Finite Group Databasebeta

← #37544963

Subgroups — #37544963

Order 23168.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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#26041836C211yesmaximal, characteristic, complemented
2#26041813C211yesmaximal, characteristic
3#26041688C211yesmaximal, characteristic, complemented
4#26041688C211yesmaximal, characteristic, complemented
5#26041639C211yesmaximal, characteristic, complemented
6#26041639C211yesmaximal, characteristic, complemented
7#26041621C212yesmaximal, complemented
8#26041604C212yesmaximal
9#26041587C212yesmaximal, complemented
10#26041580C212yesmaximal, complemented
11#432×C181C211yesmaximal, characteristic, complemented
12#19153816C2211yescharacteristic
13#19153816C2211yescharacteristic
14#19153810—21no—
15#19153808C2211yescharacteristic
16#19153808C2212yes—
17#19153804C2211yescharacteristic
18#19153799—21no—
19#19153795—21no—
20#19153795—21no—
21#19153795C2211yescharacteristic
22#19153790C2211yescharacteristic
23C4×Dic362—21no—
24C4×Dic362—21no—
25C4×Dic362C2211yescharacteristic
26C4×D724C2211yescharacteristic
27C4×C22⋊D181—21no—
28#19153775C2212yes—
29#19153773—21no—
30#19153750C2212yes—
31#19153750C2212yes—
32#19153748C2212yes—
33#19153748C2212yes—
34#19153741C2212yes—
35#19153741C2212yes—
36#19153738C2212yes—
37#19153738C2212yes—
38C2×C42×C181C2211yescharacteristic
39C4⋊C8×C181C2212yes—
40C22⋊C8×C181C2212yes—
41#97×C181C2211yescharacteristic
42#97×C181C2211yescharacteristic
43C2×Dic362—21no—
44C2×Dic362—21no—
45C2×Dic362C2311yescharacteristic
46C2×D724C2311yescharacteristic
47C2×C22⋊D181—21no—
48C2×C4×D181—21no—
49C4⋊Dic181—21no—
50C4⋊Dic181—21no—
51C4⋊Dic181C2312yes—
52C4⋊Dic181C2312yes—
53C4⋊Dic181C2311yescharacteristic
54C4⋊Dic181C2311yescharacteristic
55#15668428—21no—
56#15668428—21no—
57#15668428—21no—
58#15668428—22no—
59#15668428—22no—
60#15668428—21no—
61C22⋊Dic181—22no—
62C22⋊Dic181—21no—
63#15668426—21no—
64#15668426—21no—
65#15668426—21no—
66#15668426—21no—
67C4×Dic181—21no—
68C4×Dic181—22no—
69C22×C4×C181D411yescharacteristic
70C22×C4×C181D411yescharacteristic
71C22×C4×C181C2311yescharacteristic
72C2×C8×C181C2312yes—
73C2×C8×C181C2312yes—
74C42×C181D411yescharacteristic
75C42×C181D411yescharacteristic
76C42×C181C2311yescharacteristic
77C42×C181C2311yescharacteristic
78C22×D181—21no—
79Dic362—22no—
80Dic362—42no—
81Dic362—42no—
82D724—22no—
83C22⋊D181—42no—
84C2×Dic181—21no—
85C2×Dic181—21no—
86C2×Dic181—22no—
87C2×Dic181—22no—
88C2×Dic181—21no—
89C4×D181—42no—
90C23×C181C2×D411yescharacteristic
91C2×C4×C181—22no—
92C2×C4×C181—41no—
93C2×C4×C181—41no—
94C2×C4×C181C2×D411yescharacteristic
95C2×C4×C181C2×D411yescharacteristic
96C2×C4×C181C2×D411yescharacteristic
97C2×C4×C181C2×D411yescharacteristic
98C2×C4×C181C2×D411yescharacteristic
99C2×C4×C181C2411yescharacteristic
100C8×C181—22no—
101C8×C181—22no—
102C22×C181—21no—
103C22×C181—21no—
104C22×C181—21no—
105C22×C181C22×D411yescharacteristic
106C2×D181—41no—
107C2×D181—41no—
108C2×D181—41no—
109C4×C181—21no—
110C4×C181—21no—
111C4×C181—21no—
112C4×C181—21no—
113C4×C181—21no—
114C4×C1812−1+412yes—
115Dic181—41no—
116Dic181—41no—
117Dic181—41no—
118Dic181—42no—
119Dic181—42no—
120C2×C181—41no—
121C2×C181#53611yescharacteristic
122C2×C181#57511yescharacteristic
123C2×C181#57511yescharacteristic
124D181—81no—
125C181#324011yescharacteristic, complemented, Sylow
126#3240—1811nomaximal, Sylow
127#533—1811no—
128#529—1811no—
129#501—1811no—
130#501—1811no—
131#489—1811no—
132#489—1811no—
133#485—1812no—
134#482—1812no—
135#479—1812no—
136#478—1812no—
137#432D18111yescharacteristic, complemented
138C4⋊Q8—1811no—
139C4⋊Q8—1811no—
140#126—3621no—
141#125—1811no—
142#125—1812no—
143#124—1811no—
144#123—3621no—
145C22⋊Q8—3621no—
146C22⋊Q8—3621no—
147C22⋊Q8—1811no—
148#121—1811no—
149C4×Q8—3621no—
150C4×Q8—3621no—
151C4×Q8—1811no—
152C4×D4—3621no—
153C4×D4—1811no—
154#117—3621no—
155#117—1812no—
156C2×C42C2×D18111yescharacteristic
157#107—1812no—
158#107—1812no—
159#106—1812no—
160#106—1812no—
161C4⋊C8C2×D18112yes—
162#103—1812no—
163#103—1812no—
164#102—1812no—
165#102—1812no—
166C22⋊C8C2×D18112yes—
167#97C2×D18111yescharacteristic
168#97C2×D18111yescharacteristic
169C2×Q8—3621no—
170C2×Q8—3621no—
171C2×Q8—1811no—
172C2×D4—3621no—
173C2×D4—1811no—
174C22×C4—3621no—
175C22×C4D72411yescharacteristic
176C22×C4D72411yescharacteristic
177C22×C4C22×D18111yescharacteristic
178C2×C8C22×D18112yes—
179C2×C8C22×D18112yes—
180C4⋊C4—3621no—
181C4⋊C4—3621no—
182C4⋊C4—3621no—
183C4⋊C4—3622no—
184C4⋊C4—3622no—
185C4⋊C4—3621no—
186C4⋊C4—3621no—
187C4⋊C4—3621no—
188C4⋊C4—1812no—
189C4⋊C4—1812no—
190C4⋊C4—1811no—
191C4⋊C4—1811no—
192C22⋊C4—3622no—
193C22⋊C4—3621no—
194C22⋊C4—3621no—
195C22⋊C4—3621no—
196C22⋊C4—3621no—
197C22⋊C4—3621no—
198C42—3621no—
199C42—3622no—
200C42D72411yescharacteristic
201C42D72411yescharacteristic
202C42C22×D18111yescharacteristic
203C42C22×D18111yescharacteristic
204C23—3621no—
205C23C2×D72411yescharacteristic
206Q8—3622no—
207Q8—7242no—
208Q8—7242no—
209D4—3622no—
210D4—7242no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—3621no—
215C2×C4—3621no—
216C2×C4—3622no—
217C2×C4—3622no—
218C2×C4—3621no—
219C2×C4—7242no—
220C2×C4C2×D72411yescharacteristic
221C2×C4C2×D72411yescharacteristic
222C2×C4C2×D72411yescharacteristic
223C2×C4C2×D72411yescharacteristic
224C2×C4C2×D72411yescharacteristic
225C2×C4C23×D18111yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—7241no—
232C22—7241no—
233C22—7241no—
234C22C22×D72411yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—7241no—
241C4—7241no—
242C4—7242no—
243C4—7242no—
244C4—7241no—
245C4#1915386312yes—
246C2—41no—
247C2—14481no—
248C2#2604185511yescharacteristic
249C2#2604207911yescharacteristic
250C2#2604207911yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#432×C181C2
socleC22×C181C22×D4
prime radical#19153790C22
hypercenter#432D181
hypocenterC181#3240
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #26041836C2semidirect
3. #26041688C2semidirect
4. #26041688C2semidirect
5. #26041639C2semidirect
6. #26041639C2semidirect
7. #26041621C2semidirect
9. #26041587C2semidirect
10. #26041580C2semidirect
11. #432×C181C2semidirect
125. C181#3240semidirect
137. #432D181semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260418132
#260416882
#260416392
#260416212
#260416042
#260415872
#260415802
#432×C1812
#3240181