Finite Group Databasebeta

← #37532440

Subgroups — #37532440

Order 23168.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#26041301C211yesmaximal, characteristic, complemented
4#26041026C211yesmaximal, characteristic, complemented
5#26041024C211yesmaximal, characteristic, complemented
6#26041023C211yesmaximal, characteristic, complemented
7#331×C181C211yesmaximal, characteristic, complemented
8C2×#15668448—21no—
9C2×#15668432—21no—
10#19153816C2211yescharacteristic
11#19153803—21no—
12#19153787—21no—
13#19153787C412yes—
14D4×Dic181—21no—
15D4×Dic181C412yes—
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—42no—
26#15668448—42no—
27C2×Dic362—21no—
28C2×C22⋊D181—22no—
29C22×Dic181—22no—
30C2×C4×D181C2×C411yescharacteristic
31C2×C4×D181D411yescharacteristic
32C2×C4×D181D411yescharacteristic
33#15668432—42no—
34C2×#13089678—21no—
35C2×#13089678—21no—
36C4⋊Dic181—21no—
37C4⋊Dic181C2×C412yes—
38C22⋊Dic181—22no—
39C22⋊Dic181—22no—
40C4×Dic181C2×C411yescharacteristic
41C4×Dic181D411yescharacteristic
42C4×Dic181D411yescharacteristic
43C2×D4×C181—21no—
44C2×D4×C181—21no—
45C2×D4×C181C2×C412yes—
46C2×C8×C181—21no—
47C2×C8×C181—21no—
48C42×C181C2311yescharacteristic
49C22×D181C22⋊C411yescharacteristic
50Dic362—41no—
51Dic362—41no—
52C22⋊D181—44no—
53C2×Dic181—22no—
54C2×Dic181—44no—
55C2×Dic181C22⋊C411yescharacteristic
56C2×Dic181C22⋊C411yescharacteristic
57C2×Dic181C22⋊C411yescharacteristic
58C4×D181—21no—
59C4×D181—21no—
60C4×D181—21no—
61C4×D181—21no—
62C4×D181—41no—
63#13089678—41no—
64#13089678—41no—
65C23×C181—22no—
66D4×C181—42no—
67D4×C181—41no—
68D4×C181—41no—
69D4×C181—41no—
70D4×C181—41no—
71C2×C4×C181C22×C411yescharacteristic
72C2×C4×C181C2×D411yescharacteristic
73C2×C4×C181C2×D411yescharacteristic
74C8×C181—41no—
75C8×C181—41no—
76C22×C181—42no—
77C22×C181—42no—
78C22×C181—42no—
79C22×C181C2×C22⋊C411yescharacteristic
80C2×D181—21no—
81C2×D181—21no—
82C2×D181—21no—
83C4×C181—21no—
84C4×C181AGL(1,ℤ/8)11yescharacteristic
85C4×C181AGL(1,ℤ/8)11yescharacteristic
86C4×C181AGL(1,ℤ/8)11yescharacteristic
87C4×C181#13711yescharacteristic
88Dic181—21no—
89Dic181—21no—
90Dic181—21no—
91Dic181—42no—
92C2×C181—82no—
93C2×C181#41311yescharacteristic
94C2×C181#41711yescharacteristic
95C2×C181#41811yescharacteristic
96D181—41no—
97C181#155711yescharacteristic, complemented, Sylow
98#1557—1811nomaximal, Sylow
99#532—1811no—
100#432—1811no—
101#423—1811no—
102#332—1811no—
103#332—1811no—
104#331—1811no—
105#331D18111yescharacteristic, complemented
106C2×#41—3621no—
107C2×M16—3621no—
108C4⋊Q8—1811no—
109#127C2×D18111yescharacteristic
110#124—3621no—
111#121—3621no—
112#121—1812no—
113C4×D4—3621no—
114C4×D4—1812no—
115C2×C42—1811no—
116C4⋊C8—3621no—
117C4⋊C8—1811no—
118C4⋊C8—1811no—
119C4⋊C8C2×D18111yescharacteristic
120C4⋊C8C2×D18111yescharacteristic
121C22⋊C8—3621no—
122#97—3621no—
123#41—7242no—
124#41—7242no—
125C2×Q8—3621no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—3622no—
129C2×D4C4×D18112yes—
130C22×C4—3622no—
131C22×C4—1811no—
132C22×C4—1811no—
133C22×C4—1811no—
134M16—7242no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—3621no—
138C2×C8—3621no—
139C4⋊C4—3621no—
140C4⋊C4—1812no—
141C22⋊C4—3622no—
142C22⋊C4—3622no—
143C42—1811no—
144C42—1811no—
145C42—1811no—
146C42C22×D18111yescharacteristic
147C23—22no—
148C23—1811no—
149Q8—7241no—
150Q8—7241no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—7244no—
157C2×C4—3621no—
158C2×C4—3621no—
159C2×C4—3621no—
160C2×C4—3621no—
161C2×C4—3622no—
162C2×C4—1811no—
163C2×C4—1811no—
164C2×C4—1811no—
165C2×C4—7241no—
166C2×C4—7244no—
167C2×C4C2×C4×D18111yescharacteristic
168C2×C4D4×D18111yescharacteristic
169C2×C4D4×D18111yescharacteristic
170C8—41no—
171C8—41no—
172C8—7241no—
173C8—7241no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—3621no—
178C22—3621no—
179C22—3621no—
180C22C22⋊C4×D18111yescharacteristic
181C4—21no—
182C4—3621no—
183C4—3621no—
184C4—3621no—
185C4—7242no—
186C4#1915384011yescharacteristic
187C4#1915384011yescharacteristic
188C4#1915384311yescharacteristic
189C4#1915384511yescharacteristic
190C2—82no—
191C2—7241no—
192C2#2604126011yescharacteristic
193C2#2604127711yescharacteristic
194C2#2604128211yescharacteristic
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#1557
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. #26041301C2semidirect
4. #26041026C2semidirect
5. #26041024C2semidirect
6. #26041023C2semidirect
7. #331×C181C2semidirect
97. C181#1557semidirect
105. #331D181semidirect

Maximal subgroups

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

subgroupindex
#260418272
#260413352
#260413012
#260410262
#260410242
#260410232
#331×C1812
#1557181