Finite Group Databasebeta

← C11×#11135 #14588328

Subgroups — C11×#11135 #14588328

Order 2816.

1190 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
2C22×C11×#100C211yesmaximal, characteristic
3C11×#2309C211yesmaximal, characteristic
4C2×C11×#390C211yesmaximal, characteristic
5C11×#1736C211yesmaximal, characteristic, complemented
6C2×C11×#339C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4—22no—
15C22×C42×C11C2211yescharacteristic
16C11×#428—22no—
17C11×#428—22no—
18C2×C11×#107—21no—
19C2×C11×#106—21no—
20C2×C11×#100—22no—
21C2×C11×#100—22no—
22C2×C11×#100C414yescomplemented
23C11×#390—22no—
24C11×#390—22no—
25C11×#390—21no—
26C11×#390—21no—
27C11×#390—22no—
28C11×#379—22no—
29C11×#340—22no—
30C11×#339—22no—
31C11×#339—22no—
32C25×C11D412yes—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2×C412yes—
46C22×D4×C11Q812yes—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
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×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16C2×C412yes—
59C2×C11×M16C2×C412yes—
60C2×C11×M16D412yes—
61C2×C11×M16D412yes—
62C22×C8×C11—21no—
63C22×C8×C11—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—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D412yes—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C22⋊C4—28no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—48no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11D412yes—
95C11×#107—24no—
96C11×#106—24no—
97C11×#100—28no—
98#11135C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—44no—
106C24×C11—44no—
107C24×C11C4⋊C414yes—
108C24×C11C2×D411yescharacteristic
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—44no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×Q811yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—41no—
169C11×M16—41no—
170C11×M16C22⋊C414yescomplemented
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C22⋊C4—416no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—84no—
193C11×C22⋊C4—84no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—41no—
197C42×C11—41no—
198C42×C11—41no—
199C42×C11—41no—
200C42×C11—41no—
201C42×C11—41no—
202C2×#428C2×C1111yescharacteristic, complemented
203C22×#100C2×C1111yescharacteristic
204#2309C2×C1111yescharacteristic
205C2×#390C2×C1111yescharacteristic
206#1736C2×C1111yescharacteristic, complemented
207C2×#339C2×C1111yescharacteristic, complemented
208C2×#339C2×C1111yescharacteristic, complemented
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—48no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11—48no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—84no—
225C23×C11—82no—
226C23×C11—82no—
227C23×C11—84no—
228C23×C11C2×C4⋊C411yescharacteristic
229C23×C11#12011yescharacteristic
230C23×C11#12011yescharacteristic
231C23×C11#12111yescharacteristic
232C23×C11#12111yescharacteristic
233C23×C11#12311yescharacteristic
234C23×C11#12311yescharacteristic
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—42no—
242D4×C11—42no—
243C2×C4×C11—24no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11—42no—
248C2×C4×C11—44no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—82no—
258C2×C4×C11—82no—
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11#11711yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12111yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11C22⋊Q811yescharacteristic
273C2×C4×C11C22⋊Q811yescharacteristic
274C2×C4×C11C22⋊Q811yescharacteristic
275C2×C4×C11C22⋊Q811yescharacteristic
276C2×C4×C11C22⋊Q811yescharacteristic
277C2×C4×C11C22⋊Q811yescharacteristic
278C2×C4×C11#12311yescharacteristic
279C2×C4×C11#12311yescharacteristic
280C2×C4×C11#12311yescharacteristic
281C2×C4×C11#12411yescharacteristic
282C2×C4×C11#12411yescharacteristic
283C2×C4×C11#12411yescharacteristic
284C2×C4×C11#12611yescharacteristic
285C2×C4×C11#12611yescharacteristic
286C2×C4×C11#12711yescharacteristic
287C8×C11—24no—
288C8×C11—42no—
289C23×D4C22×C1111yescharacteristic
290C22×M16C22×C1111yescharacteristic
291C22×M16C22×C1111yescharacteristic
292C2×#117C22×C1111yescharacteristic
293C2×#117C22×C1111yescharacteristic
294C22×C4⋊C4C22×C1111yescharacteristic
295C22×C22⋊C4—22no—
296C22×C42C22×C1111yescharacteristic
297#428—22no—
298#428—22no—
299C2×#107—21no—
300C2×#106—21no—
301C2×#100—22no—
302C2×#100—22no—
303C2×#100C4×C1114yescomplemented
304#390—22no—
305#390—21no—
306#390—21no—
307#390—22no—
308#390—22no—
309#379—22no—
310#340—22no—
311#339—22no—
312#339—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—48no—
322C22×C11—48no—
323C22×C11—44no—
324C22×C11—84no—
325C22×C11—84no—
326C22×C11—84no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—84no—
330C22×C11#38011yescharacteristic
331C22×C11#38511yescharacteristic
332C22×C11#38511yescharacteristic
333C22×C11#39211yescharacteristic
334C22×C11#39411yescharacteristic
335C22×C11#39411yescharacteristic
336C22×C11#39711yescharacteristic
337C22×C11#45312yes—
338C22×C11#45512yes—
339C4×C11—44no—
340C4×C11—81no—
341C4×C11—82no—
342C4×C11—81no—
343C4×C11—82no—
344C4×C11#38611yescharacteristic
345C4×C11#38811yescharacteristic
346C4×C11#38811yescharacteristic
347C4×C11#39011yescharacteristic
348C4×C11#39311yescharacteristic
349C4×C11#39611yescharacteristic
350C4×C11#39611yescharacteristic
351C4×C11#39911yescharacteristic
352C25D4×C1112yes—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4C2×C4×C1112yes—
366C22×D4Q8×C1112yes—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4C23×C1111yescharacteristic
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16C2×C4×C1112yes—
379C2×M16C2×C4×C1112yes—
380C2×M16D4×C1112yes—
381C2×M16D4×C1112yes—
382C22×C8—21no—
383C22×C8—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4D4×C1112yes—
398C2×C4⋊C4D4×C1112yes—
399C2×C4⋊C4D4×C1111yescharacteristic
400C2×C4⋊C4D4×C1111yescharacteristic
401C2×C22⋊C4—28no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—48no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42D4×C1112yes—
415#107—24no—
416#106—24no—
417#100—28no—
418C2×C11—21no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—84no—
423C2×C11#143911yescharacteristic
424C2×C11#185612yes—
425C2×C11#200211yescharacteristic
426C2×C11#200411yescharacteristic
427C2×C11#203712yes—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—44no—
435C24—44no—
436C24C11×C4⋊C414yes—
437C24C2×D4×C1111yescharacteristic
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—42no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—44no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4C22×C4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1111yescharacteristic
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×Q8×C1111yescharacteristic
486C22×C4C11×#4111yescharacteristic
487C22×C4C11×#4111yescharacteristic
488C22×C4C11×#4111yescharacteristic
489C22×C4C11×#4111yescharacteristic
490C22×C4C11×#4111yescharacteristic
491C22×C4C11×#4111yescharacteristic
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—22no—
497M16—41no—
498M16—41no—
499M16C11×C22⋊C414yescomplemented
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—41no—
505C2×C8—41no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C22⋊C4—416no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—84no—
522C22⋊C4—84no—
523C42—22no—
524C42—22no—
525C42—41no—
526C42—41no—
527C42—41no—
528C42—41no—
529C42—41no—
530C42—41no—
531C11#1113511yescharacteristic, direct product factor, Sylow
532C23—22no—
533C23—22no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—48no—
538C23—44no—
539C23—44no—
540C23—48no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—44no—
546C23—44no—
547C23—84no—
548C23—82no—
549C23—82no—
550C23—84no—
551C23C2×C11×C4⋊C411yescharacteristic
552C23C11×#12011yescharacteristic
553C23C11×#12011yescharacteristic
554C23C11×#12111yescharacteristic
555C23C11×#12111yescharacteristic
556C23C11×#12311yescharacteristic
557C23C11×#12311yescharacteristic
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—42no—
566C2×C4—24no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4C2×C11×C22⋊C411yescharacteristic
583C2×C4C11×#11711yescharacteristic
584C2×C4C4×D4×C1111yescharacteristic
585C2×C4C4×D4×C1111yescharacteristic
586C2×C4C4×D4×C1111yescharacteristic
587C2×C4C4×D4×C1111yescharacteristic
588C2×C4C11×#12011yescharacteristic
589C2×C4C11×#12111yescharacteristic
590C2×C4C11×#12111yescharacteristic
591C2×C4C11×#12111yescharacteristic
592C2×C4C11×#12111yescharacteristic
593C2×C4C11×#12111yescharacteristic
594C2×C4C11×#12111yescharacteristic
595C2×C4C11×C22⋊Q811yescharacteristic
596C2×C4C11×C22⋊Q811yescharacteristic
597C2×C4C11×C22⋊Q811yescharacteristic
598C2×C4C11×C22⋊Q811yescharacteristic
599C2×C4C11×C22⋊Q811yescharacteristic
600C2×C4C11×C22⋊Q811yescharacteristic
601C2×C4C11×#12311yescharacteristic
602C2×C4C11×#12311yescharacteristic
603C2×C4C11×#12311yescharacteristic
604C2×C4C11×#12411yescharacteristic
605C2×C4C11×#12411yescharacteristic
606C2×C4C11×#12411yescharacteristic
607C2×C4C11×#12611yescharacteristic
608C2×C4C11×#12611yescharacteristic
609C2×C4C11×#12711yescharacteristic
610C8—24no—
611C8—42no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—48no—
621C22—44no—
622C22—48no—
623C22—84no—
624C22—84no—
625C22—84no—
626C22—82no—
627C22—82no—
628C22—84no—
629C22C11×#38011yescharacteristic
630C22C11×#38511yescharacteristic
631C22C11×#38511yescharacteristic
632C22C11×#39211yescharacteristic
633C22C11×#39411yescharacteristic
634C22C11×#39411yescharacteristic
635C22C11×#39711yescharacteristic
636C22C11×#45312yes—
637C22C11×#45512yes—
638C4—44no—
639C4—82no—
640C4—81no—
641C4—81no—
642C4—82no—
643C4C11×#38611yescharacteristic
644C4C11×#38811yescharacteristic
645C4C11×#38811yescharacteristic
646C4C11×#39011yescharacteristic
647C4C11×#39311yescharacteristic
648C4C11×#39611yescharacteristic
649C4C11×#39611yescharacteristic
650C4C11×#39911yescharacteristic
651C2—21no—
652C2—21no—
653C2—21no—
654C2—21no—
655C2—84no—
656C2C11×#143911yescharacteristic
657C2C11×#185612yes—
658C2C11×#200211yescharacteristic
659C2C11×#200411yescharacteristic
660C2C11×#203712yes—
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C11×#1736C2semidirect
6. C2×C11×#339C2semidirect
7. C2×C11×#339C2semidirect
22. C2×C11×#100C4semidirect
98. #11135C11direct (N × H)
170. C11×M16C22⋊C4semidirect
202. C2×#428C2×C11semidirect
206. #1736C2×C11semidirect
207. C2×#339C2×C11semidirect
208. C2×#339C2×C11semidirect
303. C2×#100C4×C11semidirect
499. M16C11×C22⋊C4semidirect
531. C11#11135direct (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
C22×C11×#1002
C11×#23092
C2×C11×#3902
C11×#17362
C2×C11×#3392
#1113511