Finite Group Databasebeta

← #28402885

Subgroups — #28402885

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299306C211yesmaximal, characteristic, complemented
2#20299250C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298930C211yesmaximal, characteristic, complemented
5#20298926C211yesmaximal, characteristic, complemented
6#20298887C211yesmaximal, characteristic, complemented
7#20298855C211yesmaximal, characteristic, complemented
8#20298806C211yesmaximal, characteristic, complemented
9#20298759C211yesmaximal, characteristic, complemented
10#20298758C211yesmaximal, characteristic, complemented
11#20298683C211yesmaximal, characteristic, complemented
12#20298674C211yesmaximal, characteristic, complemented
13#20298600C211yesmaximal, characteristic, complemented
14#20298598C211yesmaximal, characteristic, complemented
15#470×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813612—21no—
24#16813607—21no—
25#16813604—21no—
26#16813602—21no—
27#16813602C2211yescharacteristic
28#16813599—21no—
29#16813598C2211yescharacteristic
30#16813595—21no—
31Q8×Dic113C2211yescharacteristic
32#16813584C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813582—21no—
35C2×C4⋊Dic113C2211yescharacteristic
36C4⋊C4×D113—21no—
37C4⋊C4×D113C2211yescharacteristic
38#16813553C2211yescharacteristic
39#16813553C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61#14268647—22no—
62#14268647—41no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113D411yescharacteristic
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268637—41no—
76#14268634—22no—
77#14268630—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113—21no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626D411yescharacteristic
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624D411yescharacteristic
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101Q16×C113—41no—
102M16×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113—21no—
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—22no—
127C22⋊D113—42no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—81no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—21no—
136D452—42no—
137D452#4112yes—
138C4×D113—21no—
139C4×D113—21no—
140C4×D113—42no—
141C4×D113—42no—
142C4×D113—42no—
143C4×D113—81no—
144Dic226—21no—
145Dic226—21no—
146Dic226—81no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113C22×D411yescharacteristic
155C2×D113—21no—
156C2×D113—22no—
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—41no—
160C2×D113—41no—
161C4×C113—21no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113H(5,𝔽2)11yescharacteristic
168Dic113—21no—
169Dic113—21no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173Dic113#13712yes—
174C2×C113—41no—
175C2×C113#54611yescharacteristic
176C2×C113C2×#13711yescharacteristic
177C2×C113#57711yescharacteristic
178D113—41no—
179D113—42no—
180#3331—1131nomaximal, Sylow
181C113#333111yescharacteristic, complemented, Sylow
182#554—1131no—
183#547—1131no—
184#487—1131no—
185#483—1131no—
186#483—1131no—
187#476—1131no—
188#470—1131no—
189#470D11311yescharacteristic, complemented
190#462—1131no—
191#452—1131no—
192#452—1131no—
193C4×SD16—1131no—
194#436—1131no—
195#417—1131no—
196#417—1131no—
197C2×#41—1131no—
198C2×#41—1131no—
199C2×Q16—1131no—
200C2×Q16C2×D11311yescharacteristic
201C2×SD16—1131no—
202C2×M16—1131no—
203C2×M16C2×D11311yescharacteristic
204C4⋊Q8—1131no—
205C4⋊Q8—1131no—
206#125—2261no—
207#123—2261no—
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212C22⋊Q8—2261no—
213C22⋊Q8C2×D11311yescharacteristic
214C22⋊Q8C2×D11311yescharacteristic
215#121—2261no—
216C4×Q8—1131no—
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—2261no—
220C2×C4⋊C4—1131no—
221C2×C4⋊C4—1131no—
222C2×C4⋊C4—2261no—
223#106—1131no—
224#106—1131no—
225#106C2×D11311yescharacteristic
226C4⋊C8—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103C2×D11311yescharacteristic
233#103C2×D11311yescharacteristic
234#102—1131no—
235#102—1131no—
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239C4×C8—1131no—
240#41—4521no—
241#41—4521no—
242#41—2262no—
243#41—2262no—
244C2×Q8—1131no—
245C2×Q8—2261no—
246C2×Q8C22×D11311yescharacteristic
247C2×Q8C22×D11311yescharacteristic
248C2×D4—1131no—
249C2×D4—1131no—
250C2×D4—2261no—
251C2×D4—2261no—
252C22×C4—1131no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4C22×D11311yescharacteristic
259Q16—41no—
260Q16—4521no—
261SD16—2262no—
262M16—41no—
263M16—4521no—
264C2×C8—1131no—
265C2×C8—1131no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—1131no—
271C4⋊C4—1131no—
272C4⋊C4—1131no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4C22×D11311yescharacteristic
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1131no—
286C22⋊C4—1131no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C42—1131no—
291C42—2261no—
292C23—1131no—
293C23—2261no—
294C23D4×D11311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—9041no—
300Q8—2261no—
301Q8—2261no—
302D4—1132no—
303D4—4522no—
304D4—4522no—
305D4—2262no—
306D4—2261no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—9041no—
317C2×C4—9041no—
318C2×C4—4522no—
319C2×C4—4522no—
320C2×C4—4522no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4D4×D11311yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2261no—
331C8—2261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—4521no—
336C22—4521no—
337C22—2261no—
338C22—2261no—
339C22—2262no—
340C22—2261no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1132no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—2261no—
352C4—2261no—
353C4#41×D11311yescharacteristic
354C4#1681366711yescharacteristic
355C2—41no—
356C2—4522no—
357C2—4521no—
358C2#2029923711yescharacteristic
359C2#137×D11311yescharacteristic
360C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radical#20299250C2
hypercenter#470D113
hypocenterC113#3331
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20299306C2semidirect
3. #20298947C2semidirect
4. #20298930C2semidirect
5. #20298926C2semidirect
6. #20298887C2semidirect
7. #20298855C2semidirect
8. #20298806C2semidirect
9. #20298759C2semidirect
10. #20298758C2semidirect
11. #20298683C2semidirect
12. #20298674C2semidirect
13. #20298600C2semidirect
14. #20298598C2semidirect
15. #470×C113C2semidirect
181. C113#3331semidirect
189. #470D113semidirect

Maximal subgroups

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

subgroupindex
#202993062
#202992502
#202989472
#202989302
#202989262
#202988872
#202988552
#202988062
#202987592
#202987582
#202986832
#202986742
#202986002
#202985982
#470×C1132
#3331113