Subgroups — #21445959

Order 7808.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839786	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519688	C₂	1	1	yes	maximal, characteristic
3	#16839526	C₂	1	4	yes	maximal
4	C₆₁×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758194	C₂²	1	2	yes	—
6	C₂²×#92418	C₂²	1	2	yes	—
7	C₄⋊#92418	—	2	2	no	—
8	#14519688	C₄	1	4	yes	—
9	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
10	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₆₁	—	2	2	no	—
12	C₂²×C₄×C₆₁	Q₈	1	2	yes	—
13	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
14	M₁₆×C₆₁	—	2	4	no	—
15	C₂×C₈×C₆₁	—	2	2	no	—
16	C₄²×C₆₁	C₂×C₄	1	2	yes	—
17	C₄²×C₆₁	D₄	1	2	yes	—
18	#11758194	—	2	4	no	—
19	C₂×#92418	—	2	2	no	—
20	C₂×#92418	—	2	2	no	—
21	C₂×#92418	—	2	2	no	—
22	C₂×#92418	C₂×C₄	1	4	yes	—
23	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₆₁	—	4	2	no	—
25	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
26	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	#41	1	2	yes	—
29	C₂×C₄×C₆₁	#41	1	2	yes	—
30	C₈×C₆₁	—	4	2	no	—
31	#92418	—	2	4	no	—
32	#92418	—	4	2	no	—
33	C₂²×C₆₁	—	2	2	no	—
34	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₆₁	#125	1	2	yes	—
36	C₄×C₆₁	—	2	4	no	—
37	C₄×C₆₁	#117	1	2	yes	—
38	C₄×C₆₁	#124	1	1	yes	characteristic
39	C₄×C₆₁	#124	1	1	yes	characteristic
40	#1838	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	—	2	2	no	—
42	C₂×C₆₁	#382	1	1	yes	characteristic
43	C₂×C₆₁	#430	1	2	yes	—
44	#423	—	61	1	no	—
45	#423	D₆₁	1	1	yes	characteristic
46	C₂×#97	—	61	1	no	—
47	#341	—	61	4	no	—
48	C₆₁	#1838	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₁₆	—	61	2	no	—
50	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
51	C₂²×C₈	—	61	2	no	—
52	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
53	C₄⋊C₈	—	2	2	no	—
54	C₄⋊C₈	—	122	2	no	—
55	#97	—	61	4	no	—
56	C₂²×C₄	Dic₁₂₂	1	2	yes	—
57	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
58	M₁₆	—	2	4	no	—
59	M₁₆	—	122	4	no	—
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	—	61	4	no	—
62	C₂×C₈	—	122	2	no	—
63	C₂×C₈	—	122	2	no	—
64	C₂×C₈	—	122	2	no	—
65	C₄²	C₄×D₆₁	1	2	yes	—
66	C₄²	C₂²⋊D₆₁	1	2	yes	—
67	C₂³	C₂×Dic₁₂₂	1	1	yes	characteristic
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	#11758196	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
71	C₂×C₄	#11758224	1	2	yes	—
72	C₂×C₄	#11758226	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	122	4	no	—
76	C₈	—	244	2	no	—
77	C₂²	—	2	2	no	—
78	C₂²	C₂×#11758196	1	1	yes	characteristic
79	C₂²	#14519768	1	2	yes	—
80	C₄	—	2	4	no	—
81	C₄	#14519735	1	2	yes	—
82	C₄	#14519764	1	1	yes	characteristic
83	C₄	#14519766	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#16839627	1	1	yes	characteristic
86	C₂	#16839810	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#423	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#423	D₆₁
hypocenter	C₆₁	#1838
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
48. C₆₁	#1838	semidirect