Finite Group Databasebeta

← C11×#22623 #14599816

Subgroups — C11×#22623 #14599816

Order 2816.

782 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×#428C211yesmaximal, characteristic
2C11×#2347C211yesmaximal, characteristic
3C11×#2345C211yesmaximal, characteristic
4C11×#1944C211yesmaximal, characteristic, complemented
5C11×#1941C211yesmaximal, characteristic, complemented
6C11×#1921C211yesmaximal, characteristic, complemented
7C11×#1920C211yesmaximal, characteristic, complemented
8C11×#1919C211yesmaximal, characteristic, complemented
9C11×#1918C211yesmaximal, characteristic, complemented
10C11×#1825C211yesmaximal, characteristic
11C11×#1823C211yesmaximal, characteristic
12C11×#1809C211yesmaximal, characteristic
13C11×#1776C211yesmaximal, characteristic, complemented
14C4×C11×#107C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#428C418yescomplemented
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#389C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#389C2211yescharacteristic
33C11×#388—21no—
34C11×#388—21no—
35C11×#387—21no—
36C11×#387—21no—
37C11×#383—21no—
38C11×#380—21no—
39C11×#380C2211yescharacteristic
40C11×#380C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C22⋊C4—21no—
47C4×C11×C22⋊C4C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16C2×C414yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117—22no—
70C11×#117C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2×C414yes—
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×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×#107—22no—
99C11×#107C2×C414yes—
100C11×#107C2×C414yes—
101C11×#106—22no—
102C11×#106C2×C414yes—
103C11×#106C2×C414yes—
104C11×C22⋊C8—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×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#22623C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
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×C11C22×C412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C11×M16—28no—
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—
156C2×C8×C11#4112yes—
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—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4C22×C412yes—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4C22×C412yes—
177C11×C4⋊C4C22×C412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—81no—
183C42×C11—24no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—81no—
189C42×C11—81no—
190C42×C11—81no—
191C42×C11—81no—
192C2×#428C2×C1111yescharacteristic
193#2347C2×C1111yescharacteristic
194#2345C2×C1111yescharacteristic
195#1944C2×C1111yescharacteristic, complemented
196#1941C2×C1111yescharacteristic, complemented
197#1921C2×C1111yescharacteristic, complemented
198#1920C2×C1111yescharacteristic, complemented
199#1919C2×C1111yescharacteristic, complemented
200#1918C2×C1111yescharacteristic, complemented
201#1825C2×C1111yescharacteristic
202#1823C2×C1111yescharacteristic
203#1809C2×C1111yescharacteristic
204#1776C2×C1111yescharacteristic, complemented
205C4×#107C2×C1111yescharacteristic, complemented
206#1753C2×C1111yescharacteristic
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11C4×D412yes—
214C23×C11C22×D411yescharacteristic
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
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—41no—
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—41no—
256C2×C4×C11—84no—
257C2×C4×C11C4×D412yes—
258C2×C4×C11#13712yes—
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—41no—
267C8×C11—41no—
268C8×C11#11714yes—
269C22×M16C22×C1111yescharacteristic
270C2×#117C22×C1111yescharacteristic
271C22×C4⋊C4C22×C1111yescharacteristic
272#428C4×C1118yescomplemented
273C2×#107C22×C1111yescharacteristic
274C2×#107C22×C1111yescharacteristic
275C2×#107C22×C1111yescharacteristic
276C2×#106C22×C1111yescharacteristic
277C2×#106C22×C1111yescharacteristic
278C2×#106C22×C1111yescharacteristic
279C2×C22⋊C8C22×C1111yescharacteristic
280C2×#97C22×C1111yescharacteristic
281C2×C4×C8C22×C1111yescharacteristic
282#389C22×C1111yescharacteristic
283#389C22×C1111yescharacteristic
284#389C22×C1111yescharacteristic
285#389C22×C1111yescharacteristic
286#388—21no—
287#388—21no—
288#387—21no—
289#387—21no—
290#383—21no—
291#380—21no—
292#380C22×C1111yescharacteristic
293#380C22×C1111yescharacteristic
294C4×C4⋊C4—21no—
295C4×C4⋊C4C22×C1111yescharacteristic
296C4×C4⋊C4C22×C1111yescharacteristic
297C4×C4⋊C4C22×C1111yescharacteristic
298C4×C4⋊C4C22×C1111yescharacteristic
299C4×C22⋊C4—21no—
300C4×C22⋊C4C22×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#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#336C22×C1111yescharacteristic
312#336C22×C1111yescharacteristic
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11C2×C4×D411yescharacteristic
321C22×C11#54711yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11C2×#13711yescharacteristic
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—42no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C2×#11711yescharacteristic
341C4×C11#51911yescharacteristic
342C4×C11#55211yescharacteristic
343C4×C11#55211yescharacteristic
344C23×C4—21no—
345C23×C4C23×C1111yescharacteristic
346C2×M16—22no—
347C2×M16—22no—
348C2×M16C2×C4×C1114yes—
349C22×C8C23×C1111yescharacteristic
350C22×C8C23×C1111yescharacteristic
351C22×C8C23×C1111yescharacteristic
352C22×C8C23×C1111yescharacteristic
353#117—22no—
354#117C2×C4×C1114yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C2×C4×C1114yes—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1111yescharacteristic
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4D4×C1111yescharacteristic
374C2×C22⋊C4D4×C1111yescharacteristic
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C23×C1111yescharacteristic
381C2×C42C23×C1111yescharacteristic
382#107—22no—
383#107C2×C4×C1114yes—
384#107C2×C4×C1114yes—
385#106—22no—
386#106C2×C4×C1114yes—
387#106C2×C4×C1114yes—
388C22⋊C8—22no—
389#97—22no—
390C4×C8—22no—
391#95—21no—
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—42no—
404C2×C11#234411yescharacteristic
405C2×C11C4×#13711yescharacteristic
406C2×C11#294611yescharacteristic
407C2×C11#334611yescharacteristic
408C2×C11#335011yescharacteristic
409C2×C11#335511yescharacteristic
410C2×C11#335611yescharacteristic
411C24C2×D4×C1111yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4C22×C4×C1112yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C11×#4112yes—
434C22×C4C24×C1111yescharacteristic
435M16—28no—
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—
447C2×C8C11×#4112yes—
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—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4C22×C4×C1112yes—
466C4⋊C4C22×C4×C1112yes—
467C4⋊C4C22×C4×C1112yes—
468C4⋊C4C22×C4×C1112yes—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C42—24no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—81no—
481C42—81no—
482C42—81no—
483C11#2262311yescharacteristic, direct product factor, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23C4×D4×C1112yes—
491C23C22×D4×C1111yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
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—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4C4×D4×C1112yes—
535C2×C4C11×#13712yes—
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—41no—
544C8—41no—
545C8C11×#11714yes—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×C4×D4×C1111yescharacteristic
554C22C11×#54711yescharacteristic
555C22C11×#54711yescharacteristic
556C22C2×C11×#13711yescharacteristic
557C22C11×#57511yescharacteristic
558C22C11×#57611yescharacteristic
559C22C11×#57711yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4C2×C11×#11711yescharacteristic
574C4C11×#51911yescharacteristic
575C4C11×#55211yescharacteristic
576C4C11×#55211yescharacteristic
577C2—42no—
578C2C11×#234411yescharacteristic
579C2C4×C11×#13711yescharacteristic
580C2C11×#294611yescharacteristic
581C2C11×#334611yescharacteristic
582C2C11×#335011yescharacteristic
583C2C11×#335511yescharacteristic
584C2C11×#335611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1944C2semidirect
5. C11×#1941C2semidirect
6. C11×#1921C2semidirect
7. C11×#1920C2semidirect
8. C11×#1919C2semidirect
9. C11×#1918C2semidirect
13. C11×#1776C2semidirect
14. C4×C11×#107C2semidirect
19. C11×#428C4semidirect
119. #22623C11direct (N × H)
195. #1944C2×C11semidirect
196. #1941C2×C11semidirect
197. #1921C2×C11semidirect
198. #1920C2×C11semidirect
199. #1919C2×C11semidirect
200. #1918C2×C11semidirect
204. #1776C2×C11semidirect
205. C4×#107C2×C11semidirect
272. #428C4×C11semidirect
483. C11#22623direct (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
C11×#23472
C11×#23452
C11×#19442
C11×#19412
C11×#19212
C11×#19202
C11×#19192
C11×#19182
C11×#18252
C11×#18232
C11×#18092
C11×#17762
C4×C11×#1072
C11×#17532
#2262311