Finite Group Databasebeta

← #28403100

Subgroups — #28403100

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#20299316C211yesmaximal, characteristic
2#20299287C211yesmaximal, characteristic
3#20299005C211yesmaximal, characteristic, complemented
4#20298941C211yesmaximal, characteristic, complemented
5#20298939C211yesmaximal, characteristic, complemented
6#20298939C211yesmaximal, characteristic, complemented
7#20298935C211yesmaximal, characteristic, complemented
8#20298904C211yesmaximal, characteristic, complemented
9#20298892C211yesmaximal, characteristic, complemented
10#20298857C211yesmaximal, characteristic, complemented
11#20298839C211yesmaximal, characteristic, complemented
12#20298704C211yesmaximal, characteristic, complemented
13#20298669C211yesmaximal, characteristic
14#20298637C211yesmaximal, characteristic, complemented
15#427×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813616—21no—
20#16813615—21no—
21#16813615—21no—
22#16813614—21no—
23#16813613C2211yescharacteristic
24#16813608—21no—
25#16813604—21no—
26#16813602C2211yescharacteristic
27#16813602C2211yescharacteristic
28#16813601C2211yescharacteristic
29#16813601C2211yescharacteristic
30C4×Dic226—21no—
31#16813587C2211yescharacteristic
32#16813587C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813580C2211yescharacteristic
35#16813579—21no—
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C22×C8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×C22⋊D113D411yescharacteristic
63C2×C4×D113—21no—
64C2×C4×D113C2311yescharacteristic
65Dic452—22no—
66#14268630—22no—
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
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#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113D411yescharacteristic
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624D411yescharacteristic
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C2×C8×C113—22no—
95C2×C8×C113C2311yescharacteristic
96C2×C8×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C4⋊C4×C113C2311yescharacteristic
99C4⋊C4×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C42×C113—21no—
104C42×C113—21no—
105C23×C113C2×D411yescharacteristic
106C22×D113C2×D411yescharacteristic
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113C2×D411yescharacteristic
114C2×C4×C113C2411yescharacteristic
115C22⋊D113—41no—
116C2×Dic113—21no—
117C2×Dic113—21no—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113C2×D411yescharacteristic
121C2×Dic113C2×D411yescharacteristic
122C2×Dic113C2×D411yescharacteristic
123C4×D113—21no—
124C4×D113—21no—
125C4×D113—42no—
126Dic226—21no—
127Dic226—21no—
128Dic226—21no—
129Dic226—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#470—1131no—
173#467—1131no—
174#441—1131no—
175#435—1131no—
176#428—1131no—
177#427D11311yescharacteristic, complemented
178C2×Q16—1131no—
179C2×M16—1131no—
180C22×C8C2×D11311yescharacteristic
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—1131no—
194C4×Q8—1131no—
195C4×Q8—2261no—
196C4×D4—1131no—
197#117—1131no—
198#117—2261no—
199#117C2×D11311yescharacteristic
200#117C2×D11311yescharacteristic
201C2×C4⋊C4—1131no—
202#107—1131no—
203#107—1131no—
204#107—1131no—
205#107C2×D11311yescharacteristic
206#107C2×D11311yescharacteristic
207#106—1131no—
208#106—1131no—
209#106C2×D11311yescharacteristic
210#106C2×D11311yescharacteristic
211C4⋊C8—1131no—
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218C22⋊C8—1131no—
219C22⋊C8—1131no—
220#97—1131no—
221C2×Q8—1131no—
222C2×Q8—1131no—
223C2×Q8—2261no—
224C2×D4—1131no—
225C22×C4—1131no—
226C22×C4—2261no—
227C22×C4C22×D11311yescharacteristic
228Q16—2262no—
229M16—2262no—
230C2×C8—22no—
231C2×C8—1131no—
232C2×C8—1131no—
233C2×C8C22×D11311yescharacteristic
234C2×C8C22×D11311yescharacteristic
235C4⋊C4—1131no—
236C4⋊C4—1131no—
237C4⋊C4—1131no—
238C4⋊C4—2261no—
239C4⋊C4—2261no—
240C4⋊C4—2261no—
241C4⋊C4—2261no—
242C4⋊C4—2261no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4C22×D11311yescharacteristic
249C4⋊C4C22×D11311yescharacteristic
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—21no—
262C42—21no—
263C42—1131no—
264C42—2261no—
265C42—2261no—
266C42—2261no—
267C23—1131no—
268C23D4×D11311yescharacteristic
269Q8—4522no—
270Q8—2261no—
271Q8—2261no—
272Q8—2261no—
273Q8—2261no—
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#1426864712yes—
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×#1426864711yescharacteristic
317C4#1681367011yescharacteristic
318C2—41no—
319C2—4521no—
320C2#2029924911yescharacteristic
321C2#2029939511yescharacteristic
322C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#427×C113C2
socleC22×C113C22×D4
prime radicalC2×C22⋊D113D4
hypercenter#427D113
hypocenterC113#3349
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #20299005C2semidirect
4. #20298941C2semidirect
5. #20298939C2semidirect
6. #20298939C2semidirect
7. #20298935C2semidirect
8. #20298904C2semidirect
9. #20298892C2semidirect
10. #20298857C2semidirect
11. #20298839C2semidirect
12. #20298704C2semidirect
14. #20298637C2semidirect
15. #427×C113C2semidirect
162. C113#3349semidirect
177. #427D113semidirect

Maximal subgroups

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

subgroupindex
#202993162
#202992872
#202990052
#202989412
#202989392
#202989352
#202989042
#202988922
#202988572
#202988392
#202987042
#202986692
#202986372
#427×C1132
#3349113