Subgroups — #20298898

Order 7232.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813614	C₂	1	1	yes	maximal, characteristic, complemented
2	#16813555	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813553	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊#11744751	C₂	1	1	yes	maximal, characteristic, complemented
5	#16813543	C₂	1	1	yes	maximal, characteristic
6	#16813543	C₂	1	1	yes	maximal, characteristic
7	C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11744751	C₂²	1	1	yes	characteristic
9	C₂×#11744751	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
12	#14268626	—	2	1	no	—
13	#14268626	—	2	1	no	—
14	C₂×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₁₁₃	—	2	1	no	—
16	C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²⋊C₄×C₁₁₃	—	2	1	no	—
18	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂³×C₁₁₃	—	2	1	no	—
20	D₄×C₁₁₃	—	2	1	no	—
21	D₄×C₁₁₃	Q₈	1	2	yes	—
22	C₂×C₄×C₁₁₃	—	2	1	no	—
23	C₂×C₄×C₁₁₃	—	4	2	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	#11744751	—	2	1	no	—
30	#11744751	—	2	1	no	—
31	C₂²×C₁₁₃	—	2	2	no	—
32	C₂²×C₁₁₃	—	4	1	no	—
33	C₂²×C₁₁₃	—	4	1	no	—
34	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₁₃	—	2	1	no	—
36	C₄×C₁₁₃	—	2	1	no	—
37	C₄×C₁₁₃	—	4	1	no	—
38	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₁₁₃	#41	1	1	yes	characteristic
40	Dic₁₁₃	—	4	1	no	—
41	Dic₁₁₃	—	4	1	no	—
42	C₂×C₁₁₃	—	4	2	no	—
43	C₂×C₁₁₃	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₁₁₃	#135	1	1	yes	characteristic
45	C₂×C₁₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₁₁₃	#478	1	1	yes	characteristic, complemented, Sylow
47	#478	—	113	1	no	maximal, Sylow
48	#125	—	113	1	no	—
49	C₄×D₄	D₁₁₃	1	1	yes	characteristic
50	#107	—	113	1	no	—
51	#106	—	113	1	no	—
52	C₄⋊C₈	—	113	1	no	—
53	#102	—	113	1	no	—
54	#102	—	113	1	no	—
55	C₂×D₄	C₂×D₁₁₃	1	1	yes	characteristic
56	C₂²×C₄	—	2	1	no	—
57	C₂×C₈	—	113	1	no	—
58	C₂×C₈	—	113	1	no	—
59	C₄⋊C₄	—	113	1	no	—
60	C₄⋊C₄	—	113	1	no	—
61	C₄⋊C₄	—	226	1	no	—
62	C₄⋊C₄	—	226	1	no	—
63	C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
66	C₂³	—	2	1	no	—
67	D₄	—	2	1	no	—
68	D₄	Dic₂₂₆	1	2	yes	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	226	1	no	—
72	C₂×C₄	—	226	1	no	—
73	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
76	C₈	—	226	1	no	—
77	C₈	—	226	1	no	—
78	C₂²	—	2	2	no	—
79	C₂²	—	4	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	452	1	no	—
86	C₄	—	452	1	no	—
87	C₄	C₂×Dic₂₂₆	1	1	yes	characteristic
88	C₄	#14268647	1	1	yes	characteristic
89	C₂	—	4	2	no	—
90	C₂	#16813601	1	1	yes	characteristic
91	C₂	#16813642	1	1	yes	characteristic
92	C₂	#16813648	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₁₃
commutator	C₂×C₄×C₁₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₄×D₄×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	C₄×D₄	D₁₁₃
hypocenter	C₁₁₃	#478
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #16813614	C₂	semidirect
2. #16813555	C₂	semidirect
3. #16813553	C₂	semidirect
4. C₄⋊#11744751	C₂	semidirect
46. C₁₁₃	#478	semidirect