Subgroups — #28388647

Order 14464.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14268622	C₂	1	1	yes	maximal, characteristic
2	#20298351	C₂	1	1	yes	maximal, characteristic
3	#335×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268622	C₄	1	1	yes	characteristic
5	C₂×#14268622	C₄	1	1	yes	characteristic
6	C₄⋊#11744751	—	2	1	no	—
7	C₄⋊C₈×C₁₁₃	—	2	1	no	—
8	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂×#11744751	—	4	1	no	—
10	#14268622	—	2	1	no	—
11	#14268622	C₈	1	2	yes	complemented
12	C₂×C₈×C₁₁₃	—	4	1	no	—
13	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₁₃	Q₈	1	1	yes	characteristic
15	C₄²×C₁₁₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₁₃	D₈	1	1	yes	characteristic
18	C₂×C₄×C₁₁₃	Q₁₆	1	1	yes	characteristic
19	C₈×C₁₁₃	—	2	1	no	—
20	C₈×C₁₁₃	—	8	1	no	—
21	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
22	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
23	#11744751	—	8	1	no	—
24	C₂²×C₁₁₃	#107	1	1	yes	characteristic
25	C₄×C₁₁₃	—	2	1	no	—
26	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₁₁₃	#108	1	1	yes	characteristic
28	C₄×C₁₁₃	SD₃₂	1	1	yes	characteristic
29	C₄×C₁₁₃	SD₃₂	1	1	yes	characteristic
30	C₂×C₁₁₃	#335	1	1	yes	characteristic
31	C₂×C₁₁₃	#367	1	1	yes	characteristic
32	C₂×C₁₁₃	#368	1	1	yes	characteristic
33	#1372	—	113	1	no	maximal, Sylow
34	C₁₁₃	#1372	1	1	yes	characteristic, complemented, Sylow
35	C₄×C₁₆	—	113	1	no	—
36	#335	—	113	1	no	—
37	#335	D₁₁₃	1	1	yes	characteristic
38	C₂×C₁₆	—	113	1	no	—
39	C₂×C₁₆	—	113	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	226	1	no	—
42	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	452	1	no	—
45	C₂×C₈	Dic₂₂₆	1	1	yes	characteristic
46	C₂×C₈	C₄×D₁₁₃	1	1	yes	characteristic
47	C₄²	C₂²⋊D₁₁₃	1	1	yes	characteristic
48	C₁₆	—	113	2	no	—
49	C₁₆	—	226	1	no	—
50	C₂×C₄	#14268626	1	1	yes	characteristic
51	C₂×C₄	#14268632	1	1	yes	characteristic
52	C₂×C₄	#14268637	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	904	1	no	—
56	C₈	C₈×D₁₁₃	1	1	yes	characteristic
57	C₈	#14268630	1	1	yes	characteristic
58	C₂²	#16813555	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#16813551	1	1	yes	characteristic
61	C₄	#16813557	1	1	yes	characteristic
62	C₄	#16813565	1	1	yes	characteristic
63	C₄	#16813566	1	1	yes	characteristic
64	C₂	#20298350	1	1	yes	characteristic
65	C₂	#20298425	1	1	yes	characteristic
66	C₂	#20298427	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14268632
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₁₃
Fitting	#335×C₁₁₃	C₂
socle, prime radical	C₂²×C₁₁₃	#107
cosocle	C₄×C₈×C₁₁₃	C₂²
hypercenter	#335	D₁₁₃
hypocenter	C₁₁₃	#1372
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. #14268622	C₈	semidirect
34. C₁₁₃	#1372	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14268622	2
#20298351	2
#335×C₁₁₃	2
#1372	113