Finite Group Databasebeta

← C11×#25002 #14602195

Subgroups — C11×#25002 #14602195

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2580C211yesmaximal, characteristic
2Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3C11×#2100C211yesmaximal, characteristic, complemented
4C11×#2099C211yesmaximal, characteristic, complemented
5C11×#2071C211yesmaximal, characteristic
6C11×#2071C211yesmaximal, characteristic
7C11×#1985C211yesmaximal, characteristic, complemented
8C11×#1949C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic
10C11×#1925C211yesmaximal, characteristic
11C11×#1921C211yesmaximal, characteristic, complemented
12C11×#1920C211yesmaximal, characteristic, complemented
13C11×#1836C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic
15C11×#1762C211yesmaximal, characteristic
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C11×#399—21no—
28C11×#393—21no—
29C11×#390C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#389—21no—
32C11×#389—21no—
33C11×#389—21no—
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#385—21no—
37C11×#385—21no—
38C11×#384C2211yescharacteristic
39C11×#384C2211yescharacteristic
40C11×#384C2211yescharacteristic
41C11×#382C2211yescharacteristic
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×Q8×C11—44no—
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⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×#107—22no—
101C11×#106—22no—
102C11×C4⋊C8—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—22no—
106C11×#102—22no—
107C11×#97—22no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115#25002C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11#4112yes—
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—21no—
133C22×C4×C11—42no—
134C22×C4×C11—81no—
135C22×C4×C11—81no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
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—
154C2×C8×C11—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
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—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4—81no—
178C11×C4⋊C4—81no—
179C11×C4⋊C4#4112yes—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C11×C22⋊C4—81no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11—42no—
191C42×C11—42no—
192C42×C11#4112yes—
193C42×C11#4112yes—
194#2580C2×C1111yescharacteristic
195Q8×C4⋊C4C2×C1111yescharacteristic, complemented
196#2100C2×C1111yescharacteristic, complemented
197#2099C2×C1111yescharacteristic, complemented
198#2071C2×C1111yescharacteristic
199#2071C2×C1111yescharacteristic
200#1985C2×C1111yescharacteristic, complemented
201#1949C2×C1111yescharacteristic, complemented
202#1926C2×C1111yescharacteristic
203#1925C2×C1111yescharacteristic
204#1921C2×C1111yescharacteristic, complemented
205#1920C2×C1111yescharacteristic, complemented
206#1836C2×C1111yescharacteristic, complemented
207#1802C2×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
217Q8×C11—28no—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—41no—
221D4×C11—41no—
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—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
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—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—84no—
258C2×C4×C11#12312yes—
259C2×C4×C11#12312yes—
260C2×C4×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11#13712yes—
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C2×C4×Q8—21no—
273C2×C4×Q8C22×C1111yescharacteristic
274C2×C4×D4C22×C1111yescharacteristic
275C2×#107C22×C1111yescharacteristic
276C2×#106C22×C1111yescharacteristic
277C2×C4⋊C8C22×C1111yescharacteristic
278C2×#102C22×C1111yescharacteristic
279C2×#102C22×C1111yescharacteristic
280C2×#102C22×C1111yescharacteristic
281C2×#102C22×C1111yescharacteristic
282C2×#97C22×C1111yescharacteristic
283#399—21no—
284#393—21no—
285#390C22×C1111yescharacteristic
286#390C22×C1111yescharacteristic
287#389—21no—
288#389—21no—
289#389—21no—
290#389C22×C1111yescharacteristic
291#389C22×C1111yescharacteristic
292#385—21no—
293#385—21no—
294#384C22×C1111yescharacteristic
295#384C22×C1111yescharacteristic
296#384C22×C1111yescharacteristic
297#382C22×C1111yescharacteristic
298C4×C4⋊C4C22×C1111yescharacteristic
299C4×C4⋊C4C22×C1111yescharacteristic
300C4×C4⋊C4C22×C1111yescharacteristic
301#340C22×C1111yescharacteristic
302#340C22×C1111yescharacteristic
303#340C22×C1111yescharacteristic
304#340C22×C1111yescharacteristic
305#340C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#340C22×C1111yescharacteristic
308#340C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#336C22×C1111yescharacteristic
312#336C22×C1111yescharacteristic
313#336C22×C1111yescharacteristic
314#336C22×C1111yescharacteristic
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11C2×#12311yescharacteristic
323C22×C11#54811yescharacteristic
324C22×C11#54811yescharacteristic
325C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C11C2×#13711yescharacteristic
327C22×C11#57611yescharacteristic
328C22×C11#57711yescharacteristic
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#52911yescharacteristic
343C4×C11#54111yescharacteristic
344C4×C11#55211yescharacteristic
345C4×C11#55611yescharacteristic
346C22×Q8D4×C1111yescharacteristic
347C22×D4C23×C1111yescharacteristic
348C23×C4—21no—
349C22×C8C23×C1111yescharacteristic
350C22×C8C23×C1111yescharacteristic
351C22×C8C23×C1111yescharacteristic
352C22×C8C23×C1111yescharacteristic
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—44no—
356C4×D4—22no—
357C4×D4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4D4×C1111yescharacteristic
367C2×C4⋊C4D4×C1111yescharacteristic
368C2×C4⋊C4D4×C1111yescharacteristic
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C4⋊C4C23×C1111yescharacteristic
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C4⋊C4C23×C1111yescharacteristic
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42C23×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386C2×C42C23×C1111yescharacteristic
387#107—22no—
388#106—22no—
389C4⋊C8—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#97—22no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402C2×C11—82no—
403C2×C11#242111yescharacteristic
404C2×C11#309211yescharacteristic
405C2×C11#309611yescharacteristic
406C2×C11#336611yescharacteristic
407C2×C11#337211yescharacteristic
408C2×C11#337311yescharacteristic
409C2×C11#337511yescharacteristic
410C24—21no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4C11×#4112yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—42no—
428C22×C4—81no—
429C22×C4—81no—
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×C8—21no—
448C2×C8—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
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—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4C11×#4112yes—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—42no—
484C42—42no—
485C42—42no—
486C42C11×#4112yes—
487C42C11×#4112yes—
488C11#2500211yescharacteristic, direct product factor, Sylow
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C22×D4×C1111yescharacteristic
497Q8—28no—
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
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—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—84no—
538C2×C4C11×#12312yes—
539C2×C4C11×#12312yes—
540C2×C4C11×AGL(1,ℤ/8)12yes—
541C2×C4C11×#13712yes—
542C2×C4C2×C11×#4111yescharacteristic
543C2×C4C2×C11×#4111yescharacteristic
544C2×C4C2×C11×#4111yescharacteristic
545C2×C4C2×C11×#4111yescharacteristic
546C2×C4C11×2−1+411yescharacteristic
547C2×C4C11×2−1+411yescharacteristic
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×C11×#12311yescharacteristic
560C22C11×#54811yescharacteristic
561C22C11×#54811yescharacteristic
562C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
563C22C2×C11×#13711yescharacteristic
564C22C11×#57611yescharacteristic
565C22C11×#57711yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C11×#52911yescharacteristic
580C4C11×#54111yescharacteristic
581C4C11×#55211yescharacteristic
582C4C11×#55611yescharacteristic
583C2—82no—
584C2C11×#242111yescharacteristic
585C2C11×#309211yescharacteristic
586C2C11×#309611yescharacteristic
587C2C11×#336611yescharacteristic
588C2C11×#337211yescharacteristic
589C2C11×#337311yescharacteristic
590C2C11×#337511yescharacteristic
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. Q8×C11×C4⋊C4C2semidirect
3. C11×#2100C2semidirect
4. C11×#2099C2semidirect
7. C11×#1985C2semidirect
8. C11×#1949C2semidirect
11. C11×#1921C2semidirect
12. C11×#1920C2semidirect
13. C11×#1836C2semidirect
115. #25002C11direct (N × H)
195. Q8×C4⋊C4C2×C11semidirect
196. #2100C2×C11semidirect
197. #2099C2×C11semidirect
200. #1985C2×C11semidirect
201. #1949C2×C11semidirect
204. #1921C2×C11semidirect
205. #1920C2×C11semidirect
206. #1836C2×C11semidirect
488. C11#25002direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25802
Q8×C11×C4⋊C42
C11×#21002
C11×#20992
C11×#20712
C11×#19852
C11×#19492
C11×#19262
C11×#19252
C11×#19212
C11×#19202
C11×#18362
C11×#18022
C11×#17622
#2500211