Finite Group Databasebeta

← #14737045

Subgroups — #14737045

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#13079557C211yesmaximal, characteristic
3#13077550C211yesmaximal, characteristic, complemented
4#13068153C214yesmaximal, complemented
5#13068029C214yesmaximal, complemented
6#13067364C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067284C211yesmaximal, characteristic
9C2×C11×#486C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12#10623001C2211yescharacteristic
13C11×#486—21no—
14C11×#486—21no—
15C11×#486C2212yes—
16C11×#486C2212yes—
17C2×C11×#102—21no—
18C2×C11×#102—21no—
19C2×C4×C8×C11C2211yescharacteristic
20#10622831—22no—
21#10622715—21no—
22#10622714—21no—
23#10622706—21no—
24#10622704C2214yescomplemented
25#10622691—21no—
26#10622689—21no—
27#10622688C2214yes—
28#10622683—21no—
29#10622583—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622292—21no—
34#10622292C2212yescomplemented
35C8×Dic22—21no—
36C8×Dic22C2212yescomplemented
37#10622184C2214yescomplemented
38#10622182C2214yes—
39#10622096C2212yescomplemented
40#10622095C2212yescomplemented
41C22×Q8×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11D411yescharacteristic
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8C2312yes—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127—21no—
54C11×#127C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×#4324—24no—
59#66979—21no—
60#66977—21no—
61#66977D412yes—
62C2×#4318—21no—
63#66923—21no—
64#66922D411yescharacteristic
65#66922D411yescharacteristic
66C4×Dic22—21no—
67C4×Dic22C2312yes—
68C11×#102—22no—
69C11×#102—22no—
70C11×#102—22no—
71C11×#102—22no—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66896—24no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)—21no—
79#66879—22no—
80Dic11⋊C8—22no—
81Dic11⋊C8—22no—
82C8×Dic11—22no—
83#66874—24no—
84#66871—24no—
85C4⋊(C11⋊C8)—21no—
86C4⋊(C11⋊C8)C2312yes—
87C4⋊(C11⋊C8)C2312yes—
88C4⋊(C11⋊C8)C2312yes—
89C4×C11⋊C8—21no—
90C4×C11⋊C8—21no—
91#19212—111nomaximal, Sylow
92C24×C11—41no—
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—82no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11—82no—
105C2×D4×C11—82no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×Dic22—21no—
111C2×Dic22C2×D412yes—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11C2411yescharacteristic
126C22⋊Dic11—22no—
127#4324—84no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11C2×D412yes—
132Dic11⋊C4—22no—
133Dic11⋊C4—22no—
134C4×Dic11—22no—
135#4318—42no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139#3230—111no—
140#3208—111no—
141C2×#486D1111yescharacteristic
142#2960—111no—
143#1698—114no—
144#1678—114no—
145#1564—111no—
146#1548—111no—
147#1545—111no—
148C23×C11—42no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11#12111yescharacteristic
153Q8×C11—82no—
154Q8×C11—82no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—44no—
158D4×C11—82no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—82no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—42no—
165C2×C4×C11—82no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#13512yes—
170C2×C4×C11#13712yes—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×Dic11—22no—
175C2×Dic11—22no—
176Dic22—24no—
177Dic22—42no—
178C8×C11—21no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11—21no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185#533—111no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×#127C2×D1111yescharacteristic
188#500—221no—
189#492—221no—
190#487—221no—
191#486—21no—
192#486—21no—
193#486—221no—
194#486C2×D1112yes—
195#486C2×D1112yes—
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#431—111no—
206#424—221no—
207#423—111no—
208C2×#102—21no—
209C2×#102—21no—
210#405—221no—
211C2×C4×C8C2×D1111yescharacteristic
212#335—112no—
213#334—112no—
214#333—114no—
215#331—114no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—164no—
222C22×C11#46412yes—
223C22×C11C2×#12111yescharacteristic
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—21no—
236C22×D4—21no—
237C22×D4—21no—
238C2×SD16—224no—
239C2×M16—221no—
240C22×C8C22⋊D1111yescharacteristic
241C22×C8C22⋊D1111yescharacteristic
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—111no—
246C4⋊Q8—111no—
247C4⋊Q8C22×D1112yes—
248#127—21no—
249#127—21no—
250#127—21no—
251#127C22×D1112yes—
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—112no—
263C4⋊C8—112no—
264C4⋊C8—112no—
265C4⋊C8—222no—
266C4⋊C8—222no—
267C4⋊C8—221no—
268#103—224no—
269#102—22no—
270#102—22no—
271#102—22no—
272#102—22no—
273#102—224no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276#97—222no—
277C4×C8—222no—
278C4×C8—221no—
279C4×C8—221no—
280C4×C8C22⋊D1111yescharacteristic
281C4×C8C22⋊D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C2×C11—22no—
285C2×C11—162no—
286C2×C11C2×#46411yescharacteristic
287C2×C11#305711yescharacteristic
288C2×C11C2×#47211yescharacteristic
289C24—41no—
290C2×Q8—22no—
291C2×Q8—41no—
292C2×Q8—82no—
293C2×Q8—112no—
294C2×Q8—221no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—82no—
304C2×D4—82no—
305C22×C4—41no—
306C22×C4D4×D1111yescharacteristic
307C22×C4#434111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309SD16—884no—
310M16—442no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8C2×C22⋊D1111yescharacteristic
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C2×C22⋊D1111yescharacteristic
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—
332C42D4×D1111yescharacteristic
333C42#434111yescharacteristic
334C42C2×C22⋊D1111yescharacteristic
335C42C23×D1111yescharacteristic
336C11#1921211yescharacteristic, complemented, Sylow
337C23—42no—
338C23—82no—
339C23—82no—
340C23—82no—
341C23#6699111yescharacteristic
342Q8—82no—
343Q8—82no—
344Q8—224no—
345Q8—442no—
346D4—44no—
347D4—42no—
348D4—42no—
349D4—82no—
350D4—82no—
351D4—82no—
352D4—82no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4#6699111yescharacteristic
360C2×C4#6699111yescharacteristic
361C2×C4#6699111yescharacteristic
362C2×C4#6700312yes—
363C2×C4#6700412yes—
364C2×C4C2×D4×D1111yescharacteristic
365C2×C4C2×#434111yescharacteristic
366C2×C4C22×C22⋊D1111yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8—21no—
371C8—442no—
372C8—442no—
373C8—442no—
374C22—21no—
375C22—21no—
376C22—82no—
377C22—82no—
378C22—82no—
379C22—164no—
380C22#1062266712yes—
381C22C2×#6699111yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—442no—
386C4—442no—
387C4#1062266712yes—
388C4#1062277312yes—
389C4#1062329312yes—
390C4C2×#6700311yescharacteristic
391C4C2×#6700411yescharacteristic
392C2—22no—
393C2—162no—
394C2C2×#1062266711yescharacteristic
395C2#1307825111yescharacteristic
396C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC22×C11C2×#121
prime radicalC2×C11×#127C22
hypercenterC2×#486D11
hypocenterC11#19212
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13079767C2semidirect
3. #13077550C2semidirect
4. #13068153C2semidirect
5. #13068029C2semidirect
6. #13067364C2semidirect
7. #13067297C2semidirect
24. #10622704C22semidirect
34. #10622292C22semidirect
36. C8×Dic22C22semidirect
37. #10622184C22semidirect
39. #10622096C22semidirect
40. #10622095C22semidirect
336. C11#19212semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130795572
#130775502
#130681532
#130680292
#130673642
#130672972
#130672842
C2×C11×#4862
#1921211