Finite Group Databasebeta

← #14737052

Subgroups — #14737052

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079767C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic
3C2×#10622701C211yesmaximal, characteristic
4#13077546C211yesmaximal, characteristic, complemented
5#13068159C214yesmaximal, complemented
6#13068035C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic
9C11×#1548C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66927C2211yescharacteristic
12#10623001C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15#10622735—21no—
16#10622732—21no—
17#10622706—21no—
18#10622704C2214yescomplemented
19#10622701—21no—
20#10622701—21no—
21#10622701C2212yes—
22#10622701C2212yes—
23#10622691—21no—
24#10622583—22no—
25C2×#66873—21no—
26C2×#66873—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622461C2214yes—
30#10622444—21no—
31#10622444C2212yescomplemented
32#10622443—21no—
33#10622443C2212yescomplemented
34#10622344—22no—
35#10622307—21no—
36#10622306—21no—
37C11×#333C2214yescomplemented
38#10622123C2214yes—
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C22×Q8×C11—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C2×C11×M16—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53#66979—21no—
54#66977—21no—
55#66977D412yes—
56C22×C11⋊C8D411yescharacteristic
57C22×C11⋊C8D411yescharacteristic
58C2×#4314—24no—
59#66927—21no—
60#66927—21no—
61#66927—21no—
62#66927C2312yes—
63#66923—21no—
64#66922D411yescharacteristic
65#66922D411yescharacteristic
66C4×Dic22—21no—
67C4×Dic22C2312yes—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8—21no—
72C4×C8×C11—21no—
73C22⋊(C11⋊C8)—21no—
74#66885—24no—
75#66879—22no—
76Dic11⋊C8—22no—
77Dic11⋊C8—22no—
78C8×Dic11—22no—
79#66874—24no—
80#66873—22no—
81#66873—22no—
82#66873—22no—
83#66873—22no—
84#66871—24no—
85C4⋊(C11⋊C8)C2312yes—
86C4×C11⋊C8—21no—
87C4×C11⋊C8D411yescharacteristic
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8C2311yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91#19212—111nomaximal, Sylow
92C23×D11—41no—
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—82no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—42no—
107C2×D44—42no—
108C2×D44—82no—
109C2×D44—82no—
110C2×Dic22—21no—
111C2×Dic22C2×D412yes—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123C22⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11C2×D412yes—
128Dic11⋊C4—22no—
129Dic11⋊C4—22no—
130C4×Dic11—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138#4314—84no—
139#3230—111no—
140#3208—111no—
141C2×#486—111no—
142#2960—111no—
143#1698—114no—
144#1678—114no—
145#1564—111no—
146#1548D1111yescharacteristic, complemented
147#1545—111no—
148C23×C11#12111yescharacteristic
149C22×D11—42no—
150C22×D11—82no—
151C22×D11—82no—
152C22×D11—82no—
153Q8×C11—82no—
154Q8×C11—82no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#13512yes—
163C2×C4×C11#13712yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—22no—
169D44—42no—
170D44—42no—
171D44—44no—
172D44—82no—
173D44—82no—
174D44—82no—
175D44—82no—
176Dic22—24no—
177Dic22—42no—
178C8×C11—42no—
179C8×C11—42no—
180C11⋊C8—21no—
181C11⋊C8—21no—
182C11⋊C8—21no—
183C11⋊C8—21no—
184C11⋊C8—42no—
185#533—111no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×#127—111no—
188#500—221no—
189#492—221no—
190#487—221no—
191#486—112no—
192#486—112no—
193#486—221no—
194#486—221no—
195#486—221no—
196#484—222no—
197#477—114no—
198#460—114no—
199#450—222no—
200#446—112no—
201#446—221no—
202C8×Q8—112no—
203C8×Q8—221no—
204#431—111no—
205#431C2×D1111yescharacteristic
206#424—221no—
207#423C2×D1111yescharacteristic
208C2×#102—221no—
209C2×#102—221no—
210#405—221no—
211C2×C4×C8—111no—
212#335—112no—
213#334—112no—
214#333C2×D1114yescomplemented
215#331—114no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11#46412yes—
219C22×C11C2×#12111yescharacteristic
220C2×D11—82no—
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—164no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—82no—
227C4×C11#46412yes—
228C4×C11#47212yes—
229C4×C11C2×#13511yescharacteristic
230C4×C11C2×#13711yescharacteristic
231C4×C11#57712yes—
232Dic11—42no—
233Dic11—42no—
234C22×Q8—21no—
235C22×D4—221no—
236C22×D4—221no—
237C22×D4—221no—
238C2×SD16—224no—
239C2×M16—21no—
240C22×C8—111no—
241C22×C8—111no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—111no—
246C4⋊Q8—111no—
247C4⋊Q8C22×D1112yes—
248#127—112no—
249#127—221no—
250#127—221no—
251#127—221no—
252#125—221no—
253C22⋊Q8—112no—
254C22⋊Q8—221no—
255C4×Q8—112no—
256C4×Q8—221no—
257#117—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#107—224no—
262C4⋊C8—21no—
263C4⋊C8—112no—
264C4⋊C8—222no—
265C4⋊C8—222no—
266C4⋊C8C22×D1112yes—
267C4⋊C8C22×D1112yes—
268#103—224no—
269#102—222no—
270#102—222no—
271#102—222no—
272#102—222no—
273#102—224no—
274C22⋊C8—21no—
275C22⋊C8—221no—
276#97—222no—
277C4×C8—21no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—222no—
283C4×C8—221no—
284C2×C11—22no—
285C2×C11C2×#46411yescharacteristic
286C2×C11#305711yescharacteristic
287C2×C11C2×#47211yescharacteristic
288D11—162no—
289C24—441no—
290C2×Q8—22no—
291C2×Q8—41no—
292C2×Q8—82no—
293C2×Q8—112no—
294C2×Q8—221no—
295C2×D4—222no—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—442no—
302C2×D4—442no—
303C2×D4—882no—
304C2×D4—882no—
305C22×C4—41no—
306C22×C4#433911yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309SD16—884no—
310M16—42no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—111no—
314C2×C8—111no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—222no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—112no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—221no—
329C4⋊C4—222no—
330C22⋊C4—222no—
331C42—222no—
332C42#433911yescharacteristic
333C42D4×D1111yescharacteristic
334C42D4×D1111yescharacteristic
335C42C23×D1111yescharacteristic
336C11#1921211yescharacteristic, complemented, Sylow
337C23—442no—
338C23—882no—
339C23—882no—
340C23—882no—
341C23#6693711yescharacteristic
342Q8—82no—
343Q8—82no—
344Q8—224no—
345Q8—442no—
346D4—442no—
347D4—442no—
348D4—444no—
349D4—882no—
350D4—882no—
351D4—882no—
352D4—882no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4#6693711yescharacteristic
360C2×C4#6693711yescharacteristic
361C2×C4#6693711yescharacteristic
362C2×C4#6696912yes—
363C2×C4#6697112yes—
364C2×C4C2×#433911yescharacteristic
365C2×C4C2×D4×D1111yescharacteristic
366C2×C4C2×D4×D1111yescharacteristic
367C8—42no—
368C8—42no—
369C8—221no—
370C8—221no—
371C8—221no—
372C8—221no—
373C8—442no—
374C22—21no—
375C22—21no—
376C22—882no—
377C22—882no—
378C22—882no—
379C22—1764no—
380C22#1062241112yes—
381C22C2×#6693711yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—442no—
386C4—442no—
387C4#1062236212yes—
388C4#1062241112yes—
389C4C2×#6696911yescharacteristic
390C4C2×#6697111yescharacteristic
391C4#1062330912yes—
392C2—22no—
393C2—1762no—
394C2C2×#1062241111yescharacteristic
395C2#1307825811yescharacteristic
396C2C2×#1062236211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#1548D11
hypocenterC11#19212
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
1. #13079767C2semidirect
4. #13077546C2semidirect
5. #13068159C2semidirect
6. #13068035C2semidirect
7. #13067362C2semidirect
9. C11×#1548C2semidirect
18. #10622704C22semidirect
31. #10622444C22semidirect
33. #10622443C22semidirect
37. C11×#333C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
146. #1548D11semidirect
214. #333C2×D11semidirect
336. C11#19212semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130795592
C2×#106227012
#130775462
#130681592
#130680352
#130673622
#130672852
C11×#15482
#1921211