Subgroups — #21460834

Order 7808.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840683	C₂	1	1	yes	maximal, characteristic
2	#16840626	C₂	1	1	yes	maximal, characteristic
3	#16840140	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	—	2	1	no	—
5	C₄⋊#92420	—	2	1	no	—
6	C₂×Dic₂₄₄	C₄	1	1	yes	characteristic
7	C₂×#11758202	—	2	1	no	—
8	#14519775	—	2	1	no	—
9	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₆₁	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₆₁	—	2	1	no	—
12	C₂×Dic₁₂₂	—	2	1	no	—
13	C₂×#92420	—	4	1	no	—
14	Q₁₆×C₆₁	—	4	1	no	—
15	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	#11758202	—	4	1	no	—
17	#11758202	—	4	1	no	—
18	#11758196	—	4	1	no	—
19	#11758196	—	4	1	no	—
20	C₄×Dic₆₁	D₄	1	1	yes	characteristic
21	C₂×#92418	D₄	1	1	yes	characteristic
22	Dic₂₄₄	—	4	1	no	—
23	#11758187	—	4	1	no	—
24	Q₈×C₆₁	—	4	1	no	—
25	Q₈×C₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	—	4	1	no	—
27	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₆₁	—	4	1	no	—
29	C₂×Dic₆₁	D₈	1	1	yes	characteristic
30	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
31	Dic₁₂₂	—	4	1	no	—
32	Dic₁₂₂	—	4	1	no	—
33	#92420	—	8	1	no	—
34	C₈×C₆₁	—	2	1	no	—
35	#92418	D₈	1	1	yes	characteristic
36	#92418	SD₁₆	1	1	yes	characteristic
37	C₂²×C₆₁	#102	1	1	yes	characteristic
38	C₄×C₆₁	—	8	1	no	—
39	C₄×C₆₁	#100	1	1	yes	characteristic
40	C₄×C₆₁	#102	1	1	yes	characteristic
41	Dic₆₁	—	2	1	no	—
42	Dic₆₁	—	8	1	no	—
43	Dic₆₁	SD₃₂	1	1	yes	characteristic
44	Dic₆₁	Q₃₂	1	1	yes	characteristic
45	#1362	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	#331	1	1	yes	characteristic
47	C₂×C₆₁	#358	1	1	yes	characteristic
48	C₂×C₆₁	#362	1	1	yes	characteristic
49	#494	—	61	1	no	—
50	C₄⋊C₁₆	—	61	1	no	—
51	#335	—	61	1	no	—
52	C₆₁	#1362	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	—	61	1	no	—
54	C₂×Q₁₆	—	122	1	no	—
55	C₂×Q₁₆	#6923	1	1	yes	characteristic
56	C₄⋊Q₈	—	122	1	no	—
57	C₂×C₁₆	—	122	1	no	—
58	C₄⋊C₈	—	122	1	no	—
59	C₄×C₈	—	61	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	122	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	244	1	no	—
64	Q₁₆	—	244	1	no	—
65	Q₁₆	—	244	1	no	—
66	C₂×C₈	—	61	1	no	—
67	C₂×C₈	—	244	1	no	—
68	C₂×C₈	C₂×#6923	1	1	yes	characteristic
69	C₄⋊C₄	—	244	1	no	—
70	C₄⋊C₄	—	244	1	no	—
71	C₄²	—	61	1	no	—
72	C₁₆	—	244	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	244	1	no	—
76	Q₈	—	244	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	61	1	no	—
79	C₂×C₄	—	61	1	no	—
80	C₂×C₄	—	244	1	no	—
81	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	61	1	no	—
84	C₈	—	61	1	no	—
85	C₈	—	488	1	no	—
86	C₂²	#14519839	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	61	1	no	—
89	C₄	—	61	1	no	—
90	C₄	—	122	1	no	—
91	C₄	—	488	1	no	—
92	C₄	#14519837	1	1	yes	characteristic
93	C₄	#14519839	1	1	yes	characteristic
94	C₂	#16840620	1	1	yes	characteristic
95	C₂	#16840675	1	1	yes	characteristic
96	C₂	#16840681	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519839
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×Q₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#102
hypercenter	C₂×Q₁₆	#6923
hypocenter	C₆₁	#1362
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
52. C₆₁	#1362	semidirect