Finite Group Databasebeta

← #28403109

Subgroups — #28403109

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#20299289C211yesmaximal, characteristic
3#20299007C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298937C211yesmaximal, characteristic, complemented
6#20298937C211yesmaximal, characteristic, complemented
7#20298932C211yesmaximal, characteristic, complemented
8#20298905C211yesmaximal, characteristic, complemented
9#20298893C211yesmaximal, characteristic, complemented
10#20298853C211yesmaximal, characteristic, complemented
11#20298836C211yesmaximal, characteristic, complemented
12#20298671C211yesmaximal, characteristic
13#20298637C211yesmaximal, characteristic, complemented
14#20298633C211yesmaximal, characteristic, complemented
15#441×C113C211yesmaximal, characteristic, complemented
16C2×#14268630C2211yescharacteristic
17C2×C8×D113C2211yescharacteristic
18#16813622C2211yescharacteristic
19#16813617—21no—
20#16813617—21no—
21#16813616—21no—
22#16813614C2211yescharacteristic
23#16813612—21no—
24#16813610—21no—
25#16813607—21no—
26#16813598C2211yescharacteristic
27#16813598C2211yescharacteristic
28#16813598C2211yescharacteristic
29#16813598C2211yescharacteristic
30C4×Dic226—21no—
31C4×D452C2211yescharacteristic
32#16813580C2211yescharacteristic
33#16813580C2211yescharacteristic
34#16813580C2211yescharacteristic
35#16813579—21no—
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813553C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×D452D411yescharacteristic
61C2×C4×D113—21no—
62C2×C4×D113C2311yescharacteristic
63C2×C4×D113C2311yescharacteristic
64#14268630—22no—
65C2×#11744751C2311yescharacteristic
66C2×#11744751C2311yescharacteristic
67C8×D113—22no—
68C4⋊Dic113—21no—
69C4⋊Dic113D411yescharacteristic
70C4⋊Dic113C2311yescharacteristic
71C4⋊Dic113C2311yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74#14268626—21no—
75#14268626—21no—
76#14268626—21no—
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—
93C2×Q8×C113C2311yescharacteristic
94C2×Q8×C113C2311yescharacteristic
95Q16×C113—22no—
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C42×C113—21no—
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C22×D113C2×D411yescharacteristic
106C22×D113C2×D411yescharacteristic
107Q8×C113—21no—
108Q8×C113—21no—
109Q8×C113—21no—
110Q8×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124D452—41no—
125C4×D113—21no—
126C4×D113—21no—
127C4×D113—21no—
128C4×D113—21no—
129C4×D113—42no—
130Dic226—42no—
131C8×C113—21no—
132C8×C113#4112yes—
133#11744751—21no—
134#11744751—21no—
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#479—1131no—
171#477—1131no—
172#470—1131no—
173#467—1131no—
174#441D11311yescharacteristic, complemented
175#435—1131no—
176#428—1131no—
177#427—1131no—
178C2×Q16C2×D11311yescharacteristic
179C2×M16—1131no—
180C22×C8—1131no—
181C4⋊Q8—1131no—
182#126—2261no—
183#126—2261no—
184#126—2261no—
185#125—1131no—
186#125—2261no—
187#124—2261no—
188#123—2261no—
189C22⋊Q8—1131no—
190C22⋊Q8—1131no—
191C22⋊Q8—1131no—
192C22⋊Q8—1131no—
193C4×Q8—2261no—
194C4×Q8C2×D11311yescharacteristic
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#107—1131no—
207#106—1131no—
208#106—1131no—
209#106—1131no—
210#106C2×D11311yescharacteristic
211C4⋊C8—1131no—
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#97C2×D11311yescharacteristic
221C2×Q8—2261no—
222C2×Q8C22×D11311yescharacteristic
223C2×Q8C22×D11311yescharacteristic
224C2×D4—1131no—
225C22×C4—1131no—
226C22×C4—1131no—
227C22×C4—2261no—
228Q16—22no—
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—1131no—
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⋊C4—2261no—
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—21no—
263C42—2261no—
264C42—2261no—
265C42—2261no—
266C42C22×D11311yescharacteristic
267C23—1131no—
268C23—1131no—
269Q8—21no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—4522no—
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—2261no—
295C8—2261no—
296C8#1426864712yes—
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—
316C4C2×#1426864711yescharacteristic
317C4#1681366911yescharacteristic
318C2—4521no—
319C2—4521no—
320C2#2029925311yescharacteristic
321C2#2029939711yescharacteristic
322C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radicalC2×D452D4
hypercenter#441D113
hypocenterC113#3349
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #20299007C2semidirect
4. #20298938C2semidirect
5. #20298937C2semidirect
6. #20298937C2semidirect
7. #20298932C2semidirect
8. #20298905C2semidirect
9. #20298893C2semidirect
10. #20298853C2semidirect
11. #20298836C2semidirect
13. #20298637C2semidirect
14. #20298633C2semidirect
15. #441×C113C2semidirect
162. C113#3349semidirect
174. #441D113semidirect

Maximal subgroups

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

subgroupindex
#202993212
#202992892
#202990072
#202989382
#202989372
#202989322
#202989052
#202988932
#202988532
#202988362
#202986712
#202986372
#202986332
#441×C1132
#3349113