Finite Group Databasebeta

← D11×#2099 #14783665

Subgroups — D11×#2099 #14783665

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#389C211yesmaximal, characteristic
2D11×#384C211yesmaximal, characteristic
3#13070177C212yesmaximal, complemented
4#13070176C212yesmaximal, complemented
5#13070175C211yesmaximal, characteristic, complemented
6#13070174C211yesmaximal, characteristic, complemented
7#13070173C211yesmaximal, characteristic, complemented
8D11×#340C212yesmaximal
9D11×#340C212yesmaximal
10D11×#336C211yesmaximal, characteristic
11C11×#2099C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×C4⋊C4×D11—21no—
14C2×C4⋊C4×D11—21no—
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11C2212yes—
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C42×D11C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#384C2211yescharacteristic
22#10622598C2211yescharacteristic
23#10622589—21no—
24#10622589—21no—
25#10622589C2212yes—
26#10622586C2211yescharacteristic
27#10622585—21no—
28#10622548C2211yescharacteristic
29#10622541C2211yescharacteristic
30D11×#95—21no—
31#10622260—21no—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2211yescharacteristic
35#10622189C2212yes—
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2211yescharacteristic
43C22×C4×D11—21no—
44C22×C4×D11—22no—
45C22×C4×D11—21no—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C2×C8×D11—24no—
75C2×C8×D11—24no—
76C2×C8×D11—24no—
77C4⋊C4×D11—22no—
78C4⋊C4×D11—24no—
79C4⋊C4×D11—28no—
80C4⋊C4×D11—44no—
81C4⋊C4×D11—44no—
82C4⋊C4×D11—44no—
83C4⋊C4×D11Q814yes—
84C42×D11—24no—
85C11×#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C2×#2099—111nomaximal, Sylow
90C23×D11C2×D411yescharacteristic
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C2×C4×D11—24no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—42no—
109C2×C4×D11—44no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—44no—
113C2×C4×D11—44no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×C4×D11D814yes—
117C2×C4×D11SD1614yes—
118C2×C4×D11C2×Q812yes—
119C2×C4×D11#4112yes—
120C2×C4×D11#4114yes—
121C2×C4×D11#4114yes—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C2×Q812yes—
132C42×C11—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—24no—
136C4⋊Dic11—42no—
137C4⋊Dic11—42no—
138C4⋊Dic11—42no—
139C4⋊Dic11C2×Q812yes—
140Dic11⋊C4—24no—
141Dic11⋊C4—42no—
142Dic11⋊C4—44no—
143Dic11⋊C4—42no—
144Dic11⋊C4—44no—
145Dic11⋊C4—44no—
146Dic11⋊C4—42no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C8×D11—48no—
154C2×#389—111no—
155C2×#384—111no—
156#2099—111no—
157#2099—111no—
158#2099—112no—
159#2099—112no—
160#2099—111no—
161#2099D1111yescharacteristic, direct product factor
162C2×#340—112no—
163C2×#340—112no—
164C2×#336—111no—
165C23×C11C22×D411yescharacteristic
166C22×D11C22⋊Q812yes—
167C22×D11#12312yes—
168C22×D11#12412yes—
169C22×D11C2×D812yes—
170C22×D11C2×SD1612yes—
171C22×D11#13712yes—
172C22×D11#13712yes—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11C2×D812yes—
187C2×C4×C11C2×SD1612yes—
188C2×C4×C11C22×Q811yescharacteristic
189C2×C4×C11C2×#4112yes—
190C2×C4×C11C2×#4112yes—
191C2×C4×C11C2×#4111yescharacteristic
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—22no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11C22⋊Q812yes—
206C2×Dic11#12312yes—
207C2×Dic11#12412yes—
208C2×Dic11C2×D812yes—
209C2×Dic11C2×SD1612yes—
210C4×D11—28no—
211C4×D11—28no—
212C4×D11—48no—
213C4×D11—84no—
214C4×D11—88no—
215C4×D11#12518yes—
216C4×D11#12618yes—
217C8×C11—42no—
218C11⋊C8—42no—
219C23×C8—112no—
220C22×C4⋊C4—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—221no—
224C22×C4⋊C4—221no—
225C22×C4⋊C4—221no—
226C22×C42—111no—
227#389—111no—
228#389—111no—
229#389—111no—
230#389—221no—
231#389—221no—
232#389C2×D1111yescharacteristic
233#384—112no—
234#384—111no—
235#384—221no—
236#384—221no—
237#384C2×D1111yescharacteristic
238C2×#95—221no—
239#340—112no—
240#340—112no—
241#340—112no—
242#340—112no—
243#340—112no—
244#340—112no—
245#340C2×D1112yes—
246#340C2×D1112yes—
247#336—112no—
248#336—111no—
249#336C2×D1111yescharacteristic
250C22×C11C2×C22⋊Q811yescharacteristic
251C22×C11C2×#12311yescharacteristic
252C22×C11C2×#12411yescharacteristic
253C22×C11C22×D811yescharacteristic
254C22×C11C22×SD1611yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C22×C11C2×#13711yescharacteristic
257C2×D11#40014yes—
258C2×D11#47414yes—
259C2×D11#47514yes—
260C2×D11#48014yes—
261C2×D11#48314yes—
262C2×D11#48614yes—
263C2×D11#49114yes—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—81no—
268C4×C11—82no—
269C4×C11C2×#12512yes—
270C4×C11C2×#12612yes—
271Dic11—22no—
272Dic11—22no—
273Dic11—42no—
274Dic11—81no—
275Dic11—82no—
276Dic11#40014yes—
277C23×C4—111no—
278C23×C4—111no—
279C23×C4—111no—
280C23×C4—221no—
281C23×C4—222no—
282C23×C4—221no—
283C22×C8—112no—
284C22×C8—224no—
285C22×C8—224no—
286C22×C8—224no—
287C22×C8C22×D1112yes—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—114no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—224no—
297C2×C4⋊C4—228no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—444no—
309C2×C4⋊C4—444no—
310C2×C4⋊C4—444no—
311C2×C4⋊C4C22×D1112yes—
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C4⋊C4C22×D1111yescharacteristic
314C2×C42—111no—
315C2×C42—111no—
316C2×C42—111no—
317C2×C42—224no—
318C2×C42C22×D1111yescharacteristic
319#95—21no—
320#95—221no—
321#95—221no—
322#95—221no—
323C2×C11C2×#40011yescharacteristic
324C2×C11C2×#47411yescharacteristic
325C2×C11C2×#47511yescharacteristic
326C2×C11C2×#48011yescharacteristic
327C2×C11C2×#48311yescharacteristic
328C2×C11C2×#48611yescharacteristic
329C2×C11C2×#49111yescharacteristic
330D11#209918yesdirect product factor
331C24—111no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—111no—
336C22×C4—112no—
337C22×C4—114no—
338C22×C4—114no—
339C22×C4—112no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—114no—
343C22×C4—114no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—224no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4—444no—
356C22×C4—444no—
357C22×C4—442no—
358C22×C4—444no—
359C22×C4—442no—
360C22×C4D4×D1111yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4C23×D1111yescharacteristic
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—448no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—24no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—112no—
377C4⋊C4—224no—
378C4⋊C4—221no—
379C4⋊C4—222no—
380C4⋊C4—224no—
381C4⋊C4—442no—
382C4⋊C4—444no—
383C4⋊C4—442no—
384C4⋊C4—444no—
385C4⋊C4—444no—
386C4⋊C4—442no—
387C4⋊C4—442no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4Q8×D1112yes—
391C42—22no—
392C42—222no—
393C42—222no—
394C42—222no—
395C11C2×#209911yescharacteristic, complemented, Sylow
396C23—112no—
397C23—112no—
398C23—112no—
399C23—112no—
400C23—112no—
401C23—112no—
402C23—112no—
403C23C2×D4×D1111yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—112no—
418C2×C4—112no—
419C2×C4—112no—
420C2×C4—118no—
421C2×C4—118no—
422C2×C4—112no—
423C2×C4—112no—
424C2×C4—228no—
425C2×C4—228no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—222no—
431C2×C4—448no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—442no—
440C2×C4—888no—
441C2×C4—884no—
442C2×C4D8×D1112yes—
443C2×C4SD16×D1112yes—
444C2×C4C2×Q8×D1111yescharacteristic
445C2×C4#41×D1111yescharacteristic
446C2×C4#41×D1112yes—
447C2×C4#41×D1112yes—
448C8—42no—
449C8—442no—
450C22—114no—
451C22—114no—
452C22—114no—
453C22—114no—
454C22—114no—
455C22—114no—
456C22—114no—
457C22D11×C22⋊Q811yescharacteristic
458C22D11×#12311yescharacteristic
459C22D11×#12411yescharacteristic
460C22C2×D8×D1111yescharacteristic
461C22C2×SD16×D1111yescharacteristic
462C22D11×#13711yescharacteristic
463C22D11×#13711yescharacteristic
464C4—22no—
465C4—22no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—114no—
470C4—222no—
471C4—222no—
472C4—442no—
473C4—882no—
474C4—881no—
475C4D11×#12512yes—
476C4D11×#12612yes—
477C2—118no—
478C2D11×#40011yescharacteristic
479C2D11×#47411yescharacteristic
480C2D11×#47511yescharacteristic
481C2D11×#48011yescharacteristic
482C2D11×#48311yescharacteristic
483C2D11×#48611yescharacteristic
484C2D11×#49111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2099C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2099D11
hypocenterC11C2×#2099
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #13070177C2semidirect
4. #13070176C2semidirect
5. #13070175C2semidirect
6. #13070174C2semidirect
7. #13070173C2semidirect
11. C11×#2099C2semidirect
161. #2099D11direct (N × H)
330. D11#2099direct (N × H)
395. C11C2×#2099semidirect

Maximal subgroups

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

subgroupindex
D11×#3892
D11×#3842
#130701772
#130701762
#130701752
#130701742
#130701732
D11×#3402
D11×#3362
C11×#20992
C2×#209911