Subgroups — #21443700

Order 7808.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519688	C₂	1	2	yes	maximal
2	C₆₁×#382	C₂	1	1	yes	maximal, characteristic
3	C₂²×#92418	—	2	2	no	—
4	#14519688	—	2	2	no	—
5	#14519688	C₄	1	4	yes	complemented
6	C₂×C₄⋊C₄×C₆₁	C₄	1	2	yes	—
7	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
8	#95×C₆₁	—	2	2	no	—
9	C₂²×C₄×C₆₁	—	2	2	no	—
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₆₁	D₄	1	2	yes	—
12	C₄⋊C₄×C₆₁	—	4	2	no	—
13	C₄²×C₆₁	C₂×C₄	1	2	yes	—
14	C₄²×C₆₁	D₄	1	1	yes	characteristic
15	C₄²×C₆₁	Q₈	1	1	yes	characteristic
16	C₂×#92418	—	2	8	no	—
17	C₂×#92418	—	2	4	no	—
18	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₆₁	—	2	1	no	—
20	C₂×C₄×C₆₁	—	2	1	no	—
21	C₂×C₄×C₆₁	—	2	4	no	—
22	C₂×C₄×C₆₁	—	4	2	no	—
23	C₂×C₄×C₆₁	—	4	4	no	—
24	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
26	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
28	#92418	—	2	8	no	—
29	C₂²×C₆₁	#95	1	1	yes	characteristic
30	C₂²×C₆₁	#100	1	1	yes	characteristic
31	C₂²×C₆₁	#101	1	1	yes	characteristic
32	C₂²×C₆₁	#104	1	4	yes	—
33	C₄×C₆₁	—	2	2	no	—
34	C₄×C₆₁	—	2	2	no	—
35	C₄×C₆₁	—	2	1	no	—
36	C₄×C₆₁	—	2	1	no	—
37	C₄×C₆₁	—	8	2	no	—
38	#1295	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	#329	1	2	yes	—
40	C₂×C₆₁	#330	1	2	yes	—
41	C₂×C₆₁	#339	1	2	yes	—
42	C₂×C₆₁	#343	1	1	yes	characteristic
43	C₂×#97	—	61	2	no	—
44	#382	D₆₁	1	1	yes	characteristic
45	C₆₁	#1295	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₈	—	122	2	no	—
47	C₂×C₄⋊C₄	Dic₆₁	1	2	yes	—
48	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
49	#97	—	61	4	no	—
50	#97	—	122	2	no	—
51	#95	—	2	2	no	—
52	C₂²×C₄	—	2	2	no	—
53	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
54	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
55	C₂×C₈	—	122	8	no	—
56	C₂×C₈	—	122	4	no	—
57	C₄⋊C₄	—	4	2	no	—
58	C₄²	Dic₁₂₂	1	1	yes	characteristic
59	C₄²	C₄×D₆₁	1	2	yes	—
60	C₄²	D₂₄₄	1	1	yes	characteristic
61	C₂³	C₂²⋊Dic₆₁	1	1	yes	characteristic
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	4	4	no	—
67	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
68	C₂×C₄	#11758196	1	2	yes	—
69	C₂×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
70	C₂×C₄	#11758198	1	2	yes	—
71	C₈	—	122	8	no	—
72	C₂²	#14519684	1	1	yes	characteristic
73	C₂²	#14519694	1	1	yes	characteristic
74	C₂²	#14519696	1	1	yes	characteristic
75	C₂²	#14519704	1	4	yes	—
76	C₄	—	2	2	no	—
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	8	2	no	—
81	C₂	#16839502	1	2	yes	—
82	C₂	#16839504	1	2	yes	—
83	C₂	#16839521	1	2	yes	—
84	C₂	#16839531	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊Dic₆₁
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂×C₄²	C₂×D₆₁
Fitting	C₆₁×#382	C₂
socle	C₂³×C₆₁	C₂²⋊C₄
hypercenter	#382	D₆₁
hypocenter	C₆₁	#1295
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

Complements

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

N	H ≅ G/N	type
5. #14519688	C₄	semidirect
45. C₆₁	#1295	semidirect