Subgroups — #21448132

Order 7808.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840194	C₂	1	1	yes	maximal, characteristic, complemented
2	#16839600	C₂	1	2	yes	maximal, complemented
3	#16839597	C₂	1	2	yes	maximal, complemented
4	#16839596	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14519799	—	2	1	no	—
7	Dic₄₈₈	C₂²	1	1	yes	characteristic, complemented
8	#14519722	—	2	1	no	—
9	D₉₇₆	C₂²	1	1	yes	characteristic, complemented
10	#14519683	C₂²	1	2	yes	complemented
11	C₂×D₈×C₆₁	—	2	1	no	—
12	D₁₆×C₆₁	—	2	1	no	—
13	D₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×D₄×C₆₁	—	4	1	no	—
16	#11758222	—	4	1	no	—
17	D₈×C₆₁	—	2	2	no	—
18	D₈×C₆₁	—	4	1	no	—
19	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
20	Dic₂₄₄	—	2	1	no	—
21	D₄₈₈	—	2	1	no	—
22	#11758190	—	4	1	no	—
23	C₁₆×C₆₁	D₄	1	1	yes	characteristic
24	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
25	C₂³×C₆₁	—	8	1	no	—
26	D₄×C₆₁	—	4	2	no	—
27	D₄×C₆₁	—	8	1	no	—
28	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
29	C₂²⋊D₆₁	—	8	1	no	—
30	D₂₄₄	—	4	1	no	—
31	C₄×D₆₁	—	8	1	no	—
32	Dic₁₂₂	—	4	1	no	—
33	C₈×C₆₁	D₈	1	1	yes	characteristic
34	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₆₁	—	8	2	no	—
36	C₂²×C₆₁	—	16	2	no	—
37	C₂²×C₆₁	D₁₆	1	1	yes	characteristic
38	C₂×D₆₁	—	8	1	no	—
39	C₄×C₆₁	D₁₆	1	1	yes	characteristic
40	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
41	Dic₆₁	—	8	1	no	—
42	#2263	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	—	2	1	no	—
44	C₂×C₆₁	—	16	2	no	—
45	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
46	D₆₁	—	16	1	no	—
47	#508	—	61	1	no	—
48	C₂×D₁₆	D₆₁	1	1	yes	characteristic, complemented
49	SD₆₄	—	61	2	no	—
50	D₃₂	—	61	2	no	—
51	M₆₄	—	61	1	no	—
52	C₆₁	#2263	1	1	yes	characteristic, complemented, Sylow
53	#135	—	122	1	no	—
54	C₂×D₈	—	2	1	no	—
55	Q₃₂	—	61	1	no	—
56	SD₃₂	—	122	1	no	—
57	D₁₆	—	2	1	no	—
58	D₁₆	—	61	1	no	—
59	D₁₆	C₂×D₆₁	1	2	yes	—
60	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
61	C₃₂	—	61	2	no	—
62	#41	—	244	1	no	—
63	C₂×D₄	—	4	1	no	—
64	Q₁₆	—	122	1	no	—
65	SD₁₆	—	244	1	no	—
66	D₈	—	2	2	no	—
67	D₈	—	4	1	no	—
68	D₈	—	122	1	no	—
69	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
70	C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
71	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	244	1	no	—
74	D₄	—	4	2	no	—
75	D₄	—	8	1	no	—
76	D₄	—	488	1	no	—
77	D₄	—	244	1	no	—
78	C₂×C₄	—	488	1	no	—
79	C₂×C₄	#11758199	1	1	yes	characteristic
80	C₈	#11758199	1	1	yes	characteristic
81	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
82	C₂²	—	8	2	no	—
83	C₂²	—	16	2	no	—
84	C₂²	—	488	1	no	—
85	C₂²	#14519718	1	1	yes	characteristic
86	C₄	—	488	1	no	—
87	C₄	#14519718	1	1	yes	characteristic
88	C₄	C₂×#11758199	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	16	2	no	—
91	C₂	—	976	1	no	—
92	C₂	C₂×#14519718	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#14519718
commutator	C₁₆×C₆₁	C₂³
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₂×D₁₆×C₆₁	C₂
socle	C₂×C₆₁	C₂×D₁₆
hypercenter	C₂×D₁₆	D₆₁
hypocenter	C₆₁	#2263
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. #16840194	C₂	semidirect
2. #16839600	C₂	semidirect
3. #16839597	C₂	semidirect
4. #16839596	C₂	semidirect
5. C₂×D₁₆×C₆₁	C₂	semidirect
7. Dic₄₈₈	C₂²	semidirect
9. D₉₇₆	C₂²	semidirect
10. #14519683	C₂²	semidirect
48. C₂×D₁₆	D₆₁	semidirect
52. C₆₁	#2263	semidirect