Finite Group Databasebeta

← C11×#23071 #14600264

Subgroups — C11×#23071 #14600264

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#478C211yesmaximal, characteristic
2C11×#2370C211yesmaximal, characteristic, complemented
3C11×#2357C211yesmaximal, characteristic
4C11×#1991C211yesmaximal, characteristic, complemented
5C11×#1949C211yesmaximal, characteristic, complemented
6C11×#1936C211yesmaximal, characteristic
7C11×#1936C211yesmaximal, characteristic
8C11×#1926C211yesmaximal, characteristic
9C11×#1925C211yesmaximal, characteristic
10C11×#1920C211yesmaximal, characteristic, complemented
11C11×#1918C211yesmaximal, characteristic, complemented
12C11×#1776C211yesmaximal, characteristic, complemented
13C11×#1776C211yesmaximal, characteristic, complemented
14C11×#1770C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#478C418yescomplemented
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#389—21no—
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#388—21no—
38C11×#387—21no—
39C11×#387—21no—
40C11×#382C2211yescharacteristic
41C11×#381—21no—
42C4×C11×C4⋊C4—21no—
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125C2×C414yes—
68C4×D4×C11—22no—
69C4×D4×C11C2×C414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C11×#107—22no—
97C11×#107C2×C414yes—
98C11×#106—22no—
99C11×#106C2×C414yes—
100C11×C4⋊C8C2×C414yes—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102C2×C414yes—
104C11×#102C2×C414yes—
105C11×#97—22no—
106C11×#97—22no—
107C4×C8×C11—22no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#23071C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C22×C412yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—81no—
136C22×C4×C11—81no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
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×C11C22×C412yes—
154C2×C8×C11C22×C412yes—
155C2×C8×C11#4112yes—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
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—41no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4C22×C412yes—
173C11×C4⋊C4C22×C412yes—
174C11×C4⋊C4C22×C412yes—
175C11×C4⋊C4#4112yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—81no—
180C11×C22⋊C4—81no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186C42×C11—81no—
187C42×C11—81no—
188C42×C11—81no—
189C42×C11—81no—
190C42×C11C22×C412yes—
191C42×C11#4112yes—
192C2×#478C2×C1111yescharacteristic
193#2370C2×C1111yescharacteristic, complemented
194#2357C2×C1111yescharacteristic
195#1991C2×C1111yescharacteristic, complemented
196#1949C2×C1111yescharacteristic, complemented
197#1936C2×C1111yescharacteristic
198#1936C2×C1111yescharacteristic
199#1926C2×C1111yescharacteristic
200#1925C2×C1111yescharacteristic
201#1920C2×C1111yescharacteristic, complemented
202#1918C2×C1111yescharacteristic, complemented
203#1776C2×C1111yescharacteristic, complemented
204#1776C2×C1111yescharacteristic, complemented
205#1770C2×C1111yescharacteristic, complemented
206C4×#102C2×C1111yescharacteristic
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
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—21no—
238C2×C4×C11—21no—
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—41no—
256C2×C4×C11—84no—
257C2×C4×C11C4×D412yes—
258C2×C4×C11C4×D412yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C8×C11—22no—
266C8×C11—22no—
267C8×C11—22no—
268C8×C11—41no—
269C2×#125C22×C1111yescharacteristic
270C2×C4×D4C22×C1111yescharacteristic
271#478C4×C1118yescomplemented
272C2×#107C22×C1111yescharacteristic
273C2×#107C22×C1111yescharacteristic
274C2×#106C22×C1111yescharacteristic
275C2×#106C22×C1111yescharacteristic
276C2×C4⋊C8C22×C1111yescharacteristic
277C2×#102C22×C1111yescharacteristic
278C2×#102C22×C1111yescharacteristic
279C2×#102C22×C1111yescharacteristic
280C2×#102C22×C1111yescharacteristic
281C2×#97C22×C1111yescharacteristic
282C2×#97C22×C1111yescharacteristic
283C2×C4×C8C22×C1111yescharacteristic
284#390C22×C1111yescharacteristic
285#390C22×C1111yescharacteristic
286#389—21no—
287#389C22×C1111yescharacteristic
288#389C22×C1111yescharacteristic
289#388—21no—
290#388—21no—
291#387—21no—
292#387—21no—
293#382C22×C1111yescharacteristic
294#381—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4C22×C1111yescharacteristic
297C4×C4⋊C4C22×C1111yescharacteristic
298C4×C4⋊C4C22×C1111yescharacteristic
299C4×C4⋊C4C22×C1111yescharacteristic
300C4×C4⋊C4C22×C1111yescharacteristic
301C4×C4⋊C4C22×C1111yescharacteristic
302C4×C22⋊C4—21no—
303#340C22×C1111yescharacteristic
304#340C22×C1111yescharacteristic
305#340C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#340C22×C1111yescharacteristic
308#340C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#336C22×C1111yescharacteristic
312#336C22×C1111yescharacteristic
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11C2×C4×D411yescharacteristic
321C22×C11#54711yescharacteristic
322C22×C11#54811yescharacteristic
323C22×C11#57511yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C4×#4111yescharacteristic
341C4×C11#51911yescharacteristic
342C4×C11#55211yescharacteristic
343C4×C11#55611yescharacteristic
344C22×D4C23×C1111yescharacteristic
345C23×C4—21no—
346C22×C8C23×C1111yescharacteristic
347C22×C8C23×C1111yescharacteristic
348C22×C8C23×C1111yescharacteristic
349C22×C8C23×C1111yescharacteristic
350#125—22no—
351#125C2×C4×C1114yes—
352C4×D4—22no—
353C4×D4C2×C4×C1114yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4D4×C1111yescharacteristic
359C2×C4⋊C4D4×C1111yescharacteristic
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×C42—21no—
376C2×C42—21no—
377C2×C42C23×C1111yescharacteristic
378C2×C42C23×C1111yescharacteristic
379C2×C42C23×C1111yescharacteristic
380#107—22no—
381#107C2×C4×C1114yes—
382#106—22no—
383#106C2×C4×C1114yes—
384C4⋊C8C2×C4×C1114yes—
385#102—22no—
386#102—22no—
387#102C2×C4×C1114yes—
388#102C2×C4×C1114yes—
389#97—22no—
390#97—22no—
391C4×C8—22no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95D4×C1111yescharacteristic
402#95D4×C1111yescharacteristic
403C2×C11—82no—
404C2×C11#236211yescharacteristic
405C2×C11#294311yescharacteristic
406C2×C11#294611yescharacteristic
407C2×C11#335111yescharacteristic
408C2×C11#335511yescharacteristic
409C2×C11#337011yescharacteristic
410C2×C11#337111yescharacteristic
411C24—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C22×C4×C1112yes—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C24×C1111yescharacteristic
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×C8—21no—
444C2×C8C22×C4×C1112yes—
445C2×C8C22×C4×C1112yes—
446C2×C8C11×#4112yes—
447C4⋊C4—24no—
448C4⋊C4—24no—
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—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—42no—
462C4⋊C4—81no—
463C4⋊C4C22×C4×C1112yes—
464C4⋊C4C22×C4×C1112yes—
465C4⋊C4C22×C4×C1112yes—
466C4⋊C4C11×#4112yes—
467C22⋊C4—24no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—81no—
471C22⋊C4—81no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—42no—
477C42—81no—
478C42—81no—
479C42—81no—
480C42—81no—
481C42C22×C4×C1112yes—
482C42C11×#4112yes—
483C11#2307111yescharacteristic, direct product factor, Sylow
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×D4×C1111yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
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—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4C4×D4×C1112yes—
535C2×C4C4×D4×C1112yes—
536C2×C4C23×C4×C1111yescharacteristic
537C2×C4C2×C11×#4111yescharacteristic
538C2×C4C2×C11×#4111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C2×C4C11×2−1+411yescharacteristic
541C2×C4C11×2−1+411yescharacteristic
542C8—22no—
543C8—22no—
544C8—22no—
545C8—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×C4×D4×C1111yescharacteristic
554C22C11×#54711yescharacteristic
555C22C11×#54811yescharacteristic
556C22C11×#57511yescharacteristic
557C22C11×#57511yescharacteristic
558C22C11×#57611yescharacteristic
559C22C11×#57711yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4C4×C11×#4111yescharacteristic
574C4C11×#51911yescharacteristic
575C4C11×#55211yescharacteristic
576C4C11×#55611yescharacteristic
577C2—82no—
578C2C11×#236211yescharacteristic
579C2C11×#294311yescharacteristic
580C2C11×#294611yescharacteristic
581C2C11×#335111yescharacteristic
582C2C11×#335511yescharacteristic
583C2C11×#337011yescharacteristic
584C2C11×#337111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2370C2semidirect
4. C11×#1991C2semidirect
5. C11×#1949C2semidirect
10. C11×#1920C2semidirect
11. C11×#1918C2semidirect
12. C11×#1776C2semidirect
13. C11×#1776C2semidirect
14. C11×#1770C2semidirect
18. C11×#478C4semidirect
119. #23071C11direct (N × H)
193. #2370C2×C11semidirect
195. #1991C2×C11semidirect
196. #1949C2×C11semidirect
201. #1920C2×C11semidirect
202. #1918C2×C11semidirect
203. #1776C2×C11semidirect
204. #1776C2×C11semidirect
205. #1770C2×C11semidirect
271. #478C4×C11semidirect
483. C11#23071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4782
C11×#23702
C11×#23572
C11×#19912
C11×#19492
C11×#19362
C11×#19262
C11×#19252
C11×#19202
C11×#19182
C11×#17762
C11×#17702
C4×C11×#1022
#2307111