Finite Group Databasebeta

← #14737067

Subgroups — #14737067

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079561C211yesmaximal, characteristic, complemented
2#13079554C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic
4#13068184C214yesmaximal, complemented
5#13068060C214yesmaximal, complemented
6#13067364C211yesmaximal, characteristic, complemented
7#13067302C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic
9C11×#2960C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×#66927C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#446—21no—
14C11×#446C2212yescomplemented
15C8×Q8×C11—21no—
16C8×Q8×C11C2212yescomplemented
17C11×#424—21no—
18C11×#423C2211yescharacteristic
19C11×#405—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66885—21no—
22C2×#66885—21no—
23#10622706—21no—
24#10622705—21no—
25#10622701—21no—
26#10622698—21no—
27#10622663—22no—
28#10622659—22no—
29#10622644C2214yescomplemented
30#10622640C2214yes—
31#10622538C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622307—21no—
34#10622307—21no—
35#10622307C2212yes—
36#10622307C2212yes—
37#10622124C2214yescomplemented
38#10622123C2214yes—
39#10622096C2212yescomplemented
40#10622095C2212yescomplemented
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×Dic22—21no—
45C2×C11×M16—21no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11D411yescharacteristic
48C11×C4⋊Q8D411yescharacteristic
49C11×C4⋊Q8D411yescharacteristic
50C11×#125—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8D412yes—
53C4×Q8×C11—21no—
54C4×Q8×C11C2312yes—
55C11×#117—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4326—24no—
58C2×#4325—24no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61#66927—21no—
62#66927—21no—
63#66927—21no—
64#66927C2312yes—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922C2312yes—
69C11×C4⋊C8—22no—
70C11×C4⋊C8—22no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×#97—22no—
74C4×C8×C11—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81#66885—22no—
82#66885—22no—
83#66885—22no—
84#66885—22no—
85#66874—24no—
86#66873—24no—
87C4⋊(C11⋊C8)C2312yes—
88C4⋊(C11⋊C8)C2312yes—
89C4×C11⋊C8—21no—
90C4×C11⋊C8—21no—
91#19214—111nomaximal, Sylow
92C23×D11—41no—
93C2×Q8×C11—21no—
94C2×Q8×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—41no—
99C2×D44—22no—
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—42no—
106C2×D44—42no—
107C2×D44—82no—
108C2×D44—82no—
109C2×Dic22—22no—
110C2×Dic22—41no—
111C2×Dic22—82no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4C2×D412yes—
126C11×C22⋊C4—22no—
127C42×C11—22no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132#4326—84no—
133#4325—84no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140#3209—111no—
141#3208—111no—
142C2×#486—111no—
143#2960D1111yescharacteristic, complemented
144#1702—114no—
145#1682—114no—
146#1564—111no—
147#1549—111no—
148#1545—111no—
149C23×C11#12111yescharacteristic
150C22×D11—42no—
151C22×D11—82no—
152C22×D11—82no—
153C22×D11—82no—
154Q8×C11—24no—
155Q8×C11—42no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#13512yes—
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×Dic11—42no—
169C2×Dic11—82no—
170D44—42no—
171D44—42no—
172D44—44no—
173D44—82no—
174D44—82no—
175D44—82no—
176D44—82no—
177Dic22—44no—
178Dic22—82no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11—42no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186#533C2×D1111yescharacteristic
187C2×C4⋊Q8—111no—
188C2×#127—111no—
189#494—221no—
190#492—221no—
191#487—221no—
192#486—112no—
193#486—112no—
194#486—221no—
195#486—221no—
196#486—221no—
197#462—114no—
198#460—114no—
199#451—222no—
200#450—222no—
201#446—21no—
202#446C2×D1112yescomplemented
203C8×Q8—21no—
204C8×Q8C2×D1112yescomplemented
205#431—111no—
206#431—111no—
207#424—21no—
208#423C2×D1111yescharacteristic
209C2×#102—221no—
210C2×#102—221no—
211#405—21no—
212C2×C4×C8C2×D1111yescharacteristic
213#335—112no—
214#334—112no—
215#332—114no—
216#331—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#46412yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—82no—
224C2×D11—164no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11#46412yes—
230C4×C11#47112yes—
231C4×C11C2×#13511yescharacteristic
232C4×C11C2×#13711yescharacteristic
233C4×C11#57612yes—
234Dic11—82no—
235C22×Q8—221no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4—221no—
239C2×Q16—224no—
240C2×SD16—224no—
241C2×M16—21no—
242C22×C8C22⋊D1111yescharacteristic
243C22×C8C22⋊D1111yescharacteristic
244C4⋊Q8—112no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8D4411yescharacteristic
249C4⋊Q8D4411yescharacteristic
250#127—112no—
251#127—221no—
252#127—221no—
253#127—221no—
254#125—21no—
255C22⋊Q8—21no—
256C22⋊Q8D4412yes—
257C4×Q8—21no—
258C4×Q8C22×D1112yes—
259#117—21no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C42C22×D1111yescharacteristic
263C4⋊C8—22no—
264C4⋊C8—22no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8C22×D1112yes—
269#103—224no—
270#102—222no—
271#102—222no—
272#102—222no—
273#102—222no—
274#102—224no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#97—22no—
278C4×C8—22no—
279C4×C8—221no—
280C4×C8—221no—
281C4×C8C22⋊D1111yescharacteristic
282C4×C8C22⋊D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C2×C11—22no—
286C2×C11C2×#46411yescharacteristic
287C2×C11#305811yescharacteristic
288C2×C11C2×#47111yescharacteristic
289D11—162no—
290C24—441no—
291C2×Q8—21no—
292C2×Q8—222no—
293C2×Q8—441no—
294C2×Q8—882no—
295C2×Q8C2×D4412yes—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—222no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—882no—
305C2×D4—882no—
306C22×C4—441no—
307C22×C4C2×D4411yescharacteristic
308C22×C4#433911yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310Q16—884no—
311SD16—884no—
312M16—42no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C2×C22⋊D1111yescharacteristic
320C2×C8C2×C22⋊D1111yescharacteristic
321C2×C8C2×C22⋊D1111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4C2×D4412yes—
332C22⋊C4—22no—
333C42—22no—
334C42C2×D4411yescharacteristic
335C42#433911yescharacteristic
336C42C2×C22⋊D1111yescharacteristic
337C42C23×D1111yescharacteristic
338C11#1921411yescharacteristic, complemented, Sylow
339C23—442no—
340C23—882no—
341C23—882no—
342C23—882no—
343C23#6698311yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—444no—
347Q8—882no—
348D4—444no—
349D4—442no—
350D4—442no—
351D4—882no—
352D4—882no—
353D4—882no—
354D4—882no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—442no—
360C2×C4—882no—
361C2×C4#6698311yescharacteristic
362C2×C4#6698311yescharacteristic
363C2×C4#6698311yescharacteristic
364C2×C4#6699512yes—
365C2×C4#6700312yes—
366C2×C4C22×D4411yescharacteristic
367C2×C4C2×#433911yescharacteristic
368C2×C4C22×C22⋊D1111yescharacteristic
369C8—21no—
370C8—21no—
371C8—21no—
372C8—21no—
373C8—42no—
374C8—442no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—882no—
379C22—882no—
380C22—882no—
381C22—1764no—
382C22#1062264112yes—
383C22C2×#6698311yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—42no—
388C4—882no—
389C4#1062264112yes—
390C4#1062275412yes—
391C4#1062328312yes—
392C4C2×#6699511yescharacteristic
393C4C2×#6700311yescharacteristic
394C2—22no—
395C2—1762no—
396C2C2×#1062264111yescharacteristic
397C2#1307826411yescharacteristic
398C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#2960D11
hypocenterC11#19214
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
4. #13068184C2semidirect
5. #13068060C2semidirect
6. #13067364C2semidirect
7. #13067302C2semidirect
9. C11×#2960C2semidirect
14. C11×#446C22semidirect
16. C8×Q8×C11C22semidirect
29. #10622644C22semidirect
37. #10622124C22semidirect
39. #10622096C22semidirect
40. #10622095C22semidirect
143. #2960D11semidirect
202. #446C2×D11semidirect
204. C8×Q8C2×D11semidirect
338. C11#19214semidirect

Maximal subgroups

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

subgroupindex
#130795612
#130795542
C2×#106223072
#130681842
#130680602
#130673642
#130673022
#130672852
C11×#29602
#1921411