Finite Group Databasebeta

← C11×#24998 #14602191

Subgroups — C11×#24998 #14602191

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2580C211yesmaximal, characteristic
2C11×#2355C211yesmaximal, characteristic, complemented
3C11×#2101C211yesmaximal, characteristic, complemented
4C11×#2099C211yesmaximal, characteristic, complemented
5C11×#2073C211yesmaximal, characteristic
6C11×#2071C211yesmaximal, characteristic
7C11×#1984C211yesmaximal, characteristic, complemented
8C11×#1949C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic
10C11×#1925C211yesmaximal, characteristic
11C11×#1921C211yesmaximal, characteristic, complemented
12C11×#1919C211yesmaximal, characteristic, complemented
13C11×#1835C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic
15C4×C11×#102C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#399—21no—
27C11×#393—21no—
28C11×#391—21no—
29C11×#390C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#389C2211yescharacteristic
33C11×#387—21no—
34C11×#387—21no—
35C11×#385—21no—
36C11×#385—21no—
37C11×#384C2211yescharacteristic
38C11×#382C2211yescharacteristic
39C11×#382C2211yescharacteristic
40C11×#382C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
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⋊C4D411yescharacteristic
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×#106—22no—
97C11×C4⋊C8—22no—
98C11×#102—22no—
99C11×#102—22no—
100C11×#102—22no—
101C11×#102—22no—
102C4×C8×C11—22no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114#24998C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11#4112yes—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—42no—
133C22×C4×C11—81no—
134C22×C4×C11—81no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×C8×C11—21no—
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—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
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—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—81no—
179C11×C22⋊C4—81no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—42no—
185C42×C11—81no—
186C42×C11—81no—
187C42×C11#4112yes—
188C42×C11#4112yes—
189#2580C2×C1111yescharacteristic
190#2355C2×C1111yescharacteristic, complemented
191#2101C2×C1111yescharacteristic, complemented
192#2099C2×C1111yescharacteristic, complemented
193#2073C2×C1111yescharacteristic
194#2071C2×C1111yescharacteristic
195#1984C2×C1111yescharacteristic, complemented
196#1949C2×C1111yescharacteristic, complemented
197#1926C2×C1111yescharacteristic
198#1925C2×C1111yescharacteristic
199#1921C2×C1111yescharacteristic, complemented
200#1919C2×C1111yescharacteristic, complemented
201#1835C2×C1111yescharacteristic, complemented
202#1804C2×C1111yescharacteristic
203C4×#102C2×C1111yescharacteristic
204C23×C11—22no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11C22×D411yescharacteristic
212Q8×C11—44no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—41no—
216D4×C11—41no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
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—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
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—84no—
254C2×C4×C11#12312yes—
255C2×C4×C11#12312yes—
256C2×C4×C11#13512yes—
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C2×C4×Q8C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269C2×#107C22×C1111yescharacteristic
270C2×#106C22×C1111yescharacteristic
271C2×C4⋊C8C22×C1111yescharacteristic
272C2×#102C22×C1111yescharacteristic
273C2×#102C22×C1111yescharacteristic
274C2×#102C22×C1111yescharacteristic
275C2×#102C22×C1111yescharacteristic
276C2×C4×C8C22×C1111yescharacteristic
277#399—21no—
278#393—21no—
279#391—21no—
280#390C22×C1111yescharacteristic
281#390C22×C1111yescharacteristic
282#389C22×C1111yescharacteristic
283#389C22×C1111yescharacteristic
284#387—21no—
285#387—21no—
286#385—21no—
287#385—21no—
288#384C22×C1111yescharacteristic
289#382C22×C1111yescharacteristic
290#382C22×C1111yescharacteristic
291#382C22×C1111yescharacteristic
292C4×C4⋊C4—21no—
293C4×C4⋊C4C22×C1111yescharacteristic
294C4×C4⋊C4C22×C1111yescharacteristic
295C4×C4⋊C4C22×C1111yescharacteristic
296#340C22×C1111yescharacteristic
297#340C22×C1111yescharacteristic
298#340C22×C1111yescharacteristic
299#340C22×C1111yescharacteristic
300#340C22×C1111yescharacteristic
301#340C22×C1111yescharacteristic
302#340C22×C1111yescharacteristic
303#340C22×C1111yescharacteristic
304#340C22×C1111yescharacteristic
305#340C22×C1111yescharacteristic
306#336C22×C1111yescharacteristic
307#336C22×C1111yescharacteristic
308#336C22×C1111yescharacteristic
309#336C22×C1111yescharacteristic
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11C2×#12311yescharacteristic
318C22×C11#54811yescharacteristic
319C22×C11#54811yescharacteristic
320C22×C11C2×#13511yescharacteristic
321C22×C11#57511yescharacteristic
322C22×C11#57611yescharacteristic
323C22×C11#57711yescharacteristic
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#52911yescharacteristic
338C4×C11#54111yescharacteristic
339C4×C11#55211yescharacteristic
340C4×C11#55611yescharacteristic
341C22×Q8D4×C1111yescharacteristic
342C22×D4C23×C1111yescharacteristic
343C23×C4—21no—
344C22×C8C23×C1111yescharacteristic
345C22×C8C23×C1111yescharacteristic
346C22×C8C23×C1111yescharacteristic
347C22×C8C23×C1111yescharacteristic
348C4×Q8—22no—
349C4×Q8—22no—
350C4×D4—22no—
351C4×D4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4D4×C1111yescharacteristic
357C2×C4⋊C4D4×C1111yescharacteristic
358C2×C4⋊C4D4×C1111yescharacteristic
359C2×C4⋊C4C23×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×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C23×C1111yescharacteristic
375C2×C42C23×C1111yescharacteristic
376C2×C42C23×C1111yescharacteristic
377#107—22no—
378#106—22no—
379C4⋊C8—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384C4×C8—22no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396C2×C11—82no—
397C2×C11#242111yescharacteristic
398C2×C11#309111yescharacteristic
399C2×C11#309611yescharacteristic
400C2×C11#336111yescharacteristic
401C2×C11#336511yescharacteristic
402C2×C11#337011yescharacteristic
403C2×C11#337611yescharacteristic
404C24—21no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—41no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C11×#4112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—42no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C24×C1111yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
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—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
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—21no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4C11×#4112yes—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—81no—
468C22⋊C4—81no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—42no—
474C42—81no—
475C42—81no—
476C42C11×#4112yes—
477C42C11×#4112yes—
478C11#2499811yescharacteristic, direct product factor, Sylow
479C23—22no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23C22×D4×C1111yescharacteristic
487Q8—44no—
488D4—22no—
489D4—22no—
490D4—41no—
491D4—41no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
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—84no—
529C2×C4C11×#12312yes—
530C2×C4C11×#12312yes—
531C2×C4C11×#13512yes—
532C2×C4C2×C11×#4111yescharacteristic
533C2×C4C2×C11×#4111yescharacteristic
534C2×C4C2×C11×#4111yescharacteristic
535C2×C4C2×C11×#4111yescharacteristic
536C2×C4C11×2−1+411yescharacteristic
537C2×C4C11×2−1+411yescharacteristic
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22C2×C11×#12311yescharacteristic
550C22C11×#54811yescharacteristic
551C22C11×#54811yescharacteristic
552C22C2×C11×#13511yescharacteristic
553C22C11×#57511yescharacteristic
554C22C11×#57611yescharacteristic
555C22C11×#57711yescharacteristic
556C4—22no—
557C4—22no—
558C4—22no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—42no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C11×#52911yescharacteristic
570C4C11×#54111yescharacteristic
571C4C11×#55211yescharacteristic
572C4C11×#55611yescharacteristic
573C2—82no—
574C2C11×#242111yescharacteristic
575C2C11×#309111yescharacteristic
576C2C11×#309611yescharacteristic
577C2C11×#336111yescharacteristic
578C2C11×#336511yescharacteristic
579C2C11×#337011yescharacteristic
580C2C11×#337611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2355C2semidirect
3. C11×#2101C2semidirect
4. C11×#2099C2semidirect
7. C11×#1984C2semidirect
8. C11×#1949C2semidirect
11. C11×#1921C2semidirect
12. C11×#1919C2semidirect
13. C11×#1835C2semidirect
114. #24998C11direct (N × H)
190. #2355C2×C11semidirect
191. #2101C2×C11semidirect
192. #2099C2×C11semidirect
195. #1984C2×C11semidirect
196. #1949C2×C11semidirect
199. #1921C2×C11semidirect
200. #1919C2×C11semidirect
201. #1835C2×C11semidirect
478. C11#24998direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25802
C11×#23552
C11×#21012
C11×#20992
C11×#20732
C11×#20712
C11×#19842
C11×#19492
C11×#19262
C11×#19252
C11×#19212
C11×#19192
C11×#18352
C11×#18042
C4×C11×#1022
#2499811