Subgroups — #21443791

Order 7808.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839880	C₂	1	1	yes	maximal, characteristic
2	C₈×#92418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	#14519799	C₄	1	1	yes	characteristic
5	#14519783	—	2	1	no	—
6	#14519713	C₄	1	1	yes	characteristic
7	#14519705	—	2	1	no	—
8	C₄×#92418	—	2	1	no	—
9	M₃₂×C₆₁	—	2	1	no	—
10	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	#11758222	—	2	1	no	—
12	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₄²×C₆₁	D₄	1	1	yes	characteristic
15	#11758194	—	2	1	no	—
16	C₂×#92418	—	2	2	no	—
17	Dic₂₄₄	C₈	1	1	yes	characteristic, complemented
18	D₄₈₈	C₈	1	1	yes	characteristic, complemented
19	#11758190	—	2	1	no	—
20	#11758189	—	4	1	no	—
21	C₈×D₆₁	—	4	1	no	—
22	C₁₆×C₆₁	—	4	1	no	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₆₁	—	4	1	no	—
26	D₂₄₄	—	2	1	no	—
27	C₄×D₆₁	—	4	1	no	—
28	Dic₁₂₂	—	2	1	no	—
29	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₈×C₆₁	M₁₆	1	1	yes	characteristic
31	C₈×C₆₁	D₈	1	1	yes	characteristic
32	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
33	#92418	—	2	4	no	—
34	#92418	—	4	1	no	—
35	C₂²×C₆₁	#104	1	1	yes	characteristic
36	C₂×D₆₁	—	4	1	no	—
37	C₄×C₆₁	—	2	2	no	—
38	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₆₁	#102	1	1	yes	characteristic
40	Dic₆₁	—	4	1	no	—
41	#1335	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	—	2	1	no	—
43	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
44	D₆₁	—	8	1	no	—
45	#443	—	61	1	no	—
46	#364	D₆₁	1	1	yes	characteristic, complemented
47	C₈²	—	61	1	no	—
48	C₆₁	#1335	1	1	yes	characteristic, complemented, Sylow
49	#135	—	61	1	no	—
50	#131	—	122	1	no	—
51	M₃₂	—	2	1	no	—
52	#108	—	61	1	no	—
53	#104	—	122	1	no	—
54	C₄×C₈	—	122	1	no	—
55	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
56	#41	—	122	1	no	—
57	Q₁₆	—	61	1	no	—
58	SD₁₆	—	122	1	no	—
59	D₈	—	61	1	no	—
60	M₁₆	—	122	1	no	—
61	M₁₆	—	244	1	no	—
62	C₂×C₈	—	122	2	no	—
63	C₂×C₈	—	244	1	no	—
64	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
66	C₄²	D₂₄₄	1	1	yes	characteristic
67	C₁₆	—	4	1	no	—
68	Q₈	—	122	1	no	—
69	D₄	—	122	1	no	—
70	D₄	—	244	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	244	1	no	—
73	C₂×C₄	#11758198	1	1	yes	characteristic
74	C₈	—	122	4	no	—
75	C₈	—	244	1	no	—
76	C₈	C₈×D₆₁	1	1	yes	characteristic
77	C₈	#11758189	1	1	yes	characteristic
78	C₈	#11758199	1	1	yes	characteristic
79	C₈	#11758201	1	1	yes	characteristic
80	C₂²	—	244	1	no	—
81	C₂²	#14519703	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	244	1	no	—
84	C₄	#14519689	1	1	yes	characteristic
85	C₄	#14519697	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	488	1	no	—
88	C₂	#16839489	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#11758199
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#364	C₂
socle	C₂×C₆₁	D₄⋊C₈
hypercenter	#364	D₆₁
hypocenter	C₆₁	#1335
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. C₈×#92418	C₂	semidirect
3. C₆₁×#364	C₂	semidirect
17. Dic₂₄₄	C₈	semidirect
18. D₄₈₈	C₈	semidirect
46. #364	D₆₁	semidirect
48. C₆₁	#1335	semidirect