Finite Group Databasebeta

← #37546334

Subgroups — #37546334

Order 23168.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041997C211yesmaximal, characteristic
2#26041987C211yesmaximal, characteristic
3#26041676C211yesmaximal, characteristic, complemented
4#26041618C211yesmaximal, characteristic, complemented
5#26041611C211yesmaximal, characteristic, complemented
6#26041610C211yesmaximal, characteristic, complemented
7#26041573C211yesmaximal, characteristic, complemented
8#26041562C211yesmaximal, characteristic, complemented
9#26041536C211yesmaximal, characteristic, complemented
10#26041535C211yesmaximal, characteristic, complemented
11#26041371C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic
13#26041322C211yesmaximal, characteristic, complemented
14#26041320C211yesmaximal, characteristic, complemented
15#485×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668433C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19#19153815C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153810—21no—
22#19153809—21no—
23#19153806—21no—
24#19153802—21no—
25#19153796—21no—
26#19153796C2211yescharacteristic
27#19153795C2211yescharacteristic
28#19153793—21no—
29#19153792C2211yescharacteristic
30Q8×Dic181C2211yescharacteristic
31C4×Dic362—21no—
32#19153781C2211yescharacteristic
33C4×C22⋊D181C2211yescharacteristic
34#19153776—21no—
35#19153774C2211yescharacteristic
36C2×C4⋊Dic181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153740C2211yescharacteristic
49#19153739C2211yescharacteristic
50#19153728C2211yescharacteristic
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
62C2×C22⋊D181D411yescharacteristic
63C22×Dic181—21no—
64C2×C4×D181—21no—
65C2×C4×D181C2311yescharacteristic
66#15668439—22no—
67#15668433—22no—
68#15668432—22no—
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84C22⋊Dic181—21no—
85C22⋊Dic181D411yescharacteristic
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426D411yescharacteristic
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C2×Q8×C181C2311yescharacteristic
95C22×C4×C181C2311yescharacteristic
96C2×C8×C181C2311yescharacteristic
97C2×C8×C181C2311yescharacteristic
98C4⋊C4×C181—21no—
99C4⋊C4×C181C2311yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C22⋊C4×C181—21no—
103C22⋊C4×C181—21no—
104C42×C181—21no—
105C22×D181C2×D411yescharacteristic
106Dic362—21no—
107Dic362—21no—
108Dic362—42no—
109Dic362—81no—
110C22⋊D181—22no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—81no—
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C2×Dic181C2×D411yescharacteristic
119C4×D181—21no—
120C4×D181—21no—
121C4×D181—81no—
122#13089678—21no—
123#13089678#4112yes—
124C23×C181C2×D411yescharacteristic
125Q8×C181—21no—
126Q8×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2411yescharacteristic
135C8×C181—21no—
136C8×C181—21no—
137C22×C181—21no—
138C22×C181—21no—
139C22×C181—21no—
140C22×C181C22×D411yescharacteristic
141C2×D181—21no—
142C2×D181—21no—
143C2×D181—21no—
144C4×C181—21no—
145C4×C181—41no—
146C4×C181—41no—
147C4×C181—41no—
148C4×C181—41no—
149C4×C181C2×#4111yescharacteristic
150C4×C1812−1+411yescharacteristic
151Dic181—21no—
152Dic181—21no—
153Dic181—41no—
154Dic181—41no—
155Dic181—41no—
156Dic181—41no—
157Dic181#13712yes—
158C2×C181—41no—
159C2×C181#54711yescharacteristic
160C2×C181C2×#13711yescharacteristic
161C2×C181#57711yescharacteristic
162D181—41no—
163C181#335611yescharacteristic, complemented, Sylow
164#3356—1811nomaximal, Sylow
165#556—1811no—
166#554—1811no—
167#498—1811no—
168#485—1811no—
169#485D18111yescharacteristic, complemented
170#483—1811no—
171#483—1811no—
172#477—1811no—
173#475—1811no—
174#470—1811no—
175#470—1811no—
176C4×Q16—1811no—
177#436—1811no—
178#428—1811no—
179#428—1811no—
180C2×Q16—1811no—
181C2×M16—1811no—
182C2×M16—1811no—
183C4⋊Q8—1811no—
184C4⋊Q8—1811no—
185#126—3621no—
186#126—3621no—
187#125—3621no—
188#124—3621no—
189C22⋊Q8—3621no—
190C22⋊Q8—3621no—
191C22⋊Q8—1811no—
192C22⋊Q8—1811no—
193C22⋊Q8—1811no—
194C22⋊Q8C2×D18111yescharacteristic
195C4×Q8—3621no—
196C4×Q8—1811no—
197C4×Q8—1811no—
198C4×D4—3621no—
199C4×D4—1811no—
200#117—1811no—
201#117C2×D18111yescharacteristic
202C2×C4⋊C4—1811no—
203C2×C4⋊C4—1811no—
204#107—1811no—
205#107—1811no—
206#107C2×D18111yescharacteristic
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106—1811no—
211#106—1811no—
212#106C2×D18111yescharacteristic
213C4⋊C8—1811no—
214#103—1811no—
215#103—1811no—
216#103—1811no—
217#103—1811no—
218#103C2×D18111yescharacteristic
219#103C2×D18111yescharacteristic
220C22⋊C8—1811no—
221C22⋊C8C2×D18111yescharacteristic
222C4×C8—1811no—
223C2×Q8—3621no—
224C2×Q8—3621no—
225C2×Q8—1811no—
226C2×Q8C22×D18111yescharacteristic
227C2×D4—1811no—
228C22×C4—3621no—
229C22×C4—3621no—
230C22×C4—1811no—
231C22×C4C22×D18111yescharacteristic
232Q16—3622no—
233M16—3622no—
234M16—3622no—
235C2×C8—1811no—
236C2×C8—1811no—
237C2×C8C22×D18111yescharacteristic
238C2×C8C22×D18111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—3621no—
241C4⋊C4—3621no—
242C4⋊C4—3621no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—1811no—
250C4⋊C4—1811no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4C22×D18111yescharacteristic
254C4⋊C4C22×D18111yescharacteristic
255C4⋊C4C22×D18111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—1811no—
263C22⋊C4—1811no—
264C42—21no—
265C42—3621no—
266C42—3621no—
267C42—3621no—
268C42—1811no—
269C23—1811no—
270C23D4×D18111yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—3621no—
274Q8—3621no—
275Q8—14481no—
276Q8—7242no—
277D4—3622no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—3621no—
290C2×C4—14481no—
291C2×C4—14481no—
292C2×C4—1811no—
293C2×C4—1811no—
294C2×C4—1811no—
295C2×C4D4×D18111yescharacteristic
296C2×C4C23×D18111yescharacteristic
297C8—21no—
298C8—21no—
299C8—3621no—
300C8—1812no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—3621no—
305C22—3621no—
306C22—3621no—
307C22C2×D4×D18111yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—3621no—
314C4—3621no—
315C4—1812no—
316C4—7241no—
317C4—7241no—
318C4—7241no—
319C4—7241no—
320C4#41×D18111yescharacteristic
321C4#1915386311yescharacteristic
322C2—41no—
323C2—7241no—
324C2#2604192711yescharacteristic
325C2#137×D18111yescharacteristic
326C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#485×C181C2
socleC22×C181C22×D4
prime radicalC2×C22⋊D181D4
hypercenter#485D181
hypocenterC181#3356
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. #26041676C2semidirect
4. #26041618C2semidirect
5. #26041611C2semidirect
6. #26041610C2semidirect
7. #26041573C2semidirect
8. #26041562C2semidirect
9. #26041536C2semidirect
10. #26041535C2semidirect
11. #26041371C2semidirect
13. #26041322C2semidirect
14. #26041320C2semidirect
15. #485×C181C2semidirect
163. C181#3356semidirect
169. #485D181semidirect

Maximal subgroups

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

subgroupindex
#260419972
#260419872
#260416762
#260416182
#260416112
#260416102
#260415732
#260415622
#260415362
#260415352
#260413712
#260413542
#260413222
#260413202
#485×C1812
#3356181