Finite Group Databasebeta

← #28401443

Subgroups — #28401443

Order 14464.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299171C211yesmaximal, characteristic, complemented
2#20299165C211yesmaximal, characteristic
3#20298940C211yesmaximal, characteristic, complemented
4#20298936C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298920C211yesmaximal, characteristic, complemented
7#20298843C211yesmaximal, characteristic, complemented
8#20298841C211yesmaximal, characteristic, complemented
9#20298826C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11#20298749C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13#20298735C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic, complemented
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22#16813621—21no—
23#16813618—21no—
24#16813609—21no—
25#16813608—21no—
26#16813607—21no—
27#16813604—21no—
28#16813602C2211yescharacteristic, complemented
29#16813601C2211yescharacteristic
30#16813598C2211yescharacteristic, complemented
31#16813593C2211yescharacteristic
32#16813593C2211yescharacteristic
33#16813593C2211yescharacteristic
34#16813593C2211yescharacteristic
35#16813591—21no—
36#16813591—21no—
37#16813581C2211yescharacteristic
38#16813580C2211yescharacteristic, complemented
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—41no—
60#14268647—41no—
61C2×Dic226—21no—
62C2×Dic226D411yescharacteristic
63C2×Dic226C2311yescharacteristic
64Q8×D113—41no—
65Q8×D113—41no—
66C2×D452D411yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113D411yescharacteristic
72C2×C22⋊D113D411yescharacteristic
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75C2×C4×D113C2311yescharacteristic
76#14268635—41no—
77#14268635—41no—
78#14268630—41no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C8×D113—41no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99C24×C113—21no—
100C2×Q8×C113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113—41no—
103C2×D4×C113—41no—
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113C2311yescharacteristic
107SD16×C113—41no—
108SD16×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—42no—
117C23×C113—81no—
118C23×C113—81no—
119C23×C113C2×D411yescharacteristic
120C22×D113C2×D411yescharacteristic
121C22×D113C2×D411yescharacteristic
122Q8×C113—21no—
123Q8×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—42no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—41no—
136C22⋊D113—41no—
137C22⋊D113—81no—
138C22⋊D113—81no—
139C22⋊D113—81no—
140C22⋊D113—81no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113C2×D411yescharacteristic
146C2×Dic113C2×D411yescharacteristic
147D452—41no—
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—21no—
151C4×D113—21no—
152C4×D113—42no—
153Dic226—21no—
154Dic226—21no—
155Dic226—41no—
156Dic226—42no—
157C8×C113—21no—
158C8×C113—21no—
159#11744751—21no—
160#11744751—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—84no—
171C22×C113C22×D411yescharacteristic
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—21no—
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113H(5,𝔽2)11yescharacteristic
182C4×C113H(5,𝔽2)11yescharacteristic
183Dic113—21no—
184Dic113—21no—
185Dic113—41no—
186Dic113—41no—
187Dic113—41no—
188Dic113—41no—
189C2×C113—41no—
190C2×C113—81no—
191C2×C113—81no—
192C2×C113#53411yescharacteristic
193C2×C113#57711yescharacteristic
194C2×C113#57711yescharacteristic
195D113—41no—
196D113—41no—
197#3200—1131nomaximal, Sylow
198C113#320011yescharacteristic, complemented, Sylow
199#536—1131no—
200#535—1131no—
201#485—1131no—
202#485—1131no—
203#482—1131no—
204#482—1131no—
205#468—1131no—
206#468—1131no—
207#465—1131no—
208#465—1131no—
209#450—1131no—
210#450D11311yescharacteristic, complemented
211#448—1131no—
212#448—1131no—
213#408—1131no—
214C2×#41—1131no—
215C22×Q8—1131no—
216C22×D4C2×D11311yescharacteristic
217C2×SD16—1131no—
218C2×SD16—1131no—
219C2×SD16C2×D11311yescharacteristic
220C2×SD16C2×D11311yescharacteristic
221C2×M16—1131no—
222C22×C8—1131no—
223C4⋊Q8—2261no—
224#127—2261no—
225#124—2261no—
226#124—2261no—
227#123—2261no—
228#123—2261no—
229C22⋊Q8—1131no—
230C22⋊Q8—1131no—
231C22⋊Q8—1131no—
232C22⋊Q8C2×D11311yescharacteristic
233#121—1131no—
234#121—1131no—
235#121—1131no—
236#121—1131no—
237#120—2261no—
238#120—2261no—
239#117—1131no—
240#117—1131no—
241#107—1131no—
242#107—1131no—
243#106—1131no—
244#106—1131no—
245#103—1131no—
246#103—1131no—
247#103—1131no—
248#103—1131no—
249#102—1131no—
250#102—1131no—
251#102C2×D11311yescharacteristic
252#102C2×D11311yescharacteristic
253C22⋊C8—1131no—
254C22⋊C8—1131no—
255C22⋊C8—1131no—
256C22⋊C8C2×D11311yescharacteristic
257C24—21no—
258#41—4521no—
259#41—4521no—
260C2×Q8—1131no—
261C2×Q8—1131no—
262C2×Q8—4521no—
263C2×Q8—4521no—
264C2×Q8—2261no—
265C2×Q8C22×D11311yescharacteristic
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—1131no—
270C2×D4—1131no—
271C2×D4—1131no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4C22×D11311yescharacteristic
277C2×D4C22×D11311yescharacteristic
278C22×C4—1131no—
279C22×C4—1131no—
280C22×C4—2261no—
281C22×C4C22×D11311yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—4521no—
285SD16—4521no—
286M16—4521no—
287C2×C8—1131no—
288C2×C8—1131no—
289C2×C8—4521no—
290C2×C8C22×D11311yescharacteristic
291C2×C8C22×D11311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—1131no—
294C4⋊C4—1131no—
295C4⋊C4—1131no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
298C4⋊C4—2261no—
299C4⋊C4C22×D11311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C42—2261no—
311C42—2261no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1131no—
318C23—1131no—
319C23D4×D11311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—4521no—
323Q8—4522no—
324Q8—2261no—
325Q8—2261no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—9041no—
332D4—9041no—
333D4—9041no—
334D4—9041no—
335D4—4521no—
336D4—4521no—
337D4—4521no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—1131no—
343C2×C4—1131no—
344C2×C4—4522no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4—2261no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4D4×D11311yescharacteristic
354C2×C4C23×D11311yescharacteristic
355C8—21no—
356C8—21no—
357C8—2261no—
358C8—2261no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—2261no—
370C22—2261no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22—2261no—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—4521no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4#1681366711yescharacteristic
386C4#1681366711yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—4521no—
391C2—4521no—
392C2#2029915811yescharacteristic
393C2#2029940411yescharacteristic
394C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radical#20299165C2
hypercenter#450D113
hypocenterC113#3200
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20299171C2semidirect
3. #20298940C2semidirect
4. #20298936C2semidirect
5. #20298921C2semidirect
6. #20298920C2semidirect
7. #20298843C2semidirect
8. #20298841C2semidirect
9. #20298826C2semidirect
10. #20298824C2semidirect
11. #20298749C2semidirect
12. #20298735C2semidirect
13. #20298735C2semidirect
14. #20298563C2semidirect
15. #450×C113C2semidirect
17. C2×Q8×D113C22semidirect
20. C2×#14268630C22semidirect
21. C2×C8×D113C22semidirect
28. #16813602C22semidirect
30. #16813598C22semidirect
38. #16813580C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813546C22semidirect
50. #16813534C22semidirect
51. #16813534C22semidirect
198. C113#3200semidirect
210. #450D113semidirect

Maximal subgroups

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

subgroupindex
#202991712
#202991652
#202989402
#202989362
#202989212
#202989202
#202988432
#202988412
#202988262
#202988242
#202987492
#202987352
#202985632
#450×C1132
#3200113