Finite Group Databasebeta

← #37545952

Subgroups — #37545952

Order 23168.

448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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#26041999C211yesmaximal, characteristic, complemented
2#26041625C211yesmaximal, characteristic, complemented
3#26041600C212yesmaximal, complemented
4#26041559C211yesmaximal, characteristic, complemented
5#26041523C212yesmaximal, complemented
6#26041476C211yesmaximal, characteristic, complemented
7#26041430C212yesmaximal, complemented
8C4×#15668437C211yesmaximal, characteristic, complemented
9#26041357C211yesmaximal, characteristic, complemented
10#26041284C212yesmaximal, complemented
11D42×C181C211yesmaximal, characteristic
12C2×#15668437C2211yescharacteristic
13C2×#15668437C2212yescomplemented
14C2×#15668433C2212yescomplemented
15#19153816C2211yescharacteristic, complemented
16#19153809—22no—
17#19153803—21no—
18#19153795C2212yescomplemented
19C4×Dic362C2211yescharacteristic, complemented
20#19153781—21no—
21#19153775C2212yescomplemented
22#19153749C2212yescomplemented
23#19153747C2211yescharacteristic, complemented
24C4⋊#13089678C2211yescharacteristic, complemented
25#19153739C2211yescharacteristic, complemented
26#19153737C2211yescharacteristic
27#19153737C2212yes—
28#19153737C2212yescomplemented
29#19153737C2212yescomplemented
30#19153737C2212yescomplemented
31C22⋊#13089678C2212yescomplemented
32C4×#13089678C2211yescharacteristic, complemented
33C22×D4×C181—21no—
34C22×D4×C181C2212yes—
35#127×C181C2211yescharacteristic
36#121×C181—21no—
37#121×C181C2212yes—
38#120×C181—22no—
39C4×D4×C181C2211yescharacteristic
40C4×D4×C181C2211yescharacteristic
41C2×Dic362—21no—
42C2×Dic362C2311yescharacteristic
43#15668437—22no—
44#15668437—42no—
45#15668433—42no—
46C2×#13089678C2311yescharacteristic
47C2×#13089678C2311yescharacteristic
48C2×#13089678C2312yes—
49C4⋊Dic181—21no—
50C4⋊Dic181C2311yescharacteristic
51C4⋊Dic181C2312yes—
52#15668428—22no—
53#15668428—21no—
54C22⋊Dic181—22no—
55C22⋊Dic181—22no—
56C4×Dic181—22no—
57C4×Dic181—21no—
58C24×C181—22no—
59C2×D4×C181—24no—
60C2×D4×C181—22no—
61C2×D4×C181—22no—
62C2×D4×C181—21no—
63C2×D4×C181—21no—
64C2×D4×C181—42no—
65C2×D4×C181—44no—
66C2×D4×C181D411yescharacteristic
67C2×D4×C181C2312yes—
68C2×D4×C181C2311yescharacteristic
69C22×C4×C181—21no—
70C22×C4×C181C2312yes—
71C4⋊C4×C181D411yescharacteristic
72C4⋊C4×C181C2311yescharacteristic
73C22⋊C4×C181—21no—
74C22⋊C4×C181—22no—
75C22⋊C4×C181D412yes—
76C42×C181C2311yescharacteristic
77Dic362—21no—
78Dic362—21no—
79Dic362—42no—
80C2×Dic181—21no—
81C2×Dic181—21no—
82C2×Dic181—22no—
83#13089678—21no—
84#13089678—21no—
85#13089678—22no—
86C23×C181—21no—
87C23×C181—22no—
88C23×C181—44no—
89C23×C181—44no—
90C23×C181—82no—
91C23×C181C2×D412yes—
92D4×C181—22no—
93D4×C181—22no—
94D4×C181—21no—
95D4×C181—22no—
96D4×C181—44no—
97D4×C181—44no—
98D4×C181—42no—
99D4×C181—81no—
100D4×C181#4112yes—
101C2×C4×C181—22no—
102C2×C4×C181—22no—
103C2×C4×C181—21no—
104C2×C4×C181—42no—
105C2×C4×C181C2×D411yescharacteristic
106C2×C4×C181C2×D412yes—
107C2×C4×C181C2×D411yescharacteristic
108C2×C4×C181C2411yescharacteristic
109C22×C181—22no—
110C22×C181—22no—
111C22×C181—22no—
112C22×C181—22no—
113C22×C181—41no—
114C22×C181—41no—
115C22×C181—42no—
116C22×C181—42no—
117C22×C181—42no—
118C22×C181—88no—
119C22×C181C22×D411yescharacteristic
120C4×C181—22no—
121C4×C181—21no—
122C4×C181—41no—
123C4×C181AGL(1,ℤ/8)12yes—
124C4×C181C2×#4111yescharacteristic
125C4×C181H(5,𝔽2)11yescharacteristic
126Dic181—41no—
127Dic181—42no—
128Dic181—41no—
129C2×C181—42no—
130C2×C181—42no—
131C2×C181—82no—
132C2×C181#54611yescharacteristic
133C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C181#57711yescharacteristic
135C181#332411yescharacteristic, complemented, Sylow
136#3324—1811nomaximal, Sylow
137#556—1811no—
138D42D18111yescharacteristic
139#486—1811no—
140#482—1812no—
141#474—1811no—
142#468—1812no—
143#460—1811no—
144#450—1812no—
145C4×SD16—1811no—
146#436—1811no—
147#418—1812no—
148C22×D4—21no—
149C22×D4C2×D18112yes—
150C2×SD16—1811no—
151C2×SD16—1812no—
152C2×M16—1812no—
153C4⋊Q8—1811no—
154#127C2×D18111yescharacteristic
155#126—3622no—
156#124—3621no—
157C22⋊Q8—1812no—
158#121—21no—
159#121C2×D18112yes—
160#120—22no—
161C4×Q8—3621no—
162C4×Q8—1811no—
163C4×D4C2×D18111yescharacteristic
164C4×D4C2×D18111yescharacteristic
165#117—1812no—
166#107—1812no—
167#106—1811no—
168C4⋊C8—1811no—
169#103—1811no—
170#102—1811no—
171#102—1812no—
172#102—1812no—
173#102—1812no—
174#102—1812no—
175C22⋊C8—1812no—
176C4×C8—1811no—
177C24—22no—
178C2×Q8—3621no—
179C2×Q8—1811no—
180C2×D4—24no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—42no—
186C2×D4—44no—
187C2×D4C22⋊D18111yescharacteristic
188C2×D4C22×D18112yes—
189C2×D4C22×D18111yescharacteristic
190C22×C4—21no—
191C22×C4C22×D18112yes—
192SD16—3622no—
193SD16—7242no—
194M16—7242no—
195C2×C8—1811no—
196C2×C8—1811no—
197C2×C8—1812no—
198C4⋊C4—3622no—
199C4⋊C4—3621no—
200C4⋊C4—3621no—
201C4⋊C4—1811no—
202C4⋊C4—1812no—
203C4⋊C4C22⋊D18111yescharacteristic
204C4⋊C4C22×D18111yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—22no—
207C22⋊C4—3622no—
208C22⋊C4—3622no—
209C22⋊C4C22⋊D18112yes—
210C42—3622no—
211C42—3621no—
212C42C22×D18111yescharacteristic
213C23—21no—
214C23—22no—
215C23—44no—
216C23—44no—
217C23—82no—
218C23C2×C22⋊D18112yes—
219Q8—3621no—
220Q8—3621no—
221Q8—7242no—
222D4—22no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1566844812yes—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—3621no—
236C2×C4—3621no—
237C2×C4—3622no—
238C2×C4C2×C22⋊D18112yes—
239C2×C4C2×C22⋊D18111yescharacteristic
240C2×C4C2×C22⋊D18111yescharacteristic
241C2×C4C23×D18111yescharacteristic
242C8—3621no—
243C8—3621no—
244C8—3622no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—88no—
255C22C22×C22⋊D18111yescharacteristic
256C4—22no—
257C4—21no—
258C4—41no—
259C4—7241no—
260C4—7242no—
261C4—7241no—
262C4#1915384212yes—
263C4C2×#1566844811yescharacteristic
264C4#1915386111yescharacteristic
265C2—42no—
266C2—42no—
267C2—82no—
268C2#2604192311yescharacteristic
269C2C2×#1915384211yescharacteristic
270C2#2604209011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting, prime radicalD42×C181C2
socleC22×C181C22×D4
hypercenterD42D181
hypocenterC181#3324
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #26041999C2semidirect
2. #26041625C2semidirect
3. #26041600C2semidirect
4. #26041559C2semidirect
5. #26041523C2semidirect
6. #26041476C2semidirect
7. #26041430C2semidirect
8. C4×#15668437C2semidirect
9. #26041357C2semidirect
10. #26041284C2semidirect
13. C2×#15668437C22semidirect
14. C2×#15668433C22semidirect
15. #19153816C22semidirect
18. #19153795C22semidirect
19. C4×Dic362C22semidirect
21. #19153775C22semidirect
22. #19153749C22semidirect
23. #19153747C22semidirect
24. C4⋊#13089678C22semidirect
25. #19153739C22semidirect
28. #19153737C22semidirect
29. #19153737C22semidirect
30. #19153737C22semidirect
31. C22⋊#13089678C22semidirect
32. C4×#13089678C22semidirect
135. C181#3324semidirect

Maximal subgroups

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

subgroupindex
#260419992
#260416252
#260416002
#260415592
#260415232
#260414762
#260414302
C4×#156684372
#260413572
#260412842
D42×C1812
#3324181