Finite Group Databasebeta

← C11×#27133 #14604326

Subgroups — C11×#27133 #14604326

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2513C211yesmaximal, characteristic
2C11×#2369C211yesmaximal, characteristic, complemented
3C11×#2101C211yesmaximal, characteristic, complemented
4C11×#2067C211yesmaximal, characteristic
5C11×#2057C211yesmaximal, characteristic, complemented
6C11×#2023C211yesmaximal, characteristic
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1934C211yesmaximal, characteristic
9C11×#1926C211yesmaximal, characteristic
10C11×#1925C211yesmaximal, characteristic
11C11×#1925C211yesmaximal, characteristic
12C11×#1921C211yesmaximal, characteristic, complemented
13C11×#1920C211yesmaximal, characteristic, complemented
14C11×#1916C211yesmaximal, characteristic, complemented
15C4×C11×#107C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#397—21no—
28C11×#397—21no—
29C11×#391—21no—
30C11×#391—21no—
31C11×#390C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C11×#389—21no—
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#388—21no—
40C11×#382C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
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×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C11×#107—22no—
94C11×#107—22no—
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×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114#27133C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C2×Q8×C11—24no—
117C2×Q8×C11—81no—
118C2×Q8×C11—81no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
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×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
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#4112yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
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—81no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4#4112yes—
169C11×C4⋊C4#4112yes—
170C11×C4⋊C4#4112yes—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—81no—
174C11×C22⋊C4—81no—
175C11×C22⋊C4—81no—
176C11×C22⋊C4—81no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11—81no—
185C42×C11—81no—
186C42×C11—81no—
187#2513C2×C1111yescharacteristic
188#2369C2×C1111yescharacteristic, complemented
189#2101C2×C1111yescharacteristic, complemented
190#2067C2×C1111yescharacteristic
191#2057C2×C1111yescharacteristic, complemented
192#2023C2×C1111yescharacteristic
193#1949C2×C1111yescharacteristic, complemented
194#1934C2×C1111yescharacteristic
195#1926C2×C1111yescharacteristic
196#1925C2×C1111yescharacteristic
197#1925C2×C1111yescharacteristic
198#1921C2×C1111yescharacteristic, complemented
199#1920C2×C1111yescharacteristic, complemented
200#1916C2×C1111yescharacteristic, complemented
201C4×#107C2×C1111yescharacteristic, complemented
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11C22×D411yescharacteristic
210Q8×C11—84no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—41no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
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—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#13512yes—
253C2×C4×C11#13712yes—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C8×C11—22no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11—41no—
264C2×C4⋊Q8C22×C1111yescharacteristic
265C2×#107C22×C1111yescharacteristic
266C2×#107C22×C1111yescharacteristic
267C2×#107C22×C1111yescharacteristic
268C2×#106C22×C1111yescharacteristic
269C2×C4⋊C8C22×C1111yescharacteristic
270C2×#102C22×C1111yescharacteristic
271C2×#102C22×C1111yescharacteristic
272C2×#102C22×C1111yescharacteristic
273C2×#102C22×C1111yescharacteristic
274C2×C4×C8C22×C1111yescharacteristic
275#397—21no—
276#397—21no—
277#391—21no—
278#391—21no—
279#390C22×C1111yescharacteristic
280#390C22×C1111yescharacteristic
281#390C22×C1111yescharacteristic
282#389—21no—
283#389C22×C1111yescharacteristic
284#389C22×C1111yescharacteristic
285#389C22×C1111yescharacteristic
286#388—21no—
287#388—21no—
288#382C22×C1111yescharacteristic
289C4×C4⋊C4—21no—
290C4×C4⋊C4C22×C1111yescharacteristic
291C4×C4⋊C4C22×C1111yescharacteristic
292C4×C4⋊C4C22×C1111yescharacteristic
293C4×C4⋊C4C22×C1111yescharacteristic
294C4×C4⋊C4C22×C1111yescharacteristic
295#340C22×C1111yescharacteristic
296#340C22×C1111yescharacteristic
297#340C22×C1111yescharacteristic
298#340C22×C1111yescharacteristic
299#340C22×C1111yescharacteristic
300#340C22×C1111yescharacteristic
301#340C22×C1111yescharacteristic
302#340C22×C1111yescharacteristic
303#336C22×C1111yescharacteristic
304#336C22×C1111yescharacteristic
305#336C22×C1111yescharacteristic
306#336C22×C1111yescharacteristic
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11#52511yescharacteristic
315C22×C11#54711yescharacteristic
316C22×C11#54811yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×#13711yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57611yescharacteristic
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11#52911yescharacteristic
335C4×C11#54111yescharacteristic
336C4×C11#55611yescharacteristic
337C4×C11#55611yescharacteristic
338C22×Q8—21no—
339C22×D4C23×C1111yescharacteristic
340C22×C8C23×C1111yescharacteristic
341C22×C8C23×C1111yescharacteristic
342C22×C8C23×C1111yescharacteristic
343C22×C8C23×C1111yescharacteristic
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C4⋊C4D4×C1111yescharacteristic
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C4⋊C4C23×C1111yescharacteristic
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42C23×C1111yescharacteristic
370C2×C42C23×C1111yescharacteristic
371C2×C42C23×C1111yescharacteristic
372#107—22no—
373#107—22no—
374#107—22no—
375#106—22no—
376C4⋊C8—22no—
377#102—22no—
378#102—22no—
379#102—22no—
380#102—22no—
381C4×C8—22no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95D4×C1111yescharacteristic
392#95D4×C1111yescharacteristic
393C2×C11—161no—
394C2×C11#246911yescharacteristic
395C2×C11#310811yescharacteristic
396C2×C11#312211yescharacteristic
397C2×C11#334111yescharacteristic
398C2×C11#334611yescharacteristic
399C2×C11#336111yescharacteristic
400C2×C11#337511yescharacteristic
401C24—21no—
402C2×Q8—24no—
403C2×Q8—81no—
404C2×Q8—81no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C24×C1111yescharacteristic
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8C11×#4112yes—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—81no—
452C4⋊C4—81no—
453C4⋊C4—81no—
454C4⋊C4C11×#4112yes—
455C4⋊C4C11×#4112yes—
456C4⋊C4C11×#4112yes—
457C22⋊C4—42no—
458C22⋊C4—42no—
459C22⋊C4—81no—
460C22⋊C4—81no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—42no—
470C42—81no—
471C42—81no—
472C42—81no—
473C11#2713311yescharacteristic, direct product factor, Sylow
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×D4×C1111yescharacteristic
482Q8—84no—
483D4—41no—
484D4—41no—
485D4—41no—
486D4—41no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
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×C4C11×#13512yes—
525C2×C4C11×#13712yes—
526C2×C4C2×C11×#4111yescharacteristic
527C2×C4C2×C11×#4111yescharacteristic
528C2×C4C2×C11×#4111yescharacteristic
529C2×C4C2×C11×#4111yescharacteristic
530C2×C4C11×2−1+411yescharacteristic
531C2×C4C11×2−1+411yescharacteristic
532C8—22no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C11×#52511yescharacteristic
544C22C11×#54711yescharacteristic
545C22C11×#54811yescharacteristic
546C22C2×C11×#13511yescharacteristic
547C22C2×C11×#13711yescharacteristic
548C22C11×#57611yescharacteristic
549C22C11×#57611yescharacteristic
550C4—22no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—42no—
556C4—41no—
557C4—42no—
558C4—42no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C11×#52911yescharacteristic
564C4C11×#54111yescharacteristic
565C4C11×#55611yescharacteristic
566C4C11×#55611yescharacteristic
567C2—161no—
568C2C11×#246911yescharacteristic
569C2C11×#310811yescharacteristic
570C2C11×#312211yescharacteristic
571C2C11×#334111yescharacteristic
572C2C11×#334611yescharacteristic
573C2C11×#336111yescharacteristic
574C2C11×#337511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×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×#2369C2semidirect
3. C11×#2101C2semidirect
5. C11×#2057C2semidirect
7. C11×#1949C2semidirect
12. C11×#1921C2semidirect
13. C11×#1920C2semidirect
14. C11×#1916C2semidirect
15. C4×C11×#107C2semidirect
114. #27133C11direct (N × H)
188. #2369C2×C11semidirect
189. #2101C2×C11semidirect
191. #2057C2×C11semidirect
193. #1949C2×C11semidirect
198. #1921C2×C11semidirect
199. #1920C2×C11semidirect
200. #1916C2×C11semidirect
201. C4×#107C2×C11semidirect
473. C11#27133direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25132
C11×#23692
C11×#21012
C11×#20672
C11×#20572
C11×#20232
C11×#19492
C11×#19342
C11×#19262
C11×#19252
C11×#19212
C11×#19202
C11×#19162
C4×C11×#1072
#2713311