Finite Group Databasebeta

← #28402406

Subgroups — #28402406

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#20299286C211yesmaximal, characteristic, complemented
2#20299243C211yesmaximal, characteristic
3#20298955C211yesmaximal, characteristic, complemented
4#20298930C211yesmaximal, characteristic, complemented
5#20298925C211yesmaximal, characteristic, complemented
6#20298840C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298821C211yesmaximal, characteristic, complemented
9#20298761C211yesmaximal, characteristic, complemented
10#20298750C211yesmaximal, characteristic, complemented
11C4×#14268635C211yesmaximal, characteristic, complemented
12#20298663C211yesmaximal, characteristic, complemented
13#20298591C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#478×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic, complemented
19C2×#14268636C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic, complemented
23#16813617—21no—
24#16813613—21no—
25#16813610C2211yescharacteristic
26#16813607—21no—
27#16813606—21no—
28#16813602C2211yescharacteristic
29#16813602C2211yescharacteristic
30#16813602C2211yescharacteristic, complemented
31#16813597C2211yescharacteristic
32#16813596—21no—
33#16813592—21no—
34C4×Dic226C2211yescharacteristic, complemented
35C4×D452C2211yescharacteristic
36#16813580—21no—
37#16813580C2211yescharacteristic, complemented
38C4⋊C4×D113C2211yescharacteristic
39C2×#14268624—21no—
40#16813553C2211yescharacteristic, complemented
41#16813547C2211yescharacteristic, complemented
42#16813545C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51C4×#11744751C2211yescharacteristic, complemented
52#125×C113C2211yescharacteristic, complemented
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60#14268646—22no—
61#14268646—41no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×D452—21no—
65C2×D452D411yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69D4×D113—22no—
70D4×D113—41no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74C2×C4×D113C2311yescharacteristic
75Dic452—41no—
76#14268636—41no—
77#14268635—22no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C8×D113—41no—
82C4⋊Dic113—21no—
83C4⋊Dic113—21no—
84C4⋊Dic113—21no—
85C4⋊Dic113D411yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97#14268624D411yescharacteristic
98C4×Dic113—21no—
99C4×Dic113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113—21no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C22×D113—21no—
113C22×D113—42no—
114C22×D113—42no—
115C22×D113—81no—
116C22×D113C2×D411yescharacteristic
117C22×D113C2×D411yescharacteristic
118D4×C113—21no—
119D4×C113#4112yes—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—81no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—42no—
128C22⋊D113—42no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—42no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—22no—
136D452—21no—
137D452—21no—
138D452—81no—
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—42no—
144Dic226—21no—
145Dic226—21no—
146Dic226—21no—
147Dic226—21no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—22no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—84no—
165C2×D113#13512yes—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113C2×#4111yescharacteristic
172C4×C113H(5,𝔽2)11yescharacteristic
173Dic113—21no—
174Dic113—21no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178C2×C113—42no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—22no—
183D113—41no—
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#478D11311yescharacteristic, complemented
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—2261no—
211#125C2×D11311yescharacteristic, complemented
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#107C2×D11311yescharacteristic, complemented
229#106—1131no—
230#106C2×D11311yescharacteristic, complemented
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#102C2×D11311yescharacteristic
241#102C2×D11311yescharacteristic
242C22⋊C8—1131no—
243C22⋊C8—1131no—
244C4×C8—1131no—
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—2261no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2262no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—21no—
259C22×C4—1131no—
260C22×C4—1131no—
261C22×C4—2261no—
262C22×C4—2261no—
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—2261no—
295C42—2261no—
296C42C22×D11311yescharacteristic
297C23—21no—
298C23—1131no—
299C23—1131no—
300C23—9041no—
301C23—4522no—
302C23—4522no—
303C23—2261no—
304Q8—2261no—
305Q8—2261no—
306Q8—2261no—
307Q8—2261no—
308D4—21no—
309D4—9041no—
310D4—4522no—
311D4—4522no—
312D4—2262no—
313D4—2261no—
314D4—2261no—
315D4#1426864812yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—4522no—
323C2×C4—4522no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11311yescharacteristic
332C2×C4D4×D11311yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2261no—
337C8—2261no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—1132no—
342C22—9044no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—2261no—
347C22—2261no—
348C22—2261no—
349C22—2261no—
350C22—2261no—
351C22C2×D4×D11311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4521no—
358C4—4521no—
359C4—4521no—
360C4—2261no—
361C4—2261no—
362C4C2×#1426864811yescharacteristic
363C4#1681366811yescharacteristic
364C2—42no—
365C2—9041no—
366C2—4521no—
367C2—2262no—
368C2#2029923911yescharacteristic
369C2#135×D11311yescharacteristic
370C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
prime radical#20299243C2
hypercenter#478D113
hypocenterC113#3296
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20299286C2semidirect
3. #20298955C2semidirect
4. #20298930C2semidirect
5. #20298925C2semidirect
6. #20298840C2semidirect
7. #20298828C2semidirect
8. #20298821C2semidirect
9. #20298761C2semidirect
10. #20298750C2semidirect
11. C4×#14268635C2semidirect
12. #20298663C2semidirect
13. #20298591C2semidirect
14. #102×D113C2semidirect
15. #478×C113C2semidirect
18. C2×Dic452C22semidirect
22. C2×C8×D113C22semidirect
30. #16813602C22semidirect
34. C4×Dic226C22semidirect
37. #16813580C22semidirect
40. #16813553C22semidirect
41. #16813547C22semidirect
42. #16813545C22semidirect
43. #16813545C22semidirect
44. #16813545C22semidirect
50. #16813534C22semidirect
51. C4×#11744751C22semidirect
52. #125×C113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. C4⋊C8×C113C22semidirect
186. C113#3296semidirect
192. #478D113semidirect
211. #125C2×D113semidirect
228. #107C2×D113semidirect
230. #106C2×D113semidirect
231. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992862
#202992432
#202989552
#202989302
#202989252
#202988402
#202988282
#202988212
#202987612
#202987502
C4×#142686352
#202986632
#202985912
#102×D1132
#478×C1132
#3296113