Subgroups — #21460787

Order 7808.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11758187	C₂	1	1	yes	maximal, characteristic
2	#16840650	C₂	1	1	yes	maximal, characteristic
3	#16839893	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	—	2	1	no	—
5	C₂×#11758187	—	2	1	no	—
6	C₄⋊#92418	—	2	1	no	—
7	C₄⋊#92418	C₄	1	1	yes	characteristic
8	#14519688	—	2	1	no	—
9	C₄×#92418	C₂²	1	1	yes	characteristic
10	C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₆₁	C₈	1	1	yes	characteristic
12	C₄⋊C₄×C₆₁	—	2	1	no	—
13	C₄⋊C₄×C₆₁	C₈	1	1	yes	characteristic
14	C₄²×C₆₁	—	2	1	no	—
15	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×#92418	—	2	1	no	—
17	C₂×#92418	D₄	1	1	yes	characteristic
18	C₂×#92418	D₄	1	1	yes	characteristic
19	#11758187	—	2	2	no	—
20	#11758187	—	4	1	no	—
21	Q₈×C₆₁	—	4	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	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
27	#92418	—	2	1	no	—
28	#92418	—	4	1	no	—
29	#92418	SD₁₆	1	1	yes	characteristic
30	#92418	Q₁₆	1	1	yes	characteristic
31	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₆₁	—	2	1	no	—
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	—	4	1	no	—
35	C₄×C₆₁	—	4	1	no	—
36	C₄×C₆₁	#103	1	1	yes	characteristic
37	C₄×C₆₁	#104	1	1	yes	characteristic
38	#1338	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	Q₈⋊C₈	1	1	yes	characteristic
40	C₂×C₆₁	#349	1	1	yes	characteristic
41	C₂×C₆₁	#350	1	1	yes	characteristic
42	#446	—	61	1	no	—
43	C₄⋊C₁₆	—	61	1	no	—
44	#346	—	61	1	no	—
45	C₆₁	#1338	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₈	#6923	1	1	yes	characteristic
47	C₂×C₁₆	—	122	1	no	—
48	C₂×C₁₆	—	122	1	no	—
49	C₄⋊C₈	—	61	1	no	—
50	C₄⋊C₈	—	122	1	no	—
51	#97	—	122	1	no	—
52	C₄×C₈	—	61	1	no	—
53	C₂×Q₈	#92420	1	1	yes	characteristic
54	C₂×C₈	—	61	1	no	—
55	C₂×C₈	—	61	1	no	—
56	C₂×C₈	—	122	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	#92420	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×#6923	1	1	yes	characteristic
61	C₁₆	—	122	2	no	—
62	C₁₆	—	244	1	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂×#92420	1	1	yes	characteristic
67	C₂×C₄	#11758217	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
69	C₈	—	61	1	no	—
70	C₈	—	61	1	no	—
71	C₈	—	122	1	no	—
72	C₈	—	244	1	no	—
73	C₂²	C₂²⋊#92420	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#14519840	1	1	yes	characteristic
79	C₄	#14519842	1	1	yes	characteristic
80	C₂	Q₈⋊#92420	1	1	yes	characteristic
81	C₂	#16840658	1	1	yes	characteristic
82	C₂	#16840660	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₄²	C₂×#6923
Fitting	C₄×Q₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₄×Q₈	#6923
hypocenter	C₆₁	#1338
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
45. C₆₁	#1338	semidirect