Subgroups — #21443867

Order 7808.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840142	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11758185	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₄₄	—	2	1	no	—
5	C₂×Dic₂₄₄	C₄	1	2	yes	—
6	#14519777	—	2	1	no	—
7	C₂×#11758185	—	2	1	no	—
8	C₄⋊C₈×C₆₁	—	2	1	no	—
9	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₂₂	—	2	2	no	—
11	C₂×C₈×C₆₁	—	4	1	no	—
12	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₄²×C₆₁	D₄	1	1	yes	characteristic
15	C₄⋊Dic₆₁	—	4	1	no	—
16	C₄⋊Dic₆₁	—	4	1	no	—
17	Dic₂₄₄	—	4	2	no	—
18	Dic₂₄₄	—	4	1	no	—
19	Dic₂₄₄	—	4	1	no	—
20	#11758185	—	4	1	no	—
21	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
23	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
24	C₂×Dic₆₁	—	4	2	no	—
25	Dic₁₂₂	—	4	2	no	—
26	Dic₁₂₂	—	4	2	no	—
27	C₈×C₆₁	—	2	1	no	—
28	C₈×C₆₁	—	8	1	no	—
29	C₈×C₆₁	D₈	1	1	yes	characteristic
30	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
31	C₂²×C₆₁	#102	1	1	yes	characteristic
32	C₄×C₆₁	—	2	1	no	—
33	C₄×C₆₁	#100	1	1	yes	characteristic
34	C₄×C₆₁	#102	1	1	yes	characteristic
35	C₄×C₆₁	SD₃₂	1	1	yes	characteristic
36	C₄×C₆₁	Q₃₂	1	1	yes	characteristic
37	Dic₆₁	—	8	2	no	—
38	#1362	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	#331	1	1	yes	characteristic
40	C₂×C₆₁	#358	1	1	yes	characteristic
41	C₂×C₆₁	#362	1	1	yes	characteristic
42	#494	—	61	1	no	—
43	C₄⋊C₁₆	—	61	1	no	—
44	#335	D₆₁	1	1	yes	characteristic
45	C₆₁	#1362	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	61	2	no	—
47	C₂×Q₁₆	—	122	1	no	—
48	C₄⋊Q₈	—	122	1	no	—
49	C₂×C₁₆	—	122	1	no	—
50	C₄⋊C₈	—	2	1	no	—
51	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
52	C₂×Q₈	—	122	2	no	—
53	Q₁₆	—	244	2	no	—
54	Q₁₆	—	244	1	no	—
55	Q₁₆	—	244	1	no	—
56	C₂×C₈	—	4	1	no	—
57	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
58	C₂×C₈	D₂₄₄	1	1	yes	characteristic
59	C₄⋊C₄	—	244	1	no	—
60	C₄⋊C₄	—	244	1	no	—
61	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
62	C₁₆	—	244	1	no	—
63	Q₈	—	244	2	no	—
64	Q₈	—	244	2	no	—
65	C₂×C₄	—	244	2	no	—
66	C₂×C₄	#11758198	1	1	yes	characteristic
67	C₂×C₄	#11758199	1	1	yes	characteristic
68	C₂×C₄	#11758201	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	8	1	no	—
71	C₈	#11758190	1	1	yes	characteristic
72	C₈	D₄₈₈	1	1	yes	characteristic
73	C₂²	#14519697	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	488	2	no	—
76	C₄	#14519693	1	1	yes	characteristic
77	C₄	#14519699	1	1	yes	characteristic
78	C₄	#14519721	1	1	yes	characteristic
79	C₄	#14519723	1	1	yes	characteristic
80	C₂	#16839505	1	1	yes	characteristic
81	C₂	#16839565	1	1	yes	characteristic
82	C₂	#16839577	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519697
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#335	C₂
socle	C₂²×C₆₁	#102
hypercenter	#335	D₆₁
hypocenter	C₆₁	#1362
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

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