Finite Group Databasebeta

← #28403111

Subgroups — #28403111

Order 14464.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299321C211yesmaximal, characteristic
2#20299286C211yesmaximal, characteristic
3#20299008C211yesmaximal, characteristic, complemented
4#20298942C211yesmaximal, characteristic, complemented
5#20298941C211yesmaximal, characteristic, complemented
6#20298938C211yesmaximal, characteristic, complemented
7#20298932C211yesmaximal, characteristic, complemented
8#20298894C211yesmaximal, characteristic, complemented
9#20298855C211yesmaximal, characteristic, complemented
10#20298838C211yesmaximal, characteristic, complemented
11#20298703C211yesmaximal, characteristic, complemented
12#20298668C211yesmaximal, characteristic
13#20298637C211yesmaximal, characteristic, complemented
14#20298635C211yesmaximal, characteristic, complemented
15#479×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18C2×C8×D113C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813617—21no—
21#16813617—21no—
22#16813617—21no—
23#16813613—21no—
24#16813610—21no—
25#16813607—21no—
26#16813602C2211yescharacteristic
27#16813602C2211yescharacteristic
28#16813598C2211yescharacteristic
29#16813598C2211yescharacteristic
30C4×Dic226—21no—
31C4×Dic226C2211yescharacteristic
32C4×D452C2211yescharacteristic
33#16813580—21no—
34#16813580C2211yescharacteristic
35#16813580C2211yescharacteristic
36#16813580C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452D411yescharacteristic
62C2×C4×D113—21no—
63C2×C4×D113C2311yescharacteristic
64C2×C4×D113C2311yescharacteristic
65#14268637—22no—
66#14268630—22no—
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C8×D113—22no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113D411yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624D411yescharacteristic
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C2×Q8×C113C2311yescharacteristic
95C2×C8×C113C2311yescharacteristic
96C2×C8×C113C2311yescharacteristic
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C22×D113C2×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×C113C2×D411yescharacteristic
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2411yescharacteristic
116C2×Dic113—21no—
117C2×Dic113—21no—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113C2×D411yescharacteristic
121C2×Dic113C2×D411yescharacteristic
122D452—41no—
123C4×D113—21no—
124C4×D113—21no—
125C4×D113—21no—
126C4×D113—21no—
127C4×D113—42no—
128Dic226—21no—
129Dic226—21no—
130Dic226—42no—
131C8×C113—21no—
132C8×C113—21no—
133#11744751—21no—
134#11744751#4112yes—
135C22×C113C22×D411yescharacteristic
136C2×D113—21no—
137C2×D113—21no—
138C2×D113—21no—
139C2×D113—21no—
140C2×D113—21no—
141C2×D113—21no—
142C4×C113—21no—
143C4×C113—21no—
144C4×C113—41no—
145C4×C113—41no—
146C4×C113—41no—
147C4×C113—41no—
148C4×C113C2×#4111yescharacteristic
149C4×C1132−1+411yescharacteristic
150Dic113—21no—
151Dic113—21no—
152Dic113—41no—
153Dic113—41no—
154Dic113—41no—
155Dic113—41no—
156C2×C113#54711yescharacteristic
157C2×C113#57511yescharacteristic
158C2×C113#57811yescharacteristic
159D113—41no—
160D113—41no—
161#3349—1131nomaximal, Sylow
162C113#334911yescharacteristic, complemented, Sylow
163#556—1131no—
164#552—1131no—
165#501—1131no—
166#485—1131no—
167#485—1131no—
168#485—1131no—
169#484—1131no—
170#479D11311yescharacteristic, complemented
171#477—1131no—
172#470—1131no—
173#467—1131no—
174#441—1131no—
175#435—1131no—
176#428—1131no—
177#427—1131no—
178C2×Q16—1131no—
179C2×M16—1131no—
180C22×C8—1131no—
181C4⋊Q8—1131no—
182#126—2261no—
183#126—2261no—
184#126—2261no—
185#125—2261no—
186#125C2×D11311yescharacteristic
187#124—2261no—
188#123—2261no—
189C22⋊Q8—1131no—
190C22⋊Q8—1131no—
191C22⋊Q8—1131no—
192C22⋊Q8—1131no—
193C4×Q8—1131no—
194C4×Q8—2261no—
195C4×Q8C2×D11311yescharacteristic
196C4×D4—1131no—
197#117—1131no—
198#117—1131no—
199#117—1131no—
200#117—2261no—
201C2×C4⋊C4—1131no—
202#107—1131no—
203#107—1131no—
204#107—1131no—
205#107—1131no—
206#107C2×D11311yescharacteristic
207#106—1131no—
208#106—1131no—
209#106—1131no—
210#106C2×D11311yescharacteristic
211C4⋊C8C2×D11311yescharacteristic
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103—1131no—
216#103C2×D11311yescharacteristic
217#103C2×D11311yescharacteristic
218C22⋊C8—1131no—
219C22⋊C8—1131no—
220#97—1131no—
221C2×Q8—1131no—
222C2×Q8—2261no—
223C2×Q8C22×D11311yescharacteristic
224C2×D4—1131no—
225C22×C4—1131no—
226C22×C4—1131no—
227C22×C4—2261no—
228Q16—2262no—
229M16—2262no—
230C2×C8—1131no—
231C2×C8—1131no—
232C2×C8—2262no—
233C2×C8C22×D11311yescharacteristic
234C2×C8C22×D11311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—1131no—
239C4⋊C4—1131no—
240C4⋊C4—1131no—
241C4⋊C4—1131no—
242C4⋊C4—2261no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4C22×D11311yescharacteristic
250C4⋊C4C22×D11311yescharacteristic
251C4⋊C4C22×D11311yescharacteristic
252C22⋊C4—1131no—
253C22⋊C4—1131no—
254C22⋊C4—2261no—
255C22⋊C4—2261no—
256C22⋊C4—2261no—
257C22⋊C4—2261no—
258C22⋊C4—2261no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C42—21no—
262C42—2261no—
263C42—2261no—
264C42—2261no—
265C42—2261no—
266C42C22×D11311yescharacteristic
267C23—1131no—
268C23—1131no—
269Q8—21no—
270Q8—21no—
271Q8—4522no—
272Q8—2261no—
273Q8—2261no—
274D4—4521no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—1131no—
280C2×C4—1131no—
281C2×C4—4522no—
282C2×C4—2261no—
283C2×C4—2261no—
284C2×C4—2261no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4—2261no—
288C2×C4—2261no—
289C2×C4—2261no—
290C2×C4D4×D11311yescharacteristic
291C2×C4D4×D11311yescharacteristic
292C2×C4C23×D11311yescharacteristic
293C8—21no—
294C8—21no—
295C8—1132no—
296C8—2261no—
297C22—2261no—
298C22—2261no—
299C22—2261no—
300C22—2261no—
301C22—2261no—
302C22—2261no—
303C22C2×D4×D11311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—4521no—
311C4—4521no—
312C4—4521no—
313C4—4521no—
314C4—2261no—
315C4—2261no—
316C4#41×D11311yescharacteristic
317C4#1681367011yescharacteristic
318C2—4521no—
319C2—4521no—
320C2#2029925011yescharacteristic
321C2#2029939711yescharacteristic
322C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radicalC2×D452D4
hypercenter#479D113
hypocenterC113#3349
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #20299008C2semidirect
4. #20298942C2semidirect
5. #20298941C2semidirect
6. #20298938C2semidirect
7. #20298932C2semidirect
8. #20298894C2semidirect
9. #20298855C2semidirect
10. #20298838C2semidirect
11. #20298703C2semidirect
13. #20298637C2semidirect
14. #20298635C2semidirect
15. #479×C113C2semidirect
162. C113#3349semidirect
170. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202993212
#202992862
#202990082
#202989422
#202989412
#202989382
#202989322
#202988942
#202988552
#202988382
#202987032
#202986682
#202986372
#202986352
#479×C1132
#3349113