Finite Group Databasebeta

← #37532297

Subgroups — #37532297

Order 23168.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#26041815C211yesmaximal, characteristic
2#26041329C211yesmaximal, characteristic, complemented
3#26041146C211yesmaximal, characteristic, complemented
4#26041016C211yesmaximal, characteristic, complemented
5#26041014C211yesmaximal, characteristic
6#26041012C211yesmaximal, characteristic
7#328×C181C211yesmaximal, characteristic, complemented
8#19153811—21no—
9#19153807C411yescharacteristic, complemented
10#19153805C411yescharacteristic, complemented
11#19153800—21no—
12#19153790C2211yescharacteristic
13Q8×Dic181C411yescharacteristic, complemented
14#19153778C411yescharacteristic, complemented
15#19153776—21no—
16#19153774—21no—
17C2×C4×Dic181C2211yescharacteristic
18#19153745—21no—
19C22⋊#13089678C2211yescharacteristic
20C8×Dic181—21no—
21#19153723—21no—
22#19153723—21no—
23#19153723C2211yescharacteristic
24C22⋊Q8×C181C2211yescharacteristic
25C22⋊C8×C181C2211yescharacteristic
26#95×C181C2211yescharacteristic
27C2×D724C2×C411yescharacteristic
28C2×C22⋊D181—21no—
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×C4×D181—21no—
33C2×#13089678—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181C2×C411yescharacteristic
37#15668428—21no—
38#15668426—21no—
39#15668426—21no—
40#15668426—21no—
41#15668426—21no—
42C4×Dic181—21no—
43C4×Dic181C2×C411yescharacteristic
44C4×Dic181C2×C411yescharacteristic
45C4×Dic181D411yescharacteristic
46C4×Dic181D411yescharacteristic
47C2×Q8×C181C2×C411yescharacteristic
48C22×C4×C181—21no—
49C22×C4×C181C2311yescharacteristic
50C2×C8×C181—21no—
51C4⋊C4×C181—21no—
52C4⋊C4×C181C2×C411yescharacteristic
53C22⋊C4×C181—21no—
54C22×D181—21no—
55D724—41no—
56C22⋊D181—41no—
57C22⋊D181—41no—
58C2×Dic181—21no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181—41no—
64C2×Dic181—41no—
65C2×Dic181C22⋊C411yescharacteristic
66C2×Dic181C22⋊C411yescharacteristic
67C2×Dic181C22⋊C411yescharacteristic
68C2×Dic181C22⋊C411yescharacteristic
69C4×D181—42no—
70#13089678—41no—
71C23×C181C2×D411yescharacteristic
72Q8×C181—41no—
73C2×C4×C181—21no—
74C2×C4×C181—21no—
75C2×C4×C181—41no—
76C2×C4×C181—41no—
77C2×C4×C181—41no—
78C2×C4×C181—41no—
79C2×C4×C181C22×C411yescharacteristic
80C2×C4×C181C2×D411yescharacteristic
81C8×C181—41no—
82C22×C181—21no—
83C22×C181—21no—
84C22×C181C2×C22⋊C411yescharacteristic
85C22×C181#13511yescharacteristic
86C22×C181#13511yescharacteristic
87C2×D181—41no—
88C2×D181—41no—
89C2×D181—41no—
90C4×C181—21no—
91C4×C181—21no—
92C4×C181—41no—
93C4×C181—41no—
94C4×C181—81no—
95Dic181—21no—
96Dic181—21no—
97Dic181—21no—
98Dic181—21no—
99Dic181—41no—
100Dic181—81no—
101C2×C181—21no—
102C2×C181—21no—
103C2×C181#41011yescharacteristic
104C2×C181#41611yescharacteristic
105C2×C181#42111yescharacteristic
106D181—81no—
107C181#152111yescharacteristic, complemented, Sylow
108#1521—1811nomaximal, Sylow
109#529—1811no—
110#431—1811no—
111#383—1811no—
112#328—1811no—
113#328D18111yescharacteristic, complemented
114#327—1811no—
115#327—1811no—
116#126—3621no—
117#125—1811no—
118#124—1811no—
119#123—3621no—
120C22⋊Q8C2×D18111yescharacteristic
121#121—1811no—
122C4×Q8—1811no—
123C4×D4—3621no—
124C4×D4—1811no—
125#117—3621no—
126C2×C42—1811no—
127C4⋊C8—3621no—
128C22⋊C8—1811no—
129C22⋊C8C2×D18111yescharacteristic
130C4×C8—3621no—
131#95—3621no—
132#95—3621no—
133#95—1811no—
134#95C2×D18111yescharacteristic
135C2×Q8C4×D18111yescharacteristic
136C2×D4—3621no—
137C2×D4—1811no—
138C22×C4—21no—
139C22×C4—3621no—
140C22×C4—3621no—
141C22×C4—1811no—
142C22×C4—1811no—
143C22×C4C22×D18111yescharacteristic
144C2×C8—21no—
145C2×C8—3621no—
146C4⋊C4—21no—
147C4⋊C4—3621no—
148C4⋊C4—3621no—
149C4⋊C4—3621no—
150C4⋊C4—1811no—
151C4⋊C4C4×D18111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3621no—
154C22⋊C4—3621no—
155C22⋊C4—3621no—
156C22⋊C4—3621no—
157C42—3621no—
158C42—1811no—
159C42—1811no—
160C42—1811no—
161C42—1811no—
162C23—3621no—
163C23D4×D18111yescharacteristic
164Q8—41no—
165D4—7241no—
166D4—7241no—
167D4—7241no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3621no—
175C2×C4—3621no—
176C2×C4—3621no—
177C2×C4—1811no—
178C2×C4—1811no—
179C2×C4—1811no—
180C2×C4—1811no—
181C2×C4—7242no—
182C2×C4—7241no—
183C2×C4—7241no—
184C2×C4—7241no—
185C2×C4—7241no—
186C2×C4C2×C4×D18111yescharacteristic
187C2×C4D4×D18111yescharacteristic
188C8—41no—
189C8—7241no—
190C22—21no—
191C22—21no—
192C22—7241no—
193C22—7241no—
194C22—7241no—
195C22C22⋊C4×D18111yescharacteristic
196C22#1915383711yescharacteristic
197C22#1915383911yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—3621no—
204C4—3621no—
205C4—3621no—
206C4—3621no—
207C4—14481no—
208C4—7241no—
209C2—21no—
210C2—21no—
211C2—14481no—
212C2#2604125111yescharacteristic
213C2#2604127411yescharacteristic
214C2#2604129411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D181
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#328×C181C2
socleC22×C181C2×C22⋊C4
prime radical#19153790C22
cosocleC22×C4×C181C23
hypercenter#328D181
hypocenterC181#1521
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #26041329C2semidirect
3. #26041146C2semidirect
4. #26041016C2semidirect
7. #328×C181C2semidirect
9. #19153807C4semidirect
10. #19153805C4semidirect
13. Q8×Dic181C4semidirect
14. #19153778C4semidirect
107. C181#1521semidirect
113. #328D181semidirect

Maximal subgroups

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

subgroupindex
#260418152
#260413292
#260411462
#260410162
#260410142
#260410122
#328×C1812
#1521181