Finite Group Databasebeta

← C11×#23577 #14600770

Subgroups — C11×#23577 #14600770

Order 2816.

1144 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#441C212yesmaximal, complemented
3C4×C11×C22⋊Q8C211yesmaximal, characteristic
4C11×#2058C211yesmaximal, characteristic, complemented
5C11×#2043C211yesmaximal, characteristic, complemented
6C11×#2035C212yesmaximal
7C11×#2024C211yesmaximal, characteristic, complemented
8C11×#2016C211yesmaximal, characteristic, complemented
9C11×#2001C212yesmaximal
10C11×#1763C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C11×#533—28no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2212yes—
23C2×C11×#117—21no—
24C22×C42×C11C2211yescharacteristic
25C11×#441—28no—
26C2×C11×#106C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×C22⋊C8C2212yes—
32C2×C11×#97C2212yes—
33C11×#391C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#387—21no—
36C11×#385—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C2×C11×Q16—24no—
52C2×C11×Q16—24no—
53C2×C11×Q16—24no—
54C22×C8×C11C2312yes—
55C22×C8×C11C2312yes—
56C11×C4⋊Q8—24no—
57C11×C4⋊Q8—24no—
58C11×#125—28no—
59C11×C22⋊Q8—28no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—22no—
64C4×Q8×C11—28no—
65C4×Q8×C11—24no—
66C4×Q8×C11—24no—
67C4×Q8×C11D418yes—
68C11×#117—28no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—22no—
85C2×C42×C11—24no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C11×#106—24no—
93C11×#103—24no—
94C11×#103—24no—
95C11×#103—24no—
96C11×#103—24no—
97C11×C22⋊C8—24no—
98C11×#97—24no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104#23577C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11C2×D411yescharacteristic
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11C2×D414yes—
118C2×Q8×C11#4112yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—41no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C11×Q16—216no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11#4114yes—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C2×D414yes—
161C11×C4⋊C4#4112yes—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—42no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—28no—
168C42×C11—22no—
169C42×C11—42no—
170C42×C11—42no—
171C42×C11C2×D414yes—
172C2×#533C2×C1111yescharacteristic
173C2×#441C2×C1112yescomplemented
174C4×C22⋊Q8C2×C1111yescharacteristic
175#2058C2×C1111yescharacteristic, complemented
176#2043C2×C1111yescharacteristic, complemented
177#2035C2×C1112yes—
178#2024C2×C1111yescharacteristic, complemented
179#2016C2×C1111yescharacteristic, complemented
180#2001C2×C1112yes—
181#1763C2×C1112yescomplemented
182#1749C2×C1111yescharacteristic
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11#13712yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—24no—
192Q8×C11—24no—
193Q8×C11—24no—
194Q8×C11—48no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198C2×C4×C11—28no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
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—24no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—44no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11#12012yes—
232C2×C4×C11#12012yes—
233C2×C4×C11#13712yes—
234C2×C4×C11#13712yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4112yes—
238C2×C4×C11C2×#4111yescharacteristic
239C8×C11—24no—
240C8×C11—42no—
241C22×Q16C22×C1112yes—
242#533—28no—
243C2×C4⋊Q8C22×C1111yescharacteristic
244C2×C4⋊Q8C22×C1111yescharacteristic
245C2×#125—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8C22×C1112yes—
248C2×C22⋊Q8C22×C1111yescharacteristic
249C2×C4×Q8—21no—
250C2×C4×Q8C22×C1111yescharacteristic
251C2×C4×Q8C22×C1112yes—
252C2×#117—21no—
253C22×C42C22×C1111yescharacteristic
254#441—28no—
255C2×#106C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×#103C22×C1112yes—
258C2×#103C22×C1112yes—
259C2×#103C22×C1112yes—
260C2×C22⋊C8C22×C1112yes—
261C2×#97C22×C1112yes—
262#391C22×C1111yescharacteristic
263#389C22×C1111yescharacteristic
264#387—21no—
265#385—21no—
266#380C22×C1111yescharacteristic
267C4×C4⋊C4—21no—
268C4×C4⋊C4C22×C1111yescharacteristic
269C4×C22⋊C4—21no—
270#340C22×C1112yes—
271#340C22×C1112yes—
272#336C22×C1111yescharacteristic
273#336C22×C1111yescharacteristic
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11C2×#12011yescharacteristic
282C22×C11#52511yescharacteristic
283C22×C11#53211yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11C2×#13711yescharacteristic
287C22×C11#57511yescharacteristic
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—22no—
292C4×C11—42no—
293C4×C11—41no—
294C4×C11—44no—
295C4×C11—42no—
296C4×C11—44no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11#52512yes—
300C4×C11#53212yes—
301C22×Q8—21no—
302C22×Q8C23×C1112yes—
303C22×Q8C23×C1111yescharacteristic
304C23×C4D4×C1111yescharacteristic
305C23×C4D4×C1111yescharacteristic
306C23×C4C23×C1111yescharacteristic
307C2×Q16—24no—
308C2×Q16—24no—
309C2×Q16—24no—
310C22×C8C23×C1112yes—
311C22×C8C23×C1112yes—
312C4⋊Q8—24no—
313C4⋊Q8—24no—
314#125—28no—
315C22⋊Q8—28no—
316C22⋊Q8—24no—
317C22⋊Q8—22no—
318C22⋊Q8—24no—
319C22⋊Q8—22no—
320C4×Q8—28no—
321C4×Q8—24no—
322C4×Q8—24no—
323C4×Q8D4×C1118yes—
324#117—28no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C4⋊C4C23×C1112yes—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42—22no—
341C2×C42—24no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42D4×C1111yescharacteristic
345C2×C42D4×C1111yescharacteristic
346C2×C42C23×C1111yescharacteristic
347C2×C42C23×C1111yescharacteristic
348#106—24no—
349#103—24no—
350#103—24no—
351#103—24no—
352#103—24no—
353C22⋊C8—24no—
354#97—24no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360C2×C11—42no—
361C2×C11#238811yescharacteristic
362C2×C11#300411yescharacteristic
363C2×C11#300711yescharacteristic
364C2×C11#311311yescharacteristic
365C2×C11#311611yescharacteristic
366C2×C11#318111yescharacteristic
367C2×C11#318511yescharacteristic
368C24C2×D4×C1111yescharacteristic
369C2×Q8—24no—
370C2×Q8—22no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8C2×D4×C1114yes—
381C2×Q8C11×#4112yes—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C24×C1111yescharacteristic
404Q16—216no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8C11×#4114yes—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—28no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—28no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—42no—
423C4⋊C4C2×D4×C1114yes—
424C4⋊C4C11×#4112yes—
425C22⋊C4—28no—
426C22⋊C4—24no—
427C22⋊C4—42no—
428C42—22no—
429C42—22no—
430C42—28no—
431C42—22no—
432C42—42no—
433C42—42no—
434C42C2×D4×C1114yes—
435C11#2357711yescharacteristic, direct product factor, Sylow
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23C11×#13712yes—
443C23C22×D4×C1111yescharacteristic
444Q8—24no—
445Q8—24no—
446Q8—24no—
447Q8—48no—
448Q8—42no—
449Q8—42no—
450Q8—42no—
451C2×C4—28no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—44no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4C11×#12012yes—
485C2×C4C11×#12012yes—
486C2×C4C11×#13712yes—
487C2×C4C11×#13712yes—
488C2×C4C22×D4×C1112yes—
489C2×C4C2×C11×#4111yescharacteristic
490C2×C4C2×C11×#4112yes—
491C2×C4C2×C11×#4111yescharacteristic
492C8—24no—
493C8—42no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22C2×C11×#12011yescharacteristic
502C22C11×#52511yescharacteristic
503C22C11×#53211yescharacteristic
504C22C2×C11×#13711yescharacteristic
505C22C2×C11×#13711yescharacteristic
506C22C2×C11×#13711yescharacteristic
507C22C11×#57511yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—22no—
512C4—41no—
513C4—44no—
514C4—42no—
515C4—44no—
516C4—42no—
517C4—81no—
518C4—81no—
519C4C11×#52512yes—
520C4C11×#53212yes—
521C2—42no—
522C2C11×#238811yescharacteristic
523C2C11×#300411yescharacteristic
524C2C11×#300711yescharacteristic
525C2C11×#311311yescharacteristic
526C2C11×#311611yescharacteristic
527C2C11×#318111yescharacteristic
528C2C11×#318511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#441C2semidirect
4. C11×#2058C2semidirect
5. C11×#2043C2semidirect
7. C11×#2024C2semidirect
8. C11×#2016C2semidirect
10. C11×#1763C2semidirect
104. #23577C11direct (N × H)
173. C2×#441C2×C11semidirect
175. #2058C2×C11semidirect
176. #2043C2×C11semidirect
178. #2024C2×C11semidirect
179. #2016C2×C11semidirect
181. #1763C2×C11semidirect
435. C11#23577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4412
C4×C11×C22⋊Q82
C11×#20582
C11×#20432
C11×#20352
C11×#20242
C11×#20162
C11×#20012
C11×#17632
C11×#17492
#2357711