Group #21460868 — subgroups

Subgroups — #21460868

Order 7808.

132 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	#16840725	C₂	1	1	yes	maximal, characteristic
3	C₂×#14519716	C₂	1	1	yes	maximal, characteristic
4	D₆₁⋊M₁₆	C₄	1	1	yes	characteristic
5	#14519856	C₄	1	1	yes	characteristic
6	#14519852	—	2	1	no	—
7	#14519851	C₄	1	2	yes	complemented
8	D₆₁⋊C₁₆	—	2	1	no	—
9	#14519831	—	2	1	no	—
10	C₈×#6923	—	2	1	no	—
11	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
12	#14519716	—	2	1	no	—
13	#14519716	—	2	1	no	—
14	C₂×#11758185	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊#6923	C₈	1	2	yes	—
18	#11758217	C₈	1	2	yes	—
19	C₄⋊#6923	—	2	1	no	—
20	C₄×#6923	—	2	1	no	—
21	#11758213	—	2	1	no	—
22	D₆₁⋊C₈	—	2	1	no	—
23	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₈×D₆₁	D₄	1	1	yes	characteristic
26	C₈×D₆₁	D₄	1	1	yes	characteristic
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₈×D₆₁	Q₈	1	1	yes	characteristic
29	#11758187	—	2	2	no	—
30	C₁₆×C₆₁	—	2	1	no	—
31	#11758185	—	2	1	no	—
32	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
33	C₂×#6923	—	2	2	no	—
34	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
36	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₆₁	M₁₆	1	1	yes	characteristic
39	C₄×D₆₁	M₁₆	1	1	yes	characteristic
40	#92420	—	2	2	no	—
41	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
42	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
43	#92418	C₂²⋊C₄	1	1	yes	characteristic
44	#92418	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
46	C₂×D₆₁	—	4	1	no	—
47	C₂×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
48	C₂×D₆₁	C₄⋊C₈	1	1	yes	characteristic
49	#6923	—	4	2	no	—
50	C₄×C₆₁	#95	1	1	yes	characteristic
51	C₄×C₆₁	#97	1	1	yes	characteristic
52	Dic₆₁	C₂²⋊C₈	1	1	yes	characteristic
53	Dic₆₁	C₄⋊C₈	1	1	yes	characteristic
54	#1378	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	#336	1	1	yes	characteristic
57	D₆₁	—	2	1	no	—
58	D₆₁	—	2	1	no	—
59	C₂×M₃₂	—	61	1	no	—
60	C₂×M₃₂	—	61	1	no	—
61	#405	—	61	1	no	—
62	C₆₁	#1378	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₁₆	—	61	1	no	—
64	C₂²×C₈	—	61	1	no	—
65	#117	—	61	1	no	—
66	M₃₂	—	61	2	no	—
67	M₃₂	—	122	1	no	—
68	M₃₂	—	122	1	no	—
69	M₃₂	—	122	1	no	—
70	C₂×C₁₆	—	61	1	no	—
71	C₂×C₁₆	—	122	1	no	—
72	C₂×C₁₆	#6923	1	1	yes	characteristic, complemented
73	#97	—	122	1	no	—
74	C₄×C₈	—	122	1	no	—
75	C₂²×C₄	—	61	1	no	—
76	M₁₆	—	61	2	no	—
77	M₁₆	—	122	1	no	—
78	C₂×C₈	—	61	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	122	1	no	—
84	C₂×C₈	C₂×#6923	1	1	yes	characteristic
85	C₄⋊C₄	—	122	1	no	—
86	C₂²⋊C₄	—	61	2	no	—
87	C₄²	—	122	1	no	—
88	C₁₆	—	2	1	no	—
89	C₁₆	—	122	2	no	—
90	C₁₆	—	122	1	no	—
91	C₂³	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	122	2	no	—
98	C₂×C₄	C₄×#6923	1	1	yes	characteristic
99	C₈	—	61	1	no	—
100	C₈	—	61	1	no	—
101	C₈	—	122	2	no	—
102	C₈	C₄⋊#6923	1	1	yes	characteristic
103	C₈	C₂²⋊#6923	1	1	yes	characteristic
104	C₂²	—	61	1	no	—
105	C₂²	—	61	1	no	—
106	C₂²	—	244	1	no	—
107	C₂²	C₈×#6923	1	1	yes	characteristic
108	C₄	—	61	1	no	—
109	C₄	—	61	1	no	—
110	C₄	—	244	2	no	—
111	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
112	C₄	#14519831	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	122	1	no	—
115	C₂	—	122	1	no	—
116	C₂	(C₂×#6923)⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊M₃₂

C₂

yes

maximal, characteristic

#16840725

C₂

yes

maximal, characteristic

C₂×#14519716

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

C₄

yes

characteristic

#14519856

C₄

yes

characteristic

#14519852

—

#14519851

C₄

yes

complemented

D₆₁⋊C₁₆

—

#14519831

—

C₈×#6923

—

C₂×C₈×D₆₁

C₂²

yes

—

—

C₄

yes

characteristic, complemented

C₂×C₁₆×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂²⋊#6923

C₈

yes

—

#11758217

C₈

yes

—

C₄⋊#6923

—

C₄×#6923

—

#11758213

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

#11758187

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×#6923

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

#92420

—

C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

C₂²⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₂²⋊C₈

yes

characteristic

C₂×D₆₁

C₄⋊C₈

yes

characteristic

#6923

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

C₂²⋊C₈

yes

characteristic

Dic₆₁

C₄⋊C₈

yes

characteristic

#1378

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#336

yes

characteristic

D₆₁

—

D₆₁

—

C₂×M₃₂

—

C₂×M₃₂

—

#405

—

C₆₁

#1378

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

122

—

M₃₂

—

122

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

#6923

yes

characteristic, complemented

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

C₄²

—

122

—

C₁₆

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₄×#6923

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

122

—

102

C₈

C₄⋊#6923

yes

characteristic

103

C₈

C₂²⋊#6923

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

244

—

107

C₂²

C₈×#6923

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

244

—

111

C₄

(C₂×#6923)⋊C₄

yes

characteristic

112

C₄

#14519831

yes

characteristic

113

C₂

—

114

C₂

—

122

—

115

C₂

—

122

—

116

C₂

(C₂×#6923)⋊C₈

yes

characteristic

	subgroup	G/H
center	C₈	C₂²⋊#6923
commutator	C₂²×C₆₁	C₄×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂×C₆₁	#336
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1378
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center

C₈

C₂²⋊#6923

commutator

C₂²×C₆₁

C₄×C₈

Frattini

C₂×C₈

C₂×#6923

Fitting

C₂×C₁₆×C₆₁

C₄

C₂×C₆₁

C₂×C₁₆

C₆₁

G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
7. #14519851	C₄	semidirect
14. C₂×#11758185	C₄	semidirect
15. C₂×C₁₆×C₆₁	C₄	semidirect
62. C₆₁	#1378	semidirect
72. C₂×C₁₆	#6923	semidirect

H ≅ G/N

type

7. #14519851

C₄

semidirect

14. C₂×#11758185

C₄

semidirect

15. C₂×C₁₆×C₆₁

C₄

semidirect

62. C₆₁

#1378

semidirect

72. C₂×C₁₆

#6923

semidirect

Subgroups — #21460868

Conjugacy classes of subgroups

Complements