Finite Group Databasebeta

← C11×#27136 #14604329

Subgroups — C11×#27136 #14604329

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2513C211yesmaximal, characteristic
2C11×#2370C211yesmaximal, characteristic, complemented
3C11×#2101C211yesmaximal, characteristic, complemented
4C11×#2065C211yesmaximal, characteristic
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2025C211yesmaximal, characteristic
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1934C211yesmaximal, characteristic
9C11×#1926C211yesmaximal, characteristic
10C11×#1925C211yesmaximal, characteristic
11C11×#1925C211yesmaximal, characteristic
12C11×#1921C211yesmaximal, characteristic, complemented
13C11×#1918C211yesmaximal, characteristic, complemented
14C11×#1916C211yesmaximal, characteristic, complemented
15C4×C11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
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×#390C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#389—21no—
33C11×#389C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#388—21no—
38C11×#387—21no—
39C11×#387—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×D4×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#125—22no—
65C11×#125—22no—
66C2×C11×C4⋊C4—21no—
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×#106—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#27136C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×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×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
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#4112yes—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
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—41no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4#4112yes—
167C11×C4⋊C4#4112yes—
168C11×C4⋊C4#4112yes—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—81no—
172C11×C22⋊C4—81no—
173C11×C22⋊C4—81no—
174C11×C22⋊C4—81no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—42no—
182C42×C11—81no—
183C42×C11—81no—
184C42×C11—81no—
185#2513C2×C1111yescharacteristic
186#2370C2×C1111yescharacteristic, complemented
187#2101C2×C1111yescharacteristic, complemented
188#2065C2×C1111yescharacteristic
189#2059C2×C1111yescharacteristic, complemented
190#2025C2×C1111yescharacteristic
191#1949C2×C1111yescharacteristic, complemented
192#1934C2×C1111yescharacteristic
193#1926C2×C1111yescharacteristic
194#1925C2×C1111yescharacteristic
195#1925C2×C1111yescharacteristic
196#1921C2×C1111yescharacteristic, complemented
197#1918C2×C1111yescharacteristic, complemented
198#1916C2×C1111yescharacteristic, complemented
199C4×#106C2×C1111yescharacteristic, complemented
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C22×D411yescharacteristic
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
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—41no—
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#13512yes—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C8×C11—22no—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11—41no—
261C2×#125C22×C1111yescharacteristic
262C2×#107C22×C1111yescharacteristic
263C2×#107C22×C1111yescharacteristic
264C2×#106C22×C1111yescharacteristic
265C2×#106C22×C1111yescharacteristic
266C2×C4⋊C8C22×C1111yescharacteristic
267C2×#102C22×C1111yescharacteristic
268C2×#102C22×C1111yescharacteristic
269C2×#102C22×C1111yescharacteristic
270C2×#102C22×C1111yescharacteristic
271C2×C4×C8C22×C1111yescharacteristic
272#397—21no—
273#397—21no—
274#390C22×C1111yescharacteristic
275#390C22×C1111yescharacteristic
276#390C22×C1111yescharacteristic
277#389—21no—
278#389C22×C1111yescharacteristic
279#389C22×C1111yescharacteristic
280#389C22×C1111yescharacteristic
281#388—21no—
282#388—21no—
283#387—21no—
284#387—21no—
285#382C22×C1111yescharacteristic
286C4×C4⋊C4—21no—
287C4×C4⋊C4C22×C1111yescharacteristic
288C4×C4⋊C4C22×C1111yescharacteristic
289C4×C4⋊C4C22×C1111yescharacteristic
290C4×C4⋊C4C22×C1111yescharacteristic
291C4×C4⋊C4C22×C1111yescharacteristic
292#340C22×C1111yescharacteristic
293#340C22×C1111yescharacteristic
294#340C22×C1111yescharacteristic
295#340C22×C1111yescharacteristic
296#340C22×C1111yescharacteristic
297#340C22×C1111yescharacteristic
298#340C22×C1111yescharacteristic
299#340C22×C1111yescharacteristic
300#336C22×C1111yescharacteristic
301#336C22×C1111yescharacteristic
302#336C22×C1111yescharacteristic
303#336C22×C1111yescharacteristic
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11#52511yescharacteristic
312C22×C11#54711yescharacteristic
313C22×C11#54811yescharacteristic
314C22×C11C2×#13511yescharacteristic
315C22×C11#57511yescharacteristic
316C22×C11#57611yescharacteristic
317C22×C11#57711yescharacteristic
318C4×C11—22no—
319C4×C11—41no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—41no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11#52911yescharacteristic
332C4×C11#54111yescharacteristic
333C4×C11#55611yescharacteristic
334C4×C11#55611yescharacteristic
335C22×D4C23×C1111yescharacteristic
336C22×C8C23×C1111yescharacteristic
337C22×C8C23×C1111yescharacteristic
338C22×C8C23×C1111yescharacteristic
339C22×C8C23×C1111yescharacteristic
340#125—22no—
341#125—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4D4×C1111yescharacteristic
348C2×C4⋊C4D4×C1111yescharacteristic
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42C23×C1111yescharacteristic
367C2×C42C23×C1111yescharacteristic
368C2×C42C23×C1111yescharacteristic
369#107—22no—
370#107—22no—
371#106—22no—
372#106—22no—
373C4⋊C8—22no—
374#102—22no—
375#102—22no—
376#102—22no—
377#102—22no—
378C4×C8—22no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95D4×C1111yescharacteristic
389#95D4×C1111yescharacteristic
390C2×C11—161no—
391C2×C11#246911yescharacteristic
392C2×C11#310211yescharacteristic
393C2×C11#311911yescharacteristic
394C2×C11#333711yescharacteristic
395C2×C11#334711yescharacteristic
396C2×C11#336111yescharacteristic
397C2×C11#337111yescharacteristic
398C24—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C24×C1111yescharacteristic
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8C11×#4112yes—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—42no—
447C4⋊C4—81no—
448C4⋊C4—81no—
449C4⋊C4C11×#4112yes—
450C4⋊C4C11×#4112yes—
451C4⋊C4C11×#4112yes—
452C22⋊C4—42no—
453C22⋊C4—42no—
454C22⋊C4—81no—
455C22⋊C4—81no—
456C22⋊C4—81no—
457C22⋊C4—81no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—21no—
464C42—42no—
465C42—81no—
466C42—81no—
467C42—81no—
468C11#2713611yescharacteristic, direct product factor, Sylow
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C22×D4×C1111yescharacteristic
477D4—41no—
478D4—41no—
479D4—41no—
480D4—41no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
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—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
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×C4C11×#13512yes—
520C2×C4C2×C11×#4111yescharacteristic
521C2×C4C2×C11×#4111yescharacteristic
522C2×C4C2×C11×#4111yescharacteristic
523C2×C4C2×C11×#4111yescharacteristic
524C2×C4C11×2−1+411yescharacteristic
525C2×C4C11×2−1+411yescharacteristic
526C8—22no—
527C8—41no—
528C8—41no—
529C8—41no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22C11×#52511yescharacteristic
538C22C11×#54711yescharacteristic
539C22C11×#54811yescharacteristic
540C22C2×C11×#13511yescharacteristic
541C22C11×#57511yescharacteristic
542C22C11×#57611yescharacteristic
543C22C11×#57711yescharacteristic
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4C11×#52911yescharacteristic
558C4C11×#54111yescharacteristic
559C4C11×#55611yescharacteristic
560C4C11×#55611yescharacteristic
561C2—161no—
562C2C11×#246911yescharacteristic
563C2C11×#310211yescharacteristic
564C2C11×#311911yescharacteristic
565C2C11×#333711yescharacteristic
566C2C11×#334711yescharacteristic
567C2C11×#336111yescharacteristic
568C2C11×#337111yescharacteristic
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×#2370C2semidirect
3. C11×#2101C2semidirect
5. C11×#2059C2semidirect
7. C11×#1949C2semidirect
12. C11×#1921C2semidirect
13. C11×#1918C2semidirect
14. C11×#1916C2semidirect
15. C4×C11×#106C2semidirect
114. #27136C11direct (N × H)
186. #2370C2×C11semidirect
187. #2101C2×C11semidirect
189. #2059C2×C11semidirect
191. #1949C2×C11semidirect
196. #1921C2×C11semidirect
197. #1918C2×C11semidirect
198. #1916C2×C11semidirect
199. C4×#106C2×C11semidirect
468. C11#27136direct (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×#23702
C11×#21012
C11×#20652
C11×#20592
C11×#20252
C11×#19492
C11×#19342
C11×#19262
C11×#19252
C11×#19212
C11×#19182
C11×#19162
C4×C11×#1062
#2713611