Finite Group Databasebeta

← #37549253

Subgroups — #37549253

Order 23168.

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

normal subgroups only

This group has 246 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#26042299C211yesmaximal, characteristic, complemented
2#26042282C211yesmaximal, characteristic, complemented
3#26042138C212yesmaximal, complemented
4#26042137C212yesmaximal, complemented
5#26041824C211yesmaximal, characteristic
6C2×#15668458—21no—
7#19153883C2212yes—
8#19153883C2212yes—
9C4⋊#13089685—21no—
10C22⋊#13089685—21no—
11#19153871—21no—
12C2×#15668448—21no—
13#19153815C2211yescharacteristic
14#19153812C2211yescharacteristic
15#19153802—21no—
16#19153790C411yescharacteristic
17#19153788—21no—
18D4×Dic181C411yescharacteristic
19#19153778C411yescharacteristic
20#19153776—21no—
21C2×C4×Dic181C2211yescharacteristic
22#121×C181C411yescharacteristic
23#15668458—42no—
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—42no—
51#13089685—42no—
52C22×D181—21no—
53Dic362—42no—
54D724—41no—
55C22⋊D181—42no—
56C22⋊D181—41no—
57C22⋊D181—42no—
58C22⋊D181—41no—
59C2×Dic181—22no—
60C2×Dic181—21no—
61C2×Dic181—21no—
62C2×Dic181—21no—
63C2×Dic181—42no—
64C2×Dic181C22⋊C411yescharacteristic
65C2×Dic181C22⋊C411yescharacteristic
66C2×Dic181C2×D411yescharacteristic
67C2×Dic181C2×D411yescharacteristic
68C4×D181—42no—
69C23×C181—21no—
70C23×C181C22⋊C411yescharacteristic
71D4×C181—41no—
72D4×C181—42no—
73C2×C4×C181—21no—
74C2×C4×C181—41no—
75C2×C4×C181C22⋊C411yescharacteristic
76C2×C4×C181C22×C411yescharacteristic
77C22×C181—21no—
78C22×C181—21no—
79C22×C181—21no—
80C22×C181—41no—
81C22×C181—41no—
82C22×C181—41no—
83C22×C181C2×C22⋊C411yescharacteristic
84C2×D181—41no—
85C2×D181—41no—
86C2×D181—41no—
87C4×C181—21no—
88C4×C181—21no—
89C4×C181—41no—
90Dic181—21no—
91Dic181—21no—
92Dic181—41no—
93Dic181AGL(1,ℤ/8)11yescharacteristic
94Dic181AGL(1,ℤ/8)12yes—
95Dic181#13711yescharacteristic
96C2×C181—41no—
97C2×C181—81no—
98C2×C181#41311yescharacteristic
99C2×C181#41711yescharacteristic
100C2×C181#41811yescharacteristic
101D181—81no—
102C181#155711yescharacteristic, complemented, Sylow
103#1557—1811nomaximal, Sylow
104#532—1811no—
105#432—1811no—
106#423—1811no—
107#332—1812no—
108#331—1812no—
109C2×#41—3621no—
110C2×M16—3621no—
111C4⋊Q8—1811no—
112#127—1811no—
113#124—3621no—
114#121—3621no—
115#121—1811no—
116#121#1062438211yescharacteristic
117C4×D4—3621no—
118C4×D4—1811no—
119C4×D4—1811no—
120C2×C42—1811no—
121C4⋊C8—3621no—
122C4⋊C8—1812no—
123C4⋊C8—1812no—
124C22⋊C8—3621no—
125#97—3621no—
126#41—7244no—
127C2×Q8—3621no—
128C2×D4—21no—
129C2×D4—3621no—
130C2×D4—3621no—
131C2×D4—3621no—
132C2×D4—1811no—
133C2×D4C2×#1062438211yescharacteristic
134C22×C4—3621no—
135C22×C4—3621no—
136C22×C4—1811no—
137C22×C4—1811no—
138C22×C4C2×#1062438211yescharacteristic
139M16—7242no—
140C2×C8—3622no—
141C2×C8—3622no—
142C4⋊C4—3621no—
143C4⋊C4—1811no—
144C4⋊C4C2×#1062438211yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—3621no—
147C22⋊C4—3621no—
148C22⋊C4—3621no—
149C42—1811no—
150C42—1811no—
151C42—1811no—
152C42—1811no—
153C23—21no—
154C23—3621no—
155C23C22⋊#1062438211yescharacteristic
156Q8—7242no—
157D4—41no—
158D4—42no—
159D4—7241no—
160D4—7242no—
161D4—7241no—
162D4—7241no—
163D4—7242no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—3621no—
167C2×C4—3622no—
168C2×C4—3621no—
169C2×C4—3621no—
170C2×C4—1811no—
171C2×C4—1811no—
172C2×C4—1811no—
173C2×C4—1811no—
174C2×C4—7242no—
175C2×C4—7242no—
176C2×C4C22⋊#1062438211yescharacteristic
177C2×C4C22×#1062438211yescharacteristic
178C8—7242no—
179C8—7242no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—7241no—
187C22—7241no—
188C22—7241no—
189C22C2×C22⋊#1062438211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—3621no—
194C4—3621no—
195C4—1811no—
196C4—1811no—
197C4—1812no—
198C4—7241no—
199C2—41no—
200C2—81no—
201C2—14481no—
202C2#2604226611yescharacteristic
203C2#2604227011yescharacteristic
204C2#2604227111yescharacteristic
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#1557
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #26042299C2semidirect
2. #26042282C2semidirect
3. #26042138C2semidirect
4. #26042137C2semidirect
102. C181#1557semidirect

Maximal subgroups

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

subgroupindex
#260422992
#260422822
#260421382
#260421372
#260418242
#1557181