Finite Group Databasebeta

← #28403187

Subgroups — #28403187

Order 14464.

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#20299316C211yesmaximal, characteristic
2#20299306C211yesmaximal, characteristic
3#20298995C211yesmaximal, characteristic, complemented
4#20298937C211yesmaximal, characteristic, complemented
5#20298930C211yesmaximal, characteristic, complemented
6#20298929C211yesmaximal, characteristic, complemented
7#20298892C211yesmaximal, characteristic, complemented
8#20298881C211yesmaximal, characteristic, complemented
9#20298855C211yesmaximal, characteristic, complemented
10#20298854C211yesmaximal, characteristic, complemented
11#20298690C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic
13#20298641C211yesmaximal, characteristic, complemented
14#20298639C211yesmaximal, characteristic, complemented
15#485×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268631C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813616—21no—
22#16813615—21no—
23#16813612—21no—
24#16813608—21no—
25#16813602—21no—
26#16813602C2211yescharacteristic
27#16813601C2211yescharacteristic
28#16813599—21no—
29#16813598C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31C4×Dic226—21no—
32#16813587C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813582—21no—
35#16813580C2211yescharacteristic
36C2×C4⋊Dic113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×C22⋊D113D411yescharacteristic
63C22×Dic113—21no—
64C2×C4×D113—21no—
65C2×C4×D113C2311yescharacteristic
66#14268637—22no—
67#14268631—22no—
68#14268630—22no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113D411yescharacteristic
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113C2311yescharacteristic
94C2×Q8×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C22⋊C4×C113—21no—
103C22⋊C4×C113—21no—
104C42×C113—21no—
105C23×C113C2×D411yescharacteristic
106C22×D113C2×D411yescharacteristic
107Q8×C113—21no—
108Q8×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2411yescharacteristic
117C22⋊D113—22no—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—81no—
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C4×D113—21no—
127C4×D113—21no—
128C4×D113—81no—
129Dic226—21no—
130Dic226—21no—
131Dic226—42no—
132Dic226—81no—
133C8×C113—21no—
134C8×C113—21no—
135#11744751—21no—
136#11744751#4112yes—
137C22×C113—21no—
138C22×C113—21no—
139C22×C113—21no—
140C22×C113C22×D411yescharacteristic
141C2×D113—21no—
142C2×D113—21no—
143C2×D113—21no—
144C4×C113—21no—
145C4×C113—41no—
146C4×C113—41no—
147C4×C113—41no—
148C4×C113—41no—
149C4×C113C2×#4111yescharacteristic
150C4×C1132−1+411yescharacteristic
151Dic113—21no—
152Dic113—21no—
153Dic113—41no—
154Dic113—41no—
155Dic113—41no—
156Dic113—41no—
157Dic113#13712yes—
158C2×C113—41no—
159C2×C113#54711yescharacteristic
160C2×C113C2×#13711yescharacteristic
161C2×C113#57711yescharacteristic
162D113—41no—
163#3356—1131nomaximal, Sylow
164C113#335611yescharacteristic, complemented, Sylow
165#556—1131no—
166#554—1131no—
167#498—1131no—
168#485—1131no—
169#485D11311yescharacteristic, complemented
170#483—1131no—
171#483—1131no—
172#477—1131no—
173#475—1131no—
174#470—1131no—
175#470—1131no—
176C4×Q16—1131no—
177#436—1131no—
178#428—1131no—
179#428—1131no—
180C2×Q16—1131no—
181C2×M16—1131no—
182C2×M16—1131no—
183C4⋊Q8—1131no—
184C4⋊Q8—1131no—
185#126—2261no—
186#126—2261no—
187#125—2261no—
188#124—2261no—
189C22⋊Q8—1131no—
190C22⋊Q8—1131no—
191C22⋊Q8—1131no—
192C22⋊Q8—2261no—
193C22⋊Q8—2261no—
194C22⋊Q8C2×D11311yescharacteristic
195C4×Q8—1131no—
196C4×Q8—1131no—
197C4×Q8—2261no—
198C4×D4—1131no—
199C4×D4—2261no—
200#117—1131no—
201#117C2×D11311yescharacteristic
202C2×C4⋊C4—1131no—
203C2×C4⋊C4—1131no—
204#107—1131no—
205#107—1131no—
206#107C2×D11311yescharacteristic
207#106—1131no—
208#106—1131no—
209#106—1131no—
210#106—1131no—
211#106—1131no—
212#106C2×D11311yescharacteristic
213C4⋊C8—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218#103C2×D11311yescharacteristic
219#103C2×D11311yescharacteristic
220C22⋊C8—1131no—
221C22⋊C8C2×D11311yescharacteristic
222C4×C8—1131no—
223C2×Q8—1131no—
224C2×Q8—2261no—
225C2×Q8—2261no—
226C2×Q8C22×D11311yescharacteristic
227C2×D4—1131no—
228C22×C4—1131no—
229C22×C4—2261no—
230C22×C4—2261no—
231C22×C4C22×D11311yescharacteristic
232Q16—2262no—
233M16—2262no—
234M16—2262no—
235C2×C8—1131no—
236C2×C8—1131no—
237C2×C8C22×D11311yescharacteristic
238C2×C8C22×D11311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—1131no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—1131no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4C22×D11311yescharacteristic
254C4⋊C4C22×D11311yescharacteristic
255C4⋊C4C22×D11311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—1131no—
259C22⋊C4—1131no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C42—21no—
265C42—1131no—
266C42—2261no—
267C42—2261no—
268C42—2261no—
269C23—1131no—
270C23D4×D11311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—9041no—
274Q8—4522no—
275Q8—2261no—
276Q8—2261no—
277D4—2262no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—1131no—
285C2×C4—1131no—
286C2×C4—1131no—
287C2×C4—9041no—
288C2×C4—9041no—
289C2×C4—2261no—
290C2×C4—2261no—
291C2×C4—2261no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4D4×D11311yescharacteristic
296C2×C4C23×D11311yescharacteristic
297C8—21no—
298C8—21no—
299C8—1132no—
300C8—2261no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—2261no—
305C22—2261no—
306C22—2261no—
307C22C2×D4×D11311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—1132no—
314C4—4521no—
315C4—4521no—
316C4—4521no—
317C4—4521no—
318C4—2261no—
319C4—2261no—
320C4#41×D11311yescharacteristic
321C4#1681366911yescharacteristic
322C2—41no—
323C2—4521no—
324C2#2029924611yescharacteristic
325C2#137×D11311yescharacteristic
326C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#485×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#485D113
hypocenterC113#3356
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #20298995C2semidirect
4. #20298937C2semidirect
5. #20298930C2semidirect
6. #20298929C2semidirect
7. #20298892C2semidirect
8. #20298881C2semidirect
9. #20298855C2semidirect
10. #20298854C2semidirect
11. #20298690C2semidirect
13. #20298641C2semidirect
14. #20298639C2semidirect
15. #485×C113C2semidirect
164. C113#3356semidirect
169. #485D113semidirect

Maximal subgroups

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

subgroupindex
#202993162
#202993062
#202989952
#202989372
#202989302
#202989292
#202988922
#202988812
#202988552
#202988542
#202986902
#202986732
#202986412
#202986392
#485×C1132
#3356113