Finite Group Databasebeta

← #28403046

Subgroups — #28403046

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299294C211yesmaximal, characteristic, complemented
2#20299252C211yesmaximal, characteristic, complemented
3#20299007C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298917C211yesmaximal, characteristic, complemented
7#20298912C211yesmaximal, characteristic, complemented
8#20298899C211yesmaximal, characteristic, complemented
9#20298889C211yesmaximal, characteristic, complemented
10#20298851C211yesmaximal, characteristic, complemented
11#20298834C211yesmaximal, characteristic, complemented
12#20298711C211yesmaximal, characteristic, complemented
13#20298640C211yesmaximal, characteristic, complemented
14C2×#16813554C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×D904C2211yescharacteristic
18#16813622C2211yescharacteristic
19#16813617—21no—
20#16813614C2211yescharacteristic
21#16813606—21no—
22#16813606—21no—
23#16813604—21no—
24#16813602—21no—
25#16813596C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813596C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813594—21no—
30C4×D452C2211yescharacteristic
31C4×D452C2211yescharacteristic
32#16813582—21no—
33#16813581C2211yescharacteristic
34C2×C4⋊Dic113C2211yescharacteristic
35C2×C4⋊Dic113C2211yescharacteristic
36C2×C4⋊Dic113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813554C2211yescharacteristic
45#16813554C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52C2×M16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×D452C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C22×Dic113—21no—
68C22×Dic113—21no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72D904—22no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C2×D4×C113D411yescharacteristic
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96M16×C113—22no—
97C2×C8×C113—22no—
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113D411yescharacteristic
103C22⋊C4×C113D411yescharacteristic
104C22⋊C4×C113D411yescharacteristic
105C42×C113C2311yescharacteristic
106C23×C113C2×D411yescharacteristic
107C23×C113C2×D411yescharacteristic
108C22×D113—21no—
109C22×D113—21no—
110D4×C113—22no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C22⋊D113—42no—
121C22⋊D113—42no—
122C22⋊D113—42no—
123C22⋊D113—81no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—42no—
131C2×Dic113—42no—
132C2×Dic113—81no—
133D452—21no—
134D452—21no—
135D452—21no—
136D452—21no—
137C4×D113—42no—
138C4×D113—81no—
139Dic226—42no—
140C8×C113—21no—
141C8×C113—21no—
142C8×C113—21no—
143C8×C113#4112yescomplemented
144C22×C113—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113AGL(1,ℤ/8)12yes—
150C22×C113C22×D411yescharacteristic
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C4×C113—21no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113C2×#4111yescharacteristic
162C4×C1132−1+411yescharacteristic
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169C2×C113—22no—
170C2×C113—41no—
171C2×C113#54711yescharacteristic
172C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C113#57711yescharacteristic
174D113—81no—
175D113—81no—
176#3345—1131nomaximal, Sylow
177C113#334511yescharacteristic, complemented, Sylow
178#553—1131no—
179#547—1131no—
180#501—1131no—
181#482—1131no—
182#481—1131no—
183#481—1131no—
184#480—1131no—
185#478—1131no—
186#476—1131no—
187#469—1131no—
188#466—1131no—
189#442—1131no—
190#435D11311yescharacteristic, complemented
191#428—1131no—
192C2×#106—1131no—
193C2×#41—2261no—
194C2×D8—1131no—
195C2×M16C2×D11311yescharacteristic
196C22×C8C2×D11311yescharacteristic
197C4⋊Q8—1131no—
198#126—2261no—
199#125—1131no—
200#123—2261no—
201#123—2261no—
202#123—2261no—
203C22⋊Q8—2261no—
204#121—1131no—
205#121—1131no—
206#121—1131no—
207#121—1131no—
208#121—2261no—
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—2261no—
212C4×D4C2×D11311yescharacteristic
213#117—1131no—
214C2×C4⋊C4—1131no—
215C2×C4⋊C4—1131no—
216C2×C4⋊C4—1131no—
217#107—1131no—
218#107—1131no—
219#107—1131no—
220#106—1131no—
221#106—1131no—
222#106—1131no—
223#106—1131no—
224#106—1131no—
225#106—1131no—
226C4⋊C8C2×D11311yescharacteristic
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233C22⋊C8C2×D11311yescharacteristic
234C22⋊C8C2×D11311yescharacteristic
235#97C2×D11311yescharacteristic
236#41—4524no—
237C2×Q8—2261no—
238C2×D4—1131no—
239C2×D4—1131no—
240C2×D4—2261no—
241C2×D4—2261no—
242C2×D4—2261no—
243C2×D4—2261no—
244C2×D4D45211yescharacteristic
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4—2261no—
249C22×C4—2261no—
250C22×C4C22×D11311yescharacteristic
251C22×C4C22×D11311yescharacteristic
252D8—2262no—
253M16—22no—
254C2×C8—22no—
255C2×C8C22×D11311yescharacteristic
256C2×C8C22×D11311yescharacteristic
257C2×C8C22×D11311yescharacteristic
258C2×C8C22×D11311yescharacteristic
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—1131no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4D45211yescharacteristic
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4D45211yescharacteristic
280C22⋊C4D45211yescharacteristic
281C42—2261no—
282C42C22×D11311yescharacteristic
283C23—2261no—
284C23—2261no—
285C23C2×D45211yescharacteristic
286C23C2×D45211yescharacteristic
287Q8—4522no—
288D4—22no—
289D4—9041no—
290D4—4522no—
291D4—4522no—
292D4—4522no—
293D4—2261no—
294D4—2261no—
295D4—2261no—
296D4—2261no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—9041no—
302C2×C4—9041no—
303C2×C4—4522no—
304C2×C4—4522no—
305C2×C4—4522no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4C2×D45211yescharacteristic
313C2×C4C2×D45211yescharacteristic
314C2×C4C2×D45211yescharacteristic
315C2×C4C2×D45211yescharacteristic
316C2×C4C23×D11311yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#1426864612yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—4521no—
327C22—4521no—
328C22—4521no—
329C22—4521no—
330C22—4521no—
331C22—4521no—
332C22#1681365012yes—
333C22C22×D45211yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—4521no—
339C4—4521no—
340C4—4521no—
341C4—4521no—
342C4—4521no—
343C4—4521no—
344C4C2×#1426864611yescharacteristic
345C4#1681366911yescharacteristic
346C2—22no—
347C2—41no—
348C2—9041no—
349C2—9041no—
350C2#2029925211yescharacteristic
351C2C2×#1681365011yescharacteristic
352C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3345
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20299294C2semidirect
2. #20299252C2semidirect
3. #20299007C2semidirect
4. #20298923C2semidirect
5. #20298917C2semidirect
6. #20298917C2semidirect
7. #20298912C2semidirect
8. #20298899C2semidirect
9. #20298889C2semidirect
10. #20298851C2semidirect
11. #20298834C2semidirect
12. #20298711C2semidirect
13. #20298640C2semidirect
14. C2×#16813554C2semidirect
15. #435×C113C2semidirect
143. C8×C113#41semidirect
177. C113#3345semidirect
190. #435D113semidirect
320. C8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202992522
#202990072
#202989232
#202989172
#202989122
#202988992
#202988892
#202988512
#202988342
#202987112
#202986402
C2×#168135542
#435×C1132
#3345113