Finite Group Databasebeta

← #37532295

Subgroups — #37532295

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#26041810C211yesmaximal, characteristic
2#26041329C211yesmaximal, characteristic, complemented
3#26041146C211yesmaximal, characteristic, complemented
4#26041017C211yesmaximal, characteristic, complemented
5#26041015C211yesmaximal, characteristic, complemented
6#26041013C211yesmaximal, characteristic
7#327×C181C211yesmaximal, characteristic
8#19153809—21no—
9#19153807C411yescharacteristic, complemented
10#19153803C411yescharacteristic, complemented
11#19153797—21no—
12#19153795C2211yescharacteristic
13#19153781C411yescharacteristic, complemented
14D4×Dic181—21no—
15D4×Dic181C411yescharacteristic, complemented
16#19153772—21no—
17C2×C4×Dic181C2211yescharacteristic
18#19153745—21no—
19C22⋊#13089678C2211yescharacteristic
20C8×Dic181—21no—
21#19153723—21no—
22#19153723—21no—
23#19153723C2211yescharacteristic
24#121×C181C2211yescharacteristic
25C22⋊C8×C181C2211yescharacteristic
26#95×C181C2211yescharacteristic
27C2×Dic362C2×C411yescharacteristic
28C22×Dic181—21no—
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×#13089678—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181C2×C411yescharacteristic
35#15668428—21no—
36#15668428—21no—
37#15668428—21no—
38C22⋊Dic181—21no—
39C22⋊Dic181—21no—
40C22⋊Dic181—21no—
41C22⋊Dic181—21no—
42C4×Dic181—21no—
43C4×Dic181C2×C411yescharacteristic
44C4×Dic181C2×C411yescharacteristic
45C4×Dic181D411yescharacteristic
46C4×Dic181D411yescharacteristic
47C2×D4×C181—21no—
48C2×D4×C181C2×C411yescharacteristic
49C22×C4×C181—21no—
50C22×C4×C181C2311yescharacteristic
51C2×C8×C181—21no—
52C4⋊C4×C181C2×C411yescharacteristic
53C22⋊C4×C181—21no—
54Dic362—41no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—41no—
60C2×Dic181—42no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181—41no—
64C2×Dic181C22⋊C411yescharacteristic
65C2×Dic181C22⋊C411yescharacteristic
66C2×Dic181C22⋊C411yescharacteristic
67C2×Dic181C22⋊C411yescharacteristic
68#13089678—41no—
69C23×C181—21no—
70C23×C181C2×D411yescharacteristic
71D4×C181—41no—
72D4×C181—41no—
73D4×C181—41no—
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×C181—41no—
85C22×C181—41no—
86C22×C181—41no—
87C22×C181C2×C22⋊C411yescharacteristic
88C22×C181#13511yescharacteristic
89C22×C181#13511yescharacteristic
90C4×C181—21no—
91C4×C181—21no—
92C4×C181—41no—
93C4×C181—81no—
94Dic181—21no—
95Dic181—21no—
96Dic181—21no—
97Dic181—21no—
98Dic181—41no—
99Dic181—41no—
100Dic181—81no—
101C2×C181—21no—
102C2×C181—21no—
103C2×C181—81no—
104C2×C181#41011yescharacteristic
105C2×C181#41611yescharacteristic
106C2×C181#42111yescharacteristic
107C181#152111yescharacteristic, complemented, Sylow
108#1521—1811nomaximal, Sylow
109#529—1811no—
110#431—1811no—
111#383—1811no—
112#328—1811no—
113#328—1811no—
114#327—1811no—
115#327D18111yescharacteristic
116#126—3621no—
117#125—1811no—
118#124—1811no—
119#123—3621no—
120C22⋊Q8—1811no—
121#121C2×D18111yescharacteristic
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×Q8—1811no—
136C2×D4—21no—
137C2×D4C4×D18111yescharacteristic
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—3621no—
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—21no—
163C23D4×D18111yescharacteristic
164Q8—7241no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3621no—
174C2×C4—3621no—
175C2×C4—3621no—
176C2×C4—3621no—
177C2×C4—1811no—
178C2×C4—1811no—
179C2×C4—1811no—
180C2×C4—1811no—
181C2×C4—7241no—
182C2×C4—7242no—
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—41no—
193C22—41no—
194C22—41no—
195C22C22⋊C4×D18111yescharacteristic
196C22#1915383511yescharacteristic
197C22#1915383711yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—81no—
202C4—3621no—
203C4—3621no—
204C4—3621no—
205C4—3621no—
206C4—14481no—
207C4—7241no—
208C4—7241no—
209C2—21no—
210C2—21no—
211C2—81no—
212C2#2604125111yescharacteristic
213C2#2604127211yescharacteristic
214C2#2604129411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D181
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#327×C181C2
socleC22×C181C2×C22⋊C4
prime radical#121×C181C22
cosocleC22×C4×C181C23
hypercenter#327D181
hypocenterC181#1521
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #26041329C2semidirect
3. #26041146C2semidirect
4. #26041017C2semidirect
5. #26041015C2semidirect
9. #19153807C4semidirect
10. #19153803C4semidirect
13. #19153781C4semidirect
15. D4×Dic181C4semidirect
107. C181#1521semidirect

Maximal subgroups

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

subgroupindex
#260418102
#260413292
#260411462
#260410172
#260410152
#260410132
#327×C1812
#1521181