Finite Group Databasebeta

← #28400927

Subgroups — #28400927

Order 14464.

404 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#20299228C211yesmaximal, characteristic, complemented
2#20299166C211yesmaximal, characteristic
3#20298964C211yesmaximal, characteristic, complemented
4#20298961C211yesmaximal, characteristic, complemented
5#20298959C211yesmaximal, characteristic, complemented
6#20298957C211yesmaximal, characteristic, complemented
7#20298954C211yesmaximal, characteristic, complemented
8#20298945C211yesmaximal, characteristic, complemented
9#20298943C211yesmaximal, characteristic, complemented
10#20298601C211yesmaximal, characteristic, complemented
11#20298598C211yesmaximal, characteristic, complemented
12#20298593C211yesmaximal, characteristic, complemented
13#102×D113C211yesmaximal, characteristic, complemented
14#20298552C211yesmaximal, characteristic, complemented
15#488×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813622C2211yescharacteristic, complemented
21#16813621—21no—
22#16813621C2211yescharacteristic, complemented
23#16813619C2211yescharacteristic
24#16813618C2211yescharacteristic
25#16813613C2211yescharacteristic, complemented
26#16813612—21no—
27#16813611C2211yescharacteristic
28#16813602—21no—
29#16813600—21no—
30#16813595—21no—
31#16813595—21no—
32#16813592—21no—
33#16813592—21no—
34#16813580C2211yescharacteristic
35#16813579C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813546C2211yescharacteristic, complemented
38#16813546C2211yescharacteristic, complemented
39#16813544C2211yescharacteristic
40#16813544C2211yescharacteristic
41#16813544C2211yescharacteristic, complemented
42#16813544C2211yescharacteristic, complemented
43#16813543C2211yescharacteristic
44#16813543C2211yescharacteristic
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic, complemented
48#16813542C2211yescharacteristic, complemented
49#16813533C2211yescharacteristic, complemented
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52#125×C113C2211yescharacteristic, complemented
53#124×C113C2211yescharacteristic
54#103×C113C2211yescharacteristic, complemented
55#103×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268648—22no—
61#14268648—22no—
62C2×Dic226—21no—
63C2×Dic226—21no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72D4×D113—22no—
73D4×D113—22no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77#14268630—22no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—22no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89#14268626D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—21no—
111C22×D113—42no—
112C22×D113—81no—
113C22×D113—81no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—42no—
126C22⋊D113—81no—
127C22⋊D113—81no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133D452—21no—
134D452—21no—
135D452—21no—
136D452—21no—
137D452—42no—
138D452—81no—
139D452—81no—
140C4×D113—42no—
141C4×D113—81no—
142C4×D113#4112yes—
143C4×D113#4112yes—
144Dic226—81no—
145Dic226—81no—
146C8×C113—21no—
147C8×C113—21no—
148#11744751—21no—
149#11744751—21no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113C22×D411yescharacteristic
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—84no—
163C2×D113#12412yes—
164C4×C113—21no—
165C4×C113—21no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113C2×#4111yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—41no—
174Dic113—41no—
175Dic113#12412yes—
176C2×C113—81no—
177C2×C113C2×#12411yescharacteristic
178C2×C113#57611yescharacteristic
179C2×C113#57711yescharacteristic
180D113—22no—
181D113—81no—
182D113—81no—
183#3136—1131nomaximal, Sylow
184C113#313611yescharacteristic, complemented, Sylow
185#544—1131no—
186#535—1131no—
187#490—1131no—
188#490—1131no—
189#489—1131no—
190#489—1131no—
191#488—1131no—
192#488D11311yescharacteristic, complemented
193#486—1131no—
194#486—1131no—
195#418—1131no—
196#417—1131no—
197#416—1131no—
198C2×#102—1131no—
199#405—1131no—
200C2×#41—1131no—
201C22×D4—1131no—
202C2×M16—1131no—
203C22×C8—1131no—
204C4⋊Q8—1131no—
205C4⋊Q8—1131no—
206C4⋊Q8—2261no—
207#127—1131no—
208#127—1131no—
209#125—1131no—
210#125—2261no—
211#125C2×D11311yescharacteristic, complemented
212#124—1131no—
213#124C2×D11311yescharacteristic
214C22⋊Q8—2261no—
215C22⋊Q8—2261no—
216#121—2261no—
217#121—2261no—
218#120—2261no—
219#120—2261no—
220#117—1131no—
221#117—1131no—
222C2×C4⋊C4—1131no—
223#103—1131no—
224#103—1131no—
225#103C2×D11311yescharacteristic, complemented
226#103C2×D11311yescharacteristic, complemented
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102—1131no—
237#102C2×D11311yescharacteristic
238#102C2×D11311yescharacteristic
239#97—1131no—
240#97—1131no—
241C4×C8—1131no—
242C4×C8C2×D11311yescharacteristic, complemented
243C24—2261no—
244#41—2262no—
245#41—2262no—
246C2×Q8—2261no—
247C2×Q8—2261no—
248C2×Q8C22×D11311yescharacteristic
249C2×D4—1131no—
250C2×D4—1131no—
251C2×D4—2261no—
252C2×D4—2262no—
253C2×D4—2262no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4—2261no—
259C2×D4C22×D11311yescharacteristic
260C22×C4—1131no—
261C22×C4—2261no—
262C22×C4—2261no—
263M16—2262no—
264C2×C8—1131no—
265C2×C8—1131no—
266C2×C8—2262no—
267C2×C8C22×D11311yescharacteristic
268C2×C8C22×D11311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—1131no—
272C4⋊C4—1131no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4C22×D11311yescharacteristic
281C4⋊C4C22×D11311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1131no—
285C22⋊C4—1131no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C42—1131no—
290C42—2261no—
291C42C22×D11311yescharacteristic
292C23—21no—
293C23—1131no—
294C23—9041no—
295C23—9041no—
296C23—4522no—
297C23—2261no—
298C23—2261no—
299Q8—21no—
300Q8—21no—
301Q8—9041no—
302Q8—9041no—
303D4—21no—
304D4—21no—
305D4—9041no—
306D4—9041no—
307D4—9041no—
308D4—9041no—
309D4—4522no—
310D4—4522no—
311D4—2261no—
312D4—2261no—
313D4—2261no—
314D4—2261no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—1131no—
319C2×C4—1132no—
320C2×C4—1132no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—9041no—
324C2×C4—4522no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4D4×D11311yescharacteristic
328C2×C4D4×D11311yescharacteristic
329C2×C4C23×D11311yescharacteristic
330C8—21no—
331C8—21no—
332C8—2261no—
333C8—2261no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—1132no—
338C22—9044no—
339C22—4521no—
340C22—4521no—
341C22—4521no—
342C22—4521no—
343C22—4521no—
344C22—4521no—
345C22—2261no—
346C22—2261no—
347C22C2×D4×D11311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1132no—
354C4—4521no—
355C4—4521no—
356C4—2261no—
357C4—2261no—
358C4#41×D11311yescharacteristic
359C4#41×D11311yescharacteristic
360C2—81no—
361C2—9041no—
362C2—9041no—
363C2—2262no—
364C2#124×D11311yescharacteristic
365C2#2029940011yescharacteristic
366C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radical#20299166C2
hypercenter#488D113
hypocenterC113#3136
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299228C2semidirect
3. #20298964C2semidirect
4. #20298961C2semidirect
5. #20298959C2semidirect
6. #20298957C2semidirect
7. #20298954C2semidirect
8. #20298945C2semidirect
9. #20298943C2semidirect
10. #20298601C2semidirect
11. #20298598C2semidirect
12. #20298593C2semidirect
13. #102×D113C2semidirect
14. #20298552C2semidirect
15. #488×C113C2semidirect
20. #16813622C22semidirect
22. #16813621C22semidirect
25. #16813613C22semidirect
37. #16813546C22semidirect
38. #16813546C22semidirect
41. #16813544C22semidirect
42. #16813544C22semidirect
47. #16813542C22semidirect
48. #16813542C22semidirect
49. #16813533C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
52. #125×C113C22semidirect
54. #103×C113C22semidirect
55. #103×C113C22semidirect
58. C4×C8×C113C22semidirect
184. C113#3136semidirect
192. #488D113semidirect
211. #125C2×D113semidirect
225. #103C2×D113semidirect
226. #103C2×D113semidirect
242. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992282
#202991662
#202989642
#202989612
#202989592
#202989572
#202989542
#202989452
#202989432
#202986012
#202985982
#202985932
#102×D1132
#202985522
#488×C1132
#3136113