Finite Group Databasebeta

← D11×#2235 #14908533

Subgroups — D11×#2235 #14908533

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#467C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic
3#13070815C212yesmaximal, complemented
4#13070814C211yesmaximal, characteristic, complemented
5#13070813C211yesmaximal, characteristic, complemented
6#13070812C212yesmaximal, complemented
7#13070811C211yesmaximal, characteristic, complemented
8D11×#367C212yesmaximal, complemented
9D11×#358C212yesmaximal, complemented
10D11×C22⋊C16C211yesmaximal, characteristic
11C11×#2235C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14D11×C22⋊Q8—21no—
15C2×C4⋊C4×D11—21no—
16C11×#467C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622801C2211yescharacteristic
19#10622729C2211yescharacteristic
20C2×#66882C2211yescharacteristic
21#10622664—21no—
22C2×#66871—21no—
23C2×C16×D11C2212yes—
24#10622500C2211yescharacteristic
25D11×#107—21no—
26D11×#107—21no—
27D11×#107C2211yescharacteristic
28D11×#107C2212yes—
29D11×#107C2212yes—
30#10622426—21no—
31D11×#103—21no—
32C11×#367C2212yescomplemented
33C11×#358C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic
37(C2×D11)⋊C16C2212yes—
38#10622143C2212yescomplemented
39#10622141C2212yescomplemented
40#10622130C2212yescomplemented
41#10622128C2212yescomplemented
42#10622128C2212yescomplemented
43C2×Q8×D11—21no—
44C22×C4×D11—41no—
45C22×C4×D11D411yescharacteristic
46C2×C11×Q16C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C22⋊Q8—21no—
49C2×C11×C4⋊C4—21no—
50#66999—21no—
51C2×#4326—21no—
52C2×C4⋊Dic11—21no—
53#66977—21no—
54C2×Dic11⋊C4—41no—
55C22×C11⋊C8D411yescharacteristic
56Q16×D11—24no—
57C2×Dic44C2311yescharacteristic
58C2×C8×D11—24no—
59C2×C8×D11D411yescharacteristic
60C2×C8×D11D411yescharacteristic
61C2×C8×D11C2311yescharacteristic
62C2×C8×D11C2311yescharacteristic
63#66950—21no—
64#66949—41no—
65C4⋊C4×D11—22no—
66C4⋊C4×D11—22no—
67C4⋊C4×D11—21no—
68C4⋊C4×D11—41no—
69C4⋊C4×D11—41no—
70C4⋊C4×D11—41no—
71C22⋊C4×D11—41no—
72#66931—41no—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2312yes—
76C11×#107C2311yescharacteristic
77C11×#103—21no—
78#66899—21no—
79#66882—21no—
80#66882C2311yescharacteristic
81#66882C2312yes—
82#66880—21no—
83C2×C11⋊C16C2312yes—
84#66874—21no—
85#66871—22no—
86#66871—22no—
87#66871—21no—
88C16×D11—24no—
89C2×#2235—111nomaximal, Sylow
90C23×D11D811yescharacteristic
91C2×Q8×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—41no—
95C22×Dic11D811yescharacteristic
96Q8×D11—42no—
97Q8×D11—42no—
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C2×C4×D11—84no—
105C2×C4×D11D811yescharacteristic
106C2×C4×D11D811yescharacteristic
107C2×C4×D11C2×D411yescharacteristic
108C2×C4×D11C2×D411yescharacteristic
109C2×Dic22—21no—
110C2×Dic22—41no—
111C11×Q16—22no—
112C2×C8×C11—22no—
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C22⋊Dic11—41no—
121#4326—42no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130Dic11⋊C4—42no—
131Dic11⋊C4—42no—
132Dic11⋊C4—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136Dic44—22no—
137C8×D11—22no—
138C8×D11—22no—
139C8×D11—22no—
140C8×D11#4114yes—
141C11×C16—22no—
142C11⋊C16—22no—
143C2×#467—111no—
144C22×#107—111no—
145#2235—111no—
146#2235—111no—
147#2235—112no—
148#2235—112no—
149#2235—111no—
150#2235D1111yescharacteristic, direct product factor
151C2×#367—112no—
152C2×#358—112no—
153C2×C22⋊C16—111no—
154C23×C11C2×D811yescharacteristic
155C22×D11—22no—
156C22×D11—22no—
157C22×D11SD3214yes—
158C22×D11C2×D811yescharacteristic
159C22×D11C2×D811yescharacteristic
160Q8×C11—41no—
161Q8×C11—41no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—82no—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×Dic11—22no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—82no—
175C2×Dic11C2×D811yescharacteristic
176C2×Dic11C2×D811yescharacteristic
177C4×D11—22no—
178C4×D11—21no—
179C4×D11—21no—
180C4×D11—22no—
181C4×D11—82no—
182C4×D11—84no—
183C4×D11—84no—
184C4×D11—82no—
185C4×D11#12312yes—
186C4×D11#13712yes—
187Dic22—41no—
188Dic22—41no—
189Dic22—82no—
190C8×C11—21no—
191C8×C11C2×#4112yes—
192C11⋊C8—21no—
193C11⋊C8#12312yes—
194C22×Q16—111no—
195C23×C8—111no—
196C2×C22⋊Q8—221no—
197C22×C4⋊C4—221no—
198C22×C16—112no—
199#467—111no—
200#467—111no—
201#467—111no—
202#467—221no—
203#467—221no—
204#467C2×D1111yescharacteristic
205C2×#107—111no—
206C2×#107—112no—
207C2×#107—112no—
208C2×#107—111no—
209C2×#107—221no—
210C2×#107—221no—
211C2×#107—221no—
212C2×#107C2×D1111yescharacteristic
213C2×#103—221no—
214#367—112no—
215#367—112no—
216#367—112no—
217#367C2×D1112yescomplemented
218#358—112no—
219#358—112no—
220#358—112no—
221#358C2×D1112yescomplemented
222C22⋊C16—111no—
223C22⋊C16—112no—
224C22⋊C16C2×D1111yescharacteristic
225C22×C11—21no—
226C22×C11—21no—
227C22×C11C2×SD3212yes—
228C22×C11C22×D811yescharacteristic
229C2×D11—21no—
230C2×D11—21no—
231C2×D11—28no—
232C2×D11#48012yes—
233C2×D11C2×SD3212yes—
234C2×D11C2×SD3212yes—
235C2×D11#51012yes—
236C4×C11—21no—
237C4×C11—81no—
238C4×C11—82no—
239C4×C11—81no—
240C4×C11C2×#12311yescharacteristic
241C4×C11C2×#13711yescharacteristic
242Dic11—21no—
243Dic11—81no—
244Dic11—82no—
245Dic11—81no—
246Dic11#48012yes—
247C22×Q8—221no—
248C23×C4—111no—
249C23×C4—441no—
250C2×Q16—111no—
251C2×Q16—224no—
252C2×Q16—221no—
253C2×Q16C22×D1111yescharacteristic
254C22×C8—111no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—111no—
258C22×C8—111no—
259C22×C8—224no—
260C22×C8C22×D1111yescharacteristic
261C22⋊Q8—21no—
262C22⋊Q8—221no—
263C22⋊Q8—221no—
264C22⋊Q8—221no—
265C22⋊Q8—441no—
266C22⋊Q8—441no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—441no—
273C2×C4⋊C4—441no—
274C2×C4⋊C4—441no—
275C2×C4⋊C4—441no—
276C2×C22⋊C4—441no—
277C2×C16—112no—
278C2×C16—224no—
279C2×C16C22×D1112yes—
280#107—21no—
281#107—112no—
282#107—111no—
283#107—222no—
284#107—222no—
285#107—221no—
286#107—221no—
287#107C22×D1112yes—
288#107C22×D1111yescharacteristic
289#103—21no—
290#103—221no—
291#103—221no—
292#103—221no—
293C2×C11—22no—
294C2×C11C2×#48011yescharacteristic
295C2×C11C22×SD3211yescharacteristic
296C2×C11C2×#51011yescharacteristic
297D11—22no—
298D11#223514yesdirect product factor
299C24—111no—
300C2×Q8—21no—
301C2×Q8—221no—
302C2×Q8—441no—
303C2×Q8—442no—
304C2×Q8—442no—
305C22×C4—41no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4—441no—
318C22×C4—884no—
319C22×C4D4×D1111yescharacteristic
320Q16—22no—
321Q16—222no—
322Q16—442no—
323C2×C8—22no—
324C2×C8—111no—
325C2×C8—114no—
326C2×C8—111no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8D4×D1111yescharacteristic
332C2×C8C23×D1111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—221no—
338C4⋊C4—222no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C22⋊C4—41no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C16—22no—
351C16—222no—
352C11C2×#223511yescharacteristic, complemented, Sylow
353C23—111no—
354C23—111no—
355C23—114no—
356C23—222no—
357C23—222no—
358C23D8×D1111yescharacteristic
359Q8—41no—
360Q8—41no—
361Q8—441no—
362Q8—441no—
363Q8—882no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—82no—
370C2×C4—111no—
371C2×C4—112no—
372C2×C4—112no—
373C2×C4—111no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—442no—
382C2×C4—884no—
383C2×C4—884no—
384C2×C4—882no—
385C2×C4—882no—
386C2×C4—882no—
387C2×C4D8×D1111yescharacteristic
388C2×C4C2×D4×D1111yescharacteristic
389C8—21no—
390C8—112no—
391C8—221no—
392C8#41×D1112yes—
393C22—21no—
394C22—21no—
395C22—112no—
396C22—112no—
397C22—112no—
398C22—112no—
399C22—228no—
400C22—221no—
401C22—221no—
402C22D11×SD3212yes—
403C22C2×D8×D1111yescharacteristic
404C4—21no—
405C4—82no—
406C4—81no—
407C4—81no—
408C4—112no—
409C4—221no—
410C4—882no—
411C4—881no—
412C4—881no—
413C4D11×#12311yescharacteristic
414C4D11×#13711yescharacteristic
415C2—22no—
416C2—114no—
417C2—222no—
418C2D11×#48011yescharacteristic
419C2C2×D11×SD3211yescharacteristic
420C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2235C2
socleC22×C11C22×D8
prime radicalC23×D11D8
hypercenter#2235D11
hypocenterC11C2×#2235
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
3. #13070815C2semidirect
4. #13070814C2semidirect
5. #13070813C2semidirect
6. #13070812C2semidirect
7. #13070811C2semidirect
8. D11×#367C2semidirect
9. D11×#358C2semidirect
11. C11×#2235C2semidirect
32. C11×#367C22semidirect
33. C11×#358C22semidirect
35. #10622202C22semidirect
38. #10622143C22semidirect
39. #10622141C22semidirect
40. #10622130C22semidirect
41. #10622128C22semidirect
42. #10622128C22semidirect
150. #2235D11direct (N × H)
217. #367C2×D11semidirect
221. #358C2×D11semidirect
298. D11#2235direct (N × H)
352. C11C2×#2235semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
C2×D11×#1072
#130708152
#130708142
#130708132
#130708122
#130708112
D11×#3672
D11×#3582
D11×C22⋊C162
C11×#22352
C2×#223511