Subgroups — #21444004

Order 7808.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840194	C₂	1	1	yes	maximal, characteristic
2	#16839592	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#14519799	—	2	1	no	—
5	Dic₄₈₈	C₄	1	1	yes	characteristic
6	#14519722	—	2	1	no	—
7	D₉₇₆	C₄	1	1	yes	characteristic
8	#14519713	—	2	1	no	—
9	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
10	C₃₂×C₆₁	—	2	1	no	—
11	#11758222	—	4	1	no	—
12	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
13	#11758194	—	4	1	no	—
14	Dic₂₄₄	—	2	1	no	—
15	D₄₈₈	—	2	1	no	—
16	#11758190	—	4	1	no	—
17	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₆₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
20	C₂²⋊D₆₁	—	8	1	no	—
21	D₂₄₄	—	4	1	no	—
22	C₄×D₆₁	—	8	1	no	—
23	Dic₁₂₂	—	4	1	no	—
24	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
26	#92418	—	8	1	no	—
27	C₂²×C₆₁	SD₃₂	1	1	yes	characteristic
28	C₂×D₆₁	—	8	1	no	—
29	C₄×C₆₁	#102	1	1	yes	characteristic
30	C₄×C₆₁	D₁₆	1	1	yes	characteristic
31	Dic₆₁	—	8	1	no	—
32	#1417	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	—	2	1	no	—
34	C₂×C₆₁	#357	1	1	yes	characteristic
35	D₆₁	—	16	1	no	—
36	#508	—	61	1	no	—
37	C₂×C₃₂	D₆₁	1	1	yes	characteristic, complemented
38	#368	—	61	1	no	—
39	C₆₁	#1417	1	1	yes	characteristic, complemented, Sylow
40	#135	—	122	1	no	—
41	Q₃₂	—	61	1	no	—
42	SD₃₂	—	122	1	no	—
43	D₁₆	—	61	1	no	—
44	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
45	#108	—	122	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	244	1	no	—
48	Q₁₆	—	122	1	no	—
49	SD₁₆	—	244	1	no	—
50	D₈	—	122	1	no	—
51	M₁₆	—	244	1	no	—
52	C₂×C₈	D₂₄₄	1	1	yes	characteristic
53	C₁₆	C₄×D₆₁	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
55	Q₈	—	244	1	no	—
56	D₄	—	488	1	no	—
57	D₄	—	244	1	no	—
58	C₂×C₄	—	488	1	no	—
59	C₂×C₄	D₄₈₈	1	1	yes	characteristic
60	C₈	—	488	1	no	—
61	C₈	#11758190	1	1	yes	characteristic
62	C₈	#11758198	1	1	yes	characteristic
63	C₂²	—	488	1	no	—
64	C₂²	#14519722	1	1	yes	characteristic
65	C₄	—	488	1	no	—
66	C₄	#14519699	1	1	yes	characteristic
67	C₄	D₉₇₆	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	976	1	no	—
70	C₂	#16839564	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₉₇₆
commutator	C₁₆×C₆₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₆₁
Fitting	C₂×C₃₂×C₆₁	C₂
socle	C₂×C₆₁	#357
hypercenter	C₂×C₃₂	D₆₁
hypocenter	C₆₁	#1417
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #16839592	C₂	semidirect
3. C₂×C₃₂×C₆₁	C₂	semidirect
37. C₂×C₃₂	D₆₁	semidirect
39. C₆₁	#1417	semidirect