Group #22618583 — subgroups

Subgroups — #22618583

Order 9344.

384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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	C₄×#11924028	C₂	1	1	yes	maximal, characteristic
2	#17988646	C₂	1	4	yes	maximal, complemented
3	#17988642	C₂	1	4	yes	maximal, complemented
4	#17988615	C₂	1	2	yes	maximal, complemented
5	#17988555	C₂	1	2	yes	maximal
6	C₂×#14556502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11924028	C₂²	1	1	yes	characteristic
9	C₂²×#10596831	C₂²	1	2	yes	—
10	C₄×Dic₁₄₆	C₄	1	2	yes	—
11	C₄×D₂₉₂	C₄	1	2	yes	—
12	C₄×C₂²⋊D₇₃	C₄	1	4	yes	—
13	#14556550	C₂²	1	1	yes	characteristic
14	#14556548	C₂²	1	2	yes	—
15	C₄²×D₇₃	C₂²	1	2	yes	—
16	#14556520	C₂²	1	8	yes	—
17	#14556503	C₂²	1	8	yes	—
18	#14556502	C₂²	1	2	yes	—
19	#14556502	C₂²	1	2	yes	—
20	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
21	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
22	#97×C₇₃	C₂²	1	2	yes	—
23	C₄×C₈×C₇₃	C₂²	1	2	yes	—
24	#11924028	—	2	4	no	—
25	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
26	C₂×D₂₉₂	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
28	C₂×C₄×D₇₃	C₂×C₄	1	4	yes	—
29	C₂×C₄×D₇₃	C₂³	1	2	yes	—
30	C₂×#10596831	—	2	4	no	—
31	C₂×#10596831	C₂³	1	4	yes	—
32	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
33	#11924007	C₂×C₄	1	4	yes	—
34	C₂²⋊Dic₇₃	C₂×C₄	1	2	yes	—
35	#11924005	C₂×C₄	1	4	yes	—
36	C₄×Dic₇₃	C₂×C₄	1	4	yes	—
37	C₄×Dic₇₃	C₂³	1	2	yes	—
38	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
39	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
40	M₁₆×C₇₃	—	2	4	no	—
41	C₂×C₈×C₇₃	C₂³	1	4	yes	—
42	C₄²×C₇₃	C₂×C₄	1	2	yes	—
43	C₄²×C₇₃	C₂³	1	1	yes	characteristic
44	C₄²×C₇₃	C₂³	1	1	yes	characteristic
45	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×D₇₃	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₇₃	—	4	2	no	—
48	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
50	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₇₃	#41	1	4	yes	—
52	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
53	C₂²⋊D₇₃	—	2	4	no	—
54	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
55	C₂×Dic₇₃	C₂²×C₄	1	4	yes	—
56	D₂₉₂	—	2	2	no	—
57	C₄×D₇₃	—	2	4	no	—
58	C₄×D₇₃	—	4	4	no	—
59	Dic₁₄₆	—	2	2	no	—
60	C₈×C₇₃	—	2	4	no	—
61	#10596831	—	2	4	no	—
62	C₂²×C₇₃	—	2	2	no	—
63	C₂²×C₇₃	#117	1	2	yes	—
64	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
65	C₂×D₇₃	—	2	2	no	—
66	C₂×D₇₃	—	2	4	no	—
67	C₄×C₇₃	—	2	2	no	—
68	C₄×C₇₃	—	2	2	no	—
69	C₄×C₇₃	#117	1	2	yes	—
70	C₄×C₇₃	C₂×#41	1	2	yes	—
71	Dic₇₃	—	2	2	no	—
72	Dic₇₃	—	2	4	no	—
73	C₂×C₇₃	—	2	2	no	—
74	C₂×C₇₃	C₂×#117	1	1	yes	characteristic
75	C₂×C₇₃	#568	1	2	yes	—
76	D₇₃	—	4	2	no	—
77	#2923	—	73	1	no	maximal, Sylow
78	C₇₃	#2923	1	1	yes	characteristic, complemented, Sylow
79	C₄×#41	—	73	1	no	—
80	#433	—	73	4	no	—
81	#432	—	73	4	no	—
82	#424	—	73	2	no	—
83	#408	—	73	2	no	—
84	C₄×M₁₆	D₇₃	1	1	yes	characteristic, complemented
85	C₂×#97	—	73	1	no	—
86	C₂×#41	—	73	1	no	—
87	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
88	C₂²×C₈	—	73	2	no	—
89	C₄×Q₈	—	73	2	no	—
90	C₄×D₄	—	73	4	no	—
91	C₄×D₄	—	73	2	no	—
92	#117	—	73	1	no	—
93	#117	—	73	2	no	—
94	C₂×C₄²	—	73	2	no	—
95	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
96	C₄⋊C₈	—	73	8	no	—
97	C₂²⋊C₈	—	73	8	no	—
98	#97	—	73	2	no	—
99	#97	—	73	2	no	—
100	#97	C₂×D₇₃	1	2	yes	—
101	C₄×C₈	C₂×D₇₃	1	2	yes	—
102	#41	—	146	4	no	—
103	C₂×Q₈	—	73	1	no	—
104	C₂×D₄	—	73	2	no	—
105	C₂×D₄	—	73	1	no	—
106	C₂²×C₄	—	73	4	no	—
107	C₂²×C₄	—	73	2	no	—
108	C₂²×C₄	C₄×D₇₃	1	2	yes	—
109	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
110	M₁₆	—	2	4	no	—
111	C₂×C₈	—	73	4	no	—
112	C₂×C₈	—	146	4	no	—
113	C₂×C₈	C₂²×D₇₃	1	4	yes	—
114	C₄⋊C₄	—	73	4	no	—
115	C₄⋊C₄	—	73	2	no	—
116	C₂²⋊C₄	—	73	2	no	—
117	C₂²⋊C₄	—	73	4	no	—
118	C₄²	—	73	4	no	—
119	C₄²	—	73	2	no	—
120	C₄²	C₄×D₇₃	1	2	yes	—
121	C₄²	C₂²×D₇₃	1	1	yes	characteristic
122	C₄²	C₂²×D₇₃	1	1	yes	characteristic
123	C₂³	—	73	2	no	—
124	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
125	Q₈	—	146	2	no	—
126	D₄	—	146	4	no	—
127	D₄	—	146	2	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	292	4	no	—
130	C₂×C₄	—	73	4	no	—
131	C₂×C₄	—	73	2	no	—
132	C₂×C₄	—	146	4	no	—
133	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
134	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
135	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
136	C₂×C₄	#11924028	1	4	yes	—
137	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
138	C₈	—	2	4	no	—
139	C₈	—	146	4	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	146	2	no	—
142	C₂²	—	146	4	no	—
143	C₂²	#14556548	1	2	yes	—
144	C₂²	C₂²×C₄×D₇₃	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	146	2	no	—
148	C₄	—	146	4	no	—
149	C₄	#14556548	1	2	yes	—
150	C₄	C₂×#11924028	1	2	yes	—
151	C₂	—	2	2	no	—
152	C₂	—	292	2	no	—
153	C₂	C₂×#14556548	1	1	yes	characteristic
154	C₂	#17989353	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#11924028

C₂

yes

maximal, characteristic

#17988646

C₂

yes

maximal, complemented

#17988642

C₂

yes

maximal, complemented

#17988615

C₂

yes

maximal, complemented

#17988555

C₂

yes

maximal

C₂×#14556502

C₂

yes

maximal, characteristic, complemented

C₄×M₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

—

C₄×Dic₁₄₆

C₄

yes

—

C₄×D₂₉₂

C₄

yes

—

C₄×C₂²⋊D₇₃

C₄

yes

—

#14556550

C₂²

yes

characteristic

#14556548

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

—

#14556520

C₂²

yes

—

#14556503

C₂²

yes

—

#14556502

C₂²

yes

—

#14556502

C₂²

yes

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#97×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

—

#11924028

—

C₂×Dic₁₄₆

C₂×C₄

yes

characteristic

C₂×D₂₉₂

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

C₂×#10596831

—

C₂×#10596831

C₂³

yes

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

C₂×C₄

yes

—

C₂²⋊Dic₇₃

C₂×C₄

yes

—

#11924005

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

—

C₄²×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂²×D₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#117

yes

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#117

yes

—

C₄×C₇₃

C₂×#41

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#117

yes

characteristic

C₂×C₇₃

#568

yes

—

D₇₃

—

#2923

—

maximal, Sylow

C₇₃

#2923

yes

characteristic, complemented, Sylow

C₄×#41

—

—

—

—

—

C₄×M₁₆

D₇₃

yes

characteristic, complemented

C₂×#97

—

C₂×#41

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

100

#97

C₂×D₇₃

yes

—

101

C₄×C₈

C₂×D₇₃

yes

—

102

#41

—

146

—

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₄×D₇₃

yes

—

109

C₂²×C₄

C₂²×D₇₃

yes

characteristic

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

146

—

113

C₂×C₈

C₂²×D₇₃

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₄×D₇₃

yes

—

121

C₄²

C₂²×D₇₃

yes

characteristic

122

C₄²

C₂²×D₇₃

yes

characteristic

123

C₂³

—

124

C₂³

C₂×C₄×D₇₃

yes

characteristic

125

Q₈

—

146

—

126

D₄

—

146

—

127

D₄

—

146

—

128

C₂×C₄

—

129

C₂×C₄

—

292

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

146

—

133

C₂×C₄

C₂×C₄×D₇₃

yes

—

134

C₂×C₄

C₂×C₄×D₇₃

yes

—

135

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

136

C₂×C₄

#11924028

yes

—

137

C₂×C₄

C₂³×D₇₃

yes

characteristic

138

C₈

—

139

C₈

—

146

—

140

C₂²

—

141

C₂²

—

146

—

142

C₂²

—

146

—

143

C₂²

#14556548

yes

—

144

C₂²

C₂²×C₄×D₇₃

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

146

—

148

C₄

—

146

—

149

C₄

#14556548

yes

—

150

C₄

C₂×#11924028

yes

—

151

C₂

—

152

C₂

—

292

—

153

C₂

C₂×#14556548

yes

characteristic

154

C₂

#17989353

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂³×C₄
Fitting	C₄×M₁₆×C₇₃	C₂
hypercenter	C₄×M₁₆	D₇₃
hypocenter	C₇₃	#2923
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₇₃

commutator, socle

C₂²×C₇₃

C₂³×C₄

Fitting

C₄×M₁₆×C₇₃

C₂

hypercenter

C₄×M₁₆

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

N	H ≅ G/N	type
2. #17988646	C₂	semidirect
3. #17988642	C₂	semidirect
4. #17988615	C₂	semidirect
6. C₂×#14556502	C₂	semidirect
7. C₄×M₁₆×C₇₃	C₂	semidirect
78. C₇₃	#2923	semidirect
84. C₄×M₁₆	D₇₃	semidirect

H ≅ G/N

type

2. #17988646

C₂

semidirect

3. #17988642

C₂

semidirect

4. #17988615

C₂

semidirect

6. C₂×#14556502

C₂

semidirect

7. C₄×M₁₆×C₇₃

C₂

semidirect

78. C₇₃

#2923

semidirect

84. C₄×M₁₆

D₇₃

semidirect

Subgroups — #22618583

Conjugacy classes of subgroups

Complements