Finite Group Databasebeta

← #28402411

Subgroups — #28402411

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#20299288C211yesmaximal, characteristic, complemented
2#20299244C211yesmaximal, characteristic
3#20298953C211yesmaximal, characteristic, complemented
4#20298929C211yesmaximal, characteristic, complemented
5#20298923C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298839C211yesmaximal, characteristic, complemented
8#20298827C211yesmaximal, characteristic, complemented
9#20298821C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298751C211yesmaximal, characteristic, complemented
12C4×#14268636C211yesmaximal, characteristic, complemented
13#20298595C211yesmaximal, characteristic, complemented
14C2×#16813544C211yesmaximal, characteristic, complemented
15C8×D4×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×Dic452C2211yescharacteristic, complemented
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21#16813615—21no—
22#16813614C2211yescharacteristic, complemented
23#16813612—21no—
24#16813610C2211yescharacteristic
25#16813607—21no—
26#16813603—21no—
27#16813601C2211yescharacteristic
28#16813601C2211yescharacteristic
29#16813601C2211yescharacteristic, complemented
30#16813596C2211yescharacteristic
31#16813595—21no—
32#16813590—21no—
33C4×Dic226C2211yescharacteristic, complemented
34C4×D452C2211yescharacteristic
35#16813581C2211yescharacteristic, complemented
36#16813578—21no—
37C2×C4⋊Dic113C2211yescharacteristic
38C22⋊C4×D113—21no—
39#16813556C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813547C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52C22×C8×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic, complemented
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic, complemented
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic, complemented
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—22no—
61#14268647—41no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×D452—22no—
65C2×D452—21no—
66C2×D452—41no—
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74Dic452—41no—
75#14268636—22no—
76#14268636—41no—
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C2×D4×C113D411yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C2×C8×C113—41no—
102C2×C8×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C22⋊C4×C113D411yescharacteristic
110C42×C113C2311yescharacteristic
111C23×C113C2×D411yescharacteristic
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—81no—
118D4×C113—22no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—42no—
129C22⋊D113—81no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—42no—
137D452—21no—
138D452—21no—
139D452—21no—
140D452—42no—
141D452#4112yes—
142C4×D113—42no—
143C4×D113—81no—
144Dic226—21no—
145Dic226—21no—
146Dic226—21no—
147Dic226—21no—
148C8×C113—21no—
149C8×C113—21no—
150C8×C113—21no—
151C8×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113#13512yes—
158C22×C113C22×D411yescharacteristic
159C2×D113—22no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—84no—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—21no—
169C4×C113—21no—
170C4×C113C2×#4111yescharacteristic
171C4×C113H(5,𝔽2)11yescharacteristic
172Dic113—41no—
173Dic113—41no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178C2×C113—22no—
179C2×C113—41no—
180C2×C113#54611yescharacteristic
181C2×C113C2×#13511yescharacteristic
182C2×C113#57711yescharacteristic
183D113—42no—
184D113—81no—
185#3296—1131nomaximal, Sylow
186C113#329611yescharacteristic, complemented, Sylow
187#552—1131no—
188#546—1131no—
189#488—1131no—
190#483—1131no—
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×D4D11311yescharacteristic, complemented
200#416—1131no—
201C2×#102—1131no—
202C2×#41—1131no—
203C22×D4—1131no—
204C2×Q16—1131no—
205C2×SD16—1131no—
206C2×SD16—1131no—
207C22×C8C2×D11311yescharacteristic
208C22×C8C2×D11311yescharacteristic, complemented
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⋊Q8—1131no—
218#121—1131no—
219#121—2261no—
220#120—2261no—
221C4×Q8—1131no—
222C4×D4—1131no—
223C4×D4C2×D11311yescharacteristic
224#117—1131no—
225#117—2261no—
226C2×C4⋊C4—1131no—
227C2×C22⋊C4—2261no—
228#107—1131no—
229#106—1131no—
230#106—1131no—
231C4⋊C8C2×D11311yescharacteristic, complemented
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102—1131no—
242C22⋊C8C2×D11311yescharacteristic
243C22⋊C8C2×D11311yescharacteristic, complemented
244C4×C8C2×D11311yescharacteristic, complemented
245C24—2261no—
246#41—4521no—
247#41—2262no—
248C2×Q8—1131no—
249C2×Q8—1131no—
250C2×D4—1131no—
251C2×D4—1131no—
252C2×D4—4521no—
253C2×D4—2262no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4D45211yescharacteristic
258C22×C4—2261no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4C22×D11311yescharacteristic
262C22×C4C22×D11311yescharacteristic
263Q16—4521no—
264SD16—4521no—
265SD16—2262no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8C22×D11311yescharacteristic
269C2×C8C22×D11311yescharacteristic
270C2×C8C22×D11311yescharacteristic
271C2×C8C22×D11311yescharacteristic
272C4⋊C4—1131no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4D45211yescharacteristic
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4D45211yescharacteristic
293C22⋊C4D45211yescharacteristic
294C42—2261no—
295C42—2261no—
296C42C22×D11311yescharacteristic
297C23—9041no—
298C23—4522no—
299C23—4522no—
300C23—2261no—
301C23—2261no—
302C23C2×D45211yescharacteristic
303C23C2×D45211yescharacteristic
304Q8—2261no—
305Q8—2261no—
306Q8—2261no—
307Q8—2261no—
308D4—22no—
309D4—1132no—
310D4—9041no—
311D4—4522no—
312D4—4522no—
313D4—2261no—
314D4—2261no—
315D4—2261no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—9041no—
321C2×C4—4522no—
322C2×C4—4522no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4C2×D45211yescharacteristic
330C2×C4C2×D45211yescharacteristic
331C2×C4C2×D45211yescharacteristic
332C2×C4C2×D45211yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—9044no—
344C22—4521no—
345C22—4521no—
346C22—4521no—
347C22—4521no—
348C22—4521no—
349C22—2262no—
350C22#1681364412yes—
351C22C22×D45211yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—4521no—
357C4—4521no—
358C4—4521no—
359C4—4521no—
360C4—4521no—
361C4—4521no—
362C4#41×D11311yescharacteristic
363C4#1681366711yescharacteristic
364C2—22no—
365C2—41no—
366C2—9041no—
367C2—4522no—
368C2#2029924311yescharacteristic
369C2C2×#1681364411yescharacteristic
370C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC8×D4×C113C2
socleC22×C113C22×D4
prime radical#20299244C2
hypercenterC8×D4D113
hypocenterC113#3296
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20299288C2semidirect
3. #20298953C2semidirect
4. #20298929C2semidirect
5. #20298923C2semidirect
6. #20298899C2semidirect
7. #20298839C2semidirect
8. #20298827C2semidirect
9. #20298821C2semidirect
10. #20298762C2semidirect
11. #20298751C2semidirect
12. C4×#14268636C2semidirect
13. #20298595C2semidirect
14. C2×#16813544C2semidirect
15. C8×D4×C113C2semidirect
18. C2×Dic452C22semidirect
22. #16813614C22semidirect
29. #16813601C22semidirect
33. C4×Dic226C22semidirect
35. #16813581C22semidirect
39. #16813556C22semidirect
40. #16813554C22semidirect
41. #16813554C22semidirect
42. #16813547C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
45. #16813547C22semidirect
53. C22×C8×C113C22semidirect
55. C4⋊C8×C113C22semidirect
57. C22⋊C8×C113C22semidirect
58. C4×C8×C113C22semidirect
186. C113#3296semidirect
199. C8×D4D113semidirect
208. C22×C8C2×D113semidirect
231. C4⋊C8C2×D113semidirect
243. C22⋊C8C2×D113semidirect
244. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992882
#202992442
#202989532
#202989292
#202989232
#202988992
#202988392
#202988272
#202988212
#202987622
#202987512
C4×#142686362
#202985952
C2×#168135442
C8×D4×C1132
#3296113