Finite Group Databasebeta

← C11×#19413 #14596606

Subgroups — C11×#19413 #14596606

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3210C211yesmaximal, characteristic, complemented
2C11×#3115C211yesmaximal, characteristic
3C11×#3107C211yesmaximal, characteristic, complemented
4C11×#2988C211yesmaximal, characteristic, complemented
5C11×#1682C211yesmaximal, characteristic, complemented
6C11×#1681C211yesmaximal, characteristic, complemented
7C11×#1680C211yesmaximal, characteristic, complemented
8C11×#1679C211yesmaximal, characteristic, complemented
9C11×#1670C211yesmaximal, characteristic, complemented
10C11×#1669C211yesmaximal, characteristic, complemented
11C11×#1666C211yesmaximal, characteristic, complemented
12C11×#1665C211yesmaximal, characteristic, complemented
13C11×#1572C211yesmaximal, characteristic, complemented
14C11×#1552C211yesmaximal, characteristic, complemented
15C11×#1540C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C11×#494C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#485—21no—
24C11×#482—21no—
25C11×#475C2211yescharacteristic
26C11×#475C2211yescharacteristic
27C11×#474C2211yescharacteristic
28C11×#474C2211yescharacteristic
29C11×#464—21no—
30C11×#464—21no—
31C11×#462C2211yescharacteristic
32C11×#461C2211yescharacteristic
33C11×#460C2211yescharacteristic
34C11×#459C2211yescharacteristic
35C11×#452—21no—
36C11×#452—21no—
37C11×#452—21no—
38C11×#449—21no—
39C8×Q8×C11C2211yescharacteristic
40C8×Q8×C11C2211yescharacteristic
41C11×#442—21no—
42C11×#440—21no—
43C4×C11×Q16—21no—
44C4×C11×SD16—21no—
45C8×D4×C11—21no—
46C8×D4×C11—21no—
47C8×D4×C11C2211yescharacteristic
48C8×D4×C11C2211yescharacteristic
49C11×#432C2211yescharacteristic
50C11×#431—21no—
51C11×#431C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C2×C11×C4⋊C8—21no—
54C2×C11×C4⋊C8C2211yescharacteristic
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×#332C2211yescharacteristic
64C11×#332C2211yescharacteristic
65C11×#331C2211yescharacteristic
66C11×#331C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×C11×Q16—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×D8—21no—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C22×C8×C11—21no—
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×#127C2311yescharacteristic
84C11×#125—21no—
85C11×#124—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×#121—21no—
89C11×#121—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11D411yescharacteristic
93C4×Q8×C11C2311yescharacteristic
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11D411yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C11×#117—21no—
101C11×#117—21no—
102C11×#117D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C11×#107—21no—
106C11×#107—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8D411yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8D411yescharacteristic
137C11×C22⋊C8D411yescharacteristic
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19413C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—81no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C11×Q16—42no—
167C11×Q16—81no—
168C11×Q16—81no—
169C11×SD16—42no—
170C11×SD16—42no—
171C11×SD16—81no—
172C11×SD16—81no—
173C11×D8—42no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—81no—
181C2×C8×C11—81no—
182C2×C8×C11—81no—
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—41no—
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211C42×C11#4111yescharacteristic
212C42×C11C2411yescharacteristic
213#3210C2×C1111yescharacteristic, complemented
214#3115C2×C1111yescharacteristic
215#3107C2×C1111yescharacteristic, complemented
216#2988C2×C1111yescharacteristic, complemented
217#1682C2×C1111yescharacteristic, complemented
218#1681C2×C1111yescharacteristic, complemented
219#1680C2×C1111yescharacteristic, complemented
220#1679C2×C1111yescharacteristic, complemented
221#1670C2×C1111yescharacteristic, complemented
222#1669C2×C1111yescharacteristic, complemented
223#1666C2×C1111yescharacteristic, complemented
224#1665C2×C1111yescharacteristic, complemented
225#1572C2×C1111yescharacteristic, complemented
226#1552C2×C1111yescharacteristic, complemented
227#1540C2×C1111yescharacteristic, complemented
228C23×C11—21no—
229C23×C11—41no—
230C23×C11#12111yescharacteristic
231Q8×C11—21no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11#13512yes—
239D4×C11—24no—
240D4×C11—21no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—81no—
246D4×C11—82no—
247D4×C11#13512yes—
248C2×C4×C11—24no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—81no—
263C2×C4×C11—82no—
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11#12111yescharacteristic
266C2×C4×C11#12111yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280#533C22×C1111yescharacteristic
281#532C22×C1111yescharacteristic
282C4×#41C22×C1111yescharacteristic
283#494C22×C1111yescharacteristic
284#492C22×C1111yescharacteristic
285#487C22×C1111yescharacteristic
286#486C22×C1111yescharacteristic
287#485—21no—
288#482—21no—
289#475C22×C1111yescharacteristic
290#475C22×C1111yescharacteristic
291#474C22×C1111yescharacteristic
292#474C22×C1111yescharacteristic
293#464—21no—
294#464—21no—
295#462C22×C1111yescharacteristic
296#461C22×C1111yescharacteristic
297#460C22×C1111yescharacteristic
298#459C22×C1111yescharacteristic
299#452—21no—
300#452—21no—
301#452—21no—
302#449—21no—
303C8×Q8C22×C1111yescharacteristic
304C8×Q8C22×C1111yescharacteristic
305#442—21no—
306#440—21no—
307C4×Q16—21no—
308C4×SD16—21no—
309C8×D4—21no—
310C8×D4—21no—
311C8×D4C22×C1111yescharacteristic
312C8×D4C22×C1111yescharacteristic
313#432C22×C1111yescharacteristic
314#431—21no—
315#431C22×C1111yescharacteristic
316#431C22×C1111yescharacteristic
317C2×C4⋊C8—21no—
318C2×C4⋊C8C22×C1111yescharacteristic
319#335C22×C1111yescharacteristic
320#335C22×C1111yescharacteristic
321#334C22×C1111yescharacteristic
322#334C22×C1111yescharacteristic
323#332C22×C1111yescharacteristic
324#332C22×C1111yescharacteristic
325#332C22×C1111yescharacteristic
326#332C22×C1111yescharacteristic
327#332C22×C1111yescharacteristic
328#332C22×C1111yescharacteristic
329#331C22×C1111yescharacteristic
330#331C22×C1111yescharacteristic
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—21no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11C2×#12111yescharacteristic
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11C2×#13511yescharacteristic
352C4×C11C2×#13511yescharacteristic
353C4×C11#57611yescharacteristic
354C4×C11#57711yescharacteristic
355C2×#41—21no—
356C2×#41D4×C1111yescharacteristic
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×D8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8C23×C1111yescharacteristic
369C4⋊Q8C23×C1111yescharacteristic
370C4⋊Q8C23×C1111yescharacteristic
371#127C23×C1111yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C1111yescharacteristic
381C4×Q8C23×C1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4D4×C1111yescharacteristic
387C4×D4C23×C1111yescharacteristic
388#117—21no—
389#117—21no—
390#117D4×C1111yescharacteristic
391C2×C42—21no—
392C2×C42C23×C1111yescharacteristic
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8D4×C1111yescharacteristic
401C4⋊C8D4×C1111yescharacteristic
402C4⋊C8C23×C1111yescharacteristic
403C4⋊C8C23×C1111yescharacteristic
404C4⋊C8C23×C1111yescharacteristic
405C4⋊C8C23×C1111yescharacteristic
406C4⋊C8C23×C1111yescharacteristic
407C4⋊C8C23×C1111yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8D4×C1111yescharacteristic
425C22⋊C8D4×C1111yescharacteristic
426#97—21no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C23×C1111yescharacteristic
431C4×C8C23×C1111yescharacteristic
432C2×C11—41no—
433C2×C11—42no—
434C2×C11—161no—
435C2×C11#304511yescharacteristic
436C2×C11#305011yescharacteristic
437C2×C11#306911yescharacteristic
438#41—22no—
439#41—22no—
440#41—81no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C1111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4C2×D4×C1111yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C11×#4111yescharacteristic
459Q16—42no—
460Q16—81no—
461Q16—81no—
462SD16—42no—
463SD16—42no—
464SD16—81no—
465SD16—81no—
466D8—42no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—81no—
474C2×C8—81no—
475C2×C8—81no—
476C2×C8C2×D4×C1111yescharacteristic
477C2×C8C2×D4×C1111yescharacteristic
478C2×C8C2×D4×C1111yescharacteristic
479C2×C8C2×D4×C1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C1111yescharacteristic
491C4⋊C4C2×D4×C1111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C2×D4×C1111yescharacteristic
503C42C2×D4×C1111yescharacteristic
504C42C11×#4111yescharacteristic
505C42C24×C1111yescharacteristic
506C11#1941311yescharacteristic, direct product factor, Sylow
507C23—21no—
508C23—41no—
509C23C11×#12111yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8C11×#13512yes—
518D4—24no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4C11×#13512yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—81no—
542C2×C4—82no—
543C2×C4C11×#12111yescharacteristic
544C2×C4C11×#12111yescharacteristic
545C2×C4C11×#12111yescharacteristic
546C2×C4C22×D4×C1111yescharacteristic
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C2×C11×#4111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×C11×#12111yescharacteristic
569C4—21no—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×C11×#13511yescharacteristic
580C4C2×C11×#13511yescharacteristic
581C4C11×#57611yescharacteristic
582C4C11×#57711yescharacteristic
583C2—41no—
584C2—42no—
585C2—161no—
586C2C11×#304511yescharacteristic
587C2C11×#305011yescharacteristic
588C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3115C2
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×#3210C2semidirect
3. C11×#3107C2semidirect
4. C11×#2988C2semidirect
5. C11×#1682C2semidirect
6. C11×#1681C2semidirect
7. C11×#1680C2semidirect
8. C11×#1679C2semidirect
9. C11×#1670C2semidirect
10. C11×#1669C2semidirect
11. C11×#1666C2semidirect
12. C11×#1665C2semidirect
13. C11×#1572C2semidirect
14. C11×#1552C2semidirect
15. C11×#1540C2semidirect
144. #19413C11direct (N × H)
213. #3210C2×C11semidirect
215. #3107C2×C11semidirect
216. #2988C2×C11semidirect
217. #1682C2×C11semidirect
218. #1681C2×C11semidirect
219. #1680C2×C11semidirect
220. #1679C2×C11semidirect
221. #1670C2×C11semidirect
222. #1669C2×C11semidirect
223. #1666C2×C11semidirect
224. #1665C2×C11semidirect
225. #1572C2×C11semidirect
226. #1552C2×C11semidirect
227. #1540C2×C11semidirect
506. C11#19413direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32102
C11×#31152
C11×#31072
C11×#29882
C11×#16822
C11×#16812
C11×#16802
C11×#16792
C11×#16702
C11×#16692
C11×#16662
C11×#16652
C11×#15722
C11×#15522
C11×#15402
#1941311