Finite Group Databasebeta

← #37544995

Subgroups — #37544995

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#26041907C211yesmaximal, characteristic
2#26041889C211yesmaximal, characteristic
3#26041687C211yesmaximal, characteristic, complemented
4#26041679C211yesmaximal, characteristic, complemented
5#26041646C211yesmaximal, characteristic, complemented
6#26041628C211yesmaximal, characteristic, complemented
7#26041620C211yesmaximal, characteristic
8#26041612C211yesmaximal, characteristic
9#26041610C211yesmaximal, characteristic
10#26041589C211yesmaximal, characteristic, complemented
11#26041584C211yesmaximal, characteristic, complemented
12#26041573C211yesmaximal, characteristic, complemented
13#26041562C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic
15#485×C181C211yesmaximal, characteristic
16#19153816—21no—
17#19153815C2211yescharacteristic
18#19153815C2211yescharacteristic
19#19153814C2211yescharacteristic
20#19153809—21no—
21#19153809—21no—
22#19153808—21no—
23#19153807—21no—
24#19153807C2211yescharacteristic
25#19153807C2211yescharacteristic
26#19153807C2211yescharacteristic
27#19153806—21no—
28#19153795C2211yescharacteristic
29#19153793—21no—
30#19153793—21no—
31Q8×Dic181C2211yescharacteristic
32#19153781C2211yescharacteristic
33#19153775C2211yescharacteristic
34C2×C4⋊Dic181C2211yescharacteristic
35#19153749C2211yescharacteristic
36#19153749C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153748C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C22⋊Q8×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C22×Dic181—21no—
63C2×#13089678C2311yescharacteristic
64C2×#13089678C2311yescharacteristic
65C4⋊Dic181—21no—
66C4⋊Dic181—21no—
67C4⋊Dic181—21no—
68C4⋊Dic181—21no—
69C4⋊Dic181—21no—
70C4⋊Dic181D411yescharacteristic
71C4⋊Dic181D411yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75#15668428—21no—
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181D411yescharacteristic
86C22⋊Dic181D411yescharacteristic
87C4×Dic181—21no—
88C4×Dic181—21no—
89C4×Dic181C2311yescharacteristic
90C4×Dic181C2311yescharacteristic
91C2×Q8×C181C2311yescharacteristic
92C22×C4×C181C2311yescharacteristic
93C2×C8×C181C2311yescharacteristic
94C2×C8×C181C2311yescharacteristic
95C4⋊C4×C181—21no—
96C4⋊C4×C181C2311yescharacteristic
97C4⋊C4×C181C2311yescharacteristic
98C4⋊C4×C181C2311yescharacteristic
99C22⋊C4×C181—21no—
100C22⋊C4×C181—21no—
101C42×C181—21no—
102Dic362—21no—
103Dic362—21no—
104Dic362—81no—
105Dic362—81no—
106C2×Dic181—21no—
107C2×Dic181—21no—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181—81no—
111C2×Dic181C2×D411yescharacteristic
112C2×Dic181C2×D411yescharacteristic
113C2×Dic181C2×D411yescharacteristic
114C2×Dic181C2×D411yescharacteristic
115#13089678—21no—
116#13089678—21no—
117C23×C181C2×D411yescharacteristic
118Q8×C181—21no—
119Q8×C181—21no—
120C2×C4×C181—21no—
121C2×C4×C181—21no—
122C2×C4×C181—21no—
123C2×C4×C181—21no—
124C2×C4×C181—21no—
125C2×C4×C181—21no—
126C2×C4×C181C2×D411yescharacteristic
127C2×C4×C181C2411yescharacteristic
128C8×C181—21no—
129C8×C181—21no—
130C22×C181—21no—
131C22×C181—21no—
132C22×C181—21no—
133C22×C181C22×D411yescharacteristic
134C4×C181—21no—
135C4×C181—41no—
136C4×C181—41no—
137C4×C181—41no—
138C4×C181—41no—
139C4×C1812−1+411yescharacteristic
140C4×C1812−1+411yescharacteristic
141Dic181—21no—
142Dic181—21no—
143Dic181—21no—
144Dic181—21no—
145Dic181—41no—
146Dic181—41no—
147Dic181—41no—
148Dic181—41no—
149C2×C181—41no—
150C2×C181#53611yescharacteristic
151C2×C181#57711yescharacteristic
152C2×C181#57811yescharacteristic
153C181#324211yescharacteristic, complemented, Sylow
154#3242—1811nomaximal, Sylow
155#544—1811no—
156#541—1811no—
157#501—1811no—
158#499—1811no—
159#491—1811no—
160#487—1811no—
161#485—1811no—
162#485D18111yescharacteristic
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#125—1811no—
181#125—1811no—
182C22⋊Q8—3621no—
183C22⋊Q8—3621no—
184C22⋊Q8—1811no—
185C22⋊Q8C2×D18111yescharacteristic
186C4×Q8—1811no—
187C4×Q8—1811no—
188#117—1811no—
189#117C2×D18111yescharacteristic
190C2×C4⋊C4—1811no—
191#107—1811no—
192#107—1811no—
193#107—1811no—
194#107C2×D18111yescharacteristic
195#106—1811no—
196#106—1811no—
197#106—1811no—
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#103C2×D18111yescharacteristic
208#103C2×D18111yescharacteristic
209C22⋊C8—1811no—
210C22⋊C8C2×D18111yescharacteristic
211#97—1811no—
212C4×C8—1811no—
213C2×Q8—3621no—
214C2×Q8—3621no—
215C2×Q8—1811no—
216C2×Q8C22×D18111yescharacteristic
217C22×C4—3621no—
218C22×C4C22×D18111yescharacteristic
219C2×C8—1811no—
220C2×C8—1811no—
221C2×C8C22×D18111yescharacteristic
222C2×C8C22×D18111yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—3621no—
225C4⋊C4—3621no—
226C4⋊C4—3621no—
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⋊C4—1811no—
243C4⋊C4C22×D18111yescharacteristic
244C4⋊C4C22×D18111yescharacteristic
245C4⋊C4C22×D18111yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—3621no—
249C22⋊C4—1811no—
250C22⋊C4—1811no—
251C42—21no—
252C42—3621no—
253C42—3621no—
254C42—1811no—
255C42—1811no—
256C23D4×D18111yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—3621no—
260Q8—3621no—
261Q8—14481no—
262Q8—14481no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
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×C4—1811no—
278C2×C4D4×D18111yescharacteristic
279C2×C4C23×D18111yescharacteristic
280C8—21no—
281C8—21no—
282C8—3621no—
283C8—3621no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C2×D4×D18111yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—3621no—
294C4—3621no—
295C4—3621no—
296C4—3621no—
297C4—7241no—
298C4—7241no—
299C4—7241no—
300C4—7241no—
301C4#1915386311yescharacteristic
302C4#1915386311yescharacteristic
303C2—41no—
304C2#2604185111yescharacteristic
305C2#2604208611yescharacteristic
306C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#485×C181C2
socleC22×C181C22×D4
prime radicalC23×C181C2×D4
hypercenter#485D181
hypocenterC181#3242
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #26041687C2semidirect
4. #26041679C2semidirect
5. #26041646C2semidirect
6. #26041628C2semidirect
10. #26041589C2semidirect
11. #26041584C2semidirect
12. #26041573C2semidirect
13. #26041562C2semidirect
153. C181#3242semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260418892
#260416872
#260416792
#260416462
#260416282
#260416202
#260416122
#260416102
#260415892
#260415842
#260415732
#260415622
#260413372
#485×C1812
#3242181