Subgroups — #21460786

Order 7808.

94 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	C₄×#11758187	C₂	1	1	yes	maximal, characteristic
3	#16839886	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	—	2	1	no	—
5	C₂×#11758187	—	2	1	no	—
6	C₄×Dic₁₂₂	C₄	1	1	yes	characteristic
7	#14519706	—	2	1	no	—
8	C₄×#92418	C₂²	1	1	yes	characteristic
9	C₈×Dic₆₁	—	2	1	no	—
10	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
11	C₂×Dic₁₂₂	C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	—	2	1	no	—
13	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
15	#11758196	—	2	1	no	—
16	C₄×Dic₆₁	—	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	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
24	C₂×Dic₆₁	—	2	1	no	—
25	C₂×Dic₆₁	—	2	1	no	—
26	Dic₁₂₂	—	2	1	no	—
27	Dic₁₂₂	C₁₆	1	2	yes	complemented
28	C₈×C₆₁	—	4	1	no	—
29	#92418	—	2	1	no	—
30	#92418	SD₁₆	1	1	yes	characteristic
31	#92418	Q₁₆	1	1	yes	characteristic
32	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	#103	1	1	yes	characteristic
35	C₄×C₆₁	#104	1	1	yes	characteristic
36	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₆₁	M₃₂	1	1	yes	characteristic
38	Dic₆₁	—	2	2	no	—
39	Dic₆₁	—	4	1	no	—
40	Q₈⋊C₁₆	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	Q₈⋊C₈	1	1	yes	characteristic
42	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₂×C₆₁	#350	1	1	yes	characteristic
44	C₈×Q₈	—	61	1	no	—
45	C₄⋊C₁₆	—	61	1	no	—
46	C₄×C₁₆	—	61	1	no	—
47	C₆₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
48	C₄×Q₈	—	61	1	no	—
49	C₂×C₁₆	—	122	1	no	—
50	C₂×C₁₆	—	122	1	no	—
51	C₄⋊C₈	—	122	1	no	—
52	C₄⋊C₈	#6923	1	1	yes	characteristic
53	C₄×C₈	—	61	1	no	—
54	C₄×C₈	—	122	1	no	—
55	C₂×Q₈	—	61	1	no	—
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	—	61	1	no	—
58	C₂×C₈	—	61	1	no	—
59	C₄⋊C₄	—	61	1	no	—
60	C₄⋊C₄	—	122	1	no	—
61	C₄²	—	122	1	no	—
62	C₄²	C₂×#6923	1	1	yes	characteristic
63	C₁₆	—	122	2	no	—
64	C₁₆	—	244	1	no	—
65	Q₈	—	61	2	no	—
66	Q₈	—	122	1	no	—
67	C₂×C₄	—	122	1	no	—
68	C₂×C₄	—	122	1	no	—
69	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
70	C₂×C₄	#11758213	1	1	yes	characteristic
71	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
72	C₈	—	4	1	no	—
73	C₈	—	61	1	no	—
74	C₈	—	61	1	no	—
75	C₈	—	122	1	no	—
76	C₂²	#14519834	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	122	2	no	—
79	C₄	—	244	1	no	—
80	C₄	#14519840	1	1	yes	characteristic
81	C₄	#14519841	1	1	yes	characteristic
82	C₄	D₆₁⋊C₁₆	1	1	yes	characteristic
83	C₄	#14519852	1	1	yes	characteristic
84	C₂	#16840612	1	1	yes	characteristic
85	C₂	#16840657	1	1	yes	characteristic
86	C₂	#16840661	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₄²	C₂×#6923
Fitting	C₄⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
27. Dic₁₂₂	C₁₆	semidirect
47. C₆₁	Q₈⋊C₁₆	semidirect