Finite Group Databasebeta

← #28402733

Subgroups — #28402733

Order 14464.

414 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#20299311C211yesmaximal, characteristic, complemented
2#20299239C211yesmaximal, characteristic, complemented
3#20298959C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298877C211yesmaximal, characteristic, complemented
6#20298846C211yesmaximal, characteristic, complemented
7#20298835C211yesmaximal, characteristic, complemented
8#20298816C211yesmaximal, characteristic, complemented
9#20298746C211yesmaximal, characteristic, complemented
10#20298734C211yesmaximal, characteristic, complemented
11#20298709C211yesmaximal, characteristic, complemented
12#20298672C211yesmaximal, characteristic, complemented
13#20298602C211yesmaximal, characteristic, complemented
14#20298593C211yesmaximal, characteristic, complemented
15#485×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×#14268634C2211yescharacteristic, complemented
19C2×D904C2211yescharacteristic
20C2×D904C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic, complemented
23#16813621C2211yescharacteristic, complemented
24#16813611C2211yescharacteristic
25#16813610—21no—
26#16813608—21no—
27#16813607—21no—
28#16813597—21no—
29#16813597C2211yescharacteristic
30#16813597C2211yescharacteristic, complemented
31#16813596C2211yescharacteristic
32#16813595—21no—
33#16813592—21no—
34#16813584C2211yescharacteristic
35#16813584C2211yescharacteristic, complemented
36C4×C22⋊D113C2211yescharacteristic
37#16813580C2211yescharacteristic, complemented
38#16813579—21no—
39C22⋊C4×D113—21no—
40#16813555C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813532C2211yescharacteristic, complemented
52C22⋊Q8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113—21no—
60#14268648—22no—
61#14268648—41no—
62C2×Dic226—21no—
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—41no—
69C2×D452C2311yescharacteristic
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113D411yescharacteristic
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78#14268634—41no—
79D904—22no—
80D904—41no—
81#14268631—41no—
82C2×#11744751C2311yescharacteristic
83C2×#11744751C2311yescharacteristic
84C8×D113—41no—
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626D411yescharacteristic
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624D411yescharacteristic
98C4×Dic113—21no—
99C4×Dic113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113—21no—
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—81no—
118C22×D113C2×D411yescharacteristic
119Q8×C113—21no—
120Q8×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—41no—
130C22⋊D113—81no—
131C2×Dic113—21no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—21no—
136D452—21no—
137D452—21no—
138D452—21no—
139D452—21no—
140D452—42no—
141D452—42no—
142D452—81no—
143D452—81no—
144D452#4112yes—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—42no—
148C4×D113—42no—
149C4×D113—81no—
150Dic226—81no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—22no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
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×C113—41no—
177C4×C113C2×#4111yescharacteristic
178C4×C113H(5,𝔽2)11yescharacteristic
179Dic113—21no—
180Dic113—21no—
181Dic113—21no—
182Dic113—41no—
183C2×C113—41no—
184C2×C113#54611yescharacteristic
185C2×C113#57511yescharacteristic
186C2×C113#57611yescharacteristic
187D113—41no—
188D113—42no—
189D113—81no—
190D113—81no—
191#3319—1131nomaximal, Sylow
192C113#331911yescharacteristic, complemented, Sylow
193#555—1131no—
194#546—1131no—
195#489—1131no—
196#485D11311yescharacteristic, complemented
197#482—1131no—
198#474—1131no—
199#468—1131no—
200#466—1131no—
201#463—1131no—
202#449—1131no—
203#447—1131no—
204#442—1131no—
205#435—1131no—
206#418—1131no—
207#416—1131no—
208C2×#41—1131no—
209C22×D4—1131no—
210C2×SD16—1131no—
211C2×D8—1131no—
212C2×D8—1131no—
213C2×M16—1131no—
214C22×C8—1131no—
215C4⋊Q8—1131no—
216#124—1131no—
217#124—2261no—
218#124—2261no—
219#123—2261no—
220C22⋊Q8C2×D11311yescharacteristic
221#121—1131no—
222#121—1131no—
223#121—1131no—
224#121—2261no—
225#121—2261no—
226#120—2261no—
227C4×D4—1131no—
228C4×D4—1131no—
229C4×D4—1131no—
230#117—1131no—
231#117—2261no—
232#117C2×D11311yescharacteristic
233C2×C22⋊C4—2261no—
234#107—1131no—
235#107C2×D11311yescharacteristic, complemented
236#106C2×D11311yescharacteristic, complemented
237C4⋊C8—1131no—
238#103—1131no—
239#103C2×D11311yescharacteristic, complemented
240#103C2×D11311yescharacteristic, complemented
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248C22⋊C8—1131no—
249C22⋊C8C2×D11311yescharacteristic
250#97—1131no—
251C24—2261no—
252#41—4521no—
253#41—2262no—
254C2×Q8—2261no—
255C2×Q8C22×D11311yescharacteristic
256C2×D4—1131no—
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—1131no—
260C2×D4—4521no—
261C2×D4—2262no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4—2261no—
266C2×D4—2261no—
267C22×C4—1131no—
268C22×C4—2261no—
269C22×C4—2261no—
270C22×C4—2261no—
271C22×C4C22×D11311yescharacteristic
272SD16—4521no—
273D8—4521no—
274D8—2262no—
275M16—4521no—
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—2261no—
285C4⋊C4C22×D11311yescharacteristic
286C4⋊C4C22×D11311yescharacteristic
287C4⋊C4C22×D11311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—1131no—
291C22⋊C4—1131no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C42—21no—
301C42—1131no—
302C42—2261no—
303C23—1131no—
304C23—9041no—
305C23—4522no—
306C23—4522no—
307C23—2261no—
308C23—2261no—
309C23—2261no—
310C23D4×D11311yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—9041no—
314D4—1132no—
315D4—9041no—
316D4—9041no—
317D4—9041no—
318D4—4522no—
319D4—4522no—
320D4—4521no—
321D4—2261no—
322D4—2261no—
323D4—2261no—
324D4—2261no—
325D4—2261no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1131no—
333C2×C4—1131no—
334C2×C4—1131no—
335C2×C4—9041no—
336C2×C4—4522no—
337C2×C4—4522no—
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—21no—
350C22—9044no—
351C22—4521no—
352C22—4521no—
353C22—4521no—
354C22—4521no—
355C22—4521no—
356C22—4521no—
357C22—4521no—
358C22—4521no—
359C22—2261no—
360C22—2261no—
361C22—2262no—
362C22—2261no—
363C22C2×D4×D11311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—4521no—
370C4—2261no—
371C4—2261no—
372C4—2261no—
373C4#41×D11311yescharacteristic
374C4#1681366811yescharacteristic
375C2—41no—
376C2—9041no—
377C2—9041no—
378C2—4522no—
379C2—4521no—
380C2#2029924011yescharacteristic
381C2#2029939711yescharacteristic
382C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#485×C113C2
socleC22×C113C22×D4
hypercenter#485D113
hypocenterC113#3319
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #20299311C2semidirect
2. #20299239C2semidirect
3. #20298959C2semidirect
4. #20298924C2semidirect
5. #20298877C2semidirect
6. #20298846C2semidirect
7. #20298835C2semidirect
8. #20298816C2semidirect
9. #20298746C2semidirect
10. #20298734C2semidirect
11. #20298709C2semidirect
12. #20298672C2semidirect
13. #20298602C2semidirect
14. #20298593C2semidirect
15. #485×C113C2semidirect
18. C2×#14268634C22semidirect
22. C2×C8×D113C22semidirect
23. #16813621C22semidirect
30. #16813597C22semidirect
35. #16813584C22semidirect
37. #16813580C22semidirect
40. #16813555C22semidirect
41. #16813551C22semidirect
42. #16813546C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. #16813532C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. #103×C113C22semidirect
57. #103×C113C22semidirect
192. C113#3319semidirect
196. #485D113semidirect
235. #107C2×D113semidirect
236. #106C2×D113semidirect
239. #103C2×D113semidirect
240. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993112
#202992392
#202989592
#202989242
#202988772
#202988462
#202988352
#202988162
#202987462
#202987342
#202987092
#202986722
#202986022
#202985932
#485×C1132
#3319113