Group #22609656 — subgroups

Subgroups — #22609656

Order 9344.

372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11924011	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×D₇₃	C₂	1	2	yes	maximal
3	#17988352	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988351	C₂	1	2	yes	maximal, complemented
5	#341×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
7	C₂×#11924012	C₂²	1	2	yes	—
8	C₂×#11924011	—	2	2	no	—
9	C₂×#11924011	—	2	4	no	—
10	C₂×#11924011	C₄	1	4	yes	—
11	M₁₆×D₇₃	—	2	4	no	—
12	M₁₆×D₇₃	C₄	1	8	yes	—
13	C₂²×#10596831	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₇₃	—	2	2	no	—
15	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
16	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂³×D₇₃	Q₈	1	1	yes	characteristic
18	C₂²×Dic₇₃	Q₈	1	1	yes	characteristic
19	C₂×C₄×D₇₃	C₂×C₄	1	4	yes	—
20	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₇₃	D₄	1	2	yes	—
22	C₂×C₄×D₇₃	D₄	1	4	yes	—
23	#11924012	—	2	2	no	—
24	#11924012	C₂×C₄	1	4	yes	—
25	#11924011	—	2	8	no	—
26	#11924011	—	2	8	no	—
27	C₂×#10596831	—	2	2	no	—
28	C₂×#10596831	—	2	2	no	—
29	C₂×#10596831	C₂×C₄	1	2	yes	—
30	C₈×D₇₃	—	2	8	no	—
31	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
32	M₁₆×C₇₃	—	2	2	no	—
33	M₁₆×C₇₃	C₂×C₄	1	4	yes	—
34	C₂×C₈×C₇₃	—	2	2	no	—
35	C₂×C₈×C₇₃	—	2	2	no	—
36	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
37	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
38	C₂²×D₇₃	—	4	2	no	—
39	C₂²×D₇₃	C₄⋊C₄	1	2	yes	—
40	C₂²×D₇₃	C₄⋊C₄	1	4	yes	—
41	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₇₃	C₄⋊C₄	1	4	yes	—
46	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
47	C₄×D₇₃	C₄²	1	4	yes	—
48	C₄×D₇₃	C₂²⋊C₄	1	4	yes	—
49	C₄×D₇₃	C₂²⋊C₄	1	4	yes	—
50	C₄×D₇₃	C₂²⋊C₄	1	4	yes	—
51	C₈×C₇₃	—	2	2	no	—
52	C₈×C₇₃	—	2	4	no	—
53	#10596831	—	2	4	no	—
54	#10596831	—	2	2	no	—
55	C₂²×C₇₃	—	2	2	no	—
56	C₂²×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
57	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×D₇₃	—	2	4	no	—
59	C₂×D₇₃	—	4	4	no	—
60	C₂×D₇₃	#95	1	4	yes	—
61	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
62	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
64	Dic₇₃	#95	1	4	yes	—
65	C₂×C₇₃	—	2	2	no	—
66	C₂×C₇₃	C₂×#95	1	1	yes	characteristic
67	C₂×C₇₃	#430	1	2	yes	—
68	D₇₃	—	2	4	no	—
69	#1738	—	73	1	no	maximal, Sylow
70	C₇₃	#1738	1	1	yes	characteristic, complemented, Sylow
71	C₂²×M₁₆	—	73	1	no	—
72	C₂²×M₁₆	—	73	2	no	—
73	#341	—	73	2	no	—
74	#341	—	73	1	no	—
75	#341	D₇₃	1	1	yes	characteristic, complemented
76	C₂³×C₄	—	73	1	no	—
77	C₂×M₁₆	—	73	4	no	—
78	C₂×M₁₆	—	73	2	no	—
79	C₂×M₁₆	—	73	8	no	—
80	C₂×M₁₆	—	146	4	no	—
81	C₂×M₁₆	—	146	2	no	—
82	C₂×M₁₆	—	146	4	no	—
83	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
84	C₂²×C₈	—	73	1	no	—
85	C₂²×C₈	—	146	2	no	—
86	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
87	C₂⁴	—	73	1	no	—
88	C₂²×C₄	—	73	1	no	—
89	C₂²×C₄	—	73	4	no	—
90	C₂²×C₄	—	73	2	no	—
91	C₂²×C₄	—	73	4	no	—
92	C₂²×C₄	—	73	2	no	—
93	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
94	M₁₆	—	2	2	no	—
95	M₁₆	—	73	4	no	—
96	M₁₆	—	146	8	no	—
97	M₁₆	—	146	8	no	—
98	M₁₆	—	146	2	no	—
99	M₁₆	C₄×D₇₃	1	4	yes	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	2	2	no	—
102	C₂×C₈	—	73	2	no	—
103	C₂×C₈	—	146	8	no	—
104	C₂×C₈	—	146	2	no	—
105	C₂×C₈	—	146	2	no	—
106	C₂×C₈	C₄×D₇₃	1	2	yes	—
107	C₂³	—	292	2	no	—
108	C₂³	—	73	4	no	—
109	C₂³	—	73	2	no	—
110	C₂³	Q₈×D₇₃	1	1	yes	characteristic
111	C₂×C₄	—	73	4	no	—
112	C₂×C₄	—	73	2	no	—
113	C₂×C₄	—	73	4	no	—
114	C₂×C₄	—	73	4	no	—
115	C₂×C₄	—	73	4	no	—
116	C₂×C₄	—	73	4	no	—
117	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
118	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
119	C₂×C₄	D₄×D₇₃	1	2	yes	—
120	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
121	C₈	—	2	2	no	—
122	C₈	—	2	4	no	—
123	C₈	—	146	2	no	—
124	C₈	—	146	4	no	—
125	C₂²	—	2	2	no	—
126	C₂²	—	292	4	no	—
127	C₂²	—	73	4	no	—
128	C₂²	—	146	4	no	—
129	C₂²	C₄⋊C₄×D₇₃	1	2	yes	—
130	C₂²	C₄⋊C₄×D₇₃	1	1	yes	characteristic
131	C₄	—	73	4	no	—
132	C₄	C₄²×D₇₃	1	1	yes	characteristic
133	C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
134	C₄	C₂²⋊C₄×D₇₃	1	2	yes	—
135	C₂	—	2	2	no	—
136	C₂	—	146	4	no	—
137	C₂	#95×D₇₃	1	1	yes	characteristic
138	C₂	#17988634	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924011

C₂

yes

maximal, characteristic

C₂×M₁₆×D₇₃

C₂

yes

maximal

#17988352

C₂

yes

maximal, characteristic, complemented

#17988351

C₂

yes

maximal, complemented

#341×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₃

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

—

C₂×#11924011

—

C₂×#11924011

—

C₂×#11924011

C₄

yes

—

M₁₆×D₇₃

—

M₁₆×D₇₃

C₄

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂×C₈×D₇₃

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂³×D₇₃

Q₈

yes

characteristic

C₂²×Dic₇₃

Q₈

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

D₄

yes

—

C₂×C₄×D₇₃

D₄

yes

—

#11924012

—

#11924012

C₂×C₄

yes

—

—

—

—

—

C₂×C₄

yes

—

C₈×D₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂×Q₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

C₄⋊C₄

yes

—

C₂²×D₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

C₄²

yes

—

C₄×D₇₃

C₂²⋊C₄

yes

—

C₄×D₇₃

C₂²⋊C₄

yes

—

C₄×D₇₃

C₂²⋊C₄

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#95

yes

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×C₂²⋊C₄

yes

—

Dic₇₃

#95

yes

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#95

yes

characteristic

C₂×C₇₃

#430

yes

—

D₇₃

—

#1738

—

maximal, Sylow

C₇₃

#1738

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂²×M₁₆

—

#341

—

#341

—

#341

D₇₃

yes

characteristic, complemented

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂×M₁₆

—

146

—

C₂×M₁₆

—

146

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₂²×C₈

—

146

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

C₄×D₇₃

yes

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

146

—

104

C₂×C₈

—

146

—

105

C₂×C₈

—

146

—

106

C₂×C₈

C₄×D₇₃

yes

—

107

C₂³

—

292

—

108

C₂³

—

109

C₂³

—

110

C₂³

Q₈×D₇₃

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

118

C₂×C₄

C₂×C₄×D₇₃

yes

—

119

C₂×C₄

D₄×D₇₃

yes

—

120

C₂×C₄

D₄×D₇₃

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

146

—

124

C₈

—

146

—

125

C₂²

—

126

C₂²

—

292

—

127

C₂²

—

128

C₂²

—

146

—

129

C₂²

C₄⋊C₄×D₇₃

yes

—

130

C₂²

C₄⋊C₄×D₇₃

yes

characteristic

131

C₄

—

132

C₄

C₄²×D₇₃

yes

characteristic

133

C₄

C₂²⋊C₄×D₇₃

yes

characteristic

134

C₄

C₂²⋊C₄×D₇₃

yes

—

135

C₂

—

136

C₂

—

146

—

137

C₂

#95×D₇₃

yes

characteristic

138

C₂

#17988634

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₇₃
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#341×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#341	D₇₃
hypocenter	C₇₃	#1738
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₇₃

commutator

C₄×C₇₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#341×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₄⋊C₄

D₇₃

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
3. #17988352	C₂	semidirect
4. #17988351	C₂	semidirect
5. #341×C₇₃	C₂	semidirect
70. C₇₃	#1738	semidirect
75. #341	D₇₃	semidirect

H ≅ G/N

type

3. #17988352

C₂

semidirect

4. #17988351

C₂

semidirect

5. #341×C₇₃

C₂

semidirect

70. C₇₃

#1738

semidirect

75. #341

D₇₃

semidirect

Subgroups — #22609656

Conjugacy classes of subgroups

Complements