Group #22620345 — subgroups

Subgroups — C₂×#17988965 #22620345

Order 9344.

552 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₂²×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11924018	C₂	1	2	yes	maximal
3	C₂×#14556589	C₂	1	2	yes	maximal
4	#17988965	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
8	C₂×Dic₂₉₂	—	2	4	no	—
9	C₂×Dic₂₉₂	C₂²	1	4	yes	—
10	C₂×#11924018	—	2	8	no	—
11	C₂×#11924018	C₂²	1	8	yes	—
12	C₂²×#10596831	C₂²	1	1	yes	characteristic
13	#14556589	—	2	4	no	—
14	#14556589	C₂²	1	8	yes	—
15	C₂×#11924007	—	2	4	no	—
16	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
17	C₈×Dic₇₃	C₂²	1	4	yes	—
18	C₂²×Q₈×C₇₃	C₂²	1	2	yes	—
19	C₂×Q₁₆×C₇₃	—	2	4	no	—
20	C₂×Q₁₆×C₇₃	C₂²	1	4	yes	—
21	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×Dic₁₄₆	—	2	4	no	—
23	C₂×Dic₁₄₆	—	2	4	no	—
24	C₂×Dic₁₄₆	—	2	2	no	—
25	C₂×Dic₁₄₆	C₂³	1	4	yes	—
26	C₂²×Dic₇₃	—	2	2	no	—
27	C₂²×Dic₇₃	D₄	1	2	yes	—
28	Dic₂₉₂	—	2	8	no	—
29	#11924018	—	2	16	no	—
30	C₂×#10596831	D₄	1	4	yes	—
31	C₂×#10596831	C₂³	1	2	yes	—
32	#11924007	—	2	16	no	—
33	C₄×Dic₇₃	D₄	1	2	yes	—
34	C₄×Dic₇₃	C₂³	1	2	yes	—
35	C₂×Q₈×C₇₃	—	2	2	no	—
36	C₂×Q₈×C₇₃	—	2	4	no	—
37	C₂×Q₈×C₇₃	—	2	4	no	—
38	C₂×Q₈×C₇₃	C₂³	1	4	yes	—
39	C₂²×C₄×C₇₃	—	2	2	no	—
40	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
41	Q₁₆×C₇₃	—	2	8	no	—
42	C₂×C₈×C₇₃	D₄	1	4	yes	—
43	C₂×C₈×C₇₃	C₂³	1	2	yes	—
44	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
45	Q₈×C₇₃	—	2	4	no	—
46	Q₈×C₇₃	—	2	4	no	—
47	Q₈×C₇₃	—	4	4	no	—
48	C₂×C₄×C₇₃	—	2	4	no	—
49	C₂×C₄×C₇₃	—	4	4	no	—
50	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
54	C₂×Dic₇₃	—	2	4	no	—
55	C₂×Dic₇₃	—	4	4	no	—
56	C₂×Dic₇₃	Q₁₆	1	8	yes	complemented
57	C₂×Dic₇₃	C₂×D₄	1	4	yes	—
58	Dic₁₄₆	—	2	4	no	—
59	Dic₁₄₆	—	2	4	no	—
60	Dic₁₄₆	—	4	4	no	—
61	C₈×C₇₃	C₂×D₄	1	4	yes	—
62	#10596831	C₂×D₄	1	4	yes	—
63	C₂²×C₇₃	#127	1	2	yes	—
64	C₂²×C₇₃	C₂×Q₁₆	1	4	yes	—
65	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
66	C₄×C₇₃	—	4	4	no	—
67	C₄×C₇₃	#127	1	2	yes	—
68	C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
69	C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
70	Dic₇₃	—	4	4	no	—
71	Dic₇₃	C₂×Q₁₆	1	8	yes	complemented
72	C₂×C₇₃	#494	1	4	yes	complemented
73	C₂×C₇₃	C₂×#127	1	1	yes	characteristic
74	C₂×C₇₃	C₂²×Q₁₆	1	2	yes	—
75	C₂×#494	—	73	1	no	maximal, Sylow
76	C₇₃	C₂×#494	1	1	yes	characteristic, complemented, Sylow
77	C₂²×Q₁₆	—	73	2	no	—
78	C₂²×Q₁₆	—	73	1	no	—
79	C₂²×Q₁₆	D₇₃	1	1	yes	characteristic
80	C₂×C₄⋊Q₈	—	73	2	no	—
81	#494	—	73	8	no	—
82	C₂×C₄×C₈	—	73	1	no	—
83	C₂²×Q₈	—	73	2	no	—
84	C₂²×Q₈	C₂×D₇₃	1	2	yes	—
85	C₂×Q₁₆	—	2	4	no	—
86	C₂×Q₁₆	—	73	8	no	—
87	C₂×Q₁₆	—	73	4	no	—
88	C₂×Q₁₆	—	146	8	no	—
89	C₂×Q₁₆	—	146	4	no	—
90	C₂×Q₁₆	C₂×D₇₃	1	4	yes	—
91	C₂²×C₈	—	73	1	no	—
92	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
93	C₄⋊Q₈	—	73	8	no	—
94	C₄⋊Q₈	—	146	4	no	—
95	C₂×C₄⋊C₄	—	146	4	no	—
96	C₂×C₄²	—	73	1	no	—
97	C₄×C₈	—	73	4	no	—
98	C₂×Q₈	—	2	2	no	—
99	C₂×Q₈	—	2	4	no	—
100	C₂×Q₈	—	2	4	no	—
101	C₂×Q₈	—	73	4	no	—
102	C₂×Q₈	—	146	4	no	—
103	C₂×Q₈	—	146	4	no	—
104	C₂×Q₈	—	146	2	no	—
105	C₂×Q₈	C₂²×D₇₃	1	4	yes	—
106	C₂²×C₄	—	2	2	no	—
107	C₂²×C₄	—	73	2	no	—
108	C₂²×C₄	—	146	2	no	—
109	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
110	Q₁₆	—	2	8	no	—
111	Q₁₆	—	146	16	no	—
112	Q₁₆	—	146	8	no	—
113	C₂×C₈	—	73	4	no	—
114	C₂×C₈	—	73	2	no	—
115	C₂×C₈	C₂²⋊D₇₃	1	4	yes	—
116	C₂×C₈	C₂²×D₇₃	1	2	yes	—
117	C₄⋊C₄	—	146	16	no	—
118	C₄²	—	73	2	no	—
119	C₄²	—	73	2	no	—
120	C₂³	D₄×D₇₃	1	1	yes	characteristic
121	Q₈	—	2	4	no	—
122	Q₈	—	2	4	no	—
123	Q₈	—	4	4	no	—
124	Q₈	—	292	4	no	—
125	Q₈	—	146	4	no	—
126	Q₈	—	146	4	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	292	4	no	—
130	C₂×C₄	—	73	8	no	—
131	C₂×C₄	—	73	4	no	—
132	C₂×C₄	—	146	4	no	—
133	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
134	C₂×C₄	D₄×D₇₃	1	2	yes	—
135	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
136	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
137	C₈	—	73	4	no	—
138	C₈	C₂×C₂²⋊D₇₃	1	4	yes	—
139	C₂²	#14556587	1	2	yes	—
140	C₂²	Q₁₆×D₇₃	1	4	yes	—
141	C₂²	C₂×D₄×D₇₃	1	1	yes	characteristic
142	C₄	—	4	4	no	—
143	C₄	—	292	4	no	—
144	C₄	—	73	8	no	—
145	C₄	#14556587	1	2	yes	—
146	C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
147	C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
148	C₂	#17988965	1	4	yes	direct product factor
149	C₂	C₂×#14556587	1	1	yes	characteristic
150	C₂	C₂×Q₁₆×D₇₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₉₂

C₂

yes

maximal, characteristic

C₂²×#11924018

C₂

yes

maximal

C₂×#14556589

C₂

yes

maximal

#17988965

C₂

yes

maximal, direct product factor

C₂×C₈×Dic₇₃

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂²

yes

—

C₂×#11924018

—

C₂×#11924018

C₂²

yes

—

C₂²×#10596831

C₂²

yes

characteristic

#14556589

—

#14556589

C₂²

yes

—

C₂×#11924007

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

—

C₂²×Q₈×C₇₃

C₂²

yes

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂³

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

—

Dic₂₉₂

—

#11924018

—

C₂×#10596831

D₄

yes

—

C₂×#10596831

C₂³

yes

—

#11924007

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

C₂³

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

Q₁₆

yes

complemented

C₂×Dic₇₃

C₂×D₄

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₄

yes

—

#10596831

C₂×D₄

yes

—

C₂²×C₇₃

#127

yes

—

C₂²×C₇₃

C₂×Q₁₆

yes

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

#127

yes

—

C₄×C₇₃

C₂²×D₄

yes

characteristic

C₄×C₇₃

C₂²×D₄

yes

characteristic

Dic₇₃

—

Dic₇₃

C₂×Q₁₆

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

C₂²×Q₁₆

yes

—

C₂×#494

—

maximal, Sylow

C₇₃

C₂×#494

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂²×Q₁₆

—

C₂²×Q₁₆

D₇₃

yes

characteristic

C₂×C₄⋊Q₈

—

#494

—

C₂×C₄×C₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₇₃

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

146

—

103

C₂×Q₈

—

146

—

104

C₂×Q₈

—

146

—

105

C₂×Q₈

C₂²×D₇₃

yes

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

146

—

109

C₂²×C₄

C₂²×D₇₃

yes

characteristic

110

Q₁₆

—

111

Q₁₆

—

146

—

112

Q₁₆

—

146

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₂²⋊D₇₃

yes

—

116

C₂×C₈

C₂²×D₇₃

yes

—

117

C₄⋊C₄

—

146

—

118

C₄²

—

119

C₄²

—

120

C₂³

D₄×D₇₃

yes

characteristic

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

292

—

125

Q₈

—

146

—

126

Q₈

—

146

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

292

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

146

—

133

C₂×C₄

D₄×D₇₃

yes

characteristic

134

C₂×C₄

D₄×D₇₃

yes

—

135

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

136

C₂×C₄

C₂³×D₇₃

yes

characteristic

137

C₈

—

138

C₈

C₂×C₂²⋊D₇₃

yes

—

139

C₂²

#14556587

yes

—

140

C₂²

Q₁₆×D₇₃

yes

—

141

C₂²

C₂×D₄×D₇₃

yes

characteristic

142

C₄

—

143

C₄

—

292

—

144

C₄

—

145

C₄

#14556587

yes

—

146

C₄

C₂×D₄×D₇₃

yes

characteristic

147

C₄

C₂²×C₂²⋊D₇₃

yes

characteristic

148

C₂

#17988965

yes

direct product factor

149

C₂

C₂×#14556587

yes

characteristic

150

C₂

C₂×Q₁₆×D₇₃

yes

—

	subgroup	G/H
center	C₂³	D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	C₂²×Q₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	C₂²×Q₁₆	D₇₃
hypocenter	C₇₃	C₂×#494
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂³

D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

C₂²×Q₁₆×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

hypercenter

C₂²×Q₁₆

D₇₃

hypocenter

C₇₃

C₂×#494

LCS

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
4. #17988965	C₂	direct (N × H)
56. C₂×Dic₇₃	Q₁₆	semidirect
71. Dic₇₃	C₂×Q₁₆	semidirect
72. C₂×C₇₃	#494	semidirect
76. C₇₃	C₂×#494	semidirect
148. C₂	#17988965	direct (N × H)

H ≅ G/N

type

4. #17988965

C₂

direct (N × H)

56. C₂×Dic₇₃

Q₁₆

semidirect

71. Dic₇₃

C₂×Q₁₆

semidirect

72. C₂×C₇₃

#494

semidirect

76. C₇₃

C₂×#494

semidirect

148. C₂

#17988965

direct (N × H)

Subgroups — C₂×#17988965 #22620345

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17988965 #22620345

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17988965 #22620345