Finite Group Databasebeta

← D11×#2229 #14908404

Subgroups — D11×#2229 #14908404

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#499C211yesmaximal, characteristic
2C4×Q16×D11C211yesmaximal, characteristic
3#13070783C211yesmaximal, characteristic, complemented
4#13070782C211yesmaximal, characteristic, complemented
5#13070781C211yesmaximal, characteristic, complemented
6#13070780C211yesmaximal, characteristic, complemented
7#13070779C211yesmaximal, characteristic, complemented
8#13070778C211yesmaximal, characteristic, complemented
9#13070777C211yesmaximal, characteristic, complemented
10D11×#367C211yesmaximal, characteristic
11D11×#366C211yesmaximal, characteristic
12D11×C4⋊C16C211yesmaximal, characteristic
13D11×#358C211yesmaximal, characteristic
14D11×#358C211yesmaximal, characteristic
15C11×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17D11×#125—21no—
18C4×Q8×D11—21no—
19C11×#499C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22#10622677—21no—
23C4×#4326—21no—
24C2×C16×D11C2211yescharacteristic
25C2×C16×D11C2211yescharacteristic
26D11×#107C2211yescharacteristic
27D11×#107C2211yescharacteristic
28D11×#107C2211yescharacteristic
29#10622491C2211yescharacteristic
30#10622491C2211yescharacteristic
31#10622486C2211yescharacteristic
32D11×#106—21no—
33#10622471—21no—
34D11×#103—21no—
35#10622403—21no—
36C4×Dic44C2211yescharacteristic
37C4×C8×D11C2211yescharacteristic
38#10622296C2211yescharacteristic
39C11×#367C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622143C2211yescharacteristic
47#10622142C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×C11×Q16C2311yescharacteristic
61C11×#125—21no—
62C4×Q8×C11—21no—
63Q8×Dic11—21no—
64C2×#4326—21no—
65Q16×D11—22no—
66Q16×D11Q814yes—
67C2×Dic44C2311yescharacteristic
68C2×C8×D11D411yescharacteristic
69C2×C8×D11C2311yescharacteristic
70C4⋊C4×D11—21no—
71C4⋊C4×D11—21no—
72C4⋊C4×D11—21no—
73C4⋊C4×D11—41no—
74C4⋊C4×D11—41no—
75C4⋊C4×D11—41no—
76#66943—21no—
77#66943—21no—
78#66942—41no—
79#66942—41no—
80#66940—21no—
81#66940—41no—
82C42×D11—41no—
83C42×D11D411yescharacteristic
84#66923—21no—
85C4×Dic22—21no—
86C4×Dic22—41no—
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C11×#103—21no—
94C4×C8×C11C2311yescharacteristic
95#66899—21no—
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66881—21no—
100#66880—21no—
101C8×Dic11D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C2×C11⋊C16C2311yescharacteristic
105#66874—21no—
106#66872—21no—
107#66872—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111C4×C11⋊C8D411yescharacteristic
112C16×D11—22no—
113C16×D11—22no—
114C2×#2229—111nomaximal, Sylow
115C2×Q8×C11—21no—
116Q8×D11—24no—
117Q8×D11—42no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11D811yescharacteristic
123C2×C4×D11D811yescharacteristic
124C2×C4×D11C2×D411yescharacteristic
125C2×Dic22—21no—
126C2×Dic22—41no—
127C11×Q16—21no—
128C11×Q16C2×Q812yes—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C42×C11—41no—
138C42×C11C2×D411yescharacteristic
139#4326—24no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11D811yescharacteristic
159C4×Dic11D811yescharacteristic
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163Dic44—21no—
164Dic44C2×Q812yes—
165C8×D11—22no—
166C8×D11C2×Q812yes—
167C8×D11#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172C2×#499—111no—
173C2×C4×Q16—111no—
174#2229—111no—
175#2229—111no—
176#2229—111no—
177#2229—111no—
178#2229—111no—
179#2229—111no—
180#2229—111no—
181#2229D1111yescharacteristic, direct product factor
182C2×#367—111no—
183C2×#366—111no—
184C2×C4⋊C16—111no—
185C2×#358—111no—
186C2×#358—111no—
187C22×D11C2×D811yescharacteristic
188Q8×C11—22no—
189Q8×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11C2×D811yescharacteristic
202C2×Dic11C2×D811yescharacteristic
203C2×Dic11C2×D811yescharacteristic
204C4×D11—22no—
205C4×D11—22no—
206C4×D11—44no—
207C4×D11—82no—
208C4×D11—82no—
209C4×D11—82no—
210C4×D11C22⋊Q812yes—
211C4×D11#13712yes—
212Dic22—22no—
213Dic22—41no—
214Dic22—44no—
215C8×C11—21no—
216C8×C11C22×Q811yescharacteristic
217C8×C11C2×#4111yescharacteristic
218C11⋊C8—21no—
219C11⋊C8C22⋊Q812yes—
220C22×Q16—111no—
221C2×#125—221no—
222C2×C4×Q8—221no—
223C22×C16—111no—
224C22×C16—111no—
225#499—111no—
226#499—111no—
227#499—111no—
228#499—221no—
229#499—221no—
230#499C2×D1111yescharacteristic
231C4×Q16—111no—
232C4×Q16—111no—
233C4×Q16—111no—
234C4×Q16—221no—
235C4×Q16—221no—
236C4×Q16C2×D1111yescharacteristic
237C2×#107—111no—
238C2×#107—111no—
239C2×#107—111no—
240C2×#106—221no—
241C2×#103—221no—
242C2×C4×C8—111no—
243#367—111no—
244#367—111no—
245#367—111no—
246#367C2×D1111yescharacteristic
247#366—111no—
248#366—111no—
249#366—111no—
250#366C2×D1111yescharacteristic
251C4⋊C16—111no—
252C4⋊C16—111no—
253C4⋊C16—111no—
254C4⋊C16C2×D1111yescharacteristic
255#358—111no—
256#358—111no—
257#358—111no—
258#358—111no—
259#358—111no—
260#358—111no—
261#358C2×D1111yescharacteristic
262#358C2×D1111yescharacteristic
263C22×C11C22×D811yescharacteristic
264C2×D11#47412yes—
265C2×D11#50812yes—
266C2×D11#51012yes—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11C2×C22⋊Q811yescharacteristic
274C4×C11C2×#13711yescharacteristic
275Dic11—21no—
276Dic11—21no—
277Dic11—42no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281Dic11#47412yes—
282C22×Q8—221no—
283C2×Q16—114no—
284C2×Q16—111no—
285C2×Q16—222no—
286C2×Q16—221no—
287C2×Q16C22×D1111yescharacteristic
288C22×C8—111no—
289C22×C8—111no—
290#125—21no—
291#125—221no—
292#125—221no—
293#125—221no—
294#125—441no—
295#125—441no—
296C4×Q8—21no—
297C4×Q8—221no—
298C4×Q8—221no—
299C4×Q8—221no—
300C4×Q8—441no—
301C4×Q8—441no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—441no—
306C2×C4⋊C4—441no—
307C2×C4⋊C4—441no—
308C2×C42—111no—
309C2×C42—441no—
310C2×C16—111no—
311C2×C16—111no—
312C2×C16—222no—
313C2×C16—222no—
314C2×C16C22×D1111yescharacteristic
315C2×C16C22×D1111yescharacteristic
316#107—111no—
317#107—111no—
318#107—111no—
319#107—221no—
320#107—221no—
321#107—221no—
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#107C22×D1111yescharacteristic
325#106—21no—
326#106—221no—
327#106—221no—
328#106—221no—
329#103—21no—
330#103—221no—
331#103—221no—
332#103—221no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8—111no—
336C4×C8C22×D1111yescharacteristic
337C2×C11C2×#47411yescharacteristic
338C2×C11C2×#50811yescharacteristic
339C2×C11C2×#51011yescharacteristic
340D11#222914yesdirect product factor
341C2×Q8—21no—
342C2×Q8—224no—
343C2×Q8—221no—
344C2×Q8—441no—
345C2×Q8—442no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4—441no—
353Q16—21no—
354Q16—112no—
355Q16—224no—
356Q16—221no—
357Q16Q8×D1112yes—
358C2×C8—111no—
359C2×C8—112no—
360C2×C8—112no—
361C2×C8—111no—
362C2×C8—222no—
363C2×C8D4×D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C42—41no—
387C42—111no—
388C42—111no—
389C42—111no—
390C42—441no—
391C42—441no—
392C42—441no—
393C42D4×D1111yescharacteristic
394C16—21no—
395C16—21no—
396C16—221no—
397C16—221no—
398C11C2×#222911yescharacteristic, complemented, Sylow
399C23—111no—
400Q8—22no—
401Q8—41no—
402Q8—222no—
403Q8—444no—
404Q8—441no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—111no—
410C2×C4—112no—
411C2×C4—112no—
412C2×C4—111no—
413C2×C4—111no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—444no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—882no—
422C2×C4—882no—
423C2×C4—882no—
424C2×C4D8×D1111yescharacteristic
425C2×C4D8×D1111yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C8—21no—
428C8—112no—
429C8—221no—
430C8C2×Q8×D1111yescharacteristic
431C8#41×D1111yescharacteristic
432C22—112no—
433C22—112no—
434C22—112no—
435C22C2×D8×D1111yescharacteristic
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—112no—
443C4—221no—
444C4—221no—
445C4—442no—
446C4—881no—
447C4—881no—
448C4—881no—
449C4D11×C22⋊Q811yescharacteristic
450C4D11×#13711yescharacteristic
451C2—114no—
452C2D11×#47411yescharacteristic
453C2D11×#50811yescharacteristic
454C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2229C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2229D11
hypocenterC11C2×#2229
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #13070783C2semidirect
4. #13070782C2semidirect
5. #13070781C2semidirect
6. #13070780C2semidirect
7. #13070779C2semidirect
8. #13070778C2semidirect
9. #13070777C2semidirect
15. C11×#2229C2semidirect
181. #2229D11direct (N × H)
340. D11#2229direct (N × H)
398. C11C2×#2229semidirect

Maximal subgroups

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

subgroupindex
D11×#4992
C4×Q16×D112
#130707832
#130707822
#130707812
#130707802
#130707792
#130707782
#130707772
D11×#3672
D11×#3662
D11×C4⋊C162
D11×#3582
C11×#22292
C2×#222911