Group #22607952 — subgroups

Subgroups — #22607952

Order 9344.

162 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 37 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	#17988354	C₂	1	1	yes	maximal, characteristic
2	#17988311	C₂	1	1	yes	maximal, characteristic
3	#393×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊Dic₇₃	—	2	1	no	—
5	C₂²⋊#10596831	—	2	1	no	—
6	C₂²×Q₈×C₇₃	C₄	1	1	yes	characteristic, complemented
7	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
8	C₂×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
9	#95×C₇₃	—	2	1	no	—
10	#95×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂²×Dic₇₃	—	4	1	no	—
12	C₂×#10596831	—	4	1	no	—
13	C₂²⋊Dic₇₃	—	2	2	no	—
14	C₂²⋊Dic₇₃	—	4	1	no	—
15	C₂⁴×C₇₃	D₄	1	1	yes	characteristic
16	C₂×Q₈×C₇₃	—	4	2	no	—
17	C₂×Q₈×C₇₃	—	4	1	no	—
18	C₂²×C₄×C₇₃	—	2	1	no	—
19	C₂²×C₄×C₇₃	—	2	1	no	—
20	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
22	C₂²⋊C₄×C₇₃	—	4	1	no	—
23	C₂²⋊C₄×C₇₃	—	4	2	no	—
24	C₂³×C₇₃	—	2	1	no	—
25	C₂³×C₇₃	—	2	1	no	—
26	C₂³×C₇₃	—	4	1	no	—
27	C₂³×C₇₃	—	4	1	no	—
28	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂³×C₇₃	SD₁₆	1	1	yes	characteristic
30	C₂³×C₇₃	Q₁₆	1	1	yes	characteristic
31	Q₈×C₇₃	—	4	2	no	—
32	Q₈×C₇₃	—	4	2	no	—
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	—	2	1	no	—
35	C₂×C₄×C₇₃	—	2	1	no	—
36	C₂×C₄×C₇₃	—	4	1	no	—
37	C₂×C₄×C₇₃	—	4	1	no	—
38	C₂×C₄×C₇₃	—	4	1	no	—
39	C₂×C₄×C₇₃	—	4	1	no	—
40	C₂×C₄×C₇₃	—	4	1	no	—
41	C₂×C₄×C₇₃	—	4	1	no	—
42	C₂×C₄×C₇₃	—	4	1	no	—
43	C₂×Dic₇₃	—	4	2	no	—
44	C₂×Dic₇₃	—	8	1	no	—
45	C₂×Dic₇₃	—	8	1	no	—
46	#10596831	—	8	1	no	—
47	C₂²×C₇₃	—	2	1	no	—
48	C₂²×C₇₃	—	2	1	no	—
49	C₂²×C₇₃	—	2	1	no	—
50	C₂²×C₇₃	—	2	1	no	—
51	C₂²×C₇₃	—	4	1	no	—
52	C₂²×C₇₃	—	4	1	no	—
53	C₂²×C₇₃	—	4	1	no	—
54	C₂²×C₇₃	—	4	1	no	—
55	C₂²×C₇₃	—	8	1	no	—
56	C₂²×C₇₃	#99	1	1	yes	characteristic
57	C₂²×C₇₃	#103	1	1	yes	characteristic
58	C₂²×C₇₃	#104	1	1	yes	characteristic
59	C₄×C₇₃	—	4	2	no	—
60	C₄×C₇₃	—	4	1	no	—
61	C₄×C₇₃	—	4	1	no	—
62	C₄×C₇₃	—	8	1	no	—
63	Dic₇₃	—	8	2	no	—
64	C₂×C₇₃	—	2	1	no	—
65	C₂×C₇₃	—	2	1	no	—
66	C₂×C₇₃	—	4	1	no	—
67	C₂×C₇₃	—	4	1	no	—
68	C₂×C₇₃	#328	1	1	yes	characteristic
69	C₂×C₇₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
70	C₂×C₇₃	#354	1	1	yes	characteristic
71	#1351	—	73	1	no	maximal, Sylow
72	C₇₃	#1351	1	1	yes	characteristic, complemented, Sylow
73	#393	D₇₃	1	1	yes	characteristic
74	#342	—	73	1	no	—
75	#323	—	73	1	no	—
76	C₂²×Q₈	Dic₇₃	1	1	yes	characteristic, complemented
77	C₂×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₂²⋊C₄	—	146	1	no	—
79	C₂×C₂²⋊C₄	C₂×D₇₃	1	1	yes	characteristic
80	C₂²⋊C₈	—	146	1	no	—
81	#95	—	2	1	no	—
82	#95	Dic₇₃	1	1	yes	characteristic, complemented
83	C₂⁴	C₂²⋊D₇₃	1	1	yes	characteristic
84	C₂×Q₈	—	4	2	no	—
85	C₂×Q₈	—	4	1	no	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	292	1	no	—
89	C₂²×C₄	C₂×Dic₇₃	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
91	C₂×C₈	—	292	1	no	—
92	C₂²⋊C₄	—	4	1	no	—
93	C₂²⋊C₄	—	4	2	no	—
94	C₂²⋊C₄	—	292	1	no	—
95	C₂²⋊C₄	—	146	2	no	—
96	C₂³	—	2	1	no	—
97	C₂³	—	2	1	no	—
98	C₂³	—	4	1	no	—
99	C₂³	—	4	1	no	—
100	C₂³	C₂²⋊Dic₇₃	1	1	yes	characteristic
101	C₂³	#11924015	1	1	yes	characteristic
102	C₂³	#11924018	1	1	yes	characteristic
103	Q₈	—	4	2	no	—
104	Q₈	—	4	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	292	2	no	—
116	C₂×C₄	—	584	1	no	—
117	C₂×C₄	—	584	1	no	—
118	C₈	—	584	1	no	—
119	C₂²	—	2	1	no	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	4	1	no	—
124	C₂²	—	4	1	no	—
125	C₂²	—	4	1	no	—
126	C₂²	—	4	1	no	—
127	C₂²	—	8	1	no	—
128	C₂²	#14556506	1	1	yes	characteristic
129	C₂²	#14556515	1	1	yes	characteristic
130	C₂²	#14556518	1	1	yes	characteristic
131	C₄	—	4	2	no	—
132	C₄	—	4	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	8	1	no	—
135	C₄	—	584	2	no	—
136	C₂	—	2	1	no	—
137	C₂	—	2	1	no	—
138	C₂	—	4	1	no	—
139	C₂	—	4	1	no	—
140	C₂	#17988324	1	1	yes	characteristic
141	C₂	#17988374	1	1	yes	characteristic
142	C₂	#17988382	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988354

C₂

yes

maximal, characteristic

#17988311

C₂

yes

maximal, characteristic

#393×C₇₃

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₇₃

—

C₂²⋊#10596831

—

C₂²×Q₈×C₇₃

C₄

yes

characteristic, complemented

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

C₂²

yes

characteristic

#95×C₇₃

—

#95×C₇₃

C₄

yes

characteristic, complemented

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂⁴×C₇₃

D₄

yes

characteristic

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂³×C₇₃

SD₁₆

yes

characteristic

C₂³×C₇₃

Q₁₆

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#328

yes

characteristic

C₂×C₇₃

AΣL(1,𝔽₁₆)

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#393

D₇₃

yes

characteristic

#342

—

#323

—

C₂²×Q₈

Dic₇₃

yes

characteristic, complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

146

—

C₂×C₂²⋊C₄

C₂×D₇₃

yes

characteristic

C₂²⋊C₈

—

146

—

#95

—

#95

Dic₇₃

yes

characteristic, complemented

C₂⁴

C₂²⋊D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

C₂×Dic₇₃

yes

characteristic

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

—

292

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

292

—

C₂²⋊C₄

—

146

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

C₂²⋊Dic₇₃

yes

characteristic

101

C₂³

#11924015

yes

characteristic

102

C₂³

#11924018

yes

characteristic

103

Q₈

—

104

Q₈

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

292

—

116

C₂×C₄

—

584

—

117

C₂×C₄

—

584

—

118

C₈

—

584

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

#14556506

yes

characteristic

129

C₂²

#14556515

yes

characteristic

130

C₂²

#14556518

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

584

—

136

C₂

—

137

C₂

—

138

C₂

—

139

C₂

—

140

C₂

#17988324

yes

characteristic

141

C₂

#17988374

yes

characteristic

142

C₂

#17988382

yes

characteristic

	subgroup	G/H
center	C₂²	#14556506
commutator	C₂²×C₄×C₇₃	C₂×C₄
Frattini	C₂×C₂²⋊C₄	C₂×D₇₃
Fitting	#393×C₇₃	C₂
socle	C₂²×C₇₃	#99
hypercenter	#393	D₇₃
hypocenter	C₇₃	#1351
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #393

subgroup

G/H

center

C₂²

#14556506

commutator

C₂²×C₄×C₇₃

C₂×C₄

Frattini

C₂×C₂²⋊C₄

C₂×D₇₃

Fitting

#393×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #393

N	H ≅ G/N	type
6. C₂²×Q₈×C₇₃	C₄	semidirect
10. #95×C₇₃	C₄	semidirect
72. C₇₃	#1351	semidirect
76. C₂²×Q₈	Dic₇₃	semidirect
82. #95	Dic₇₃	semidirect

H ≅ G/N

type

6. C₂²×Q₈×C₇₃

C₄

semidirect

10. #95×C₇₃

C₄

semidirect

72. C₇₃

#1351

semidirect

76. C₂²×Q₈

Dic₇₃

semidirect

82. #95

Dic₇₃

semidirect

Subgroups — #22607952

Conjugacy classes of subgroups

Complements