Group #22625032 — subgroups

Subgroups — #22625032

Order 9344.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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	#17989573	C₂	1	1	yes	maximal, characteristic
2	#17989566	C₂	1	1	yes	maximal, characteristic
3	#17988555	C₂	1	1	yes	maximal, characteristic
4	D₇₃⋊M₁₆	—	2	1	no	—
5	#14556670	—	2	1	no	—
6	#14556652	C₄	1	2	yes	complemented
7	#14556651	—	2	1	no	—
8	#14556650	C₄	1	2	yes	—
9	#14556649	—	2	1	no	—
10	C₂×#11924028	C₂²	1	1	yes	characteristic
11	C₂²×#10596831	C₄	1	1	yes	characteristic, complemented
12	#14556503	—	2	1	no	—
13	#14556503	—	2	1	no	—
14	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
15	#11924038	—	4	1	no	—
16	#11924037	—	2	2	no	—
17	#11924036	—	4	1	no	—
18	C₄⋊#64408	—	4	1	no	—
19	C₂²⋊#64408	—	2	2	no	—
20	C₄×#64408	—	4	1	no	—
21	#11924028	—	4	1	no	—
22	#11924028	—	4	1	no	—
23	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
24	C₂×D₂₉₂	C₂×C₄	1	1	yes	characteristic
25	C₂×C₂²⋊D₇₃	D₄	1	1	yes	characteristic
26	C₂×C₂²⋊D₇₃	Q₈	1	1	yes	characteristic
27	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
28	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
29	C₂×#10596831	—	2	1	no	—
30	C₂×#10596831	—	4	1	no	—
31	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
32	M₁₆×C₇₃	—	4	1	no	—
33	C₂×C₈×C₇₃	—	2	1	no	—
34	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×#64408	—	4	2	no	—
38	C₂×C₄×C₇₃	—	2	1	no	—
39	C₂×C₄×C₇₃	—	2	1	no	—
40	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
41	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²⋊D₇₃	—	4	1	no	—
43	C₂²⋊D₇₃	—	4	1	no	—
44	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
46	D₂₉₂	—	4	1	no	—
47	C₄×D₇₃	—	2	1	no	—
48	C₄×D₇₃	—	2	1	no	—
49	C₄×D₇₃	—	2	1	no	—
50	C₄×D₇₃	—	2	1	no	—
51	Dic₁₄₆	—	4	1	no	—
52	#10596833	—	4	2	no	—
53	C₈×C₇₃	—	4	1	no	—
54	#10596831	—	4	1	no	—
55	C₂²×C₇₃	—	2	1	no	—
56	C₂²×C₇₃	—	4	1	no	—
57	C₂²×C₇₃	#95	1	1	yes	characteristic
58	C₂×D₇₃	—	2	1	no	—
59	C₂×D₇₃	—	2	1	no	—
60	C₂×D₇₃	—	4	1	no	—
61	C₂×D₇₃	—	4	1	no	—
62	#64408	—	8	2	no	—
63	C₄×C₇₃	—	2	1	no	—
64	C₄×C₇₃	#99	1	1	yes	characteristic
65	C₄×C₇₃	#99	1	1	yes	characteristic
66	Dic₇₃	—	2	1	no	—
67	Dic₇₃	—	2	1	no	—
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	—	4	1	no	—
70	C₂×C₇₃	#342	1	1	yes	characteristic
71	D₇₃	—	4	1	no	—
72	D₇₃	—	4	1	no	—
73	#1395	—	73	1	no	maximal, Sylow
74	C₇₃	#1395	1	1	yes	characteristic, complemented, Sylow
75	#413	—	73	1	no	—
76	#410	—	73	1	no	—
77	#408	—	73	1	no	—
78	C₂×#41	—	73	1	no	—
79	C₂×M₁₆	—	146	1	no	—
80	C₂×M₁₆	#64408	1	1	yes	characteristic, complemented
81	C₂²×C₈	—	73	1	no	—
82	#117	—	146	1	no	—
83	#101	—	73	2	no	—
84	#100	—	146	1	no	—
85	#99	—	73	2	no	—
86	#99	—	146	1	no	—
87	C₂²⋊C₈	—	146	1	no	—
88	C₂²⋊C₈	—	146	1	no	—
89	#41	—	292	1	no	—
90	#41	—	292	1	no	—
91	C₂×Q₈	—	73	1	no	—
92	C₂×D₄	—	73	1	no	—
93	C₂×D₄	—	73	1	no	—
94	C₂×D₄	—	73	1	no	—
95	C₂²×C₄	—	73	1	no	—
96	C₂²×C₄	—	73	1	no	—
97	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
98	M₁₆	—	4	1	no	—
99	M₁₆	—	292	1	no	—
100	M₁₆	—	146	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	292	1	no	—
103	C₂×C₈	—	292	1	no	—
104	C₂×C₈	—	146	1	no	—
105	C₄⋊C₄	—	292	1	no	—
106	C₂²⋊C₄	—	146	2	no	—
107	C₄²	—	292	1	no	—
108	C₂³	—	73	1	no	—
109	C₂³	—	73	1	no	—
110	C₂³	C₄⋊#64408	1	1	yes	characteristic
111	Q₈	—	292	1	no	—
112	D₄	—	292	1	no	—
113	D₄	—	292	1	no	—
114	D₄	—	292	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	292	2	no	—
118	C₂×C₄	—	73	1	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	146	1	no	—
121	C₂×C₄	—	146	1	no	—
122	C₂×C₄	—	146	1	no	—
123	C₂×C₄	—	146	1	no	—
124	C₂×C₄	C₄×#64408	1	1	yes	characteristic
125	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
126	C₈	—	4	1	no	—
127	C₈	—	292	2	no	—
128	C₈	—	292	1	no	—
129	C₂²	—	2	1	no	—
130	C₂²	—	4	1	no	—
131	C₂²	—	292	1	no	—
132	C₂²	—	292	1	no	—
133	C₂²	—	146	1	no	—
134	C₂²	—	146	1	no	—
135	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
136	C₄	—	2	1	no	—
137	C₄	—	584	2	no	—
138	C₄	—	146	1	no	—
139	C₄	—	146	1	no	—
140	C₄	#14556649	1	1	yes	characteristic
141	C₄	#14556650	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	4	1	no	—
144	C₂	—	292	1	no	—
145	C₂	—	292	1	no	—
146	C₂	#17989465	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989573

C₂

yes

maximal, characteristic

#17989566

C₂

yes

maximal, characteristic

#17988555

C₂

yes

maximal, characteristic

D₇₃⋊M₁₆

—

#14556670

—

#14556652

C₄

yes

complemented

#14556651

—

#14556650

C₄

yes

—

#14556649

—

C₂×#11924028

C₂²

yes

characteristic

C₂²×#10596831

C₄

yes

characteristic, complemented

#14556503

—

#14556503

—

C₂×M₁₆×C₇₃

C₄

yes

characteristic, complemented

—

—

—

—

—

—

—

—

C₂×Dic₁₄₆

C₂×C₄

yes

characteristic

C₂×D₂₉₂

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₇₃

D₄

yes

characteristic

C₂×C₂²⋊D₇₃

Q₈

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×#10596831

—

C₂×#10596831

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

C₂×#64408

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#95

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#342

yes

characteristic

D₇₃

—

D₇₃

—

#1395

—

maximal, Sylow

C₇₃

#1395

yes

characteristic, complemented, Sylow

#413

—

#410

—

#408

—

C₂×#41

—

C₂×M₁₆

—

146

—

C₂×M₁₆

#64408

yes

characteristic, complemented

C₂²×C₈

—

#117

—

146

—

#101

—

#100

—

146

—

#99

—

#99

—

146

—

C₂²⋊C₈

—

146

—

C₂²⋊C₈

—

146

—

#41

—

292

—

#41

—

292

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

M₁₆

—

292

—

100

M₁₆

—

146

—

101

C₂×C₈

—

102

C₂×C₈

—

292

—

103

C₂×C₈

—

292

—

104

C₂×C₈

—

146

—

105

C₄⋊C₄

—

292

—

106

C₂²⋊C₄

—

146

—

107

C₄²

—

292

—

108

C₂³

—

109

C₂³

—

110

C₂³

C₄⋊#64408

yes

characteristic

111

Q₈

—

292

—

112

D₄

—

292

—

113

D₄

—

292

—

114

D₄

—

292

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

292

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

146

—

121

C₂×C₄

—

146

—

122

C₂×C₄

—

146

—

123

C₂×C₄

—

146

—

124

C₂×C₄

C₄×#64408

yes

characteristic

125

C₂×C₄

C₂²⋊#64408

yes

characteristic

126

C₈

—

127

C₈

—

292

—

128

C₈

—

292

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

292

—

132

C₂²

—

292

—

133

C₂²

—

146

—

134

C₂²

—

146

—

135

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

136

C₄

—

137

C₄

—

584

—

138

C₄

—

146

—

139

C₄

—

146

—

140

C₄

#14556649

yes

characteristic

141

C₄

#14556650

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

—

292

—

145

C₂

—

292

—

146

C₂

#17989465

yes

characteristic

	subgroup	G/H
center	C₄	#14556649
commutator	C₂×C₄×C₇₃	C₄²
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂×M₁₆×C₇₃	C₄
socle	C₂×C₇₃	#342
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	#1395
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₄

#14556649

commutator

C₂×C₄×C₇₃

C₄²

Frattini

C₂²×C₄

C₂×#64408

Fitting

C₂×M₁₆×C₇₃

C₄

C₂×C₇₃

C₂×M₁₆

C₇₃

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

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
6. #14556652	C₄	semidirect
11. C₂²×#10596831	C₄	semidirect
14. C₂×M₁₆×C₇₃	C₄	semidirect
74. C₇₃	#1395	semidirect
80. C₂×M₁₆	#64408	semidirect

H ≅ G/N

type

6. #14556652

C₄

semidirect

11. C₂²×#10596831

C₄

semidirect

14. C₂×M₁₆×C₇₃

C₄

semidirect

74. C₇₃

#1395

semidirect

80. C₂×M₁₆

#64408

semidirect

Subgroups — #22625032

Conjugacy classes of subgroups

Complements