Finite Group Databasebeta

← C11×#23791 #14600984

Subgroups — C11×#23791 #14600984

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2330C211yesmaximal, characteristic, complemented
2C11×#2319C211yesmaximal, characteristic
3C11×#2100C211yesmaximal, characteristic, complemented
4C11×#2093C211yesmaximal, characteristic
5C11×#2087C211yesmaximal, characteristic, complemented
6C11×#2086C211yesmaximal, characteristic, complemented
7C11×#2067C211yesmaximal, characteristic
8C11×#2065C211yesmaximal, characteristic
9C11×#2059C211yesmaximal, characteristic, complemented
10C11×#2025C211yesmaximal, characteristic
11C11×#1776C211yesmaximal, characteristic, complemented
12C4×C11×#107C211yesmaximal, characteristic, complemented
13C11×#1768C211yesmaximal, characteristic, complemented
14C11×#1762C211yesmaximal, characteristic
15C4×C11×#102C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#389—21no—
33C11×#389—21no—
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#388—21no—
40C11×#387—21no—
41C11×#387—21no—
42C11×#384C2211yescharacteristic
43C11×#381—21no—
44C11×#380—21no—
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C11×#376C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#125—22no—
66C11×#125—22no—
67C4×D4×C11—22no—
68C4×D4×C11Q814yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—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⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C11×#107—22no—
96C11×#107—22no—
97C11×#107—22no—
98C11×#106—22no—
99C11×C4⋊C8—22no—
100C11×C4⋊C8—22no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#97—22no—
106C4×C8×C11—22no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#23791C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11C2×Q812yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—81no—
135C22×C4×C11—81no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11#4112yes—
154C2×C8×C11#4112yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4—81no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4C2×Q812yes—
175C11×C4⋊C4#4112yes—
176C11×C4⋊C4#4112yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—81no—
179C11×C22⋊C4—81no—
180C11×C22⋊C4—81no—
181C11×C22⋊C4—81no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—81no—
187C42×C11—81no—
188C42×C11—81no—
189C42×C11C2×Q812yes—
190C42×C11#4112yes—
191#2330C2×C1111yescharacteristic, complemented
192#2319C2×C1111yescharacteristic
193#2100C2×C1111yescharacteristic, complemented
194#2093C2×C1111yescharacteristic
195#2087C2×C1111yescharacteristic, complemented
196#2086C2×C1111yescharacteristic, complemented
197#2067C2×C1111yescharacteristic
198#2065C2×C1111yescharacteristic
199#2059C2×C1111yescharacteristic, complemented
200#2025C2×C1111yescharacteristic
201#1776C2×C1111yescharacteristic, complemented
202C4×#107C2×C1111yescharacteristic, complemented
203#1768C2×C1111yescharacteristic, complemented
204#1762C2×C1111yescharacteristic
205C4×#102C2×C1111yescharacteristic
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11C22×D411yescharacteristic
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—41no—
217D4×C11—41no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—84no—
256C2×C4×C11C22⋊Q812yes—
257C2×C4×C11C22⋊Q812yes—
258C2×C4×C11C22×Q811yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C8×C11—22no—
265C8×C11—22no—
266C8×C11—41no—
267C8×C11—41no—
268C2×#125C22×C1111yescharacteristic
269C2×C4×D4C22×C1111yescharacteristic
270C2×#107C22×C1111yescharacteristic
271C2×#107C22×C1111yescharacteristic
272C2×#107C22×C1111yescharacteristic
273C2×#106C22×C1111yescharacteristic
274C2×C4⋊C8C22×C1111yescharacteristic
275C2×C4⋊C8C22×C1111yescharacteristic
276C2×#102C22×C1111yescharacteristic
277C2×#102C22×C1111yescharacteristic
278C2×#102C22×C1111yescharacteristic
279C2×#102C22×C1111yescharacteristic
280C2×#97C22×C1111yescharacteristic
281C2×C4×C8C22×C1111yescharacteristic
282#390C22×C1111yescharacteristic
283#390C22×C1111yescharacteristic
284#389—21no—
285#389—21no—
286#389C22×C1111yescharacteristic
287#389C22×C1111yescharacteristic
288#389C22×C1111yescharacteristic
289#389C22×C1111yescharacteristic
290#388—21no—
291#388—21no—
292#387—21no—
293#387—21no—
294#384C22×C1111yescharacteristic
295#381—21no—
296#380—21no—
297C4×C4⋊C4C22×C1111yescharacteristic
298C4×C4⋊C4C22×C1111yescharacteristic
299C4×C4⋊C4C22×C1111yescharacteristic
300#376C22×C1111yescharacteristic
301#340C22×C1111yescharacteristic
302#340C22×C1111yescharacteristic
303#340C22×C1111yescharacteristic
304#340C22×C1111yescharacteristic
305#340C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#340C22×C1111yescharacteristic
308#340C22×C1111yescharacteristic
309#336C22×C1111yescharacteristic
310#336C22×C1111yescharacteristic
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11C2×C22⋊Q811yescharacteristic
319C22×C11#52511yescharacteristic
320C22×C11#53211yescharacteristic
321C22×C11#57611yescharacteristic
322C22×C11#57611yescharacteristic
323C22×C11#57711yescharacteristic
324C22×C11#57811yescharacteristic
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—41no—
329C4×C11—42no—
330C4×C11—41no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#52911yescharacteristic
339C4×C11#52911yescharacteristic
340C4×C11#53311yescharacteristic
341C4×C11#53311yescharacteristic
342C22×D4C23×C1111yescharacteristic
343C23×C4—21no—
344C22×C8C23×C1111yescharacteristic
345C22×C8C23×C1111yescharacteristic
346C22×C8C23×C1111yescharacteristic
347C22×C8C23×C1111yescharacteristic
348#125—22no—
349#125—22no—
350C4×D4—22no—
351C4×D4Q8×C1114yes—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42C23×C1111yescharacteristic
376C2×C42C23×C1111yescharacteristic
377C2×C42C23×C1111yescharacteristic
378#107—22no—
379#107—22no—
380#107—22no—
381#106—22no—
382C4⋊C8—22no—
383C4⋊C8—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388#97—22no—
389C4×C8—22no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95D4×C1111yescharacteristic
398#95D4×C1111yescharacteristic
399#95D4×C1111yescharacteristic
400#95D4×C1111yescharacteristic
401C2×C11—82no—
402C2×C11#239611yescharacteristic
403C2×C11#308111yescharacteristic
404C2×C11#308311yescharacteristic
405C2×C11#311911yescharacteristic
406C2×C11#312411yescharacteristic
407C2×C11#317611yescharacteristic
408C2×C11#317811yescharacteristic
409C24—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4C2×Q8×C1112yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—81no—
425C22×C4—81no—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C24×C1111yescharacteristic
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8C11×#4112yes—
444C2×C8C11×#4112yes—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4C2×Q8×C1112yes—
465C4⋊C4C11×#4112yes—
466C4⋊C4C11×#4112yes—
467C22⋊C4—24no—
468C22⋊C4—81no—
469C22⋊C4—81no—
470C22⋊C4—81no—
471C22⋊C4—81no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—81no—
477C42—81no—
478C42—81no—
479C42C2×Q8×C1112yes—
480C42C11×#4112yes—
481C11#2379111yescharacteristic, direct product factor, Sylow
482C23—22no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23C22×D4×C1111yescharacteristic
490D4—22no—
491D4—22no—
492D4—41no—
493D4—41no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4C11×C22⋊Q812yes—
533C2×C4C11×C22⋊Q812yes—
534C2×C4C22×Q8×C1111yescharacteristic
535C2×C4C2×C11×#4111yescharacteristic
536C2×C4C2×C11×#4111yescharacteristic
537C2×C4C2×C11×#4111yescharacteristic
538C2×C4C2×C11×#4111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C8—22no—
541C8—22no—
542C8—41no—
543C8—41no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22C2×C11×C22⋊Q811yescharacteristic
552C22C11×#52511yescharacteristic
553C22C11×#53211yescharacteristic
554C22C11×#57611yescharacteristic
555C22C11×#57611yescharacteristic
556C22C11×#57711yescharacteristic
557C22C11×#57811yescharacteristic
558C4—22no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—42no—
563C4—41no—
564C4—42no—
565C4—41no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C11×#52911yescharacteristic
572C4C11×#52911yescharacteristic
573C4C11×#53311yescharacteristic
574C4C11×#53311yescharacteristic
575C2—82no—
576C2C11×#239611yescharacteristic
577C2C11×#308111yescharacteristic
578C2C11×#308311yescharacteristic
579C2C11×#311911yescharacteristic
580C2C11×#312411yescharacteristic
581C2C11×#317611yescharacteristic
582C2C11×#317811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2330C2semidirect
3. C11×#2100C2semidirect
5. C11×#2087C2semidirect
6. C11×#2086C2semidirect
9. C11×#2059C2semidirect
11. C11×#1776C2semidirect
12. C4×C11×#107C2semidirect
13. C11×#1768C2semidirect
118. #23791C11direct (N × H)
191. #2330C2×C11semidirect
193. #2100C2×C11semidirect
195. #2087C2×C11semidirect
196. #2086C2×C11semidirect
199. #2059C2×C11semidirect
201. #1776C2×C11semidirect
202. C4×#107C2×C11semidirect
203. #1768C2×C11semidirect
481. C11#23791direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23302
C11×#23192
C11×#21002
C11×#20932
C11×#20872
C11×#20862
C11×#20672
C11×#20652
C11×#20592
C11×#20252
C11×#17762
C4×C11×#1072
C11×#17682
C11×#17622
C4×C11×#1022
#2379111