Finite Group Databasebeta

← #28401137

Subgroups — #28401137

Order 14464.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299134C211yesmaximal, characteristic, complemented
2#20299129C211yesmaximal, characteristic, complemented
3#20298998C211yesmaximal, characteristic, complemented
4#20298979C211yesmaximal, characteristic, complemented
5#20298954C211yesmaximal, characteristic, complemented
6#20298951C211yesmaximal, characteristic, complemented
7#20298837C211yesmaximal, characteristic, complemented
8#20298832C211yesmaximal, characteristic
9#20298827C211yesmaximal, characteristic, complemented
10#20298690C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12#20298685C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14C2×C8×Dic113C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C22×#11744751C2211yescharacteristic
20#16813617—21no—
21#16813615—21no—
22#16813613C2211yescharacteristic
23#16813613C2211yescharacteristic
24#16813611C2211yescharacteristic
25#16813609C2211yescharacteristic
26#16813606—21no—
27#16813603—21no—
28#16813601C2211yescharacteristic
29#16813596C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31#16813587C2211yescharacteristic
32D4×Dic113—21no—
33D4×Dic113C2211yescharacteristic
34#16813584C2211yescharacteristic
35#16813582—21no—
36#16813580—21no—
37#16813578—21no—
38C2×C4×Dic113C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48C8×Dic113C2211yescharacteristic
49C8×Dic113C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C22×Dic113D411yescharacteristic
64C22×Dic113D411yescharacteristic
65C2×C4×D113—21no—
66#14268637—22no—
67#14268636—22no—
68#14268632—22no—
69C2×#11744751—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113D411yescharacteristic
92C4×Dic113D411yescharacteristic
93C4×Dic113C2311yescharacteristic
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×D4×C113—21no—
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99SD16×C113—22no—
100C2×C8×C113—22no—
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113D4×C113—21no—
114D4×C113—21no—
115D4×C113—42no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C22⋊D113—42no—
124C2×Dic113—22no—
125C2×Dic113—22no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—42no—
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134D452—21no—
135D452—21no—
136C4×D113—42no—
137Dic226—21no—
138Dic226—21no—
139C8×C113—21no—
140C8×C113#4112yes—
141#11744751—21no—
142#11744751#4112yes—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113#13512yes—
149C22×C113C22×D411yescharacteristic
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C4×C113—21no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113C2×#4111yescharacteristic
158C4×C113C2×#4111yescharacteristic
159Dic113—21no—
160Dic113—21no—
161Dic113—21no—
162Dic113—41no—
163Dic113—41no—
164Dic113—41no—
165Dic113#13512yes—
166C2×C113—22no—
167C2×C113—81no—
168C2×C113#53211yescharacteristic
169C2×C113C2×#13511yescharacteristic
170C2×C113C2×#13511yescharacteristic
171D113—81no—
172#3168—1131nomaximal, Sylow
173C113#316811yescharacteristic, complemented, Sylow
174#529—1131no—
175#529—1131no—
176#499—1131no—
177#495—1131no—
178#488—1131no—
179#488—1131no—
180#467—1131no—
181#466—1131no—
182#465—1131no—
183#465D11311yescharacteristic, complemented
184C4×Q16—1131no—
185C4×SD16—1131no—
186C4×SD16—1131no—
187C4×D8—1131no—
188C2×C4×C8—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16C2×D11311yescharacteristic
192C2×D8—1131no—
193C22×C8—1131no—
194C22×C8C2×D11311yescharacteristic
195#126—2261no—
196#126—2261no—
197#125—1131no—
198#125—1131no—
199#124—1131no—
200#124—1131no—
201#123—2261no—
202#123—2261no—
203C22⋊Q8—1131no—
204C22⋊Q8C2×D11311yescharacteristic
205#121—1131no—
206#121C2×D11311yescharacteristic
207C4×Q8—1131no—
208C4×Q8—1131no—
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—2261no—
212C4×D4—2261no—
213#117—2261no—
214#117—2261no—
215C2×C42—1131no—
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106C2×D11311yescharacteristic
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102—1131no—
226#102—1131no—
227#102C2×D11311yescharacteristic
228C4×C8—1131no—
229C4×C8—1131no—
230C4×C8—1131no—
231C4×C8—1131no—
232C2×Q8—1131no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—21no—
235C2×D4—1131no—
236C2×D4—2261no—
237C2×D4C22×D11311yescharacteristic
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—2261no—
241C22×C4—2261no—
242C22×C4C22×D11311yescharacteristic
243Q16—2262no—
244SD16—22no—
245SD16—2262no—
246D8—2262no—
247C2×C8—22no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8—2262no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C42—1131no—
276C42—1131no—
277C42—1131no—
278C42—1131no—
279C42—2261no—
280C42—2261no—
281C23—21no—
282C23—2261no—
283C23D4×D11311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—2261no—
287Q8—2261no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—4522no—
292D4—2261no—
293D4—2261no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—1131no—
300C2×C4—1131no—
301C2×C4—1131no—
302C2×C4—1131no—
303C2×C4—4522no—
304C2×C4—4522no—
305C2×C4—2262no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2262no—
310C2×C4D4×D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—21no—
313C8—1132no—
314C8—2261no—
315C8#1426864612yes—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—4521no—
322C22—4521no—
323C22—4521no—
324C22#1681364312yes—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—1132no—
331C4—4521no—
332C4—4521no—
333C4—4521no—
334C4—2261no—
335C4—2261no—
336C4—2261no—
337C4#41×D11311yescharacteristic
338C4C2×#1426864611yescharacteristic
339C2—22no—
340C2—81no—
341C2—9041no—
342C2#2029914311yescharacteristic
343C2#135×D11311yescharacteristic
344C2C2×#1681364311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20298832C2
hypercenter#465D113
hypocenterC113#3168
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #20299134C2semidirect
2. #20299129C2semidirect
3. #20298998C2semidirect
4. #20298979C2semidirect
5. #20298954C2semidirect
6. #20298951C2semidirect
7. #20298837C2semidirect
9. #20298827C2semidirect
10. #20298690C2semidirect
11. SD16×Dic113C2semidirect
12. #20298685C2semidirect
13. #20298678C2semidirect
14. C2×C8×Dic113C2semidirect
15. #465×C113C2semidirect
173. C113#3168semidirect
183. #465D113semidirect

Maximal subgroups

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

subgroupindex
#202991342
#202991292
#202989982
#202989792
#202989542
#202989512
#202988372
#202988322
#202988272
#202986902
SD16×Dic1132
#202986852
#202986782
C2×C8×Dic1132
#465×C1132
#3168113