Finite Group Databasebeta

← #28403154

Subgroups — #28403154

Order 14464.

374 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#20299316C211yesmaximal, characteristic, complemented
2#20299249C211yesmaximal, characteristic
3#20299002C211yesmaximal, characteristic, complemented
4#20298935C211yesmaximal, characteristic, complemented
5#20298933C211yesmaximal, characteristic, complemented
6#20298924C211yesmaximal, characteristic, complemented
7#20298922C211yesmaximal, characteristic, complemented
8#20298882C211yesmaximal, characteristic, complemented
9#20298877C211yesmaximal, characteristic, complemented
10#20298845C211yesmaximal, characteristic, complemented
11#20298844C211yesmaximal, characteristic, complemented
12#20298685C211yesmaximal, characteristic, complemented
13#20298674C211yesmaximal, characteristic, complemented
14#20298637C211yesmaximal, characteristic, complemented
15#428×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×#14268636C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813616—21no—
22#16813615—21no—
23#16813608—21no—
24#16813607—21no—
25#16813605—21no—
26#16813602C2211yescharacteristic
27#16813601C2211yescharacteristic
28#16813600—21no—
29#16813597C2211yescharacteristic
30#16813596C2211yescharacteristic
31C4×Dic226—21no—
32#16813587C2211yescharacteristic
33#16813584C2211yescharacteristic
34C4×C22⋊D113C2211yescharacteristic
35#16813580C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×M16×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic
59#14268647—44no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113D411yescharacteristic
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113C2311yescharacteristic
70#14268636—22no—
71#14268630—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84C22⋊Dic113D411yescharacteristic
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113C2311yescharacteristic
94C22×C4×C113—21no—
95C22×C4×C113C2311yescharacteristic
96M16×C113—22no—
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C42×C113—21no—
106C23×C113C2×D411yescharacteristic
107C22×D113—21no—
108C22×D113C2×D411yescharacteristic
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—42no—
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—22no—
119C22⋊D113—42no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126D452—21no—
127D452—21no—
128D452—42no—
129C4×D113—21no—
130C4×D113—21no—
131C4×D113—42no—
132C4×D113—42no—
133Dic226—21no—
134Dic226—21no—
135Dic226—42no—
136Dic226—42no—
137C8×C113—21no—
138C8×C113#4112yescomplemented
139#11744751—21no—
140#11744751—21no—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113C22×D411yescharacteristic
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—21no—
148C2×D113—41no—
149C2×D113—41no—
150C2×D113—41no—
151C4×C113—21no—
152C4×C113—41no—
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—
163Dic113AGL(1,ℤ/8)12yes—
164C2×C113—41no—
165C2×C113#54711yescharacteristic
166C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C113#57811yescharacteristic
168D113—41no—
169D113—81no—
170#3353—1131nomaximal, Sylow
171C113#335311yescharacteristic, complemented, Sylow
172#556—1131no—
173#547—1131no—
174#500—1131no—
175#484—1131no—
176#484—1131no—
177#482—1131no—
178#482—1131no—
179#475—1131no—
180#474—1131no—
181#468—1131no—
182#468—1131no—
183C4×SD16—1131no—
184#436—1131no—
185#428—1131no—
186#428D11311yescharacteristic, complemented
187C2×#41—2261no—
188C2×SD16—1131no—
189C2×M16—1131no—
190C2×M16C2×D11311yescharacteristic
191C4⋊Q8—1131no—
192C4⋊Q8—1131no—
193#126—2261no—
194#126—2261no—
195#124—2261no—
196#123—2261no—
197#123—2261no—
198C22⋊Q8—1131no—
199C22⋊Q8—1131no—
200C22⋊Q8—2261no—
201#121—1131no—
202#121—1131no—
203C4×Q8—1131no—
204C4×Q8—2261no—
205C4×D4—1131no—
206C4×D4—1131no—
207#117—1131no—
208#117C2×D11311yescharacteristic
209C2×C4⋊C4—1131no—
210C2×C4⋊C4C2×D11311yescharacteristic
211#107—1131no—
212#107—1131no—
213#107—1131no—
214#107—1131no—
215#107C2×D11311yescharacteristic
216#107C2×D11311yescharacteristic
217#106—1131no—
218#106C2×D11311yescharacteristic
219#106C2×D11311yescharacteristic
220C4⋊C8—1131no—
221#103—1131no—
222#103—1131no—
223#103—1131no—
224#102—1131no—
225#102—1131no—
226#102—1131no—
227C22⋊C8—1131no—
228C22⋊C8—1131no—
229C4×C8—1131no—
230#41—4524no—
231C2×Q8—1131no—
232C2×Q8—2261no—
233C2×Q8—2261no—
234C2×D4—1131no—
235C2×D4—1131no—
236C2×D4—2261no—
237C2×D4—2261no—
238C22×C4—21no—
239C22×C4—1131no—
240C22×C4—2261no—
241C22×C4—2261no—
242C22×C4C22×D11311yescharacteristic
243SD16—2262no—
244M16—22no—
245M16—2262no—
246C2×C8—1131no—
247C2×C8—1131no—
248C2×C8C22×D11311yescharacteristic
249C2×C8C22×D11311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—1131no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4C22×D11311yescharacteristic
261C4⋊C4C22×D11311yescharacteristic
262C4⋊C4C22×D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—1131no—
266C22⋊C4—1131no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C42—21no—
274C42—1131no—
275C42—2261no—
276C42—2261no—
277C23—1131no—
278C23—2261no—
279C23D4×D11311yescharacteristic
280Q8—4522no—
281Q8—4522no—
282Q8—2261no—
283Q8—2261no—
284D4—4522no—
285D4—4522no—
286D4—2262no—
287D4—2261no—
288D4—2261no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—4522no—
300C2×C4—4522no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4D4×D11311yescharacteristic
307C2×C4C23×D11311yescharacteristic
308C8—21no—
309C8—2261no—
310C8—2261no—
311C8#1426864712yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—4521no—
316C22—4521no—
317C22—4521no—
318C22—2261no—
319C22—2261no—
320C22—2261no—
321C22C2×D4×D11311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—1132no—
328C4—4521no—
329C4—4521no—
330C4—4521no—
331C4—2261no—
332C4—2261no—
333C4C2×#1426864711yescharacteristic
334C4#1681367011yescharacteristic
335C2—41no—
336C2—9041no—
337C2—4521no—
338C2#2029924911yescharacteristic
339C2AGL(1,ℤ/8)×D11311yescharacteristic
340C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#428×C113C2
socleC22×C113C22×D4
prime radical#20299249C2
hypercenter#428D113
hypocenterC113#3353
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #20299316C2semidirect
3. #20299002C2semidirect
4. #20298935C2semidirect
5. #20298933C2semidirect
6. #20298924C2semidirect
7. #20298922C2semidirect
8. #20298882C2semidirect
9. #20298877C2semidirect
10. #20298845C2semidirect
11. #20298844C2semidirect
12. #20298685C2semidirect
13. #20298674C2semidirect
14. #20298637C2semidirect
15. #428×C113C2semidirect
138. C8×C113#41semidirect
171. C113#3353semidirect
186. #428D113semidirect
311. C8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202993162
#202992492
#202990022
#202989352
#202989332
#202989242
#202989222
#202988822
#202988772
#202988452
#202988442
#202986852
#202986742
#202986372
#428×C1132
#3353113