Finite Group Databasebeta

← C11×#16295 #14593488

Subgroups — C11×#16295 #14593488

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#397C211yesmaximal, characteristic
2C2×C11×#396C211yesmaximal, characteristic
3C2×C11×#395C211yesmaximal, characteristic, complemented
4C2×C11×#393C211yesmaximal, characteristic
5C2×C11×#391C211yesmaximal, characteristic, complemented
6C2×C11×#388C211yesmaximal, characteristic
7C11×#1445C211yesmaximal, characteristic, complemented
8C11×#1442C211yesmaximal, characteristic, complemented
9C11×#1442C211yesmaximal, characteristic, complemented
10C11×#1441C211yesmaximal, characteristic, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C11×#1440C211yesmaximal, characteristic
13C11×#1440C211yesmaximal, characteristic
14C11×#1439C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C11×#397—24no—
32C11×#396—24no—
33C11×#395—24no—
34C11×#393—24no—
35C11×#391—24no—
36C11×#388—24no—
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C25×C11C2311yescharacteristic
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—41no—
64C22×Q8×C11—41no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4—41no—
113C2×C11×C22⋊C4—41no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4D414yes—
118C2×C42×C11—22no—
119C2×C42×C11—22no—
120C2×C42×C11—41no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—22no—
126C11×#95—22no—
127C11×#95—22no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134C11×#95—22no—
135C11×#95—41no—
136C11×#95—41no—
137C11×#95—41no—
138C11×#95—41no—
139C11×#95D414yes—
140C11×#95D414yes—
141#16295C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11C2×D412yes—
157C24×C11C2411yescharacteristic
158C2×Q8×C11—28no—
159C2×Q8×C11—44no—
160C2×Q8×C11—44no—
161C2×Q8×C11—44no—
162C2×Q8×C11—44no—
163C2×Q8×C11—44no—
164C2×Q8×C11—44no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11#4112yes—
260C22×C4×C11#4112yes—
261C22×C4×C11#4112yes—
262C22×C4×C11#4112yes—
263C11×C4⋊C4—44no—
264C11×C4⋊C4—44no—
265C11×C4⋊C4—44no—
266C11×C4⋊C4—44no—
267C11×C4⋊C4—44no—
268C11×C4⋊C4—44no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—44no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C11×C22⋊C4—44no—
274C11×C22⋊C4—44no—
275C11×C22⋊C4—44no—
276C42×C11—44no—
277C2×#397C2×C1111yescharacteristic
278C2×#396C2×C1111yescharacteristic
279C2×#395C2×C1111yescharacteristic, complemented
280C2×#393C2×C1111yescharacteristic
281C2×#391C2×C1111yescharacteristic, complemented
282C2×#388C2×C1111yescharacteristic
283#1445C2×C1111yescharacteristic, complemented
284#1442C2×C1111yescharacteristic, complemented
285#1442C2×C1111yescharacteristic, complemented
286#1441C2×C1111yescharacteristic, complemented
287#1441C2×C1111yescharacteristic, complemented
288#1440C2×C1111yescharacteristic
289#1440C2×C1111yescharacteristic
290#1439C2×C1111yescharacteristic
291#1436C2×C1111yescharacteristic, complemented
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11C22×D411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C112−1+411yescharacteristic
338C23×C112−1+411yescharacteristic
339C23×C112−1+411yescharacteristic
340C23×C112−1+411yescharacteristic
341C23×C112−1+411yescharacteristic
342Q8×C11—416no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11#12114yes—
441C23×Q8C22×C1111yescharacteristic
442C22×C4⋊C4C22×C1111yescharacteristic
443C22×C4⋊C4C22×C1111yescharacteristic
444C22×C4⋊C4C22×C1111yescharacteristic
445C22×C4⋊C4C22×C1111yescharacteristic
446C22×C4⋊C4C22×C1111yescharacteristic
447C22×C4⋊C4C22×C1111yescharacteristic
448C22×C22⋊C4C22×C1111yescharacteristic
449C22×C22⋊C4C22×C1111yescharacteristic
450C22×C22⋊C4C22×C1111yescharacteristic
451C22×C22⋊C4C22×C1111yescharacteristic
452C22×C22⋊C4C22×C1111yescharacteristic
453C22×C22⋊C4C22×C1111yescharacteristic
454C22×C22⋊C4C22×C1111yescharacteristic
455C22×C42C22×C1111yescharacteristic
456#397—24no—
457#396—24no—
458#395—24no—
459#393—24no—
460#391—24no—
461#388—24no—
462C2×#95C22×C1111yescharacteristic
463C2×#95C22×C1111yescharacteristic
464C2×#95C22×C1111yescharacteristic
465C2×#95C22×C1111yescharacteristic
466C2×#95C22×C1111yescharacteristic
467C2×#95C22×C1111yescharacteristic
468C2×#95C22×C1111yescharacteristic
469C2×#95C22×C1111yescharacteristic
470C2×#95C22×C1111yescharacteristic
471C2×#95C22×C1111yescharacteristic
472C2×#95C22×C1111yescharacteristic
473C2×#95C22×C1111yescharacteristic
474C2×#95C22×C1111yescharacteristic
475C2×#95C22×C1111yescharacteristic
476C2×#95C22×C1111yescharacteristic
477C2×#95C22×C1111yescharacteristic
478C2×#95C22×C1111yescharacteristic
479C2×#95C22×C1111yescharacteristic
480C2×#95C22×C1111yescharacteristic
481C2×#95C22×C1111yescharacteristic
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11—81no—
496C22×C11—81no—
497C22×C11C2×#12111yescharacteristic
498C22×C11#52511yescharacteristic
499C22×C11#52911yescharacteristic
500C22×C11#53611yescharacteristic
501C22×C11#53611yescharacteristic
502C22×C11#53611yescharacteristic
503C22×C11#53611yescharacteristic
504C22×C11#53611yescharacteristic
505C22×C11#53711yescharacteristic
506C22×C11#53811yescharacteristic
507C22×C11#53911yescharacteristic
508C22×C11#54111yescharacteristic
509C22×C11#54111yescharacteristic
510C22×C11#54111yescharacteristic
511C22×C11#54211yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11#54211yescharacteristic
515C22×C11#54211yescharacteristic
516C22×C11D4211yescharacteristic
517C22×C11D4211yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54611yescharacteristic
520C22×C11#54611yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54711yescharacteristic
523C22×C11#54711yescharacteristic
524C22×C11#54811yescharacteristic
525C22×C11#54811yescharacteristic
526C22×C11#55611yescharacteristic
527C22×C11#55611yescharacteristic
528C22×C11#56211yescharacteristic
529C22×C11#56211yescharacteristic
530C22×C11#56311yescharacteristic
531C22×C11#56311yescharacteristic
532C4×C11—24no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—81no—
543C4×C11—81no—
544C4×C11—81no—
545C4×C11—81no—
546C25C23×C1111yescharacteristic
547C22×Q8—22no—
548C22×Q8—22no—
549C22×Q8—22no—
550C22×Q8—22no—
551C22×Q8—22no—
552C22×Q8—41no—
553C22×Q8—41no—
554C23×C4C23×C1111yescharacteristic
555C23×C4C23×C1111yescharacteristic
556C23×C4C23×C1111yescharacteristic
557C23×C4C23×C1111yescharacteristic
558C23×C4C23×C1111yescharacteristic
559C23×C4C23×C1111yescharacteristic
560C23×C4C23×C1111yescharacteristic
561C23×C4C23×C1111yescharacteristic
562C23×C4C23×C1111yescharacteristic
563C23×C4C23×C1111yescharacteristic
564C23×C4C23×C1111yescharacteristic
565C23×C4C23×C1111yescharacteristic
566C23×C4C23×C1111yescharacteristic
567C23×C4C23×C1111yescharacteristic
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4D4×C1114yes—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—41no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95D4×C1114yes—
629#95D4×C1114yes—
630C2×C11—82no—
631C2×C11#242411yescharacteristic
632C2×C11#242711yescharacteristic
633C2×C11#246911yescharacteristic
634C2×C11#262111yescharacteristic
635C2×C11#263711yescharacteristic
636C2×C11#265011yescharacteristic
637C2×C11#267211yescharacteristic
638C2×C11#267411yescharacteristic
639C2×C11#267411yescharacteristic
640C2×C11#268111yescharacteristic
641C2×C11#268911yescharacteristic
642C2×C11#270011yescharacteristic
643C2×C11#270011yescharacteristic
644C2×C11#271611yescharacteristic
645C2×C11#283111yescharacteristic
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24C2×D4×C1112yes—
661C24C24×C1111yescharacteristic
662C2×Q8—28no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4C2×D4×C1112yes—
756C22×C4C2×D4×C1112yes—
757C22×C4C2×D4×C1112yes—
758C22×C4C2×D4×C1112yes—
759C22×C4C2×D4×C1112yes—
760C22×C4C2×D4×C1112yes—
761C22×C4C2×D4×C1112yes—
762C22×C4C2×D4×C1112yes—
763C22×C4C11×#4112yes—
764C22×C4C11×#4112yes—
765C22×C4C11×#4112yes—
766C22×C4C11×#4112yes—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C22⋊C4—28no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C42—44no—
781C11#1629511yescharacteristic, direct product factor, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23C22×D4×C1111yescharacteristic
818C23C22×D4×C1111yescharacteristic
819C23C22×D4×C1111yescharacteristic
820C23C2×C11×#4111yescharacteristic
821C23C2×C11×#4111yescharacteristic
822C23C2×C11×#4111yescharacteristic
823C23C2×C11×#4111yescharacteristic
824C23C11×H(5,𝔽2)11yescharacteristic
825C23C11×H(5,𝔽2)11yescharacteristic
826C23C11×H(5,𝔽2)11yescharacteristic
827C23C11×2−1+411yescharacteristic
828C23C11×2−1+411yescharacteristic
829C23C11×2−1+411yescharacteristic
830C23C11×2−1+411yescharacteristic
831C23C11×2−1+411yescharacteristic
832Q8—416no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4C11×#12114yes—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22C2×C11×#12111yescharacteristic
947C22C11×#52511yescharacteristic
948C22C11×#52911yescharacteristic
949C22C11×#53611yescharacteristic
950C22C11×#53611yescharacteristic
951C22C11×#53611yescharacteristic
952C22C11×#53611yescharacteristic
953C22C11×#53611yescharacteristic
954C22C11×#53711yescharacteristic
955C22C11×#53811yescharacteristic
956C22C11×#53911yescharacteristic
957C22C11×#54111yescharacteristic
958C22C11×#54111yescharacteristic
959C22C11×#54111yescharacteristic
960C22C11×#54211yescharacteristic
961C22C11×#54211yescharacteristic
962C22C11×#54211yescharacteristic
963C22C11×#54211yescharacteristic
964C22C11×#54211yescharacteristic
965C22D42×C1111yescharacteristic
966C22D42×C1111yescharacteristic
967C22C11×#54611yescharacteristic
968C22C11×#54611yescharacteristic
969C22C11×#54611yescharacteristic
970C22C11×#54611yescharacteristic
971C22C11×#54711yescharacteristic
972C22C11×#54711yescharacteristic
973C22C11×#54811yescharacteristic
974C22C11×#54811yescharacteristic
975C22C11×#55611yescharacteristic
976C22C11×#55611yescharacteristic
977C22C11×#56211yescharacteristic
978C22C11×#56211yescharacteristic
979C22C11×#56311yescharacteristic
980C22C11×#56311yescharacteristic
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—81no—
995C2—82no—
996C2C11×#242411yescharacteristic
997C2C11×#242711yescharacteristic
998C2C11×#246911yescharacteristic
999C2C11×#262111yescharacteristic
1000C2C11×#263711yescharacteristic
1001C2C11×#265011yescharacteristic
1002C2C11×#267211yescharacteristic
1003C2C11×#267411yescharacteristic
1004C2C11×#267411yescharacteristic
1005C2C11×#268111yescharacteristic
1006C2C11×#268911yescharacteristic
1007C2C11×#270011yescharacteristic
1008C2C11×#270011yescharacteristic
1009C2C11×#271611yescharacteristic
1010C2C11×#283111yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#395C2semidirect
5. C2×C11×#391C2semidirect
7. C11×#1445C2semidirect
8. C11×#1442C2semidirect
9. C11×#1442C2semidirect
10. C11×#1441C2semidirect
11. C11×#1441C2semidirect
15. C11×#1436C2semidirect
141. #16295C11direct (N × H)
279. C2×#395C2×C11semidirect
281. C2×#391C2×C11semidirect
283. #1445C2×C11semidirect
284. #1442C2×C11semidirect
285. #1442C2×C11semidirect
286. #1441C2×C11semidirect
287. #1441C2×C11semidirect
291. #1436C2×C11semidirect
781. C11#16295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3972
C2×C11×#3962
C2×C11×#3952
C2×C11×#3932
C2×C11×#3912
C2×C11×#3882
C11×#14452
C11×#14422
C11×#14412
C11×#14402
C11×#14392
C11×#14362
#1629511