Finite Group Databasebeta

← C11×#23784 #14600977

Subgroups — C11×#23784 #14600977

Order 2816.

756 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#125C211yesmaximal, characteristic, complemented
2C11×#2293C211yesmaximal, characteristic
3C11×#2101C211yesmaximal, characteristic, complemented
4C11×#2092C211yesmaximal, characteristic
5C11×#2088C211yesmaximal, characteristic, complemented
6C11×#2086C211yesmaximal, characteristic, complemented
7C11×#2067C211yesmaximal, characteristic
8C11×#2065C211yesmaximal, characteristic
9C11×#2059C211yesmaximal, characteristic, complemented
10C11×#2025C211yesmaximal, characteristic
11C11×#1776C211yesmaximal, characteristic, complemented
12C11×#1776C211yesmaximal, characteristic, complemented
13C11×#1767C211yesmaximal, characteristic, complemented
14C11×#1762C211yesmaximal, characteristic
15C11×#1762C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117—21no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×C11×#97C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#388—21no—
39C11×#387—21no—
40C11×#387—21no—
41C11×#382C2211yescharacteristic
42C4×C11×C4⋊C4—21no—
43C4×C11×C4⋊C4—21no—
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4—21no—
48C43×C11C2211yescharacteristic
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—
69C11×#117—44no—
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⋊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×C11D411yescharacteristic
92C2×C42×C11D411yescharacteristic
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×#107—22no—
99C11×#107—22no—
100C11×#106—22no—
101C11×#106—22no—
102C11×C4⋊C8—22no—
103C11×C4⋊C8—22no—
104C11×#102—22no—
105C11×#102—22no—
106C11×#102—22no—
107C11×#102—22no—
108C11×#97—22no—
109C11×#97—22no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119#23784C1111yesmaximal, 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×C11C2×Q812yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
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×C11—21no—
154C2×C8×C11#4112yes—
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—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4C2×Q812yes—
174C11×C4⋊C4#4112yes—
175C11×C4⋊C4#4112yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C42×C11—22no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—41no—
187C42×C11—41no—
188C42×C11—41no—
189C42×C11—42no—
190C42×C11—42no—
191C42×C11—42no—
192C42×C11C2×Q812yes—
193C42×C11#4112yes—
194C4×#125C2×C1111yescharacteristic, complemented
195#2293C2×C1111yescharacteristic
196#2101C2×C1111yescharacteristic, complemented
197#2092C2×C1111yescharacteristic
198#2088C2×C1111yescharacteristic, complemented
199#2086C2×C1111yescharacteristic, complemented
200#2067C2×C1111yescharacteristic
201#2065C2×C1111yescharacteristic
202#2059C2×C1111yescharacteristic, complemented
203#2025C2×C1111yescharacteristic
204#1776C2×C1111yescharacteristic, complemented
205#1776C2×C1111yescharacteristic, complemented
206#1767C2×C1111yescharacteristic, complemented
207#1762C2×C1111yescharacteristic
208#1762C2×C1111yescharacteristic
209C23×C11—22no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11C22×D411yescharacteristic
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—41no—
220D4×C11—41no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
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—48no—
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—41no—
257C2×C4×C11—41no—
258C2×C4×C11C22⋊Q812yes—
259C2×C4×C11C22⋊Q812yes—
260C2×C4×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C8×C11—22no—
268C8×C11—22no—
269C8×C11—41no—
270C8×C11—41no—
271C2×#125C22×C1111yescharacteristic
272C2×C4×D4C22×C1111yescharacteristic
273C2×#117—21no—
274C2×#107C22×C1111yescharacteristic
275C2×#107C22×C1111yescharacteristic
276C2×#106C22×C1111yescharacteristic
277C2×#106C22×C1111yescharacteristic
278C2×C4⋊C8C22×C1111yescharacteristic
279C2×C4⋊C8C22×C1111yescharacteristic
280C2×#102C22×C1111yescharacteristic
281C2×#102C22×C1111yescharacteristic
282C2×#102C22×C1111yescharacteristic
283C2×#102C22×C1111yescharacteristic
284C2×#97C22×C1111yescharacteristic
285C2×#97C22×C1111yescharacteristic
286#390C22×C1111yescharacteristic
287#390C22×C1111yescharacteristic
288#389C22×C1111yescharacteristic
289#389C22×C1111yescharacteristic
290#389C22×C1111yescharacteristic
291#389C22×C1111yescharacteristic
292#388—21no—
293#388—21no—
294#387—21no—
295#387—21no—
296#382C22×C1111yescharacteristic
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4C22×C1111yescharacteristic
300C4×C4⋊C4C22×C1111yescharacteristic
301C4×C4⋊C4C22×C1111yescharacteristic
302C4×C22⋊C4—21no—
303C43C22×C1111yescharacteristic
304#340C22×C1111yescharacteristic
305#340C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#340C22×C1111yescharacteristic
308#340C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#336C22×C1111yescharacteristic
313#336C22×C1111yescharacteristic
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11#52511yescharacteristic
323C22×C11#53211yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57511yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#52911yescharacteristic
342C4×C11#52911yescharacteristic
343C4×C11#53311yescharacteristic
344C4×C11#53311yescharacteristic
345C22×D4C23×C1111yescharacteristic
346C23×C4—21no—
347C22×C8C23×C1111yescharacteristic
348C22×C8C23×C1111yescharacteristic
349C22×C8C23×C1111yescharacteristic
350C22×C8C23×C1111yescharacteristic
351#125—22no—
352#125—22no—
353C4×D4—22no—
354C4×D4Q8×C1114yes—
355#117—44no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
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×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42D4×C1111yescharacteristic
378C2×C42D4×C1111yescharacteristic
379C2×C42D4×C1111yescharacteristic
380C2×C42D4×C1111yescharacteristic
381C2×C42C23×C1111yescharacteristic
382C2×C42C23×C1111yescharacteristic
383C2×C42C23×C1111yescharacteristic
384#107—22no—
385#107—22no—
386#106—22no—
387#106—22no—
388C4⋊C8—22no—
389C4⋊C8—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#97—22no—
395#97—22no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405C2×C11—82no—
406C2×C11#239611yescharacteristic
407C2×C11#307711yescharacteristic
408C2×C11#308011yescharacteristic
409C2×C11#311111yescharacteristic
410C2×C11#311511yescharacteristic
411C2×C11#318011yescharacteristic
412C2×C11#318311yescharacteristic
413C24—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4C2×Q8×C1112yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C24×C1111yescharacteristic
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8C11×#4112yes—
448C2×C8C11×#4112yes—
449C4⋊C4—24no—
450C4⋊C4—24no—
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—21no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4C2×Q8×C1112yes—
467C4⋊C4C11×#4112yes—
468C4⋊C4C11×#4112yes—
469C22⋊C4—24no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—41no—
480C42—41no—
481C42—41no—
482C42—42no—
483C42—42no—
484C42—42no—
485C42C2×Q8×C1112yes—
486C42C11×#4112yes—
487C11#2378411yescharacteristic, direct product factor, Sylow
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C22×D4×C1111yescharacteristic
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—48no—
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—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4C11×C22⋊Q812yes—
538C2×C4C11×C22⋊Q812yes—
539C2×C4C11×AGL(1,ℤ/8)12yes—
540C2×C4C22×Q8×C1111yescharacteristic
541C2×C4C2×C11×#4111yescharacteristic
542C2×C4C2×C11×#4111yescharacteristic
543C2×C4C2×C11×#4111yescharacteristic
544C2×C4C2×C11×#4111yescharacteristic
545C2×C4C2×C11×#4111yescharacteristic
546C8—22no—
547C8—22no—
548C8—41no—
549C8—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C11×C22⋊Q811yescharacteristic
558C22C11×#52511yescharacteristic
559C22C11×#53211yescharacteristic
560C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
561C22C11×#57511yescharacteristic
562C22C11×#57511yescharacteristic
563C22C11×#57511yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C11×#52911yescharacteristic
578C4C11×#52911yescharacteristic
579C4C11×#53311yescharacteristic
580C4C11×#53311yescharacteristic
581C2—82no—
582C2C11×#239611yescharacteristic
583C2C11×#307711yescharacteristic
584C2C11×#308011yescharacteristic
585C2C11×#311111yescharacteristic
586C2C11×#311511yescharacteristic
587C2C11×#318011yescharacteristic
588C2C11×#318311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C11×#125C2semidirect
3. C11×#2101C2semidirect
5. C11×#2088C2semidirect
6. C11×#2086C2semidirect
9. C11×#2059C2semidirect
11. C11×#1776C2semidirect
12. C11×#1776C2semidirect
13. C11×#1767C2semidirect
119. #23784C11direct (N × H)
194. C4×#125C2×C11semidirect
196. #2101C2×C11semidirect
198. #2088C2×C11semidirect
199. #2086C2×C11semidirect
202. #2059C2×C11semidirect
204. #1776C2×C11semidirect
205. #1776C2×C11semidirect
206. #1767C2×C11semidirect
487. C11#23784direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1252
C11×#22932
C11×#21012
C11×#20922
C11×#20882
C11×#20862
C11×#20672
C11×#20652
C11×#20592
C11×#20252
C11×#17762
C11×#17672
C11×#17622
#2378411