Group #22626593 — subgroups

Subgroups — #22626593

Order 9344.

440 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 198 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	#17989666	C₂	1	2	yes	maximal
2	#17989602	C₂	1	6	yes	maximal, complemented
3	C₂×#14556662	C₂	1	3	yes	maximal, complemented
4	D₇₃⋊#108	C₂	1	3	yes	maximal, complemented
5	#131×D₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556679	—	2	2	no	—
7	#14556678	—	2	6	no	—
8	C₂×#11924038	C₂²	1	6	yes	—
9	D₇₃⋊M₁₆	C₂²	1	6	yes	—
10	#14556662	C₂²	1	1	yes	characteristic
11	#14556662	C₂²	1	3	yes	—
12	#14556662	C₂²	1	6	yes	—
13	#14556661	C₂²	1	6	yes	—
14	#41×D₇₃	C₂²	1	1	yes	characteristic
15	#14556599	C₄	1	3	yes	—
16	#14556598	C₄	1	1	yes	characteristic
17	#14556597	C₄	1	3	yes	—
18	M₁₆×D₇₃	C₂²	1	3	yes	—
19	C₂×C₈×D₇₃	C₂²	1	3	yes	—
20	#131×C₇₃	C₄	1	1	yes	characteristic
21	#11924038	—	2	6	no	—
22	#11924038	C₂³	1	2	yes	—
23	#11924038	C₂³	1	6	yes	—
24	#11924037	—	2	6	no	—
25	#11924036	—	2	6	no	—
26	C₂×#10596833	—	2	6	no	—
27	#11924029	D₄	1	1	yes	characteristic
28	#11924028	C₂×C₄	1	3	yes	—
29	#11924027	D₄	1	3	yes	—
30	Q₈×D₇₃	Q₈	1	1	yes	characteristic
31	D₄×D₇₃	Q₈	1	3	yes	—
32	C₂×C₄×D₇₃	C₂³	1	3	yes	—
33	#11924012	C₂×C₄	1	3	yes	—
34	#11924011	C₂×C₄	1	6	yes	—
35	C₂×#10596831	C₂×C₄	1	3	yes	—
36	C₈×D₇₃	C₂×C₄	1	3	yes	—
37	C₈×D₇₃	C₂×C₄	1	3	yes	—
38	C₈×D₇₃	C₂³	1	1	yes	characteristic
39	C₈×D₇₃	C₂³	1	3	yes	—
40	#41×C₇₃	C₂×C₄	1	1	yes	characteristic
41	M₁₆×C₇₃	C₂×C₄	1	3	yes	—
42	C₂×C₈×C₇₃	C₂×C₄	1	3	yes	—
43	C₂²×D₇₃	C₂×Q₈	1	3	yes	—
44	Q₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
45	D₄×C₇₃	C₄⋊C₄	1	3	yes	—
46	C₂×C₄×C₇₃	C₂²×C₄	1	3	yes	—
47	C₂²⋊D₇₃	C₄⋊C₄	1	6	yes	—
48	C₂×Dic₇₃	C₂×D₄	1	3	yes	—
49	D₂₉₂	C₄⋊C₄	1	3	yes	—
50	C₄×D₇₃	C₂²×C₄	1	3	yes	—
51	C₄×D₇₃	C₂×D₄	1	3	yes	—
52	C₄×D₇₃	C₂×Q₈	1	3	yes	—
53	C₄×D₇₃	C₂⁴	1	1	yes	characteristic
54	Dic₁₄₆	C₄⋊C₄	1	3	yes	—
55	#10596833	—	2	6	no	—
56	#10596833	—	2	2	no	—
57	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
58	C₈×C₇₃	C₂²×C₄	1	3	yes	—
59	#10596831	C₂²×C₄	1	1	yes	characteristic
60	#10596831	C₂²×C₄	1	3	yes	—
61	C₂²×C₇₃	C₂×C₄⋊C₄	1	3	yes	—
62	C₂×D₇₃	—	4	3	no	—
63	C₂×D₇₃	C₂×C₄⋊C₄	1	3	yes	—
64	C₂×D₇₃	C₂²×Q₈	1	1	yes	characteristic
65	C₄×C₇₃	C₂×C₄⋊C₄	1	3	yes	—
66	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
67	Dic₇₃	C₂×C₄⋊C₄	1	3	yes	—
68	Dic₇₃	C₂²×D₄	1	1	yes	characteristic
69	C₂×C₇₃	—	2	3	no	—
70	C₂×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
71	D₇₃	—	2	1	no	—
72	D₇₃	—	2	3	no	—
73	#2916	—	73	1	no	maximal, Sylow
74	C₇₃	#2916	1	1	yes	characteristic, complemented, Sylow
75	#568	—	73	2	no	—
76	C₂×#131	—	73	1	no	—
77	#430	—	73	6	no	—
78	C₂×#108	—	73	3	no	—
79	C₂×#108	—	73	3	no	—
80	C₂×#41	—	73	1	no	—
81	#131	—	73	1	no	—
82	#131	—	73	3	no	—
83	#131	—	73	3	no	—
84	#131	—	146	6	no	—
85	#131	—	146	2	no	—
86	#131	#64408	1	1	yes	characteristic
87	C₂×M₁₆	—	73	3	no	—
88	C₂×M₁₆	—	73	6	no	—
89	C₂×M₁₆	—	73	6	no	—
90	C₂²×C₈	—	73	3	no	—
91	#108	—	73	1	no	—
92	#108	—	73	3	no	—
93	#108	—	73	6	no	—
94	#108	—	73	6	no	—
95	#41	—	73	1	no	—
96	#41	—	73	3	no	—
97	#41	—	73	3	no	—
98	#41	C₂×#64408	1	1	yes	characteristic
99	C₂×Q₈	—	73	1	no	—
100	C₂×D₄	—	73	3	no	—
101	C₂²×C₄	—	73	3	no	—
102	M₁₆	—	73	3	no	—
103	M₁₆	—	73	6	no	—
104	M₁₆	—	73	2	no	—
105	M₁₆	—	73	6	no	—
106	M₁₆	—	146	6	no	—
107	M₁₆	—	146	6	no	—
108	M₁₆	C₂×#64408	1	3	yes	—
109	C₂×C₈	—	73	3	no	—
110	C₂×C₈	—	73	3	no	—
111	C₂×C₈	—	73	3	no	—
112	C₂×C₈	—	73	1	no	—
113	C₂×C₈	—	73	3	no	—
114	C₂×C₈	—	146	6	no	—
115	C₂×C₈	—	146	6	no	—
116	C₂×C₈	C₂×#64408	1	3	yes	—
117	C₂³	—	73	3	no	—
118	Q₈	—	73	3	no	—
119	Q₈	C₄⋊#64408	1	1	yes	characteristic
120	D₄	—	73	6	no	—
121	D₄	—	73	3	no	—
122	D₄	C₄⋊#64408	1	3	yes	—
123	C₂×C₄	—	73	3	no	—
124	C₂×C₄	—	73	1	no	—
125	C₂×C₄	—	73	3	no	—
126	C₂×C₄	—	73	3	no	—
127	C₂×C₄	—	73	3	no	—
128	C₂×C₄	C₂²×#64408	1	3	yes	—
129	C₈	—	73	1	no	—
130	C₈	—	73	3	no	—
131	C₈	—	146	6	no	—
132	C₈	—	146	2	no	—
133	C₈	C₂²×#64408	1	1	yes	characteristic
134	C₈	C₂²×#64408	1	3	yes	—
135	C₂²	—	292	3	no	—
136	C₂²	—	73	1	no	—
137	C₂²	—	73	3	no	—
138	C₂²	C₂×C₄⋊#64408	1	3	yes	—
139	C₄	—	73	1	no	—
140	C₄	—	73	3	no	—
141	C₄	C₂×C₄⋊#64408	1	3	yes	—
142	C₄	C₂³×#64408	1	1	yes	characteristic
143	C₂	—	2	3	no	—
144	C₂	—	146	1	no	—
145	C₂	—	146	3	no	—
146	C₂	C₂²×C₄⋊#64408	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989666

C₂

yes

maximal

#17989602

C₂

yes

maximal, complemented

C₂×#14556662

C₂

yes

maximal, complemented

D₇₃⋊#108

C₂

yes

maximal, complemented

#131×D₇₃

C₂

yes

maximal, characteristic

#14556679

—

#14556678

—

C₂×#11924038

C₂²

yes

—

D₇₃⋊M₁₆

C₂²

yes

—

#14556662

C₂²

yes

characteristic

#14556662

C₂²

yes

—

#14556662

C₂²

yes

—

#14556661

C₂²

yes

—

#41×D₇₃

C₂²

yes

characteristic

#14556599

C₄

yes

—

#14556598

C₄

yes

characteristic

#14556597

C₄

yes

—

M₁₆×D₇₃

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

#131×C₇₃

C₄

yes

characteristic

#11924038

—

#11924038

C₂³

yes

—

#11924038

C₂³

yes

—

—

—

—

D₄

yes

characteristic

#11924028

C₂×C₄

yes

—

#11924027

D₄

yes

—

Q₈×D₇₃

Q₈

yes

characteristic

D₄×D₇₃

Q₈

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

#11924012

C₂×C₄

yes

—

#11924011

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂³

yes

characteristic

C₈×D₇₃

C₂³

yes

—

#41×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂²×D₇₃

C₂×Q₈

yes

—

Q₈×C₇₃

C₄⋊C₄

yes

characteristic

D₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂²⋊D₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

—

D₂₉₂

C₄⋊C₄

yes

—

C₄×D₇₃

C₂²×C₄

yes

—

C₄×D₇₃

C₂×D₄

yes

—

C₄×D₇₃

C₂×Q₈

yes

—

C₄×D₇₃

C₂⁴

yes

characteristic

Dic₁₄₆

C₄⋊C₄

yes

—

#10596833

—

#10596833

—

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

C₂²×C₄

yes

—

#10596831

C₂²×C₄

yes

characteristic

#10596831

C₂²×C₄

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₄⋊C₄

yes

—

C₂×D₇₃

C₂²×Q₈

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₄×C₇₃

C₂³×C₄

yes

characteristic

Dic₇₃

C₂×C₄⋊C₄

yes

—

Dic₇₃

C₂²×D₄

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂²×C₄⋊C₄

yes

characteristic

D₇₃

—

D₇₃

—

#2916

—

maximal, Sylow

C₇₃

#2916

yes

characteristic, complemented, Sylow

—

—

—

—

—

C₂×#41

—

—

—

—

—

146

—

#131

—

146

—

#131

#64408

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

—

—

—

—

—

—

—

yes

C₂×Q₈

—

100

C₂×D₄

—

101

C₂²×C₄

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

146

—

107

M₁₆

—

146

—

108

M₁₆

C₂×#64408

yes

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

146

—

115

C₂×C₈

—

146

—

116

C₂×C₈

C₂×#64408

yes

—

117

C₂³

—

118

Q₈

—

119

Q₈

C₄⋊#64408

yes

characteristic

120

D₄

—

121

D₄

—

122

D₄

C₄⋊#64408

yes

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂²×#64408

yes

—

129

C₈

—

130

C₈

—

131

C₈

—

146

—

132

C₈

—

146

—

133

C₈

C₂²×#64408

yes

characteristic

134

C₈

C₂²×#64408

yes

—

135

C₂²

—

292

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂×C₄⋊#64408

yes

—

139

C₄

—

140

C₄

—

141

C₄

C₂×C₄⋊#64408

yes

—

142

C₄

C₂³×#64408

yes

characteristic

143

C₂

—

144

C₂

—

146

—

145

C₂

—

146

—

146

C₂

C₂²×C₄⋊#64408

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×C₄⋊#64408
commutator	C₄×C₇₃	C₂³×C₄
Frattini	C₄	C₂³×#64408
Fitting	#131×C₇₃	C₄
socle	C₂×C₇₃	C₂²×C₄⋊C₄
hypercenter	#131	#64408
hypocenter	C₇₃	#2916
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

subgroup

G/H

center

C₂

C₂²×C₄⋊#64408

commutator

C₄×C₇₃

C₂³×C₄

Frattini

C₄

C₂³×#64408

Fitting

#131×C₇₃

C₄

socle

C₂×C₇₃

C₂²×C₄⋊C₄

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ #41 ◁ #131

N	H ≅ G/N	type
2. #17989602	C₂	semidirect
3. C₂×#14556662	C₂	semidirect
4. D₇₃⋊#108	C₂	semidirect
74. C₇₃	#2916	semidirect

H ≅ G/N

type

2. #17989602

C₂

semidirect

3. C₂×#14556662

C₂

semidirect

4. D₇₃⋊#108

C₂

semidirect

74. C₇₃

#2916

semidirect

Subgroups — #22626593

Conjugacy classes of subgroups

Complements