Finite Group Databasebeta

← D11×#1695 #14736304

Subgroups — D11×#1695 #14736304

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#500C211yesmaximal, characteristic, complemented
2D11×#476C212yesmaximal
3D11×#436C211yesmaximal, characteristic
4#13068140C211yesmaximal, characteristic, complemented
5#13068139C211yesmaximal, characteristic, complemented
6#13068138C212yesmaximal, complemented
7#13068137C212yesmaximal, complemented
8#13068136C211yesmaximal, characteristic, complemented
9D11×#334C211yesmaximal, characteristic, complemented
10D11×#333C212yesmaximal, complemented
11C11×#1695C211yesmaximal, characteristic, complemented
12C2×M16×D11—21no—
13D11×C4⋊Q8C2212yes—
14C4×D4×D11C2211yescharacteristic
15C11×#500C2211yescharacteristic, complemented
16C11×#476C2212yes—
17C11×#436C2211yescharacteristic
18#10622741—21no—
19#10622697C2212yes—
20#10622691C2212yescomplemented
21#10622625C2211yescharacteristic
22#10622621C2212yes—
23D11×#107—21no—
24D11×#107—21no—
25#10622487—21no—
26#10622487—21no—
27#10622483—22no—
28D11×#106—22no—
29#10622455C2212yes—
30#10622451C2211yescharacteristic
31D11×C4⋊C8C2211yescharacteristic
32D11×C4⋊C8C2212yes—
33D11×#102—22no—
34#10622374—22no—
35#10622342—21no—
36D11×C22⋊C8—21no—
37#10622301C2211yescharacteristic
38C4×C8×D11C2211yescharacteristic
39#10622295C2211yescharacteristic, complemented
40C11×#334C2211yescharacteristic, complemented
41C11×#333C2212yescomplemented
42#10622184C2212yescomplemented
43#10622119C2212yescomplemented
44#10622119C2212yescomplemented
45#10622118C2212yescomplemented
46#10622095C2211yescharacteristic, complemented
47C2×Q8×D11—22no—
48C2×D4×D11D411yescharacteristic
49C22×C4×D11—21no—
50C2×C11×M16—21no—
51C11×C4⋊Q8C2312yes—
52C4×D4×C11C2311yescharacteristic
53#66997—22no—
54D4×Dic11D411yescharacteristic
55C4×C22⋊D11—21no—
56C2×#4318—21no—
57M16×D11—44no—
58C2×#4313—21no—
59C2×#4313—21no—
60C2×C8×D11—22no—
61C2×C8×D11—21no—
62C2×C8×D11D411yescharacteristic
63C2×C8×D11D411yescharacteristic
64#66946D411yescharacteristic
65C4⋊C4×D11—22no—
66C4⋊C4×D11—22no—
67C4⋊C4×D11D411yescharacteristic
68#66941—22no—
69#66941—22no—
70(C22⋊D11)⋊C4—21no—
71C22⋊C4×D11—21no—
72C4×D44C2311yescharacteristic
73C42×D11C2311yescharacteristic
74#66922C2312yes—
75C11×#107—21no—
76C11×#107—21no—
77C11×#106—22no—
78C11×C4⋊C8C2311yescharacteristic
79C11×C4⋊C8C2312yes—
80C11×#102—22no—
81C11×C22⋊C8—21no—
82C4×C8×C11C2311yescharacteristic
83#66896—22no—
84C22⋊(C11⋊C8)—21no—
85#66885—22no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88#66882—21no—
89#66882—21no—
90#66881—22no—
91Dic11⋊C8—22no—
92Dic11⋊C8—21no—
93C8×Dic11D411yescharacteristic
94C8×Dic11D411yescharacteristic
95#66873—22no—
96#66872—22no—
97#66872—22no—
98#66871—22no—
99#66871—22no—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2312yes—
102C4×C11⋊C8C2311yescharacteristic
103C2×#1695—111nomaximal, Sylow
104C23×D11—21no—
105C2×Q8×C11—22no—
106C2×D4×C11C2×D411yescharacteristic
107C22×C4×C11—21no—
108C2×C22⋊D11—21no—
109C22×Dic11—21no—
110Q8×D11—84no—
111D4×D11—24no—
112C2×D44C2×D411yescharacteristic
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11C2×D411yescharacteristic
120C2×C4×D11C2×D411yescharacteristic
121C2×C4×D11#4111yescharacteristic
122C2×Dic22—22no—
123C2×Dic22—42no—
124C11×M16—42no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4C2×D411yescharacteristic
132C11×C22⋊C4—21no—
133C42×C11C2411yescharacteristic
134C22⋊Dic11—21no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11C2×D411yescharacteristic
140Dic11⋊C4—21no—
141Dic11⋊C4—42no—
142Dic11⋊C4—42no—
143C4×Dic11C2×D411yescharacteristic
144C4×Dic11C2×D411yescharacteristic
145C4×Dic11#4111yescharacteristic
146#4318—42no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8C2×D411yescharacteristic
150C2×C11⋊C8C2×D411yescharacteristic
151#4313—42no—
152#4313—42no—
153C8×D11—22no—
154C8×D11—42no—
155C8×D11—44no—
156C8×D11SD1614yes—
157C2×#500—111no—
158C2×#476—112no—
159C2×#436—111no—
160#1695—111no—
161#1695—112no—
162#1695—111no—
163#1695—111no—
164#1695—112no—
165#1695D1111yescharacteristic, direct product factor
166C2×#334—111no—
167C2×#333—112no—
168C23×C11—21no—
169C22×D11—21no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—42no—
173C22×D11#12111yescharacteristic
174Q8×C11—82no—
175D4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C22⋊D11—42no—
184C2×Dic11—21no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11#12111yescharacteristic
188C2×Dic11#12111yescharacteristic
189C2×Dic11#12111yescharacteristic
190D44—22no—
191C4×D11—22no—
192C4×D11—42no—
193C4×D11—41no—
194C4×D11—41no—
195C4×D11—42no—
196C4×D11—84no—
197C4×D11C2×SD1612yes—
198C4×D11#13712yes—
199C4×D11#13714yes—
200Dic22—84no—
201Dic22—82no—
202C8×C11—21no—
203C8×C11—41no—
204C8×C11—42no—
205C8×C11C2×SD1612yes—
206C11⋊C8—21no—
207C11⋊C8—41no—
208C11⋊C8—42no—
209C11⋊C8C2×SD1612yes—
210C22×M16—221no—
211C2×C4⋊Q8—112no—
212C2×C4×D4—111no—
213#500—112no—
214#500—111no—
215#500—221no—
216#500—221no—
217#500C2×D1111yescharacteristic, complemented
218#476—112no—
219#476—112no—
220#476—112no—
221#476—222no—
222#476—222no—
223#476C2×D1112yes—
224#436—111no—
225#436—111no—
226#436—111no—
227#436—221no—
228#436—221no—
229#436C2×D1111yescharacteristic
230C2×#107—221no—
231C2×#107—221no—
232C2×#106—222no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—112no—
235C2×#102—222no—
236C2×C22⋊C8—221no—
237C2×C4×C8—111no—
238#334—112no—
239#334—111no—
240#334C2×D1111yescharacteristic, complemented
241#333—112no—
242#333—112no—
243#333—112no—
244#333C2×D1112yescomplemented
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11C2×#12111yescharacteristic
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—84no—
253C2×D11#46112yes—
254C2×D11#47012yes—
255C2×D11#47212yes—
256C4×C11—21no—
257C4×C11—41no—
258C4×C11—82no—
259C4×C11C22×SD1611yescharacteristic
260C4×C11C2×#13711yescharacteristic
261C4×C11C2×#13712yes—
262Dic11—21no—
263Dic11—41no—
264Dic11—82no—
265Dic11#46112yes—
266Dic11#47012yes—
267C22×Q8—222no—
268C22×D4—111no—
269C23×C4—221no—
270C2×M16—21no—
271C2×M16—221no—
272C2×M16—221no—
273C2×M16—221no—
274C2×M16—444no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—221no—
278C22×C8—222no—
279C4⋊Q8—112no—
280C4⋊Q8—222no—
281C4⋊Q8—222no—
282C4⋊Q8—222no—
283C4⋊Q8C22×D1112yes—
284C4×D4—111no—
285C4×D4—111no—
286C4×D4—111no—
287C4×D4—221no—
288C4×D4—221no—
289C4×D4C22×D1111yescharacteristic
290C2×C4⋊C4—111no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C22⋊C4—221no—
294C2×C42—111no—
295#107—21no—
296#107—21no—
297#107—222no—
298#107—222no—
299#107—221no—
300#107—221no—
301#106—22no—
302#106—222no—
303#106—222no—
304#106—222no—
305C4⋊C8—111no—
306C4⋊C8—112no—
307C4⋊C8—221no—
308C4⋊C8—222no—
309C4⋊C8C22×D1111yescharacteristic
310C4⋊C8C22×D1112yes—
311#102—22no—
312#102—222no—
313#102—222no—
314#102—222no—
315C22⋊C8—21no—
316C22⋊C8—221no—
317C22⋊C8—221no—
318C22⋊C8—221no—
319C4×C8—111no—
320C4×C8—111no—
321C4×C8—111no—
322C4×C8C22×D1111yescharacteristic
323C2×C11—81no—
324C2×C11C2×#46111yescharacteristic
325C2×C11C2×#47011yescharacteristic
326C2×C11C2×#47211yescharacteristic
327D11—81no—
328D11#169514yesdirect product factor
329C24—221no—
330C2×Q8—22no—
331C2×Q8—222no—
332C2×Q8—442no—
333C2×Q8—884no—
334C2×D4—111no—
335C2×D4—224no—
336C2×D4—221no—
337C2×D4D4×D1111yescharacteristic
338C22×C4—21no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4—442no—
349M16—42no—
350M16—442no—
351M16—442no—
352M16—442no—
353C2×C8—21no—
354C2×C8—22no—
355C2×C8—111no—
356C2×C8—114no—
357C2×C8—111no—
358C2×C8—222no—
359C2×C8—221no—
360C2×C8—222no—
361C2×C8—442no—
362C2×C8—444no—
363C2×C8D4×D1111yescharacteristic
364C2×C8D4×D1111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—111no—
368C4⋊C4—221no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4D4×D1111yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—221no—
376C22⋊C4—221no—
377C22⋊C4—221no—
378C42—111no—
379C42—111no—
380C42—111no—
381C42C23×D1111yescharacteristic
382C11C2×#169511yescharacteristic, complemented, Sylow
383C23—21no—
384C23—111no—
385C23—221no—
386C23—442no—
387C23—442no—
388C23—442no—
389Q8—82no—
390Q8—882no—
391Q8—884no—
392D4—22no—
393D4—222no—
394D4—442no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—111no—
400C2×C4—111no—
401C2×C4—112no—
402C2×C4—112no—
403C2×C4—114no—
404C2×C4—111no—
405C2×C4—222no—
406C2×C4—221no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—442no—
413C2×C4—884no—
414C2×C4C2×D4×D1111yescharacteristic
415C2×C4C2×D4×D1111yescharacteristic
416C2×C4#41×D1111yescharacteristic
417C8—21no—
418C8—41no—
419C8—42no—
420C8—112no—
421C8—221no—
422C8—441no—
423C8—442no—
424C8SD16×D1112yes—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—112no—
429C22—112no—
430C22—112no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22—884no—
435C22D11×#12111yescharacteristic
436C4—21no—
437C4—41no—
438C4—82no—
439C4—112no—
440C4—112no—
441C4—221no—
442C4—441no—
443C4—882no—
444C4C2×SD16×D1111yescharacteristic
445C4D11×#13711yescharacteristic
446C4D11×#13712yes—
447C2—81no—
448C2—114no—
449C2—881no—
450C2D11×#46111yescharacteristic
451C2D11×#47011yescharacteristic
452C2D11×#47211yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1695C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1695D11
hypocenterC11C2×#1695
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1695

Complements

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

NH ≅ G/Ntype
1. D11×#500C2semidirect
4. #13068140C2semidirect
5. #13068139C2semidirect
6. #13068138C2semidirect
7. #13068137C2semidirect
8. #13068136C2semidirect
9. D11×#334C2semidirect
10. D11×#333C2semidirect
11. C11×#1695C2semidirect
15. C11×#500C22semidirect
20. #10622691C22semidirect
39. #10622295C22semidirect
40. C11×#334C22semidirect
41. C11×#333C22semidirect
42. #10622184C22semidirect
43. #10622119C22semidirect
44. #10622119C22semidirect
45. #10622118C22semidirect
46. #10622095C22semidirect
165. #1695D11direct (N × H)
217. #500C2×D11semidirect
240. #334C2×D11semidirect
244. #333C2×D11semidirect
328. D11#1695direct (N × H)
382. C11C2×#1695semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
D11×#4762
D11×#4362
#130681402
#130681392
#130681382
#130681372
#130681362
D11×#3342
D11×#3332
C11×#16952
C2×#169511