Subgroups — #21460783

Order 7808.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840684	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840603	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839879	C₂	1	1	yes	maximal, characteristic
4	#14519851	—	2	1	no	—
5	C₄×#92420	—	2	1	no	—
6	#14519784	—	2	1	no	—
7	#14519713	C₄	1	1	yes	characteristic
8	#14519704	—	2	1	no	—
9	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
10	#135×C₆₁	C₄	1	1	yes	characteristic
11	#41×C₆₁	—	2	1	no	—
12	C₂×#92420	—	2	2	no	—
13	Q₁₆×C₆₁	C₈	1	1	yes	characteristic, complemented
14	SD₁₆×C₆₁	—	2	1	no	—
15	D₈×C₆₁	C₈	1	1	yes	characteristic, complemented
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₆₁	D₄	1	1	yes	characteristic
18	#11758194	—	2	1	no	—
19	#11758194	—	4	1	no	—
20	C₂×#92418	—	4	1	no	—
21	C₂×#92418	D₄	1	1	yes	characteristic
22	#11758187	—	4	1	no	—
23	Q₈×C₆₁	—	2	1	no	—
24	D₄×C₆₁	—	2	1	no	—
25	D₄×C₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	—	4	1	no	—
27	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₆₁	—	2	1	no	—
29	#92420	—	4	2	no	—
30	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
31	C₈×C₆₁	M₁₆	1	1	yes	characteristic
32	#92418	—	4	1	no	—
33	#92418	D₈	1	1	yes	characteristic
34	#92418	SD₁₆	1	1	yes	characteristic
35	C₂²×C₆₁	—	4	1	no	—
36	C₂²×C₆₁	#104	1	1	yes	characteristic
37	C₄×C₆₁	—	4	1	no	—
38	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₆₁	#102	1	1	yes	characteristic
40	Dic₆₁	—	2	2	no	—
41	#1336	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	—	2	1	no	—
43	C₂×C₆₁	—	8	1	no	—
44	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
45	#443	—	61	1	no	—
46	#364	—	61	1	no	—
47	#322	—	61	1	no	—
48	C₆₁	#1336	1	1	yes	characteristic, complemented, Sylow
49	#135	#6923	1	1	yes	characteristic
50	#131	—	122	1	no	—
51	M₃₂	—	122	1	no	—
52	#108	—	61	1	no	—
53	#104	—	122	1	no	—
54	C₄×C₈	—	61	1	no	—
55	C₄×C₈	—	122	1	no	—
56	#41	—	2	1	no	—
57	Q₁₆	#92420	1	1	yes	characteristic, complemented
58	SD₁₆	—	2	1	no	—
59	D₈	#92420	1	1	yes	characteristic, complemented
60	M₁₆	—	122	1	no	—
61	M₁₆	—	244	1	no	—
62	C₂×C₈	—	61	1	no	—
63	C₂×C₈	—	122	2	no	—
64	C₂×C₈	—	244	1	no	—
65	C₂×C₈	C₂×#6923	1	1	yes	characteristic
66	C₄²	—	61	1	no	—
67	C₁₆	—	244	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	—	122	1	no	—
73	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
74	C₈	—	61	1	no	—
75	C₈	—	61	1	no	—
76	C₈	—	244	2	no	—
77	C₈	—	244	1	no	—
78	C₈	C₂×#92420	1	1	yes	characteristic
79	C₈	#11758217	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#14519841	1	1	yes	characteristic
82	C₄	—	4	1	no	—
83	C₄	—	122	2	no	—
84	C₄	C₂²⋊#92420	1	1	yes	characteristic
85	C₄	#14519839	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	D₄⋊#92420	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519839
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	#135×C₆₁	C₄
socle	C₂×C₆₁	D₄⋊C₈
hypercenter	#135	#6923
hypocenter	C₆₁	#1336
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #16840684	C₂	semidirect
2. #16840603	C₂	semidirect
13. Q₁₆×C₆₁	C₈	semidirect
15. D₈×C₆₁	C₈	semidirect
48. C₆₁	#1336	semidirect
57. Q₁₆	#92420	semidirect
59. D₈	#92420	semidirect