Finite Group Databasebeta

← #28403358

Subgroups — #28403358

Order 14464.

340 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299326C211yesmaximal, characteristic, complemented
2#20299304C211yesmaximal, characteristic
3#20298968C211yesmaximal, characteristic, complemented
4#20298965C211yesmaximal, characteristic, complemented
5#20298947C211yesmaximal, characteristic, complemented
6#20298908C211yesmaximal, characteristic, complemented
7#20298892C211yesmaximal, characteristic, complemented
8#20298804C211yesmaximal, characteristic
9#20298802C211yesmaximal, characteristic
10#20298802C211yesmaximal, characteristic
11#20298727C211yesmaximal, characteristic, complemented
12#20298697C211yesmaximal, characteristic
13#20298696C211yesmaximal, characteristic
14#20298685C211yesmaximal, characteristic
15#479×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813614—21no—
24#16813613C2211yescharacteristic
25#16813612—21no—
26#16813612—21no—
27#16813602—21no—
28#16813600—21no—
29#16813600—21no—
30C4×Dic226—21no—
31C4×Dic226C2211yescharacteristic
32#16813587C2211yescharacteristic
33#16813587C2211yescharacteristic
34C4×D452C2211yescharacteristic
35#16813584C2211yescharacteristic
36#16813584C2211yescharacteristic
37C4⋊C4×D113—21no—
38#16813555C2211yescharacteristic
39#16813551C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813533C2211yescharacteristic
50#16813532C2211yescharacteristic
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—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67#14268636—22no—
68#14268636—22no—
69#14268634—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113D411yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86#14268626D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624—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#4112yes—
124C4×D113—42no—
125C4×D113—81no—
126C4×D113—81no—
127Dic226—22no—
128Dic226—21no—
129Dic226—21no—
130Dic226—21no—
131Dic226—21no—
132Dic226—81no—
133C8×C113—21no—
134C8×C113—21no—
135#11744751—21no—
136#11744751—21no—
137C22×C113C22×D411yescharacteristic
138C2×D113—22no—
139C2×D113—41no—
140C2×D113—41no—
141C4×C113—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#13712yes—
156C2×C113#54811yescharacteristic
157C2×C113C2×#13711yescharacteristic
158C2×C113#57711yescharacteristic
159D113—42no—
160#3372—1131nomaximal, Sylow
161C113#337211yescharacteristic, complemented, Sylow
162#557—1131no—
163#554—1131no—
164#491—1131no—
165#491—1131no—
166#487—1131no—
167#479—1131no—
168#479D11311yescharacteristic, complemented
169#477—1131no—
170#461—1131no—
171#461—1131no—
172#461—1131no—
173#446—1131no—
174#440—1131no—
175#440—1131no—
176C4×SD16—1131no—
177C2×SD16—1131no—
178C2×SD16—1131no—
179C2×SD16—1131no—
180C4⋊Q8—1131no—
181C4⋊Q8—1131no—
182C4⋊Q8—1131no—
183C4⋊Q8—1131no—
184#125—1131no—
185#125—2261no—
186#125—2261no—
187#125—2261no—
188#125C2×D11311yescharacteristic
189C22⋊Q8—2261no—
190C22⋊Q8—2261no—
191C22⋊Q8—2261no—
192C4×Q8—1131no—
193C4×Q8—1131no—
194C4×Q8—1131no—
195C4×Q8—2261no—
196C4×Q8C2×D11311yescharacteristic
197C4×D4—1131no—
198C4×D4—1131no—
199C4×D4—1131no—
200C2×C4⋊C4—2261no—
201#107—1131no—
202#107C2×D11311yescharacteristic
203#106C2×D11311yescharacteristic
204C4⋊C8—1131no—
205C4⋊C8—1131no—
206C4⋊C8C2×D11311yescharacteristic
207#103—1131no—
208#103—1131no—
209#103—1131no—
210#103—1131no—
211#103—1131no—
212#103—1131no—
213#103—1131no—
214#103C2×D11311yescharacteristic
215#103C2×D11311yescharacteristic
216#102—1131no—
217#97—1131no—
218#97—1131no—
219C4×C8—1131no—
220C2×Q8—1131no—
221C2×Q8—1131no—
222C2×Q8—1131no—
223C2×Q8—2261no—
224C2×Q8C22×D11311yescharacteristic
225C2×D4—1131no—
226C22×C4—2261no—
227C22×C4—2261no—
228C22×C4—2261no—
229SD16—2262no—
230SD16—2262no—
231SD16—2262no—
232C2×C8—1131no—
233C2×C8—1131no—
234C2×C8C22×D11311yescharacteristic
235C2×C8C22×D11311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—1131no—
240C4⋊C4—1131no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—2261no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
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
256C4⋊C4C22×D11311yescharacteristic
257C22⋊C4—2261no—
258C22⋊C4—2261no—
259C22⋊C4—2261no—
260C42—21no—
261C42—1131no—
262C42—1131no—
263C42—2261no—
264C42—2261no—
265C42C22×D11311yescharacteristic
266C23—2261no—
267Q8—21no—
268Q8—21no—
269Q8—9041no—
270Q8—2262no—
271Q8—2261no—
272Q8—2261no—
273Q8—2261no—
274Q8—2261no—
275D4—1132no—
276D4—2261no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—1131no—
282C2×C4—1131no—
283C2×C4—1131no—
284C2×C4—1131no—
285C2×C4—9041no—
286C2×C4—9041no—
287C2×C4—4522no—
288C2×C4—2261no—
289C2×C4—2261no—
290C2×C4—2261no—
291C2×C4D4×D11311yescharacteristic
292C2×C4D4×D11311yescharacteristic
293C2×C4C23×D11311yescharacteristic
294C8—21no—
295C8—21no—
296C8—2261no—
297C8—2261no—
298C22—4521no—
299C22—4521no—
300C22—2262no—
301C22C2×D4×D11311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—1132no—
309C4—4521no—
310C4—4521no—
311C4—4521no—
312C4—2261no—
313C4—2261no—
314C4—2261no—
315C4#41×D11311yescharacteristic
316C4#1681367011yescharacteristic
317C2—4522no—
318C2#2029925811yescharacteristic
319C2#137×D11311yescharacteristic
320C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radicalC2×D452C23
hypercenter#479D113
hypocenterC113#3372
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. #20299326C2semidirect
3. #20298968C2semidirect
4. #20298965C2semidirect
5. #20298947C2semidirect
6. #20298908C2semidirect
7. #20298892C2semidirect
11. #20298727C2semidirect
15. #479×C113C2semidirect
161. C113#3372semidirect
168. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202993262
#202993042
#202989682
#202989652
#202989472
#202989082
#202988922
#202988042
#202988022
#202987272
#202986972
#202986962
#202986852
#479×C1132
#3372113