Finite Group Databasebeta

← #28403099

Subgroups — #28403099

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#20299319C211yesmaximal, characteristic
2#20299290C211yesmaximal, characteristic
3#20299005C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298937C211yesmaximal, characteristic, complemented
6#20298936C211yesmaximal, characteristic, complemented
7#20298931C211yesmaximal, characteristic, complemented
8#20298903C211yesmaximal, characteristic, complemented
9#20298891C211yesmaximal, characteristic, complemented
10#20298836C211yesmaximal, characteristic, complemented
11#20298705C211yesmaximal, characteristic, complemented
12#20298667C211yesmaximal, characteristic
13#20298640C211yesmaximal, characteristic, complemented
14#20298633C211yesmaximal, characteristic, complemented
15#470×C113C211yesmaximal, characteristic, complemented
16C2×C8×D113C2211yescharacteristic
17#16813621C2211yescharacteristic
18#16813617—21no—
19#16813617—21no—
20#16813615—21no—
21#16813613—21no—
22#16813613C2211yescharacteristic
23#16813608—21no—
24#16813606—21no—
25#16813598C2211yescharacteristic
26#16813598C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic
29#16813587—21no—
30C4×C22⋊D113C2211yescharacteristic
31#16813581C2211yescharacteristic
32#16813580C2211yescharacteristic
33#16813580C2211yescharacteristic
34#16813578—21no—
35C2×C4⋊Dic113C2211yescharacteristic
36#16813556C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×C22⋊D113D411yescharacteristic
61C22×Dic113—21no—
62C2×C4×D113C2311yescharacteristic
63C2×#11744751C2311yescharacteristic
64C2×#11744751C2311yescharacteristic
65C8×D113—22no—
66C4⋊Dic113—21no—
67C4⋊Dic113—21no—
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113C2311yescharacteristic
71C4⋊Dic113C2311yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74#14268626—21no—
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626D411yescharacteristic
79C22⋊Dic113—21no—
80C22⋊Dic113D411yescharacteristic
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624D411yescharacteristic
86C4×Dic113—21no—
87C4×Dic113—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113C2311yescharacteristic
92C2×Q8×C113C2311yescharacteristic
93C2×Q8×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95Q16×C113—22no—
96M16×C113—22no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C23×C113C2×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×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2411yescharacteristic
119C22⋊D113—41no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—42no—
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C4×D113—21no—
129C4×D113—21no—
130Dic226—42no—
131C8×C113—21no—
132C8×C113#4112yes—
133#11744751—21no—
134#11744751—21no—
135C22×C113—21no—
136C22×C113—21no—
137C22×C113—21no—
138C22×C113C22×D411yescharacteristic
139C2×D113—21no—
140C2×D113—21no—
141C2×D113—21no—
142C4×C113—21no—
143C4×C113—41no—
144C4×C113—41no—
145C4×C113—41no—
146C4×C113—41no—
147C4×C113C2×#4111yescharacteristic
148C4×C1132−1+411yescharacteristic
149Dic113—21no—
150Dic113—21no—
151Dic113—21no—
152Dic113—41no—
153Dic113—41no—
154Dic113—41no—
155Dic113—41no—
156C2×C113—41no—
157C2×C113#54711yescharacteristic
158C2×C113#57511yescharacteristic
159C2×C113#57811yescharacteristic
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#470D11311yescharacteristic, complemented
173#467—1131no—
174#441—1131no—
175#435—1131no—
176#428—1131no—
177#427—1131no—
178C2×Q16C2×D11311yescharacteristic
179C2×M16C2×D11311yescharacteristic
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⋊Q8C2×D11311yescharacteristic
192C22⋊Q8C2×D11311yescharacteristic
193C4×Q8—1131no—
194C4×Q8—1131no—
195C4×Q8—2261no—
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#97—1131no—
221C2×Q8—2261no—
222C2×Q8C22×D11311yescharacteristic
223C2×Q8C22×D11311yescharacteristic
224C2×D4—1131no—
225C22×C4—1131no—
226C22×C4—2261no—
227C22×C4C22×D11311yescharacteristic
228Q16—22no—
229M16—22no—
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—21no—
253C22⋊C4—21no—
254C22⋊C4—1131no—
255C22⋊C4—1131no—
256C22⋊C4—2261no—
257C22⋊C4—2261no—
258C22⋊C4—2261no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C42—1131no—
262C42—2261no—
263C42—2261no—
264C42—2261no—
265C42—2261no—
266C42—2261no—
267C23—1131no—
268C23D4×D11311yescharacteristic
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—21no—
280C2×C4—21no—
281C2×C4—1131no—
282C2×C4—1131no—
283C2×C4—1131no—
284C2×C4—4522no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4—2261no—
288C2×C4—2261no—
289C2×C4—2261no—
290C2×C4—2261no—
291C2×C4D4×D11311yescharacteristic
292C2×C4C23×D11311yescharacteristic
293C8—21no—
294C8—2261no—
295C8—2261no—
296C8#1426864612yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—2261no—
301C22—2261no—
302C22—2261no—
303C22C2×D4×D11311yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—4521no—
310C4—4521no—
311C4—4521no—
312C4—4521no—
313C4—2261no—
314C4—2261no—
315C4—2261no—
316C4C2×#1426864611yescharacteristic
317C4#1681366911yescharacteristic
318C2—41no—
319C2—4521no—
320C2#2029924811yescharacteristic
321C2#2029939711yescharacteristic
322C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#470D113
hypocenterC113#3349
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #20299005C2semidirect
4. #20298938C2semidirect
5. #20298937C2semidirect
6. #20298936C2semidirect
7. #20298931C2semidirect
8. #20298903C2semidirect
9. #20298891C2semidirect
10. #20298836C2semidirect
11. #20298705C2semidirect
13. #20298640C2semidirect
14. #20298633C2semidirect
15. #470×C113C2semidirect
162. C113#3349semidirect
172. #470D113semidirect

Maximal subgroups

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

subgroupindex
#202993192
#202992902
#202990052
#202989382
#202989372
#202989362
#202989312
#202989032
#202988912
#202988362
#202987052
#202986672
#202986402
#202986332
#470×C1132
#3349113