Finite Group Databasebeta

← #37549983

Subgroups — #37549983

Order 23168.

234 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 54 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#26042265C211yesmaximal, characteristic
2#26042258C211yesmaximal, characteristic
3#26042181C214yesmaximal, complemented
4#26041853C211yesmaximal, characteristic
5D181⋊M16—21no—
6#19153895—21no—
7#19153877—21no—
8#19153876C2212yes—
9#19153875—21no—
10#19153874C2212yes—
11C2×#15668449C2211yescharacteristic
12#19153814—21no—
13#19153805—21no—
14#19153799C412yescomplemented
15#19153799C2212yes—
16#19153792—21no—
17#19153792—21no—
18#19153775C411yescharacteristic, complemented
19C22×Q8×C181C411yescharacteristic, complemented
20#15668459—41no—
21#15668458—22no—
22D181⋊C8—41no—
23C4⋊#10624382—41no—
24C22⋊#10624382—22no—
25C4×#10624382—41no—
26#15668449—41no—
27#15668449—41no—
28C2×Dic362D411yescharacteristic
29C2×D724D411yescharacteristic
30C2×C22⋊D181C2×C411yescharacteristic
31C2×C22⋊D181C2311yescharacteristic
32C2×C4×D181D411yescharacteristic
33C2×C4×D181D411yescharacteristic
34C4⋊Dic181—21no—
35#15668428—22no—
36#15668428—22no—
37C22⋊Dic181C2×C412yes—
38#15668426—22no—
39#15668426—22no—
40C4×Dic181—21no—
41C2×Q8×C181—21no—
42C2×Q8×C181—21no—
43C2×Q8×C181—41no—
44C2×Q8×C181—41no—
45C22×C4×C181C2×C412yes—
46C22×C4×C181C2×C411yescharacteristic
47C2×#10624382—42no—
48#13089685—42no—
49C22×D181C22⋊C411yescharacteristic
50C22×D181C2×D411yescharacteristic
51Dic362—41no—
52D724—41no—
53C22⋊D181—41no—
54C22⋊D181—41no—
55C2×Dic181—22no—
56C2×Dic181C22⋊C411yescharacteristic
57C2×Dic181C2×D411yescharacteristic
58C4×D181—21no—
59C4×D181—21no—
60C4×D181—21no—
61C4×D181—21no—
62C23×C181C22×C411yescharacteristic
63Q8×C181—42no—
64Q8×C181—41no—
65Q8×C181—41no—
66C2×C4×C181—21no—
67C2×C4×C181—21no—
68C2×C4×C181—22no—
69C2×C4×C181—42no—
70C2×C4×C181C22⋊C411yescharacteristic
71C2×C4×C181C22⋊C411yescharacteristic
72C22×C181—21no—
73C22×C181—41no—
74C22×C181C2×C22⋊C411yescharacteristic
75C2×D181—21no—
76C2×D181—21no—
77C2×D181—41no—
78C2×D181—41no—
79#10624382—82no—
80C4×C181—21no—
81C4×C181—42no—
82C4×C181#9911yescharacteristic
83C4×C181#9911yescharacteristic
84Dic181—21no—
85Dic181—21no—
86Dic181—42no—
87C2×C181—21no—
88C2×C181—41no—
89C2×C181C2×#9911yescharacteristic
90D181—41no—
91D181—41no—
92C181#212311yescharacteristic, complemented, Sylow
93#2123—1811nomaximal, Sylow
94#536—1811no—
95#413—1811no—
96#410—1811no—
97#352—1814no—
98C2×#41—1811no—
99C22×Q8#1062438211yescharacteristic, complemented
100C2×M16—3621no—
101C4⋊Q8—3621no—
102#124—3621no—
103#123—1812no—
104#123—1812no—
105C22⋊Q8—3621no—
106C22⋊Q8—3621no—
107#117—3621no—
108#117—1811no—
109#101—3621no—
110#100—1812no—
111#99—3621no—
112#99—1812no—
113#41—7241no—
114#41—7241no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8—1811no—
120C2×D4—1811no—
121C2×D4—1811no—
122C2×D4—1811no—
123C22×C4—1811no—
124C22×C4—1811no—
125C22×C4C2×#1062438212yes—
126C22×C4C2×#1062438211yescharacteristic
127M16—3622no—
128M16—7241no—
129C2×C8—7241no—
130C4⋊C4—3622no—
131C4⋊C4—3622no—
132C4⋊C4—3621no—
133C4⋊C4—7241no—
134C22⋊C4—3622no—
135C22⋊C4—3622no—
136C22⋊C4—3622no—
137C22⋊C4—1812no—
138C42—3621no—
139C42—7241no—
140C23—1811no—
141C23—1811no—
142C23C22×#1062438211yescharacteristic
143Q8—42no—
144Q8—41no—
145Q8—41no—
146Q8—7241no—
147D4—7241no—
148D4—7241no—
149D4—7241no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—3621no—
155C2×C4—3621no—
156C2×C4—3621no—
157C2×C4—3621no—
158C2×C4—3622no—
159C2×C4—1811no—
160C2×C4—1811no—
161C2×C4—7242no—
162C2×C4C22⋊#1062438211yescharacteristic
163C2×C4C22⋊#1062438211yescharacteristic
164C8—7242no—
165C22—21no—
166C22—41no—
167C22—3621no—
168C22—3621no—
169C22—7241no—
170C22—7241no—
171C22C2×C22⋊#1062438211yescharacteristic
172C4—21no—
173C4—42no—
174C4—3621no—
175C4—3621no—
176C4—14482no—
177C4—7242no—
178C4#1915387411yescharacteristic
179C4#1915387411yescharacteristic
180C2—21no—
181C2—41no—
182C2—7241no—
183C2—7241no—
184C2C2×#1915387411yescharacteristic
subgroupG/H
centerC2C2×#19153874
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC22×Q8×C181C4
socleC2×C181C2×#99
prime radicalC2×#15668449C22
cosocleC2×C22⋊D181C23
hypercenterC22×Q8#10624382
hypocenterC181#2123
LCSG ▷ C23×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #26042181C2semidirect
14. #19153799C4semidirect
18. #19153775C4semidirect
19. C22×Q8×C181C4semidirect
92. C181#2123semidirect
99. C22×Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422652
#260422582
#260421812
#260418532
#2123181