Finite Group Databasebeta

← #28403220

Subgroups — #28403220

Order 14464.

350 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299317C211yesmaximal, characteristic, complemented
2#20299304C211yesmaximal, characteristic, complemented
3#20298951C211yesmaximal, characteristic, complemented
4#20298947C211yesmaximal, characteristic, complemented
5#20298903C211yesmaximal, characteristic, complemented
6#20298902C211yesmaximal, characteristic, complemented
7#20298886C211yesmaximal, characteristic, complemented
8#20298812C211yesmaximal, characteristic
9#20298810C211yesmaximal, characteristic
10#20298802C211yesmaximal, characteristic, complemented
11C8×Dic226C211yesmaximal, characteristic, complemented
12C4×#14268636C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14#20298678C211yesmaximal, characteristic
15#488×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813620C2211yescharacteristic
21#16813615—21no—
22#16813615—21no—
23#16813613C2211yescharacteristic
24#16813609C2211yescharacteristic
25#16813602—21no—
26#16813600—21no—
27#16813600—21no—
28#16813599—21no—
29Q8×Dic113C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31C4×Dic226C2211yescharacteristic
32C4×D452C2211yescharacteristic
33D4×Dic113C2211yescharacteristic
34#16813584C2211yescharacteristic
35#16813584C2211yescharacteristic
36#16813578—21no—
37C4⋊C4×D113—21no—
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813543C2211yescharacteristic
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×Dic226—21no—
60C2×Dic226D411yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C22×Dic113—21no—
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67#14268636—22no—
68#14268634—22no—
69#14268632—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113D411yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626D411yescharacteristic
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C4×Dic113C2311yescharacteristic
94C2×Q8×C113C2311yescharacteristic
95C2×D4×C113C2311yescharacteristic
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C22⋊C4×C113—21no—
103C22⋊C4×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106C22×D113—21no—
107Q8×C113—21no—
108Q8×C113—21no—
109D4×C113—21no—
110D4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2411yescharacteristic
117C2×Dic113—21no—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—42no—
121C2×Dic113C2×D411yescharacteristic
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125D452—21no—
126D452#4112yes—
127C4×D113—42no—
128C4×D113—81no—
129C4×D113—81no—
130Dic226—22no—
131Dic226—21no—
132Dic226—21no—
133Dic226—81no—
134C8×C113—21no—
135C8×C113—21no—
136#11744751—21no—
137#11744751—21no—
138C22×C113—41no—
139C22×C113—41no—
140C22×C113—41no—
141C22×C113C22×D411yescharacteristic
142C2×D113—22no—
143C2×D113—41no—
144C2×D113—41no—
145C4×C113—21no—
146C4×C113—21no—
147C4×C113—41no—
148C4×C113—41no—
149C4×C113—41no—
150C4×C113C2×#4111yescharacteristic
151C4×C1132−1+411yescharacteristic
152Dic113—21no—
153Dic113—21no—
154Dic113—21no—
155Dic113—41no—
156Dic113—41no—
157Dic113—41no—
158Dic113#13512yes—
159C2×C113—81no—
160C2×C113#54811yescharacteristic
161C2×C113C2×#13511yescharacteristic
162C2×C113#57711yescharacteristic
163D113—42no—
164#3360—1131nomaximal, Sylow
165C113#336011yescharacteristic, complemented, Sylow
166#556—1131no—
167#554—1131no—
168#488—1131no—
169#488D11311yescharacteristic, complemented
170#487—1131no—
171#479—1131no—
172#479—1131no—
173#476—1131no—
174#463—1131no—
175#463—1131no—
176#461—1131no—
177C8×Q8—1131no—
178C4×SD16—1131no—
179C4×SD16—1131no—
180C4×D8—1131no—
181C2×SD16—1131no—
182C2×SD16—1131no—
183C2×D8—1131no—
184C4⋊Q8—1131no—
185C4⋊Q8—1131no—
186#126—2261no—
187#126—2261no—
188#125—1131no—
189#125C2×D11311yescharacteristic
190#124—1131no—
191#124C2×D11311yescharacteristic
192C22⋊Q8—2261no—
193C22⋊Q8—2261no—
194C22⋊Q8—2261no—
195C22⋊Q8—2261no—
196C4×Q8—1131no—
197C4×Q8—1131no—
198C4×Q8—1131no—
199C4×D4—1131no—
200C4×D4—1131no—
201C4×D4—1131no—
202C4×D4—1131no—
203#117—2261no—
204C2×C4⋊C4—2261no—
205#107—1131no—
206#106—1131no—
207#106—1131no—
208C4⋊C8—1131no—
209C4⋊C8—1131no—
210C4⋊C8—1131no—
211#103—1131no—
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103C2×D11311yescharacteristic
216#103C2×D11311yescharacteristic
217#102—1131no—
218#102—1131no—
219#102C2×D11311yescharacteristic
220#102C2×D11311yescharacteristic
221C4×C8—1131no—
222C4×C8—1131no—
223C4×C8C2×D11311yescharacteristic
224C2×Q8—1131no—
225C2×Q8—1131no—
226C2×Q8—2261no—
227C2×Q8C22×D11311yescharacteristic
228C2×D4—1131no—
229C2×D4C22×D11311yescharacteristic
230C22×C4—2261no—
231C22×C4—2261no—
232C22×C4—2261no—
233C22×C4—2261no—
234SD16—2262no—
235SD16—2262no—
236D8—2262no—
237C2×C8—1131no—
238C2×C8—1131no—
239C2×C8C22×D11311yescharacteristic
240C2×C8C22×D11311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—1131no—
244C4⋊C4—1131no—
245C4⋊C4—1131no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4C22×D11311yescharacteristic
256C4⋊C4C22×D11311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—2261no—
260C22⋊C4—2261no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C42—1131no—
266C42—1131no—
267C42—2261no—
268C42—2261no—
269C42C22×D11311yescharacteristic
270C23—21no—
271C23—2261no—
272Q8—21no—
273Q8—21no—
274Q8—9041no—
275Q8—2262no—
276Q8—2261no—
277Q8—2261no—
278D4—21no—
279D4—21no—
280D4—1132no—
281D4—2261no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—1131no—
286C2×C4—1131no—
287C2×C4—1131no—
288C2×C4—1131no—
289C2×C4—9041no—
290C2×C4—9041no—
291C2×C4—4522no—
292C2×C4—4522no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4D4×D11311yescharacteristic
297C2×C4D4×D11311yescharacteristic
298C2×C4C23×D11311yescharacteristic
299C8—21no—
300C8—21no—
301C8—2261no—
302C8—2261no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—4521no—
307C22—4521no—
308C22—2262no—
309C22C2×D4×D11311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—1132no—
316C4—4521no—
317C4—4521no—
318C4—4521no—
319C4—2261no—
320C4—2261no—
321C4—2261no—
322C4#41×D11311yescharacteristic
323C4#1681366911yescharacteristic
324C2—81no—
325C2—4522no—
326C2#2029925611yescharacteristic
327C2#135×D11311yescharacteristic
328C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268632C22
hypercenter#488D113
hypocenterC113#3360
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. #20299317C2semidirect
2. #20299304C2semidirect
3. #20298951C2semidirect
4. #20298947C2semidirect
5. #20298903C2semidirect
6. #20298902C2semidirect
7. #20298886C2semidirect
10. #20298802C2semidirect
11. C8×Dic226C2semidirect
12. C4×#14268636C2semidirect
13. #20298683C2semidirect
15. #488×C113C2semidirect
165. C113#3360semidirect
169. #488D113semidirect

Maximal subgroups

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

subgroupindex
#202993172
#202993042
#202989512
#202989472
#202989032
#202989022
#202988862
#202988122
#202988102
#202988022
C8×Dic2262
C4×#142686362
#202986832
#202986782
#488×C1132
#3360113