Group #22625889 — subgroups

Subgroups — #22625889

Order 9344.

252 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 66 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	#17989667	C₂	1	1	yes	maximal, characteristic
2	#17989602	C₂	1	2	yes	maximal, complemented
3	#17989562	C₂	1	1	yes	maximal, characteristic
4	#17989462	C₂	1	2	yes	maximal, complemented
5	#17988570	C₂	1	1	yes	maximal, characteristic
6	#14556679	—	2	2	no	—
7	#14556679	—	2	2	no	—
8	C₂×#11924038	C₂²	1	1	yes	characteristic
9	D₇₃⋊M₁₆	—	2	2	no	—
10	D₇₃⋊M₁₆	C₂²	1	2	yes	—
11	C₂×#11924036	C₂²	1	1	yes	characteristic
12	#14556662	—	2	2	no	—
13	#14556661	—	2	2	no	—
14	#14556648	—	2	2	no	—
15	C₂×#11924029	C₂²	1	1	yes	characteristic
16	M₁₆×D₇₃	C₂²	1	2	yes	—
17	#14556510	C₄	1	1	yes	characteristic
18	#14556507	C₄	1	2	yes	—
19	#101×C₇₃	C₄	1	1	yes	characteristic
20	#11924038	—	2	2	no	—
21	#11924038	—	2	2	no	—
22	#11924038	—	2	2	no	—
23	#11924038	D₄	1	2	yes	—
24	#11924038	D₄	1	2	yes	—
25	#11924037	—	2	2	no	—
26	#11924036	—	2	4	no	—
27	#11924036	—	2	2	no	—
28	#11924036	—	2	2	no	—
29	C₂×#10596833	—	2	1	no	—
30	C₂×#10596833	—	2	1	no	—
31	#11924029	—	2	2	no	—
32	#11924029	—	2	2	no	—
33	C₂×D₂₉₂	C₂×C₄	1	1	yes	characteristic
34	C₂×D₂₉₂	Q₈	1	2	yes	—
35	C₂×C₄×D₇₃	D₄	1	2	yes	—
36	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
37	#11924012	C₂×C₄	1	2	yes	—
38	#11924011	—	2	2	no	—
39	C₈×D₇₃	—	2	2	no	—
40	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
41	M₁₆×C₇₃	C₂×C₄	1	2	yes	—
42	C₂²×D₇₃	C₄⋊C₄	1	2	yes	—
43	C₂²×D₇₃	C₂×Q₈	1	1	yes	characteristic
44	Q₈×C₇₃	—	2	2	no	—
45	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
46	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
48	D₂₉₂	—	2	4	no	—
49	D₂₉₂	—	2	2	no	—
50	C₄×D₇₃	—	2	2	no	—
51	C₄×D₇₃	—	2	2	no	—
52	C₄×D₇₃	C₂×D₄	1	2	yes	—
53	C₄×D₇₃	#41	1	2	yes	—
54	#10596833	—	2	2	no	—
55	#10596833	—	2	2	no	—
56	#10596833	—	4	1	no	—
57	#10596833	—	4	1	no	—
58	C₈×C₇₃	—	2	2	no	—
59	#10596831	—	2	2	no	—
60	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×D₇₃	—	2	2	no	—
62	C₂×D₇₃	—	4	1	no	—
63	C₂×D₇₃	—	4	2	no	—
64	C₂×D₇₃	C₂²⋊Q₈	1	2	yes	—
65	C₄×C₇₃	—	2	2	no	—
66	C₄×C₇₃	C₄×D₄	1	2	yes	—
67	Dic₇₃	#120	1	1	yes	characteristic
68	Dic₇₃	#123	1	1	yes	characteristic
69	C₂×C₇₃	—	2	1	no	—
70	C₂×C₇₃	#385	1	1	yes	characteristic
71	D₇₃	—	2	2	no	—
72	D₇₃	—	4	2	no	—
73	#1858	—	73	1	no	maximal, Sylow
74	C₇₃	#1858	1	1	yes	characteristic, complemented, Sylow
75	#568	—	73	1	no	—
76	#430	—	73	2	no	—
77	#413	—	73	1	no	—
78	#408	—	73	1	no	—
79	#341	—	73	2	no	—
80	C₂×#41	—	73	1	no	—
81	#131	—	146	2	no	—
82	#131	—	146	2	no	—
83	C₂×M₁₆	—	73	2	no	—
84	C₂×M₁₆	—	73	2	no	—
85	C₂×M₁₆	—	73	1	no	—
86	C₂×M₁₆	—	146	2	no	—
87	C₂²×C₈	—	73	1	no	—
88	#108	—	146	2	no	—
89	#108	—	146	2	no	—
90	#101	—	73	1	no	—
91	#101	#64408	1	1	yes	characteristic
92	#100	—	73	2	no	—
93	C₂²⋊C₈	—	146	2	no	—
94	#41	—	146	2	no	—
95	#41	—	146	2	no	—
96	C₂×Q₈	C₂×#64408	1	1	yes	characteristic
97	C₂×D₄	—	73	2	no	—
98	C₂×D₄	—	73	1	no	—
99	C₂²×C₄	—	73	1	no	—
100	C₂²×C₄	—	73	2	no	—
101	M₁₆	—	73	2	no	—
102	M₁₆	—	73	2	no	—
103	M₁₆	—	73	2	no	—
104	M₁₆	—	146	2	no	—
105	M₁₆	—	146	2	no	—
106	M₁₆	—	146	2	no	—
107	M₁₆	—	146	2	no	—
108	M₁₆	—	146	2	no	—
109	M₁₆	C₂×#64408	1	2	yes	—
110	C₂×C₈	—	146	2	no	—
111	C₂×C₈	—	146	1	no	—
112	C₂×C₈	—	146	1	no	—
113	C₂×C₈	—	146	2	no	—
114	C₂×C₈	—	146	2	no	—
115	C₂×C₈	—	146	4	no	—
116	C₂³	—	73	1	no	—
117	C₂³	—	73	2	no	—
118	Q₈	—	2	2	no	—
119	D₄	—	146	4	no	—
120	D₄	—	146	2	no	—
121	C₂×C₄	—	73	1	no	—
122	C₂×C₄	—	73	2	no	—
123	C₂×C₄	—	73	2	no	—
124	C₂×C₄	—	146	2	no	—
125	C₂×C₄	—	146	2	no	—
126	C₂×C₄	C₄⋊#64408	1	2	yes	—
127	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
128	C₈	—	2	2	no	—
129	C₈	—	292	1	no	—
130	C₈	—	292	1	no	—
131	C₈	—	146	2	no	—
132	C₈	—	146	2	no	—
133	C₈	—	146	2	no	—
134	C₂²	—	292	2	no	—
135	C₂²	—	292	1	no	—
136	C₂²	—	73	2	no	—
137	C₂²	—	146	2	no	—
138	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	73	1	no	—
141	C₄	—	73	1	no	—
142	C₄	D₄×#64408	1	2	yes	—
143	C₂	—	2	1	no	—
144	C₂	—	292	2	no	—
145	C₂	—	146	2	no	—
146	C₂	#17989534	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989667

C₂

yes

maximal, characteristic

#17989602

C₂

yes

maximal, complemented

#17989562

C₂

yes

maximal, characteristic

#17989462

C₂

yes

maximal, complemented

#17988570

C₂

yes

maximal, characteristic

#14556679

—

#14556679

—

C₂×#11924038

C₂²

yes

characteristic

D₇₃⋊M₁₆

—

D₇₃⋊M₁₆

C₂²

yes

—

C₂×#11924036

C₂²

yes

—

—

—

C₂²

yes

characteristic

M₁₆×D₇₃

C₂²

yes

—

#14556510

C₄

yes

characteristic

#14556507

C₄

yes

—

#101×C₇₃

C₄

yes

—

—

—

D₄

yes

—

#11924038

D₄

yes

—

—

—

—

—

—

—

—

—

C₂×D₂₉₂

C₂×C₄

yes

characteristic

C₂×D₂₉₂

Q₈

yes

—

C₂×C₄×D₇₃

D₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

#11924012

C₂×C₄

yes

—

#11924011

—

C₈×D₇₃

—

C₂×Q₈×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

C₂×C₄

yes

—

C₂²×D₇₃

C₄⋊C₄

yes

—

C₂²×D₇₃

C₂×Q₈

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

C₂×D₄

yes

—

C₄×D₇₃

#41

yes

—

—

—

—

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

#385

yes

characteristic

D₇₃

—

D₇₃

—

#1858

—

maximal, Sylow

C₇₃

#1858

yes

characteristic, complemented, Sylow

—

—

—

—

—

C₂×#41

—

#131

—

146

—

#131

—

146

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

#108

—

146

—

#108

—

146

—

—

yes

—

C₂²⋊C₈

—

146

—

#41

—

146

—

#41

—

146

—

C₂×Q₈

C₂×#64408

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

146

—

105

M₁₆

—

146

—

106

M₁₆

—

146

—

107

M₁₆

—

146

—

108

M₁₆

—

146

—

109

M₁₆

C₂×#64408

yes

—

110

C₂×C₈

—

146

—

111

C₂×C₈

—

146

—

112

C₂×C₈

—

146

—

113

C₂×C₈

—

146

—

114

C₂×C₈

—

146

—

115

C₂×C₈

—

146

—

116

C₂³

—

117

C₂³

—

118

Q₈

—

119

D₄

—

146

—

120

D₄

—

146

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

146

—

125

C₂×C₄

—

146

—

126

C₂×C₄

C₄⋊#64408

yes

—

127

C₂×C₄

C₂²×#64408

yes

characteristic

128

C₈

—

129

C₈

—

292

—

130

C₈

—

292

—

131

C₈

—

146

—

132

C₈

—

146

—

133

C₈

—

146

—

134

C₂²

—

292

—

135

C₂²

—

292

—

136

C₂²

—

137

C₂²

—

146

—

138

C₂²

C₂×C₄⋊#64408

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

D₄×#64408

yes

—

143

C₂

—

144

C₂

—

292

—

145

C₂

—

146

—

146

C₂

#17989534

yes

characteristic

	subgroup	G/H
center	C₂	#17989534
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#101×C₇₃	C₄
socle	C₂×C₇₃	#385
hypercenter	#101	#64408
hypocenter	C₇₃	#1858
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

subgroup

G/H

center

C₂

#17989534

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#101×C₇₃

C₄

C₂×C₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

N	H ≅ G/N	type
2. #17989602	C₂	semidirect
4. #17989462	C₂	semidirect
74. C₇₃	#1858	semidirect

H ≅ G/N

type

2. #17989602

C₂

semidirect

4. #17989462

C₂

semidirect

74. C₇₃

#1858

semidirect

Subgroups — #22625889

Conjugacy classes of subgroups

Complements