Subgroups — #20299618

Order 7232.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813689	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11744753	C₂	1	2	yes	maximal
3	#16813677	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11744753	C₂²	1	4	yes	—
6	C₂²×Dic₁₁₃	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₁₃	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
9	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
10	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
11	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₁₁₃	C₄	1	1	yes	characteristic
13	C₂³×C₁₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	—	2	2	no	—
15	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₁₃	—	2	2	no	—
18	C₂×Dic₁₁₃	—	2	2	no	—
19	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₁₁₃	C₂³	1	1	yes	characteristic
23	#11744753	—	2	4	no	—
24	C₂²×C₁₁₃	—	2	1	no	—
25	C₂²×C₁₁₃	—	2	1	no	—
26	C₂²×C₁₁₃	M₁₆	1	2	yes	—
27	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₁₁₃	—	2	1	no	—
29	C₄×C₁₁₃	—	2	1	no	—
30	Dic₁₁₃	—	2	1	no	—
31	Dic₁₁₃	—	2	1	no	—
32	Dic₁₁₃	M₁₆	1	2	yes	—
33	Dic₁₁₃	#41	1	2	yes	—
34	C₂×C₁₁₃	—	2	2	no	—
35	C₂×C₁₁₃	#117	1	1	yes	characteristic
36	C₂×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
38	C₁₁₃	#432	1	1	yes	characteristic, complemented, Sylow
39	#432	—	113	1	no	maximal, Sylow
40	C₂×C₄²	—	113	1	no	—
41	C₄⋊C₈	—	113	2	no	—
42	C₂²⋊C₈	—	113	2	no	—
43	#97	—	113	2	no	—
44	C₂²×C₄	—	113	1	no	—
45	C₂²×C₄	—	113	1	no	—
46	C₂²×C₄	#90673	1	1	yes	characteristic
47	C₂×C₈	—	113	4	no	—
48	C₄²	—	113	1	no	—
49	C₄²	—	113	1	no	—
50	C₄²	—	113	1	no	—
51	C₄²	—	113	1	no	—
52	C₂³	C₂×#90673	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	113	1	no	—
55	C₂×C₄	—	113	1	no	—
56	C₂×C₄	—	113	1	no	—
57	C₂×C₄	—	113	1	no	—
58	C₂×C₄	—	226	2	no	—
59	C₂×C₄	—	226	2	no	—
60	C₂×C₄	C₂×#90673	1	1	yes	characteristic
61	C₂×C₄	C₂×#90673	1	1	yes	characteristic
62	C₈	—	226	4	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	2	1	no	—
65	C₂²	#14268656	1	2	yes	—
66	C₂²	C₂²×#90673	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	2	1	no	—
69	C₄	—	113	2	no	—
70	C₄	—	113	2	no	—
71	C₄	—	226	1	no	—
72	C₄	—	226	1	no	—
73	C₂	—	2	2	no	—
74	C₂	#16813701	1	1	yes	characteristic
75	C₂	C₂×#14268656	1	1	yes	characteristic
76	C₂	D₁₁₃⋊M₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#90673
commutator, socle	C₂²×C₁₁₃	C₂²×C₄
Fitting	C₂²×C₄×C₁₁₃	C₄
hypercenter	C₂²×C₄	#90673
hypocenter	C₁₁₃	#432
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #16813689	C₂	semidirect
3. #16813677	C₂	semidirect
38. C₁₁₃	#432	semidirect