Subgroups — #21462786

Order 7808.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840820	C₂	1	8	yes	maximal, complemented
2	C₂×#14519851	C₂	1	6	yes	maximal, complemented
3	C₂×#14519784	C₂	1	1	yes	maximal, characteristic
4	#14519851	C₂²	1	4	yes	—
5	#14519851	C₂²	1	12	yes	complemented
6	C₂×#11758187	C₂²	1	12	yes	complemented
7	#14519784	C₄	1	4	yes	—
8	#14519784	C₂²	1	4	yes	—
9	C₂×#11758194	C₄	1	3	yes	—
10	C₂²×#92418	C₂²	1	3	yes	—
11	C₂×#41×C₆₁	C₄	1	1	yes	characteristic
12	#41×C₆₁	C₈	1	4	yes	—
13	#41×C₆₁	C₂×C₄	1	4	yes	—
14	C₂×Q₈×C₆₁	C₈	1	1	yes	characteristic
15	C₂×D₄×C₆₁	C₈	1	3	yes	—
16	C₂²×C₄×C₆₁	C₂×C₄	1	3	yes	—
17	#11758194	C₂×C₄	1	12	yes	—
18	C₂×#92418	C₂×C₄	1	3	yes	—
19	C₂×#92418	C₂×C₄	1	6	yes	—
20	C₂×#92418	C₂³	1	6	yes	—
21	C₂×#92418	C₂³	1	1	yes	characteristic
22	#11758187	C₂³	1	8	yes	—
23	C₂³×C₆₁	C₂×C₈	1	3	yes	—
24	Q₈×C₆₁	C₂×C₈	1	4	yes	—
25	D₄×C₆₁	C₂×C₈	1	12	yes	—
26	C₂×C₄×C₆₁	C₂×C₈	1	3	yes	—
27	C₂×C₄×C₆₁	C₂×C₈	1	6	yes	—
28	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂²×C₄	1	6	yes	—
30	#92418	C₂²×C₄	1	1	yes	characteristic
31	#92418	C₂²×C₄	1	6	yes	—
32	#92418	C₂⁴	1	1	yes	characteristic
33	C₂²×C₆₁	—	4	3	no	—
34	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
35	C₂²×C₆₁	C₂²×C₈	1	6	yes	—
36	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
37	C₄×C₆₁	C₂²×C₈	1	6	yes	—
38	C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
39	#3407	—	61	1	no	maximal, Sylow
40	C₂×C₆₁	—	2	1	no	—
41	C₂×C₆₁	—	2	6	no	—
42	C₂×C₆₁	C₂³×C₈	1	1	yes	characteristic
43	C₂×#131	—	61	1	no	—
44	#504	—	61	8	no	—
45	C₂×M₃₂	—	61	6	no	—
46	C₆₁	#3407	1	1	yes	characteristic, complemented, Sylow
47	C₂×#41	#6923	1	1	yes	characteristic
48	#131	—	61	4	no	—
49	#131	—	61	4	no	—
50	C₂×M₁₆	—	61	3	no	—
51	C₂²×C₈	—	61	3	no	—
52	M₃₂	—	61	4	no	—
53	M₃₂	—	61	12	no	—
54	C₂×C₁₆	—	61	12	no	—
55	#41	#92420	1	4	yes	—
56	#41	C₂×#6923	1	4	yes	—
57	C₂×Q₈	#92420	1	1	yes	characteristic
58	C₂×D₄	#92420	1	3	yes	—
59	C₂²×C₄	C₂×#6923	1	3	yes	—
60	M₁₆	—	61	12	no	—
61	C₂×C₈	—	61	6	no	—
62	C₂×C₈	—	61	1	no	—
63	C₂×C₈	—	61	3	no	—
64	C₂×C₈	—	61	6	no	—
65	C₁₆	—	61	8	no	—
66	C₂³	C₂×#92420	1	3	yes	—
67	Q₈	C₂×#92420	1	4	yes	—
68	D₄	C₂×#92420	1	12	yes	—
69	C₂×C₄	C₂×#92420	1	3	yes	—
70	C₂×C₄	C₂×#92420	1	6	yes	—
71	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
72	C₂×C₄	C₂²×#6923	1	6	yes	—
73	C₈	—	61	1	no	—
74	C₈	—	61	6	no	—
75	C₈	—	61	1	no	—
76	C₂²	—	4	3	no	—
77	C₂²	C₂²×#92420	1	1	yes	characteristic
78	C₂²	C₂²×#92420	1	6	yes	—
79	C₄	C₂²×#92420	1	1	yes	characteristic
80	C₄	C₂²×#92420	1	6	yes	—
81	C₄	C₂³×#6923	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	2	6	no	—
84	C₂	C₂³×#92420	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂³×#6923
commutator, socle	C₂×C₆₁	C₂³×C₈
Fitting	C₂×#41×C₆₁	C₄
hypercenter	C₂×#41	#6923
hypocenter	C₆₁	#3407
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #16840820	C₂	semidirect
2. C₂×#14519851	C₂	semidirect
5. #14519851	C₂²	semidirect
6. C₂×#11758187	C₂²	semidirect
46. C₆₁	#3407	semidirect