Subgroups — #21460742

Order 7808.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#11758187	C₂	1	2	yes	maximal, complemented
2	#16839730	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758187	—	2	2	no	—
4	C₂×#11758222	C₄	1	1	yes	characteristic
5	C₂²×#92418	C₂²	1	1	yes	characteristic
6	#14519689	—	2	2	no	—
7	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₆₁	—	2	1	no	—
10	#11758222	—	4	1	no	—
11	#11758222	—	4	1	no	—
12	C₂×D₂₄₄	C₈	1	1	yes	characteristic
13	C₂×C₄×D₆₁	—	2	1	no	—
14	C₂×Dic₁₂₂	C₈	1	1	yes	characteristic
15	M₁₆×C₆₁	—	4	1	no	—
16	C₂×C₈×C₆₁	—	2	1	no	—
17	C₂×#92418	—	4	1	no	—
18	C₂×#92418	D₄	1	2	yes	—
19	#11758187	—	4	2	no	—
20	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
21	C₂²×D₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
26	C₂²⋊D₆₁	—	4	2	no	—
27	C₂×Dic₆₁	—	2	1	no	—
28	D₂₄₄	—	4	1	no	—
29	C₄×D₆₁	—	4	1	no	—
30	C₄×D₆₁	—	4	1	no	—
31	Dic₁₂₂	—	4	1	no	—
32	C₈×C₆₁	—	4	1	no	—
33	#92418	—	2	2	no	—
34	C₂²×C₆₁	—	2	1	no	—
35	C₂²×C₆₁	—	2	2	no	—
36	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₆₁	—	4	1	no	—
38	C₂×D₆₁	—	4	2	no	—
39	C₄×C₆₁	—	2	1	no	—
40	C₄×C₆₁	#99	1	1	yes	characteristic
41	C₄×C₆₁	#100	1	1	yes	characteristic
42	Dic₆₁	—	4	1	no	—
43	#1315	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	—	4	1	no	—
45	C₂×C₆₁	#323	1	1	yes	characteristic
46	C₂×C₆₁	#350	1	2	yes	—
47	D₆₁	—	8	1	no	—
48	#408	—	61	1	no	—
49	C₂²⋊C₁₆	—	61	2	no	—
50	C₆₁	#1315	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	—	61	1	no	—
52	C₂×M₁₆	#6923	1	1	yes	characteristic
53	C₂²×C₈	—	61	1	no	—
54	C₂×C₁₆	—	122	2	no	—
55	C₂²⋊C₈	—	122	2	no	—
56	#41	—	244	1	no	—
57	#41	—	244	1	no	—
58	C₂×Q₈	—	61	1	no	—
59	C₂×D₄	—	61	1	no	—
60	C₂×D₄	—	122	1	no	—
61	C₂²×C₄	—	122	1	no	—
62	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
63	M₁₆	—	4	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	61	2	no	—
66	C₂×C₈	—	244	1	no	—
67	C₁₆	—	244	2	no	—
68	C₂³	—	122	1	no	—
69	C₂³	#11758213	1	1	yes	characteristic
70	Q₈	—	244	1	no	—
71	D₄	—	244	1	no	—
72	D₄	—	244	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	122	1	no	—
76	C₂×C₄	—	244	1	no	—
77	C₂×C₄	—	244	1	no	—
78	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	122	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	244	1	no	—
85	C₂²	—	244	2	no	—
86	C₂²	#14519834	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	244	1	no	—
89	C₄	#14519836	1	1	yes	characteristic
90	C₄	#14519837	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	488	1	no	—
93	C₂	#16840606	1	1	yes	characteristic
94	C₂	#16840661	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×M₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#1315
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#11758187	C₂	semidirect
50. C₆₁	#1315	semidirect