Finite Group Databasebeta

← C11×#19805 #14596998

Subgroups — C11×#19805 #14596998

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C11×SD16C211yesmaximal, characteristic, complemented
2Q8×C11×SD16C211yesmaximal, characteristic, complemented
3C11×#3298C211yesmaximal, characteristic
4C11×#3276C211yesmaximal, characteristic
5C11×#1716C211yesmaximal, characteristic, complemented
6C11×#1691C211yesmaximal, characteristic, complemented
7C11×#1680C211yesmaximal, characteristic, complemented
8C11×#1671C211yesmaximal, characteristic, complemented
9C11×#1670C211yesmaximal, characteristic, complemented
10C11×#1651C211yesmaximal, characteristic, complemented
11C11×#1651C211yesmaximal, characteristic, complemented
12C11×#1645C211yesmaximal, characteristic, complemented
13C11×#1635C211yesmaximal, characteristic
14C11×#1583C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#137—21no—
17Q82×C11C2211yescharacteristic
18D4×Q8×C11C2211yescharacteristic
19D4×Q8×C11C2211yescharacteristic
20C11×#547C2211yescharacteristic
21C11×#498—21no—
22C11×#498—21no—
23C11×#498C2211yescharacteristic
24C11×#498C2211yescharacteristic
25C11×#498C2211yescharacteristic
26C11×#494C2211yescharacteristic
27C11×#487C2211yescharacteristic
28C11×#487C2211yescharacteristic
29C11×#483—21no—
30C11×#476—21no—
31C11×#476—21no—
32C11×#476C2211yescharacteristic
33C11×#476C2211yescharacteristic
34C11×#475—21no—
35C11×#475—21no—
36C11×#475C2211yescharacteristic
37C11×#475C2211yescharacteristic
38C11×#475C2211yescharacteristic
39C11×#470—21no—
40C11×#465—21no—
41C11×#462C2211yescharacteristic
42C11×#461C2211yescharacteristic
43C11×#461C2211yescharacteristic
44C11×#452—21no—
45C11×#451—21no—
46C11×#448—21no—
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C4×C11×SD16—21no—
50C4×C11×SD16—21no—
51C4×C11×SD16C2211yescharacteristic
52C4×C11×SD16C2211yescharacteristic
53C11×#436C2211yescharacteristic
54C8×D4×C11C2211yescharacteristic
55C2×C11×#103—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C22×Q8×C11—21no—
69C22×Q8×C11—21no—
70C11×#137—44no—
71C2×C11×Q16—21no—
72C2×C11×Q16—21no—
73C2×C11×Q16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16D411yescharacteristic
77C2×C11×SD16D411yescharacteristic
78C2×C11×M16—21no—
79C22×C8×C11—21no—
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—41no—
85C11×C4⋊Q8C2311yescharacteristic
86C11×C4⋊Q8C2311yescharacteristic
87C11×C4⋊Q8C2311yescharacteristic
88C11×C4⋊Q8C2311yescharacteristic
89C11×#123—41no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—41no—
94C11×C22⋊Q8—41no—
95C11×#121—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11C2311yescharacteristic
99C4×Q8×C11C2311yescharacteristic
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11C2311yescharacteristic
103C4×D4×C11C2311yescharacteristic
104C2×C11×C4⋊C4—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×#106—21no—
112C11×#106—21no—
113C11×#106—21no—
114C11×#106—41no—
115C11×#106D411yescharacteristic
116C11×#106D411yescharacteristic
117C11×C4⋊C8—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×C4⋊C8C2311yescharacteristic
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—21no—
129C11×#103—21no—
130C11×#103—21no—
131C11×#103—41no—
132C11×#103D411yescharacteristic
133C11×#103D411yescharacteristic
134C11×#102—21no—
135C11×#102—21no—
136C11×#102D411yescharacteristic
137C11×#102D411yescharacteristic
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145#19805C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—42no—
147C11×#41—81no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—41no—
153C2×Q8×C11—41no—
154C2×Q8×C11—41no—
155C2×Q8×C11—42no—
156C2×Q8×C11—42no—
157C2×Q8×C11—81no—
158C2×Q8×C11—81no—
159C2×Q8×C11C2×D411yescharacteristic
160C2×Q8×C11C2×D411yescharacteristic
161C2×D4×C11—41no—
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C11×Q16—42no—
170C11×Q16—42no—
171C11×Q16—81no—
172C11×SD16—22no—
173C11×SD16—42no—
174C11×SD16—81no—
175C11×SD16SD1614yescomplemented
176C11×M16—42no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
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—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4—41no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C22⋊C4—21no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—41no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—41no—
214C42×C11C2411yescharacteristic
215Q8×SD16C2×C1111yescharacteristic, complemented
216Q8×SD16C2×C1111yescharacteristic, complemented
217#3298C2×C1111yescharacteristic
218#3276C2×C1111yescharacteristic
219#1716C2×C1111yescharacteristic, complemented
220#1691C2×C1111yescharacteristic, complemented
221#1680C2×C1111yescharacteristic, complemented
222#1671C2×C1111yescharacteristic, complemented
223#1670C2×C1111yescharacteristic, complemented
224#1651C2×C1111yescharacteristic, complemented
225#1651C2×C1111yescharacteristic, complemented
226#1645C2×C1111yescharacteristic, complemented
227#1635C2×C1111yescharacteristic
228#1583C2×C1111yescharacteristic, complemented
229SD16⋊C8C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—82no—
241Q8×C11—82no—
242Q8×C11—81no—
243Q8×C11—161no—
244Q8×C11C2×SD1612yes—
245Q8×C11#13712yescomplemented
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11—82no—
250D4×C11C2×SD1612yes—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—82no—
266C2×C4×C11—82no—
267C2×C4×C11—82no—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
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×C11C2×SD1612yes—
280C2×#137—21no—
281Q82C22×C1111yescharacteristic
282D4×Q8C22×C1111yescharacteristic
283D4×Q8C22×C1111yescharacteristic
284#547C22×C1111yescharacteristic
285#498—21no—
286#498—21no—
287#498C22×C1111yescharacteristic
288#498C22×C1111yescharacteristic
289#498C22×C1111yescharacteristic
290#494C22×C1111yescharacteristic
291#487C22×C1111yescharacteristic
292#487C22×C1111yescharacteristic
293#483—21no—
294#476—21no—
295#476—21no—
296#476C22×C1111yescharacteristic
297#476C22×C1111yescharacteristic
298#475—21no—
299#475—21no—
300#475C22×C1111yescharacteristic
301#475C22×C1111yescharacteristic
302#475C22×C1111yescharacteristic
303#470—21no—
304#465—21no—
305#462C22×C1111yescharacteristic
306#461C22×C1111yescharacteristic
307#461C22×C1111yescharacteristic
308#452—21no—
309#451—21no—
310#448—21no—
311C8×Q8C22×C1111yescharacteristic
312C8×Q8C22×C1111yescharacteristic
313C4×SD16—21no—
314C4×SD16—21no—
315C4×SD16C22×C1111yescharacteristic
316C4×SD16C22×C1111yescharacteristic
317#436C22×C1111yescharacteristic
318C8×D4C22×C1111yescharacteristic
319C2×#103—21no—
320#335C22×C1111yescharacteristic
321#334C22×C1111yescharacteristic
322#333C22×C1111yescharacteristic
323#332C22×C1111yescharacteristic
324#332C22×C1111yescharacteristic
325#332C22×C1111yescharacteristic
326Q8⋊C8C22×C1111yescharacteristic
327Q8⋊C8C22×C1111yescharacteristic
328D4⋊C8C22×C1111yescharacteristic
329D4⋊C8C22×C1111yescharacteristic
330#322C22×C1111yescharacteristic
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11D4211yescharacteristic
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C22×SD1611yescharacteristic
350C4×C11C2×#13711yescharacteristic
351C4×C11#57711yescharacteristic
352C4×C11#57711yescharacteristic
353C2×#41—21no—
354C22×Q8—21no—
355C22×Q8—21no—
356#137—44no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16D4×C1111yescharacteristic
363C2×SD16D4×C1111yescharacteristic
364C2×M16—21no—
365C22×C8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—41no—
371C4⋊Q8C23×C1111yescharacteristic
372C4⋊Q8C23×C1111yescharacteristic
373C4⋊Q8C23×C1111yescharacteristic
374C4⋊Q8C23×C1111yescharacteristic
375#123—41no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C22⋊Q8—41no—
381#121—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8C23×C1111yescharacteristic
385C4×Q8C23×C1111yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C23×C1111yescharacteristic
389C4×D4C23×C1111yescharacteristic
390C2×C4⋊C4—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—41no—
401#106D4×C1111yescharacteristic
402#106D4×C1111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C1111yescharacteristic
406C4⋊C8C23×C1111yescharacteristic
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#103D4×C1111yescharacteristic
419#103D4×C1111yescharacteristic
420#102—21no—
421#102—21no—
422#102D4×C1111yescharacteristic
423#102D4×C1111yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8C23×C1111yescharacteristic
429C4×C8C23×C1111yescharacteristic
430C4×C8C23×C1111yescharacteristic
431C2×C11—42no—
432C2×C11—81no—
433C2×C11#326611yescharacteristic
434C2×C11D4×SD1611yescharacteristic
435C2×C11#328911yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—81no—
448C2×Q8—81no—
449C2×Q8C2×D4×C1111yescharacteristic
450C2×Q8C2×D4×C1111yescharacteristic
451C2×D4—41no—
452C2×D4C2×D4×C1111yescharacteristic
453C2×D4C2×D4×C1111yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—42no—
460Q16—42no—
461Q16—81no—
462SD16—22no—
463SD16—42no—
464SD16—81no—
465SD16C11×SD1614yescomplemented
466M16—42no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—81no—
473C2×C8C2×D4×C1111yescharacteristic
474C2×C8C2×D4×C1111yescharacteristic
475C2×C8C2×D4×C1111yescharacteristic
476C2×C8C2×D4×C1111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C1111yescharacteristic
493C4⋊C4C2×D4×C1111yescharacteristic
494C4⋊C4C2×D4×C1111yescharacteristic
495C4⋊C4C2×D4×C1111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42—41no—
504C42C24×C1111yescharacteristic
505C11#1980511yescharacteristic, direct product factor, Sylow
506C23—21no—
507C23—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—82no—
517Q8—82no—
518Q8—81no—
519Q8—161no—
520Q8C2×C11×SD1612yes—
521Q8C11×#13712yescomplemented
522D4—21no—
523D4—21no—
524D4—21no—
525D4—82no—
526D4C2×C11×SD1612yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C11×H(5,𝔽2)11yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8C2×C11×SD1612yes—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22D42×C1111yescharacteristic
563C4—22no—
564C4—22no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4C22×C11×SD1611yescharacteristic
575C4C2×C11×#13711yescharacteristic
576C4C11×#57711yescharacteristic
577C4C11×#57711yescharacteristic
578C2—42no—
579C2—81no—
580C2C11×#326611yescharacteristic
581C2D4×C11×SD1611yescharacteristic
582C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#547C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. Q8×C11×SD16C2semidirect
2. Q8×C11×SD16C2semidirect
5. C11×#1716C2semidirect
6. C11×#1691C2semidirect
7. C11×#1680C2semidirect
8. C11×#1671C2semidirect
9. C11×#1670C2semidirect
10. C11×#1651C2semidirect
11. C11×#1651C2semidirect
12. C11×#1645C2semidirect
14. C11×#1583C2semidirect
15. C11×SD16⋊C8C2semidirect
145. #19805C11direct (N × H)
175. C11×SD16SD16semidirect
215. Q8×SD16C2×C11semidirect
216. Q8×SD16C2×C11semidirect
219. #1716C2×C11semidirect
220. #1691C2×C11semidirect
221. #1680C2×C11semidirect
222. #1671C2×C11semidirect
223. #1670C2×C11semidirect
224. #1651C2×C11semidirect
225. #1651C2×C11semidirect
226. #1645C2×C11semidirect
228. #1583C2×C11semidirect
229. SD16⋊C8C2×C11semidirect
245. Q8×C11#137semidirect
465. SD16C11×SD16semidirect
505. C11#19805direct (N × H)
521. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
Q8×C11×SD162
C11×#32982
C11×#32762
C11×#17162
C11×#16912
C11×#16802
C11×#16712
C11×#16702
C11×#16512
C11×#16452
C11×#16352
C11×#15832
C11×SD16⋊C82
#1980511