Finite Group Databasebeta

← #28400723

Subgroups — #28400723

Order 14464.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299145C211yesmaximal, characteristic, complemented
2C4×#14268648C211yesmaximal, characteristic, complemented
3#20298925C211yesmaximal, characteristic, complemented
4#20298921C211yesmaximal, characteristic, complemented
5#20298881C211yesmaximal, characteristic, complemented
6#20298877C211yesmaximal, characteristic, complemented
7#20298796C211yesmaximal, characteristic, complemented
8#20298792C211yesmaximal, characteristic, complemented
9#20298746C211yesmaximal, characteristic, complemented
10#20298742C211yesmaximal, characteristic, complemented
11#20298711C211yesmaximal, characteristic, complemented
12#20298708C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298653C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647—21no—
18C2×#14268634C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813618C2211yescharacteristic
23#16813608—21no—
24#16813597C2211yescharacteristic
25#16813595—21no—
26#16813593C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic
28C4×D452—21no—
29C4×D452C2211yescharacteristic
30C4×D452C2211yescharacteristic
31#16813584—21no—
32#16813584C2211yescharacteristic
33C4×C22⋊D113—21no—
34#16813580—21no—
35#16813580C2211yescharacteristic
36C42×D113—21no—
37C42×D113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—22no—
61#14268647—44no—
62C2×Dic226—21no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113D411yescharacteristic
75C2×C4×D113D411yescharacteristic
76C2×C4×D113C2311yescharacteristic
77#14268634—22no—
78D904—22no—
79#14268632—22no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100SD16×C113—22no—
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C42×C113C2311yescharacteristic
109C23×C113—21no—
110C22×D113—21no—
111C22×D113—21no—
112C22×D113C2×D411yescharacteristic
113Q8×C113—21no—
114Q8×C113#4112yescomplemented
115D4×C113—21no—
116D4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—42no—
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—42no—
125C22⋊D113—42no—
126C22⋊D113—42no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—24no—
133D452—21no—
134D452—21no—
135D452—21no—
136D452—42no—
137D452#4112yescomplemented
138C4×D113—24no—
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—22no—
142C4×D113—41no—
143C4×D113—42no—
144C4×D113—42no—
145C4×D113—42no—
146Dic226—42no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—21no—
156C2×D113—22no—
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C4×C113—22no—
165C4×C113—21no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113C2×#4111yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—41no—
174Dic113—41no—
175Dic113AGL(1,ℤ/8)12yes—
176C2×C113—81no—
177C2×C113#52511yescharacteristic
178C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C113#57511yescharacteristic
180D113—41no—
181D113—42no—
182D113—81no—
183#3115—1131nomaximal, Sylow
184C113#311511yescharacteristic, complemented, Sylow
185#532—1131no—
186C4×#41—1131no—
187#482—1131no—
188#482—1131no—
189#475—1131no—
190#474—1131no—
191#460—1131no—
192#459—1131no—
193#449—1131no—
194#449—1131no—
195#442—1131no—
196#442—1131no—
197#440—1131no—
198#440D11311yescharacteristic, complemented
199#432—1131no—
200C2×#41—1131no—
201C2×#41—2261no—
202C2×SD16—1131no—
203C2×SD16C2×D11311yescharacteristic
204C2×D8—1131no—
205C2×D8—1131no—
206C4⋊Q8—1131no—
207#127—1131no—
208#124—2261no—
209#121—1131no—
210#121—1131no—
211#121—2261no—
212C4×Q8—1131no—
213C4×Q8C2×D11311yescharacteristic
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—1131no—
217C4×D4—2261no—
218C4×D4—2261no—
219C4×D4—2261no—
220C4×D4C2×D11311yescharacteristic
221#117—1131no—
222#117—2261no—
223C2×C42—1131no—
224C2×C42—2261no—
225#107—1131no—
226#107C2×D11311yescharacteristic
227#106—1131no—
228#106—1131no—
229C4⋊C8—1131no—
230C4⋊C8—1131no—
231#103—1131no—
232#103C2×D11311yescharacteristic
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102—1131no—
237#102—1131no—
238#102C2×D11311yescharacteristic
239C22⋊C8—1131no—
240C22⋊C8—1131no—
241#97—1131no—
242#97C2×D11311yescharacteristic
243#41—4524no—
244#41—2262no—
245#41—2262no—
246C2×Q8—2261no—
247C2×Q8C22×D11311yescharacteristic
248C2×D4—1131no—
249C2×D4—1131no—
250C2×D4—2261no—
251C2×D4—2261no—
252C2×D4—2261no—
253C2×D4—2261no—
254C2×D4—2261no—
255C2×D4C22×D11311yescharacteristic
256C22×C4—21no—
257C22×C4—1131no—
258C22×C4—1131no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4—2261no—
264SD16—22no—
265SD16—2262no—
266D8—2262no—
267D8—2262no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8C22×D11311yescharacteristic
271C2×C8C22×D11311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4C22×D11311yescharacteristic
278C4⋊C4C22×D11311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—1131no—
288C42—1131no—
289C42—1131no—
290C42—2261no—
291C42—2261no—
292C42C22×D11311yescharacteristic
293C23—21no—
294C23—1131no—
295C23—2261no—
296C23—2261no—
297Q8—21no—
298Q8—4522no—
299Q8#1426864712yescomplemented
300D4—21no—
301D4—21no—
302D4—1132no—
303D4—4522no—
304D4—4522no—
305D4—4522no—
306D4—4522no—
307D4—2264no—
308D4—2261no—
309D4—2261no—
310D4—2261no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—1131no—
318C2×C4—4522no—
319C2×C4—4522no—
320C2×C4—4521no—
321C2×C4—4522no—
322C2×C4—2262no—
323C2×C4—2264no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4D4×D11311yescharacteristic
329C2×C4D4×D11311yescharacteristic
330C2×C4C23×D11311yescharacteristic
331C8—21no—
332C8—21no—
333C8—2261no—
334C8—2261no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—4521no—
339C22—4521no—
340C22—4521no—
341C22—4521no—
342C22—4521no—
343C22—2262no—
344C22—2261no—
345C22—2261no—
346C22—2261no—
347C22C2×D4×D11311yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—1132no—
354C4—4521no—
355C4—4521no—
356C4—2261no—
357C4—2261no—
358C4#41×D11311yescharacteristic
359C4C2×#1426864711yescharacteristic
360C2—81no—
361C2—9041no—
362C2—4522no—
363C2—4521no—
364C2#2029910711yescharacteristic
365C2AGL(1,ℤ/8)×D11311yescharacteristic
366C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
hypercenter#440D113
hypocenterC113#3115
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. #20299145C2semidirect
2. C4×#14268648C2semidirect
3. #20298925C2semidirect
4. #20298921C2semidirect
5. #20298881C2semidirect
6. #20298877C2semidirect
7. #20298796C2semidirect
8. #20298792C2semidirect
9. #20298746C2semidirect
10. #20298742C2semidirect
11. #20298711C2semidirect
12. #20298708C2semidirect
13. #20298696C2semidirect
14. #20298653C2semidirect
15. #440×C113C2semidirect
114. Q8×C113#41semidirect
137. D452#41semidirect
184. C113#3115semidirect
198. #440D113semidirect
299. Q8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202991452
C4×#142686482
#202989252
#202989212
#202988812
#202988772
#202987962
#202987922
#202987462
#202987422
#202987112
#202987082
#202986962
#202986532
#440×C1132
#3115113