Subgroups — #20298416

Order 7232.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268622	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11744751	C₄	1	1	yes	characteristic
5	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
6	#14268622	—	2	1	no	—
7	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₁₃	—	2	1	no	—
9	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₁₃	C₈	1	1	yes	characteristic
11	C₂×Dic₁₁₃	C₈	1	1	yes	characteristic
12	C₈×C₁₁₃	D₄	1	1	yes	characteristic
13	C₈×C₁₁₃	Q₈	1	1	yes	characteristic
14	#11744751	—	2	1	no	—
15	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₁₃	M₁₆	1	1	yes	characteristic
18	Dic₁₁₃	—	2	1	no	—
19	Dic₁₁₃	C₁₆	1	2	yes	complemented
20	C₂×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₁₃	M₃₂	1	1	yes	characteristic
23	C₁₁₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	113	1	no	maximal, Sylow
25	C₂×C₁₆	—	113	1	no	—
26	C₂×C₁₆	D₁₁₃	1	1	yes	characteristic
27	C₄×C₈	—	113	1	no	—
28	C₂×C₈	—	113	1	no	—
29	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
30	C₄²	—	113	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	226	1	no	—
33	C₂×C₄	—	113	1	no	—
34	C₂×C₄	—	113	1	no	—
35	C₂×C₄	C₄×D₁₁₃	1	1	yes	characteristic
36	C₈	—	226	1	no	—
37	C₈	Dic₂₂₆	1	1	yes	characteristic
38	C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
39	C₂²	C₈×D₁₁₃	1	1	yes	characteristic
40	C₄	—	113	2	no	—
41	C₄	—	226	1	no	—
42	C₄	#14268626	1	1	yes	characteristic
43	C₄	#14268630	1	1	yes	characteristic
44	C₂	#16813551	1	1	yes	characteristic
45	C₂	C₁₆×D₁₁₃	1	1	yes	characteristic
46	C₂	#16813561	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₁₃
commutator	C₂×C₁₁₃	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×C₈
hypercenter	C₂×C₁₆	D₁₁₃
hypocenter	C₁₁₃	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₁₁₃	C₁₆	semidirect
23. C₁₁₃	C₄⋊C₁₆	semidirect