Subgroups — #20298564

Order 7232.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268647	C₂	1	1	yes	maximal, characteristic
2	C₂×#14268631	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813534	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#14268647	—	2	2	no	—
6	#14268647	—	2	2	no	—
7	C₂×Dic₂₂₆	C₄	1	1	yes	characteristic
8	C₂×D₄₅₂	C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₁₁₃	C₄	1	2	yes	—
10	C₂×C₄×D₁₁₃	C₂²	1	2	yes	—
11	#14268631	—	2	2	no	—
12	C₂×#11744751	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₁₃	—	2	2	no	—
15	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
16	C₂³×C₁₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×D₁₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
20	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
21	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
22	C₂²⋊D₁₁₃	—	2	4	no	—
23	C₂×Dic₁₁₃	C₂×C₄	1	2	yes	—
24	D₄₅₂	—	2	2	no	—
25	C₄×D₁₁₃	—	2	2	no	—
26	C₄×D₁₁₃	—	2	2	no	—
27	Dic₂₂₆	—	2	2	no	—
28	C₈×C₁₁₃	—	2	2	no	—
29	#11744751	—	2	2	no	—
30	C₂²×C₁₁₃	—	2	2	no	—
31	C₂²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₁₁₃	—	2	2	no	—
34	C₂×D₁₁₃	—	2	4	no	—
35	C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
36	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
37	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
38	Dic₁₁₃	—	2	2	no	—
39	C₂×C₁₁₃	—	2	2	no	—
40	C₂×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₁₁₃	#131	1	2	yes	—
42	D₁₁₃	—	4	2	no	—
43	C₁₁₃	#408	1	1	yes	characteristic, complemented, Sylow
44	#408	—	113	1	no	maximal, Sylow
45	C₂×#41	—	113	1	no	—
46	C₂×M₁₆	—	113	1	no	—
47	C₂²×C₈	D₁₁₃	1	1	yes	characteristic, complemented
48	C₂²⋊C₈	—	113	4	no	—
49	#41	—	226	2	no	—
50	#41	—	226	2	no	—
51	C₂×Q₈	—	113	1	no	—
52	C₂×D₄	—	113	2	no	—
53	C₂×D₄	—	113	1	no	—
54	C₂²×C₄	—	113	2	no	—
55	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
56	M₁₆	—	226	2	no	—
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	—	113	2	no	—
59	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
60	C₂³	—	113	2	no	—
61	C₂³	C₄×D₁₁₃	1	1	yes	characteristic
62	Q₈	—	226	2	no	—
63	D₄	—	226	4	no	—
64	D₄	—	226	2	no	—
65	C₂×C₄	—	113	2	no	—
66	C₂×C₄	—	226	2	no	—
67	C₂×C₄	—	226	2	no	—
68	C₂×C₄	C₄×D₁₁₃	1	1	yes	characteristic
69	C₂×C₄	D₄₅₂	1	2	yes	—
70	C₂×C₄	C₂²⋊D₁₁₃	1	2	yes	—
71	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₈	—	226	2	no	—
74	C₂²	—	2	2	no	—
75	C₂²	—	226	2	no	—
76	C₂²	—	226	4	no	—
77	C₂²	#14268624	1	2	yes	—
78	C₂²	C₂×C₄×D₁₁₃	1	1	yes	characteristic
79	C₄	—	226	2	no	—
80	C₄	#14268624	1	2	yes	—
81	C₄	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
82	C₄	C₂×D₄₅₂	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	452	2	no	—
85	C₂	C₂×#14268624	1	1	yes	characteristic
86	C₂	#16813628	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₁₃
commutator, socle	C₂²×C₁₁₃	C₂²×C₄
Fitting	C₂²×C₈×C₁₁₃	C₂
hypercenter	C₂²×C₈	D₁₁₃
hypocenter	C₁₁₃	#408
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#14268631	C₂	semidirect
3. #16813534	C₂	semidirect
4. C₂²×C₈×C₁₁₃	C₂	semidirect
43. C₁₁₃	#408	semidirect
47. C₂²×C₈	D₁₁₃	semidirect