Group #22610681 — subgroups

Subgroups — #22610681

Order 9344.

200 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14556526	C₂	1	1	yes	maximal, characteristic
2	#17988623	C₂	1	1	yes	maximal, characteristic
3	#17988613	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556501	C₂	1	1	yes	maximal, characteristic
5	#17988348	C₂	1	1	yes	maximal, characteristic
6	#17988346	C₂	1	1	yes	maximal, characteristic
7	#424×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924012	C₂²	1	1	yes	characteristic
9	C₂²×#10596831	C₂²	1	1	yes	characteristic
10	#14556550	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
12	#14556526	—	2	2	no	—
13	#14556524	C₄	1	2	yes	complemented
14	#14556522	C₄	1	2	yes	complemented
15	#14556520	—	2	2	no	—
16	#14556501	—	2	2	no	—
17	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	#117×C₇₃	C₂²	1	1	yes	characteristic
20	C₄⋊C₈×C₇₃	—	2	2	no	—
21	C₂²×Dic₇₃	—	2	1	no	—
22	#11924012	—	2	1	no	—
23	#11924012	—	2	1	no	—
24	C₂×#10596831	—	2	1	no	—
25	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
26	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
27	C₂×#10596831	D₄	1	2	yes	—
28	C₂×#10596831	Q₈	1	2	yes	—
29	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
30	C₂²⋊Dic₇₃	—	2	1	no	—
31	C₄×Dic₇₃	—	2	1	no	—
32	C₄×Dic₇₃	—	2	1	no	—
33	C₄×Dic₇₃	Q₈	1	2	yes	—
34	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
35	M₁₆×C₇₃	—	2	1	no	—
36	M₁₆×C₇₃	—	2	1	no	—
37	C₂×C₈×C₇₃	—	2	1	no	—
38	C₂×C₈×C₇₃	—	2	1	no	—
39	C₂×C₈×C₇₃	—	2	1	no	—
40	C₂×C₈×C₇₃	D₄	1	2	yes	—
41	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
42	C₂²⋊C₄×C₇₃	—	2	1	no	—
43	C₄²×C₇₃	—	2	1	no	—
44	C₂³×C₇₃	#41	1	1	yes	characteristic
45	C₂×C₄×C₇₃	—	2	2	no	—
46	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
52	C₂×Dic₇₃	—	2	2	no	—
53	C₂×Dic₇₃	—	2	2	no	—
54	C₂×Dic₇₃	—	4	2	no	—
55	C₈×C₇₃	—	2	2	no	—
56	C₈×C₇₃	—	4	1	no	—
57	#10596831	—	4	1	no	—
58	#10596831	C₄⋊C₄	1	2	yes	—
59	#10596831	C₄⋊C₄	1	2	yes	—
60	C₂²×C₇₃	—	2	2	no	—
61	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
62	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂²×C₇₃	#125	1	1	yes	characteristic
64	C₄×C₇₃	—	4	2	no	—
65	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
67	C₄×C₇₃	#121	1	1	yes	characteristic
68	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
69	Dic₇₃	—	4	2	no	—
70	Dic₇₃	—	4	2	no	—
71	C₂×C₇₃	—	2	1	no	—
72	C₂×C₇₃	—	2	1	no	—
73	C₂×C₇₃	#389	1	1	yes	characteristic
74	C₂×C₇₃	#444	1	2	yes	—
75	#1946	—	73	1	no	maximal, Sylow
76	C₇₃	#1946	1	1	yes	characteristic, complemented, Sylow
77	C₂×#108	—	73	1	no	—
78	#427	—	73	1	no	—
79	#424	—	73	1	no	—
80	#424	D₇₃	1	1	yes	characteristic
81	C₂×#97	—	73	1	no	—
82	#339	—	73	1	no	—
83	#339	—	73	1	no	—
84	C₂×M₁₆	—	73	1	no	—
85	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
86	C₂²×C₈	—	73	1	no	—
87	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
88	#117	—	73	1	no	—
89	#117	C₂×D₇₃	1	1	yes	characteristic
90	C₂×C₄²	—	73	1	no	—
91	#108	—	146	2	no	—
92	#107	—	73	2	no	—
93	#106	—	73	2	no	—
94	C₄⋊C₈	—	2	2	no	—
95	C₄⋊C₈	—	146	2	no	—
96	#97	—	146	2	no	—
97	C₂²×C₄	—	146	1	no	—
98	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
99	M₁₆	—	2	1	no	—
100	M₁₆	—	2	1	no	—
101	M₁₆	—	146	1	no	—
102	M₁₆	—	146	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	73	1	no	—
107	C₂×C₈	—	73	1	no	—
108	C₂×C₈	—	73	2	no	—
109	C₂×C₈	—	73	2	no	—
110	C₂×C₈	—	146	1	no	—
111	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
112	C₄⋊C₄	—	73	2	no	—
113	C₄⋊C₄	C₄×D₇₃	1	2	yes	—
114	C₂²⋊C₄	—	2	1	no	—
115	C₂²⋊C₄	—	146	1	no	—
116	C₄²	—	2	1	no	—
117	C₄²	—	73	2	no	—
118	C₄²	—	146	1	no	—
119	C₄²	—	146	1	no	—
120	C₂³	#11924028	1	1	yes	characteristic
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	292	2	no	—
123	C₂×C₄	—	146	2	no	—
124	C₂×C₄	—	146	2	no	—
125	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
126	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
127	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
128	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
129	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
130	C₂×C₄	#11924027	1	1	yes	characteristic
131	C₈	—	2	2	no	—
132	C₈	—	4	1	no	—
133	C₈	—	292	1	no	—
134	C₈	—	73	2	no	—
135	C₈	—	73	2	no	—
136	C₂²	—	2	2	no	—
137	C₂²	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
138	C₂²	#14556569	1	1	yes	characteristic
139	C₂²	#14556581	1	1	yes	characteristic
140	C₄	—	4	2	no	—
141	C₄	—	292	2	no	—
142	C₄	—	292	2	no	—
143	C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
144	C₄	#14556556	1	1	yes	characteristic
145	C₄	#14556563	1	1	yes	characteristic
146	C₄	#14556589	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	#17988482	1	1	yes	characteristic
150	C₂	#17988707	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556526

C₂

yes

maximal, characteristic

#17988623

C₂

yes

maximal, characteristic

#17988613

C₂

yes

maximal, characteristic

C₂×#14556501

C₂

yes

maximal, characteristic

#17988348

C₂

yes

maximal, characteristic

#17988346

C₂

yes

maximal, characteristic

#424×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556550

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556526

—

#14556524

C₄

yes

complemented

#14556522

C₄

yes

complemented

#14556520

—

#14556501

—

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²×Dic₇₃

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

D₄

yes

—

C₂×#10596831

Q₈

yes

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

C₄⋊C₄

yes

—

#10596831

C₄⋊C₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₃

#125

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₄×Q₈

yes

characteristic

C₄×C₇₃

#121

yes

characteristic

C₄×C₇₃

C₄⋊Q₈

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#389

yes

characteristic

C₂×C₇₃

#444

yes

—

#1946

—

maximal, Sylow

C₇₃

#1946

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic

C₂×#97

—

#339

—

#339

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

—

#117

C₂×D₇₃

yes

characteristic

C₂×C₄²

—

#108

—

146

—

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

#97

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

100

M₁₆

—

101

M₁₆

—

146

—

102

M₁₆

—

146

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

146

—

111

C₂×C₈

C₂²⋊D₇₃

yes

—

112

C₄⋊C₄

—

113

C₄⋊C₄

C₄×D₇₃

yes

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

146

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

146

—

119

C₄²

—

146

—

120

C₂³

#11924028

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

292

—

123

C₂×C₄

—

146

—

124

C₂×C₄

—

146

—

125

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

126

C₂×C₄

D₄×D₇₃

yes

characteristic

127

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

128

C₂×C₄

Q₈×D₇₃

yes

characteristic

129

C₂×C₄

Q₈×D₇₃

yes

characteristic

130

C₂×C₄

#11924027

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

292

—

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

C₄×C₂²⋊D₇₃

yes

characteristic

138

C₂²

#14556569

yes

characteristic

139

C₂²

#14556581

yes

characteristic

140

C₄

—

141

C₄

—

292

—

142

C₄

—

292

—

143

C₄

C₄⋊C₄×D₇₃

yes

characteristic

144

C₄

#14556556

yes

characteristic

145

C₄

#14556563

yes

characteristic

146

C₄

#14556589

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

#17988482

yes

characteristic

150

C₂

#17988707

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#424×C₇₃	C₂
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#424	D₇₃
hypocenter	C₇₃	#1946
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #424

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#424×C₇₃

C₂

socle

C₂²×C₇₃

C₄×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #424

N	H ≅ G/N	type
13. #14556524	C₄	semidirect
14. #14556522	C₄	semidirect
76. C₇₃	#1946	semidirect

H ≅ G/N

type

13. #14556524

C₄

semidirect

14. #14556522

C₄

semidirect

76. C₇₃

#1946

semidirect

Subgroups — #22610681

Conjugacy classes of subgroups

Complements