Finite Group Databasebeta

← C11×#29441 #14606634

Subgroups — C11×#29441 #14606634

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2645C211yesmaximal, characteristic, complemented
2C11×#2319C211yesmaximal, characteristic
3C11×#2088C211yesmaximal, characteristic, complemented
4C11×#2068C211yesmaximal, characteristic, complemented
5C11×#2067C211yesmaximal, characteristic
6C11×#2055C211yesmaximal, characteristic
7C11×#1968C211yesmaximal, characteristic
8C11×#1942C211yesmaximal, characteristic, complemented
9C11×#1936C211yesmaximal, characteristic
10C11×#1935C211yesmaximal, characteristic, complemented
11C11×#1928C211yesmaximal, characteristic, complemented
12C11×#1920C211yesmaximal, characteristic, complemented
13C11×#1877C211yesmaximal, characteristic
14C11×#1862C211yesmaximal, characteristic
15C11×#1768C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#401—21no—
32C11×#400—21no—
33C11×#400—21no—
34C11×#400—21no—
35C11×#391C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#391C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#388—21no—
46C11×#388—21no—
47C11×#381—21no—
48C11×#380—21no—
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#376C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×D4×C11—22no—
70C4×D4×C11—22no—
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×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C11×#107—22no—
92C11×#107—41no—
93C11×#106—22no—
94C11×C4⋊C8—22no—
95C11×C4⋊C8—22no—
96C11×#103—22no—
97C11×#103—22no—
98C11×#103—41no—
99C11×#102—22no—
100C11×#102—22no—
101C11×#102—41no—
102C11×#97—41no—
103C4×C8×C11—41no—
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—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120#29441C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—81no—
143C22×C4×C11—81no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C11×SD16—44no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11#4112yes—
163C2×C8×C11#4112yes—
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—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4—81no—
178C11×C4⋊C4—81no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4#4112yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—81no—
183C11×C22⋊C4—81no—
184C11×C22⋊C4—81no—
185C11×C22⋊C4—81no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—81no—
193#2645C2×C1111yescharacteristic, complemented
194#2319C2×C1111yescharacteristic
195#2088C2×C1111yescharacteristic, complemented
196#2068C2×C1111yescharacteristic, complemented
197#2067C2×C1111yescharacteristic
198#2055C2×C1111yescharacteristic
199#1968C2×C1111yescharacteristic
200#1942C2×C1111yescharacteristic, complemented
201#1936C2×C1111yescharacteristic
202#1935C2×C1111yescharacteristic, complemented
203#1928C2×C1111yescharacteristic, complemented
204#1920C2×C1111yescharacteristic, complemented
205#1877C2×C1111yescharacteristic
206#1862C2×C1111yescharacteristic
207#1768C2×C1111yescharacteristic, complemented
208C23×C11—22no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11C22×D411yescharacteristic
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—41no—
223D4×C11—41no—
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—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
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×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—84no—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C8×C11—22no—
271C8×C11—22no—
272C8×C11—41no—
273C8×C11—41no—
274C22×SD16C22×C1111yescharacteristic
275C2×C4×D4C22×C1111yescharacteristic
276C2×#107C22×C1111yescharacteristic
277C2×#107C22×C1111yescharacteristic
278C2×#106C22×C1111yescharacteristic
279C2×C4⋊C8C22×C1111yescharacteristic
280C2×C4⋊C8C22×C1111yescharacteristic
281C2×#103C22×C1111yescharacteristic
282C2×#103C22×C1111yescharacteristic
283C2×#103C22×C1111yescharacteristic
284C2×#102C22×C1111yescharacteristic
285C2×#102C22×C1111yescharacteristic
286C2×#102C22×C1111yescharacteristic
287C2×#97C22×C1111yescharacteristic
288C2×C4×C8C22×C1111yescharacteristic
289#401—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#391C22×C1111yescharacteristic
294#391C22×C1111yescharacteristic
295#391C22×C1111yescharacteristic
296#390C22×C1111yescharacteristic
297#390C22×C1111yescharacteristic
298#389C22×C1111yescharacteristic
299#389C22×C1111yescharacteristic
300#389C22×C1111yescharacteristic
301#389C22×C1111yescharacteristic
302#389C22×C1111yescharacteristic
303#388—21no—
304#388—21no—
305#381—21no—
306#380—21no—
307C4×C4⋊C4C22×C1111yescharacteristic
308#376C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#340C22×C1111yescharacteristic
313#340C22×C1111yescharacteristic
314#340C22×C1111yescharacteristic
315#336C22×C1111yescharacteristic
316#336C22×C1111yescharacteristic
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11#52511yescharacteristic
325C22×C11#53211yescharacteristic
326C22×C11#53711yescharacteristic
327C22×C11#57611yescharacteristic
328C22×C11#57711yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57811yescharacteristic
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#55111yescharacteristic
345C4×C11#55211yescharacteristic
346C4×C11#55311yescharacteristic
347C4×C11#55611yescharacteristic
348C22×Q8C23×C1111yescharacteristic
349C22×D4C23×C1111yescharacteristic
350C23×C4—21no—
351C2×SD16—22no—
352C2×SD16—22no—
353C2×SD16—41no—
354C22×C8C23×C1111yescharacteristic
355C22×C8C23×C1111yescharacteristic
356C22×C8C23×C1111yescharacteristic
357C22×C8C23×C1111yescharacteristic
358C4×D4—22no—
359C4×D4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1111yescharacteristic
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42C23×C1111yescharacteristic
378C2×C42C23×C1111yescharacteristic
379C2×C42C23×C1111yescharacteristic
380#107—22no—
381#107—41no—
382#106—22no—
383C4⋊C8—22no—
384C4⋊C8—22no—
385#103—22no—
386#103—22no—
387#103—41no—
388#102—22no—
389#102—22no—
390#102—41no—
391#97—41no—
392C4×C8—41no—
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#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95D4×C1111yescharacteristic
406#95D4×C1111yescharacteristic
407#95D4×C1111yescharacteristic
408#95D4×C1111yescharacteristic
409C2×C11—82no—
410C2×C11#260111yescharacteristic
411C2×C11#311811yescharacteristic
412C2×C11#312011yescharacteristic
413C2×C11#317411yescharacteristic
414C2×C11#317511yescharacteristic
415C2×C11#325711yescharacteristic
416C2×C11#325811yescharacteristic
417C24—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4C11×#4112yes—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—81no—
439C22×C4—81no—
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C24×C1111yescharacteristic
447SD16—44no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C11×#4112yes—
459C2×C8C11×#4112yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4C11×#4112yes—
477C22⋊C4—24no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C22⋊C4—81no—
481C22⋊C4—81no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—81no—
489C11#2944111yescharacteristic, direct product factor, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C22×D4×C1111yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
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×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C2×C11×#4111yescharacteristic
548C2×C4C2×C11×#4111yescharacteristic
549C2×C4C2×C11×#4111yescharacteristic
550C2×C4C11×H(5,𝔽2)11yescharacteristic
551C2×C4C11×2−1+411yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C11×#52511yescharacteristic
564C22C11×#53211yescharacteristic
565C22C11×#53711yescharacteristic
566C22C11×#57611yescharacteristic
567C22C11×#57711yescharacteristic
568C22C11×#57711yescharacteristic
569C22C11×#57811yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4C11×#55111yescharacteristic
584C4C11×#55211yescharacteristic
585C4C11×#55311yescharacteristic
586C4C11×#55611yescharacteristic
587C2—82no—
588C2C11×#260111yescharacteristic
589C2C11×#311811yescharacteristic
590C2C11×#312011yescharacteristic
591C2C11×#317411yescharacteristic
592C2C11×#317511yescharacteristic
593C2C11×#325711yescharacteristic
594C2C11×#325811yescharacteristic
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×#2645C2semidirect
3. C11×#2088C2semidirect
4. C11×#2068C2semidirect
8. C11×#1942C2semidirect
10. C11×#1935C2semidirect
11. C11×#1928C2semidirect
12. C11×#1920C2semidirect
15. C11×#1768C2semidirect
120. #29441C11direct (N × H)
193. #2645C2×C11semidirect
195. #2088C2×C11semidirect
196. #2068C2×C11semidirect
200. #1942C2×C11semidirect
202. #1935C2×C11semidirect
203. #1928C2×C11semidirect
204. #1920C2×C11semidirect
207. #1768C2×C11semidirect
489. C11#29441direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26452
C11×#23192
C11×#20882
C11×#20682
C11×#20672
C11×#20552
C11×#19682
C11×#19422
C11×#19362
C11×#19352
C11×#19282
C11×#19202
C11×#18772
C11×#18622
C11×#17682
#2944111