Finite Group Databasebeta

← #37544992

Subgroups — #37544992

Order 23168.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041909C211yesmaximal, characteristic
2#26041892C211yesmaximal, characteristic
3#26041689C211yesmaximal, characteristic, complemented
4#26041649C211yesmaximal, characteristic, complemented
5#26041630C211yesmaximal, characteristic, complemented
6#26041623C211yesmaximal, characteristic
7#26041622C211yesmaximal, characteristic
8#26041616C211yesmaximal, characteristic
9#26041611C211yesmaximal, characteristic
10#26041589C211yesmaximal, characteristic, complemented
11#26041585C211yesmaximal, characteristic, complemented
12#26041573C211yesmaximal, characteristic, complemented
13#26041563C211yesmaximal, characteristic, complemented
14#26041338C211yesmaximal, characteristic
15#499×C181C211yesmaximal, characteristic, complemented
16#19153816C2211yescharacteristic
17#19153816C2211yescharacteristic
18#19153815—21no—
19#19153815C2211yescharacteristic
20#19153811—21no—
21#19153811—21no—
22#19153807—21no—
23#19153807—21no—
24#19153807C2211yescharacteristic
25#19153806—21no—
26#19153796—21no—
27#19153796C2211yescharacteristic
28#19153796C2211yescharacteristic
29#19153794—21no—
30#19153781C2211yescharacteristic
31#19153781C2211yescharacteristic
32#19153774C2211yescharacteristic
33#19153773C2211yescharacteristic
34C4⋊C4×D181C2211yescharacteristic
35#19153749C2211yescharacteristic
36#19153749C2211yescharacteristic
37#19153747C2211yescharacteristic
38#19153747C2211yescharacteristic
39#19153745C2211yescharacteristic
40#19153745C2211yescharacteristic
41#19153741C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153727C2211yescharacteristic
52#125×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#106×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×Dic362C2311yescharacteristic
63C2×C4×D181—21no—
64C2×C4×D181C2311yescharacteristic
65C2×#13089678C2311yescharacteristic
66C2×#13089678C2311yescharacteristic
67C4⋊Dic181—21no—
68C4⋊Dic181—21no—
69C4⋊Dic181—21no—
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75#15668428—21no—
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428D411yescharacteristic
81#15668428D411yescharacteristic
82#15668426—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426D411yescharacteristic
86#15668426D411yescharacteristic
87C4×Dic181—21no—
88C4×Dic181—21no—
89C4×Dic181—21no—
90C4×Dic181C2311yescharacteristic
91C2×C8×C181C2311yescharacteristic
92C2×C8×C181C2311yescharacteristic
93C4⋊C4×C181—21no—
94C4⋊C4×C181—21no—
95C4⋊C4×C181—21no—
96C4⋊C4×C181—21no—
97C4⋊C4×C181C2311yescharacteristic
98C4⋊C4×C181C2311yescharacteristic
99C4⋊C4×C181C2311yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C42×C181C2311yescharacteristic
102C22×D181C2×D411yescharacteristic
103Dic362—21no—
104Dic362—21no—
105Dic362—21no—
106Dic362—21no—
107Dic362—81no—
108Dic362—81no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181C2×D411yescharacteristic
114C2×Dic181C2×D411yescharacteristic
115C2×Dic181C2×D411yescharacteristic
116C4×D181—21no—
117C4×D181—21no—
118C4×D181—81no—
119#13089678—21no—
120#13089678—21no—
121C2×C4×C181—21no—
122C2×C4×C181—21no—
123C2×C4×C181—21no—
124C2×C4×C181—21no—
125C2×C4×C181C2×D411yescharacteristic
126C2×C4×C181C2×D411yescharacteristic
127C2×C4×C181C2411yescharacteristic
128C8×C181—21no—
129C8×C181—21no—
130C22×C181C22×D411yescharacteristic
131C2×D181—21no—
132C2×D181—21no—
133C2×D181—21no—
134C4×C181—21no—
135C4×C181—21no—
136C4×C181—41no—
137C4×C181—41no—
138C4×C181—41no—
139C4×C181—41no—
140C4×C1812−1+411yescharacteristic
141C4×C1812−1+411yescharacteristic
142Dic181—21no—
143Dic181—21no—
144Dic181—21no—
145Dic181—41no—
146Dic181—41no—
147Dic181—41no—
148Dic181—41no—
149C2×C181#53611yescharacteristic
150C2×C181#57711yescharacteristic
151C2×C181#57811yescharacteristic
152D181—41no—
153C181#324211yescharacteristic, complemented, Sylow
154#3242—1811nomaximal, Sylow
155#544—1811no—
156#541—1811no—
157#501—1811no—
158#499D18111yescharacteristic, complemented
159#491—1811no—
160#487—1811no—
161#485—1811no—
162#485—1811no—
163#484—1811no—
164#483—1811no—
165#479—1811no—
166#479—1811no—
167#477—1811no—
168#475—1811no—
169#433—1811no—
170C4⋊Q8—3621no—
171C4⋊Q8—1811no—
172C4⋊Q8—1811no—
173C4⋊Q8—1811no—
174#126—3621no—
175#126—3621no—
176#125—3621no—
177#125—3621no—
178#125—3621no—
179#125—1811no—
180#125C2×D18111yescharacteristic
181#125C2×D18111yescharacteristic
182C22⋊Q8—3621no—
183C22⋊Q8—3621no—
184C22⋊Q8—1811no—
185C22⋊Q8—1811no—
186C4×Q8—1811no—
187C4×Q8—1811no—
188#117—1811no—
189#117—1811no—
190C2×C4⋊C4—1811no—
191#107—1811no—
192#107—1811no—
193#107C2×D18111yescharacteristic
194#107C2×D18111yescharacteristic
195#106—1811no—
196#106—1811no—
197#106C2×D18111yescharacteristic
198#106C2×D18111yescharacteristic
199C4⋊C8—1811no—
200C4⋊C8—1811no—
201#103—1811no—
202#103—1811no—
203#103—1811no—
204#103—1811no—
205#103—1811no—
206#103—1811no—
207#103—1811no—
208#103—1811no—
209C22⋊C8—1811no—
210C22⋊C8—1811no—
211#97—1811no—
212C4×C8C2×D18111yescharacteristic
213C2×Q8—3621no—
214C2×Q8—3621no—
215C2×Q8—1811no—
216C2×Q8—1811no—
217C22×C4—3621no—
218C22×C4—1811no—
219C2×C8—1811no—
220C2×C8—1811no—
221C2×C8C22×D18111yescharacteristic
222C2×C8C22×D18111yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—3621no—
228C4⋊C4—3621no—
229C4⋊C4—3621no—
230C4⋊C4—3621no—
231C4⋊C4—3621no—
232C4⋊C4—3621no—
233C4⋊C4—3621no—
234C4⋊C4—3621no—
235C4⋊C4—3621no—
236C4⋊C4—3621no—
237C4⋊C4—3621no—
238C4⋊C4—1811no—
239C4⋊C4—1811no—
240C4⋊C4—1811no—
241C4⋊C4—1811no—
242C4⋊C4C22×D18111yescharacteristic
243C4⋊C4C22×D18111yescharacteristic
244C4⋊C4C22×D18111yescharacteristic
245C4⋊C4C22×D18111yescharacteristic
246C22⋊C4—3621no—
247C22⋊C4—3621no—
248C22⋊C4—3621no—
249C22⋊C4—1811no—
250C22⋊C4—1811no—
251C42—3621no—
252C42—3621no—
253C42—3621no—
254C42—1811no—
255C42C22×D18111yescharacteristic
256C23—1811no—
257Q8—3621no—
258Q8—3621no—
259Q8—3621no—
260Q8—3621no—
261Q8—14481no—
262Q8—14481no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—3621no—
268C2×C4—3621no—
269C2×C4—3621no—
270C2×C4—3621no—
271C2×C4—3621no—
272C2×C4—3621no—
273C2×C4—14481no—
274C2×C4—1811no—
275C2×C4—1811no—
276C2×C4—1811no—
277C2×C4D4×D18111yescharacteristic
278C2×C4D4×D18111yescharacteristic
279C2×C4C23×D18111yescharacteristic
280C8—21no—
281C8—21no—
282C8—3621no—
283C8—3621no—
284C22—3621no—
285C22—3621no—
286C22—3621no—
287C22C2×D4×D18111yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—3621no—
295C4—3621no—
296C4—3621no—
297C4—7241no—
298C4—7241no—
299C4—7241no—
300C4—7241no—
301C4#1915386411yescharacteristic
302C4#1915386411yescharacteristic
303C2—7241no—
304C2#2604185411yescharacteristic
305C2#2604208611yescharacteristic
306C2#2604209311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#499×C181C2
socleC22×C181C22×D4
prime radicalC22×D181C2×D4
hypercenter#499D181
hypocenterC181#3242
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
3. #26041689C2semidirect
4. #26041649C2semidirect
5. #26041630C2semidirect
10. #26041589C2semidirect
11. #26041585C2semidirect
12. #26041573C2semidirect
13. #26041563C2semidirect
15. #499×C181C2semidirect
153. C181#3242semidirect
158. #499D181semidirect

Maximal subgroups

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

subgroupindex
#260419092
#260418922
#260416892
#260416492
#260416302
#260416232
#260416222
#260416162
#260416112
#260415892
#260415852
#260415732
#260415632
#260413382
#499×C1812
#3242181