Subgroups — #21448136

Order 7808.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#16839602	C₂	1	2	yes	maximal, complemented
3	#16839600	C₂	1	2	yes	maximal, complemented
4	#16839596	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#508	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₄₄	—	2	1	no	—
7	Dic₄₈₈	—	2	1	no	—
8	Dic₄₈₈	C₂²	1	2	yes	—
9	#14519683	C₂²	1	2	yes	—
10	#135×C₆₁	—	2	1	no	—
11	Q₃₂×C₆₁	C₂²	1	1	yes	characteristic
12	SD₃₂×C₆₁	—	2	1	no	—
13	D₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	#41×C₆₁	—	4	1	no	—
16	C₂×Dic₁₂₂	—	4	1	no	—
17	Q₁₆×C₆₁	—	2	1	no	—
18	SD₁₆×C₆₁	—	4	1	no	—
19	D₈×C₆₁	—	2	1	no	—
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	Dic₂₄₄	—	2	2	no	—
22	Dic₂₄₄	—	4	1	no	—
23	C₁₆×C₆₁	D₄	1	1	yes	characteristic
24	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
25	Q₈×C₆₁	—	4	1	no	—
26	D₄×C₆₁	—	4	1	no	—
27	D₄×C₆₁	—	8	1	no	—
28	C₂×C₄×C₆₁	—	8	1	no	—
29	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
30	C₂×Dic₆₁	—	8	1	no	—
31	Dic₁₂₂	—	4	2	no	—
32	Dic₁₂₂	—	8	1	no	—
33	C₈×C₆₁	D₈	1	1	yes	characteristic
34	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₆₁	—	8	1	no	—
36	C₂²×C₆₁	D₁₆	1	1	yes	characteristic
37	C₄×C₆₁	—	8	1	no	—
38	C₄×C₆₁	D₁₆	1	1	yes	characteristic
39	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
40	Dic₆₁	—	8	2	no	—
41	#2264	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	—	2	1	no	—
43	C₂×C₆₁	—	16	1	no	—
44	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
45	#508	D₆₁	1	1	yes	characteristic
46	C₂×Q₃₂	—	61	1	no	—
47	Q₆₄	—	61	2	no	—
48	SD₆₄	—	61	2	no	—
49	M₆₄	—	61	1	no	—
50	C₆₁	#2264	1	1	yes	characteristic, complemented, Sylow
51	#135	—	2	1	no	—
52	C₂×Q₁₆	—	122	1	no	—
53	Q₃₂	—	61	2	no	—
54	Q₃₂	—	122	1	no	—
55	Q₃₂	C₂×D₆₁	1	1	yes	characteristic
56	SD₃₂	—	2	1	no	—
57	D₁₆	C₂×D₆₁	1	1	yes	characteristic
58	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
59	C₃₂	—	61	2	no	—
60	#41	—	4	1	no	—
61	C₂×Q₈	—	244	1	no	—
62	Q₁₆	—	2	1	no	—
63	Q₁₆	—	122	2	no	—
64	Q₁₆	—	244	1	no	—
65	SD₁₆	—	4	1	no	—
66	D₈	—	2	1	no	—
67	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
68	C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
69	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
70	Q₈	—	4	1	no	—
71	Q₈	—	488	1	no	—
72	Q₈	—	244	2	no	—
73	D₄	—	4	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	488	1	no	—
77	C₂×C₄	#11758199	1	1	yes	characteristic
78	C₈	#11758199	1	1	yes	characteristic
79	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
80	C₂²	—	8	1	no	—
81	C₂²	#14519718	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	488	2	no	—
84	C₄	#14519718	1	1	yes	characteristic
85	C₄	C₂×#11758199	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	1	no	—
88	C₂	C₂×#14519718	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#14519718
commutator	C₁₆×C₆₁	C₂³
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₆₁×#508	C₂
socle	C₂×C₆₁	C₂×D₁₆
hypercenter	#508	D₆₁
hypocenter	C₆₁	#2264
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₄₈₈	C₂	semidirect
2. #16839602	C₂	semidirect
3. #16839600	C₂	semidirect
4. #16839596	C₂	semidirect
50. C₆₁	#2264	semidirect