Subgroups — #21443760

Order 7808.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839788	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#11758185	C₂	1	1	yes	maximal, characteristic
3	C₆₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758194	C₄	1	1	yes	characteristic
5	#14519736	C₄	1	1	yes	characteristic
6	C₂×#11758185	—	2	1	no	—
7	#14519706	—	2	1	no	—
8	#14519706	—	2	1	no	—
9	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₆₁	—	2	1	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₆₁	—	4	1	no	—
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
15	C₂²⋊Dic₆₁	—	2	1	no	—
16	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
17	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
18	C₄×Dic₆₁	—	2	1	no	—
19	#11758194	—	4	1	no	—
20	C₂×#92418	—	2	1	no	—
21	C₁₆×C₆₁	—	4	1	no	—
22	#11758185	—	4	1	no	—
23	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₆₁	—	2	1	no	—
25	C₂×C₄×C₆₁	—	2	1	no	—
26	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₆₁	—	2	1	no	—
29	C₂×Dic₆₁	—	2	1	no	—
30	C₈×C₆₁	—	2	1	no	—
31	C₈×C₆₁	—	2	1	no	—
32	#92418	—	4	1	no	—
33	C₂²×C₆₁	—	2	1	no	—
34	C₂²×C₆₁	—	2	1	no	—
35	C₂²×C₆₁	—	2	1	no	—
36	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₆₁	—	2	1	no	—
38	C₄×C₆₁	#99	1	1	yes	characteristic
39	C₄×C₆₁	#101	1	1	yes	characteristic
40	Dic₆₁	—	4	1	no	—
41	Dic₆₁	—	4	1	no	—
42	#1323	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	—	4	1	no	—
44	C₂×C₆₁	#324	1	1	yes	characteristic
45	C₂×C₆₁	#350	1	1	yes	characteristic
46	C₂×C₆₁	#350	1	1	yes	characteristic
47	#424	—	61	1	no	—
48	C₂²⋊C₁₆	—	61	1	no	—
49	C₂²⋊C₁₆	D₆₁	1	1	yes	characteristic
50	C₆₁	#1323	1	1	yes	characteristic, complemented, Sylow
51	C₂×M₁₆	—	61	1	no	—
52	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
53	#117	—	61	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	C₂×C₁₆	—	122	1	no	—
56	C₄⋊C₈	—	122	1	no	—
57	C₄⋊C₈	—	122	1	no	—
58	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
59	M₁₆	—	244	1	no	—
60	C₂×C₈	—	4	1	no	—
61	C₂×C₈	—	122	1	no	—
62	C₂×C₈	D₂₄₄	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
64	C₄⋊C₄	—	61	1	no	—
65	C₄⋊C₄	—	61	1	no	—
66	C₂²⋊C₄	—	122	1	no	—
67	C₄²	—	122	1	no	—
68	C₁₆	—	4	1	no	—
69	C₁₆	—	244	1	no	—
70	C₂³	#11758189	1	1	yes	characteristic
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	122	1	no	—
74	C₂×C₄	—	122	1	no	—
75	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
76	C₂×C₄	#11758198	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	244	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#14519689	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	244	1	no	—
86	C₄	—	244	1	no	—
87	C₄	#14519691	1	1	yes	characteristic
88	C₄	#14519695	1	1	yes	characteristic
89	C₂	—	4	1	no	—
90	C₂	#16839487	1	1	yes	characteristic
91	C₂	#16839545	1	1	yes	characteristic
92	C₂	#16839547	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11758198
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₈	C₂×D₆₁
Fitting	C₆₁×C₂²⋊C₁₆	C₂
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₂²⋊C₁₆	D₆₁
hypocenter	C₆₁	#1323
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
50. C₆₁	#1323	semidirect