Finite Group Databasebeta

← #28402926

Subgroups — #28402926

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299306C211yesmaximal, characteristic, complemented
2#20299248C211yesmaximal, characteristic
3#20298995C211yesmaximal, characteristic, complemented
4#20298927C211yesmaximal, characteristic, complemented
5#20298926C211yesmaximal, characteristic, complemented
6#20298915C211yesmaximal, characteristic, complemented
7#20298914C211yesmaximal, characteristic, complemented
8#20298886C211yesmaximal, characteristic, complemented
9#20298881C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12C8×C22⋊D113C211yesmaximal, characteristic, complemented
13C2×#16813554C211yesmaximal, characteristic, complemented
14#106×D113C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×C8×D113C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813612—21no—
21#16813604—21no—
22#16813603—21no—
23#16813602—21no—
24#16813599—21no—
25#16813599—21no—
26#16813598C2211yescharacteristic
27#16813593C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30C4×C22⋊D113C2211yescharacteristic
31#16813582—21no—
32C2×C4⋊Dic113C2211yescharacteristic
33C2×C4⋊Dic113C2211yescharacteristic
34C4⋊C4×D113C2211yescharacteristic
35C4⋊C4×D113C2211yescharacteristic
36#16813554C2211yescharacteristic
37#16813554C2211yescharacteristic
38#16813554C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×C22⋊D113—21no—
63C2×C22⋊D113D411yescharacteristic
64C22×Dic113—21no—
65C22×Dic113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C8×D113—22no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624D411yescharacteristic
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C2×Q8×C113C2311yescharacteristic
94C2×D4×C113—21no—
95C2×D4×C113C2311yescharacteristic
96C22×C4×C113C2311yescharacteristic
97SD16×C113—22no—
98C2×C8×C113—22no—
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C23×C113—21no—
107C23×C113C2×D411yescharacteristic
108C22×D113C2×D411yescharacteristic
109Q8×C113—21no—
110Q8×C113—21no—
111D4×C113—21no—
112D4×C113—21no—
113D4×C113—42no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—42no—
122C22⋊D113SD1614yescomplemented
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—42no—
128C2×Dic113—42no—
129C2×Dic113—81no—
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—42no—
136C4×D113—81no—
137Dic226—42no—
138Dic226—81no—
139C8×C113—21no—
140C8×C113#4112yescomplemented
141#11744751—21no—
142#11744751—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C2×SD1612yes—
149C22×C113C22×D411yescharacteristic
150C2×D113—21no—
151C2×D113—21no—
152C2×D113C2×SD1612yes—
153C4×C113—21no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113C2×#4111yescharacteristic
158C4×C1132−1+411yescharacteristic
159Dic113—21no—
160Dic113—21no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164Dic113—41no—
165Dic113C2×SD1612yes—
166C2×C113—22no—
167C2×C113—81no—
168C2×C113#54711yescharacteristic
169C2×C113C22×SD1611yescharacteristic
170C2×C113#57711yescharacteristic
171D113—22no—
172#3335—1131nomaximal, Sylow
173C113#333511yescharacteristic, complemented, Sylow
174#554—1131no—
175#547—1131no—
176#498—1131no—
177#483—1131no—
178#483—1131no—
179#481—1131no—
180#481—1131no—
181#476—1131no—
182#475—1131no—
183#465—1131no—
184#465D11311yescharacteristic, complemented
185C4×SD16—1131no—
186C8×D4—1131no—
187C2×#106—1131no—
188C2×#106—1131no—
189C2×#41—2261no—
190C2×SD16C2×D11311yescharacteristic
191C22×C8—1131no—
192C22×C8C2×D11311yescharacteristic
193C4⋊Q8—1131no—
194C4⋊Q8—1131no—
195#125—2261no—
196#123—2261no—
197#123—2261no—
198C22⋊Q8—1131no—
199C22⋊Q8—2261no—
200C22⋊Q8—2261no—
201C22⋊Q8—2261no—
202C22⋊Q8C2×D11311yescharacteristic
203#121—1131no—
204#121C2×D11311yescharacteristic
205C4×Q8—1131no—
206C4×D4—1131no—
207C4×D4—1131no—
208C4×D4—2261no—
209C2×C4⋊C4—1131no—
210C2×C4⋊C4—1131no—
211C2×C4⋊C4—1131no—
212C2×C4⋊C4—1131no—
213#106—1131no—
214#106—1131no—
215#106—1131no—
216#106—1131no—
217#106—1131no—
218#106—1131no—
219#106—1131no—
220#106—1131no—
221#106C2×D11311yescharacteristic
222C4⋊C8—1131no—
223#103—1131no—
224#103—1131no—
225#103C2×D11311yescharacteristic
226#102—1131no—
227#102—1131no—
228#102C2×D11311yescharacteristic
229C22⋊C8—1131no—
230C22⋊C8—1131no—
231C4×C8—1131no—
232#41—4524no—
233C2×Q8—2261no—
234C2×Q8—2261no—
235C2×Q8C22×D11311yescharacteristic
236C2×D4—21no—
237C2×D4—1131no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—1131no—
241C22×C4—2261no—
242C22×C4—2261no—
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4—2261no—
246C22×C4C22×D11311yescharacteristic
247SD16—22no—
248C2×C8—22no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8—2262no—
252C2×C8C22×D11311yescharacteristic
253C2×C8C22×D11311yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C4⋊C4C22×D11311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—1131no—
273C22⋊C4—1131no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C42—1131no—
278C42—2261no—
279C23—21no—
280C23—1131no—
281C23D4×D11311yescharacteristic
282Q8—21no—
283Q8—21no—
284Q8—9041no—
285Q8—4522no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—1134no—
290D4—4522no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—9041no—
300C2×C4—9041no—
301C2×C4—4522no—
302C2×C4—4522no—
303C2×C4—4522no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4D4×D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—21no—
313C8—2261no—
314C8—2261no—
315C8#1426864612yescomplemented
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1132no—
322C22—2261no—
323C22—2261no—
324C22SD16×D11312yes—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—1132no—
331C4—4521no—
332C4—4521no—
333C4—4521no—
334C4—4521no—
335C4—2261no—
336C4—2261no—
337C4C2×#1426864611yescharacteristic
338C4#1681366911yescharacteristic
339C2—22no—
340C2—81no—
341C2—2262no—
342C2#2029924811yescharacteristic
343C2C2×SD16×D11311yescharacteristic
344C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20299248C2
hypercenter#465D113
hypocenterC113#3335
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. #20299306C2semidirect
3. #20298995C2semidirect
4. #20298927C2semidirect
5. #20298926C2semidirect
6. #20298915C2semidirect
7. #20298914C2semidirect
8. #20298886C2semidirect
9. #20298881C2semidirect
10. #20298824C2semidirect
11. SD16×Dic113C2semidirect
12. C8×C22⋊D113C2semidirect
13. C2×#16813554C2semidirect
14. #106×D113C2semidirect
15. #465×C113C2semidirect
122. C22⋊D113SD16semidirect
140. C8×C113#41semidirect
173. C113#3335semidirect
184. #465D113semidirect
315. C8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202993062
#202992482
#202989952
#202989272
#202989262
#202989152
#202989142
#202988862
#202988812
#202988242
SD16×Dic1132
C8×C22⋊D1132
C2×#168135542
#106×D1132
#465×C1132
#3335113