Finite Group Databasebeta

← C11×#25010 #14602203

Subgroups — C11×#25010 #14602203

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C212yesmaximal, complemented
2C11×#2537C211yesmaximal, characteristic
3D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4C11×#2075C212yesmaximal, complemented
5C11×#2033C212yesmaximal, complemented
6C11×#1954C211yesmaximal, characteristic, complemented
7C11×#1947C211yesmaximal, characteristic, complemented
8C11×#1852C212yesmaximal, complemented
9C11×#1845C211yesmaximal, characteristic, complemented
10C11×#1802C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C11×#480—28no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2212yes—
21C2×C11×#107C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C11×#394—22no—
30C11×#389—21no—
31C11×#385—22no—
32C11×#384C2211yescharacteristic
33C11×#384C2211yescharacteristic
34C11×#380—21no—
35C11×#380C2212yes—
36C11×#380C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#340C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11D411yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—22no—
46C23×C4×C11—21no—
47C23×C4×C11C2312yes—
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×#121—24no—
52C11×#121—42no—
53C11×#121—44no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—44no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C11×#107—24no—
80C11×#107—24no—
81C11×#107—42no—
82C11×C4⋊C8—22no—
83C11×#102—24no—
84C11×#102—22no—
85C11×#102D414yescomplemented
86C11×C22⋊C8—24no—
87C11×C22⋊C8—24no—
88C4×C8×C11—22no—
89C11×#95—21no—
90C11×#95—22no—
91C11×#95—22no—
92#25010C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—21no—
94C24×C11C2×D412yes—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—44no—
103C2×D4×C11—44no—
104C2×D4×C11—82no—
105C2×D4×C11D814yes—
106C2×D4×C11C2×D412yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—82no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C2×D412yes—
136C2×C8×C11#4112yes—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—44no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—81no—
151C11×C4⋊C4—81no—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—42no—
158C42×C11—42no—
159C42×C11#4112yes—
160C42×C11#4112yes—
161C2×#480C2×C1112yescomplemented
162#2537C2×C1111yescharacteristic
163D4×C4⋊C4C2×C1111yescharacteristic, complemented
164#2075C2×C1112yescomplemented
165#2033C2×C1112yescomplemented
166#1954C2×C1111yescharacteristic, complemented
167#1947C2×C1111yescharacteristic, complemented
168#1852C2×C1112yescomplemented
169#1845C2×C1111yescharacteristic, complemented
170#1802C2×C1111yescharacteristic, complemented
171C4×#102C2×C1111yescharacteristic, complemented
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11C2×D814yes—
186C23×C11C22×D411yescharacteristic
187D4×C11—22no—
188D4×C11—22no—
189D4×C11—28no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—88no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—88no—
218C2×C4×C11—84no—
219C2×C4×C11#12312yes—
220C2×C4×C11#12312yes—
221C2×C4×C11C2×D812yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C8×C11—22no—
230C8×C11—22no—
231C8×C11—42no—
232C2×#121—21no—
233C2×#121C22×C1112yes—
234C2×C4×D4—21no—
235C2×C4×D4C22×C1111yescharacteristic
236C2×C4×D4C22×C1111yescharacteristic
237C22×C4⋊C4C22×C1112yes—
238#480—28no—
239C2×#107C22×C1112yes—
240C2×#107C22×C1112yes—
241C2×#107C22×C1112yes—
242C2×C4⋊C8C22×C1111yescharacteristic
243C2×#102C22×C1112yes—
244C2×#102C22×C1111yescharacteristic
245C2×#102C22×C1111yescharacteristic
246C2×C22⋊C8C22×C1112yes—
247C2×C22⋊C8C22×C1112yes—
248C2×C4×C8C22×C1111yescharacteristic
249#394—22no—
250#389—21no—
251#385—22no—
252#384C22×C1111yescharacteristic
253#384C22×C1111yescharacteristic
254#380—21no—
255#380C22×C1112yes—
256#380C22×C1112yes—
257C4×C4⋊C4C22×C1111yescharacteristic
258#340C22×C1112yes—
259#340C22×C1111yescharacteristic
260#340C22×C1112yes—
261#340C22×C1111yescharacteristic
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—24no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11C2×#12311yescharacteristic
277C22×C11D4211yescharacteristic
278C22×C11#54711yescharacteristic
279C22×C11C22×D811yescharacteristic
280C22×C11C2×#13711yescharacteristic
281C22×C11#57611yescharacteristic
282C22×C11#57811yescharacteristic
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11—82no—
289C4×C11—82no—
290C4×C11#48014yescomplemented
291C4×C11#53211yescharacteristic
292C4×C11#54211yescharacteristic
293C4×C11#54711yescharacteristic
294C4×C11#55311yescharacteristic
295C22×D4—22no—
296C22×D4D4×C1111yescharacteristic
297C22×D4C23×C1111yescharacteristic
298C23×C4—22no—
299C23×C4—21no—
300C23×C4C23×C1112yes—
301C22×C8C23×C1112yes—
302C22×C8C23×C1111yescharacteristic
303C22×C8C23×C1111yescharacteristic
304#121—24no—
305#121—42no—
306#121—44no—
307C4×D4—22no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—44no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4D4×C1111yescharacteristic
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1111yescharacteristic
322C2×C4⋊C4C23×C1112yes—
323C2×C4⋊C4C23×C1111yescharacteristic
324C2×C4⋊C4C23×C1111yescharacteristic
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4D4×C1112yes—
330C2×C42—21no—
331C2×C42C23×C1111yescharacteristic
332#107—24no—
333#107—24no—
334#107—42no—
335C4⋊C8—22no—
336#102—24no—
337#102—22no—
338#102D4×C1114yescomplemented
339C22⋊C8—24no—
340C22⋊C8—24no—
341C4×C8—22no—
342#95—21no—
343#95—22no—
344#95—22no—
345C2×C11—44no—
346C2×C11—82no—
347C2×C11#242211yescharacteristic
348C2×C11C2×#48011yescharacteristic
349C2×C11#309811yescharacteristic
350C2×C11#327611yescharacteristic
351C2×C11D4×D811yescharacteristic
352C2×C11#333411yescharacteristic
353C2×C11#335711yescharacteristic
354C24—21no—
355C24C2×D4×C1112yes—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—44no—
364C2×D4—44no—
365C2×D4—82no—
366C2×D4C11×D814yes—
367C2×D4C2×D4×C1112yes—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—44no—
380C22×C4—44no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—82no—
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C24×C1111yescharacteristic
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8C2×D4×C1112yes—
397C2×C8C11×#4112yes—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—44no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—81no—
412C4⋊C4—81no—
413C4⋊C4C2×D4×C1112yes—
414C22⋊C4—24no—
415C22⋊C4—44no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—42no—
419C42—42no—
420C42C11×#4112yes—
421C42C11×#4112yes—
422C11#2501011yescharacteristic, direct product factor, Sylow
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23C2×C11×D814yes—
437C23C22×D4×C1111yescharacteristic
438D4—22no—
439D4—22no—
440D4—28no—
441D4—41no—
442D4—41no—
443D4—88no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—88no—
469C2×C4—84no—
470C2×C4C11×#12312yes—
471C2×C4C11×#12312yes—
472C2×C4C2×C11×D812yes—
473C2×C4C11×#13712yes—
474C2×C4C22×D4×C1111yescharacteristic
475C2×C4C2×C11×#4111yescharacteristic
476C2×C4C2×C11×#4111yescharacteristic
477C2×C4C2×C11×#4111yescharacteristic
478C2×C4C11×H(5,𝔽2)11yescharacteristic
479C2×C4C11×2−1+411yescharacteristic
480C8—22no—
481C8—22no—
482C8—42no—
483C22—24no—
484C22—24no—
485C22—24no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22C2×C11×#12311yescharacteristic
498C22D42×C1111yescharacteristic
499C22C11×#54711yescharacteristic
500C22C22×C11×D811yescharacteristic
501C22C2×C11×#13711yescharacteristic
502C22C11×#57611yescharacteristic
503C22C11×#57811yescharacteristic
504C4—22no—
505C4—42no—
506C4—42no—
507C4—82no—
508C4—82no—
509C4—81no—
510C4—81no—
511C4C11×#48014yescomplemented
512C4C11×#53211yescharacteristic
513C4C11×#54211yescharacteristic
514C4C11×#54711yescharacteristic
515C4C11×#55311yescharacteristic
516C2—44no—
517C2—82no—
518C2C11×#242211yescharacteristic
519C2C2×C11×#48011yescharacteristic
520C2C11×#309811yescharacteristic
521C2C11×#327611yescharacteristic
522C2D4×C11×D811yescharacteristic
523C2C11×#333411yescharacteristic
524C2C11×#335711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2537C2
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×#480C2semidirect
3. D4×C11×C4⋊C4C2semidirect
4. C11×#2075C2semidirect
5. C11×#2033C2semidirect
6. C11×#1954C2semidirect
7. C11×#1947C2semidirect
8. C11×#1852C2semidirect
9. C11×#1845C2semidirect
10. C11×#1802C2semidirect
11. C4×C11×#102C2semidirect
85. C11×#102D4semidirect
92. #25010C11direct (N × H)
161. C2×#480C2×C11semidirect
163. D4×C4⋊C4C2×C11semidirect
164. #2075C2×C11semidirect
165. #2033C2×C11semidirect
166. #1954C2×C11semidirect
167. #1947C2×C11semidirect
168. #1852C2×C11semidirect
169. #1845C2×C11semidirect
170. #1802C2×C11semidirect
171. C4×#102C2×C11semidirect
290. C4×C11#480semidirect
338. #102D4×C11semidirect
422. C11#25010direct (N × H)
511. C4C11×#480semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C11×#25372
D4×C11×C4⋊C42
C11×#20752
C11×#20332
C11×#19542
C11×#19472
C11×#18522
C11×#18452
C11×#18022
C4×C11×#1022
#2501011