Subgroups — #28407839

Order 14464.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14268661	C₂	1	2	yes	maximal
2	C₈×#11744762	C₂	1	1	yes	maximal, characteristic
3	C₂×#14268661	—	2	2	no	—
4	C₄×#11744762	C₄	1	1	yes	characteristic
5	C₄×#11744762	C₂²	1	1	yes	characteristic
6	C₈×#90673	C₄	1	1	yes	characteristic
7	#14268661	—	4	2	no	—
8	C₂×#11744762	—	2	1	no	—
9	C₂×#11744762	D₄	1	1	yes	characteristic
10	C₂×#11744762	Q₈	1	1	yes	characteristic
11	#14268655	C₈	1	1	yes	characteristic
12	C₄×#90673	C₂×C₄	1	1	yes	characteristic
13	C₈×D₁₁₃	C₈	1	1	yes	characteristic
14	C₂×#90673	C₄⋊C₄	1	1	yes	characteristic
15	C₂×#90673	M₁₆	1	1	yes	characteristic
16	#11744762	—	2	2	no	—
17	#11744762	—	2	1	no	—
18	#11744762	D₈	1	1	yes	characteristic
19	#11744762	Q₁₆	1	1	yes	characteristic
20	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
21	#11744753	—	2	1	no	—
22	C₈×C₁₁₃	C₁₆	1	1	yes	characteristic, complemented
23	#11744751	C₁₆	1	1	yes	characteristic, complemented
24	C₂×D₁₁₃	C₄⋊C₈	1	1	yes	characteristic
25	#90673	—	2	1	no	—
26	#90673	#107	1	1	yes	characteristic
27	#90673	#108	1	1	yes	characteristic
28	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
29	Dic₁₁₃	M₃₂	1	1	yes	characteristic
30	C₂×C₁₁₃	C₄⋊C₁₆	1	1	yes	characteristic
31	D₁₁₃	#335	1	1	yes	characteristic
32	D₁₁₃	#364	1	1	yes	characteristic
33	#1370	—	113	1	no	maximal, Sylow
34	C₁₁₃	#1370	1	1	yes	characteristic, complemented, Sylow
35	C₄⋊C₁₆	—	113	2	no	—
36	C₈²	—	113	1	no	—
37	C₂×C₁₆	—	226	2	no	—
38	C₄×C₈	—	113	1	no	—
39	C₄×C₈	—	113	1	no	—
40	C₄×C₈	—	113	1	no	—
41	C₂×C₈	—	113	1	no	—
42	C₂×C₈	—	113	1	no	—
43	C₂×C₈	—	113	1	no	—
44	C₂×C₈	—	113	1	no	—
45	C₂×C₈	—	226	1	no	—
46	C₄²	—	113	1	no	—
47	C₁₆	—	452	2	no	—
48	C₂×C₄	—	113	1	no	—
49	C₂×C₄	—	113	1	no	—
50	C₂×C₄	—	113	1	no	—
51	C₈	—	113	1	no	—
52	C₈	—	113	1	no	—
53	C₈	—	113	1	no	—
54	C₈	—	226	1	no	—
55	C₈	—	226	1	no	—
56	C₈	—	226	2	no	—
57	C₈	#14268661	1	1	yes	characteristic, complemented
58	C₂²	—	113	1	no	—
59	C₄	—	113	1	no	—
60	C₄	—	113	1	no	—
61	C₄	—	113	1	no	—
62	C₄	—	226	1	no	—
63	C₄	C₂×#14268661	1	1	yes	characteristic
64	C₂	—	113	1	no	—
65	C₂	—	113	1	no	—
66	C₂	C₄⋊#14268661	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₄⋊#14268661
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₄	C₂×#14268661
Fitting	C₈×C₁₁₃	C₁₆
socle	C₂×C₁₁₃	C₄⋊C₁₆
prime radical	C₂×D₁₁₃	C₄⋊C₈
cosocle	C₄×#11744762	C₂²
hypercenter	C₈	#14268661
hypocenter	C₁₁₃	#1370
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
22. C₈×C₁₁₃	C₁₆	semidirect
23. #11744751	C₁₆	semidirect
34. C₁₁₃	#1370	semidirect
57. C₈	#14268661	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14268661	2
C₈×#11744762	2
#1370	113