Finite Group Databasebeta

← C11×#11117 #14588310

Subgroups — C11×#11117 #14588310

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C11×#2896C211yesmaximal, characteristic
4C11×#2311C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C11×#1740C211yesmaximal, characteristic, complemented
7C11×#1736C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C11×#428—22no—
16C11×#428—22no—
17C2×C11×#107—21no—
18C2×C11×#106—21no—
19C11×#421—22no—
20C11×#421C414yescomplemented
21C2×C11×#104—22no—
22C11×#419—21no—
23C11×#418—21no—
24C11×#417—21no—
25C11×#417—21no—
26C11×#416—22no—
27C11×#391—21no—
28C11×#390—21no—
29C11×#386—22no—
30C11×#380—22no—
31C11×#344—22no—
32C11×#342—22no—
33C11×#340—22no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41C2×C412yes—
45C2×C11×#41Q812yes—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16C2×C412yes—
62C2×C11×M16D412yes—
63C2×C11×M16D412yes—
64C22×C8×C11—21no—
65C22×C8×C11D412yes—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—21no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117C2×C412yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4D412yes—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C11×#107—24no—
96C11×#106—24no—
97C11×#104—28no—
98C11×#103—22no—
99C11×#103—22no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#95—24no—
103#11117C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—21no—
105C24×C11C2×D411yescharacteristic
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—22no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41—41no—
121C11×#41—41no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11C4⋊C412yes—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11C4⋊C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11—82no—
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×Q811yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C11×M16—22no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—41no—
173C11×M16—41no—
174C11×M16—41no—
175C11×M16—41no—
176C11×M16C22⋊C414yescomplemented
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—84no—
202C42×C11—22no—
203C42×C11—41no—
204C42×C11—41no—
205C42×C11—41no—
206C42×C11—41no—
207C42×C11—41no—
208C2×#428C2×C1111yescharacteristic, complemented
209C2×#421C2×C1111yescharacteristic
210#2896C2×C1111yescharacteristic
211#2311C2×C1111yescharacteristic
212C2×#344C2×C1111yescharacteristic, complemented
213#1740C2×C1111yescharacteristic, complemented
214#1736C2×C1111yescharacteristic, complemented
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11C4×D411yescharacteristic
223C23×C11#12011yescharacteristic
224C23×C11#12111yescharacteristic
225C23×C11#12111yescharacteristic
226C23×C11C22⋊Q811yescharacteristic
227C23×C11#12311yescharacteristic
228C23×C11#12711yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—41no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—41no—
240D4×C11—41no—
241C2×C4×C11—22no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—81no—
257C2×C4×C11—81no—
258C2×C4×C11—82no—
259C2×C4×C11—82no—
260C2×C4×C11—81no—
261C2×C4×C11—81no—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C4⋊C411yescharacteristic
264C2×C4×C11#11711yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C4×D411yescharacteristic
267C2×C4×C11C4×D411yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11#12111yescharacteristic
273C2×C4×C11#12111yescharacteristic
274C2×C4×C11#12111yescharacteristic
275C2×C4×C11#12111yescharacteristic
276C2×C4×C11C22⋊Q811yescharacteristic
277C2×C4×C11C22⋊Q811yescharacteristic
278C2×C4×C11C22⋊Q811yescharacteristic
279C2×C4×C11C22⋊Q811yescharacteristic
280C2×C4×C11C22⋊Q811yescharacteristic
281C2×C4×C11#12311yescharacteristic
282C2×C4×C11#12311yescharacteristic
283C2×C4×C11#12311yescharacteristic
284C2×C4×C11#12311yescharacteristic
285C2×C4×C11#12411yescharacteristic
286C2×C4×C11#12411yescharacteristic
287C2×C4×C11#12411yescharacteristic
288C2×C4×C11#12611yescharacteristic
289C2×C4×C11#12611yescharacteristic
290C8×C11—24no—
291C8×C11—42no—
292C22×#41C22×C1111yescharacteristic
293C22×M16C22×C1111yescharacteristic
294C22×M16C22×C1111yescharacteristic
295C2×#117C22×C1111yescharacteristic
296C2×#117C22×C1111yescharacteristic
297C2×#117C22×C1111yescharacteristic
298C22×C4⋊C4C22×C1111yescharacteristic
299#428—22no—
300#428—22no—
301C2×#107—21no—
302C2×#106—21no—
303#421—22no—
304#421C4×C1114yescomplemented
305C2×#104—22no—
306#419—21no—
307#418—21no—
308#417—21no—
309#417—21no—
310#416—22no—
311#391—21no—
312#390—21no—
313#386—22no—
314#380—22no—
315#344—22no—
316#342—22no—
317#340—22no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—44no—
329C22×C11—42no—
330C22×C11—82no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11#38511yescharacteristic
334C22×C11#38811yescharacteristic
335C22×C11#39011yescharacteristic
336C22×C11#39211yescharacteristic
337C22×C11#39411yescharacteristic
338C22×C11#39611yescharacteristic
339C22×C11#39911yescharacteristic
340C4×C11—42no—
341C4×C11—82no—
342C4×C11—82no—
343C4×C11—82no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11#38011yescharacteristic
347C4×C11#38511yescharacteristic
348C4×C11#38611yescharacteristic
349C4×C11#38811yescharacteristic
350C4×C11#39311yescharacteristic
351C4×C11#39411yescharacteristic
352C4×C11#39611yescharacteristic
353C4×C11#39711yescharacteristic
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41C2×C4×C1112yes—
365C2×#41Q8×C1112yes—
366C22×Q8D4×C1111yescharacteristic
367C22×D4—21no—
368C22×D4D4×C1111yescharacteristic
369C23×C4—21no—
370C23×C4—21no—
371C23×C4C23×C1111yescharacteristic
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16C2×C4×C1112yes—
382C2×M16D4×C1112yes—
383C2×M16D4×C1112yes—
384C22×C8—21no—
385C22×C8D4×C1112yes—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117C2×C4×C1112yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4D4×C1112yes—
406C2×C4⋊C4D4×C1111yescharacteristic
407C2×C4⋊C4D4×C1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4D4×C1112yes—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415#107—24no—
416#106—24no—
417#104—28no—
418#103—22no—
419#103—22no—
420#102—22no—
421#102—22no—
422#95—24no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11—21no—
426C2×C11—21no—
427C2×C11—21no—
428C2×C11—21no—
429C2×C11—82no—
430C2×C11#143911yescharacteristic
431C2×C11#200811yescharacteristic
432C2×C11#200911yescharacteristic
433C24—21no—
434C24C2×D4×C1111yescharacteristic
435#41—22no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—22no—
440#41—22no—
441#41—22no—
442#41—22no—
443#41—41no—
444#41—41no—
445#41—41no—
446#41—41no—
447#41—41no—
448#41—41no—
449#41—41no—
450#41—41no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C11×C4⋊C412yes—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C11×C4⋊C412yes—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—82no—
484C22×C4C22×C4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×Q8×C1111yescharacteristic
492C22×C4C11×#4111yescharacteristic
493C22×C4C11×#4111yescharacteristic
494C22×C4C11×#4111yescharacteristic
495C22×C4C11×#4111yescharacteristic
496C22×C4C11×#4111yescharacteristic
497C22×C4C11×#4111yescharacteristic
498M16—22no—
499M16—22no—
500M16—22no—
501M16—41no—
502M16—41no—
503M16—41no—
504M16—41no—
505M16C11×C22⋊C414yescomplemented
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—84no—
531C42—22no—
532C42—41no—
533C42—41no—
534C42—41no—
535C42—41no—
536C42—41no—
537C11#1111711yescharacteristic, direct product factor, Sylow
538C23—22no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—41no—
545C23C4×D4×C1111yescharacteristic
546C23C11×#12011yescharacteristic
547C23C11×#12111yescharacteristic
548C23C11×#12111yescharacteristic
549C23C11×C22⋊Q811yescharacteristic
550C23C11×#12311yescharacteristic
551C23C11×#12711yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556D4—22no—
557D4—22no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—41no—
563D4—41no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—81no—
584C2×C4—81no—
585C2×C4C2×C11×C22⋊C411yescharacteristic
586C2×C4C2×C11×C4⋊C411yescharacteristic
587C2×C4C11×#11711yescharacteristic
588C2×C4C4×D4×C1111yescharacteristic
589C2×C4C4×D4×C1111yescharacteristic
590C2×C4C4×D4×C1111yescharacteristic
591C2×C4C11×#12011yescharacteristic
592C2×C4C11×#12011yescharacteristic
593C2×C4C11×#12111yescharacteristic
594C2×C4C11×#12111yescharacteristic
595C2×C4C11×#12111yescharacteristic
596C2×C4C11×#12111yescharacteristic
597C2×C4C11×#12111yescharacteristic
598C2×C4C11×#12111yescharacteristic
599C2×C4C11×C22⋊Q811yescharacteristic
600C2×C4C11×C22⋊Q811yescharacteristic
601C2×C4C11×C22⋊Q811yescharacteristic
602C2×C4C11×C22⋊Q811yescharacteristic
603C2×C4C11×C22⋊Q811yescharacteristic
604C2×C4C11×#12311yescharacteristic
605C2×C4C11×#12311yescharacteristic
606C2×C4C11×#12311yescharacteristic
607C2×C4C11×#12311yescharacteristic
608C2×C4C11×#12411yescharacteristic
609C2×C4C11×#12411yescharacteristic
610C2×C4C11×#12411yescharacteristic
611C2×C4C11×#12611yescharacteristic
612C2×C4C11×#12611yescharacteristic
613C8—24no—
614C8—42no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—44no—
626C22—42no—
627C22—82no—
628C22—81no—
629C22—81no—
630C22C11×#38511yescharacteristic
631C22C11×#38811yescharacteristic
632C22C11×#39011yescharacteristic
633C22C11×#39211yescharacteristic
634C22C11×#39411yescharacteristic
635C22C11×#39611yescharacteristic
636C22C11×#39911yescharacteristic
637C4—42no—
638C4—82no—
639C4—82no—
640C4—82no—
641C4—81no—
642C4—81no—
643C4C11×#38011yescharacteristic
644C4C11×#38511yescharacteristic
645C4C11×#38611yescharacteristic
646C4C11×#38811yescharacteristic
647C4C11×#39311yescharacteristic
648C4C11×#39411yescharacteristic
649C4C11×#39611yescharacteristic
650C4C11×#39711yescharacteristic
651C2—21no—
652C2—21no—
653C2—21no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—82no—
658C2C11×#143911yescharacteristic
659C2C11×#200811yescharacteristic
660C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C2×C11×#344C2semidirect
6. C11×#1740C2semidirect
7. C11×#1736C2semidirect
20. C11×#421C4semidirect
103. #11117C11direct (N × H)
176. C11×M16C22⋊C4semidirect
208. C2×#428C2×C11semidirect
212. C2×#344C2×C11semidirect
213. #1740C2×C11semidirect
214. #1736C2×C11semidirect
304. #421C4×C11semidirect
505. M16C11×C22⋊C4semidirect
537. C11#11117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4212
C11×#28962
C11×#23112
C2×C11×#3442
C11×#17402
C11×#17362
#1111711