Subgroups — #20298703

Order 7232.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268637	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic
3	#16813553	C₂	1	1	yes	maximal, characteristic
4	#16813546	C₂	1	1	yes	maximal, characteristic
5	#16813545	C₂	1	1	yes	maximal, characteristic
6	#16813533	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₂₆	C₂²	1	1	yes	characteristic
9	#14268637	C₄	1	4	yes	complemented
10	C₂×#11744751	C₂²	1	1	yes	characteristic
11	C₂×#11744751	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
13	#14268626	—	2	1	no	—
14	C₄×Dic₁₁₃	—	2	1	no	—
15	C₂×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₁₁₃	—	2	1	no	—
17	C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₄²×C₁₁₃	—	2	1	no	—
19	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
20	Q₈×C₁₁₃	—	2	1	no	—
21	Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₁₁₃	—	2	1	no	—
23	C₂×C₄×C₁₁₃	—	2	1	no	—
24	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
26	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
27	C₂×Dic₁₁₃	—	2	1	no	—
28	C₂×Dic₁₁₃	—	2	1	no	—
29	Dic₂₂₆	—	2	1	no	—
30	Dic₂₂₆	C₂×C₄	1	2	yes	—
31	#11744751	—	2	1	no	—
32	#11744751	C₂×C₄	1	2	yes	—
33	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₁₃	—	2	2	no	—
35	C₄×C₁₁₃	—	2	1	no	—
36	C₄×C₁₁₃	—	2	1	no	—
37	C₄×C₁₁₃	—	4	1	no	—
38	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₁₁₃	#41	1	1	yes	characteristic
40	Dic₁₁₃	—	2	2	no	—
41	Dic₁₁₃	—	4	1	no	—
42	C₂×C₁₁₃	C₄×D₄	1	1	yes	characteristic
43	C₂×C₁₁₃	#137	1	1	yes	characteristic
44	C₂×C₁₁₃	#137	1	1	yes	characteristic
45	C₁₁₃	#441	1	1	yes	characteristic, complemented, Sylow
46	#441	—	113	1	no	maximal, Sylow
47	C₂×Q₁₆	—	113	1	no	—
48	C₄×Q₈	—	113	1	no	—
49	C₄×Q₈	D₁₁₃	1	1	yes	characteristic
50	#106	—	113	1	no	—
51	#103	—	113	1	no	—
52	#103	—	113	1	no	—
53	#97	—	113	1	no	—
54	C₂×Q₈	—	113	1	no	—
55	C₂×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
56	Q₁₆	—	113	4	no	—
57	C₂×C₈	—	113	1	no	—
58	C₂×C₈	—	113	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	113	1	no	—
61	C₄⋊C₄	—	226	1	no	—
62	C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
63	C₄²	—	2	1	no	—
64	C₄²	—	226	1	no	—
65	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
66	Q₈	—	2	1	no	—
67	Q₈	—	113	2	no	—
68	Q₈	—	226	1	no	—
69	Q₈	C₄×D₁₁₃	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	226	1	no	—
73	C₂×C₄	—	226	1	no	—
74	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
77	C₈	—	113	2	no	—
78	C₈	—	226	1	no	—
79	C₂²	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	452	1	no	—
85	C₄	—	226	2	no	—
86	C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
87	C₄	#14268647	1	1	yes	characteristic
88	C₂	C₄×C₂²⋊D₁₁₃	1	1	yes	characteristic
89	C₂	#16813652	1	1	yes	characteristic
90	C₂	#16813653	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₁₃
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₄×Q₈×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	C₄×Q₈	D₁₁₃
hypocenter	C₁₁₃	#441
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. #14268637	C₄	semidirect
45. C₁₁₃	#441	semidirect