Finite Group Databasebeta

← #28402506

Subgroups — #28402506

Order 14464.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299319C211yesmaximal, characteristic, complemented
2#20299267C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298920C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298829C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298796C211yesmaximal, characteristic, complemented
10#20298759C211yesmaximal, characteristic, complemented
11Q16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298594C211yesmaximal, characteristic, complemented
14#20298593C211yesmaximal, characteristic, complemented
15#452×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813618—21no—
22#16813618C2211yescharacteristic
23#16813617—21no—
24#16813615—21no—
25#16813608—21no—
26#16813598C2211yescharacteristic
27#16813596—21no—
28#16813596C2211yescharacteristic
29#16813593—21no—
30#16813593C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33#16813587—21no—
34C4×C22⋊D113—21no—
35C4×C22⋊D113C2211yescharacteristic
36#16813581C2211yescharacteristic
37#16813580C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61C2×Dic226—21no—
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113D411yescharacteristic
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71#14268634—41no—
72C2×#11744751—41no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C8×D113—41no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96#41×C113—22no—
97#41×C113—41no—
98C2×Q8×C113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104Q16×C113—22no—
105SD16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113#4112yes—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—42no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—42no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—22no—
131C22⋊D113—42no—
132C22⋊D113—81no—
133C22⋊D113—81no—
134C22⋊D113—81no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141D452—21no—
142D452—21no—
143D452—42no—
144C4×D113—21no—
145C4×D113—21no—
146C4×D113—42no—
147Dic226—42no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C4×C113—22no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—41no—
174Dic113—41no—
175Dic113—41no—
176Dic113#13512yes—
177C2×C113—41no—
178C2×C113—81no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—41no—
183D113—81no—
184#3304—1131nomaximal, Sylow
185C113#330411yescharacteristic, complemented, Sylow
186#556—1131no—
187#550—1131no—
188#486—1131no—
189#482—1131no—
190#482—1131no—
191#475—1131no—
192#465—1131no—
193#465—1131no—
194#460—1131no—
195#452—1131no—
196#452D11311yescharacteristic, complemented
197C4×Q16—1131no—
198C8×D4—1131no—
199#416—1131no—
200#416—1131no—
201C2×#41—1131no—
202C2×#41C2×D11311yescharacteristic
203C2×Q16C2×D11311yescharacteristic
204C2×SD16—1131no—
205C2×SD16C2×D11311yescharacteristic
206C22×C8—1131no—
207C22×C8—1131no—
208C4⋊Q8—1131no—
209#127—1131no—
210#127—2261no—
211#126—2261no—
212#126—2261no—
213#124—2261no—
214C22⋊Q8—1131no—
215C22⋊Q8C2×D11311yescharacteristic
216#121—1131no—
217#121—1131no—
218#121—2261no—
219#121—2261no—
220C4×Q8—1131no—
221C4×Q8—1131no—
222C4×Q8—2261no—
223C4×D4—1131no—
224C4×D4—2261no—
225#117—1131no—
226#117—1131no—
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103C2×D11311yescharacteristic
235#102—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102C2×D11311yescharacteristic
241C22⋊C8—1131no—
242C22⋊C8C2×D11311yescharacteristic
243C4×C8—1131no—
244#41—22no—
245#41—41no—
246#41—4521no—
247#41—2262no—
248C2×Q8—2261no—
249C2×Q8C22×D11311yescharacteristic
250C2×Q8C22×D11311yescharacteristic
251C2×D4—21no—
252C2×D4—1131no—
253C2×D4—1131no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4—2261no—
259C2×D4C22×D11311yescharacteristic
260C22×C4—21no—
261C22×C4—1131no—
262C22×C4—2261no—
263C22×C4C22×D11311yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—4521no—
267C2×C8—1131no—
268C2×C8—1131no—
269C2×C8—4521no—
270C2×C8—4521no—
271C2×C8C22×D11311yescharacteristic
272C2×C8C22×D11311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—1131no—
285C22⋊C4—1131no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C42—1131no—
292C42—2261no—
293C42—2261no—
294C42—2261no—
295C42—2261no—
296C23—21no—
297C23—1131no—
298C23—2261no—
299C23D4×D11311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—4522no—
304Q8#1426864612yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—9041no—
309D4—9041no—
310D4—9041no—
311D4—4522no—
312D4—4522no—
313D4—2262no—
314D4—2261no—
315D4—2261no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—1131no—
323C2×C4—1131no—
324C2×C4—1131no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11311yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—21no—
334C8—21no—
335C8—2261no—
336C8—2261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—2261no—
347C22—2261no—
348C22—2261no—
349C22C2×D4×D11311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—1132no—
355C4—4521no—
356C4—4521no—
357C4—4521no—
358C4—2261no—
359C4—2261no—
360C4C2×#1426864611yescharacteristic
361C4#1681366711yescharacteristic
362C2—41no—
363C2—81no—
364C2—9041no—
365C2—4521no—
366C2#2029923511yescharacteristic
367C2#135×D11311yescharacteristic
368C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#452×C113C2
socleC22×C113C22×D4
prime radical#20299267C2
hypercenter#452D113
hypocenterC113#3304
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #20299319C2semidirect
3. #20298943C2semidirect
4. #20298923C2semidirect
5. #20298920C2semidirect
6. #20298881C2semidirect
7. #20298829C2semidirect
8. #20298824C2semidirect
9. #20298796C2semidirect
10. #20298759C2semidirect
11. Q16×Dic113C2semidirect
12. #20298661C2semidirect
13. #20298594C2semidirect
14. #20298593C2semidirect
15. #452×C113C2semidirect
185. C113#3304semidirect
196. #452D113semidirect

Maximal subgroups

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

subgroupindex
#202993192
#202992672
#202989432
#202989232
#202989202
#202988812
#202988292
#202988242
#202987962
#202987592
Q16×Dic1132
#202986612
#202985942
#202985932
#452×C1132
#3304113