Subgroups — #20299507

Order 7232.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813683	C₂	1	2	yes	maximal, complemented
2	#16813610	C₂	1	1	yes	maximal, characteristic
3	#14268656	—	2	2	no	—
4	C₂×Dic₂₂₆	C₂²	1	1	yes	characteristic
5	C₂×D₄₅₂	C₄	1	1	yes	characteristic
6	#14268624	—	2	2	no	—
7	C₄²×C₁₁₃	C₄	1	1	yes	characteristic
8	C₂²×D₁₁₃	—	2	1	no	—
9	C₂×C₄×C₁₁₃	—	2	1	no	—
10	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₁₁₃	D₄	1	2	yes	—
12	D₄₅₂	—	4	1	no	—
13	Dic₂₂₆	—	4	1	no	—
14	#11744753	—	4	2	no	—
15	C₂²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₁₁₃	—	4	2	no	—
17	C₂×D₁₁₃	—	4	1	no	—
18	C₄×C₁₁₃	—	2	1	no	—
19	C₄×C₁₁₃	—	4	1	no	—
20	Dic₁₁₃	—	2	2	no	—
21	C₂×C₁₁₃	—	2	1	no	—
22	C₂×C₁₁₃	#99	1	1	yes	characteristic
23	D₁₁₃	—	8	1	no	—
24	C₁₁₃	#355	1	1	yes	characteristic, complemented, Sylow
25	#355	—	113	1	no	maximal, Sylow
26	#124	—	113	1	no	—
27	#101	—	113	2	no	—
28	C₂×Q₈	—	113	1	no	—
29	C₂×D₄	—	113	1	no	—
30	M₁₆	—	226	2	no	—
31	C₂²⋊C₄	—	226	2	no	—
32	C₄²	#90673	1	1	yes	characteristic
33	C₂³	—	226	1	no	—
34	Q₈	—	452	1	no	—
35	D₄	—	452	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	113	2	no	—
38	C₂×C₄	C₂×#90673	1	1	yes	characteristic
39	C₈	—	452	2	no	—
40	C₂²	—	452	2	no	—
41	C₂²	—	452	1	no	—
42	C₂²	C₂²⋊#90673	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	226	2	no	—
46	C₂	—	2	1	no	—
47	C₂	—	904	1	no	—
48	C₂	#16813681	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16813683	C₂	semidirect
24. C₁₁₃	#355	semidirect