Group #21460856 — subgroups

Subgroups — (C₂×#6923)⋊C₁₆ #21460856

Order 7808.

160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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	C₂×D₆₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#6923	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×D₆₁⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₄×#6923	C₄	1	1	yes	characteristic
6	D₆₁⋊C₁₆	—	2	1	no	—
7	D₆₁⋊C₁₆	—	2	1	no	—
8	C₂×#11758187	C₄	1	2	yes	complemented
9	C₈×#6923	—	2	1	no	—
10	C₈×#6923	—	2	1	no	—
11	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
12	C₂×#11758185	C₄	1	1	yes	characteristic, complemented
13	C₁₆×D₆₁	—	2	1	no	—
14	C₁₆×D₆₁	—	2	1	no	—
15	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
16	C₂²×#6923	C₈	1	2	yes	—
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×#92420	C₈	1	2	yes	—
19	C₄×#6923	—	2	1	no	—
20	C₄×#6923	—	2	1	no	—
21	D₆₁⋊C₈	—	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×#6923	—	2	2	no	—
35	C₂×#6923	C₁₆	1	4	yes	complemented
36	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
38	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₆₁	M₁₆	1	1	yes	characteristic
41	C₄×D₆₁	M₁₆	1	1	yes	characteristic
42	#92420	—	2	2	no	—
43	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
44	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
45	#92418	C₂²⋊C₄	1	1	yes	characteristic
46	#92418	C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
48	C₂×D₆₁	C₂²⋊C₈	1	1	yes	characteristic
49	C₂×D₆₁	C₄⋊C₈	1	1	yes	characteristic
50	C₂×D₆₁	C₂×C₁₆	1	2	yes	—
51	C₂×D₆₁	M₃₂	1	2	yes	—
52	#6923	—	2	4	no	—
53	C₄×C₆₁	#95	1	1	yes	characteristic
54	C₄×C₆₁	#97	1	1	yes	characteristic
55	Dic₆₁	C₂²⋊C₈	1	1	yes	characteristic
56	Dic₆₁	C₄⋊C₈	1	1	yes	characteristic
57	#1374	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	#336	1	1	yes	characteristic
59	C₂×C₆₁	C₄×C₁₆	1	1	yes	characteristic
60	C₂×C₆₁	#346	1	1	yes	characteristic
61	D₆₁	C₂²⋊C₁₆	1	2	yes	—
62	D₆₁	C₄⋊C₁₆	1	2	yes	—
63	C₂²×C₁₆	—	61	1	no	—
64	C₂²×C₁₆	—	61	1	no	—
65	C₂×C₄×C₈	—	61	1	no	—
66	C₆₁	#1374	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	61	1	no	—
68	C₂²×C₈	—	61	1	no	—
69	C₂×C₄²	—	61	1	no	—
70	C₂×C₁₆	—	61	2	no	—
71	C₂×C₁₆	—	61	1	no	—
72	C₂×C₁₆	—	122	1	no	—
73	C₂×C₁₆	—	122	1	no	—
74	C₂×C₁₆	—	122	1	no	—
75	C₂×C₁₆	—	122	1	no	—
76	C₂×C₁₆	#6923	1	1	yes	characteristic, complemented
77	C₄×C₈	—	122	1	no	—
78	C₄×C₈	—	122	1	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	—	61	2	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	61	1	no	—
85	C₂×C₈	—	61	1	no	—
86	C₂×C₈	—	61	2	no	—
87	C₂×C₈	—	122	1	no	—
88	C₂×C₈	—	122	1	no	—
89	C₂×C₈	C₂×#6923	1	1	yes	characteristic
90	C₄²	—	122	1	no	—
91	C₄²	—	122	1	no	—
92	C₁₆	—	2	1	no	—
93	C₁₆	—	122	2	no	—
94	C₁₆	—	122	1	no	—
95	C₂³	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	4	no	—
102	C₂×C₄	—	122	2	no	—
103	C₂×C₄	—	122	2	no	—
104	C₂×C₄	C₄×#6923	1	1	yes	characteristic
105	C₈	—	61	1	no	—
106	C₈	—	61	1	no	—
107	C₈	—	122	2	no	—
108	C₈	C₄⋊#6923	1	1	yes	characteristic
109	C₈	C₂²⋊#6923	1	1	yes	characteristic
110	C₂²	—	61	1	no	—
111	C₂²	—	61	1	no	—
112	C₂²	—	61	2	no	—
113	C₂²	—	61	2	no	—
114	C₂²	C₈×#6923	1	1	yes	characteristic
115	C₄	—	61	1	no	—
116	C₄	—	61	1	no	—
117	C₄	—	122	4	no	—
118	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
119	C₄	#14519831	1	1	yes	characteristic
120	C₂	—	61	2	no	—
121	C₂	—	61	2	no	—
122	C₂	(C₂×#6923)⋊C₈	1	1	yes	characteristic
123	C₂	C₁₆×#6923	1	1	yes	characteristic
124	C₂	#16840649	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₆₁⋊C₁₆

C₂

yes

maximal, characteristic

C₂×C₈×#6923

C₂

yes

maximal, characteristic

C₂×C₁₆×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

C₄

yes

characteristic

C₂×C₄×#6923

C₄

yes

characteristic

D₆₁⋊C₁₆

—

D₆₁⋊C₁₆

—

C₂×#11758187

C₄

yes

complemented

C₈×#6923

—

C₈×#6923

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂×#11758185

C₄

yes

characteristic, complemented

C₁₆×D₆₁

—

C₁₆×D₆₁

—

C₂×C₁₆×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

C₈

yes

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×#92420

C₈

yes

—

C₄×#6923

—

C₄×#6923

—

D₆₁⋊C₈

—

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

—

—

C₁₆

yes

complemented

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

C₂²⋊C₈

yes

characteristic

C₂×D₆₁

C₄⋊C₈

yes

characteristic

C₂×D₆₁

C₂×C₁₆

yes

—

C₂×D₆₁

M₃₂

yes

—

#6923

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

C₂²⋊C₈

yes

characteristic

Dic₆₁

C₄⋊C₈

yes

—

C₂×C₆₁

yes

C₂×C₆₁

C₄×C₁₆

yes

characteristic

C₂×C₆₁

#346

yes

characteristic

D₆₁

C₂²⋊C₁₆

yes

—

D₆₁

C₄⋊C₁₆

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₆₁

#1374

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

—

122

—

C₂×C₁₆

—

122

—

C₂×C₁₆

—

122

—

C₂×C₁₆

#6923

yes

characteristic, complemented

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄²

—

122

—

C₄²

—

122

—

C₁₆

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

122

—

103

C₂×C₄

—

122

—

104

C₂×C₄

C₄×#6923

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

122

—

108

C₈

C₄⋊#6923

yes

characteristic

109

C₈

C₂²⋊#6923

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₈×#6923

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

122

—

118

C₄

(C₂×#6923)⋊C₄

yes

characteristic

119

C₄

#14519831

yes

characteristic

120

C₂

—

121

C₂

—

122

C₂

(C₂×#6923)⋊C₈

yes

characteristic

123

C₂

C₁₆×#6923

yes

characteristic

124

C₂

#16840649

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#6923
commutator	C₂×C₆₁	C₄×C₁₆
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₄×C₈
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1374
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂×#6923

commutator

C₂×C₆₁

C₄×C₁₆

Fitting

C₂×C₁₆×C₆₁

C₄

socle

C₂²×C₆₁

C₄×C₈

C₂×C₁₆

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
8. C₂×#11758187	C₄	semidirect
12. C₂×#11758185	C₄	semidirect
15. C₂×C₁₆×C₆₁	C₄	semidirect
35. C₂×#6923	C₁₆	semidirect
66. C₆₁	#1374	semidirect
76. C₂×C₁₆	#6923	semidirect

H ≅ G/N

type

8. C₂×#11758187

C₄

semidirect

12. C₂×#11758185

C₄

semidirect

15. C₂×C₁₆×C₆₁

C₄

semidirect

35. C₂×#6923

C₁₆

semidirect

66. C₆₁

#1374

semidirect

76. C₂×C₁₆

#6923

semidirect

Subgroups — (C₂×#6923)⋊C₁₆ #21460856

Conjugacy classes of subgroups

Complements

Subgroups — (C2×#6923)⋊C16 #21460856

Conjugacy classes of subgroups

Complements

Subgroups — (C₂×#6923)⋊C₁₆ #21460856