Subgroups — #28405724

Order 14464.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299529	C₂	1	1	yes	maximal, characteristic
2	#20299524	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#16813691	—	2	1	no	—
5	#16813672	—	2	1	no	—
6	Q₁₆×D₁₁₃	—	2	1	no	—
7	Dic₉₀₄	C₄	1	1	yes	characteristic, complemented
8	#16813568	—	2	1	no	—
9	C₁₆×D₁₁₃	C₂²	1	1	yes	characteristic
10	Q₃₂×C₁₁₃	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#90673	—	4	1	no	—
12	Q₈×D₁₁₃	—	4	1	no	—
13	Dic₄₅₂	—	2	1	no	—
14	#14268637	—	4	1	no	—
15	C₈×D₁₁₃	D₄	1	1	yes	characteristic
16	#14268622	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₁₃	—	2	1	no	—
18	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#90673	—	8	1	no	—
20	Q₈×C₁₁₃	—	4	1	no	—
21	C₄×D₁₁₃	—	8	1	no	—
22	C₄×D₁₁₃	D₈	1	1	yes	characteristic
23	Dic₂₂₆	—	4	1	no	—
24	Dic₂₂₆	—	8	1	no	—
25	C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	#11744751	SD₁₆	1	1	yes	characteristic
27	C₂×D₁₁₃	D₁₆	1	1	yes	characteristic
28	#90673	—	16	1	no	—
29	C₄×C₁₁₃	—	8	1	no	—
30	C₄×C₁₁₃	#102	1	1	yes	characteristic
31	Dic₁₁₃	—	8	1	no	—
32	Dic₁₁₃	SD₃₂	1	1	yes	characteristic
33	C₂×C₁₁₃	#357	1	1	yes	characteristic
34	D₁₁₃	SD₆₄	1	1	yes	characteristic
35	D₁₁₃	Q₆₄	1	1	yes	characteristic
36	#1416	—	113	1	no	maximal, Sylow
37	C₁₁₃	#1416	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₃₂	—	113	1	no	—
39	C₂×C₃₂	—	113	1	no	—
40	#366	—	113	1	no	—
41	C₂×Q₁₆	—	226	1	no	—
42	Q₃₂	—	113	1	no	—
43	Q₃₂	—	226	1	no	—
44	Q₃₂	#90673	1	1	yes	characteristic, complemented
45	C₂×C₁₆	—	113	1	no	—
46	#107	—	226	1	no	—
47	C₃₂	—	226	1	no	—
48	C₂×Q₈	—	452	1	no	—
49	Q₁₆	—	2	1	no	—
50	Q₁₆	—	452	1	no	—
51	Q₁₆	—	226	1	no	—
52	C₂×C₈	—	113	1	no	—
53	C₄⋊C₄	—	452	1	no	—
54	C₁₆	—	113	1	no	—
55	C₁₆	C₂×#90673	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	Q₈	—	904	1	no	—
58	Q₈	—	452	1	no	—
59	C₂×C₄	—	113	1	no	—
60	C₂×C₄	—	904	1	no	—
61	C₂×C₄	—	904	1	no	—
62	C₈	—	113	1	no	—
63	C₈	C₂²⋊#90673	1	1	yes	characteristic
64	C₂²	—	113	1	no	—
65	C₄	—	8	1	no	—
66	C₄	—	1808	1	no	—
67	C₄	—	113	1	no	—
68	C₄	—	904	1	no	—
69	C₄	#16813684	1	1	yes	characteristic
70	C₂	—	113	1	no	—
71	C₂	—	113	1	no	—
72	C₂	#20299510	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20299510
commutator	C₁₆×C₁₁₃	C₂×C₄
Frattini	C₁₆	C₂×#90673
Fitting	Q₃₂×C₁₁₃	C₄
socle	C₂×C₁₁₃	#357
prime radical	C₂×D₁₁₃	D₁₆
cosocle	C₁₆×D₁₁₃	C₂²
hypercenter	Q₃₂	#90673
hypocenter	C₁₁₃	#1416
LCS	G ▷ C₁₆×C₁₁₃ ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
7. Dic₉₀₄	C₄	semidirect
10. Q₃₂×C₁₁₃	C₄	semidirect
37. C₁₁₃	#1416	semidirect
44. Q₃₂	#90673	semidirect

Maximal subgroups

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

subgroup	index
#20299529	2
#20299524	2
Q₃₂×D₁₁₃	2
#1416	113