Finite Group Databasebeta

← #28401143

Subgroups — #28401143

Order 14464.

380 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#20299133C211yesmaximal, characteristic, complemented
2#20299127C211yesmaximal, characteristic, complemented
3#20298997C211yesmaximal, characteristic, complemented
4#20298980C211yesmaximal, characteristic, complemented
5#20298953C211yesmaximal, characteristic, complemented
6#20298838C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic
8#20298830C211yesmaximal, characteristic, complemented
9#20298826C211yesmaximal, characteristic, complemented
10#20298690C211yesmaximal, characteristic, complemented
11#20298689C211yesmaximal, characteristic, complemented
12#20298683C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14C4×C8×D113C211yesmaximal, characteristic, complemented
15#488×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813617—21no—
23#16813615—21no—
24#16813614C2211yescharacteristic
25#16813610C2211yescharacteristic
26#16813607—21no—
27#16813604—21no—
28#16813602C2211yescharacteristic
29#16813598C2211yescharacteristic
30#16813597C2211yescharacteristic
31#16813593C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33#16813587C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35#16813584—21no—
36#16813584C2211yescharacteristic
37#16813582—21no—
38#16813580—21no—
39#16813578—21no—
40C42×D113C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813555C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49C4×#11744751C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#125×C113C2211yescharacteristic
53#124×C113C2211yescharacteristic
54#103×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×D452—21no—
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C22×Dic113—21no—
64C2×C4×D113—21no—
65C2×C4×D113D411yescharacteristic
66C2×C4×D113D411yescharacteristic
67C2×C4×D113C2311yescharacteristic
68#14268637—22no—
69#14268635—22no—
70#14268634—22no—
71#14268632—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C8×D113—22no—
75C8×D113—22no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84C22⋊Dic113—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—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×C113—21no—
113D4×C113—21no—
114D4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—42no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—42no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129D452—21no—
130D452—21no—
131D452—42no—
132C4×D113—22no—
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—22no—
136C4×D113—42no—
137Dic226—21no—
138Dic226—21no—
139C8×C113—21no—
140C8×C113—21no—
141#11744751#4112yes—
142#11744751#4112yes—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113C22×D411yescharacteristic
147C2×D113—21no—
148C2×D113—21no—
149C2×D113—41no—
150C2×D113—41no—
151C2×D113—41no—
152C2×D113#13512yes—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113C2×#4111yescharacteristic
159C4×C113C2×#4111yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—41no—
163Dic113—41no—
164Dic113—41no—
165Dic113#13512yes—
166C2×C113—81no—
167C2×C113#53211yescharacteristic
168C2×C113C2×#13511yescharacteristic
169C2×C113C2×#13511yescharacteristic
170D113—22no—
171D113—81no—
172#3168—1131nomaximal, Sylow
173C113#316811yescharacteristic, complemented, Sylow
174#529—1131no—
175#529—1131no—
176#499—1131no—
177#495—1131no—
178#488—1131no—
179#488D11311yescharacteristic, complemented
180#467—1131no—
181#466—1131no—
182#465—1131no—
183#465—1131no—
184C4×Q16—1131no—
185C4×SD16—1131no—
186C4×SD16—1131no—
187C4×D8—1131no—
188C2×C4×C8—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×D8—1131no—
193C22×C8—1131no—
194C22×C8—1131no—
195#126—2261no—
196#126—2261no—
197#125—1131no—
198#125C2×D11311yescharacteristic
199#124—1131no—
200#124C2×D11311yescharacteristic
201#123—2261no—
202#123—2261no—
203C22⋊Q8—1131no—
204C22⋊Q8—1131no—
205#121—1131no—
206#121—1131no—
207C4×Q8—1131no—
208C4×Q8—1131no—
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—2261no—
212C4×D4—2261no—
213#117—2261no—
214#117—2261no—
215C2×C42—1131no—
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106—1131no—
220#103—1131no—
221#103—1131no—
222#103C2×D11311yescharacteristic
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102—1131no—
226#102C2×D11311yescharacteristic
227#102C2×D11311yescharacteristic
228C4×C8—1131no—
229C4×C8—1131no—
230C4×C8—1131no—
231C4×C8C2×D11311yescharacteristic
232C2×Q8—1131no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—1131no—
235C2×D4—2261no—
236C2×D4—2261no—
237C2×D4C22×D11311yescharacteristic
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—2261no—
242C22×C4—2261no—
243Q16—2262no—
244SD16—2262no—
245SD16—2262no—
246D8—2262no—
247C2×C8—1131no—
248C2×C8—1131no—
249C2×C8—2262no—
250C2×C8—2262no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C42—1131no—
276C42—1131no—
277C42—1131no—
278C42—2261no—
279C42—2261no—
280C42C22×D11311yescharacteristic
281C23—21no—
282C23—1131no—
283C23—2261no—
284Q8—21no—
285Q8—21no—
286Q8—2261no—
287Q8—2261no—
288D4—21no—
289D4—21no—
290D4—4522no—
291D4—4522no—
292D4—2261no—
293D4—2261no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—1131no—
300C2×C4—4522no—
301C2×C4—4522no—
302C2×C4—2262no—
303C2×C4—2262no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4D4×D11311yescharacteristic
310C2×C4D4×D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—21no—
313C8—21no—
314C8—1132no—
315C8—1132no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—1132no—
320C22—4521no—
321C22—4521no—
322C22—4521no—
323C22—2261no—
324C22—2261no—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1132no—
332C4—4521no—
333C4—4521no—
334C4—4521no—
335C4—2261no—
336C4—2261no—
337C4#41×D11311yescharacteristic
338C4#41×D11311yescharacteristic
339C2—81no—
340C2—9041no—
341C2—2262no—
342C2#2029914711yescharacteristic
343C2#135×D11311yescharacteristic
344C2#135×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radical#20298833C2
hypercenter#488D113
hypocenterC113#3168
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299133C2semidirect
2. #20299127C2semidirect
3. #20298997C2semidirect
4. #20298980C2semidirect
5. #20298953C2semidirect
6. #20298838C2semidirect
8. #20298830C2semidirect
9. #20298826C2semidirect
10. #20298690C2semidirect
11. #20298689C2semidirect
12. #20298683C2semidirect
13. #20298678C2semidirect
14. C4×C8×D113C2semidirect
15. #488×C113C2semidirect
173. C113#3168semidirect
179. #488D113semidirect

Maximal subgroups

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

subgroupindex
#202991332
#202991272
#202989972
#202989802
#202989532
#202988382
#202988332
#202988302
#202988262
#202986902
#202986892
#202986832
#202986782
C4×C8×D1132
#488×C1132
#3168113