Finite Group Databasebeta

← #28402430

Subgroups — #28402430

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299300C211yesmaximal, characteristic, complemented
2#20299239C211yesmaximal, characteristic, complemented
3#20298954C211yesmaximal, characteristic, complemented
4#20298931C211yesmaximal, characteristic, complemented
5#20298924C211yesmaximal, characteristic, complemented
6#20298897C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298742C211yesmaximal, characteristic, complemented
10#20298731C211yesmaximal, characteristic, complemented
11#20298678C211yesmaximal, characteristic, complemented
12C8×C22⋊D113C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14C2×#16813544C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic, complemented
21#16813615—21no—
22#16813613C2211yescharacteristic, complemented
23#16813611C2211yescharacteristic
24#16813607—21no—
25#16813606—21no—
26#16813597—21no—
27#16813597C2211yescharacteristic
28#16813594—21no—
29#16813593C2211yescharacteristic, complemented
30#16813592—21no—
31D4×Dic113—21no—
32D4×Dic113C2211yescharacteristic, complemented
33#16813584C2211yescharacteristic
34C4×C22⋊D113C2211yescharacteristic
35#16813580C2211yescharacteristic, complemented
36C2×C4⋊Dic113C2211yescharacteristic
37C22⋊C4×D113—21no—
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813551C2211yescharacteristic, complemented
41#16813546C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic, complemented
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268648—22no—
61#14268648—41no—
62C2×D452—22no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—41no—
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113D411yescharacteristic
71C22×Dic113—21no—
72C22×Dic113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113C2311yescharacteristic
76#14268632—22no—
77#14268632—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624D411yescharacteristic
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102SD16×C113—41no—
103C2×C8×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—81no—
118C22×D113C2×D411yescharacteristic
119Q8×C113—21no—
120Q8×C113—21no—
121D4×C113—21no—
122D4×C113—21no—
123D4×C113—42no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—22no—
132C22⋊D113—81no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—81no—
136C2×Dic113—81no—
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140D452—21no—
141D452—21no—
142D452—21no—
143D452—42no—
144D452—42no—
145D452—81no—
146D452#4112yes—
147C4×D113—21no—
148C4×D113—21no—
149C4×D113—42no—
150C4×D113—81no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113#13512yes—
161C22×C113C22×D411yescharacteristic
162C2×D113—21no—
163C2×D113—22no—
164C2×D113—21no—
165C2×D113—21no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—84no—
172C4×C113—21no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113—41no—
176C4×C113C2×#4111yescharacteristic
177C4×C113H(5,𝔽2)11yescharacteristic
178Dic113—21no—
179Dic113—21no—
180Dic113—21no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—22no—
184C2×C113—81no—
185C2×C113#54611yescharacteristic
186C2×C113C2×#13511yescharacteristic
187C2×C113#57611yescharacteristic
188D113—41no—
189D113—42no—
190D113—81no—
191#3297—1131nomaximal, Sylow
192C113#329711yescharacteristic, complemented, Sylow
193#553—1131no—
194#546—1131no—
195#488—1131no—
196#484—1131no—
197#482—1131no—
198#478—1131no—
199#466—1131no—
200#465D11311yescharacteristic, complemented
201#463—1131no—
202#449—1131no—
203#447—1131no—
204C4×D8—1131no—
205C8×D4—1131no—
206#416—1131no—
207C2×#102—1131no—
208C2×#41—1131no—
209C22×D4—1131no—
210C2×SD16C2×D11311yescharacteristic, complemented
211C2×D8—1131no—
212C2×D8—1131no—
213C22×C8—1131no—
214C22×C8C2×D11311yescharacteristic
215#126—2261no—
216#125—1131no—
217#124—1131no—
218#123—2261no—
219#123—2261no—
220C22⋊Q8C2×D11311yescharacteristic
221#121—1131no—
222#121—1131no—
223#121—2261no—
224#121—2261no—
225#121C2×D11311yescharacteristic
226#120—2261no—
227C4×D4—1131no—
228C4×D4—1131no—
229C4×D4—1131no—
230C4×D4—2261no—
231#117—1131no—
232C2×C4⋊C4—1131no—
233C2×C22⋊C4—2261no—
234#107—1131no—
235#107—1131no—
236#106C2×D11311yescharacteristic, complemented
237C4⋊C8—1131no—
238#103—1131no—
239#103—1131no—
240#103C2×D11311yescharacteristic, complemented
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102C2×D11311yescharacteristic, complemented
248C22⋊C8—1131no—
249C22⋊C8—1131no—
250C4×C8—1131no—
251C24—2261no—
252#41—4521no—
253#41—2262no—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—21no—
256C2×D4—1131no—
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—4521no—
260C2×D4—2262no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4C22×D11311yescharacteristic
266C22×C4—1131no—
267C22×C4—2261no—
268C22×C4—2261no—
269C22×C4—2261no—
270C22×C4—2261no—
271C22×C4C22×D11311yescharacteristic
272SD16—41no—
273D8—4521no—
274D8—2262no—
275C2×C8—41no—
276C2×C8—1131no—
277C2×C8—1131no—
278C2×C8—4521no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—1131no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4C22×D11311yescharacteristic
289C4⋊C4C22×D11311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1131no—
293C22⋊C4—1131no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C42—1131no—
302C42—2261no—
303C23—21no—
304C23—1131no—
305C23—9041no—
306C23—4522no—
307C23—4522no—
308C23—2261no—
309C23—2261no—
310C23D4×D11311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—1132no—
317D4—9041no—
318D4—9041no—
319D4—4522no—
320D4—4522no—
321D4—2262no—
322D4—2261no—
323D4—2261no—
324D4—2261no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—9041no—
334C2×C4—9041no—
335C2×C4—9041no—
336C2×C4—4522no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4D4×D11311yescharacteristic
342C2×C4C23×D11311yescharacteristic
343C8—21no—
344C8—21no—
345C8—2261no—
346C8—2261no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—9044no—
353C22—4521no—
354C22—4521no—
355C22—4521no—
356C22—4521no—
357C22—4521no—
358C22—2261no—
359C22—2261no—
360C22—2262no—
361C22—2261no—
362C22#1681364312yes—
363C22C2×D4×D11311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—4521no—
369C4—4521no—
370C4—2261no—
371C4—2261no—
372C4—2261no—
373C4#41×D11311yescharacteristic
374C4#1681366711yescharacteristic
375C2—22no—
376C2—81no—
377C2—9041no—
378C2—4522no—
379C2—4521no—
380C2#2029923711yescharacteristic
381C2C2×#1681364311yescharacteristic
382C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
hypercenter#465D113
hypocenterC113#3297
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #20299300C2semidirect
2. #20299239C2semidirect
3. #20298954C2semidirect
4. #20298931C2semidirect
5. #20298924C2semidirect
6. #20298897C2semidirect
7. #20298833C2semidirect
8. #20298815C2semidirect
9. #20298742C2semidirect
10. #20298731C2semidirect
11. #20298678C2semidirect
12. C8×C22⋊D113C2semidirect
13. #20298593C2semidirect
14. C2×#16813544C2semidirect
15. #465×C113C2semidirect
20. C2×C8×D113C22semidirect
22. #16813613C22semidirect
29. #16813593C22semidirect
32. D4×Dic113C22semidirect
35. #16813580C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813551C22semidirect
41. #16813546C22semidirect
42. #16813546C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
52. C2×SD16×C113C22semidirect
56. #106×C113C22semidirect
57. #103×C113C22semidirect
58. #102×C113C22semidirect
192. C113#3297semidirect
200. #465D113semidirect
210. C2×SD16C2×D113semidirect
236. #106C2×D113semidirect
240. #103C2×D113semidirect
247. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993002
#202992392
#202989542
#202989312
#202989242
#202988972
#202988332
#202988152
#202987422
#202987312
#202986782
C8×C22⋊D1132
#202985932
C2×#168135442
#465×C1132
#3297113