Subgroups — #21460791

Order 7808.

104 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	#16840630	C₂	1	1	yes	maximal, characteristic
3	#16840017	C₂	1	1	yes	maximal, characteristic
4	#14519856	—	2	1	no	—
5	#14519851	—	2	1	no	—
6	C₂×#11758189	C₂²	1	1	yes	characteristic
7	#14519753	—	2	1	no	—
8	#14519709	C₄	1	1	yes	characteristic, complemented
9	#14519701	—	2	1	no	—
10	C₂×Q₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₆₁	—	2	1	no	—
12	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
13	C₂²⋊#6923	—	4	1	no	—
14	C₄⋊#6923	—	4	1	no	—
15	C₄×#6923	—	2	2	no	—
16	Q₁₆×C₆₁	—	4	1	no	—
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	#11758198	—	4	1	no	—
19	C₄⋊Dic₆₁	—	2	1	no	—
20	#11758196	—	4	1	no	—
21	C₂×#92418	D₄	1	1	yes	characteristic
22	#11758189	—	4	1	no	—
23	#11758187	—	4	1	no	—
24	C₂²×D₆₁	D₈	1	1	yes	characteristic
25	C₂×#6923	—	4	2	no	—
26	Q₈×C₆₁	—	4	1	no	—
27	Q₈×C₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	—	4	1	no	—
29	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₆₁	—	4	1	no	—
31	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
32	C₄×D₆₁	—	2	1	no	—
33	C₄×D₆₁	—	2	1	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	#6923	—	8	2	no	—
40	C₄×C₆₁	—	8	1	no	—
41	C₄×C₆₁	#99	1	1	yes	characteristic
42	C₄×C₆₁	#104	1	1	yes	characteristic
43	Dic₆₁	—	2	1	no	—
44	Dic₆₁	—	8	1	no	—
45	#1340	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	—	2	1	no	—
47	C₂×C₆₁	#327	1	1	yes	characteristic
48	D₆₁	—	4	1	no	—
49	#470	—	61	1	no	—
50	#349	—	61	1	no	—
51	H(3,ℤ/4)	—	61	1	no	—
52	C₆₁	#1340	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	#6923	1	1	yes	characteristic, complemented
54	C₂×M₁₆	—	61	1	no	—
55	C₂²⋊Q₈	—	122	1	no	—
56	#117	—	122	1	no	—
57	M₃₂	—	122	1	no	—
58	#106	—	61	1	no	—
59	#103	—	122	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	—	61	1	no	—
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	244	1	no	—
64	C₂×C₈	—	61	1	no	—
65	C₂×C₈	C₂×#6923	1	1	yes	characteristic
66	C₄⋊C₄	—	122	1	no	—
67	C₄⋊C₄	—	244	1	no	—
68	C₄⋊C₄	—	244	1	no	—
69	C₂²⋊C₄	—	244	1	no	—
70	C₂²⋊C₄	—	244	1	no	—
71	C₄²	—	122	2	no	—
72	C₁₆	—	244	1	no	—
73	C₂³	—	61	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	61	1	no	—
78	C₂×C₄	—	122	1	no	—
79	C₂×C₄	—	122	1	no	—
80	C₂×C₄	—	244	2	no	—
81	C₂×C₄	—	244	1	no	—
82	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	122	1	no	—
85	C₂²	—	122	1	no	—
86	C₂²	—	244	1	no	—
87	C₂²	#14519839	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	122	1	no	—
90	C₄	—	488	1	no	—
91	C₄	—	488	2	no	—
92	C₄	#14519835	1	1	yes	characteristic
93	C₄	#14519841	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	244	1	no	—
96	C₂	#16840613	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840613
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×Q₁₆×C₆₁	C₄
socle	C₂×C₆₁	#327
hypercenter	C₂×Q₁₆	#6923
hypocenter	C₆₁	#1340
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
8. #14519709	C₄	semidirect
10. C₂×Q₁₆×C₆₁	C₄	semidirect
52. C₆₁	#1340	semidirect
53. C₂×Q₁₆	#6923	semidirect