Finite Group Databasebeta

← D11×#1694 #14736397

Subgroups — D11×#1694 #14736397

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#500C211yesmaximal, characteristic
2D11×#462C212yesmaximal
3D11×#446C211yesmaximal, characteristic
4#13068135C211yesmaximal, characteristic, complemented
5#13068134C211yesmaximal, characteristic, complemented
6#13068133C212yesmaximal, complemented
7#13068132C212yesmaximal, complemented
8#13068131C211yesmaximal, characteristic, complemented
9D11×#334C211yesmaximal, characteristic
10D11×#332C212yesmaximal
11C11×#1694C211yesmaximal, characteristic, complemented
12C2×Q16×D11—22no—
13D11×C4⋊Q8C2212yes—
14C4×Q8×D11C2211yescharacteristic
15C11×#500C2211yescharacteristic
16C11×#462C2212yes—
17C11×#446C2211yescharacteristic
18#10622795—22no—
19#10622703C2212yes—
20#10622691C2212yes—
21#10622644C2212yes—
22#10622637C2211yescharacteristic
23D11×#107—21no—
24D11×#107—21no—
25#10622487—21no—
26#10622487—21no—
27#10622462C2212yes—
28D11×C4⋊C8—21no—
29D11×C4⋊C8C2212yes—
30D11×C4⋊C8C2211yescharacteristic
31#10622444C2211yescharacteristic
32#10622441—21no—
33D11×#103—22no—
34#10622406—22no—
35D11×#97—21no—
36#10622314—21no—
37C4×C8×D11C2211yescharacteristic
38#10622295C2211yescharacteristic
39#10622292C2211yescharacteristic
40C11×#334C2211yescharacteristic
41C11×#332C2212yes—
42#10622185C2212yes—
43#10622124C2212yes—
44#10622120C2212yes—
45#10622118C2212yes—
46#10622095C2211yescharacteristic
47C2×Q8×D11—22no—
48C2×Q8×D11D411yescharacteristic
49C2×C11×Q16—22no—
50C11×C4⋊Q8C2312yes—
51C4×Q8×C11C2311yescharacteristic
52Q8×Dic11D411yescharacteristic
53#66997—22no—
54C2×#4326—22no—
55C2×#4326—22no—
56Q16×D11—48no—
57C2×Dic44—22no—
58C2×C8×D11—22no—
59C2×C8×D11—21no—
60C2×C8×D11D411yescharacteristic
61C2×C8×D11D411yescharacteristic
62C4⋊C4×D11—21no—
63C4⋊C4×D11—22no—
64C4⋊C4×D11—22no—
65C4⋊C4×D11D411yescharacteristic
66#66941—22no—
67#66941—22no—
68#66940—21no—
69#66940D411yescharacteristic
70C42×D11—21no—
71C42×D11C2311yescharacteristic
72#66922C2312yes—
73C4×Dic22—21no—
74C4×Dic22C2311yescharacteristic
75C11×#107—21no—
76C11×#107—21no—
77C11×C4⋊C8—21no—
78C11×C4⋊C8C2311yescharacteristic
79C11×C4⋊C8C2312yes—
80C11×#103—22no—
81C11×#97—21no—
82C4×C8×C11C2311yescharacteristic
83#66899—22no—
84#66882—21no—
85#66882—21no—
86#66880—22no—
87#66879—21no—
88#66879—21no—
89Dic11⋊C8—21no—
90Dic11⋊C8—22no—
91Dic11⋊C8—21no—
92Dic11⋊C8—21no—
93C8×Dic11D411yescharacteristic
94C8×Dic11D411yescharacteristic
95#66874—22no—
96#66871—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2312yes—
101#66867—21no—
102C4×C11⋊C8C2311yescharacteristic
103C2×#1694—111nomaximal, Sylow
104C2×Q8×C11—22no—
105C2×Q8×C11C2×D411yescharacteristic
106Q8×D11—24no—
107Q8×D11—44no—
108Q8×D11—44no—
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—42no—
112C2×C4×D11C2×D411yescharacteristic
113C2×C4×D11C2×D411yescharacteristic
114C2×C4×D11#4111yescharacteristic
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—42no—
118C2×Dic22C2×D411yescharacteristic
119C11×Q16—44no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4C2×D411yescharacteristic
128C42×C11—21no—
129C42×C11C2411yescharacteristic
130#4326—44no—
131#4326—44no—
132C4⋊Dic11—21no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11C2×D411yescharacteristic
136Dic11⋊C4—21no—
137Dic11⋊C4—21no—
138Dic11⋊C4—21no—
139Dic11⋊C4—42no—
140Dic11⋊C4—42no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144C4×Dic11C2×D411yescharacteristic
145C4×Dic11C2×D411yescharacteristic
146C4×Dic11#4111yescharacteristic
147C2×C11⋊C8—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8C2×D411yescharacteristic
150C2×C11⋊C8C2×D411yescharacteristic
151Dic44—44no—
152C8×D11—22no—
153C8×D11—44no—
154C8×D11—42no—
155C8×D11Q1614yescomplemented
156C2×#500—111no—
157C2×#462—112no—
158C2×#446—111no—
159#1694—111no—
160#1694—112no—
161#1694—111no—
162#1694—111no—
163#1694—112no—
164#1694D1111yescharacteristic, direct product factor
165C2×#334—111no—
166C2×#332—112no—
167C22×D11#12111yescharacteristic
168Q8×C11—22no—
169Q8×C11—42no—
170Q8×C11—42no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—42no—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—42no—
180C2×Dic11#12111yescharacteristic
181C2×Dic11#12111yescharacteristic
182C2×Dic11#12111yescharacteristic
183C4×D11—22no—
184C4×D11—42no—
185C4×D11—42no—
186C4×D11—84no—
187C4×D11C2×Q1612yes—
188C4×D11AGL(1,ℤ/8)14yes—
189C4×D11#13712yes—
190Dic22—22no—
191Dic22—42no—
192Dic22—42no—
193Dic22—42no—
194Dic22—84no—
195C8×C11—21no—
196C8×C11—42no—
197C8×C11—41no—
198C8×C11C2×Q1612yescomplemented
199C11⋊C8—21no—
200C11⋊C8—42no—
201C11⋊C8—41no—
202C11⋊C8C2×Q1612yescomplemented
203C22×Q16—222no—
204C2×C4⋊Q8—112no—
205C2×C4×Q8—111no—
206#500—112no—
207#500—111no—
208#500—221no—
209#500—221no—
210#500C2×D1111yescharacteristic
211#462—112no—
212#462—112no—
213#462—112no—
214#462—222no—
215#462—222no—
216#462C2×D1112yes—
217#446—111no—
218#446—111no—
219#446—111no—
220#446—221no—
221#446—221no—
222#446C2×D1111yescharacteristic
223C2×#107—221no—
224C2×#107—221no—
225C2×C4⋊C8—111no—
226C2×C4⋊C8—112no—
227C2×C4⋊C8—221no—
228C2×#103—222no—
229C2×#97—221no—
230C2×C4×C8—111no—
231#334—112no—
232#334—111no—
233#334C2×D1111yescharacteristic
234#332—112no—
235#332—112no—
236#332—112no—
237#332C2×D1112yes—
238C22×C11C2×#12111yescharacteristic
239C2×D11#46212yes—
240C2×D11#46912yes—
241C2×D11#47312yes—
242C4×C11—21no—
243C4×C11—41no—
244C4×C11—41no—
245C4×C11—82no—
246C4×C11C22×Q1611yescharacteristic
247C4×C11C2×AGL(1,ℤ/8)12yes—
248C4×C11C2×#13711yescharacteristic
249Dic11—21no—
250Dic11—41no—
251Dic11—41no—
252Dic11—82no—
253Dic11#46212yes—
254Dic11#46912yes—
255C22×Q8—111no—
256C22×Q8—222no—
257C2×Q16—22no—
258C2×Q16—222no—
259C2×Q16—222no—
260C2×Q16—222no—
261C2×Q16—448no—
262C22×C8—111no—
263C22×C8—111no—
264C22×C8—222no—
265C22×C8—221no—
266C4⋊Q8—112no—
267C4⋊Q8—222no—
268C4⋊Q8—222no—
269C4⋊Q8—222no—
270C4⋊Q8C22×D1112yes—
271C4×Q8—111no—
272C4×Q8—111no—
273C4×Q8—111no—
274C4×Q8—221no—
275C4×Q8—221no—
276C4×Q8C22×D1111yescharacteristic
277C2×C4⋊C4—111no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—222no—
281C2×C42—111no—
282C2×C42—221no—
283#107—21no—
284#107—21no—
285#107—222no—
286#107—222no—
287#107—221no—
288#107—221no—
289C4⋊C8—21no—
290C4⋊C8—111no—
291C4⋊C8—112no—
292C4⋊C8—221no—
293C4⋊C8—221no—
294C4⋊C8—222no—
295C4⋊C8—221no—
296C4⋊C8—221no—
297C4⋊C8C22×D1111yescharacteristic
298C4⋊C8C22×D1112yes—
299#103—22no—
300#103—222no—
301#103—222no—
302#103—222no—
303#97—21no—
304#97—221no—
305#97—221no—
306#97—221no—
307C4×C8—111no—
308C4×C8—111no—
309C4×C8—111no—
310C4×C8C22×D1111yescharacteristic
311C2×C11C2×#46211yescharacteristic
312C2×C11C2×#46911yescharacteristic
313C2×C11C2×#47311yescharacteristic
314D11#169414yesdirect product factor
315C2×Q8—22no—
316C2×Q8—111no—
317C2×Q8—221no—
318C2×Q8—224no—
319C2×Q8—222no—
320C2×Q8—442no—
321C2×Q8—444no—
322C2×Q8—444no—
323C2×Q8D4×D1111yescharacteristic
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—442no—
330Q16—44no—
331Q16—444no—
332Q16—444no—
333Q16—444no—
334C2×C8—21no—
335C2×C8—22no—
336C2×C8—111no—
337C2×C8—114no—
338C2×C8—111no—
339C2×C8—222no—
340C2×C8—221no—
341C2×C8—222no—
342C2×C8—444no—
343C2×C8—442no—
344C2×C8D4×D1111yescharacteristic
345C2×C8D4×D1111yescharacteristic
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—111no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C4⋊C4—221no—
354C4⋊C4—222no—
355C4⋊C4—222no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4D4×D1111yescharacteristic
359C42—21no—
360C42—111no—
361C42—111no—
362C42—111no—
363C42—221no—
364C42—221no—
365C42—221no—
366C42C23×D1111yescharacteristic
367C11C2×#169411yescharacteristic, complemented, Sylow
368C23—111no—
369Q8—22no—
370Q8—42no—
371Q8—42no—
372Q8—222no—
373Q8—442no—
374Q8—442no—
375Q8—442no—
376Q8—884no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—111no—
381C2×C4—111no—
382C2×C4—112no—
383C2×C4—114no—
384C2×C4—112no—
385C2×C4—111no—
386C2×C4—222no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—884no—
393C2×C4C2×D4×D1111yescharacteristic
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4#41×D1111yescharacteristic
396C8—21no—
397C8—42no—
398C8—41no—
399C8—112no—
400C8—221no—
401C8—442no—
402C8—441no—
403C8Q16×D1112yescomplemented
404C22—112no—
405C22—112no—
406C22—112no—
407C22D11×#12111yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—82no—
412C4—112no—
413C4—112no—
414C4—221no—
415C4—441no—
416C4—441no—
417C4—882no—
418C4C2×Q16×D1111yescharacteristic
419C4D11×AGL(1,ℤ/8)12yes—
420C4D11×#13711yescharacteristic
421C2—114no—
422C2D11×#46211yescharacteristic
423C2D11×#46911yescharacteristic
424C2D11×#47311yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1694C2
socleC22×C11C2×#121
prime radicalC22×D11#121
hypercenter#1694D11
hypocenterC11C2×#1694
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1694

Complements

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

NH ≅ G/Ntype
4. #13068135C2semidirect
5. #13068134C2semidirect
6. #13068133C2semidirect
7. #13068132C2semidirect
8. #13068131C2semidirect
11. C11×#1694C2semidirect
155. C8×D11Q16semidirect
164. #1694D11direct (N × H)
198. C8×C11C2×Q16semidirect
202. C11⋊C8C2×Q16semidirect
314. D11#1694direct (N × H)
367. C11C2×#1694semidirect
403. C8Q16×D11semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
D11×#4622
D11×#4462
#130681352
#130681342
#130681332
#130681322
#130681312
D11×#3342
D11×#3322
C11×#16942
C2×#169411