Finite Group Databasebeta

← #28403295

Subgroups — #28403295

Order 14464.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299320C211yesmaximal, characteristic, complemented
2#20299263C211yesmaximal, characteristic, complemented
3#20298960C211yesmaximal, characteristic, complemented
4#20298959C211yesmaximal, characteristic, complemented
5#20298947C211yesmaximal, characteristic, complemented
6#20298892C211yesmaximal, characteristic, complemented
7#20298877C211yesmaximal, characteristic, complemented
8#20298816C211yesmaximal, characteristic
9#20298814C211yesmaximal, characteristic
10#20298802C211yesmaximal, characteristic, complemented
11#20298727C211yesmaximal, characteristic, complemented
12#20298697C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298680C211yesmaximal, characteristic
15#477×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113—21no—
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×D904C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813617—21no—
24#16813616—21no—
25#16813611C2211yescharacteristic
26#16813610C2211yescharacteristic
27#16813600—21no—
28#16813600—21no—
29#16813600—21no—
30#16813598—21no—
31C4×Dic226C2211yescharacteristic
32#16813587C2211yescharacteristic
33C4×D452C2211yescharacteristic
34#16813584C2211yescharacteristic
35#16813584C2211yescharacteristic
36#16813584C2211yescharacteristic
37#16813579—21no—
38#16813555C2211yescharacteristic
39#16813551C2211yescharacteristic
40#16813551C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813533C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226D411yescharacteristic
62C2×Dic226C2311yescharacteristic
63Q8×D113—44no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70#14268636—22no—
71#14268634—22no—
72D904—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113D411yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626D411yescharacteristic
83#14268626D411yescharacteristic
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C4×Dic113C2311yescharacteristic
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113—21no—
96C2×Q8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C42×C113—21no—
105C42×C113C2311yescharacteristic
106C22×D113—21no—
107C22×D113—21no—
108Q8×C113—21no—
109Q8×C113—21no—
110Q8×C113—42no—
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×C113C2411yescharacteristic
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113C2×D411yescharacteristic
121C2×Dic113C2×D411yescharacteristic
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124D452—21no—
125D452—21no—
126D452—21no—
127D452#4112yes—
128C4×D113—42no—
129C4×D113—42no—
130C4×D113—42no—
131C4×D113—42no—
132Dic226—22no—
133Dic226—21no—
134Dic226—21no—
135Dic226—42no—
136Dic226—42no—
137C8×C113—21no—
138C8×C113—21no—
139#11744751—21no—
140#11744751—21no—
141C22×C113C22×D411yescharacteristic
142C2×D113—22no—
143C2×D113—41no—
144C2×D113—41no—
145C2×D113—41no—
146C2×D113—41no—
147C2×D113—41no—
148C4×C113—21no—
149C4×C113—21no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113C2×#4111yescharacteristic
155C4×C1132−1+411yescharacteristic
156Dic113—21no—
157Dic113—21no—
158Dic113—21no—
159Dic113—41no—
160Dic113—41no—
161Dic113AGL(1,ℤ/8)12yes—
162C2×C113#54811yescharacteristic
163C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C113#57811yescharacteristic
165D113—42no—
166D113—81no—
167#3367—1131nomaximal, Sylow
168C113#336711yescharacteristic, complemented, Sylow
169#556—1131no—
170D4×Q8—1131no—
171#489—1131no—
172#489—1131no—
173#487—1131no—
174#477—1131no—
175#477D11311yescharacteristic, complemented
176#474—1131no—
177#463—1131no—
178#463—1131no—
179#461—1131no—
180#446—1131no—
181#440—1131no—
182#440—1131no—
183C4×D8—1131no—
184C22×Q8—2261no—
185C2×SD16—1131no—
186C2×SD16—1131no—
187C2×D8—1131no—
188C4⋊Q8—1131no—
189C4⋊Q8—1131no—
190C4⋊Q8—1131no—
191C4⋊Q8C2×D11311yescharacteristic
192#126—2261no—
193#126—2261no—
194#124—1131no—
195#124—1131no—
196C22⋊Q8—2261no—
197C22⋊Q8—2261no—
198C22⋊Q8—2261no—
199C22⋊Q8—2261no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8C2×D11311yescharacteristic
203C4×D4—1131no—
204C4×D4—1131no—
205C4×D4—1131no—
206C4×D4—1131no—
207#117—2261no—
208#107—1131no—
209#107C2×D11311yescharacteristic
210#107C2×D11311yescharacteristic
211C4⋊C8—1131no—
212C4⋊C8—1131no—
213C4⋊C8C2×D11311yescharacteristic
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218#103C2×D11311yescharacteristic
219#103C2×D11311yescharacteristic
220#102—1131no—
221#102—1131no—
222#102—1131no—
223#102—1131no—
224#97—1131no—
225#97—1131no—
226C4×C8—1131no—
227C2×Q8—21no—
228C2×Q8—1131no—
229C2×Q8—1131no—
230C2×Q8—4524no—
231C2×Q8—2261no—
232C2×Q8—2261no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—1131no—
235C2×D4—1131no—
236C22×C4—2261no—
237C22×C4—2261no—
238C22×C4—2261no—
239C22×C4—2261no—
240SD16—2262no—
241SD16—2262no—
242D8—2262no—
243C2×C8—1131no—
244C2×C8—1131no—
245C2×C8C22×D11311yescharacteristic
246C2×C8C22×D11311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4C22×D11311yescharacteristic
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C42—21no—
270C42—1131no—
271C42—1131no—
272C42—2261no—
273C42C22×D11311yescharacteristic
274C23—2261no—
275C23—2261no—
276Q8—21no—
277Q8—21no—
278Q8—42no—
279Q8—4522no—
280Q8—4522no—
281Q8—2262no—
282Q8—2261no—
283Q8—2261no—
284D4—1132no—
285D4—2261no—
286D4—2261no—
287D4—2261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—1131no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—4522no—
297C2×C4—4522no—
298C2×C4—4522no—
299C2×C4—4522no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4D4×D11311yescharacteristic
303C2×C4D4×D11311yescharacteristic
304C2×C4C23×D11311yescharacteristic
305C8—21no—
306C8—21no—
307C8—2261no—
308C8—2261no—
309C22—4521no—
310C22—4521no—
311C22—4521no—
312C22—4521no—
313C22—4521no—
314C22—2262no—
315C22C2×D4×D11311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—1132no—
323C4—4521no—
324C4—4521no—
325C4—2261no—
326C4—2261no—
327C4—2261no—
328C4#41×D11311yescharacteristic
329C4#1681367011yescharacteristic
330C2—9041no—
331C2—4522no—
332C2#2029925811yescharacteristic
333C2AGL(1,ℤ/8)×D11311yescharacteristic
334C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#477×C113C2
socleC22×C113C22×D4
prime radicalC2×D904C22
hypercenter#477D113
hypocenterC113#3367
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #20299320C2semidirect
2. #20299263C2semidirect
3. #20298960C2semidirect
4. #20298959C2semidirect
5. #20298947C2semidirect
6. #20298892C2semidirect
7. #20298877C2semidirect
10. #20298802C2semidirect
11. #20298727C2semidirect
12. #20298697C2semidirect
13. #20298696C2semidirect
15. #477×C113C2semidirect
168. C113#3367semidirect
175. #477D113semidirect

Maximal subgroups

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

subgroupindex
#202993202
#202992632
#202989602
#202989592
#202989472
#202988922
#202988772
#202988162
#202988142
#202988022
#202987272
#202986972
#202986962
#202986802
#477×C1132
#3367113