Subgroups — #21460796

Order 7808.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840659	C₂	1	1	yes	maximal, characteristic
2	#16840631	C₂	1	1	yes	maximal, characteristic
3	#16840021	C₂	1	1	yes	maximal, characteristic
4	D₆₁⋊M₁₆	—	2	1	no	—
5	#14519851	—	2	1	no	—
6	C₂×Dic₂₄₄	C₄	1	1	yes	characteristic
7	C₂×#11758189	C₂²	1	1	yes	characteristic
8	#14519757	—	2	1	no	—
9	#14519700	—	2	1	no	—
10	#106×C₆₁	C₄	1	1	yes	characteristic
11	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
12	C₂×Dic₁₂₂	—	2	1	no	—
13	#11758217	—	4	1	no	—
14	#11758213	—	4	1	no	—
15	D₆₁⋊C₈	—	2	2	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄⋊C₄×C₆₁	—	2	1	no	—
18	#11758198	—	4	1	no	—
19	C₄⋊Dic₆₁	—	4	1	no	—
20	C₂×#92418	D₄	1	1	yes	characteristic
21	Dic₂₄₄	—	4	1	no	—
22	#11758189	—	4	1	no	—
23	#11758187	—	4	1	no	—
24	C₂²×D₆₁	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₆₁	—	4	1	no	—
28	C₂×Dic₆₁	D₈	1	1	yes	characteristic
29	C₄×D₆₁	—	2	1	no	—
30	C₄×D₆₁	—	2	1	no	—
31	Dic₁₂₂	—	4	1	no	—
32	Dic₁₂₂	—	4	1	no	—
33	#92420	—	4	2	no	—
34	C₈×C₆₁	—	2	1	no	—
35	#92418	—	2	1	no	—
36	C₂²×C₆₁	#102	1	1	yes	characteristic
37	C₂×D₆₁	—	2	1	no	—
38	C₂×D₆₁	—	4	1	no	—
39	C₄×C₆₁	—	8	1	no	—
40	C₄×C₆₁	#99	1	1	yes	characteristic
41	C₄×C₆₁	#104	1	1	yes	characteristic
42	Dic₆₁	—	2	1	no	—
43	Dic₆₁	—	8	1	no	—
44	#1342	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	—	2	1	no	—
46	C₂×C₆₁	#327	1	1	yes	characteristic
47	D₆₁	—	4	1	no	—
48	#470	—	61	1	no	—
49	#349	—	61	1	no	—
50	#338	—	61	1	no	—
51	C₆₁	#1342	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	61	1	no	—
53	C₂×M₁₆	—	61	1	no	—
54	C₂×M₁₆	—	122	1	no	—
55	C₂²⋊Q₈	—	122	1	no	—
56	M₃₂	—	122	1	no	—
57	#106	#6923	1	1	yes	characteristic
58	#103	—	122	1	no	—
59	C₂×Q₈	—	122	1	no	—
60	C₂²×C₄	—	61	1	no	—
61	Q₁₆	—	244	1	no	—
62	M₁₆	—	244	1	no	—
63	M₁₆	—	244	1	no	—
64	M₁₆	—	244	1	no	—
65	C₂×C₈	—	61	1	no	—
66	C₂×C₈	—	122	2	no	—
67	C₂×C₈	C₂×#6923	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	244	1	no	—
70	C₂²⋊C₄	—	244	1	no	—
71	C₁₆	—	244	1	no	—
72	C₂³	—	61	1	no	—
73	Q₈	—	244	1	no	—
74	Q₈	—	244	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	61	1	no	—
77	C₂×C₄	—	122	1	no	—
78	C₂×C₄	—	122	1	no	—
79	C₂×C₄	—	244	1	no	—
80	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	122	1	no	—
83	C₈	—	244	2	no	—
84	C₂²	—	122	1	no	—
85	C₂²	—	244	1	no	—
86	C₂²	#14519839	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	122	1	no	—
89	C₄	—	488	1	no	—
90	C₄	#14519836	1	1	yes	characteristic
91	C₄	#14519842	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	244	1	no	—
94	C₂	#16840614	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840614
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₂×C₈	C₂×#6923
Fitting	#106×C₆₁	C₄
socle	C₂×C₆₁	#327
hypercenter	#106	#6923
hypocenter	C₆₁	#1342
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
51. C₆₁	#1342	semidirect