Subgroups — #21460948

Order 7808.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840671	C₂	1	1	yes	maximal, characteristic
2	#16840669	C₂	1	1	yes	maximal, characteristic
3	#16840154	C₂	1	1	yes	maximal, characteristic
4	#14519838	—	2	1	no	—
5	#14519836	—	2	1	no	—
6	C₂×#11758202	—	2	1	no	—
7	C₂×#11758201	—	2	1	no	—
8	#14519765	C₂²	1	1	yes	characteristic
9	#14519688	C₄	1	1	yes	characteristic, complemented
10	C₄⋊Q₈×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₆₁	—	2	1	no	—
12	C₂×D₂₄₄	D₄	1	1	yes	characteristic
13	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
14	C₂²⋊#6923	—	4	1	no	—
15	#11758217	—	4	1	no	—
16	C₄⋊C₄×C₆₁	—	4	1	no	—
17	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
18	#11758202	—	4	2	no	—
19	#11758201	—	4	2	no	—
20	#11758198	—	4	1	no	—
21	C₂×#92418	—	2	1	no	—
22	C₂²×D₆₁	—	2	1	no	—
23	C₂×#6923	—	8	1	no	—
24	Q₈×C₆₁	—	4	1	no	—
25	Q₈×C₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₆₁	—	2	1	no	—
30	D₂₄₄	—	4	1	no	—
31	Dic₁₂₂	—	4	1	no	—
32	#92420	—	8	1	no	—
33	#92418	—	2	2	no	—
34	C₂²×C₆₁	#99	1	1	yes	characteristic
35	C₂×D₆₁	—	4	1	no	—
36	C₂×D₆₁	—	8	1	no	—
37	#6923	—	16	1	no	—
38	C₄×C₆₁	—	2	1	no	—
39	C₄×C₆₁	—	4	1	no	—
40	C₄×C₆₁	—	8	1	no	—
41	Dic₆₁	—	4	1	no	—
42	#1407	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	—	2	1	no	—
44	C₂×C₆₁	#353	1	1	yes	characteristic
45	D₆₁	—	8	1	no	—
46	#497	—	61	1	no	—
47	#355	—	61	1	no	—
48	#354	—	61	1	no	—
49	C₆₁	#1407	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	122	1	no	—
51	C₂×SD₁₆	—	122	1	no	—
52	C₄⋊Q₈	#6923	1	1	yes	characteristic, complemented
53	#124	—	61	1	no	—
54	#101	—	122	1	no	—
55	#99	—	122	1	no	—
56	#97	—	61	1	no	—
57	C₂×Q₈	—	2	1	no	—
58	C₂×Q₈	—	61	1	no	—
59	C₂×D₄	—	61	1	no	—
60	Q₁₆	—	244	2	no	—
61	SD₁₆	—	244	2	no	—
62	M₁₆	—	244	1	no	—
63	C₂×C₈	—	122	1	no	—
64	C₄⋊C₄	—	4	1	no	—
65	C₂²⋊C₄	—	244	1	no	—
66	C₂²⋊C₄	—	244	1	no	—
67	C₄²	C₂×#6923	1	1	yes	characteristic
68	C₂³	—	122	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	Q₈	—	244	1	no	—
72	D₄	—	244	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	122	1	no	—
76	C₂×C₄	—	488	1	no	—
77	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
78	C₈	—	122	2	no	—
79	C₈	—	488	1	no	—
80	C₂²	—	488	1	no	—
81	C₂²	—	244	1	no	—
82	C₂²	#14519835	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	976	1	no	—
87	C₄	—	244	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	488	1	no	—
90	C₂	#16840666	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840666
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	C₄⋊Q₈×C₆₁	C₄
socle	C₂×C₆₁	#353
hypercenter	C₄⋊Q₈	#6923
hypocenter	C₆₁	#1407
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
9. #14519688	C₄	semidirect
10. C₄⋊Q₈×C₆₁	C₄	semidirect
49. C₆₁	#1407	semidirect
52. C₄⋊Q₈	#6923	semidirect