Finite Group Databasebeta

← #37549244

Subgroups — #37549244

Order 23168.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#26042302C211yesmaximal, characteristic, complemented
2#26042297C211yesmaximal, characteristic, complemented
3#26042138C212yesmaximal, complemented
4#26042137C212yesmaximal, complemented
5#26041826C211yesmaximal, characteristic
6#19153883C2212yes—
7#19153883C2212yes—
8#19153873—21no—
9#19153873—21no—
10#19153871—21no—
11C4×#13089685—21no—
12C2×#15668449—21no—
13#19153815C2211yescharacteristic
14#19153812C2211yescharacteristic
15#19153802—21no—
16#19153791C411yescharacteristic
17#19153789—21no—
18#19153787C411yescharacteristic
19C4×D724C411yescharacteristic
20C4×C22⋊D181—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25#15668449—44no—
26C2×Dic362—21no—
27C2×D724—21no—
28C2×D724C2×C411yescharacteristic
29C2×C22⋊D181—21no—
30C2×C22⋊D181—21no—
31C2×C22⋊D181—21no—
32C2×C4×D181—21no—
33C2×C4×D181C2×C411yescharacteristic
34C2×C4×D181D411yescharacteristic
35C2×C4×D181D411yescharacteristic
36C4⋊Dic181C2×C411yescharacteristic
37#15668428—21no—
38C22⋊Dic181—21no—
39#15668426—21no—
40#15668426—21no—
41C4×Dic181D411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181C2311yescharacteristic
44C2×D4×C181C2×C411yescharacteristic
45C22×C4×C181—21no—
46C4⋊C4×C181C2×C411yescharacteristic
47C22⋊C4×C181—21no—
48C42×C181C2×C411yescharacteristic
49#13089685—42no—
50#13089685—42no—
51C22×D181—21no—
52C22×D181C22⋊C411yescharacteristic
53Dic362—42no—
54D724—41no—
55D724—42no—
56C22⋊D181—42no—
57C22⋊D181—42no—
58C22⋊D181—42no—
59C2×Dic181—21no—
60C2×Dic181C22⋊C411yescharacteristic
61C2×Dic181C2×D411yescharacteristic
62C2×Dic181C2×D411yescharacteristic
63C4×D181—22no—
64C4×D181—22no—
65C4×D181—41no—
66C4×D181—42no—
67C23×C181—21no—
68D4×C181—41no—
69C2×C4×C181—21no—
70C2×C4×C181—42no—
71C2×C4×C181C22⋊C411yescharacteristic
72C2×C4×C181C22⋊C411yescharacteristic
73C2×C4×C181C22×C411yescharacteristic
74C22×C181—41no—
75C22×C181—41no—
76C22×C181—41no—
77C22×C181C2×C22⋊C411yescharacteristic
78C2×D181—21no—
79C2×D181—21no—
80C2×D181—21no—
81C2×D181—41no—
82C2×D181—41no—
83C2×D181—41no—
84C4×C181—21no—
85C4×C181—21no—
86C4×C181—21no—
87C4×C181—41no—
88Dic181—21no—
89Dic181—41no—
90Dic181#13512yes—
91Dic181AGL(1,ℤ/8)12yes—
92C2×C181—81no—
93C2×C181#41311yescharacteristic
94C2×C181#41611yescharacteristic
95C2×C181#41811yescharacteristic
96D181—41no—
97D181—81no—
98C181#155311yescharacteristic, complemented, Sylow
99#1553—1811nomaximal, Sylow
100#532—1811no—
101#432—1811no—
102#431—1811no—
103#332—1812no—
104#331—1812no—
105C2×#41—3621no—
106C4⋊Q8—1811no—
107#127—1811no—
108#124—3621no—
109#121—3621no—
110#121—1811no—
111#121—1811no—
112C4×D4—3621no—
113C4×D4—1811no—
114C4×D4#1062438211yescharacteristic
115C2×C42—1811no—
116C4⋊C8—1812no—
117C4⋊C8—1812no—
118C22⋊C8—3621no—
119C22⋊C8—3621no—
120#97—3621no—
121C4×C8—3621no—
122#41—7244no—
123C2×Q8—3621no—
124C2×D4—3621no—
125C2×D4—3621no—
126C2×D4—3621no—
127C2×D4—3621no—
128C2×D4—1811no—
129C2×D4C2×#1062438211yescharacteristic
130C22×C4—21no—
131C22×C4—3621no—
132C22×C4—1811no—
133C22×C4—1811no—
134C22×C4—1811no—
135C2×C8—3622no—
136C2×C8—3622no—
137C4⋊C4—3621no—
138C4⋊C4—1811no—
139C4⋊C4C2×#1062438211yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—3621no—
142C22⋊C4—3621no—
143C22⋊C4—3621no—
144C42—1811no—
145C42—1811no—
146C42—1811no—
147C42C2×#1062438211yescharacteristic
148C23—21no—
149C23—3621no—
150C23—1811no—
151Q8—7242no—
152D4—41no—
153D4—7241no—
154D4—7242no—
155D4—7242no—
156D4—7242no—
157D4—7242no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—3622no—
161C2×C4—3622no—
162C2×C4—3621no—
163C2×C4—1811no—
164C2×C4—1811no—
165C2×C4—1811no—
166C2×C4—7241no—
167C2×C4—7242no—
168C2×C4C22⋊#1062438211yescharacteristic
169C2×C4C22⋊#1062438211yescharacteristic
170C2×C4C22×#1062438211yescharacteristic
171C8—7242no—
172C8—7242no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—3621no—
177C22—3621no—
178C22—3621no—
179C22—7241no—
180C22—7241no—
181C22—7241no—
182C22C2×C22⋊#1062438211yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—3621no—
188C4—1812no—
189C4—1812no—
190C4—7241no—
191C2—81no—
192C2—14481no—
193C2—7241no—
194C2#2604226511yescharacteristic
195C2#2604226911yescharacteristic
196C2#2604227111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041826C2
cosocleC4×Dic181C23
hypercenterC4×D4#10624382
hypocenterC181#1553
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042302C2semidirect
2. #26042297C2semidirect
3. #26042138C2semidirect
4. #26042137C2semidirect
98. C181#1553semidirect

Maximal subgroups

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

subgroupindex
#260423022
#260422972
#260421382
#260421372
#260418262
#1553181