Finite Group Databasebeta

← C11×#19218 #14596411

Subgroups — C11×#19218 #14596411

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3233C211yesmaximal, characteristic, complemented
2C11×#3212C211yesmaximal, characteristic
3C11×#3167C211yesmaximal, characteristic, complemented
4C11×#2966C211yesmaximal, characteristic, complemented
5C11×#1700C211yesmaximal, characteristic, complemented
6C11×#1699C211yesmaximal, characteristic, complemented
7C11×#1698C211yesmaximal, characteristic, complemented
8C11×#1697C211yesmaximal, characteristic, complemented
9C11×#1672C211yesmaximal, characteristic, complemented
10C11×#1671C211yesmaximal, characteristic, complemented
11C11×#1666C211yesmaximal, characteristic, complemented
12C11×#1665C211yesmaximal, characteristic, complemented
13C11×#1564C211yesmaximal, characteristic, complemented
14C11×#1554C211yesmaximal, characteristic, complemented
15C11×#1553C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C11×#529C2211yescharacteristic
19C11×#499—21no—
20C11×#498C2211yescharacteristic
21C11×#495—21no—
22C11×#492C2211yescharacteristic
23C11×#488—21no—
24C11×#488—21no—
25C11×#487C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#485—21no—
28C11×#482—21no—
29C11×#477C2211yescharacteristic
30C11×#476C2211yescharacteristic
31C11×#475C2211yescharacteristic
32C11×#474C2211yescharacteristic
33C11×#465—21no—
34C11×#465—21no—
35C11×#462C2211yescharacteristic
36C11×#461C2211yescharacteristic
37C11×#460C2211yescharacteristic
38C11×#459C2211yescharacteristic
39C11×#452—21no—
40C11×#449—21no—
41C11×#446C2211yescharacteristic
42C8×Q8×C11C2211yescharacteristic
43C4×C11×SD16—21no—
44C4×C11×SD16—21no—
45C11×#436C2211yescharacteristic
46C11×#435—21no—
47C8×D4×C11—21no—
48C8×D4×C11C2211yescharacteristic
49C11×#433—21no—
50C11×#432C2211yescharacteristic
51C11×#431C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C11×#405—21no—
54C2×C4×C8×C11C2211yescharacteristic
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×#332C2211yescharacteristic
64C11×#332C2211yescharacteristic
65C11×#331C2211yescharacteristic
66C11×#331C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×D8—21no—
74C2×C11×M16—21no—
75C22×C8×C11—21no—
76C22×C8×C11D411yescharacteristic
77C22×C8×C11D411yescharacteristic
78C11×C4⋊Q8C2311yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×#127C2311yescharacteristic
82C11×#126—21no—
83C11×#125—21no—
84C11×#125D411yescharacteristic
85C11×#124—21no—
86C11×#124D411yescharacteristic
87C11×#123—21no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8D411yescharacteristic
91C11×#121—21no—
92C11×#121—21no—
93C11×#121D411yescharacteristic
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11C2311yescharacteristic
101C11×#117—21no—
102C11×#117—21no—
103C2×C42×C11C2311yescharacteristic
104C11×#107—21no—
105C11×#107—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8C2311yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×#103—21no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#102—21no—
125C11×#102—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×C22⋊C8—21no—
131C11×C22⋊C8—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×#97—21no—
136C11×#97—21no—
137C4×C8×C11—21no—
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11D411yescharacteristic
141C4×C8×C11D411yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19218C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—41no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C11×Q16—81no—
163C11×SD16—42no—
164C11×SD16—42no—
165C11×SD16—81no—
166C11×SD16—81no—
167C11×D8—81no—
168C11×M16—42no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—41no—
177C2×C8×C11—42no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C42×C11—21no—
205C42×C11—41no—
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11#4111yescharacteristic
209C42×C11C2411yescharacteristic
210#3233C2×C1111yescharacteristic, complemented
211#3212C2×C1111yescharacteristic
212#3167C2×C1111yescharacteristic, complemented
213#2966C2×C1111yescharacteristic, complemented
214#1700C2×C1111yescharacteristic, complemented
215#1699C2×C1111yescharacteristic, complemented
216#1698C2×C1111yescharacteristic, complemented
217#1697C2×C1111yescharacteristic, complemented
218#1672C2×C1111yescharacteristic, complemented
219#1671C2×C1111yescharacteristic, complemented
220#1666C2×C1111yescharacteristic, complemented
221#1665C2×C1111yescharacteristic, complemented
222#1564C2×C1111yescharacteristic, complemented
223#1554C2×C1111yescharacteristic, complemented
224#1553C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11—41no—
227C23×C11#12111yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—81no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—42no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—81no—
243D4×C11—82no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—82no—
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11#13512yes—
274#533C22×C1111yescharacteristic
275#532C22×C1111yescharacteristic
276#529C22×C1111yescharacteristic
277#499—21no—
278#498C22×C1111yescharacteristic
279#495—21no—
280#492C22×C1111yescharacteristic
281#488—21no—
282#488—21no—
283#487C22×C1111yescharacteristic
284#486C22×C1111yescharacteristic
285#485—21no—
286#482—21no—
287#477C22×C1111yescharacteristic
288#476C22×C1111yescharacteristic
289#475C22×C1111yescharacteristic
290#474C22×C1111yescharacteristic
291#465—21no—
292#465—21no—
293#462C22×C1111yescharacteristic
294#461C22×C1111yescharacteristic
295#460C22×C1111yescharacteristic
296#459C22×C1111yescharacteristic
297#452—21no—
298#449—21no—
299#446C22×C1111yescharacteristic
300C8×Q8C22×C1111yescharacteristic
301C4×SD16—21no—
302C4×SD16—21no—
303#436C22×C1111yescharacteristic
304#435—21no—
305C8×D4—21no—
306C8×D4C22×C1111yescharacteristic
307#433—21no—
308#432C22×C1111yescharacteristic
309#431C22×C1111yescharacteristic
310#431C22×C1111yescharacteristic
311#405—21no—
312C2×C4×C8C22×C1111yescharacteristic
313#335C22×C1111yescharacteristic
314#335C22×C1111yescharacteristic
315#334C22×C1111yescharacteristic
316#334C22×C1111yescharacteristic
317#333C22×C1111yescharacteristic
318#333C22×C1111yescharacteristic
319#332C22×C1111yescharacteristic
320#332C22×C1111yescharacteristic
321#332C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#331C22×C1111yescharacteristic
324#331C22×C1111yescharacteristic
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11C2×#12111yescharacteristic
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×#13511yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57711yescharacteristic
348C4×C11#57711yescharacteristic
349C2×#41—21no—
350C2×Q16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×D8—21no—
356C2×M16—21no—
357C22×C8—21no—
358C22×C8D4×C1111yescharacteristic
359C22×C8D4×C1111yescharacteristic
360C4⋊Q8C23×C1111yescharacteristic
361C4⋊Q8C23×C1111yescharacteristic
362C4⋊Q8C23×C1111yescharacteristic
363#127C23×C1111yescharacteristic
364#126—21no—
365#125—21no—
366#125D4×C1111yescharacteristic
367#124—21no—
368#124D4×C1111yescharacteristic
369#123—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8D4×C1111yescharacteristic
373#121—21no—
374#121—21no—
375#121D4×C1111yescharacteristic
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C23×C1111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C23×C1111yescharacteristic
383#117—21no—
384#117—21no—
385C2×C42C23×C1111yescharacteristic
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C1111yescharacteristic
395C4⋊C8C23×C1111yescharacteristic
396C4⋊C8C23×C1111yescharacteristic
397C4⋊C8C23×C1111yescharacteristic
398C4⋊C8C23×C1111yescharacteristic
399C4⋊C8C23×C1111yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417#97—21no—
418#97—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8D4×C1111yescharacteristic
423C4×C8D4×C1111yescharacteristic
424C4×C8C23×C1111yescharacteristic
425C4×C8C23×C1111yescharacteristic
426C2×C11—41no—
427C2×C11—81no—
428C2×C11—161no—
429C2×C11#303511yescharacteristic
430C2×C11#305711yescharacteristic
431C2×C11#306711yescharacteristic
432#41—81no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×D4×C1111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4C2×D4×C1111yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C11×#4111yescharacteristic
449Q16—81no—
450SD16—42no—
451SD16—42no—
452SD16—81no—
453SD16—81no—
454D8—81no—
455M16—42no—
456C2×C8—22no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—41no—
464C2×C8—42no—
465C2×C8C2×D4×C1111yescharacteristic
466C2×C8C2×D4×C1111yescharacteristic
467C2×C8C2×D4×C1111yescharacteristic
468C2×C8C2×D4×C1111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C1111yescharacteristic
482C4⋊C4C2×D4×C1111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—41no—
493C42C2×D4×C1111yescharacteristic
494C42C2×D4×C1111yescharacteristic
495C42C11×#4111yescharacteristic
496C42C24×C1111yescharacteristic
497C11#1921811yescharacteristic, direct product factor, Sylow
498C23—21no—
499C23—41no—
500C23C11×#12111yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4C11×#12111yescharacteristic
532C2×C4C11×#12111yescharacteristic
533C2×C4C11×#12111yescharacteristic
534C2×C4C22×D4×C1111yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C2×C11×#4111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8C11×#13512yes—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22C2×C11×#12111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×C11×#13511yescharacteristic
568C4C11×#57511yescharacteristic
569C4C11×#57711yescharacteristic
570C4C11×#57711yescharacteristic
571C2—41no—
572C2—81no—
573C2—161no—
574C2C11×#303511yescharacteristic
575C2C11×#305711yescharacteristic
576C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3212C2
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×#3233C2semidirect
3. C11×#3167C2semidirect
4. C11×#2966C2semidirect
5. C11×#1700C2semidirect
6. C11×#1699C2semidirect
7. C11×#1698C2semidirect
8. C11×#1697C2semidirect
9. C11×#1672C2semidirect
10. C11×#1671C2semidirect
11. C11×#1666C2semidirect
12. C11×#1665C2semidirect
13. C11×#1564C2semidirect
14. C11×#1554C2semidirect
15. C11×#1553C2semidirect
144. #19218C11direct (N × H)
210. #3233C2×C11semidirect
212. #3167C2×C11semidirect
213. #2966C2×C11semidirect
214. #1700C2×C11semidirect
215. #1699C2×C11semidirect
216. #1698C2×C11semidirect
217. #1697C2×C11semidirect
218. #1672C2×C11semidirect
219. #1671C2×C11semidirect
220. #1666C2×C11semidirect
221. #1665C2×C11semidirect
222. #1564C2×C11semidirect
223. #1554C2×C11semidirect
224. #1553C2×C11semidirect
497. C11#19218direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32332
C11×#32122
C11×#31672
C11×#29662
C11×#17002
C11×#16992
C11×#16982
C11×#16972
C11×#16722
C11×#16712
C11×#16662
C11×#16652
C11×#15642
C11×#15542
C11×#15532
#1921811