Subgroups — #28407842

Order 14464.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299727	C₂	1	2	yes	maximal
2	#20299691	C₂	1	1	yes	maximal, characteristic
3	#16813721	C₄	1	4	yes	complemented
4	#16813717	C₄	1	1	yes	characteristic
5	#16813717	C₂²	1	1	yes	characteristic
6	C₈×#90673	C₄	1	1	yes	characteristic
7	#14268659	C₈	1	2	yes	—
8	#14268659	C₂×C₄	1	2	yes	—
9	#14268655	C₂×C₄	1	1	yes	characteristic
10	C₄×#90673	C₈	1	1	yes	characteristic
11	C₈×D₁₁₃	C₈	1	1	yes	characteristic
12	C₂×#90673	C₁₆	1	2	yes	—
13	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
14	#11744753	C₄²	1	1	yes	characteristic
15	#11744753	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₁₃	C₁₆	1	1	yes	characteristic
17	#11744751	C₁₆	1	1	yes	characteristic
18	C₂×D₁₁₃	C₂×C₁₆	1	1	yes	characteristic
19	#90673	C₃₂	1	4	yes	complemented
20	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
21	Dic₁₁₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₁₁₃	C₄×C₁₆	1	1	yes	characteristic
23	D₁₁₃	C₂×C₃₂	1	2	yes	—
24	C₄×C₃₂	—	113	1	no	maximal, Sylow
25	C₁₁₃	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃₂	—	113	2	no	—
27	C₄×C₁₆	—	113	1	no	—
28	C₂×C₁₆	—	113	1	no	—
29	C₂×C₁₆	—	113	1	no	—
30	C₄×C₈	—	113	1	no	—
31	C₃₂	—	113	4	no	—
32	C₂×C₈	—	113	1	no	—
33	C₂×C₈	—	113	1	no	—
34	C₄²	—	113	1	no	—
35	C₁₆	—	113	2	no	—
36	C₁₆	—	113	2	no	—
37	C₂×C₄	—	113	2	no	—
38	C₂×C₄	—	113	1	no	—
39	C₈	—	113	1	no	—
40	C₈	—	113	1	no	—
41	C₈	—	113	1	no	—
42	C₈	#14268661	1	1	yes	characteristic
43	C₂²	—	113	1	no	—
44	C₄	—	113	4	no	—
45	C₄	—	113	1	no	—
46	C₄	C₂×#14268661	1	1	yes	characteristic
47	C₂	—	113	2	no	—
48	C₂	C₄×#14268661	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	#14268661
commutator, hypocenter	C₁₁₃	C₄×C₃₂
Frattini	C₄	C₂×#14268661
Fitting	C₈×C₁₁₃	C₁₆
socle	C₂×C₁₁₃	C₄×C₁₆
prime radical	C₂×D₁₁₃	C₂×C₁₆
cosocle	#16813717	C₂²
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
3. #16813721	C₄	semidirect
19. #90673	C₃₂	semidirect
25. C₁₁₃	C₄×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
#20299727	2
#20299691	2
C₄×C₃₂	113