Group #22611992 — subgroups

Subgroups — #22611992

Order 9344.

158 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 47 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×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556535	C₂	1	1	yes	maximal, characteristic
3	#17988970	C₂	1	1	yes	maximal, characteristic
4	#17988681	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988405	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988390	C₂	1	1	yes	maximal, characteristic, complemented
7	#357×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
10	C₂×#11924016	—	2	1	no	—
11	#14556578	—	2	1	no	—
12	#14556556	—	2	1	no	—
13	Dic₅₈₄	—	2	2	no	—
14	#14556535	—	2	2	no	—
15	C₂×#11924003	C₂²	1	1	yes	characteristic
16	#14556514	—	2	1	no	—
17	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
18	C₂×D₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	#107×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₄₆	—	2	1	no	—
22	C₂×Dic₁₄₆	—	2	1	no	—
23	Dic₂₉₂	—	2	1	no	—
24	Dic₂₉₂	—	2	1	no	—
25	Dic₂₉₂	—	2	1	no	—
26	Dic₂₉₂	D₄	1	2	yes	—
27	#11924016	—	4	2	no	—
28	C₂×#10596831	D₄	1	1	yes	characteristic
29	#11924007	—	4	1	no	—
30	C₂²⋊Dic₇₃	—	4	1	no	—
31	C₂²⋊Dic₇₃	—	4	1	no	—
32	C₄×Dic₇₃	—	4	1	no	—
33	C₄×Dic₇₃	D₄	1	1	yes	characteristic
34	#11924003	—	2	1	no	—
35	C₂×D₄×C₇₃	—	2	1	no	—
36	D₈×C₇₃	—	2	1	no	—
37	D₈×C₇₃	—	2	1	no	—
38	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
39	C₄⋊C₄×C₇₃	—	2	1	no	—
40	C₁₆×C₇₃	—	2	1	no	—
41	C₂³×C₇₃	—	4	1	no	—
42	D₄×C₇₃	—	4	1	no	—
43	D₄×C₇₃	—	4	1	no	—
44	C₂×C₄×C₇₃	—	4	1	no	—
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₇₃	—	4	1	no	—
47	C₂×Dic₇₃	—	4	1	no	—
48	C₂×Dic₇₃	D₈	1	1	yes	characteristic
49	C₂×Dic₇₃	D₈	1	1	yes	characteristic
50	Dic₁₄₆	—	2	2	no	—
51	Dic₁₄₆	—	4	1	no	—
52	Dic₁₄₆	—	4	1	no	—
53	Dic₁₄₆	—	4	1	no	—
54	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
55	C₈×C₇₃	#41	1	1	yes	characteristic
56	#10596831	—	2	1	no	—
57	C₂²×C₇₃	—	8	1	no	—
58	C₂²×C₇₃	—	8	1	no	—
59	C₂²×C₇₃	—	8	1	no	—
60	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
61	C₄×C₇₃	—	8	1	no	—
62	C₄×C₇₃	#121	1	1	yes	characteristic
63	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
64	Dic₇₃	—	2	1	no	—
65	Dic₇₃	—	2	1	no	—
66	Dic₇₃	—	4	2	no	—
67	Dic₇₃	—	8	1	no	—
68	C₂×C₇₃	—	16	1	no	—
69	C₂×C₇₃	#459	1	1	yes	characteristic
70	C₂×C₇₃	#508	1	1	yes	characteristic
71	C₂×C₇₃	#510	1	1	yes	characteristic
72	#2211	—	73	1	no	maximal, Sylow
73	C₇₃	#2211	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₃₂	—	73	1	no	—
75	C₂×SD₃₂	—	73	1	no	—
76	#495	—	73	1	no	—
77	C₄×Q₁₆	—	73	1	no	—
78	C₄⋊C₁₆	—	73	1	no	—
79	#358	—	73	1	no	—
80	#357	D₇₃	1	1	yes	characteristic
81	C₂×Q₁₆	—	73	1	no	—
82	C₂×Q₁₆	—	73	1	no	—
83	C₂×SD₁₆	—	146	1	no	—
84	C₂×D₈	C₂×D₇₃	1	1	yes	characteristic
85	#124	—	146	1	no	—
86	C₄×Q₈	—	146	1	no	—
87	Q₃₂	—	146	2	no	—
88	SD₃₂	—	146	2	no	—
89	C₂×C₁₆	—	73	1	no	—
90	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
91	#107	C₂×D₇₃	1	1	yes	characteristic
92	#103	—	146	1	no	—
93	C₄×C₈	—	73	1	no	—
94	C₂×Q₈	—	146	1	no	—
95	C₂×Q₈	—	146	1	no	—
96	C₂×D₄	—	2	1	no	—
97	Q₁₆	—	73	2	no	—
98	Q₁₆	—	146	1	no	—
99	Q₁₆	—	146	1	no	—
100	Q₁₆	—	146	1	no	—
101	SD₁₆	—	292	2	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	C₂×C₈	—	73	1	no	—
105	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	292	1	no	—
108	C₂²⋊C₄	—	292	1	no	—
109	C₂²⋊C₄	—	292	1	no	—
110	C₄²	—	292	1	no	—
111	C₄²	—	73	1	no	—
112	C₁₆	—	2	1	no	—
113	C₁₆	—	146	1	no	—
114	C₂³	—	4	1	no	—
115	Q₈	—	292	1	no	—
116	Q₈	—	292	1	no	—
117	Q₈	—	292	1	no	—
118	Q₈	—	146	2	no	—
119	D₄	—	4	1	no	—
120	D₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	292	1	no	—
123	C₂×C₄	—	292	1	no	—
124	C₂×C₄	—	73	1	no	—
125	C₂×C₄	—	73	1	no	—
126	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
127	C₈	—	146	1	no	—
128	C₈	D₄×D₇₃	1	1	yes	characteristic
129	C₈	#11924028	1	1	yes	characteristic
130	C₂²	—	8	1	no	—
131	C₂²	—	8	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	D₈×D₇₃	1	1	yes	characteristic
134	C₄	—	8	1	no	—
135	C₄	—	292	2	no	—
136	C₄	—	584	1	no	—
137	C₄	—	146	1	no	—
138	C₄	—	146	1	no	—
139	C₄	#14556564	1	1	yes	characteristic
140	C₄	#14556618	1	1	yes	characteristic
141	C₂	—	16	1	no	—
142	C₂	#17988781	1	1	yes	characteristic
143	C₂	#17989016	1	1	yes	characteristic
144	C₂	#17989026	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₈₄

C₂

yes

maximal, characteristic, complemented

C₂×#14556535

C₂

yes

maximal, characteristic

#17988970

C₂

yes

maximal, characteristic

#17988681

C₂

yes

maximal, characteristic, complemented

#17988405

C₂

yes

maximal, characteristic, complemented

#17988390

C₂

yes

maximal, characteristic, complemented

#357×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×Dic₂₉₂

C₂²

yes

—

—

—

Dic₅₈₄

—

#14556535

—

C₂×#11924003

C₂²

yes

characteristic

#14556514

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×D₈×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

#107×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

D₄

yes

—

#11924016

—

C₂×#10596831

D₄

yes

characteristic

#11924007

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

D₈

yes

characteristic

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

#357

D₇₃

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

146

—

C₂×D₈

C₂×D₇₃

yes

characteristic

#124

—

146

—

C₄×Q₈

—

146

—

Q₃₂

—

146

—

SD₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#107

C₂×D₇₃

yes

characteristic

#103

—

146

—

C₄×C₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

146

—

Q₁₆

—

146

—

100

Q₁₆

—

146

—

101

SD₁₆

—

292

—

102

D₈

—

103

D₈

—

104

C₂×C₈

—

105

C₂×C₈

C₂²×D₇₃

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

292

—

108

C₂²⋊C₄

—

292

—

109

C₂²⋊C₄

—

292

—

110

C₄²

—

292

—

111

C₄²

—

112

C₁₆

—

113

C₁₆

—

146

—

114

C₂³

—

115

Q₈

—

292

—

116

Q₈

—

292

—

117

Q₈

—

292

—

118

Q₈

—

146

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

292

—

123

C₂×C₄

—

292

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

D₄×D₇₃

yes

characteristic

127

C₈

—

146

—

128

C₈

D₄×D₇₃

yes

characteristic

129

C₈

#11924028

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

D₈×D₇₃

yes

characteristic

134

C₄

—

135

C₄

—

292

—

136

C₄

—

584

—

137

C₄

—

146

—

138

C₄

—

146

—

139

C₄

#14556564

yes

characteristic

140

C₄

#14556618

yes

characteristic

141

C₂

—

142

C₂

#17988781

yes

characteristic

143

C₂

#17989016

yes

characteristic

144

C₂

#17989026

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#357×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#357	D₇₃
hypocenter	C₇₃	#2211
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#357×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×Dic₅₈₄	C₂	semidirect
4. #17988681	C₂	semidirect
5. #17988405	C₂	semidirect
6. #17988390	C₂	semidirect
73. C₇₃	#2211	semidirect

H ≅ G/N

type

1. C₂×Dic₅₈₄

C₂

semidirect

4. #17988681

C₂

semidirect

5. #17988405

C₂

semidirect

6. #17988390

C₂

semidirect

73. C₇₃

#2211

semidirect

Subgroups — #22611992

Conjugacy classes of subgroups

Complements