Finite Group Databasebeta

← #28402416

Subgroups — #28402416

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299289C211yesmaximal, characteristic, complemented
2#20299241C211yesmaximal, characteristic
3#20298952C211yesmaximal, characteristic, complemented
4#20298927C211yesmaximal, characteristic, complemented
5#20298920C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298836C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298759C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11C4×#14268634C211yesmaximal, characteristic, complemented
12#20298663C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic, complemented
21#16813616—21no—
22#16813614C2211yescharacteristic, complemented
23#16813612—21no—
24#16813607—21no—
25#16813604—21no—
26#16813598C2211yescharacteristic
27#16813598C2211yescharacteristic
28#16813598C2211yescharacteristic, complemented
29#16813595—21no—
30#16813593C2211yescharacteristic
31#16813592—21no—
32C4×D452C2211yescharacteristic
33C4×D452C2211yescharacteristic
34#16813580C2211yescharacteristic, complemented
35#16813579—21no—
36C4⋊C4×D113C2211yescharacteristic
37C22⋊C4×D113—21no—
38#16813556C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813546C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51C4×#11744751C2211yescharacteristic, complemented
52C2×Q16×C113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60#14268648—22no—
61#14268648—41no—
62C2×D452—21no—
63C2×D452D411yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67D4×D113—22no—
68D4×D113—41no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113C2311yescharacteristic
73C2×C4×D113C2311yescharacteristic
74#14268634—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C8×D113—41no—
78C8×D113—41no—
79C4⋊Dic113D411yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624D411yescharacteristic
96#14268624D411yescharacteristic
97C4×Dic113—21no—
98C2×Q8×C113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113C2311yescharacteristic
101Q16×C113—41no—
102SD16×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C22×D113—21no—
113C22×D113—42no—
114C22×D113—42no—
115C22×D113—81no—
116C22×D113C2×D411yescharacteristic
117C22×D113C2×D411yescharacteristic
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121Q8×C113—21no—
122D4×C113—21no—
123D4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—42no—
131C22⋊D113—81no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—22no—
138D452—21no—
139D452—42no—
140D452#4112yes—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—21no—
145C4×D113—42no—
146C4×D113—42no—
147C4×D113—81no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—22no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—84no—
165C2×D113#13512yes—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113C2×#4111yescharacteristic
172C4×C113H(5,𝔽2)11yescharacteristic
173Dic113—21no—
174Dic113—21no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178C2×C113—81no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—22no—
183D113—41no—
184D113—42no—
185#3296—1131nomaximal, Sylow
186C113#329611yescharacteristic, complemented, Sylow
187#552—1131no—
188#546—1131no—
189#488—1131no—
190#483—1131no—
191#482—1131no—
192#478—1131no—
193#467—1131no—
194#465—1131no—
195#464D11311yescharacteristic, complemented
196#452—1131no—
197#450—1131no—
198C4×SD16—1131no—
199C8×D4—1131no—
200#416—1131no—
201C2×#102—1131no—
202C2×#41—1131no—
203C22×D4—1131no—
204C2×Q16C2×D11311yescharacteristic, complemented
205C2×SD16—1131no—
206C2×SD16C2×D11311yescharacteristic
207C22×C8—1131no—
208C22×C8—1131no—
209#126—2261no—
210#125—1131no—
211#125—2261no—
212#124C2×D11311yescharacteristic
213#123—2261no—
214#123—2261no—
215C22⋊Q8—1131no—
216C22⋊Q8—1131no—
217C22⋊Q8—1131no—
218#121—1131no—
219#121—2261no—
220#120—2261no—
221C4×Q8C2×D11311yescharacteristic, complemented
222C4×D4—1131no—
223C4×D4—1131no—
224#117—1131no—
225#117—2261no—
226C2×C4⋊C4—1131no—
227C2×C22⋊C4—2261no—
228#107—1131no—
229#106—1131no—
230#106—1131no—
231C4⋊C8C2×D11311yescharacteristic, complemented
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103C2×D11311yescharacteristic, complemented
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102C2×D11311yescharacteristic
242C22⋊C8—1131no—
243C22⋊C8—1131no—
244C4×C8—1131no—
245C24—2261no—
246#41—4521no—
247#41—2262no—
248C2×Q8C22×D11311yescharacteristic
249C2×Q8C22×D11311yescharacteristic
250C2×D4—1131no—
251C2×D4—1131no—
252C2×D4—4521no—
253C2×D4—2261no—
254C2×D4—2261no—
255C2×D4—2262no—
256C2×D4—2261no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—1131no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263Q16—41no—
264SD16—41no—
265SD16—2262no—
266C2×C8—1131no—
267C2×C8—1131no—
268C2×C8—4521no—
269C2×C8—4521no—
270C2×C8C22×D11311yescharacteristic
271C2×C8C22×D11311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4C22×D11311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1131no—
287C22⋊C4—1131no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C42—21no—
295C42—2261no—
296C42C22×D11311yescharacteristic
297C23—21no—
298C23—1131no—
299C23—1131no—
300C23—9041no—
301C23—4522no—
302C23—4522no—
303C23—2261no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—1132no—
311D4—9041no—
312D4—4522no—
313D4—4522no—
314D4—2262no—
315D4—2261no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—9041no—
322C2×C4—4522no—
323C2×C4—4522no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11311yescharacteristic
332C2×C4D4×D11311yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2261no—
337C8—2261no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1132no—
342C22—9044no—
343C22—4521no—
344C22—4521no—
345C22—2261no—
346C22—2261no—
347C22—2262no—
348C22—2261no—
349C22—2261no—
350C22—2261no—
351C22C2×D4×D11311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4521no—
358C4—4521no—
359C4—4521no—
360C4—2261no—
361C4—2261no—
362C4#41×D11311yescharacteristic
363C4#1681366711yescharacteristic
364C2—81no—
365C2—4522no—
366C2—4521no—
367C2—2262no—
368C2#2029924511yescharacteristic
369C2#135×D11311yescharacteristic
370C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#20299241C2
hypercenter#464D113
hypocenterC113#3296
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299289C2semidirect
3. #20298952C2semidirect
4. #20298927C2semidirect
5. #20298920C2semidirect
6. #20298899C2semidirect
7. #20298836C2semidirect
8. #20298824C2semidirect
9. #20298759C2semidirect
10. #20298747C2semidirect
11. C4×#14268634C2semidirect
12. #20298663C2semidirect
13. #20298593C2semidirect
14. #102×D113C2semidirect
15. #464×C113C2semidirect
20. C2×C8×D113C22semidirect
22. #16813614C22semidirect
28. #16813598C22semidirect
34. #16813580C22semidirect
38. #16813556C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813546C22semidirect
42. #16813546C22semidirect
43. #16813546C22semidirect
50. #16813534C22semidirect
51. C4×#11744751C22semidirect
52. C2×Q16×C113C22semidirect
55. C4×Q8×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #103×C113C22semidirect
186. C113#3296semidirect
195. #464D113semidirect
204. C2×Q16C2×D113semidirect
221. C4×Q8C2×D113semidirect
231. C4⋊C8C2×D113semidirect
235. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992892
#202992412
#202989522
#202989272
#202989202
#202988992
#202988362
#202988242
#202987592
#202987472
C4×#142686342
#202986632
#202985932
#102×D1132
#464×C1132
#3296113