Finite Group Databasebeta

← C11×#19093 #14596286

Subgroups — C11×#19093 #14596286

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3563C211yesmaximal, characteristic
2C11×#3240C211yesmaximal, characteristic
3C11×#3237C211yesmaximal, characteristic, complemented
4C11×#3236C211yesmaximal, characteristic, complemented
5C11×#1664C212yesmaximal, complemented
6C11×#1664C212yesmaximal, complemented
7C11×#1663C212yesmaximal, complemented
8C11×#1663C212yesmaximal, complemented
9C11×#1537C211yesmaximal, characteristic, complemented
10C11×#1535C211yesmaximal, characteristic
11C11×#1534C211yesmaximal, characteristic, complemented
12C11×#564C2212yes—
13C11×#563C2212yes—
14C11×#557—21no—
15C11×#554—21no—
16C11×#552—21no—
17C11×#552—22no—
18C11×#552—21no—
19C11×#544—21no—
20C11×#544—21no—
21C11×#541—21no—
22C11×#541—22no—
23C11×#539—21no—
24C11×#533C2211yescharacteristic
25C11×#533C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic
28C11×#501C2211yescharacteristic
29C11×#501C2211yescharacteristic
30C11×#501C2212yes—
31C11×#501C2212yes—
32C11×#491C2212yes—
33C11×#491C2212yes—
34C11×#489C2211yescharacteristic
35C11×#489C2211yescharacteristic
36C11×#485—21no—
37C11×#485—22no—
38C11×#484—21no—
39C11×#483—21no—
40C11×#482—21no—
41C11×#479—22no—
42C11×#479—21no—
43C11×#478—21no—
44C11×#477—21no—
45C11×#475—21no—
46C11×#432C2211yescharacteristic
47C11×#432C2211yescharacteristic
48C11×#432C2211yescharacteristic
49C11×#330C2212yes—
50C11×#330C2212yes—
51C11×#330C2212yes—
52C11×#330C2212yes—
53C11×#330C2212yes—
54C11×#329C2212yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×#126—22no—
63C11×#126—22no—
64C11×#126—22no—
65C11×#126—22no—
66C11×#126—21no—
67C11×#125—22no—
68C11×#125—22no—
69C11×#125—21no—
70C11×#125—22no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#125—22no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#125—21no—
77C11×#125—21no—
78C11×#125—21no—
79C11×#125D412yes—
80C11×#125C2312yes—
81C11×#125C2312yes—
82C11×#125C2311yescharacteristic
83C11×#124C2311yescharacteristic
84C11×#123—22no—
85C11×#123—22no—
86C11×#123—21no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8D411yescharacteristic
98C11×#121D411yescharacteristic
99C4×Q8×C11—21no—
100C4×Q8×C11—22no—
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C4×Q8×C11—21no—
104C4×Q8×C11—21no—
105C4×Q8×C11—21no—
106C4×Q8×C11D411yescharacteristic
107C4×D4×C11—22no—
108C4×D4×C11—21no—
109C4×D4×C11D411yescharacteristic
110C11×#117—22no—
111C11×#117—21no—
112C11×#117—22no—
113C11×#117—21no—
114C11×#117—21no—
115C11×#117D412yes—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C11×#107—22no—
123C11×#107—21no—
124C11×#107—21no—
125C11×#107—22no—
126C11×#106—22no—
127C11×#106—21no—
128C11×#106—21no—
129C11×#106—22no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—21no—
134C11×#103—21no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—22no—
139C11×#102—21no—
140C11×#102—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97C2311yescharacteristic
145C11×#97C2311yescharacteristic
146C11×#97C2312yes—
147C11×#97C2312yes—
148#19093C1111yesmaximal, characteristic, direct product factor, Sylow
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4C2×D412yes—
197C11×C4⋊C4C2×D412yes—
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—41no—
212C42×C11—22no—
213C42×C11—22no—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—21no—
217C42×C11—41no—
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221C42×C11C2411yescharacteristic
222#3563C2×C1111yescharacteristic
223#3240C2×C1111yescharacteristic
224#3237C2×C1111yescharacteristic, complemented
225#3236C2×C1111yescharacteristic, complemented
226#1664C2×C1112yescomplemented
227#1664C2×C1112yescomplemented
228#1663C2×C1112yescomplemented
229#1663C2×C1112yescomplemented
230#1537C2×C1111yescharacteristic, complemented
231#1535C2×C1111yescharacteristic
232#1534C2×C1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11#12011yescharacteristic
235Q8×C11—41no—
236Q8×C11—42no—
237Q8×C11—42no—
238Q8×C11—42no—
239Q8×C11—81no—
240Q8×C11—82no—
241D4×C11—41no—
242D4×C11—42no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—81no—
258C2×C4×C11—82no—
259C2×C4×C11#12011yescharacteristic
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11#12011yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C8×C11—42no—
266C8×C11—42no—
267C8×C11—41no—
268C8×C11—41no—
269#564C22×C1112yes—
270#563C22×C1112yes—
271#557—21no—
272#554—21no—
273#552—21no—
274#552—22no—
275#552—21no—
276#544—21no—
277#544—21no—
278#541—21no—
279#541—22no—
280#539—21no—
281#533C22×C1111yescharacteristic
282#533C22×C1111yescharacteristic
283#529C22×C1111yescharacteristic
284C2×#125C22×C1111yescharacteristic
285#501C22×C1111yescharacteristic
286#501C22×C1111yescharacteristic
287#501C22×C1112yes—
288#501C22×C1112yes—
289#491C22×C1112yes—
290#491C22×C1112yes—
291#489C22×C1111yescharacteristic
292#489C22×C1111yescharacteristic
293#485—21no—
294#485—22no—
295#484—21no—
296#483—21no—
297#482—21no—
298#479—22no—
299#479—21no—
300#478—21no—
301#477—21no—
302#475—21no—
303#432C22×C1111yescharacteristic
304#432C22×C1111yescharacteristic
305#432C22×C1111yescharacteristic
306#330C22×C1112yes—
307#330C22×C1112yes—
308#330C22×C1112yes—
309#330C22×C1112yes—
310#330C22×C1112yes—
311#329C22×C1112yes—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11C2×#12011yescharacteristic
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—81no—
333C4×C11—81no—
334C4⋊Q8—22no—
335C4⋊Q8—21no—
336C4⋊Q8—22no—
337C4⋊Q8D4×C1111yescharacteristic
338C4⋊Q8D4×C1111yescharacteristic
339C4⋊Q8C23×C1111yescharacteristic
340C4⋊Q8C23×C1111yescharacteristic
341#126—22no—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—21no—
346#125—22no—
347#125—22no—
348#125—21no—
349#125—22no—
350#125—22no—
351#125—22no—
352#125—22no—
353#125—22no—
354#125—22no—
355#125—21no—
356#125—21no—
357#125—21no—
358#125D4×C1112yes—
359#125C23×C1112yes—
360#125C23×C1111yescharacteristic
361#125C23×C1112yes—
362#124C23×C1111yescharacteristic
363#123—22no—
364#123—22no—
365#123—21no—
366C22⋊Q8—22no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8D4×C1111yescharacteristic
377#121D4×C1111yescharacteristic
378C4×Q8—21no—
379C4×Q8—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8D4×C1111yescharacteristic
386C4×D4—22no—
387C4×D4—21no—
388C4×D4D4×C1111yescharacteristic
389#117—22no—
390#117—21no—
391#117—22no—
392#117—21no—
393#117—21no—
394#117D4×C1112yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C1111yescharacteristic
399C2×C4⋊C4D4×C1111yescharacteristic
400C2×C42C23×C1111yescharacteristic
401#107—22no—
402#107—21no—
403#107—21no—
404#107—22no—
405#106—22no—
406#106—21no—
407#106—21no—
408#106—22no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412#103—21no—
413#103—21no—
414#103—22no—
415#103—22no—
416#103—22no—
417#103—22no—
418#102—21no—
419#102—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423#97C23×C1112yes—
424#97C23×C1112yes—
425#97C23×C1111yescharacteristic
426#97C23×C1111yescharacteristic
427C2×C11—41no—
428C2×C11—81no—
429C2×C11#302011yescharacteristic
430C2×C11#302011yescharacteristic
431C2×C11#302211yescharacteristic
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×D4×C1111yescharacteristic
438C2×D4—21no—
439C2×D4C2×D4×C1111yescharacteristic
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—22no—
450C2×C8—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C1112yes—
480C4⋊C4C2×D4×C1112yes—
481C4⋊C4C2×D4×C1112yes—
482C4⋊C4C2×D4×C1112yes—
483C4⋊C4C2×D4×C1111yescharacteristic
484C4⋊C4C2×D4×C1111yescharacteristic
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—21no—
500C42—41no—
501C42C2×D4×C1111yescharacteristic
502C42C2×D4×C1111yescharacteristic
503C42C2×D4×C1111yescharacteristic
504C42C24×C1111yescharacteristic
505C11#1909311yescharacteristic, direct product factor, Sylow
506C23—21no—
507C23C11×#12011yescharacteristic
508Q8—41no—
509Q8—42no—
510Q8—42no—
511Q8—42no—
512Q8—81no—
513Q8—82no—
514D4—41no—
515D4—42no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4—82no—
532C2×C4C11×#12011yescharacteristic
533C2×C4C11×#12011yescharacteristic
534C2×C4C11×#12011yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C22×D4×C1111yescharacteristic
538C8—42no—
539C8—42no—
540C8—41no—
541C8—41no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22C2×C11×#12011yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—41no—
562C4—81no—
563C4—81no—
564C2—41no—
565C2—81no—
566C2C11×#302011yescharacteristic
567C2C11×#302011yescharacteristic
568C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#3237C2semidirect
4. C11×#3236C2semidirect
5. C11×#1664C2semidirect
6. C11×#1664C2semidirect
7. C11×#1663C2semidirect
8. C11×#1663C2semidirect
9. C11×#1537C2semidirect
11. C11×#1534C2semidirect
148. #19093C11direct (N × H)
224. #3237C2×C11semidirect
225. #3236C2×C11semidirect
226. #1664C2×C11semidirect
227. #1664C2×C11semidirect
228. #1663C2×C11semidirect
229. #1663C2×C11semidirect
230. #1537C2×C11semidirect
232. #1534C2×C11semidirect
505. C11#19093direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35632
C11×#32402
C11×#32372
C11×#32362
C11×#16642
C11×#16632
C11×#15372
C11×#15352
C11×#15342
#1909311