Finite Group Databasebeta

← C11×#10943 #14588136

Subgroups — C11×#10943 #14588136

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#418C211yesmaximal, characteristic
2C22×C11×#102C211yesmaximal, characteristic
3C22×C11×#100C211yesmaximal, characteristic
4C2×C11×#405C211yesmaximal, characteristic, complemented
5C2×C11×#343C211yesmaximal, characteristic, complemented
6C2×C11×#341C211yesmaximal, characteristic, complemented
7C11×#1736C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C11×#418—22no—
16C11×#418C414yescomplemented
17C2×C11×#102—22no—
18C2×C11×#102—21no—
19C2×C11×#102—21no—
20C2×C11×#102—22no—
21C2×C11×#102C414yescomplemented
22C2×C11×#100—22no—
23C2×C11×#100—22no—
24C2×C11×#100C414yescomplemented
25C11×#405—22no—
26C11×#405—22no—
27C2×C11×#97—21no—
28C2×C4×C8×C11—21no—
29C11×#343—22no—
30C11×#341—22no—
31C11×#340—22no—
32C25×C11—21no—
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×C11C2×C412yes—
45C22×D4×C11C2×C412yes—
46C22×D4×C11C2×C412yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
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×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16C2×C412yes—
63C2×C11×M16C2×C412yes—
64C2×C11×M16C2×C412yes—
65C2×C11×M16D412yes—
66C2×C11×M16D412yes—
67C22×C8×C11—21no—
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11C2×C412yes—
75C22×C8×C11D412yes—
76C22×C8×C11D411yescharacteristic
77C22×C8×C11D411yescharacteristic
78C11×#117—21no—
79C11×#117—21no—
80C11×#117C2×C412yes—
81C11×#117D412yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2×C412yes—
88C2×C11×C4⋊C4D412yes—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C11×#102—24no—
92C11×#102—24no—
93C11×#102—28no—
94C11×#100—28no—
95C11×#97—24no—
96C4×C8×C11—24no—
97#10943C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—41no—
102C24×C11—41no—
103C24×C11—41no—
104C24×C11—41no—
105C24×C11—82no—
106C24×C11—82no—
107C24×C11#4111yescharacteristic
108C2×D4×C11—22no—
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—22no—
122C2×D4×C11—22no—
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×C11C4214yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—82no—
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—41no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16C22⋊C414yes—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11C22⋊C412yes—
185C2×C8×C11C22⋊C412yes—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4C22⋊C414yes—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C42×C11—22no—
195C42×C11—22no—
196C2×#418C2×C1111yescharacteristic
197C22×#102C2×C1111yescharacteristic
198C22×#100C2×C1111yescharacteristic
199C2×#405C2×C1111yescharacteristic, complemented
200C2×#343C2×C1111yescharacteristic, complemented
201C2×#341C2×C1111yescharacteristic, complemented
202#1736C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—84no—
213C23×C11—84no—
214C23×C11—82no—
215C23×C11—82no—
216C23×C11—84no—
217C23×C11—84no—
218C23×C11—82no—
219C23×C11—82no—
220C23×C11—82no—
221C23×C11—82no—
222C23×C11#11711yescharacteristic
223C23×C11C4×D411yescharacteristic
224C23×C11C4×D411yescharacteristic
225C23×C11#12111yescharacteristic
226C23×C11#12311yescharacteristic
227C23×C11#12411yescharacteristic
228C23×C11#12611yescharacteristic
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—42no—
237C2×C4×C11—24no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—82no—
242C2×C4×C11—82no—
243C2×C4×C11—82no—
244C2×C4×C11C2×C4211yescharacteristic
245C2×C4×C11C2×C22⋊C411yescharacteristic
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11#11711yescharacteristic
249C2×C4×C11#11711yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C4×D411yescharacteristic
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11#12111yescharacteristic
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11#12111yescharacteristic
266C2×C4×C11#12311yescharacteristic
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12411yescharacteristic
269C2×C4×C11#12411yescharacteristic
270C2×C4×C11#12611yescharacteristic
271C2×C4×C11#12711yescharacteristic
272C8×C11—22no—
273C8×C11—22no—
274C8×C11—24no—
275C8×C11—42no—
276C8×C11—42no—
277C23×D4C22×C1111yescharacteristic
278C22×M16C22×C1111yescharacteristic
279C22×M16C22×C1111yescharacteristic
280C22×M16C22×C1111yescharacteristic
281C23×C8C22×C1111yescharacteristic
282C2×#117C22×C1111yescharacteristic
283C22×C4⋊C4C22×C1111yescharacteristic
284#418—22no—
285#418C4×C1114yescomplemented
286C2×#102—22no—
287C2×#102—21no—
288C2×#102—21no—
289C2×#102—22no—
290C2×#102C4×C1114yescomplemented
291C2×#100—22no—
292C2×#100—22no—
293C2×#100C4×C1114yescomplemented
294#405—22no—
295#405—22no—
296C2×#97—21no—
297C2×C4×C8—21no—
298#343—22no—
299#341—22no—
300#340—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—44no—
310C22×C11—84no—
311C22×C11—84no—
312C22×C11—84no—
313C22×C11—84no—
314C22×C11—84no—
315C22×C11—84no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11C4×C22⋊C411yescharacteristic
319C22×C11#38611yescharacteristic
320C22×C11#38811yescharacteristic
321C22×C11#38811yescharacteristic
322C22×C11#38811yescharacteristic
323C22×C11#38811yescharacteristic
324C22×C11#39011yescharacteristic
325C22×C11#47112yes—
326C22×C11#47212yes—
327C4×C11—44no—
328C4×C11—82no—
329C4×C11C4×C22⋊C411yescharacteristic
330C4×C11C4×C22⋊C411yescharacteristic
331C4×C11#38611yescharacteristic
332C4×C11#38611yescharacteristic
333C4×C11#38811yescharacteristic
334C4×C11#38811yescharacteristic
335C4×C11#39011yescharacteristic
336C4×C11#39011yescharacteristic
337C25—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4C2×C4×C1112yes—
350C22×D4C2×C4×C1112yes—
351C22×D4C2×C4×C1112yes—
352C23×C4—21no—
353C23×C4C23×C1111yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16C2×C4×C1112yes—
368C2×M16C2×C4×C1112yes—
369C2×M16C2×C4×C1112yes—
370C2×M16D4×C1112yes—
371C2×M16D4×C1112yes—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8C2×C4×C1112yes—
380C22×C8D4×C1112yes—
381C22×C8D4×C1111yescharacteristic
382C22×C8D4×C1111yescharacteristic
383#117—21no—
384#117—21no—
385#117C2×C4×C1112yes—
386#117D4×C1112yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C2×C4×C1112yes—
393C2×C4⋊C4D4×C1112yes—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396#102—24no—
397#102—24no—
398#102—28no—
399#100—28no—
400#97—24no—
401C4×C8—24no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—84no—
407C2×C11#143711yescharacteristic
408C2×C11#190712yes—
409C2×C11#193112yes—
410C2×C11#197711yescharacteristic
411C2×C11#197811yescharacteristic
412C24—22no—
413C24—22no—
414C24—22no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—82no—
420C24—82no—
421C24C11×#4111yescharacteristic
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4C42×C1114yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—82no—
455C22×C4C22×C4×C1111yescharacteristic
456C22×C4C22×C4×C1111yescharacteristic
457C22×C4C22×C4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C11×#4111yescharacteristic
465C22×C4C11×#4111yescharacteristic
466C22×C4C11×#4111yescharacteristic
467C22×C4C11×#4111yescharacteristic
468C22×C4C11×#4111yescharacteristic
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16C11×C22⋊C414yes—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—21no—
485C2×C8—22no—
486C2×C8—21no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8C11×C22⋊C412yes—
499C2×C8C11×C22⋊C412yes—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4C11×C22⋊C414yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C42—22no—
509C42—22no—
510C11#1094311yescharacteristic, direct product factor, Sylow
511C23—22no—
512C23—22no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—84no—
521C23—84no—
522C23—82no—
523C23—82no—
524C23—84no—
525C23—84no—
526C23—82no—
527C23—82no—
528C23—82no—
529C23—82no—
530C23C11×#11711yescharacteristic
531C23C4×D4×C1111yescharacteristic
532C23C4×D4×C1111yescharacteristic
533C23C11×#12111yescharacteristic
534C23C11×#12311yescharacteristic
535C23C11×#12411yescharacteristic
536C23C11×#12611yescharacteristic
537D4—24no—
538D4—24no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4C2×C42×C1111yescharacteristic
553C2×C4C2×C11×C22⋊C411yescharacteristic
554C2×C4C2×C11×C22⋊C411yescharacteristic
555C2×C4C2×C11×C22⋊C411yescharacteristic
556C2×C4C11×#11711yescharacteristic
557C2×C4C11×#11711yescharacteristic
558C2×C4C4×D4×C1111yescharacteristic
559C2×C4C4×D4×C1111yescharacteristic
560C2×C4C4×D4×C1111yescharacteristic
561C2×C4C4×D4×C1111yescharacteristic
562C2×C4C4×D4×C1111yescharacteristic
563C2×C4C4×D4×C1111yescharacteristic
564C2×C4C4×D4×C1111yescharacteristic
565C2×C4C4×D4×C1111yescharacteristic
566C2×C4C4×D4×C1111yescharacteristic
567C2×C4C4×D4×C1111yescharacteristic
568C2×C4C11×#12011yescharacteristic
569C2×C4C11×#12111yescharacteristic
570C2×C4C11×#12111yescharacteristic
571C2×C4C11×#12111yescharacteristic
572C2×C4C11×#12111yescharacteristic
573C2×C4C11×#12111yescharacteristic
574C2×C4C11×#12311yescharacteristic
575C2×C4C11×#12311yescharacteristic
576C2×C4C11×#12411yescharacteristic
577C2×C4C11×#12411yescharacteristic
578C2×C4C11×#12611yescharacteristic
579C2×C4C11×#12711yescharacteristic
580C8—22no—
581C8—22no—
582C8—24no—
583C8—42no—
584C8—42no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—44no—
594C22—84no—
595C22—84no—
596C22—84no—
597C22—84no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22—82no—
602C22C4×C11×C22⋊C411yescharacteristic
603C22C11×#38611yescharacteristic
604C22C11×#38811yescharacteristic
605C22C11×#38811yescharacteristic
606C22C11×#38811yescharacteristic
607C22C11×#38811yescharacteristic
608C22C11×#39011yescharacteristic
609C22C11×#47112yes—
610C22C11×#47212yes—
611C4—44no—
612C4—82no—
613C4C4×C11×C22⋊C411yescharacteristic
614C4C4×C11×C22⋊C411yescharacteristic
615C4C11×#38611yescharacteristic
616C4C11×#38611yescharacteristic
617C4C11×#38811yescharacteristic
618C4C11×#38811yescharacteristic
619C4C11×#39011yescharacteristic
620C4C11×#39011yescharacteristic
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—84no—
626C2C11×#143711yescharacteristic
627C2C11×#190712yes—
628C2C11×#193112yes—
629C2C11×#197711yescharacteristic
630C2C11×#197811yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutatorC2×C4C2×C42×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#405C2semidirect
5. C2×C11×#343C2semidirect
6. C2×C11×#341C2semidirect
7. C11×#1736C2semidirect
16. C11×#418C4semidirect
21. C2×C11×#102C4semidirect
24. C2×C11×#100C4semidirect
97. #10943C11direct (N × H)
199. C2×#405C2×C11semidirect
200. C2×#343C2×C11semidirect
201. C2×#341C2×C11semidirect
202. #1736C2×C11semidirect
285. #418C4×C11semidirect
290. C2×#102C4×C11semidirect
293. C2×#100C4×C11semidirect
510. C11#10943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4182
C22×C11×#1022
C22×C11×#1002
C2×C11×#4052
C2×C11×#3432
C2×C11×#3412
C11×#17362
#1094311