Finite Group Databasebeta

← #37549040

Subgroups — #37549040

Order 23168.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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
2C4×#15668458C211yesmaximal, characteristic, complemented
3#26042127C212yesmaximal, complemented
4D4⋊#13089685C212yesmaximal, complemented
5#26041824C211yesmaximal, characteristic
6C2×#15668458—21no—
7C4⋊#13089685C2212yes—
8C22⋊#13089685—21no—
9#19153871—21no—
10C4×#13089685—21no—
11C4×#13089685C2212yes—
12C2×#15668448—21no—
13#19153815C411yescharacteristic
14#19153812C411yescharacteristic
15#19153802—21no—
16#19153790C411yescharacteristic
17#19153788—21no—
18D4×Dic181C2211yescharacteristic
19#19153778C2211yescharacteristic
20#19153776—21no—
21C2×C4×Dic181C2211yescharacteristic
22#121×C181C411yescharacteristic
23#15668458—24no—
24C2×#13089685—22no—
25C2×#13089685—22no—
26#15668448—44no—
27C2×Dic362—21no—
28C2×D724C2×C411yescharacteristic
29C2×C22⋊D181—21no—
30C2×C22⋊D181—21no—
31C2×C22⋊D181—21no—
32C22×Dic181—21no—
33C22×Dic181D411yescharacteristic
34C22×Dic181D411yescharacteristic
35C2×C4×D181—21no—
36C4⋊Dic181C2×C411yescharacteristic
37#15668428—21no—
38C22⋊Dic181—21no—
39#15668426—21no—
40#15668426—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C4×Dic181C2311yescharacteristic
45C2×D4×C181—21no—
46C2×D4×C181C2×C411yescharacteristic
47C22×C4×C181C2×C411yescharacteristic
48C4⋊C4×C181C2×C411yescharacteristic
49C22⋊C4×C181—21no—
50#13089685—24no—
51#13089685—42no—
52C22×D181—21no—
53Dic362—42no—
54D724—22no—
55C22⋊D181—42no—
56C22⋊D181—42no—
57C22⋊D181—42no—
58C2×Dic181—22no—
59C2×Dic181—22no—
60C2×Dic181—21no—
61C2×Dic181—42no—
62C2×Dic181C22⋊C411yescharacteristic
63C2×Dic181C22⋊C411yescharacteristic
64C2×Dic181C2×D411yescharacteristic
65C2×Dic181C2×D411yescharacteristic
66C4×D181—42no—
67C23×C181—21no—
68C23×C181C22⋊C411yescharacteristic
69D4×C181—22no—
70D4×C181—42no—
71C2×C4×C181—22no—
72C2×C4×C181—21no—
73C2×C4×C181C22⋊C411yescharacteristic
74C2×C4×C181C22×C411yescharacteristic
75C22×C181—21no—
76C22×C181—21no—
77C22×C181—21no—
78C22×C181—41no—
79C22×C181—41no—
80C22×C181—41no—
81C22×C181C2×C22⋊C411yescharacteristic
82C2×D181—41no—
83C2×D181—41no—
84C2×D181—41no—
85C4×C181—21no—
86C4×C181—41no—
87C4×C181#13112yes—
88Dic181—21no—
89Dic181—21no—
90Dic181—41no—
91Dic181#10412yes—
92Dic181AGL(1,ℤ/8)12yes—
93C2×C181—41no—
94C2×C181—81no—
95C2×C181#40811yescharacteristic
96C2×C181#41811yescharacteristic
97C2×C181C2×#10411yescharacteristic
98D181—81no—
99C181#148411yescharacteristic, complemented, Sylow
100#1484—1811nomaximal, Sylow
101#532—1811no—
102#431—1811no—
103C4×M16—1811no—
104D4⋊C8—1812no—
105D4⋊C8—1812no—
106C2×#41—3621no—
107C2×M16—3621no—
108C4⋊Q8—1811no—
109#127—1811no—
110#124—3621no—
111#121—3621no—
112#121—1811no—
113#121#1062438211yescharacteristic
114C4×D4—3621no—
115C4×D4—1811no—
116C4×D4—1811no—
117C2×C42—1811no—
118C4⋊C8—1812no—
119C22⋊C8—3621no—
120#97—3621no—
121C4×C8—3621no—
122C4×C8—1812no—
123#41—7244no—
124C2×Q8—3621no—
125C2×D4—21no—
126C2×D4—3621no—
127C2×D4—3621no—
128C2×D4—3621no—
129C2×D4—1811no—
130C2×D4C2×#1062438211yescharacteristic
131C22×C4—3621no—
132C22×C4—3621no—
133C22×C4—1811no—
134C22×C4—1811no—
135C22×C4C2×#1062438211yescharacteristic
136M16—3624no—
137C2×C8—3622no—
138C2×C8—3622no—
139C4⋊C4—3621no—
140C4⋊C4—1811no—
141C4⋊C4C2×#1062438211yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—3621no—
144C22⋊C4—3621no—
145C22⋊C4—3621no—
146C42—1811no—
147C42—1811no—
148C42—1811no—
149C42—1811no—
150C23—21no—
151C23—3621no—
152C23C22⋊#1062438211yescharacteristic
153Q8—7242no—
154D4—22no—
155D4—42no—
156D4—3622no—
157D4—7242no—
158D4—7242no—
159D4—7242no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—3622no—
163C2×C4—3622no—
164C2×C4—3621no—
165C2×C4—1811no—
166C2×C4—1811no—
167C2×C4—1811no—
168C2×C4—1811no—
169C2×C4—7242no—
170C2×C4—7242no—
171C2×C4C22⋊#1062438211yescharacteristic
172C2×C4C22×#1062438211yescharacteristic
173C8—3624no—
174C8—7242no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—7241no—
182C22—7241no—
183C22—7241no—
184C22C2×C22⋊#1062438211yescharacteristic
185C4—21no—
186C4—41no—
187C4—3621no—
188C4—3621no—
189C4—1812no—
190C4—1812no—
191C4—7241no—
192C4#1915390312yes—
193C2—41no—
194C2—81no—
195C2—14481no—
196C2#2604225211yescharacteristic
197C2#2604227111yescharacteristic
198C2D181⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#121×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041824C2
cosocleC4×Dic181C23
hypercenter#121#10624382
hypocenterC181#1484
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #26042295C2semidirect
2. C4×#15668458C2semidirect
3. #26042127C2semidirect
4. D4⋊#13089685C2semidirect
99. C181#1484semidirect

Maximal subgroups

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

subgroupindex
#260422952
C4×#156684582
#260421272
D4⋊#130896852
#260418242
#1484181