6	C₄×#11744751	C₂²	1	1	yes	characteristic
7	C₄⋊Q₈×C₁₁₃	C₄	1	1	yes	characteristic
8	#14268650	—	4	2	no	—
9	C₂×Dic₂₂₆	—	2	1	no	—
10	#14268637	—	4	2	no	—
11	#14268637	—	4	2	no	—
12	C₂×#11744751	D₄	1	2	yes	—
13	C₄⋊Dic₁₁₃	—	4	1	no	—
14	C₂×Q₈×C₁₁₃	—	2	1	no	—
15	C₄⋊C₄×C₁₁₃	—	4	1	no	—
16	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
17	Q₈×C₁₁₃	—	4	2	no	—
18	C₂×C₄×C₁₁₃	—	2	1	no	—
19	C₂×C₄×C₁₁₃	—	4	1	no	—
20	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₁₁₃	—	4	1	no	—
22	Dic₂₂₆	—	4	2	no	—
23	#11744751	D₈	1	2	yes	—
24	#11744751	SD₁₆	1	2	yes	—
25	C₂²×C₁₁₃	#100	1	1	yes	characteristic
26	C₄×C₁₁₃	—	2	2	no	—
27	C₄×C₁₁₃	—	8	1	no	—
28	C₄×C₁₁₃	#102	1	2	yes	—
29	Dic₁₁₃	—	8	1	no	—
30	C₂×C₁₁₃	—	2	1	no	—
31	C₂×C₁₁₃	#331	1	1	yes	characteristic
32	#1358	—	113	1	no	maximal, Sylow
33	C₁₁₃	#1358	1	1	yes	characteristic, complemented, Sylow
34	#494	—	113	1	no	—
35	#364	—	113	2	no	—
36	C₂×Q₁₆	—	226	2	no	—
37	C₄⋊Q₈	—	113	1	no	—
38	C₄⋊Q₈	#90673	1	1	yes	characteristic
39	M₃₂	—	226	2	no	—
40	C₄×C₈	—	113	1	no	—
41	C₂×Q₈	—	2	1	no	—
42	C₂×Q₈	—	226	1	no	—
43	Q₁₆	—	452	2	no	—
44	Q₁₆	—	452	2	no	—
45	C₂×C₈	—	113	2	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄⋊C₄	—	452	1	no	—
48	C₄²	C₂×#90673	1	1	yes	characteristic
49	C₁₆	—	452	2	no	—
50	Q₈	—	4	2	no	—
51	Q₈	—	452	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	452	1	no	—
55	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
56	C₈	—	113	2	no	—
57	C₈	—	113	2	no	—
58	C₂²	#16813682	1	1	yes	characteristic
59	C₄	—	2	2	no	—
60	C₄	—	8	1	no	—
61	C₄	—	904	1	no	—
62	C₄	#16813684	1	2	yes	—
63	C₂	—	2	1	no	—
64	C₂	#20299456	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20299456
commutator	C₄²×C₁₁₃	C₂×C₄
Frattini	C₄²	C₂×#90673
Fitting	C₄⋊Q₈×C₁₁₃	C₄
socle	C₂×C₁₁₃	#331
prime radical	C₂²×C₁₁₃	#100
cosocle	C₄×#11744751	C₂²
hypercenter	C₄⋊Q₈	#90673
hypocenter	C₁₁₃	#1358
LCS	G ▷ C₄²×C₁₁₃ ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
33. C₁₁₃	#1358	semidirect

Maximal subgroups

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

subgroup	index
#20299521	2
#20298977	2
#1358	113