Finite Group Databasebeta

← C11×#18936 #14596129

Subgroups — C11×#18936 #14596129

Order 2816.

948 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic, complemented
2C11×#3245C211yesmaximal, characteristic, complemented
3C11×#3216C211yesmaximal, characteristic, complemented
4C11×#3207C211yesmaximal, characteristic, complemented
5C11×#1644C212yesmaximal, complemented
6C11×#1641C212yesmaximal, complemented
7C11×#1622C212yesmaximal, complemented
8C11×#1621C212yesmaximal, complemented
9C11×#1551C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1481C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#554—21no—
14C11×#554C2212yes—
15C11×#550—21no—
16C11×#550C2212yes—
17C11×#547—21no—
18C11×#547—21no—
19C11×#540—22no—
20C11×#537—22no—
21C11×#537—22no—
22C11×#533C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#497—21no—
27C11×#493C2211yescharacteristic
28C11×#492C2211yescharacteristic
29C11×#489—21no—
30C11×#487C2211yescharacteristic
31C11×#486C2211yescharacteristic
32C11×#474—21no—
33C11×#474C2212yes—
34C11×#466—22no—
35C11×#463—22no—
36C11×#462C2212yes—
37C11×#460C2212yes—
38C11×#459—21no—
39C11×#459C2212yes—
40C11×#452—22no—
41C11×#449—22no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#333C2212yes—
46C11×#331C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×D4⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41D412yes—
56C2×C11×Q16—22no—
57C2×C11×SD16—22no—
58C2×C11×SD16—22no—
59C2×C11×D8—22no—
60C2×C11×D8—22no—
61C22×C8×C11—21no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2311yescharacteristic
67C11×#127—22no—
68C11×#127D411yescharacteristic
69C11×#127C2311yescharacteristic
70C11×#127C2311yescharacteristic
71C11×#125—22no—
72C11×#125—21no—
73C11×#124—21no—
74C11×#124—21no—
75C11×#124D412yes—
76C11×#123—24no—
77C11×#123—24no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8D412yes—
84C11×#121—24no—
85C11×#121—24no—
86C11×#121—22no—
87C11×#121—24no—
88C11×#121—24no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—22no—
93C11×#121—21no—
94C11×#121—21no—
95C11×#121D412yes—
96C4×Q8×C11—21no—
97C4×Q8×C11C2312yes—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11C2312yes—
106C11×#117—21no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—22no—
109C2×C42×C11C2311yescharacteristic
110C11×#107—22no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×#103—22no—
116C11×#103—22no—
117C11×#102—22no—
118C11×#102—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18936C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—82no—
128C11×#41—82no—
129C11×#41—82no—
130C11×#41—82no—
131C11×#41—82no—
132C11×#41—84no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×D412yes—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—41no—
150C2×D4×C11C2×D412yes—
151C2×D4×C11C2×D412yes—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—41no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C11×Q16—82no—
161C11×SD16—82no—
162C11×SD16—82no—
163C11×D8—82no—
164C11×D8—82no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—81no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4C2×D412yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C42×C11—22no—
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2411yescharacteristic
198#3548C2×C1111yescharacteristic, complemented
199#3245C2×C1111yescharacteristic, complemented
200#3216C2×C1111yescharacteristic, complemented
201#3207C2×C1111yescharacteristic, complemented
202#1644C2×C1112yescomplemented
203#1641C2×C1112yescomplemented
204#1622C2×C1112yescomplemented
205#1621C2×C1112yescomplemented
206#1551C2×C1111yescharacteristic, complemented
207#1496C2×C1111yescharacteristic, complemented
208#1481C2×C1111yescharacteristic, complemented
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11#12011yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—81no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—41no—
230D4×C11—81no—
231D4×C11—82no—
232D4×C11—82no—
233D4×C11—84no—
234D4×C11—84no—
235D4×C11—82no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—82no—
249C2×C4×C11—84no—
250C2×C4×C11—84no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C8×C11—41no—
258C8×C11—41no—
259C8×C11—42no—
260C8×C11—42no—
261#562—22no—
262#554—21no—
263#554C22×C1112yes—
264#550—21no—
265#550C22×C1112yes—
266#547—21no—
267#547—21no—
268#540—22no—
269#537—22no—
270#537—22no—
271#533C22×C1111yescharacteristic
272#532C22×C1111yescharacteristic
273#532C22×C1111yescharacteristic
274#532C22×C1111yescharacteristic
275#497—21no—
276#493C22×C1111yescharacteristic
277#492C22×C1111yescharacteristic
278#489—21no—
279#487C22×C1111yescharacteristic
280#486C22×C1111yescharacteristic
281#474—21no—
282#474C22×C1112yes—
283#466—22no—
284#463—22no—
285#462C22×C1112yes—
286#460C22×C1112yes—
287#459—21no—
288#459C22×C1112yes—
289#452—22no—
290#449—22no—
291#432C22×C1111yescharacteristic
292#431C22×C1111yescharacteristic
293C2×C4⋊C8C22×C1111yescharacteristic
294#333C22×C1112yes—
295#331C22×C1112yes—
296Q8⋊C8C22×C1112yes—
297Q8⋊C8C22×C1112yes—
298D4⋊C8C22×C1112yes—
299D4⋊C8C22×C1112yes—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11C2×#12011yescharacteristic
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11—81no—
322C4×C11#57612yes—
323C4×C11#57711yescharacteristic
324C4×C11#57811yescharacteristic
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41D4×C1112yes—
330C2×Q16—22no—
331C2×SD16—22no—
332C2×SD16—22no—
333C2×D8—22no—
334C2×D8—22no—
335C22×C8—21no—
336C4⋊Q8D4×C1111yescharacteristic
337C4⋊Q8D4×C1111yescharacteristic
338C4⋊Q8D4×C1111yescharacteristic
339C4⋊Q8C23×C1111yescharacteristic
340C4⋊Q8C23×C1111yescharacteristic
341#127—22no—
342#127D4×C1111yescharacteristic
343#127C23×C1111yescharacteristic
344#127C23×C1111yescharacteristic
345#125—22no—
346#125—21no—
347#124—21no—
348#124—21no—
349#124D4×C1112yes—
350#123—24no—
351#123—24no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—22no—
355C22⋊Q8—24no—
356C22⋊Q8—21no—
357C22⋊Q8D4×C1112yes—
358#121—24no—
359#121—24no—
360#121—22no—
361#121—24no—
362#121—24no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—22no—
367#121—21no—
368#121—21no—
369#121D4×C1112yes—
370C4×Q8—21no—
371C4×Q8C23×C1112yes—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C23×C1112yes—
380#117—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C42C23×C1111yescharacteristic
384#107—22no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C23×C1112yes—
388C4⋊C8C23×C1112yes—
389#103—22no—
390#103—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397#97—21no—
398C4×C8C23×C1111yescharacteristic
399C4×C8C23×C1111yescharacteristic
400C2×C11—41no—
401C2×C11—82no—
402C2×C11—82no—
403C2×C11—161no—
404C2×C11#300811yescharacteristic
405C2×C11#301311yescharacteristic
406C2×C11#301911yescharacteristic
407#41—82no—
408#41—82no—
409#41—82no—
410#41—82no—
411#41—82no—
412#41—84no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8C2×D4×C1112yes—
417C2×Q8C2×D4×C1112yes—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—41no—
430C2×D4C2×D4×C1112yes—
431C2×D4C2×D4×C1112yes—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440Q16—82no—
441SD16—82no—
442SD16—82no—
443D8—82no—
444D8—82no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—81no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4C2×D4×C1112yes—
463C4⋊C4C2×D4×C1112yes—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—22no—
474C42C2×D4×C1111yescharacteristic
475C42C2×D4×C1111yescharacteristic
476C42C2×D4×C1111yescharacteristic
477C42C24×C1111yescharacteristic
478C11#1893611yescharacteristic, direct product factor, Sylow
479C23—22no—
480C23—22no—
481C23—41no—
482C23C11×#12011yescharacteristic
483Q8—22no—
484Q8—22no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488Q8—81no—
489D4—22no—
490D4—22no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—42no—
495D4—42no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—81no—
501D4—82no—
502D4—82no—
503D4—84no—
504D4—84no—
505D4—82no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—82no—
519C2×C4—84no—
520C2×C4—84no—
521C2×C4C11×#12011yescharacteristic
522C2×C4C11×#12011yescharacteristic
523C2×C4C11×#12011yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C22×D4×C1111yescharacteristic
526C2×C4C22×D4×C1111yescharacteristic
527C8—41no—
528C8—41no—
529C8—42no—
530C8—42no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C2×C11×#12011yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—81no—
553C4C11×#57612yes—
554C4C11×#57711yescharacteristic
555C4C11×#57811yescharacteristic
556C2—41no—
557C2—82no—
558C2—82no—
559C2—161no—
560C2C11×#300811yescharacteristic
561C2C11×#301311yescharacteristic
562C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
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
1. C11×#3548C2semidirect
2. C11×#3245C2semidirect
3. C11×#3216C2semidirect
4. C11×#3207C2semidirect
5. C11×#1644C2semidirect
6. C11×#1641C2semidirect
7. C11×#1622C2semidirect
8. C11×#1621C2semidirect
9. C11×#1551C2semidirect
10. C11×#1496C2semidirect
11. C11×#1481C2semidirect
126. #18936C11direct (N × H)
198. #3548C2×C11semidirect
199. #3245C2×C11semidirect
200. #3216C2×C11semidirect
201. #3207C2×C11semidirect
202. #1644C2×C11semidirect
203. #1641C2×C11semidirect
204. #1622C2×C11semidirect
205. #1621C2×C11semidirect
206. #1551C2×C11semidirect
207. #1496C2×C11semidirect
208. #1481C2×C11semidirect
478. C11#18936direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#32452
C11×#32162
C11×#32072
C11×#16442
C11×#16412
C11×#16222
C11×#16212
C11×#15512
C11×#14962
C11×#14812
#1893611