Finite Group Databasebeta

← #28403019

Subgroups — #28403019

Order 14464.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299289C211yesmaximal, characteristic, complemented
2#20299253C211yesmaximal, characteristic
3#20299007C211yesmaximal, characteristic, complemented
4#20298932C211yesmaximal, characteristic, complemented
5#20298927C211yesmaximal, characteristic, complemented
6#20298921C211yesmaximal, characteristic, complemented
7#20298910C211yesmaximal, characteristic, complemented
8#20298898C211yesmaximal, characteristic, complemented
9#20298893C211yesmaximal, characteristic, complemented
10#20298841C211yesmaximal, characteristic, complemented
11#20298824C211yesmaximal, characteristic, complemented
12#20298671C211yesmaximal, characteristic, complemented
13#20298639C211yesmaximal, characteristic, complemented
14#107×D113C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×#14268630C2211yescharacteristic
18C2×C8×D113C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813616—21no—
21#16813614C2211yescharacteristic
22#16813612—21no—
23#16813607—21no—
24#16813604—21no—
25#16813604—21no—
26#16813601—21no—
27#16813598C2211yescharacteristic
28#16813598C2211yescharacteristic
29#16813593C2211yescharacteristic
30#16813593C2211yescharacteristic
31C4×D452C2211yescharacteristic
32#16813580C2211yescharacteristic
33#16813579—21no—
34C4⋊C4×D113C2211yescharacteristic
35C4⋊C4×D113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813553C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268647—44no—
60C2×Dic226—21no—
61C2×D452D411yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68C2×C4×D113C2311yescharacteristic
69#14268630—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C8×D113—22no—
73C4⋊Dic113—21no—
74C4⋊Dic113D411yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C2×Q8×C113C2311yescharacteristic
95C2×D4×C113C2311yescharacteristic
96C22×C4×C113—21no—
97SD16×C113—22no—
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C42×C113—21no—
105C42×C113C2311yescharacteristic
106C23×C113—21no—
107C22×D113C2×D411yescharacteristic
108C22×D113C2×D411yescharacteristic
109Q8×C113—21no—
110Q8×C113—21no—
111D4×C113—21no—
112D4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—42no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C22⋊D113—42no—
121C22⋊D113—42no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128D452—22no—
129C4×D113—21no—
130C4×D113—21no—
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—42no—
134C4×D113—42no—
135C4×D113—42no—
136Dic226—42no—
137C8×C113—21no—
138C8×C113#4112yescomplemented
139#11744751—21no—
140#11744751—21no—
141C22×C113—41no—
142C22×C113—41no—
143C22×C113—41no—
144C22×C113C22×D411yescharacteristic
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—21no—
148C2×D113—21no—
149C2×D113—21no—
150C2×D113AGL(1,ℤ/8)12yes—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113C2×#4111yescharacteristic
157C4×C1132−1+411yescharacteristic
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164C2×C113—81no—
165C2×C113#54711yescharacteristic
166C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C113#57811yescharacteristic
168D113—22no—
169D113—41no—
170#3343—1131nomaximal, Sylow
171C113#334311yescharacteristic, complemented, Sylow
172#552—1131no—
173#547—1131no—
174#501—1131no—
175#484—1131no—
176#483—1131no—
177#482—1131no—
178#480—1131no—
179#478—1131no—
180#477—1131no—
181#468—1131no—
182#465—1131no—
183#440D11311yescharacteristic, complemented
184#435—1131no—
185#428—1131no—
186C2×#107—1131no—
187C2×#41—2261no—
188C2×SD16C2×D11311yescharacteristic
189C2×M16—1131no—
190C22×C8—1131no—
191C4⋊Q8—1131no—
192#126—2261no—
193#125—1131no—
194#125—2261no—
195#123—2261no—
196#123—2261no—
197#123—2261no—
198C22⋊Q8—1131no—
199C22⋊Q8—1131no—
200C22⋊Q8—2261no—
201#121—1131no—
202#121—1131no—
203C4×Q8C2×D11311yescharacteristic
204C4×D4—1131no—
205C4×D4C2×D11311yescharacteristic
206#117—1131no—
207#117—2261no—
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—1131no—
210C2×C4⋊C4—1131no—
211#107—1131no—
212#107—1131no—
213#107—1131no—
214#107—1131no—
215#107—1131no—
216#107C2×D11311yescharacteristic
217#106—1131no—
218#106—1131no—
219#106—1131no—
220C4⋊C8—1131no—
221#103—1131no—
222#103—1131no—
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102—1131no—
226#102C2×D11311yescharacteristic
227C22⋊C8—1131no—
228C22⋊C8—1131no—
229#97C2×D11311yescharacteristic
230#41—4524no—
231C2×Q8—2261no—
232C2×Q8C22×D11311yescharacteristic
233C2×D4—1131no—
234C2×D4—2261no—
235C2×D4—2261no—
236C2×D4C22×D11311yescharacteristic
237C22×C4—21no—
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—2261no—
241C22×C4—2261no—
242C22×C4—2261no—
243SD16—22no—
244M16—2262no—
245C2×C8—1131no—
246C2×C8—1131no—
247C2×C8—2262no—
248C2×C8C22×D11311yescharacteristic
249C2×C8C22×D11311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—1131no—
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⋊C4—2261no—
264C4⋊C4C22×D11311yescharacteristic
265C4⋊C4C22×D11311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—1131no—
268C22⋊C4—1131no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C42—21no—
275C42—2261no—
276C42C22×D11311yescharacteristic
277C23—21no—
278C23—1131no—
279C23—1131no—
280Q8—21no—
281Q8—21no—
282Q8—4522no—
283D4—21no—
284D4—21no—
285D4—4522no—
286D4—4522no—
287D4—2262no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—1131no—
293C2×C4—1131no—
294C2×C4—4522no—
295C2×C4—4522no—
296C2×C4—4522no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4D4×D11311yescharacteristic
306C2×C4D4×D11311yescharacteristic
307C2×C4C23×D11311yescharacteristic
308C8—21no—
309C8—2261no—
310C8—2261no—
311C8#1426864712yescomplemented
312C22—41no—
313C22—41no—
314C22—41no—
315C22—1132no—
316C22—2261no—
317C22—2261no—
318C22—2261no—
319C22—2261no—
320C22—2261no—
321C22C2×D4×D11311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—4521no—
328C4—4521no—
329C4—4521no—
330C4—4521no—
331C4—2261no—
332C4—2261no—
333C4C2×#1426864711yescharacteristic
334C4#1681366911yescharacteristic
335C2—81no—
336C2—4521no—
337C2—2262no—
338C2#2029925311yescharacteristic
339C2AGL(1,ℤ/8)×D11311yescharacteristic
340C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radical#20299253C2
hypercenter#440D113
hypocenterC113#3343
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #20299289C2semidirect
3. #20299007C2semidirect
4. #20298932C2semidirect
5. #20298927C2semidirect
6. #20298921C2semidirect
7. #20298910C2semidirect
8. #20298898C2semidirect
9. #20298893C2semidirect
10. #20298841C2semidirect
11. #20298824C2semidirect
12. #20298671C2semidirect
13. #20298639C2semidirect
14. #107×D113C2semidirect
15. #440×C113C2semidirect
138. C8×C113#41semidirect
171. C113#3343semidirect
183. #440D113semidirect
311. C8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202992892
#202992532
#202990072
#202989322
#202989272
#202989212
#202989102
#202988982
#202988932
#202988412
#202988242
#202986712
#202986392
#107×D1132
#440×C1132
#3343113