Finite Group Databasebeta

← #37549022

Subgroups — #37549022

Order 23168.

312 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042295C211yesmaximal, characteristic, complemented
2#26042295C211yesmaximal, characteristic, complemented
3#26042127C214yesmaximal, complemented
4C2×#19153778C211yesmaximal, characteristic
5C4⋊#13089685—21no—
6C4⋊#13089685C2212yescomplemented
7C22⋊#13089685—21no—
8C22⋊#13089685—21no—
9C4×#13089685—21no—
10C4×#13089685C2212yescomplemented
11C22×D724C411yescharacteristic
12C22×C4×D181—21no—
13#19153778—21no—
14#19153778—21no—
15#19153778C412yes—
16#19153778C2212yes—
17C2×#15668426—21no—
18C2×C4×Dic181C2211yescharacteristic
19C2×C4⋊C4×C181C411yescharacteristic
20C2×#13089685—22no—
21C2×#13089685—22no—
22C23×D181—21no—
23C2×D724—21no—
24C2×D724—22no—
25C2×D724C814yescomplemented
26C2×D724C2×C412yes—
27C22×Dic181D411yescharacteristic
28C22×Dic181D411yescharacteristic
29C2×C4×D181—22no—
30C2×C4×D181—22no—
31C2×C4×D181—44no—
32#15668426—22no—
33#15668426—22no—
34C4×Dic181C2×C411yescharacteristic
35C4×Dic181D411yescharacteristic
36C4×Dic181D411yescharacteristic
37C4×Dic181C2311yescharacteristic
38C22×C4×C181—21no—
39C22×C4×C181C2×C411yescharacteristic
40C4⋊C4×C181—21no—
41C4⋊C4×C181C2×C412yes—
42#13089685—42no—
43#13089685—42no—
44C22×D181—24no—
45C22×D181—22no—
46C22×D181—42no—
47C22×D181—42no—
48D724—24no—
49D724—22no—
50D724C2×C814yes—
51C2×Dic181—22no—
52C2×Dic181—41no—
53C2×Dic181C22⋊C411yescharacteristic
54C2×Dic181C22⋊C411yescharacteristic
55C2×Dic181C2×D411yescharacteristic
56C2×Dic181C2×D411yescharacteristic
57C4×D181—44no—
58C4×D181—44no—
59C23×C181C22⋊C411yescharacteristic
60C2×C4×C181—22no—
61C2×C4×C181—42no—
62C2×C4×C181C22⋊C411yescharacteristic
63C2×C4×C181C2×C812yes—
64C2×C4×C181M1612yes—
65C2×C4×C181C22×C411yescharacteristic
66C22×C181—21no—
67C22×C181—21no—
68C22×C181C22⋊C812yes—
69C22×C181C2×C22⋊C411yescharacteristic
70C2×D181—24no—
71C2×D181—48no—
72C2×D181—42no—
73C2×D181—42no—
74C4×C181—42no—
75C4×C181C22⋊C812yes—
76C4×C181C22×C811yescharacteristic
77C4×C181C2×M1611yescharacteristic
78Dic181—21no—
79Dic181—21no—
80Dic181—21no—
81Dic181AGL(1,ℤ/8)12yes—
82C2×C181—22no—
83C2×C181C2×C22⋊C811yescharacteristic
84C2×C181#41811yescharacteristic
85C2×C181#42111yescharacteristic
86D181—44no—
87C181#147811yescharacteristic, complemented, Sylow
88#1478—1811nomaximal, Sylow
89C2×C4×D4—1811no—
90#431—1811no—
91#431—1811no—
92D4⋊C8—1814no—
93C22×D4—1811no—
94C23×C4—3621no—
95C4×D4—3621no—
96C4×D4—3621no—
97C4×D4—1812no—
98C4×D4—1812no—
99C2×C4⋊C4#1062438211yescharacteristic
100C2×C22⋊C4—3621no—
101C2×C42—1811no—
102C4⋊C8—3621no—
103C4⋊C8—1812no—
104C22⋊C8—3621no—
105C22⋊C8—3621no—
106C4×C8—3621no—
107C4×C8—1812no—
108C24—3621no—
109C2×D4—3621no—
110C2×D4—3622no—
111C2×D4—1814no—
112C2×D4—1812no—
113C22×C4—21no—
114C22×C4—3622no—
115C22×C4—3622no—
116C22×C4—1811no—
117C22×C4—1811no—
118C22×C4—7244no—
119C22×C4C2×#1062438211yescharacteristic
120C2×C8—3622no—
121C2×C8—3622no—
122C4⋊C4—21no—
123C4⋊C4C2×#1062438212yes—
124C22⋊C4—3622no—
125C22⋊C4—3622no—
126C42—1811no—
127C42—1811no—
128C42—1811no—
129C42—1811no—
130C23—3624no—
131C23—3622no—
132C23—7242no—
133C23—7242no—
134C23C22⋊#1062438211yescharacteristic
135D4—3624no—
136D4—3622no—
137D4—1814no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—3622no—
141C2×C4—1811no—
142C2×C4—1811no—
143C2×C4—1811no—
144C2×C4—1811no—
145C2×C4—7244no—
146C2×C4—7244no—
147C2×C4—7241no—
148C2×C4C22⋊#1062438211yescharacteristic
149C2×C4D181⋊C812yes—
150C2×C4#1566845912yes—
151C2×C4C22×#1062438211yescharacteristic
152C8—7242no—
153C8—7242no—
154C22—21no—
155C22—21no—
156C22—3624no—
157C22—7248no—
158C22—7242no—
159C22—7242no—
160C22#1915387312yes—
161C22C2×C22⋊#1062438211yescharacteristic
162C4—42no—
163C4—3621no—
164C4—3621no—
165C4—3621no—
166C4—1812no—
167C4#1915387312yes—
168C4C2×D181⋊C811yescharacteristic
169C4C2×#1566845911yescharacteristic
170C2—22no—
171C2—7244no—
172C2C2×#1915387311yescharacteristic
173C2#2604227111yescharacteristic
174C2#2604227811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC4×C181C22×C8
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D724C4
cosocleC4×Dic181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1478
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26042295C2semidirect
2. #26042295C2semidirect
3. #26042127C2semidirect
6. C4⋊#13089685C22semidirect
10. C4×#13089685C22semidirect
25. C2×D724C8semidirect
87. C181#1478semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260422952
#260421272
C2×#191537782
#1478181