Subgroups — #21460946

Order 7808.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840671	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840669	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840149	C₂	1	1	yes	maximal, characteristic
4	#14519838	—	2	1	no	—
5	#14519836	—	2	1	no	—
6	C₂×#11758200	—	2	1	no	—
7	C₂×#11758199	—	2	1	no	—
8	#14519765	C₂²	1	1	yes	characteristic
9	#14519688	C₄	1	1	yes	characteristic, complemented
10	#127×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄×C₆₁	—	2	1	no	—
12	C₂×D₄×C₆₁	—	4	1	no	—
13	C₂×D₂₄₄	D₄	1	1	yes	characteristic
14	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
15	C₂²⋊#6923	—	4	1	no	—
16	#11758217	—	4	1	no	—
17	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
18	#11758200	—	4	2	no	—
19	#11758199	—	4	2	no	—
20	#11758198	—	4	1	no	—
21	C₂×#92418	—	2	1	no	—
22	C₂³×C₆₁	—	4	1	no	—
23	C₂²×D₆₁	—	2	1	no	—
24	C₂×#6923	—	8	1	no	—
25	D₄×C₆₁	—	4	1	no	—
26	D₄×C₆₁	—	4	1	no	—
27	D₄×C₆₁	—	8	2	no	—
28	C₂×C₄×C₆₁	—	2	1	no	—
29	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₆₁	—	2	1	no	—
31	D₂₄₄	—	4	1	no	—
32	Dic₁₂₂	—	4	1	no	—
33	#92420	—	8	1	no	—
34	#92418	—	2	2	no	—
35	C₂²×C₆₁	—	8	2	no	—
36	C₂²×C₆₁	—	8	1	no	—
37	C₂²×C₆₁	#99	1	1	yes	characteristic
38	C₂×D₆₁	—	4	1	no	—
39	C₂×D₆₁	—	8	1	no	—
40	#6923	—	16	1	no	—
41	C₄×C₆₁	—	2	1	no	—
42	C₄×C₆₁	—	4	1	no	—
43	Dic₆₁	—	4	1	no	—
44	#1406	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	—	2	1	no	—
46	C₂×C₆₁	—	16	1	no	—
47	C₂×C₆₁	#353	1	1	yes	characteristic
48	D₆₁	—	8	1	no	—
49	#496	—	61	1	no	—
50	#355	—	61	1	no	—
51	#354	—	61	1	no	—
52	C₆₁	#1406	1	1	yes	characteristic, complemented, Sylow
53	C₂×SD₁₆	—	122	1	no	—
54	C₂×D₈	—	122	1	no	—
55	#127	#6923	1	1	yes	characteristic, complemented
56	#124	—	61	1	no	—
57	#101	—	122	1	no	—
58	#99	—	122	1	no	—
59	#97	—	61	1	no	—
60	C₂×Q₈	—	61	1	no	—
61	C₂×D₄	—	2	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×D₄	—	61	1	no	—
64	SD₁₆	—	244	2	no	—
65	D₈	—	244	2	no	—
66	M₁₆	—	244	1	no	—
67	C₂×C₈	—	122	1	no	—
68	C₂²⋊C₄	—	244	1	no	—
69	C₂²⋊C₄	—	244	1	no	—
70	C₄²	C₂×#6923	1	1	yes	characteristic
71	C₂³	—	4	1	no	—
72	C₂³	—	122	1	no	—
73	Q₈	—	244	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	8	2	no	—
77	D₄	—	244	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	122	1	no	—
80	C₂×C₄	—	488	1	no	—
81	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
82	C₈	—	122	2	no	—
83	C₈	—	488	1	no	—
84	C₂²	—	8	2	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	488	1	no	—
87	C₂²	—	244	1	no	—
88	C₂²	#14519835	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	976	1	no	—
92	C₄	—	244	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	16	1	no	—
95	C₂	—	488	1	no	—
96	C₂	#16840666	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840666
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	#127×C₆₁	C₄
socle	C₂×C₆₁	#353
hypercenter	#127	#6923
hypocenter	C₆₁	#1406
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #16840671	C₂	semidirect
2. #16840669	C₂	semidirect
9. #14519688	C₄	semidirect
10. #127×C₆₁	C₄	semidirect
52. C₆₁	#1406	semidirect
55. #127	#6923	semidirect