Finite Group Databasebeta

← #28402407

Subgroups — #28402407

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299283C211yesmaximal, characteristic, complemented
2#20299239C211yesmaximal, characteristic
3#20298954C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298897C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298823C211yesmaximal, characteristic, complemented
9#20298763C211yesmaximal, characteristic, complemented
10#20298751C211yesmaximal, characteristic, complemented
11#20298685C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14C2×#16813542C211yesmaximal, characteristic, complemented
15#483×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C22×#11744751C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic, complemented
23#16813617—21no—
24#16813613C2211yescharacteristic, complemented
25#16813612—21no—
26#16813611C2211yescharacteristic
27#16813607—21no—
28#16813605—21no—
29#16813602C2211yescharacteristic, complemented
30#16813601C2211yescharacteristic
31#16813597—21no—
32#16813597C2211yescharacteristic
33#16813592—21no—
34#16813587C2211yescharacteristic, complemented
35#16813584C2211yescharacteristic
36C4×C22⋊D113C2211yescharacteristic
37#16813581—21no—
38#16813580C2211yescharacteristic, complemented
39C22⋊C4×D113—21no—
40#16813555C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22⋊Q8×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54#106×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113—21no—
60#14268648—22no—
61#14268648—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—41no—
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×C22⋊D113D411yescharacteristic
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268637—41no—
75#14268636—22no—
76#14268636—41no—
77C2×#11744751—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626D411yescharacteristic
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97C4×Dic113—21no—
98C4×Dic113—21no—
99C4×Dic113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101C22×C4×C113—21no—
102C22×C4×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113—21no—
113C22×D113—21no—
114C22×D113—42no—
115C22×D113—42no—
116C22×D113—81no—
117C22×D113C2×D411yescharacteristic
118Q8×C113—21no—
119Q8×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—42no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—22no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—21no—
136D452—21no—
137D452—21no—
138D452—42no—
139D452—42no—
140D452—81no—
141D452#4112yes—
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—42no—
145C4×D113—81no—
146Dic226—21no—
147Dic226—21no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113#13512yes—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—22no—
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—84no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113C2×#4111yescharacteristic
172C4×C113H(5,𝔽2)11yescharacteristic
173Dic113—21no—
174Dic113—21no—
175Dic113—21no—
176Dic113—41no—
177Dic113—41no—
178C2×C113—22no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—41no—
183D113—42no—
184D113—81no—
185#3296—1131nomaximal, Sylow
186C113#329611yescharacteristic, complemented, Sylow
187#552—1131no—
188#546—1131no—
189#488—1131no—
190#483D11311yescharacteristic, complemented
191#482—1131no—
192#478—1131no—
193#467—1131no—
194#465—1131no—
195#464—1131no—
196#452—1131no—
197#450—1131no—
198C4×SD16—1131no—
199C8×D4—1131no—
200#416—1131no—
201C2×#102—1131no—
202C2×#41—1131no—
203C22×D4—1131no—
204C2×Q16—1131no—
205C2×SD16—1131no—
206C2×SD16—1131no—
207C22×C8—1131no—
208C22×C8—1131no—
209#126—2261no—
210#125—1131no—
211#125—2261no—
212#124—1131no—
213#123—2261no—
214#123—2261no—
215C22⋊Q8—1131no—
216C22⋊Q8—1131no—
217C22⋊Q8C2×D11311yescharacteristic
218#121—1131no—
219#121—2261no—
220#120—2261no—
221C4×Q8—1131no—
222C4×D4—1131no—
223C4×D4—1131no—
224#117—1131no—
225#117—2261no—
226C2×C4⋊C4C2×D11311yescharacteristic
227C2×C22⋊C4—2261no—
228#107—1131no—
229#106C2×D11311yescharacteristic, complemented
230#106C2×D11311yescharacteristic, complemented
231C4⋊C8—1131no—
232#103—1131no—
233#103—1131no—
234#103C2×D11311yescharacteristic, complemented
235#103C2×D11311yescharacteristic, complemented
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102—1131no—
242C22⋊C8—1131no—
243C22⋊C8C2×D11311yescharacteristic
244C4×C8—1131no—
245C24—2261no—
246#41—4521no—
247#41—2262no—
248C2×Q8—1131no—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—1131no—
251C2×D4—1131no—
252C2×D4—1131no—
253C2×D4—4521no—
254C2×D4—2262no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4—2261no—
258C22×C4—21no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4C22×D11311yescharacteristic
263Q16—4521no—
264SD16—4521no—
265SD16—2262no—
266C2×C8—1131no—
267C2×C8—1131no—
268C2×C8—4521no—
269C2×C8—4521no—
270C2×C8C22×D11311yescharacteristic
271C2×C8C22×D11311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C4⋊C4C22×D11311yescharacteristic
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—
293C22⋊C4—2261no—
294C42—1131no—
295C42—2261no—
296C42—2261no—
297C23—1131no—
298C23—9041no—
299C23—4522no—
300C23—4522no—
301C23—2261no—
302C23—2261no—
303C23D4×D11311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2261no—
307Q8—2261no—
308D4—1132no—
309D4—9041no—
310D4—4522no—
311D4—4522no—
312D4—2262no—
313D4—2261no—
314D4—2261no—
315D4—2261no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—1131no—
324C2×C4—1131no—
325C2×C4—1131no—
326C2×C4—9041no—
327C2×C4—4522no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4D4×D11311yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2261no—
337C8—2261no—
338C22—21no—
339C22—21no—
340C22—9044no—
341C22—4521no—
342C22—4521no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—2261no—
347C22—2261no—
348C22—2262no—
349C22—2261no—
350C22#1681364312yes—
351C22C2×D4×D11311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4521no—
358C4—4521no—
359C4—2261no—
360C4—2261no—
361C4—2261no—
362C4#41×D11311yescharacteristic
363C4#1681366811yescharacteristic
364C2—22no—
365C2—9041no—
366C2—4522no—
367C2—4521no—
368C2#2029924011yescharacteristic
369C2C2×#1681364311yescharacteristic
370C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#483×C113C2
socleC22×C113C22×D4
prime radical#20299239C2
hypercenter#483D113
hypocenterC113#3296
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #20299283C2semidirect
3. #20298954C2semidirect
4. #20298924C2semidirect
5. #20298897C2semidirect
6. #20298837C2semidirect
7. #20298828C2semidirect
8. #20298823C2semidirect
9. #20298763C2semidirect
10. #20298751C2semidirect
11. #20298685C2semidirect
12. #20298661C2semidirect
13. #20298593C2semidirect
14. C2×#16813542C2semidirect
15. #483×C113C2semidirect
18. C2×#14268637C22semidirect
22. C2×C8×D113C22semidirect
24. #16813613C22semidirect
29. #16813602C22semidirect
34. #16813587C22semidirect
38. #16813580C22semidirect
40. #16813555C22semidirect
41. #16813551C22semidirect
42. #16813546C22semidirect
43. #16813545C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
54. #106×C113C22semidirect
55. #106×C113C22semidirect
56. #103×C113C22semidirect
57. #103×C113C22semidirect
186. C113#3296semidirect
190. #483D113semidirect
229. #106C2×D113semidirect
230. #106C2×D113semidirect
234. #103C2×D113semidirect
235. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992832
#202992392
#202989542
#202989242
#202988972
#202988372
#202988282
#202988232
#202987632
#202987512
#202986852
#202986612
#202985932
C2×#168135422
#483×C1132
#3296113