Finite Group Databasebeta

← #37532413

Subgroups — #37532413

Order 23168.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#26041827C211yesmaximal, characteristic
2#26041335C211yesmaximal, characteristic, complemented
3C4⋊C8×D181C211yesmaximal, characteristic, complemented
4#26041027C211yesmaximal, characteristic, complemented
5#26041027C211yesmaximal, characteristic, complemented
6#26041023C211yesmaximal, characteristic, complemented
7#331×C181C211yesmaximal, characteristic, complemented
8C2×#15668448C412yes—
9C2×C8×D181—21no—
10#19153816C2211yescharacteristic
11#19153803C412yes—
12#19153787—21no—
13#19153787—21no—
14D4×Dic181—21no—
15D4×Dic181—21no—
16C42×D181C2211yescharacteristic
17C4⋊#13089678C2211yescharacteristic
18C4⋊#13089678C2211yescharacteristic
19#19153745—21no—
20#19153728—21no—
21#19153726—21no—
22#127×C181C2211yescharacteristic
23C4⋊C8×C181C2211yescharacteristic
24C4⋊C8×C181C2211yescharacteristic
25#15668448—44no—
26C2×Dic362C2×C412yes—
27C2×C22⋊D181—22no—
28C22×Dic181—22no—
29C2×C4×D181C2×C411yescharacteristic
30C2×C4×D181D411yescharacteristic
31C2×C4×D181D411yescharacteristic
32C2×#13089678—21no—
33C2×#13089678—21no—
34C8×D181—42no—
35C4⋊Dic181—21no—
36C4⋊Dic181—21no—
37C22⋊Dic181—22no—
38C22⋊Dic181—22no—
39C4×Dic181C2×C411yescharacteristic
40C4×Dic181D411yescharacteristic
41C4×Dic181D411yescharacteristic
42C2×D4×C181—21no—
43C2×D4×C181—21no—
44C2×D4×C181C2×C412yes—
45C2×C8×C181—21no—
46C2×C8×C181—21no—
47C42×C181C2311yescharacteristic
48C22×D181C22⋊C411yescharacteristic
49Dic362—42no—
50C22⋊D181—44no—
51C2×Dic181—22no—
52C2×Dic181—44no—
53C2×Dic181C22⋊C411yescharacteristic
54C2×Dic181C22⋊C411yescharacteristic
55C2×Dic181C22⋊C411yescharacteristic
56C4×D181—22no—
57C4×D181—21no—
58C4×D181—21no—
59C4×D181—21no—
60C4×D181—21no—
61#13089678—41no—
62#13089678—41no—
63C23×C181—22no—
64D4×C181—42no—
65D4×C181—41no—
66D4×C181—41no—
67D4×C181—41no—
68D4×C181—41no—
69C2×C4×C181C22×C411yescharacteristic
70C2×C4×C181C2×D411yescharacteristic
71C2×C4×C181C2×D411yescharacteristic
72C8×C181—41no—
73C8×C181—41no—
74C22×C181—42no—
75C22×C181—42no—
76C22×C181—42no—
77C22×C181C2×C22⋊C411yescharacteristic
78C2×D181—21no—
79C2×D181—21no—
80C2×D181#10012yes—
81C4×C181—21no—
82C4×C181#13511yescharacteristic
83C4×C181#13511yescharacteristic
84C4×C181AGL(1,ℤ/8)11yescharacteristic
85C4×C181#13711yescharacteristic
86Dic181—21no—
87Dic181—21no—
88Dic181—21no—
89Dic181—42no—
90C2×C181—82no—
91C2×C181C2×#10011yescharacteristic
92C2×C181#41611yescharacteristic
93C2×C181#41711yescharacteristic
94D181—22no—
95C181#155111yescharacteristic, complemented, Sylow
96#1551—1811nomaximal, Sylow
97#532—1811no—
98#432—1811no—
99C2×C4⋊C8—1811no—
100#333—1811no—
101#333—1811no—
102#331—1811no—
103#331D18111yescharacteristic, complemented
104C2×#41—1812no—
105C22×C8—3621no—
106C4⋊Q8—1811no—
107#127C2×D18111yescharacteristic
108#124—1812no—
109#121—3621no—
110#121—3621no—
111C4×D4—3621no—
112C4×D4—3621no—
113C2×C42—1811no—
114C4⋊C8—3621no—
115C4⋊C8—1811no—
116C4⋊C8—1811no—
117C4⋊C8C2×D18111yescharacteristic
118C4⋊C8C2×D18111yescharacteristic
119C22⋊C8—3621no—
120#97—3621no—
121#41—7244no—
122C2×Q8—1812no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—3622no—
126C2×D4C4×D18112yes—
127C22×C4—3622no—
128C22×C4—1811no—
129C22×C4—1811no—
130C22×C4—1811no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—3621no—
134C2×C8—3621no—
135C2×C8—7242no—
136C4⋊C4—3621no—
137C4⋊C4—3621no—
138C22⋊C4—3622no—
139C22⋊C4—3622no—
140C42—1811no—
141C42—1811no—
142C42—1811no—
143C42C22×D18111yescharacteristic
144C23—22no—
145C23—1811no—
146Q8—7242no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—7244no—
153C2×C4—3622no—
154C2×C4—3621no—
155C2×C4—3621no—
156C2×C4—3621no—
157C2×C4—3621no—
158C2×C4—3622no—
159C2×C4—1811no—
160C2×C4—1811no—
161C2×C4—1811no—
162C2×C4—7244no—
163C2×C4C2×C4×D18111yescharacteristic
164C2×C4D4×D18111yescharacteristic
165C2×C4D4×D18111yescharacteristic
166C8—41no—
167C8—41no—
168C8—7241no—
169C8—7241no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—3621no—
174C22—3621no—
175C22—1812no—
176C22C22⋊C4×D18111yescharacteristic
177C4—21no—
178C4—3621no—
179C4—3621no—
180C4—3621no—
181C4—7242no—
182C4#1915383511yescharacteristic
183C4#1915383711yescharacteristic
184C4#1915384011yescharacteristic
185C4#1915384511yescharacteristic
186C2—82no—
187C2—3622no—
188C2#100×D18111yescharacteristic
189C2#2604127211yescharacteristic
190C2#2604127711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D181
commutatorC2×C4×C181C22×C4
FrattiniC42C22×D181
Fitting#331×C181C2
socleC22×C181C2×C22⋊C4
prime radical#26041827C2
cosocleC42×C181C23
hypercenter#331D181
hypocenterC181#1551
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #26041335C2semidirect
3. C4⋊C8×D181C2semidirect
4. #26041027C2semidirect
5. #26041027C2semidirect
6. #26041023C2semidirect
7. #331×C181C2semidirect
95. C181#1551semidirect
103. #331D181semidirect

Maximal subgroups

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

subgroupindex
#260418272
#260413352
C4⋊C8×D1812
#260410272
#260410232
#331×C1812
#1551181