Subgroups — #21448071

Order 7808.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519723	C₂	1	4	yes	maximal
2	#16840142	C₂	1	1	yes	maximal, characteristic
3	C₄×#11758185	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₄₄	—	2	1	no	—
6	C₂×Dic₂₄₄	C₂²	1	2	yes	—
7	#14519777	—	2	1	no	—
8	#14519723	—	2	8	no	—
9	C₂×#11758185	C₂²	1	2	yes	—
10	C₂×Q₁₆×C₆₁	—	2	1	no	—
11	C₂×Q₁₆×C₆₁	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₆₁	—	2	1	no	—
13	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₆₁	—	2	2	no	—
15	C₂×Dic₁₂₂	—	2	2	no	—
16	Q₁₆×C₆₁	—	2	4	no	—
17	Q₁₆×C₆₁	—	4	2	no	—
18	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₆₁	—	4	2	no	—
21	C₄²×C₆₁	D₄	1	1	yes	characteristic
22	C₄⋊Dic₆₁	—	4	2	no	—
23	Dic₂₄₄	—	2	4	no	—
24	Dic₂₄₄	—	4	2	no	—
25	#11758185	D₄	1	4	yes	—
26	Q₈×C₆₁	—	4	2	no	—
27	Q₈×C₆₁	—	4	2	no	—
28	C₂×C₄×C₆₁	—	4	2	no	—
29	C₂×C₄×C₆₁	D₈	1	2	yes	—
30	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₆₁	—	4	2	no	—
32	Dic₁₂₂	—	4	2	no	—
33	Dic₁₂₂	—	4	2	no	—
34	C₈×C₆₁	D₈	1	2	yes	—
35	C₈×C₆₁	C₂×D₄	1	2	yes	—
36	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
37	C₄×C₆₁	—	8	2	no	—
38	C₄×C₆₁	Q₃₂	1	4	yes	complemented
39	C₄×C₆₁	#127	1	1	yes	characteristic
40	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
41	Dic₆₁	—	8	2	no	—
42	#2247	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	#493	1	1	yes	characteristic
44	C₂×C₆₁	C₂×Q₃₂	1	2	yes	—
45	C₂×Q₃₂	—	61	4	no	—
46	#494	—	61	1	no	—
47	#494	D₆₁	1	1	yes	characteristic
48	C₄×C₁₆	—	61	1	no	—
49	C₆₁	#2247	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	2	1	no	—
51	C₂×Q₁₆	—	61	2	no	—
52	C₂×Q₁₆	—	122	1	no	—
53	C₂×Q₁₆	C₂×D₆₁	1	2	yes	—
54	C₄⋊Q₈	—	2	1	no	—
55	C₄⋊Q₈	—	122	1	no	—
56	Q₃₂	—	122	8	no	—
57	C₂×C₁₆	—	61	2	no	—
58	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
59	C₂×Q₈	—	2	2	no	—
60	C₂×Q₈	—	122	2	no	—
61	Q₁₆	—	2	4	no	—
62	Q₁₆	—	4	2	no	—
63	Q₁₆	—	122	4	no	—
64	Q₁₆	—	244	2	no	—
65	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
67	C₄⋊C₄	—	4	2	no	—
68	C₄⋊C₄	—	244	2	no	—
69	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
70	C₁₆	—	61	4	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	244	2	no	—
74	Q₈	—	244	2	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	244	2	no	—
77	C₂×C₄	#11758199	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
79	C₈	#11758199	1	2	yes	—
80	C₈	D₄×D₆₁	1	2	yes	—
81	C₂²	C₂×#11758199	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	488	2	no	—
84	C₄	#14519723	1	4	yes	complemented
85	C₄	#14519773	1	1	yes	characteristic
86	C₄	C₂×#11758199	1	1	yes	characteristic
87	C₂	#16840138	1	1	yes	characteristic
88	C₂	C₂×#14519723	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#494	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#494	D₆₁
hypocenter	C₆₁	#2247
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
38. C₄×C₆₁	Q₃₂	semidirect
49. C₆₁	#2247	semidirect
84. C₄	#14519723	semidirect