Finite Group Databasebeta

← C11×#25014 #14602207

Subgroups — C11×#25014 #14602207

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C212yesmaximal, complemented
2C11×#2538C211yesmaximal, characteristic
3D4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#2077C212yesmaximal, complemented
5C11×#2035C212yesmaximal, complemented
6C11×#1954C211yesmaximal, characteristic
7C11×#1948C211yesmaximal, characteristic, complemented
8C11×#1853C212yesmaximal, complemented
9C11×#1844C211yesmaximal, characteristic, complemented
10C11×#1803C211yesmaximal, characteristic, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C11×#483—28no—
18C2×C11×#106C2212yes—
19C2×C11×#106C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×C22⋊C8C2212yes—
26C2×C11×C22⋊C8C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#396—22no—
29C11×#390—21no—
30C11×#389—21no—
31C11×#389—21no—
32C11×#385—22no—
33C11×#384C2211yescharacteristic
34C11×#384C2211yescharacteristic
35C11×#380C2212yes—
36C11×#380C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#340C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11D411yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11C2312yes—
46C22×C8×C11C2312yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—42no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—44no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C11×#106—24no—
79C11×#106—24no—
80C11×#106—42no—
81C11×C4⋊C8—22no—
82C11×#103—24no—
83C11×#103—22no—
84C11×#103D414yescomplemented
85C11×C22⋊C8—24no—
86C11×C22⋊C8—24no—
87C4×C8×C11—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95—22no—
91#25014C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2×D412yes—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C2×D412yes—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11SD1614yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—44no—
115C22×C4×C11—44no—
116C22×C4×C11—82no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C2×D412yes—
129C2×C8×C11#4112yes—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—44no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—81no—
146C11×C4⋊C4—81no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—82no—
152C42×C11—42no—
153C42×C11—42no—
154C42×C11#4112yes—
155C42×C11#4112yes—
156C2×#483C2×C1112yescomplemented
157#2538C2×C1111yescharacteristic
158D4×C4⋊C4C2×C1111yescharacteristic
159#2077C2×C1112yescomplemented
160#2035C2×C1112yescomplemented
161#1954C2×C1111yescharacteristic
162#1948C2×C1111yescharacteristic, complemented
163#1853C2×C1112yescomplemented
164#1844C2×C1111yescharacteristic, complemented
165#1803C2×C1111yescharacteristic, complemented
166C4×#103C2×C1111yescharacteristic, complemented
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11C2×SD1614yes—
174C23×C11C22×D411yescharacteristic
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—41no—
178Q8×C11—41no—
179D4×C11—28no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—88no—
208C2×C4×C11#12312yes—
209C2×C4×C11#12312yes—
210C2×C4×C11C2×SD1612yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C8×C11—22no—
219C8×C11—22no—
220C8×C11—42no—
221C2×C22⋊Q8C22×C1112yes—
222C2×C4×Q8C22×C1111yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C22×C1111yescharacteristic
225C22×C4⋊C4C22×C1112yes—
226#483—28no—
227C2×#106C22×C1112yes—
228C2×#106C22×C1112yes—
229C2×#106C22×C1112yes—
230C2×C4⋊C8C22×C1111yescharacteristic
231C2×#103C22×C1112yes—
232C2×#103C22×C1111yescharacteristic
233C2×#103C22×C1111yescharacteristic
234C2×C22⋊C8C22×C1112yes—
235C2×C22⋊C8C22×C1112yes—
236C2×C4×C8C22×C1111yescharacteristic
237#396—22no—
238#390—21no—
239#389—21no—
240#389—21no—
241#385—22no—
242#384C22×C1111yescharacteristic
243#384C22×C1111yescharacteristic
244#380C22×C1112yes—
245#380C22×C1112yes—
246C4×C4⋊C4C22×C1111yescharacteristic
247#340C22×C1112yes—
248#340C22×C1111yescharacteristic
249#340C22×C1112yes—
250#340C22×C1111yescharacteristic
251C22×C11—24no—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11C2×#12311yescharacteristic
259C22×C11D4211yescharacteristic
260C22×C11#54711yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×#13711yescharacteristic
263C22×C11#57711yescharacteristic
264C22×C11#57711yescharacteristic
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—82no—
272C4×C11—82no—
273C4×C11#48314yescomplemented
274C4×C11#53211yescharacteristic
275C4×C11#54211yescharacteristic
276C4×C11#54711yescharacteristic
277C4×C11#55311yescharacteristic
278C22×Q8C23×C1111yescharacteristic
279C22×D4D4×C1111yescharacteristic
280C23×C4—22no—
281C23×C4C23×C1112yes—
282C22×C8C23×C1112yes—
283C22×C8C23×C1111yescharacteristic
284C22×C8C23×C1111yescharacteristic
285C22⋊Q8—24no—
286C22⋊Q8—42no—
287C4×Q8—22no—
288C4×Q8—22no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—44no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4D4×C1111yescharacteristic
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C4⋊C4C23×C1112yes—
305C2×C4⋊C4C23×C1111yescharacteristic
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4D4×C1112yes—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42C23×C1111yescharacteristic
314#106—24no—
315#106—24no—
316#106—42no—
317C4⋊C8—22no—
318#103—24no—
319#103—22no—
320#103D4×C1114yescomplemented
321C22⋊C8—24no—
322C22⋊C8—24no—
323C4×C8—22no—
324#95—21no—
325#95—22no—
326#95—22no—
327C2×C11—44no—
328C2×C11#242211yescharacteristic
329C2×C11C2×#48311yescharacteristic
330C2×C11#309911yescharacteristic
331C2×C11#327811yescharacteristic
332C2×C11D4×SD1611yescharacteristic
333C2×C11#333511yescharacteristic
334C2×C11#335611yescharacteristic
335C24C2×D4×C1112yes—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8C2×D4×C1112yes—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4C11×SD1614yes—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—82no—
360C22×C4C2×D4×C1112yes—
361C22×C4C2×D4×C1111yescharacteristic
362C22×C4C2×D4×C1111yescharacteristic
363C22×C4C24×C1111yescharacteristic
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8C2×D4×C1112yes—
372C2×C8C11×#4112yes—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—44no—
384C4⋊C4—44no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—81no—
389C4⋊C4—81no—
390C4⋊C4C2×D4×C1112yes—
391C22⋊C4—24no—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4—82no—
395C42—42no—
396C42—42no—
397C42C11×#4112yes—
398C42C11×#4112yes—
399C11#2501411yescharacteristic, direct product factor, Sylow
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23C2×C11×SD1614yes—
407C23C22×D4×C1111yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—41no—
411Q8—41no—
412D4—28no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—88no—
441C2×C4C11×#12312yes—
442C2×C4C11×#12312yes—
443C2×C4C2×C11×SD1612yes—
444C2×C4C11×#13712yes—
445C2×C4C22×D4×C1111yescharacteristic
446C2×C4C2×C11×#4111yescharacteristic
447C2×C4C2×C11×#4111yescharacteristic
448C2×C4C2×C11×#4111yescharacteristic
449C2×C4C11×H(5,𝔽2)11yescharacteristic
450C2×C4C11×2−1+411yescharacteristic
451C8—22no—
452C8—22no—
453C8—42no—
454C22—24no—
455C22—24no—
456C22—24no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22C2×C11×#12311yescharacteristic
462C22D42×C1111yescharacteristic
463C22C11×#54711yescharacteristic
464C22C22×C11×SD1611yescharacteristic
465C22C2×C11×#13711yescharacteristic
466C22C11×#57711yescharacteristic
467C22C11×#57711yescharacteristic
468C4—22no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—82no—
473C4—82no—
474C4—81no—
475C4—81no—
476C4C11×#48314yescomplemented
477C4C11×#53211yescharacteristic
478C4C11×#54211yescharacteristic
479C4C11×#54711yescharacteristic
480C4C11×#55311yescharacteristic
481C2—44no—
482C2C11×#242211yescharacteristic
483C2C2×C11×#48311yescharacteristic
484C2C11×#309911yescharacteristic
485C2C11×#327811yescharacteristic
486C2D4×C11×SD1611yescharacteristic
487C2C11×#333511yescharacteristic
488C2C11×#335611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
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
1. C2×C11×#483C2semidirect
4. C11×#2077C2semidirect
5. C11×#2035C2semidirect
7. C11×#1948C2semidirect
8. C11×#1853C2semidirect
9. C11×#1844C2semidirect
10. C11×#1803C2semidirect
11. C4×C11×#103C2semidirect
84. C11×#103D4semidirect
91. #25014C11direct (N × H)
156. C2×#483C2×C11semidirect
159. #2077C2×C11semidirect
160. #2035C2×C11semidirect
162. #1948C2×C11semidirect
163. #1853C2×C11semidirect
164. #1844C2×C11semidirect
165. #1803C2×C11semidirect
166. C4×#103C2×C11semidirect
273. C4×C11#483semidirect
320. #103D4×C11semidirect
399. C11#25014direct (N × H)
476. C4C11×#483semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C11×#25382
D4×C11×C4⋊C42
C11×#20772
C11×#20352
C11×#19542
C11×#19482
C11×#18532
C11×#18442
C11×#18032
C4×C11×#1032
#2501411