Finite Group Databasebeta

← #37549233

Subgroups — #37549233

Order 23168.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#26042282C211yesmaximal, characteristic, complemented
2C2×#19153883C211yesmaximal, characteristic, complemented
3#26042138C212yesmaximal, complemented
4#26042137C212yesmaximal, complemented
5#26041824C211yesmaximal, characteristic
6C2×#15668458—21no—
7C22×#13089685—21no—
8#19153883—21no—
9#19153883C2212yes—
10#19153883C2212yes—
11C4⋊#13089685—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—
26C2×#13089685—42no—
27#15668448—42no—
28#15668448—42no—
29C2×Dic362—21no—
30C2×D724C2×C411yescharacteristic
31C2×C22⋊D181—21no—
32C2×C22⋊D181—21no—
33C2×C22⋊D181—21no—
34C22×Dic181—21no—
35C22×Dic181D411yescharacteristic
36C22×Dic181D411yescharacteristic
37C2×C4×D181—21no—
38C4⋊Dic181C2×C411yescharacteristic
39#15668428—21no—
40C22⋊Dic181—21no—
41#15668426—21no—
42#15668426—21no—
43C4×Dic181C2×C411yescharacteristic
44C4×Dic181D411yescharacteristic
45C4×Dic181D411yescharacteristic
46C4×Dic181C2311yescharacteristic
47C2×D4×C181—21no—
48C2×D4×C181C2×C411yescharacteristic
49C22×C4×C181C2×C411yescharacteristic
50C4⋊C4×C181C2×C411yescharacteristic
51C22⋊C4×C181—21no—
52#13089685—42no—
53#13089685—42no—
54C22×D181—21no—
55Dic362—41no—
56Dic362—41no—
57D724—41no—
58C22⋊D181—42no—
59C22⋊D181—41no—
60C22⋊D181—41no—
61C22⋊D181—41no—
62C22⋊D181—41no—
63C2×Dic181—21no—
64C2×Dic181—21no—
65C2×Dic181—21no—
66C2×Dic181—42no—
67C2×Dic181C22⋊C411yescharacteristic
68C2×Dic181C22⋊C411yescharacteristic
69C2×Dic181D812yes—
70C2×Dic181SD1612yes—
71C2×Dic181C2×D411yescharacteristic
72C2×Dic181C2×D411yescharacteristic
73C4×D181—42no—
74C23×C181—21no—
75C23×C181C22⋊C411yescharacteristic
76D4×C181—41no—
77D4×C181—42no—
78C2×C4×C181—21no—
79C2×C4×C181—41no—
80C2×C4×C181C22⋊C411yescharacteristic
81C2×C4×C181C22×C411yescharacteristic
82C22×C181—21no—
83C22×C181—21no—
84C22×C181—41no—
85C22×C181—41no—
86C22×C181—41no—
87C22×C181#10212yes—
88C22×C181C2×C22⋊C411yescharacteristic
89C2×D181—41no—
90C2×D181—41no—
91C2×D181—41no—
92C4×C181—21no—
93C4×C181—21no—
94C4×C181—41no—
95Dic181—21no—
96Dic181—41no—
97Dic181#10212yes—
98Dic181C2×D811yescharacteristic
99Dic181C2×SD1611yescharacteristic
100Dic181AGL(1,ℤ/8)11yescharacteristic
101Dic181#13711yescharacteristic
102C2×C181—22no—
103C2×C181—81no—
104C2×C181#41311yescharacteristic
105C2×C181C2×#10211yescharacteristic
106C2×C181#41711yescharacteristic
107D181—81no—
108C181#154711yescharacteristic, complemented, Sylow
109#1547—1811nomaximal, Sylow
110#532—1811no—
111#423—1811no—
112C2×C4⋊C8—1811no—
113#332—1812no—
114#331—1812no—
115C2×#41—3621no—
116C2×M16—3621no—
117C22×C8—3621no—
118C4⋊Q8—1811no—
119#127—1811no—
120#124—3621no—
121#121—3621no—
122#121—1811no—
123#121#1062438211yescharacteristic
124C4×D4—3621no—
125C4×D4—1811no—
126C4×D4—1811no—
127C2×C42—1811no—
128C4⋊C8—3621no—
129C4⋊C8—3621no—
130C4⋊C8—1812no—
131C4⋊C8—1812no—
132#41—7242no—
133#41—7242no—
134C2×Q8—3621no—
135C2×D4—21no—
136C2×D4—3621no—
137C2×D4—3621no—
138C2×D4—3621no—
139C2×D4—1811no—
140C2×D4C2×#1062438211yescharacteristic
141C22×C4—3621no—
142C22×C4—3621no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4C2×#1062438211yescharacteristic
146M16—7242no—
147C2×C8—3622no—
148C2×C8—3622no—
149C2×C8—7242no—
150C4⋊C4—3621no—
151C4⋊C4—1811no—
152C4⋊C4C2×#1062438211yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—3621no—
155C22⋊C4—3621no—
156C22⋊C4—3621no—
157C42—1811no—
158C42—1811no—
159C42—1811no—
160C42—1811no—
161C23—21no—
162C23—3621no—
163C23C22⋊#1062438211yescharacteristic
164Q8—7241no—
165Q8—7241no—
166D4—41no—
167D4—42no—
168D4—7241no—
169D4—7241no—
170D4—7241no—
171D4—7241no—
172D4—7241no—
173D4—7242no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—3621no—
177C2×C4—3621no—
178C2×C4—3621no—
179C2×C4—1811no—
180C2×C4—1812no—
181C2×C4—1812no—
182C2×C4—1811no—
183C2×C4—1811no—
184C2×C4—1811no—
185C2×C4—7242no—
186C2×C4—7242no—
187C2×C4C22⋊#1062438211yescharacteristic
188C2×C4C22×#1062438211yescharacteristic
189C8—7242no—
190C8—7242no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—7241no—
197C22—7241no—
198C22—7241no—
199C22#1915387812yes—
200C22C2×C22⋊#1062438211yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—3621no—
205C4—1811no—
206C4—1812no—
207C4—1811no—
208C4—1811no—
209C4—1811no—
210C4—7241no—
211C2—22no—
212C2—81no—
213C2—14481no—
214C2#2604226611yescharacteristic
215C2C2×#1915387811yescharacteristic
216C2#2604227011yescharacteristic
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#1547
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. #26042282C2semidirect
2. C2×#19153883C2semidirect
3. #26042138C2semidirect
4. #26042137C2semidirect
108. C181#1547semidirect

Maximal subgroups

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

subgroupindex
#260422822
C2×#191538832
#260421382
#260421372
#260418242
#1547181