Subgroups — #21460828

Order 7808.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840685	C₂	1	2	yes	maximal
2	#16840141	C₂	1	1	yes	maximal, characteristic
3	#14519851	—	2	2	no	—
4	C₂×#11758202	—	2	2	no	—
5	#14519777	C₄	1	1	yes	characteristic
6	C₄×#92418	C₂²	1	1	yes	characteristic
7	C₄⋊Q₈×C₆₁	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₆₁	—	2	1	no	—
9	C₂×Dic₁₂₂	—	2	1	no	—
10	C₄⋊C₄×C₆₁	—	4	1	no	—
11	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
12	#11758202	—	4	2	no	—
13	#11758202	—	4	2	no	—
14	C₄⋊Dic₆₁	—	4	1	no	—
15	C₂×#92418	D₄	1	2	yes	—
16	#11758187	—	4	2	no	—
17	Q₈×C₆₁	—	4	2	no	—
18	C₂×C₄×C₆₁	—	2	1	no	—
19	C₂×C₄×C₆₁	—	4	1	no	—
20	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₆₁	—	4	1	no	—
22	Dic₁₂₂	—	4	2	no	—
23	#92418	D₈	1	2	yes	—
24	#92418	SD₁₆	1	2	yes	—
25	C₂²×C₆₁	#100	1	1	yes	characteristic
26	C₄×C₆₁	—	2	2	no	—
27	C₄×C₆₁	—	8	1	no	—
28	C₄×C₆₁	#102	1	2	yes	—
29	Dic₆₁	—	8	1	no	—
30	#1358	—	61	1	no	maximal, Sylow
31	C₂×C₆₁	—	2	1	no	—
32	C₂×C₆₁	#331	1	1	yes	characteristic
33	#494	—	61	1	no	—
34	#364	—	61	2	no	—
35	C₆₁	#1358	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₁₆	—	122	2	no	—
37	C₄⋊Q₈	—	61	1	no	—
38	C₄⋊Q₈	#6923	1	1	yes	characteristic
39	M₃₂	—	122	2	no	—
40	C₄×C₈	—	61	1	no	—
41	C₂×Q₈	—	2	1	no	—
42	C₂×Q₈	—	122	1	no	—
43	Q₁₆	—	244	2	no	—
44	Q₁₆	—	244	2	no	—
45	C₂×C₈	—	61	2	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄⋊C₄	—	244	1	no	—
48	C₄²	C₂×#6923	1	1	yes	characteristic
49	C₁₆	—	244	2	no	—
50	Q₈	—	4	2	no	—
51	Q₈	—	244	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	244	1	no	—
55	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
56	C₈	—	61	2	no	—
57	C₈	—	61	2	no	—
58	C₂²	#14519837	1	1	yes	characteristic
59	C₄	—	2	2	no	—
60	C₄	—	8	1	no	—
61	C₄	—	488	1	no	—
62	C₄	#14519839	1	2	yes	—
63	C₂	—	2	1	no	—
64	C₂	#16840620	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840620
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	C₄⋊Q₈×C₆₁	C₄
socle	C₂×C₆₁	#331
hypercenter	C₄⋊Q₈	#6923
hypocenter	C₆₁	#1358
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
35. C₆₁	#1358	semidirect