Subgroups — #20299605

Order 7232.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268657	C₂	1	1	yes	maximal, characteristic
2	C₂×#14268655	C₂	1	1	yes	maximal, characteristic
3	#16813689	C₂	1	2	yes	maximal, complemented
4	C₄⋊#11744753	C₂	1	2	yes	maximal, complemented
5	#16813580	C₂	1	1	yes	maximal, characteristic
6	#14268657	—	2	2	no	—
7	#14268655	—	2	2	no	—
8	C₂×#11744753	C₂²	1	1	yes	characteristic
9	C₂×#11744753	C₂²	1	2	yes	—
10	C₂×#11744753	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₁₃	C₄	1	1	yes	characteristic
13	#14268624	C₄	1	2	yes	—
14	C₄×Dic₁₁₃	C₂²	1	2	yes	—
15	C₄⋊C₄×C₁₁₃	C₄	1	1	yes	characteristic
16	C₂²×D₁₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₁₃	C₂×C₄	1	2	yes	—
20	C₂×Dic₁₁₃	C₂³	1	1	yes	characteristic
21	C₄×D₁₁₃	D₄	1	2	yes	—
22	C₄×D₁₁₃	Q₈	1	2	yes	—
23	#11744753	—	2	1	no	—
24	#11744753	—	2	1	no	—
25	#11744753	—	2	2	no	—
26	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₁₁₃	—	2	1	no	—
28	C₂×D₁₁₃	—	2	1	no	—
29	C₂×D₁₁₃	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₁₃	—	2	2	no	—
31	C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
32	Dic₁₁₃	—	2	2	no	—
33	Dic₁₁₃	C₂×D₄	1	1	yes	characteristic
34	Dic₁₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₁₁₃	#131	1	1	yes	characteristic
37	C₂×C₁₁₃	#131	1	1	yes	characteristic
38	D₁₁₃	—	2	2	no	—
39	C₁₁₃	#424	1	1	yes	characteristic, complemented, Sylow
40	#424	—	113	1	no	maximal, Sylow
41	C₂×M₁₆	—	113	1	no	—
42	C₂²×C₈	—	113	1	no	—
43	#117	—	113	1	no	—
44	C₄⋊C₈	—	113	2	no	—
45	C₄⋊C₈	—	113	2	no	—
46	C₂²×C₄	—	113	1	no	—
47	M₁₆	—	226	2	no	—
48	C₂×C₈	—	113	1	no	—
49	C₂×C₈	—	113	1	no	—
50	C₂×C₈	—	113	2	no	—
51	C₂×C₈	—	226	2	no	—
52	C₄⋊C₄	—	113	1	no	—
53	C₄⋊C₄	#90673	1	1	yes	characteristic
54	C₂²⋊C₄	—	113	2	no	—
55	C₄²	—	113	2	no	—
56	C₂³	—	113	1	no	—
57	C₂×C₄	—	113	1	no	—
58	C₂×C₄	—	113	2	no	—
59	C₂×C₄	—	113	2	no	—
60	C₂×C₄	—	113	2	no	—
61	C₂×C₄	C₂×#90673	1	2	yes	—
62	C₂×C₄	C₂×#90673	1	1	yes	characteristic
63	C₈	—	226	1	no	—
64	C₈	—	226	1	no	—
65	C₈	—	226	2	no	—
66	C₂²	—	113	2	no	—
67	C₂²	—	226	1	no	—
68	C₂²	—	226	1	no	—
69	C₂²	C₂²×#90673	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	113	1	no	—
72	C₄	—	113	1	no	—
73	C₄	—	226	2	no	—
74	C₄	C₄⋊#90673	1	2	yes	—
75	C₂	—	226	2	no	—
76	C₂	C₂×C₄⋊#90673	1	1	yes	characteristic
77	C₂	#16813709	1	1	yes	characteristic
78	C₂	#16813710	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#90673
commutator, socle	C₂²×C₁₁₃	C₂²×C₄
Fitting	C₄⋊C₄×C₁₁₃	C₄
hypercenter	C₄⋊C₄	#90673
hypocenter	C₁₁₃	#424
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #16813689	C₂	semidirect
4. C₄⋊#11744753	C₂	semidirect
39. C₁₁₃	#424	semidirect