Subgroups — #20299557

Order 7232.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268655	C₂	1	2	yes	maximal
2	#16813677	C₂	1	4	yes	maximal, complemented
3	C₄²×D₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268655	C₄	1	8	yes	complemented
5	C₂×#11744753	C₂²	1	4	yes	—
6	C₂×C₄×D₁₁₃	C₄	1	2	yes	—
7	C₂×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
9	C₄×Dic₁₁₃	C₂²	1	2	yes	—
10	C₄²×C₁₁₃	C₄	1	1	yes	characteristic
11	C₂²×D₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₁₃	C₂×C₄	1	2	yes	—
15	C₂×Dic₁₁₃	C₂³	1	1	yes	characteristic
16	C₄×D₁₁₃	—	2	4	no	—
17	C₄×D₁₁₃	C₂×C₄	1	4	yes	—
18	#11744753	C₂×C₄	1	8	yes	complemented
19	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
20	C₂×D₁₁₃	C₄²	1	2	yes	—
21	C₂×D₁₁₃	M₁₆	1	4	yes	—
22	C₄×C₁₁₃	—	2	2	no	—
23	C₄×C₁₁₃	C₄²	1	2	yes	—
24	Dic₁₁₃	—	2	2	no	—
25	Dic₁₁₃	C₂²×C₄	1	2	yes	—
26	C₂×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₁₁₃	C₂×M₁₆	1	2	yes	—
28	D₁₁₃	#97	1	4	yes	complemented
29	C₁₁₃	C₂×#97	1	1	yes	characteristic, complemented, Sylow
30	C₂×#97	—	113	1	no	maximal, Sylow
31	C₂²×C₈	—	113	2	no	—
32	C₂×C₄²	—	113	1	no	—
33	#97	—	113	4	no	—
34	C₂²×C₄	—	113	1	no	—
35	C₂²×C₄	—	113	2	no	—
36	C₂×C₈	—	113	4	no	—
37	C₂×C₈	—	113	8	no	—
38	C₄²	—	113	2	no	—
39	C₄²	—	113	1	no	—
40	C₄²	#90673	1	1	yes	characteristic
41	C₂³	—	113	1	no	—
42	C₂×C₄	—	113	1	no	—
43	C₂×C₄	—	113	4	no	—
44	C₂×C₄	—	113	2	no	—
45	C₂×C₄	—	226	4	no	—
46	C₂×C₄	C₂×#90673	1	2	yes	—
47	C₂×C₄	C₂×#90673	1	1	yes	characteristic
48	C₈	—	113	8	no	—
49	C₂²	—	113	2	no	—
50	C₂²	—	113	4	no	—
51	C₂²	C₂²×#90673	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	—	113	2	no	—
54	C₄	—	226	2	no	—
55	C₄	C₄×#90673	1	2	yes	—
56	C₂	—	113	4	no	—
57	C₂	C₂×C₄×#90673	1	1	yes	characteristic
58	C₂	D₁₁₃⋊M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#90673
commutator	C₂×C₁₁₃	C₂×C₄²
Frattini	C₂²	C₂²×#90673
Fitting	C₄²×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₂²×C₄
hypercenter	C₄²	#90673
hypocenter	C₁₁₃	C₂×#97
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #16813677	C₂	semidirect
4. #14268655	C₄	semidirect
18. #11744753	C₂×C₄	semidirect
28. D₁₁₃	#97	semidirect
29. C₁₁₃	C₂×#97	semidirect