Finite Group Databasebeta

← #28402497

Subgroups — #28402497

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299312C211yesmaximal, characteristic, complemented
2#20299250C211yesmaximal, characteristic, complemented
3#20298947C211yesmaximal, characteristic, complemented
4#20298942C211yesmaximal, characteristic, complemented
5#20298936C211yesmaximal, characteristic, complemented
6#20298887C211yesmaximal, characteristic, complemented
7#20298826C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298742C211yesmaximal, characteristic, complemented
10#20298741C211yesmaximal, characteristic, complemented
11#20298678C211yesmaximal, characteristic, complemented
12C8×C22⋊D113C211yesmaximal, characteristic, complemented
13#20298595C211yesmaximal, characteristic, complemented
14#20298593C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813609—21no—
24#16813608—21no—
25#16813607—21no—
26#16813604—21no—
27#16813602C2211yescharacteristic
28#16813595—21no—
29#16813594—21no—
30#16813593C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32#16813584C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813581C2211yescharacteristic
35#16813580C2211yescharacteristic
36#16813578—21no—
37C4⋊C4×D113—21no—
38#16813555C2211yescharacteristic
39#16813553C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61#14268647—22no—
62#14268647—41no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113D411yescharacteristic
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268635—41no—
76#14268632—22no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C8×D113—41no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102SD16×C113—41no—
103C2×C8×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—81no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—22no—
128C22⋊D113—42no—
129C22⋊D113—81no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—42no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—21no—
138D452—42no—
139D452#4112yes—
140C4×D113—21no—
141C4×D113—21no—
142C4×D113—42no—
143C4×D113—42no—
144C4×D113—42no—
145Dic226—21no—
146Dic226—21no—
147Dic226—81no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—22no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—41no—
164C2×D113—41no—
165C4×C113—21no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—41no—
174Dic113—41no—
175Dic113—41no—
176Dic113#13512yes—
177C2×C113—41no—
178C2×C113—81no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—41no—
183D113—42no—
184#3303—1131nomaximal, Sylow
185C113#330311yescharacteristic, complemented, Sylow
186#555—1131no—
187#547—1131no—
188#487—1131no—
189#485—1131no—
190#485—1131no—
191#476—1131no—
192#465—1131no—
193#465D11311yescharacteristic, complemented
194#461—1131no—
195#449—1131no—
196#449—1131no—
197C4×D8—1131no—
198C8×D4—1131no—
199#416—1131no—
200#416—1131no—
201C2×#41—1131no—
202C2×#41—1131no—
203C2×SD16—1131no—
204C2×SD16C2×D11311yescharacteristic
205C2×D8—1131no—
206C22×C8—1131no—
207C22×C8C2×D11311yescharacteristic
208C4⋊Q8—1131no—
209C4⋊Q8—1131no—
210#124—2261no—
211#124—2261no—
212#123—2261no—
213#123—2261no—
214C22⋊Q8—1131no—
215C22⋊Q8C2×D11311yescharacteristic
216#121—1131no—
217#121—2261no—
218#121—2261no—
219#121C2×D11311yescharacteristic
220C4×D4—1131no—
221C4×D4—1131no—
222C4×D4—1131no—
223#117—1131no—
224#117—1131no—
225#117—2261no—
226C2×C4⋊C4—2261no—
227#107—1131no—
228#106—1131no—
229#106C2×D11311yescharacteristic
230C4⋊C8—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103C2×D11311yescharacteristic
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102C2×D11311yescharacteristic
241C22⋊C8—1131no—
242C22⋊C8—1131no—
243C4×C8—1131no—
244#41—4521no—
245#41—4521no—
246#41—2262no—
247#41—2262no—
248C2×Q8—1131no—
249C2×Q8—2261no—
250C2×Q8C22×D11311yescharacteristic
251C2×D4—21no—
252C2×D4—1131no—
253C2×D4—1131no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—1131no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4C22×D11311yescharacteristic
264SD16—41no—
265SD16—4521no—
266D8—2262no—
267C2×C8—41no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8—4521no—
271C2×C8C22×D11311yescharacteristic
272C2×C8C22×D11311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1131no—
286C22⋊C4—1131no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C42—1131no—
294C42—2261no—
295C42—2261no—
296C23—21no—
297C23—1131no—
298C23—2261no—
299C23D4×D11311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—9041no—
303Q8—2261no—
304Q8—2261no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—1132no—
309D4—9041no—
310D4—4522no—
311D4—4522no—
312D4—2262no—
313D4—2261no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—4522no—
323C2×C4—4522no—
324C2×C4—4522no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11311yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—21no—
334C8—21no—
335C8—2261no—
336C8—2261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—4521no—
344C22—4521no—
345C22—2261no—
346C22—2261no—
347C22—2262no—
348C22—2261no—
349C22C2×D4×D11311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—1132no—
355C4—4521no—
356C4—4521no—
357C4—4521no—
358C4—2261no—
359C4—2261no—
360C4#41×D11311yescharacteristic
361C4#1681366711yescharacteristic
362C2—41no—
363C2—81no—
364C2—4522no—
365C2—4521no—
366C2#2029923711yescharacteristic
367C2#135×D11311yescharacteristic
368C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
hypercenter#465D113
hypocenterC113#3303
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. #20299312C2semidirect
2. #20299250C2semidirect
3. #20298947C2semidirect
4. #20298942C2semidirect
5. #20298936C2semidirect
6. #20298887C2semidirect
7. #20298826C2semidirect
8. #20298801C2semidirect
9. #20298742C2semidirect
10. #20298741C2semidirect
11. #20298678C2semidirect
12. C8×C22⋊D113C2semidirect
13. #20298595C2semidirect
14. #20298593C2semidirect
15. #465×C113C2semidirect
185. C113#3303semidirect
193. #465D113semidirect

Maximal subgroups

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

subgroupindex
#202993122
#202992502
#202989472
#202989422
#202989362
#202988872
#202988262
#202988012
#202987422
#202987412
#202986782
C8×C22⋊D1132
#202985952
#202985932
#465×C1132
#3303113