Finite Group Databasebeta

← C11×#11138 #14588331

Subgroups — C11×#11138 #14588331

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2911C211yesmaximal, characteristic, complemented
2C2×C11×#413C211yesmaximal, characteristic
3C2×C11×#410C211yesmaximal, characteristic
4C2×C11×#410C211yesmaximal, characteristic
5C11×#1733C211yesmaximal, characteristic, complemented
6C11×#1733C211yesmaximal, characteristic, complemented
7C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#428—22no—
16C11×#428—22no—
17C11×#427—22no—
18C11×#413—22no—
19C11×#413—22no—
20C2×C11×#101C412yescomplemented
21C2×C11×#100C412yescomplemented
22C11×#410—22no—
23C11×#410—22no—
24C11×#410—22no—
25C11×#410—22no—
26C2×C11×#99—22no—
27C2×C11×#99—22no—
28C11×#339—22no—
29C11×#339—22no—
30C11×H(3,ℤ/4)—22no—
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
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—
43C22×Q8×C11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C22×D4×C11D412yes—
46C23×C4×C11Q812yes—
47C23×C4×C11C2311yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16C2×C412yes—
57C2×C11×M16C2×C412yes—
58C2×C11×M16D412yes—
59C2×C11×M16D412yes—
60C22×C8×C11—21no—
61C22×C8×C11—21no—
62C11×#117—21no—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117—21no—
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×#117D412yes—
75C11×#117D412yes—
76C11×#117D412yes—
77C11×#117D412yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C11×#107—24no—
91C11×#106—24no—
92C11×#101—24no—
93C11×#100—24no—
94C11×#99—28no—
95C11×#99—28no—
96#11138C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11C4⋊C412yes—
98C24×C11C2×D411yescharacteristic
99C11×#41—41no—
100C11×#41—41no—
101C11×#41—41no—
102C11×#41—41no—
103C11×#41—41no—
104C11×#41—41no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11C4⋊C412yes—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×Q811yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16C22⋊C414yes—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—41no—
193C42×C11—41no—
194C42×C11—41no—
195C42×C11—41no—
196#2911C2×C1111yescharacteristic, complemented
197C2×#413C2×C1111yescharacteristic
198C2×#410C2×C1111yescharacteristic
199C2×#410C2×C1111yescharacteristic
200#1733C2×C1111yescharacteristic, complemented
201#1733C2×C1111yescharacteristic, complemented
202C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—81no—
207C23×C11—82no—
208C23×C11C2×C4⋊C411yescharacteristic
209C23×C11#12011yescharacteristic
210C23×C11#12011yescharacteristic
211C23×C11#12111yescharacteristic
212C23×C11#12111yescharacteristic
213C23×C11#12311yescharacteristic
214C23×C11#12311yescharacteristic
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—41no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—82no—
239C2×C4×C11—82no—
240C2×C4×C11—82no—
241C2×C4×C11—82no—
242C2×C4×C11C2×C22⋊C411yescharacteristic
243C2×C4×C11#11711yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11C22⋊Q811yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12411yescharacteristic
267C2×C4×C11#12611yescharacteristic
268C2×C4×C11#12611yescharacteristic
269C2×C4×C11#12711yescharacteristic
270C8×C11—24no—
271C8×C11—42no—
272C22×#41C22×C1111yescharacteristic
273C22×M16C22×C1111yescharacteristic
274C22×M16C22×C1111yescharacteristic
275C2×#117C22×C1111yescharacteristic
276C2×#117C22×C1111yescharacteristic
277C2×#117C22×C1111yescharacteristic
278C2×#117C22×C1111yescharacteristic
279#428—22no—
280#428—22no—
281#427—22no—
282#413—22no—
283#413—22no—
284C2×#101C4×C1112yescomplemented
285C2×#100C4×C1112yescomplemented
286#410—22no—
287#410—22no—
288#410—22no—
289#410—22no—
290C2×#99—22no—
291C2×#99—22no—
292#339—22no—
293#339—22no—
294H(3,ℤ/4)—22no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11#38011yescharacteristic
307C22×C11#38511yescharacteristic
308C22×C11#38511yescharacteristic
309C22×C11#39211yescharacteristic
310C22×C11#39411yescharacteristic
311C22×C11#39411yescharacteristic
312C22×C11#39711yescharacteristic
313C4×C11—42no—
314C4×C11—82no—
315C4×C11—82no—
316C4×C11—82no—
317C4×C11—82no—
318C4×C11#38611yescharacteristic
319C4×C11#38811yescharacteristic
320C4×C11#38811yescharacteristic
321C4×C11#39011yescharacteristic
322C4×C11#39311yescharacteristic
323C4×C11#39611yescharacteristic
324C4×C11#39611yescharacteristic
325C4×C11#39911yescharacteristic
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C22×Q8C2×C4×C1111yescharacteristic
339C22×D4C2×C4×C1111yescharacteristic
340C22×D4D4×C1112yes—
341C23×C4Q8×C1112yes—
342C23×C4C23×C1111yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16C2×C4×C1112yes—
352C2×M16C2×C4×C1112yes—
353C2×M16D4×C1112yes—
354C2×M16D4×C1112yes—
355C22×C8—21no—
356C22×C8—21no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117D4×C1112yes—
370#117D4×C1112yes—
371#117D4×C1112yes—
372#117D4×C1112yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385#107—24no—
386#106—24no—
387#101—24no—
388#100—24no—
389#99—28no—
390#99—28no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—82no—
399C2×C11#143911yescharacteristic
400C24C11×C4⋊C412yes—
401C24C2×D4×C1111yescharacteristic
402#41—41no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4C11×C4⋊C412yes—
447C22×C4C22×C4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×Q8×C1111yescharacteristic
455C22×C4C11×#4111yescharacteristic
456C22×C4C11×#4111yescharacteristic
457C22×C4C11×#4111yescharacteristic
458C22×C4C11×#4111yescharacteristic
459C22×C4C11×#4111yescharacteristic
460C22×C4C11×#4111yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—41no—
467M16—41no—
468M16C11×C22⋊C414yes—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—22no—
492C42—22no—
493C42—22no—
494C42—22no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42—41no—
499C11#1113811yescharacteristic, direct product factor, Sylow
500C23—22no—
501C23—22no—
502C23—22no—
503C23—81no—
504C23—82no—
505C23C2×C11×C4⋊C411yescharacteristic
506C23C11×#12011yescharacteristic
507C23C11×#12011yescharacteristic
508C23C11×#12111yescharacteristic
509C23C11×#12111yescharacteristic
510C23C11×#12311yescharacteristic
511C23C11×#12311yescharacteristic
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4C2×C11×C22⋊C411yescharacteristic
540C2×C4C11×#11711yescharacteristic
541C2×C4C4×D4×C1111yescharacteristic
542C2×C4C4×D4×C1111yescharacteristic
543C2×C4C4×D4×C1111yescharacteristic
544C2×C4C4×D4×C1111yescharacteristic
545C2×C4C11×#12011yescharacteristic
546C2×C4C11×#12111yescharacteristic
547C2×C4C11×#12111yescharacteristic
548C2×C4C11×#12111yescharacteristic
549C2×C4C11×#12111yescharacteristic
550C2×C4C11×#12111yescharacteristic
551C2×C4C11×#12111yescharacteristic
552C2×C4C11×C22⋊Q811yescharacteristic
553C2×C4C11×C22⋊Q811yescharacteristic
554C2×C4C11×C22⋊Q811yescharacteristic
555C2×C4C11×C22⋊Q811yescharacteristic
556C2×C4C11×C22⋊Q811yescharacteristic
557C2×C4C11×C22⋊Q811yescharacteristic
558C2×C4C11×#12311yescharacteristic
559C2×C4C11×#12311yescharacteristic
560C2×C4C11×#12311yescharacteristic
561C2×C4C11×#12411yescharacteristic
562C2×C4C11×#12411yescharacteristic
563C2×C4C11×#12411yescharacteristic
564C2×C4C11×#12611yescharacteristic
565C2×C4C11×#12611yescharacteristic
566C2×C4C11×#12711yescharacteristic
567C8—24no—
568C8—42no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22C11×#38011yescharacteristic
581C22C11×#38511yescharacteristic
582C22C11×#38511yescharacteristic
583C22C11×#39211yescharacteristic
584C22C11×#39411yescharacteristic
585C22C11×#39411yescharacteristic
586C22C11×#39711yescharacteristic
587C4—42no—
588C4—82no—
589C4—82no—
590C4—82no—
591C4—82no—
592C4C11×#38611yescharacteristic
593C4C11×#38811yescharacteristic
594C4C11×#38811yescharacteristic
595C4C11×#39011yescharacteristic
596C4C11×#39311yescharacteristic
597C4C11×#39611yescharacteristic
598C4C11×#39611yescharacteristic
599C4C11×#39911yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—82no—
608C2C11×#143911yescharacteristic
subgroupG/H
centerC4×C11#396
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC2×C11#1439
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2911C2semidirect
5. C11×#1733C2semidirect
6. C11×#1733C2semidirect
7. C2×C11×H(3,ℤ/4)C2semidirect
20. C2×C11×#101C4semidirect
21. C2×C11×#100C4semidirect
96. #11138C11direct (N × H)
196. #2911C2×C11semidirect
200. #1733C2×C11semidirect
201. #1733C2×C11semidirect
202. C2×H(3,ℤ/4)C2×C11semidirect
284. C2×#101C4×C11semidirect
285. C2×#100C4×C11semidirect
499. C11#11138direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29112
C2×C11×#4132
C2×C11×#4102
C11×#17332
C2×C11×H(3,ℤ/4)2
#1113811