Subgroups — #20299519

Order 7232.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268650	C₂	1	2	yes	maximal
2	C₈×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#14268650	—	2	2	no	—
4	C₂×#11744751	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₁₃	C₈	1	1	yes	characteristic
9	C₂×Dic₁₁₃	C₈	1	1	yes	characteristic
10	C₈×C₁₁₃	—	2	1	no	—
11	#11744751	D₄	1	1	yes	characteristic
12	#11744751	Q₈	1	1	yes	characteristic
13	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₁₃	M₁₆	1	1	yes	characteristic
16	Dic₁₁₃	—	2	1	no	—
17	Dic₁₁₃	C₁₆	1	2	yes	complemented
18	C₂×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₁₃	M₃₂	1	1	yes	characteristic
21	C₁₁₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	113	1	no	maximal, Sylow
23	C₂×C₁₆	—	113	2	no	—
24	C₄×C₈	—	113	1	no	—
25	C₂×C₈	—	113	1	no	—
26	C₂×C₈	#90673	1	1	yes	characteristic
27	C₄²	—	113	1	no	—
28	C₁₆	—	226	2	no	—
29	C₂×C₄	—	113	1	no	—
30	C₂×C₄	—	113	1	no	—
31	C₂×C₄	C₂×#90673	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	113	1	no	—
34	C₈	—	113	1	no	—
35	C₂²	#14268655	1	1	yes	characteristic
36	C₄	—	113	2	no	—
37	C₄	—	226	1	no	—
38	C₄	C₄⋊#90673	1	1	yes	characteristic
39	C₄	#14268656	1	1	yes	characteristic
40	C₂	#16813689	1	1	yes	characteristic
41	C₂	#16813695	1	1	yes	characteristic
42	C₂	#16813697	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#90673
commutator	C₂×C₁₁₃	C₂×C₁₆
Fitting	C₂×C₈×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₂×C₈
hypercenter	C₂×C₈	#90673
hypocenter	C₁₁₃	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
17. Dic₁₁₃	C₁₆	semidirect
21. C₁₁₃	C₄⋊C₁₆	semidirect