Finite Group Databasebeta

← C11×#25568 #14602761

Subgroups — C11×#25568 #14602761

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic
2C2×C11×#487C211yesmaximal, characteristic, complemented
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C11×#2542C211yesmaximal, characteristic, complemented
5C11×#2000C214yesmaximal, complemented
6C11×#1987C211yesmaximal, characteristic, complemented
7C11×#1954C211yesmaximal, characteristic, complemented
8C11×#1873C214yesmaximal, complemented
9C4×C11×#102C211yesmaximal, characteristic, complemented
10C22×C11×SD16C2212yes—
11C11×#555—24no—
12C11×#555—24no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124—22no—
16C2×C11×C22⋊Q8C2214yes—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C2×C11×#117C2212yes—
23C11×#487—24no—
24C11×#461—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#103C2214yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2214yes—
30C2×C4×C8×C11C2211yescharacteristic
31C11×#399—22no—
32C11×#390—21no—
33C11×#384—21no—
34C4×C11×C4⋊C4C2211yescharacteristic
35C11×#340C2212yes—
36C11×#340C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11C2312yes—
39C22×D4×C11—22no—
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11C2312yes—
44C2×C11×SD16—24no—
45C2×C11×SD16—44no—
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8D414yes—
52C11×#124—216no—
53C11×C22⋊Q8—28no—
54C11×C22⋊Q8—44no—
55C11×#121—28no—
56C11×#121—24no—
57C11×#121—24no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11D414yes—
62C11×#117—28no—
63C11×#117—24no—
64C11×#117—24no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11—22no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C11×C4⋊C8—22no—
82C11×#103—24no—
83C11×#103—28no—
84C11×#102—24no—
85C11×C22⋊C8—44no—
86C4×C8×C11—22no—
87C11×#95—21no—
88#25568C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—21no—
90C24×C11C2×D412yes—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—24no—
95C2×Q8×C11—24no—
96C2×Q8×C11—82no—
97C2×D4×C11—28no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—84no—
105C2×D4×C11C2×D412yes—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C11×SD16—48no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—48no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4C2×D412yes—
136C11×C4⋊C4C2×D414yes—
137C11×C4⋊C4#4114yes—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—28no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—48no—
143C42×C11—28no—
144C42×C11—42no—
145C42×C11C2×D412yes—
146C42×C11C2×D412yes—
147C2×#555C2×C1111yescharacteristic
148C2×#487C2×C1111yescharacteristic, complemented
149C2×#461C2×C1111yescharacteristic, complemented
150#2542C2×C1111yescharacteristic, complemented
151#2000C2×C1114yescomplemented
152#1987C2×C1111yescharacteristic, complemented
153#1954C2×C1111yescharacteristic, complemented
154#1873C2×C1114yescomplemented
155C4×#102C2×C1111yescharacteristic, complemented
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—24no—
162C23×C11—42no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—42no—
166C23×C11C22×D411yescharacteristic
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—44no—
170Q8×C11—84no—
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—42no—
174D4×C11—44no—
175D4×C11—88no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—44no—
190C2×C4×C11—48no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11#12012yes—
194C2×C4×C11#12012yes—
195C2×C4×C11#13512yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4112yes—
200C2×C4×C11H(5,𝔽2)12yes—
201C8×C11—42no—
202C8×C11—42no—
203C22×SD16C22×C1112yes—
204#555—24no—
205#555—24no—
206C2×C4⋊Q8C22×C1111yescharacteristic
207C2×C4⋊Q8C22×C1111yescharacteristic
208C2×#124—22no—
209C2×C22⋊Q8C22×C1114yes—
210C2×#121—21no—
211C2×#121C22×C1112yes—
212C2×C4×D4C22×C1111yescharacteristic
213C2×C4×D4C22×C1111yescharacteristic
214C2×#117—21no—
215C2×#117C22×C1112yes—
216#487—24no—
217#461—24no—
218C2×C4⋊C8C22×C1111yescharacteristic
219C2×#103C22×C1114yes—
220C2×#103C22×C1112yes—
221C2×#102C22×C1112yes—
222C2×C22⋊C8C22×C1114yes—
223C2×C4×C8C22×C1111yescharacteristic
224#399—22no—
225#390—21no—
226#384—21no—
227C4×C4⋊C4C22×C1111yescharacteristic
228#340C22×C1112yes—
229#340C22×C1114yes—
230C22×C11—44no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—44no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11C2×#12011yescharacteristic
241C22×C11#54612yes—
242C22×C11C2×#13511yescharacteristic
243C22×C11C2×#13711yescharacteristic
244C22×C11#57712yes—
245C4×C11—22no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—44no—
249C4×C11—44no—
250C4×C11—82no—
251C4×C11#45214yes—
252C4×C11#53211yescharacteristic
253C4×C11#53511yescharacteristic
254C4×C11#55012yes—
255C22×Q8—21no—
256C22×Q8C23×C1112yes—
257C22×D4—22no—
258C22×D4D4×C1111yescharacteristic
259C22×D4C23×C1111yescharacteristic
260C23×C4—21no—
261C23×C4C23×C1112yes—
262C2×SD16—24no—
263C2×SD16—44no—
264C22×C8C23×C1112yes—
265C22×C8C23×C1112yes—
266C4⋊Q8—22no—
267C4⋊Q8—22no—
268C4⋊Q8—22no—
269C4⋊Q8D4×C1114yes—
270#124—216no—
271C22⋊Q8—28no—
272C22⋊Q8—44no—
273#121—28no—
274#121—24no—
275#121—24no—
276C4×D4—22no—
277C4×D4—22no—
278C4×D4—22no—
279C4×D4D4×C1114yes—
280#117—28no—
281#117—24no—
282#117—24no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4D4×C1111yescharacteristic
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4D4×C1112yes—
296C2×C42—22no—
297C2×C42—21no—
298C2×C42C23×C1111yescharacteristic
299C4⋊C8—22no—
300#103—24no—
301#103—28no—
302#102—24no—
303C22⋊C8—44no—
304C4×C8—22no—
305#95—21no—
306C2×C11—82no—
307C2×C11—82no—
308C2×C11#243111yescharacteristic
309C2×C11C2×#45211yescharacteristic
310C2×C11#300911yescharacteristic
311C2×C11#330312yes—
312C2×C11#332912yes—
313C24—21no—
314C24C2×D4×C1112yes—
315C2×Q8—24no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—24no—
319C2×Q8—24no—
320C2×Q8—82no—
321C2×D4—28no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—84no—
329C2×D4C2×D4×C1112yes—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4C2×D4×C1112yes—
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C24×C1111yescharacteristic
345SD16—48no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—24no—
351C4⋊C4—24no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—48no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4C2×D4×C1112yes—
360C4⋊C4C2×D4×C1114yes—
361C4⋊C4C11×#4114yes—
362C22⋊C4—28no—
363C22⋊C4—28no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—48no—
367C42—28no—
368C42—42no—
369C42C2×D4×C1112yes—
370C42C2×D4×C1112yes—
371C11#2556811yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—22no—
377C23—24no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23C22×D4×C1111yescharacteristic
383Q8—42no—
384Q8—42no—
385Q8—44no—
386Q8—84no—
387D4—22no—
388D4—22no—
389D4—42no—
390D4—44no—
391D4—88no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—48no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4C11×#12012yes—
410C2×C4C11×#12012yes—
411C2×C4C11×#13512yes—
412C2×C4C11×#13712yes—
413C2×C4C22×D4×C1111yescharacteristic
414C2×C4C22×D4×C1111yescharacteristic
415C2×C4C2×C11×#4112yes—
416C2×C4C11×H(5,𝔽2)12yes—
417C8—42no—
418C8—42no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—44no—
426C22—44no—
427C22—82no—
428C22—82no—
429C22C2×C11×#12011yescharacteristic
430C22C11×#54612yes—
431C22C2×C11×#13511yescharacteristic
432C22C2×C11×#13711yescharacteristic
433C22C11×#57712yes—
434C4—22no—
435C4—42no—
436C4—42no—
437C4—44no—
438C4—44no—
439C4—82no—
440C4C11×#45214yes—
441C4C11×#53211yescharacteristic
442C4C11×#53511yescharacteristic
443C4C11×#55012yes—
444C2—82no—
445C2—82no—
446C2C11×#243111yescharacteristic
447C2C2×C11×#45211yescharacteristic
448C2C11×#300911yescharacteristic
449C2C11×#330312yes—
450C2C11×#332912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#555C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#487C2semidirect
3. C2×C11×#461C2semidirect
4. C11×#2542C2semidirect
5. C11×#2000C2semidirect
6. C11×#1987C2semidirect
7. C11×#1954C2semidirect
8. C11×#1873C2semidirect
9. C4×C11×#102C2semidirect
88. #25568C11direct (N × H)
148. C2×#487C2×C11semidirect
149. C2×#461C2×C11semidirect
150. #2542C2×C11semidirect
151. #2000C2×C11semidirect
152. #1987C2×C11semidirect
153. #1954C2×C11semidirect
154. #1873C2×C11semidirect
155. C4×#102C2×C11semidirect
371. C11#25568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#4872
C2×C11×#4612
C11×#25422
C11×#20002
C11×#19872
C11×#19542
C11×#18732
C4×C11×#1022
#2556811