Subgroups — #21448074

Order 7808.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519721	C₂	1	4	yes	maximal, complemented
2	#16840142	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#11758185	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#493	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	#14519721	—	2	8	no	—
9	C₂×#11758185	C₂²	1	2	yes	—
10	C₂×D₈×C₆₁	—	2	1	no	—
11	C₂×D₈×C₆₁	C₂²	1	2	yes	—
12	#127×C₆₁	—	2	1	no	—
13	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₆₁	—	2	2	no	—
15	C₂×D₄×C₆₁	—	4	2	no	—
16	C₂×Dic₁₂₂	—	2	2	no	—
17	D₈×C₆₁	—	2	4	no	—
18	D₈×C₆₁	—	4	2	no	—
19	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
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	complemented
26	C₂³×C₆₁	—	4	2	no	—
27	D₄×C₆₁	—	4	2	no	—
28	D₄×C₆₁	—	4	2	no	—
29	D₄×C₆₁	—	8	4	no	—
30	C₂×C₄×C₆₁	D₈	1	2	yes	—
31	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₆₁	—	4	2	no	—
33	Dic₁₂₂	—	4	2	no	—
34	Dic₁₂₂	—	4	2	no	—
35	C₈×C₆₁	D₈	1	2	yes	—
36	C₈×C₆₁	C₂×D₄	1	2	yes	—
37	C₂²×C₆₁	—	8	2	no	—
38	C₂²×C₆₁	—	8	4	no	—
39	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
40	C₄×C₆₁	SD₃₂	1	4	yes	complemented
41	C₄×C₆₁	#127	1	1	yes	characteristic
42	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
43	Dic₆₁	—	8	2	no	—
44	#2248	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	—	16	2	no	—
46	C₂×C₆₁	#493	1	1	yes	characteristic
47	C₂×C₆₁	C₂×SD₃₂	1	2	yes	—
48	C₂×SD₃₂	—	61	4	no	—
49	#494	—	61	1	no	—
50	#493	D₆₁	1	1	yes	characteristic
51	C₄×C₁₆	—	61	1	no	—
52	C₆₁	#2248	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	—	61	2	no	—
54	C₂×Q₁₆	—	122	1	no	—
55	C₂×D₈	—	2	1	no	—
56	C₂×D₈	C₂×D₆₁	1	2	yes	—
57	C₄⋊Q₈	—	122	1	no	—
58	#127	—	2	1	no	—
59	SD₃₂	—	122	8	no	—
60	C₂×C₁₆	—	61	2	no	—
61	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
62	C₂×Q₈	—	122	2	no	—
63	C₂×D₄	—	2	2	no	—
64	C₂×D₄	—	4	2	no	—
65	Q₁₆	—	122	4	no	—
66	Q₁₆	—	244	2	no	—
67	D₈	—	2	4	no	—
68	D₈	—	4	2	no	—
69	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
71	C₄⋊C₄	—	244	2	no	—
72	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
73	C₁₆	—	61	4	no	—
74	C₂³	—	4	2	no	—
75	Q₈	—	244	2	no	—
76	Q₈	—	244	2	no	—
77	D₄	—	4	2	no	—
78	D₄	—	4	2	no	—
79	D₄	—	8	4	no	—
80	C₂×C₄	—	244	2	no	—
81	C₂×C₄	#11758199	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
83	C₈	#11758199	1	2	yes	—
84	C₈	D₄×D₆₁	1	2	yes	—
85	C₂²	—	8	2	no	—
86	C₂²	—	8	4	no	—
87	C₂²	C₂×#11758199	1	1	yes	characteristic
88	C₄	—	488	2	no	—
89	C₄	#14519721	1	4	yes	complemented
90	C₄	#14519773	1	1	yes	characteristic
91	C₄	C₂×#11758199	1	1	yes	characteristic
92	C₂	—	16	2	no	—
93	C₂	#16840138	1	1	yes	characteristic
94	C₂	C₂×#14519721	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#493	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#493	D₆₁
hypocenter	C₆₁	#2248
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. C₂×#14519721	C₂	semidirect
2. #16840142	C₂	semidirect
3. C₄×#11758185	C₂	semidirect
25. #11758185	D₄	semidirect
40. C₄×C₆₁	SD₃₂	semidirect
52. C₆₁	#2248	semidirect
89. C₄	#14519721	semidirect