Finite Group Databasebeta

← #28401621

Subgroups — #28401621

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299199C211yesmaximal, characteristic, complemented
2#20299166C211yesmaximal, characteristic, complemented
3#20298984C211yesmaximal, characteristic, complemented
4#20298973C211yesmaximal, characteristic, complemented
5#20298961C211yesmaximal, characteristic, complemented
6#20298954C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298794C211yesmaximal, characteristic, complemented
9#20298793C211yesmaximal, characteristic, complemented
10#20298746C211yesmaximal, characteristic, complemented
11#20298742C211yesmaximal, characteristic, complemented
12#20298733C211yesmaximal, characteristic, complemented
13#20298730C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268634C2211yescharacteristic, complemented
19C2×D904C2211yescharacteristic
20C2×D904C2211yescharacteristic, complemented
21C2×#14268632C2211yescharacteristic
22C2×#14268632C2211yescharacteristic
23C2×#14268632C2211yescharacteristic, complemented
24#16813619C2211yescharacteristic
25#16813618C2211yescharacteristic
26#16813618C2211yescharacteristic, complemented
27#16813613C2211yescharacteristic, complemented
28#16813611C2211yescharacteristic
29#16813605—21no—
30#16813604—21no—
31#16813597C2211yescharacteristic
32#16813596—21no—
33#16813595—21no—
34#16813595—21no—
35#16813595—21no—
36#16813593C2211yescharacteristic
37#16813592—21no—
38#16813592—21no—
39C4×D452C2211yescharacteristic, complemented
40#16813579C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic, complemented
53C2×D8×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60#14268648—41no—
61#14268648—41no—
62C2×D452—21no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75D4×D113—41no—
76D4×D113—41no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113C2311yescharacteristic
80#14268634—41no—
81D904—41no—
82D904—41no—
83#14268632—41no—
84#14268632—41no—
85#14268632—41no—
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C4⋊Dic113—21no—
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91#14268626D411yescharacteristic
92#14268626D411yescharacteristic
93C22⋊Dic113—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624D411yescharacteristic
99#14268624D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113—21no—
105SD16×C113—41no—
106D8×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C23×C113—21no—
116C22×D113—21no—
117C22×D113—21no—
118C22×D113—21no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122C22×D113C2×D411yescharacteristic
123Q8×C113—21no—
124Q8×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—81no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—42no—
136C22⋊D113—81no—
137C22⋊D113—81no—
138C22⋊D113—81no—
139C22⋊D113—81no—
140C22⋊D113—81no—
141C2×Dic113—21no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145D452—21no—
146D452—21no—
147D452—21no—
148D452—21no—
149D452—21no—
150D452—21no—
151D452—42no—
152D452—81no—
153D452—81no—
154D452—81no—
155C4×D113—21no—
156C4×D113—21no—
157C4×D113—42no—
158C4×D113—81no—
159C8×C113—21no—
160C8×C113—21no—
161#11744751—21no—
162#11744751—21no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113C22×D411yescharacteristic
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—84no—
183C4×C113—21no—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113—41no—
187C4×C113H(5,𝔽2)11yescharacteristic
188C4×C113H(5,𝔽2)11yescharacteristic
189Dic113—21no—
190Dic113—21no—
191Dic113—21no—
192Dic113—41no—
193C2×C113—81no—
194C2×C113—81no—
195C2×C113#53511yescharacteristic
196C2×C113#57611yescharacteristic
197C2×C113#57611yescharacteristic
198D113—41no—
199D113—81no—
200D113—81no—
201D113—81no—
202#3220—1131nomaximal, Sylow
203C113#322011yescharacteristic, complemented, Sylow
204#540—1131no—
205#535—1131no—
206#496—1131no—
207#493—1131no—
208#490—1131no—
209#488—1131no—
210#463—1131no—
211#463D11311yescharacteristic, complemented
212#459—1131no—
213#459—1131no—
214#449—1131no—
215#449—1131no—
216#447—1131no—
217#447—1131no—
218#433—1131no—
219C2×#41—1131no—
220C22×D4—1131no—
221C2×SD16—1131no—
222C2×SD16C2×D11311yescharacteristic, complemented
223C2×D8—1131no—
224C2×D8—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×D8—1131no—
228C2×D8C2×D11311yescharacteristic
229#127—1131no—
230#127—1131no—
231#127—1131no—
232#125—1131no—
233#124—1131no—
234#124C2×D11311yescharacteristic
235#123—2261no—
236#123—2261no—
237#121—1131no—
238#121—1131no—
239#121—2261no—
240#121—2261no—
241#121—2261no—
242#121—2261no—
243#120—2261no—
244#120—2261no—
245C4×D4—1131no—
246C4×D4C2×D11311yescharacteristic, complemented
247#117—1131no—
248C4⋊C8—1131no—
249C4⋊C8C2×D11311yescharacteristic, complemented
250#103—1131no—
251#103C2×D11311yescharacteristic, complemented
252#102—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102C2×D11311yescharacteristic
258C22⋊C8—1131no—
259C22⋊C8—1131no—
260#97—1131no—
261C4×C8—1131no—
262C24—2261no—
263#41—4521no—
264#41—4521no—
265C2×Q8C22×D11311yescharacteristic
266C2×D4—1131no—
267C2×D4—1131no—
268C2×D4—1131no—
269C2×D4—4521no—
270C2×D4—4521no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4C22×D11311yescharacteristic
282C2×D4C22×D11311yescharacteristic
283C22×C4—21no—
284C22×C4—1131no—
285C22×C4—2261no—
286C22×C4—2261no—
287SD16—41no—
288SD16—4521no—
289D8—41no—
290D8—4521no—
291D8—4521no—
292D8—4521no—
293D8—4521no—
294D8—4521no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8C22×D11311yescharacteristic
298C2×C8C22×D11311yescharacteristic
299C4⋊C4—1131no—
300C4⋊C4—1131no—
301C4⋊C4—1131no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4C22×D11311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—1131no—
309C22⋊C4—1131no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C42—1131no—
316C42C22×D11311yescharacteristic
317C23—21no—
318C23—21no—
319C23—1131no—
320C23—9041no—
321C23—9041no—
322C23—4522no—
323C23—2261no—
324C23—2261no—
325C23—2261no—
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—9041no—
333D4—9041no—
334D4—9041no—
335D4—9041no—
336D4—9041no—
337D4—9041no—
338D4—9041no—
339D4—9041no—
340D4—4522no—
341D4—4522no—
342D4—2261no—
343D4—2261no—
344D4—2261no—
345D4—2261no—
346D4—2261no—
347D4—2261no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—1131no—
352C2×C4—1131no—
353C2×C4—1131no—
354C2×C4—9041no—
355C2×C4—4522no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4D4×D11311yescharacteristic
360C2×C4D4×D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—21no—
363C8—21no—
364C8—2261no—
365C8—2261no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—9044no—
373C22—4521no—
374C22—4521no—
375C22—4521no—
376C22—4521no—
377C22—4521no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—4521no—
382C22—2261no—
383C22—2261no—
384C22—2261no—
385C22C2×D4×D11311yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—4521no—
391C4—2261no—
392C4—2261no—
393C4—2261no—
394C4#1681366711yescharacteristic
395C4#1681366811yescharacteristic
396C2—81no—
397C2—81no—
398C2—9041no—
399C2—9041no—
400C2—9041no—
401C2—4521no—
402C2#2029916411yescharacteristic
403C2#2029940011yescharacteristic
404C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
hypercenter#463D113
hypocenterC113#3220
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #20299199C2semidirect
2. #20299166C2semidirect
3. #20298984C2semidirect
4. #20298973C2semidirect
5. #20298961C2semidirect
6. #20298954C2semidirect
7. #20298810C2semidirect
8. #20298794C2semidirect
9. #20298793C2semidirect
10. #20298746C2semidirect
11. #20298742C2semidirect
12. #20298733C2semidirect
13. #20298730C2semidirect
14. #20298658C2semidirect
15. #463×C113C2semidirect
18. C2×#14268634C22semidirect
20. C2×D904C22semidirect
23. C2×#14268632C22semidirect
26. #16813618C22semidirect
27. #16813613C22semidirect
39. C4×D452C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813546C22semidirect
44. #16813544C22semidirect
47. #16813542C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
52. C2×SD16×C113C22semidirect
55. C4×D4×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #103×C113C22semidirect
203. C113#3220semidirect
211. #463D113semidirect
222. C2×SD16C2×D113semidirect
246. C4×D4C2×D113semidirect
249. C4⋊C8C2×D113semidirect
251. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991992
#202991662
#202989842
#202989732
#202989612
#202989542
#202988102
#202987942
#202987932
#202987462
#202987422
#202987332
#202987302
#202986582
#463×C1132
#3220113