Finite Group Databasebeta

← #28403262

Subgroups — #28403262

Order 14464.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299325C211yesmaximal, characteristic, complemented
2#20299320C211yesmaximal, characteristic
3#20298955C211yesmaximal, characteristic
4#20298954C211yesmaximal, characteristic
5#20298947C211yesmaximal, characteristic, complemented
6#20298908C211yesmaximal, characteristic, complemented
7#20298877C211yesmaximal, characteristic
8#20298823C211yesmaximal, characteristic
9#20298821C211yesmaximal, characteristic
10#20298807C211yesmaximal, characteristic, complemented
11#20298722C211yesmaximal, characteristic, complemented
12#20298692C211yesmaximal, characteristic, complemented
13C4×#14268637C211yesmaximal, characteristic, complemented
14#20298685C211yesmaximal, characteristic
15#479×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19#16813621—21no—
20#16813621C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813617—21no—
23#16813616—21no—
24#16813613C2211yescharacteristic
25#16813612—21no—
26#16813612—21no—
27#16813611C2211yescharacteristic
28#16813610C2211yescharacteristic
29#16813600—21no—
30C4×Dic226C2211yescharacteristic
31C4×Dic226C2211yescharacteristic
32#16813587—21no—
33#16813587C2211yescharacteristic
34#16813587C2211yescharacteristic
35#16813587C2211yescharacteristic
36#16813584C2211yescharacteristic
37#16813579—21no—
38#16813555C2211yescharacteristic
39#16813551C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C4×#11744751C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
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×Dic226D411yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C4×D113—21no—
65Dic452—22no—
66#14268637—22no—
67#14268636—22no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C4⋊Dic113—21no—
71C4⋊Dic113D411yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73#14268626—21no—
74#14268626—21no—
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C4×Dic113C2311yescharacteristic
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×D113—21no—
106Q8×C113—21no—
107Q8×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113C2×D411yescharacteristic
113C2×C4×C113C2×D411yescharacteristic
114C2×C4×C113C2411yescharacteristic
115C2×Dic113—21no—
116C2×Dic113—21no—
117C2×Dic113—21no—
118C2×Dic113C2×D411yescharacteristic
119C2×Dic113C2×D411yescharacteristic
120C2×Dic113C2×D411yescharacteristic
121C2×Dic113C2×D411yescharacteristic
122D452—21no—
123D452—21no—
124C4×D113—42no—
125Dic226—21no—
126Dic226—22no—
127Dic226—21no—
128Dic226—21no—
129Dic226—42no—
130Dic226#4112yes—
131C8×C113—21no—
132C8×C113—21no—
133#11744751—21no—
134#11744751—21no—
135C22×C113C22×D411yescharacteristic
136C2×D113—41no—
137C2×D113—41no—
138C2×D113—41no—
139C4×C113—21no—
140C4×C113—21no—
141C4×C113—41no—
142C4×C113—41no—
143C4×C113—41no—
144C4×C113—41no—
145C4×C113C2×#4111yescharacteristic
146C4×C1132−1+411yescharacteristic
147Dic113—22no—
148Dic113—21no—
149Dic113—21no—
150Dic113—21no—
151Dic113—41no—
152Dic113—41no—
153Dic113#13512yes—
154C2×C113#54811yescharacteristic
155C2×C113C2×#13511yescharacteristic
156C2×C113#57811yescharacteristic
157D113—81no—
158#3364—1131nomaximal, Sylow
159C113#336411yescharacteristic, complemented, Sylow
160#557—1131no—
161#556—1131no—
162#488—1131no—
163#488—1131no—
164#487—1131no—
165#479—1131no—
166#479D11311yescharacteristic, complemented
167#474—1131no—
168#464—1131no—
169#464—1131no—
170#462—1131no—
171C8×Q8—1131no—
172C4×Q16—1131no—
173C4×Q16—1131no—
174C4×SD16—1131no—
175C2×Q16—1131no—
176C2×Q16—1131no—
177C2×SD16—1131no—
178C4⋊Q8—1131no—
179C4⋊Q8—1131no—
180C4⋊Q8—2261no—
181#126—2261no—
182#126—2261no—
183#125—1131no—
184#125—2261no—
185#125—2261no—
186#125C2×D11311yescharacteristic
187#124—1131no—
188#124—1131no—
189C22⋊Q8—2261no—
190C4×Q8—1131no—
191C4×Q8—1131no—
192C4×Q8—1131no—
193C4×Q8—1131no—
194C4×Q8—1131no—
195C4×Q8—2261no—
196C4×Q8C2×D11311yescharacteristic
197C4×D4—1131no—
198#117—2261no—
199#107—1131no—
200#107C2×D11311yescharacteristic
201#106C2×D11311yescharacteristic
202C4⋊C8—1131no—
203C4⋊C8—1131no—
204C4⋊C8C2×D11311yescharacteristic
205#103—1131no—
206#103—1131no—
207#103—1131no—
208#103—1131no—
209#103—1131no—
210#103C2×D11311yescharacteristic
211#103C2×D11311yescharacteristic
212#102—1131no—
213#102—1131no—
214#102—1131no—
215C4×C8—1131no—
216C4×C8—1131no—
217C4×C8—1131no—
218C2×Q8—1131no—
219C2×Q8—1131no—
220C2×Q8—1131no—
221C2×Q8—2261no—
222C2×Q8C22×D11311yescharacteristic
223C2×D4—1131no—
224C22×C4—2261no—
225Q16—2262no—
226Q16—2262no—
227SD16—2262no—
228C2×C8—1131no—
229C2×C8—1131no—
230C2×C8C22×D11311yescharacteristic
231C2×C8C22×D11311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—1131no—
236C4⋊C4—1131no—
237C4⋊C4—1131no—
238C4⋊C4—1131no—
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
251C22⋊C4—2261no—
252C22⋊C4—2261no—
253C22⋊C4—2261no—
254C22⋊C4—2261no—
255C22⋊C4—2261no—
256C42—21no—
257C42—1131no—
258C42—1131no—
259C42—2261no—
260C42—2261no—
261C42—2261no—
262C42—2261no—
263C42C22×D11311yescharacteristic
264C23—2261no—
265Q8—21no—
266Q8—21no—
267Q8—1132no—
268Q8—4522no—
269Q8—2262no—
270Q8—2261no—
271Q8—2261no—
272Q8—2261no—
273D4—2261no—
274D4—2261no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—1131no—
280C2×C4—1131no—
281C2×C4—1131no—
282C2×C4—1131no—
283C2×C4—4522no—
284C2×C4—2261no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4D4×D11311yescharacteristic
288C2×C4D4×D11311yescharacteristic
289C2×C4C23×D11311yescharacteristic
290C8—21no—
291C8—21no—
292C8—2261no—
293C8—2261no—
294C22—4521no—
295C22—4521no—
296C22—4521no—
297C22C2×D4×D11311yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—1132no—
305C4—4521no—
306C4—4521no—
307C4—2261no—
308C4—2261no—
309C4—2261no—
310C4—2262no—
311C4#41×D11311yescharacteristic
312C4#1681367011yescharacteristic
313C2—9041no—
314C2#2029925811yescharacteristic
315C2#135×D11311yescharacteristic
316C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radicalC2×D452C23
hypercenter#479D113
hypocenterC113#3364
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
1. #20299325C2semidirect
5. #20298947C2semidirect
6. #20298908C2semidirect
10. #20298807C2semidirect
11. #20298722C2semidirect
12. #20298692C2semidirect
13. C4×#14268637C2semidirect
15. #479×C113C2semidirect
159. C113#3364semidirect
166. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202993252
#202993202
#202989552
#202989542
#202989472
#202989082
#202988772
#202988232
#202988212
#202988072
#202987222
#202986922
C4×#142686372
#202986852
#479×C1132
#3364113