Finite Group Databasebeta

← #28403184

Subgroups — #28403184

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#20299319C211yesmaximal, characteristic
2#20299306C211yesmaximal, characteristic
3#20298995C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298936C211yesmaximal, characteristic, complemented
6#20298927C211yesmaximal, characteristic, complemented
7#20298926C211yesmaximal, characteristic, complemented
8#20298891C211yesmaximal, characteristic, complemented
9#20298881C211yesmaximal, characteristic, complemented
10#20298853C211yesmaximal, characteristic, complemented
11Q16×Dic113C211yesmaximal, characteristic, complemented
12#20298674C211yesmaximal, characteristic
13#20298640C211yesmaximal, characteristic, complemented
14#20298637C211yesmaximal, characteristic, complemented
15#470×C113C211yesmaximal, characteristic, complemented
16C2×#14268630C2211yescharacteristic
17#16813621C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813617—21no—
20#16813615—21no—
21#16813612—21no—
22#16813608—21no—
23#16813602—21no—
24#16813599—21no—
25#16813598C2211yescharacteristic
26#16813598C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic
29#16813587—21no—
30C4×C22⋊D113C2211yescharacteristic
31#16813582—21no—
32#16813581C2211yescharacteristic
33#16813580C2211yescharacteristic
34C2×C4⋊Dic113C2211yescharacteristic
35C4⋊C4×D113C2211yescharacteristic
36#16813556C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
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×Dic226—21no—
61C2×C22⋊D113D411yescharacteristic
62C22×Dic113—21no—
63C2×C4×D113—21no—
64C2×C4×D113C2311yescharacteristic
65#14268630—22no—
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113C2311yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626D411yescharacteristic
81C22⋊Dic113—21no—
82C22⋊Dic113D411yescharacteristic
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624D411yescharacteristic
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—22no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—81no—
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C4×D113—21no—
129C4×D113—21no—
130C4×D113—81no—
131Dic226—42no—
132Dic226—81no—
133C8×C113—21no—
134C8×C113#4112yes—
135#11744751—21no—
136#11744751—21no—
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#485—1131no—
170#483—1131no—
171#483—1131no—
172#477—1131no—
173#475—1131no—
174#470—1131no—
175#470D11311yescharacteristic, complemented
176C4×Q16—1131no—
177#436—1131no—
178#428—1131no—
179#428—1131no—
180C2×Q16C2×D11311yescharacteristic
181C2×M16—1131no—
182C2×M16C2×D11311yescharacteristic
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—2261no—
192C22⋊Q8—2261no—
193C22⋊Q8C2×D11311yescharacteristic
194C22⋊Q8C2×D11311yescharacteristic
195C4×Q8—1131no—
196C4×Q8—1131no—
197C4×Q8—2261no—
198C4×D4—1131no—
199C4×D4—2261no—
200#117—1131no—
201#117—1131no—
202C2×C4⋊C4—1131no—
203C2×C4⋊C4—1131no—
204#107—1131no—
205#107—1131no—
206#107—1131no—
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⋊C8—1131no—
222C4×C8—1131no—
223C2×Q8—2261no—
224C2×Q8—2261no—
225C2×Q8C22×D11311yescharacteristic
226C2×Q8C22×D11311yescharacteristic
227C2×D4—1131no—
228C22×C4—1131no—
229C22×C4—2261no—
230C22×C4—2261no—
231C22×C4C22×D11311yescharacteristic
232Q16—22no—
233M16—22no—
234M16—2262no—
235C2×C8—1131no—
236C2×C8—1131no—
237C2×C8C22×D11311yescharacteristic
238C2×C8C22×D11311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—1131no—
244C4⋊C4—1131no—
245C4⋊C4—1131no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
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—1131no—
265C42—2261no—
266C42—2261no—
267C42—2261no—
268C42—2261no—
269C23—1131no—
270C23D4×D11311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—9041no—
276Q8—4522no—
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—2261no—
299C8—2261no—
300C8#1426864612yes—
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—
320C4C2×#1426864611yescharacteristic
321C4#1681366911yescharacteristic
322C2—41no—
323C2—4521no—
324C2#2029924811yescharacteristic
325C2#137×D11311yescharacteristic
326C2#2029940711yescharacteristic
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#3356
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. #20298995C2semidirect
4. #20298938C2semidirect
5. #20298936C2semidirect
6. #20298927C2semidirect
7. #20298926C2semidirect
8. #20298891C2semidirect
9. #20298881C2semidirect
10. #20298853C2semidirect
11. Q16×Dic113C2semidirect
13. #20298640C2semidirect
14. #20298637C2semidirect
15. #470×C113C2semidirect
164. C113#3356semidirect
175. #470D113semidirect

Maximal subgroups

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

subgroupindex
#202993192
#202993062
#202989952
#202989382
#202989362
#202989272
#202989262
#202988912
#202988812
#202988532
Q16×Dic1132
#202986742
#202986402
#202986372
#470×C1132
#3356113