Subgroups — #21447218

Order 7808.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839810	C₂	1	3	yes	maximal, complemented
2	C₂×#14519693	C₂	1	3	yes	maximal
3	C₆₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₂₄₄	C₂²	1	1	yes	characteristic
5	C₂×#11758194	C₂²	1	3	yes	—
6	#14519712	—	2	6	no	—
7	#14519693	—	2	6	no	—
8	C₂×M₁₆×C₆₁	C₂²	1	3	yes	—
9	C₂³×D₆₁	Q₈	1	2	yes	—
10	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
11	C₂×D₂₄₄	—	2	3	no	—
12	C₂×D₂₄₄	—	2	3	no	—
13	M₁₆×C₆₁	—	2	3	no	—
14	M₁₆×C₆₁	—	2	3	no	—
15	C₂×C₈×C₆₁	—	2	3	no	—
16	#11758194	—	2	3	no	—
17	#11758194	D₄	1	6	yes	—
18	C₂×#92418	—	2	3	no	—
19	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
20	C₂²×D₆₁	—	2	6	no	—
21	C₂²×D₆₁	—	8	2	no	—
22	C₂×C₄×C₆₁	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₆₁	#41	1	3	yes	—
24	D₂₄₄	—	4	3	no	—
25	D₂₄₄	—	4	1	no	—
26	C₈×C₆₁	—	4	3	no	—
27	#92418	—	2	6	no	—
28	C₂²×C₆₁	—	4	1	no	—
29	C₂²×C₆₁	C₂²⋊Q₈	1	3	yes	—
30	C₂×D₆₁	—	4	2	no	—
31	C₂×D₆₁	—	8	6	no	—
32	C₄×C₆₁	#121	1	3	yes	—
33	C₄×C₆₁	#126	1	1	yes	characteristic
34	#2069	—	61	1	no	maximal, Sylow
35	C₂×C₆₁	—	2	3	no	—
36	C₂×C₆₁	#396	1	1	yes	characteristic
37	D₆₁	—	8	2	no	—
38	#430	—	61	3	no	—
39	C₂×#100	—	61	3	no	—
40	#338	D₆₁	1	1	yes	characteristic, complemented
41	C₆₁	#2069	1	1	yes	characteristic, complemented, Sylow
42	C₂²×D₄	—	61	1	no	—
43	C₂×M₁₆	—	61	3	no	—
44	C₂×M₁₆	C₂×D₆₁	1	3	yes	—
45	#108	—	122	6	no	—
46	#100	—	122	6	no	—
47	C₂⁴	—	61	2	no	—
48	C₂×D₄	—	122	3	no	—
49	C₂×D₄	—	122	3	no	—
50	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
51	M₁₆	—	2	3	no	—
52	M₁₆	—	2	3	no	—
53	M₁₆	—	61	6	no	—
54	M₁₆	—	122	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	—	122	3	no	—
57	C₂³	—	122	6	no	—
58	C₂³	—	488	2	no	—
59	C₂³	Q₈×D₆₁	1	1	yes	characteristic
60	D₄	—	244	3	no	—
61	D₄	—	244	1	no	—
62	C₂×C₄	#11758222	1	3	yes	—
63	C₂×C₄	D₄×D₆₁	1	3	yes	—
64	C₈	—	4	3	no	—
65	C₈	—	122	6	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	488	6	no	—
68	C₂²	—	244	2	no	—
69	C₂²	#14519755	1	3	yes	—
70	C₄	#14519750	1	3	yes	—
71	C₄	#14519771	1	1	yes	characteristic
72	C₂	—	2	3	no	—
73	C₂	—	488	2	no	—
74	C₂	#16839686	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839686
commutator	C₂²×C₄×C₆₁	C₂³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#338	C₂
socle	C₂×C₆₁	#396
hypercenter	#338	D₆₁
hypocenter	C₆₁	#2069
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #16839810	C₂	semidirect
3. C₆₁×#338	C₂	semidirect
40. #338	D₆₁	semidirect
41. C₆₁	#2069	semidirect