Group #22611264 — subgroups

Subgroups — #22611264

Order 9344.

282 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14556591	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556522	C₂	1	2	yes	maximal
3	#17988349	C₂	1	2	yes	maximal
4	#17988342	C₂	1	1	yes	maximal, characteristic
5	#389×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	—	2	1	no	—
7	C₂²×#10596831	C₂²	1	2	yes	—
8	#14556591	—	2	4	no	—
9	C₂×C₄⋊Dic₇₃	—	2	1	no	—
10	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
11	#14556522	—	2	4	no	—
12	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
13	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
16	#95×C₇₃	—	2	1	no	—
17	C₂×Dic₁₄₆	—	2	4	no	—
18	C₂×Dic₁₄₆	—	4	2	no	—
19	C₂×Dic₁₄₆	—	4	2	no	—
20	C₂²×Dic₇₃	—	2	2	no	—
21	C₂×#10596831	—	2	2	no	—
22	C₂×#10596831	—	2	2	no	—
23	C₂×#10596831	Q₈	1	4	yes	complemented
24	C₄⋊Dic₇₃	—	2	4	no	—
25	C₄⋊Dic₇₃	—	2	2	no	—
26	C₄⋊Dic₇₃	D₄	1	4	yes	—
27	C₂²×C₄×C₇₃	—	2	1	no	—
28	C₂²×C₄×C₇₃	—	2	1	no	—
29	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
32	C₄⋊C₄×C₇₃	—	2	1	no	—
33	C₄⋊C₄×C₇₃	—	2	2	no	—
34	C₄⋊C₄×C₇₃	—	4	2	no	—
35	C₄⋊C₄×C₇₃	Q₈	1	2	yes	complemented
36	C₄²×C₇₃	—	2	2	no	—
37	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	—	2	1	no	—
39	C₂×C₄×C₇₃	—	2	1	no	—
40	C₂×C₄×C₇₃	—	2	1	no	—
41	C₂×C₄×C₇₃	—	2	1	no	—
42	C₂×C₄×C₇₃	—	2	2	no	—
43	C₂×C₄×C₇₃	—	4	1	no	—
44	C₂×C₄×C₇₃	—	4	1	no	—
45	C₂×C₄×C₇₃	—	4	1	no	—
46	C₂×C₄×C₇₃	—	4	1	no	—
47	C₂×C₄×C₇₃	—	4	1	no	—
48	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
49	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
50	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
52	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
54	C₂×Dic₇₃	—	2	4	no	—
55	C₂×Dic₇₃	—	4	2	no	—
56	C₂×Dic₇₃	—	4	2	no	—
57	Dic₁₄₆	—	4	8	no	—
58	#10596831	—	2	4	no	—
59	C₂²×C₇₃	#120	1	1	yes	characteristic
60	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
61	C₂²×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
62	C₂²×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
63	C₂²×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
64	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂²×C₇₃	#137	1	1	yes	characteristic
66	C₄×C₇₃	—	2	2	no	—
67	C₄×C₇₃	—	2	2	no	—
68	C₄×C₇₃	—	4	2	no	—
69	C₄×C₇₃	—	8	1	no	—
70	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
71	C₄×C₇₃	C₄⋊Q₈	1	2	yes	—
72	Dic₇₃	—	4	4	no	—
73	C₂×C₇₃	#395	1	1	yes	characteristic
74	C₂×C₇₃	#448	1	1	yes	characteristic
75	C₂×C₇₃	#450	1	1	yes	characteristic
76	C₂×C₇₃	#475	1	1	yes	characteristic
77	C₂×C₇₃	#476	1	1	yes	characteristic
78	C₂×C₇₃	#498	1	1	yes	characteristic
79	C₂×C₇₃	#501	1	1	yes	characteristic
80	#2058	—	73	1	no	maximal, Sylow
81	C₇₃	#2058	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₄⋊Q₈	—	73	1	no	—
83	C₂×#106	—	73	2	no	—
84	#389	D₇₃	1	1	yes	characteristic
85	#340	—	73	2	no	—
86	#336	—	73	1	no	—
87	C₂²×Q₈	—	146	1	no	—
88	C₂²×C₈	—	73	2	no	—
89	C₄⋊Q₈	—	146	4	no	—
90	C₂×C₄⋊C₄	—	2	1	no	—
91	C₂×C₄⋊C₄	—	73	2	no	—
92	C₂×C₄⋊C₄	—	146	1	no	—
93	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
94	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
95	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
96	#106	—	146	4	no	—
97	#95	—	2	1	no	—
98	C₂×Q₈	—	292	2	no	—
99	C₂×Q₈	—	292	2	no	—
100	C₂×Q₈	—	146	4	no	—
101	C₂²×C₄	—	2	1	no	—
102	C₂²×C₄	—	2	1	no	—
103	C₂²×C₄	—	146	2	no	—
104	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
105	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
106	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
107	C₂×C₈	—	73	4	no	—
108	C₂×C₈	—	146	2	no	—
109	C₂×C₈	—	146	2	no	—
110	C₄⋊C₄	—	2	1	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	4	2	no	—
113	C₄⋊C₄	—	73	4	no	—
114	C₄⋊C₄	—	146	4	no	—
115	C₄⋊C₄	—	146	2	no	—
116	C₄⋊C₄	Dic₁₄₆	1	2	yes	complemented
117	C₄²	—	2	2	no	—
118	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
119	Q₈	—	292	8	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	292	2	no	—
131	C₂×C₄	—	292	2	no	—
132	C₂×C₄	—	146	4	no	—
133	C₂×C₄	#11924015	1	2	yes	—
134	C₂×C₄	#11924016	1	2	yes	—
135	C₂×C₄	D₄×D₇₃	1	2	yes	—
136	C₂×C₄	Q₈×D₇₃	1	2	yes	—
137	C₂×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
138	C₂×C₄	#11924028	1	1	yes	characteristic
139	C₈	—	146	4	no	—
140	C₂²	#14556559	1	1	yes	characteristic
141	C₂²	#14556570	1	1	yes	characteristic
142	C₂²	#14556589	1	1	yes	characteristic
143	C₂²	C₂×#11924015	1	1	yes	characteristic
144	C₂²	C₂×#11924016	1	1	yes	characteristic
145	C₂²	#14556616	1	1	yes	characteristic
146	C₂²	#14556621	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	2	2	no	—
149	C₄	—	4	2	no	—
150	C₄	—	8	1	no	—
151	C₄	—	292	4	no	—
152	C₄	#14556569	1	2	yes	—
153	C₄	#14556590	1	2	yes	—
154	C₂	#17988507	1	1	yes	characteristic
155	C₂	#17988725	1	1	yes	characteristic
156	C₂	#17988737	1	1	yes	characteristic
157	C₂	#17988872	1	1	yes	characteristic
158	C₂	#17988877	1	1	yes	characteristic
159	C₂	#17988983	1	1	yes	characteristic
160	C₂	#17988997	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556591

C₂

yes

maximal, characteristic

C₂×#14556522

C₂

yes

maximal

#17988349

C₂

yes

maximal

#17988342

C₂

yes

maximal, characteristic

#389×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

—

C₂²×#10596831

C₂²

yes

—

#14556591

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

#14556522

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

Q₈

yes

complemented

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

Q₈

yes

complemented

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

#10596831

—

C₂²×C₇₃

#120

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₃

C₄⋊Q₈

yes

characteristic

C₂²×C₇₃

C₂×SD₁₆

yes

characteristic

C₂²×C₇₃

C₂×SD₁₆

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

C₄⋊Q₈

yes

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

C₂×#106

—

#389

D₇₃

yes

characteristic

#340

—

#336

—

C₂²×Q₈

—

146

—

C₂²×C₈

—

C₄⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

characteristic

#106

—

146

—

#95

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

100

C₂×Q₈

—

146

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

146

—

104

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

105

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

106

C₂²×C₄

C₂²×D₇₃

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

146

—

109

C₂×C₈

—

146

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

146

—

115

C₄⋊C₄

—

146

—

116

C₄⋊C₄

Dic₁₄₆

yes

complemented

117

C₄²

—

118

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

119

Q₈

—

292

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

292

—

131

C₂×C₄

—

292

—

132

C₂×C₄

—

146

—

133

C₂×C₄

#11924015

yes

—

134

C₂×C₄

#11924016

yes

—

135

C₂×C₄

D₄×D₇₃

yes

—

136

C₂×C₄

Q₈×D₇₃

yes

—

137

C₂×C₄

C₂×Dic₁₄₆

yes

characteristic

138

C₂×C₄

#11924028

yes

characteristic

139

C₈

—

146

—

140

C₂²

#14556559

yes

characteristic

141

C₂²

#14556570

yes

characteristic

142

C₂²

#14556589

yes

characteristic

143

C₂²

C₂×#11924015

yes

characteristic

144

C₂²

C₂×#11924016

yes

characteristic

145

C₂²

#14556616

yes

characteristic

146

C₂²

#14556621

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

292

—

152

C₄

#14556569

yes

—

153

C₄

#14556590

yes

—

154

C₂

#17988507

yes

characteristic

155

C₂

#17988725

yes

characteristic

156

C₂

#17988737

yes

characteristic

157

C₂

#17988872

yes

characteristic

158

C₂

#17988877

yes

characteristic

159

C₂

#17988983

yes

characteristic

160

C₂

#17988997

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₃
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#389×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#389	D₇₃
hypocenter	C₇₃	#2058
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₃

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#389×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

N	H ≅ G/N	type
23. C₂×#10596831	Q₈	semidirect
35. C₄⋊C₄×C₇₃	Q₈	semidirect
81. C₇₃	#2058	semidirect
116. C₄⋊C₄	Dic₁₄₆	semidirect

H ≅ G/N

type

23. C₂×#10596831

Q₈

semidirect

35. C₄⋊C₄×C₇₃

Q₈

semidirect

81. C₇₃

#2058

semidirect

116. C₄⋊C₄

Dic₁₄₆

semidirect

Subgroups — #22611264

Conjugacy classes of subgroups

Complements