Group #22620334 — subgroups

Subgroups — #22620334

Order 9344.

392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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	#17989137	C₂	1	1	yes	maximal, characteristic
2	#17988957	C₂	1	2	yes	maximal, complemented
3	#17988953	C₂	1	2	yes	maximal, complemented
4	#17988944	C₂	1	4	yes	maximal, complemented
5	#17988586	C₂	1	4	yes	maximal, complemented
6	C₄×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11924028	C₂²	1	2	yes	—
9	C₂×#11924012	C₂²	1	2	yes	—
10	#14556591	C₂²	1	1	yes	characteristic
11	#14556588	C₂²	1	1	yes	characteristic
12	#14556579	C₂²	1	2	yes	—
13	#14556565	—	2	2	no	—
14	C₄×D₂₉₂	—	2	2	no	—
15	#14556514	C₂²	1	8	yes	—
16	#14556511	C₂²	1	8	yes	—
17	#14556502	C₂²	1	2	yes	—
18	C₄×#10596831	C₂²	1	2	yes	—
19	#125×C₇₃	—	2	2	no	—
20	#125×C₇₃	C₂²	1	2	yes	—
21	#125×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
23	C₂×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
24	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
25	#11924028	—	2	8	no	—
26	C₂×Dic₁₄₆	C₂³	1	2	yes	—
27	C₂×D₂₉₂	—	2	2	no	—
28	C₂×D₂₉₂	C₂³	1	2	yes	—
29	C₂×C₂²⋊D₇₃	—	2	2	no	—
30	C₂×C₄×D₇₃	—	2	2	no	—
31	#11924012	—	2	4	no	—
32	C₂×#10596831	C₂³	1	4	yes	—
33	C₄⋊Dic₇₃	—	2	2	no	—
34	#11924005	—	2	4	no	—
35	C₂²×C₄×C₇₃	—	2	2	no	—
36	C₂²×C₄×C₇₃	D₄	1	2	yes	—
37	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
38	C₄⋊C₄×C₇₃	—	2	4	no	—
39	C₄⋊C₄×C₇₃	—	2	4	no	—
40	C₄⋊C₄×C₇₃	—	2	2	no	—
41	C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
42	C₄²×C₇₃	D₄	1	2	yes	—
43	C₄²×C₇₃	C₂³	1	1	yes	characteristic
44	C₄²×C₇₃	C₂³	1	1	yes	characteristic
45	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×D₇₃	—	2	2	no	—
47	C₂×C₄×C₇₃	—	2	4	no	—
48	C₂×C₄×C₇₃	—	4	2	no	—
49	C₂×C₄×C₇₃	—	4	4	no	—
50	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₇₃	#41	1	4	yes	—
54	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
55	C₂²⋊D₇₃	—	4	4	no	—
56	C₂×Dic₇₃	—	2	2	no	—
57	D₂₉₂	—	2	4	no	—
58	D₂₉₂	—	4	4	no	—
59	C₄×D₇₃	—	4	4	no	—
60	Dic₁₄₆	—	2	4	no	—
61	#10596831	—	2	4	no	—
62	C₂²×C₇₃	—	2	2	no	—
63	C₂²×C₇₃	#124	1	2	yes	—
64	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
65	C₂×D₇₃	—	4	2	no	—
66	C₂×D₇₃	—	4	4	no	—
67	C₄×C₇₃	—	2	2	no	—
68	C₄×C₇₃	—	2	2	no	—
69	C₄×C₇₃	—	4	4	no	—
70	C₄×C₇₃	#124	1	2	yes	—
71	C₄×C₇₃	C₂×#41	1	2	yes	—
72	Dic₇₃	—	4	2	no	—
73	C₂×C₇₃	—	2	2	no	—
74	C₂×C₇₃	C₂×#124	1	1	yes	characteristic
75	C₂×C₇₃	#575	1	2	yes	—
76	D₇₃	—	8	2	no	—
77	#3142	—	73	1	no	maximal, Sylow
78	C₇₃	#3142	1	1	yes	characteristic, complemented, Sylow
79	#532	—	73	1	no	—
80	C₂×#125	D₇₃	1	1	yes	characteristic, complemented
81	#491	—	73	2	no	—
82	#490	—	73	2	no	—
83	#488	—	73	4	no	—
84	#417	—	73	4	no	—
85	C₄×M₁₆	—	73	1	no	—
86	C₂×#41	—	73	2	no	—
87	C₂×M₁₆	—	73	2	no	—
88	C₄⋊Q₈	—	73	1	no	—
89	#127	—	73	1	no	—
90	#125	—	2	2	no	—
91	#125	C₂×D₇₃	1	2	yes	—
92	#125	C₂×D₇₃	1	2	yes	—
93	#124	—	73	2	no	—
94	#121	—	146	2	no	—
95	C₄×D₄	—	146	2	no	—
96	C₂×C₄⋊C₄	—	2	2	no	—
97	C₂×C₄⋊C₄	C₂×D₇₃	1	2	yes	—
98	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
99	#103	—	73	8	no	—
100	#102	—	73	8	no	—
101	#97	—	73	2	no	—
102	C₄×C₈	—	73	2	no	—
103	#41	—	146	8	no	—
104	C₂×Q₈	—	73	2	no	—
105	C₂×D₄	—	73	2	no	—
106	C₂×D₄	—	146	2	no	—
107	C₂×D₄	—	146	2	no	—
108	C₂²×C₄	—	2	2	no	—
109	C₂²×C₄	—	146	2	no	—
110	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
111	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
112	M₁₆	—	146	4	no	—
113	C₂×C₈	—	73	4	no	—
114	C₄⋊C₄	—	2	4	no	—
115	C₄⋊C₄	—	2	4	no	—
116	C₄⋊C₄	—	2	2	no	—
117	C₄⋊C₄	—	146	2	no	—
118	C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
119	C₂²⋊C₄	—	146	4	no	—
120	C₄²	C₂²⋊D₇₃	1	2	yes	—
121	C₄²	C₂²×D₇₃	1	1	yes	characteristic
122	C₄²	C₂²×D₇₃	1	1	yes	characteristic
123	C₂³	—	146	2	no	—
124	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
125	Q₈	—	146	4	no	—
126	D₄	—	292	4	no	—
127	D₄	—	292	4	no	—
128	D₄	—	146	4	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	—	292	4	no	—
133	C₂×C₄	—	146	2	no	—
134	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
135	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
136	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
137	C₂×C₄	#11924029	1	4	yes	—
138	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
139	C₈	—	146	4	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	292	4	no	—
142	C₂²	—	292	2	no	—
143	C₂²	#14556580	1	2	yes	—
144	C₂²	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	4	4	no	—
148	C₄	—	292	2	no	—
149	C₄	#14556580	1	2	yes	—
150	C₄	C₂×#11924029	1	2	yes	—
151	C₂	—	2	2	no	—
152	C₂	—	584	2	no	—
153	C₂	C₂×#14556580	1	1	yes	characteristic
154	C₂	#17989385	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989137

C₂

yes

maximal, characteristic

#17988957

C₂

yes

maximal, complemented

#17988953

C₂

yes

maximal, complemented

#17988944

C₂

yes

maximal, complemented

#17988586

C₂

yes

maximal, complemented

C₄×#11924012

C₂

yes

maximal, characteristic, complemented

C₂×#125×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

—

C₂×#11924012

C₂²

yes

—

#14556591

C₂²

yes

characteristic

#14556588

C₂²

yes

characteristic

#14556579

C₂²

yes

—

#14556565

—

C₄×D₂₉₂

—

#14556514

C₂²

yes

—

#14556511

C₂²

yes

—

#14556502

C₂²

yes

—

C₄×#10596831

C₂²

yes

—

#125×C₇₃

—

#125×C₇₃

C₂²

yes

—

#125×C₇₃

C₂²

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#11924028

—

C₂×Dic₁₄₆

C₂³

yes

—

C₂×D₂₉₂

—

C₂×D₂₉₂

C₂³

yes

—

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

—

#11924012

—

C₂×#10596831

C₂³

yes

—

C₄⋊Dic₇₃

—

#11924005

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂³

yes

—

C₄²×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

Dic₁₄₆

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#124

yes

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#124

yes

—

C₄×C₇₃

C₂×#41

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#124

yes

characteristic

C₂×C₇₃

#575

yes

—

D₇₃

—

#3142

—

maximal, Sylow

C₇₃

#3142

yes

characteristic, complemented, Sylow

#532

—

C₂×#125

D₇₃

yes

characteristic, complemented

—

—

—

—

C₄×M₁₆

—

C₂×#41

—

C₂×M₁₆

—

C₄⋊Q₈

—

#127

—

#125

—

#125

C₂×D₇₃

yes

—

#125

C₂×D₇₃

yes

—

#124

—

#121

—

146

—

C₄×D₄

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#103

—

100

#102

—

101

#97

—

102

C₄×C₈

—

103

#41

—

146

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂×D₄

—

146

—

107

C₂×D₄

—

146

—

108

C₂²×C₄

—

109

C₂²×C₄

—

146

—

110

C₂²×C₄

C₂²⋊D₇₃

yes

—

111

C₂²×C₄

C₂²×D₇₃

yes

characteristic

112

M₁₆

—

146

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

146

—

118

C₄⋊C₄

C₂²×D₇₃

yes

—

119

C₂²⋊C₄

—

146

—

120

C₄²

C₂²⋊D₇₃

yes

—

121

C₄²

C₂²×D₇₃

yes

characteristic

122

C₄²

C₂²×D₇₃

yes

characteristic

123

C₂³

—

146

—

124

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

125

Q₈

—

146

—

126

D₄

—

292

—

127

D₄

—

292

—

128

D₄

—

146

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

292

—

133

C₂×C₄

—

146

—

134

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

135

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

136

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

137

C₂×C₄

#11924029

yes

—

138

C₂×C₄

C₂³×D₇₃

yes

characteristic

139

C₈

—

146

—

140

C₂²

—

141

C₂²

—

292

—

142

C₂²

—

292

—

143

C₂²

#14556580

yes

—

144

C₂²

C₂²×C₂²⋊D₇₃

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

292

—

149

C₄

#14556580

yes

—

150

C₄

C₂×#11924029

yes

—

151

C₂

—

152

C₂

—

584

—

153

C₂

C₂×#14556580

yes

characteristic

154

C₂

#17989385

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	C₂×#125×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×D₄
hypercenter	C₂×#125	D₇₃
hypocenter	C₇₃	#3142
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

C₂×#125×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
2. #17988957	C₂	semidirect
3. #17988953	C₂	semidirect
4. #17988944	C₂	semidirect
5. #17988586	C₂	semidirect
6. C₄×#11924012	C₂	semidirect
7. C₂×#125×C₇₃	C₂	semidirect
78. C₇₃	#3142	semidirect
80. C₂×#125	D₇₃	semidirect

H ≅ G/N

type

2. #17988957

C₂

semidirect

3. #17988953

C₂

semidirect

4. #17988944

C₂

semidirect

5. #17988586

C₂

semidirect

6. C₄×#11924012

C₂

semidirect

7. C₂×#125×C₇₃

C₂

semidirect

78. C₇₃

#3142

semidirect

80. C₂×#125

D₇₃

semidirect

Subgroups — #22620334

Conjugacy classes of subgroups

Complements