Finite Group Databasebeta

← C11×#21873 #14599066

Subgroups — C11×#21873 #14599066

Order 2816.

1022 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
1C2×C11×#541C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic
3C11×#2317C211yesmaximal, characteristic
4C11×#1992C211yesmaximal, characteristic, complemented
5C11×#1991C211yesmaximal, characteristic, complemented
6C11×#1960C211yesmaximal, characteristic, complemented
7C11×#1956C211yesmaximal, characteristic, complemented
8C11×#1873C212yesmaximal
9C11×#1872C212yesmaximal
10C11×#1805C212yesmaximal, complemented
11C11×#1803C212yesmaximal, complemented
12C11×#541—24no—
13C11×#541C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#125—22no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#433—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×#97C2211yescharacteristic
31C2×C4×C8×C11C2211yescharacteristic
32C11×#389—22no—
33C11×#385—22no—
34C11×#384C2211yescharacteristic
35C11×#384C2211yescharacteristic
36C11×#382C2211yescharacteristic
37C11×#382C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2312yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8C2×C414yescomplemented
49C11×#126—216no—
50C11×#125—216no—
51C11×#125—22no—
52C11×#125C2×C414yescomplemented
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8C2×C418yes—
55C4×Q8×C11—24no—
56C4×Q8×C11C2×C418yescomplemented
57C11×#117—42no—
58C11×#117C2×C414yes—
59C11×#117D414yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—42no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11—22no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C11×C4⋊C8—24no—
82C11×#103—42no—
83C11×#103—42no—
84C11×#103—42no—
85C11×#103—42no—
86C11×C22⋊C8—24no—
87C11×#97—22no—
88C4×C8×C11—22no—
89C11×#95—22no—
90C11×#95—22no—
91#21873C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C22×C414yes—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—42no—
108C22×C4×C11—82no—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2411yescharacteristic
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C11×C4⋊C4—28no—
122C11×C4⋊C4—28no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—82no—
132C11×C4⋊C4—82no—
133C11×C4⋊C4C22⋊C418yes—
134C11×C4⋊C4C22×C414yes—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4C22⋊C418yes—
138C42×C11—28no—
139C42×C11—42no—
140C42×C11C22×C412yes—
141C42×C11C22×C412yes—
142C42×C11C2×D412yes—
143C42×C11C2×D412yes—
144C2×#541C2×C1111yescharacteristic
145C2×#433C2×C1111yescharacteristic
146#2317C2×C1111yescharacteristic
147#1992C2×C1111yescharacteristic, complemented
148#1991C2×C1111yescharacteristic, complemented
149#1960C2×C1111yescharacteristic, complemented
150#1956C2×C1111yescharacteristic, complemented
151#1873C2×C1112yes—
152#1872C2×C1112yes—
153#1805C2×C1112yescomplemented
154#1803C2×C1112yescomplemented
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11C2×C22⋊C412yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—24no—
162Q8×C11—24no—
163Q8×C11—42no—
164Q8×C11—42no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—84no—
188C2×C4×C11C2×C22⋊C414yes—
189C2×C4×C11C2×C22⋊C414yes—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11H(5,𝔽2)12yes—
194C2×C4×C112−1+412yes—
195C8×C11—42no—
196C8×C11—42no—
197#541—24no—
198#541C4×C1118yescomplemented
199C2×C4⋊Q8C22×C1111yescharacteristic
200C2×#126—22no—
201C2×#125—22no—
202C2×#125C22×C1111yescharacteristic
203C2×C22⋊Q8C22×C1112yes—
204C2×C4×Q8C22×C1112yes—
205C2×#117C22×C1111yescharacteristic
206C2×#117C22×C1111yescharacteristic
207C22×C4⋊C4C22×C1111yescharacteristic
208#433—24no—
209C2×C4⋊C8C22×C1112yes—
210C2×#103C22×C1112yes—
211C2×#103C22×C1112yes—
212C2×#103C22×C1112yes—
213C2×#103C22×C1112yes—
214C2×C22⋊C8C22×C1112yes—
215C2×#97C22×C1111yescharacteristic
216C2×C4×C8C22×C1111yescharacteristic
217#389—22no—
218#385—22no—
219#384C22×C1111yescharacteristic
220#384C22×C1111yescharacteristic
221#382C22×C1111yescharacteristic
222#382C22×C1111yescharacteristic
223#340C22×C1112yes—
224#340C22×C1112yes—
225#340C22×C1112yes—
226#340C22×C1112yes—
227C22×C11—22no—
228C22×C11—24no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—42no—
232C22×C11C22×C22⋊C411yescharacteristic
233C22×C11#53511yescharacteristic
234C22×C11#53611yescharacteristic
235C22×C11#57712yes—
236C22×C11#57812yes—
237C4×C11—22no—
238C4×C11—24no—
239C4×C11—24no—
240C4×C11—44no—
241C4×C11—44no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11#52012yes—
247C4×C11#53712yes—
248C22×Q8C23×C1112yes—
249C23×C4—21no—
250C23×C4C23×C1111yescharacteristic
251C22×C8C23×C1112yes—
252C22×C8C23×C1112yes—
253C4⋊Q8—22no—
254C4⋊Q8C2×C4×C1114yescomplemented
255#126—216no—
256#125—216no—
257#125—22no—
258#125C2×C4×C1114yescomplemented
259C22⋊Q8—24no—
260C22⋊Q8C2×C4×C1118yes—
261C4×Q8—24no—
262C4×Q8C2×C4×C1118yescomplemented
263#117—42no—
264#117C2×C4×C1114yes—
265#117D4×C1114yes—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4D4×C1112yes—
275C2×C4⋊C4C23×C1111yescharacteristic
276C2×C4⋊C4C23×C1111yescharacteristic
277C2×C4⋊C4C23×C1111yescharacteristic
278C2×C4⋊C4C23×C1111yescharacteristic
279C2×C4⋊C4C23×C1112yes—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4D4×C1112yes—
283C2×C42—22no—
284C2×C42—21no—
285C2×C42C23×C1111yescharacteristic
286C2×C42C23×C1111yescharacteristic
287C4⋊C8—24no—
288#103—42no—
289#103—42no—
290#103—42no—
291#103—42no—
292C22⋊C8—24no—
293#97—22no—
294C4×C8—22no—
295#95—22no—
296#95—22no—
297C2×C11—42no—
298C2×C11#231111yescharacteristic
299C2×C11#289812yes—
300C2×C11#322211yescharacteristic
301C2×C11#322311yescharacteristic
302C2×C11#324212yes—
303C24C2×D4×C1111yescharacteristic
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8C22×C4×C1114yes—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—82no—
320C22×C4C22×C4×C1112yes—
321C22×C4C2×D4×C1112yes—
322C22×C4C2×D4×C1112yes—
323C22×C4C2×D4×C1111yescharacteristic
324C22×C4C2×D4×C1112yes—
325C22×C4C24×C1111yescharacteristic
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C4⋊C4—28no—
333C4⋊C4—28no—
334C4⋊C4—28no—
335C4⋊C4—28no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—42no—
342C4⋊C4—82no—
343C4⋊C4—82no—
344C4⋊C4C11×C22⋊C418yes—
345C4⋊C4C22×C4×C1114yes—
346C22⋊C4—28no—
347C22⋊C4—42no—
348C22⋊C4C11×C22⋊C418yes—
349C42—28no—
350C42—42no—
351C42C22×C4×C1112yes—
352C42C22×C4×C1112yes—
353C42C2×D4×C1112yes—
354C42C2×D4×C1112yes—
355C11#2187311yescharacteristic, direct product factor, Sylow
356C23—21no—
357C23—21no—
358C23—22no—
359C23—22no—
360C23C2×C11×C22⋊C412yes—
361C23C22×D4×C1111yescharacteristic
362Q8—24no—
363Q8—24no—
364Q8—42no—
365Q8—42no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—84no—
389C2×C4C2×C11×C22⋊C414yes—
390C2×C4C2×C11×C22⋊C414yes—
391C2×C4C2×C11×C22⋊C412yes—
392C2×C4C23×C4×C1111yescharacteristic
393C2×C4C22×D4×C1111yescharacteristic
394C2×C4C11×H(5,𝔽2)12yes—
395C2×C4C11×2−1+412yes—
396C8—42no—
397C8—42no—
398C22—24no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22C22×C11×C22⋊C411yescharacteristic
404C22C11×#53511yescharacteristic
405C22C11×#53611yescharacteristic
406C22C11×#57712yes—
407C22C11×#57812yes—
408C4—24no—
409C4—24no—
410C4—22no—
411C4—44no—
412C4—44no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4C11×#52012yes—
418C4C11×#53712yes—
419C2—42no—
420C2C11×#231111yescharacteristic
421C2C11×#289812yes—
422C2C11×#322211yescharacteristic
423C2C11×#322311yescharacteristic
424C2C11×#324212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1992C2semidirect
5. C11×#1991C2semidirect
6. C11×#1960C2semidirect
7. C11×#1956C2semidirect
10. C11×#1805C2semidirect
11. C11×#1803C2semidirect
13. C11×#541C4semidirect
48. C11×C4⋊Q8C2×C4semidirect
52. C11×#125C2×C4semidirect
56. C4×Q8×C11C2×C4semidirect
91. #21873C11direct (N × H)
147. #1992C2×C11semidirect
148. #1991C2×C11semidirect
149. #1960C2×C11semidirect
150. #1956C2×C11semidirect
153. #1805C2×C11semidirect
154. #1803C2×C11semidirect
198. #541C4×C11semidirect
254. C4⋊Q8C2×C4×C11semidirect
258. #125C2×C4×C11semidirect
262. C4×Q8C2×C4×C11semidirect
355. C11#21873direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C2×C11×#4332
C11×#23172
C11×#19922
C11×#19912
C11×#19602
C11×#19562
C11×#18732
C11×#18722
C11×#18052
C11×#18032
#2187311