Finite Group Databasebeta

← C11×#21524 #14598717

Subgroups — C11×#21524 #14598717

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C2×C11×#405C211yesmaximal, characteristic, complemented
4C11×#2324C212yesmaximal, complemented
5C11×#1970C211yesmaximal, characteristic, complemented
6C11×#1942C211yesmaximal, characteristic, complemented
7C11×#1936C212yesmaximal, complemented
8C11×#1895C212yesmaximal, complemented
9C11×#1808C211yesmaximal, characteristic, complemented
10C4×C11×#107C211yesmaximal, characteristic, complemented
11C11×#1762C212yesmaximal, complemented
12C22×C11×D8C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#121C2212yes—
16C2×C4×D4×C11C2212yes—
17C2×C11×#117C2211yescharacteristic
18C11×#466C418yescomplemented
19C4×C11×D8—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C11×#405—24no—
27C2×C11×#97C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#390—22no—
32C11×#390C2212yes—
33C11×#389C2212yes—
34C11×#388—22no—
35C11×#386—22no—
36C11×#385—22no—
37C11×#380C2212yes—
38C4×C11×C4⋊C4C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11C2312yes—
44C23×C4×C11—22no—
45C23×C4×C11C2311yescharacteristic
46C2×C11×D8—22no—
47C2×C11×D8—22no—
48C2×C11×D8C2×C414yes—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C22×C8×C11—22no—
53C22×C8×C11—22no—
54C22×C8×C11C2×C414yescomplemented
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×#121—24no—
60C11×#121C2×C418yescomplemented
61C4×D4×C11—24no—
62C4×D4×C11—24no—
63C11×#117—22no—
64C11×#117—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11—22no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C11×#107—22no—
82C11×#107—22no—
83C11×#107C2×C414yescomplemented
84C11×#102—24no—
85C11×#102—24no—
86C11×#102C2×C418yescomplemented
87C11×#97—22no—
88C11×#97—22no—
89C4×C8×C11—22no—
90C4×C8×C11D414yescomplemented
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94#21524C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—22no—
96C24×C11C2×D411yescharacteristic
97C2×D4×C11—28no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C2×D4×C11C22×C414yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—44no—
114C22×C4×C11—82no—
115C22×C4×C11—82no—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C11×D8—28no—
125C11×M16—28no—
126C2×C8×C11—28no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C22×C412yes—
134C2×C8×C11C22×C412yes—
135C2×C8×C11C2×D412yes—
136C2×C8×C11C2×D412yes—
137C2×C8×C11#4112yes—
138C2×C8×C11#4112yes—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—82no—
147C11×C4⋊C4C22×C414yes—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—82no—
153C11×C22⋊C4—82no—
154C11×C22⋊C4—82no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—82no—
158C42×C11C2×D412yes—
159C42×C11#4112yes—
160C2×#466C2×C1111yescharacteristic
161C2×C4×D8C2×C1111yescharacteristic, complemented
162C2×#405C2×C1111yescharacteristic, complemented
163#2324C2×C1112yescomplemented
164#1970C2×C1111yescharacteristic, complemented
165#1942C2×C1111yescharacteristic, complemented
166#1936C2×C1112yescomplemented
167#1895C2×C1112yescomplemented
168#1808C2×C1111yescharacteristic, complemented
169C4×#107C2×C1111yescharacteristic, complemented
170#1762C2×C1112yescomplemented
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—24no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11C4×D412yes—
185C23×C11C22×D411yescharacteristic
186D4×C11—24no—
187D4×C11—24no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—88no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—88no—
217C2×C4×C11C4×D412yes—
218C2×C4×C11#12112yes—
219C2×C4×C11#12112yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C8×C11—22no—
227C8×C11—22no—
228C8×C11—22no—
229C8×C11C4×D414yes—
230C22×D8C22×C1111yescharacteristic
231C22×M16C22×C1111yescharacteristic
232C23×C8C22×C1111yescharacteristic
233C2×#121C22×C1112yes—
234C2×C4×D4C22×C1112yes—
235C2×#117C22×C1111yescharacteristic
236#466C4×C1118yescomplemented
237C4×D8—24no—
238C2×#107C22×C1111yescharacteristic
239C2×#107C22×C1111yescharacteristic
240C2×#107C22×C1111yescharacteristic
241C2×#102C22×C1112yes—
242C2×#102C22×C1112yes—
243C2×#102C22×C1112yes—
244#405—24no—
245C2×#97C22×C1111yescharacteristic
246C2×#97C22×C1111yescharacteristic
247C2×C4×C8C22×C1111yescharacteristic
248C2×C4×C8C22×C1111yescharacteristic
249#390—22no—
250#390C22×C1112yes—
251#389C22×C1112yes—
252#388—22no—
253#386—22no—
254#385—22no—
255#380C22×C1112yes—
256C4×C4⋊C4C22×C1112yes—
257#340C22×C1112yes—
258#340C22×C1112yes—
259#340C22×C1112yes—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11C2×C4×D411yescharacteristic
275C22×C11C2×#12111yescharacteristic
276C22×C11#53211yescharacteristic
277C22×C11#57611yescharacteristic
278C22×C11#57611yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57811yescharacteristic
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—44no—
285C4×C11—41no—
286C4×C11—41no—
287C4×C11—82no—
288C4×C11—82no—
289C4×C11C2×C4×D411yescharacteristic
290C4×C11C4×#4111yescharacteristic
291C4×C11#52511yescharacteristic
292C4×C11#52911yescharacteristic
293C22×D4—22no—
294C22×D4C23×C1112yes—
295C23×C4—22no—
296C23×C4C23×C1111yescharacteristic
297C2×D8—22no—
298C2×D8—22no—
299C2×D8C2×C4×C1114yes—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8C2×C4×C1114yescomplemented
306C22×C8C23×C1111yescharacteristic
307C22×C8C23×C1111yescharacteristic
308C22×C8C23×C1111yescharacteristic
309C22×C8C23×C1111yescharacteristic
310#121—24no—
311#121C2×C4×C1118yescomplemented
312C4×D4—24no—
313C4×D4—24no—
314#117—22no—
315#117—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4D4×C1111yescharacteristic
318C2×C4⋊C4D4×C1111yescharacteristic
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1112yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4D4×C1111yescharacteristic
328C2×C22⋊C4D4×C1111yescharacteristic
329C2×C42—22no—
330C2×C42C23×C1111yescharacteristic
331C2×C42C23×C1111yescharacteristic
332#107—22no—
333#107—22no—
334#107C2×C4×C1114yescomplemented
335#102—24no—
336#102—24no—
337#102C2×C4×C1118yescomplemented
338#97—22no—
339#97—22no—
340C4×C8—22no—
341C4×C8D4×C1114yescomplemented
342#95—22no—
343#95—22no—
344#95—22no—
345C2×C11—42no—
346C2×C11—84no—
347C2×C11C4×#12111yescharacteristic
348C2×C11#294811yescharacteristic
349C2×C11#295111yescharacteristic
350C2×C11#305811yescharacteristic
351C2×C11#306111yescharacteristic
352C2×C11#317511yescharacteristic
353C2×C11#317611yescharacteristic
354C24—22no—
355C24C2×D4×C1111yescharacteristic
356C2×D4—28no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—82no—
363C2×D4—82no—
364C2×D4C22×C4×C1114yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—44no—
373C22×C4—82no—
374C22×C4—82no—
375C22×C4C22×C4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C11×#4112yes—
382C22×C4C24×C1111yescharacteristic
383D8—28no—
384M16—28no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—28no—
392C2×C8C22×C4×C1112yes—
393C2×C8C22×C4×C1112yes—
394C2×C8C2×D4×C1112yes—
395C2×C8C2×D4×C1112yes—
396C2×C8C11×#4112yes—
397C2×C8C11×#4112yes—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—82no—
406C4⋊C4C22×C4×C1114yes—
407C22⋊C4—28no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—44no—
411C22⋊C4—82no—
412C22⋊C4—82no—
413C22⋊C4—82no—
414C42—21no—
415C42—21no—
416C42—82no—
417C42C2×D4×C1112yes—
418C42C11×#4112yes—
419C11#2152411yescharacteristic, direct product factor, Sylow
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—24no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23C4×D4×C1112yes—
434C23C22×D4×C1111yescharacteristic
435D4—24no—
436D4—24no—
437D4—42no—
438D4—42no—
439D4—88no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—88no—
466C2×C4C4×D4×C1112yes—
467C2×C4C11×#12112yes—
468C2×C4C11×#12112yes—
469C2×C4C23×C4×C1111yescharacteristic
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C2×C11×#4111yescharacteristic
473C2×C4C2×C11×#4111yescharacteristic
474C2×C4C2×C11×#4111yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8C4×D4×C1114yes—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22—82no—
490C22—82no—
491C22—82no—
492C22—82no—
493C22C2×C4×D4×C1111yescharacteristic
494C22C2×C11×#12111yescharacteristic
495C22C11×#53211yescharacteristic
496C22C11×#57611yescharacteristic
497C22C11×#57611yescharacteristic
498C22C11×#57611yescharacteristic
499C22C11×#57811yescharacteristic
500C4—22no—
501C4—22no—
502C4—22no—
503C4—44no—
504C4—41no—
505C4—41no—
506C4—82no—
507C4—82no—
508C4C2×C4×D4×C1111yescharacteristic
509C4C4×C11×#4111yescharacteristic
510C4C11×#52511yescharacteristic
511C4C11×#52911yescharacteristic
512C2—42no—
513C2—84no—
514C2C4×C11×#12111yescharacteristic
515C2C11×#294811yescharacteristic
516C2C11×#295111yescharacteristic
517C2C11×#305811yescharacteristic
518C2C11×#306111yescharacteristic
519C2C11×#317511yescharacteristic
520C2C11×#317611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#466C2
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
2. C2×C4×C11×D8C2semidirect
3. C2×C11×#405C2semidirect
4. C11×#2324C2semidirect
5. C11×#1970C2semidirect
6. C11×#1942C2semidirect
7. C11×#1936C2semidirect
8. C11×#1895C2semidirect
9. C11×#1808C2semidirect
10. C4×C11×#107C2semidirect
11. C11×#1762C2semidirect
18. C11×#466C4semidirect
54. C22×C8×C11C2×C4semidirect
60. C11×#121C2×C4semidirect
83. C11×#107C2×C4semidirect
86. C11×#102C2×C4semidirect
90. C4×C8×C11D4semidirect
94. #21524C11direct (N × H)
161. C2×C4×D8C2×C11semidirect
162. C2×#405C2×C11semidirect
163. #2324C2×C11semidirect
164. #1970C2×C11semidirect
165. #1942C2×C11semidirect
166. #1936C2×C11semidirect
167. #1895C2×C11semidirect
168. #1808C2×C11semidirect
169. C4×#107C2×C11semidirect
170. #1762C2×C11semidirect
236. #466C4×C11semidirect
305. C22×C8C2×C4×C11semidirect
311. #121C2×C4×C11semidirect
334. #107C2×C4×C11semidirect
337. #102C2×C4×C11semidirect
341. C4×C8D4×C11semidirect
419. C11#21524direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C2×C4×C11×D82
C2×C11×#4052
C11×#23242
C11×#19702
C11×#19422
C11×#19362
C11×#18952
C11×#18082
C4×C11×#1072
C11×#17622
#2152411