Finite Group Databasebeta

← C11×#18415 #14595608

Subgroups — C11×#18415 #14595608

Order 2816.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3534C211yesmaximal, characteristic
2C11×#3196C211yesmaximal, characteristic, complemented
3C11×#3187C211yesmaximal, characteristic, complemented
4C11×#2663C211yesmaximal, characteristic, complemented
5C11×#1618C211yesmaximal, characteristic, complemented
6C11×#1616C211yesmaximal, characteristic, complemented
7C11×#1615C211yesmaximal, characteristic, complemented
8C11×#1613C211yesmaximal, characteristic, complemented
9C11×#1606C211yesmaximal, characteristic, complemented
10C11×#1604C211yesmaximal, characteristic, complemented
11C11×#1603C211yesmaximal, characteristic, complemented
12C11×#1601C211yesmaximal, characteristic, complemented
13C11×#1507C211yesmaximal, characteristic, complemented
14C11×#1501C211yesmaximal, characteristic, complemented
15C11×#1468C211yesmaximal, characteristic, complemented
16C11×#562—21no—
17C11×#560—21no—
18C11×#553—21no—
19C11×#551—21no—
20C11×#546—21no—
21C11×#546—21no—
22C11×#546—21no—
23D42×C11—21no—
24C11×#540—21no—
25C11×#539—21no—
26C11×#539C2211yescharacteristic
27C11×#538—21no—
28C11×#538C2211yescharacteristic
29C11×#537C2211yescharacteristic
30C11×#534—21no—
31C11×#534C2211yescharacteristic
32C11×#525C2211yescharacteristic
33C2×C11×#123C2211yescharacteristic
34C2×C11×C22⋊Q8C2211yescharacteristic, complemented
35C2×C11×#121C2211yescharacteristic
36C11×#485—21no—
37C11×#484C2211yescharacteristic, complemented
38C11×#483—21no—
39C11×#481C2211yescharacteristic
40C11×#481C2211yescharacteristic, complemented
41C11×#481C2211yescharacteristic, complemented
42C11×#470—21no—
43C11×#468—21no—
44C11×#465—21no—
45C11×#465—21no—
46C11×#452—21no—
47C11×#451C2211yescharacteristic, complemented
48C11×#450—21no—
49C11×#448C2211yescharacteristic
50C11×#448C2211yescharacteristic, complemented
51C11×#448C2211yescharacteristic, complemented
52C11×#407C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#400C2211yescharacteristic, complemented
55C11×#399C2211yescharacteristic, complemented
56C11×#397—21no—
57C11×#395C2211yescharacteristic, complemented
58C11×#394—21no—
59C11×#393C2211yescharacteristic, complemented
60C11×#389—21no—
61C11×#388—21no—
62C4×C11×C22⋊C4C2211yescharacteristic, complemented
63C11×#328C2211yescharacteristic, complemented
64C11×#328C2211yescharacteristic, complemented
65C11×#327C2211yescharacteristic
66C11×#327C2211yescharacteristic
67C11×#327C2211yescharacteristic, complemented
68C11×#327C2211yescharacteristic, complemented
69C11×#327C2211yescharacteristic, complemented
70C11×#327C2211yescharacteristic, complemented
71C11×#324C2211yescharacteristic, complemented
72C11×#324C2211yescharacteristic, complemented
73C11×#323C2211yescharacteristic, complemented
74C11×#323C2211yescharacteristic, complemented
75C2×C11×#41—21no—
76C2×C11×#41D411yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11D411yescharacteristic
82C22×D4×C11D411yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C2×C11×Q16—21no—
85C2×C11×SD16—21no—
86C2×C11×SD16—21no—
87C2×C11×SD16—21no—
88C2×C11×M16—21no—
89C22×C8×C11—21no—
90C11×#127—21no—
91C11×#126—21no—
92C11×#126—21no—
93C11×#126—21no—
94C11×#126—21no—
95C11×#125—21no—
96C11×#125—21no—
97C11×#124—21no—
98C11×#124—21no—
99C11×#124—21no—
100C11×#123—21no—
101C11×#123—21no—
102C11×#123—21no—
103C11×#123—21no—
104C11×#123—21no—
105C11×#123—21no—
106C11×#123—21no—
107C11×#123—21no—
108C11×#123—21no—
109C11×#123—21no—
110C11×#123—21no—
111C11×#123—21no—
112C11×#123—21no—
113C11×#123—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8D411yescharacteristic
124C11×C22⋊Q8C2311yescharacteristic
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—21no—
130C11×#121—21no—
131C11×#121—21no—
132C11×#121—21no—
133C11×#121—21no—
134C11×#121—21no—
135C11×#121—21no—
136C11×#121—21no—
137C11×#121—21no—
138C11×#121—21no—
139C11×#121—21no—
140C11×#121D411yescharacteristic
141C11×#121D411yescharacteristic
142C11×#121D411yescharacteristic
143C11×#121C2311yescharacteristic
144C11×#121C2311yescharacteristic
145C11×#121C2311yescharacteristic
146C11×#120—21no—
147C11×#120—21no—
148C11×#120—21no—
149C11×#120—21no—
150C11×#120—21no—
151C11×#120—21no—
152C11×#120—21no—
153C11×#120—21no—
154C4×D4×C11—21no—
155C4×D4×C11—21no—
156C4×D4×C11—21no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11—21no—
160C4×D4×C11—21no—
161C4×D4×C11—21no—
162C11×#117—21no—
163C11×#117D411yescharacteristic
164C2×C11×C4⋊C4—21no—
165C2×C11×C4⋊C4—21no—
166C2×C11×C4⋊C4—21no—
167C2×C11×C4⋊C4D411yescharacteristic
168C2×C11×C4⋊C4D411yescharacteristic
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4—21no—
172C2×C11×C22⋊C4—21no—
173C2×C11×C22⋊C4—21no—
174C2×C11×C22⋊C4—21no—
175C2×C11×C22⋊C4—21no—
176C2×C11×C22⋊C4—21no—
177C2×C11×C22⋊C4—21no—
178C2×C11×C22⋊C4D411yescharacteristic
179C2×C11×C22⋊C4D411yescharacteristic
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C42×C11—21no—
182C11×#107—21no—
183C11×#106—21no—
184C11×#106—21no—
185C11×#106—21no—
186C11×#103—21no—
187C11×#103—21no—
188C11×#103—21no—
189C11×#103—21no—
190C11×#103—21no—
191C11×#102—21no—
192C11×#102—21no—
193C11×#102—21no—
194C11×C22⋊C8—21no—
195C11×C22⋊C8—21no—
196C11×C22⋊C8C2311yescharacteristic
197C11×C22⋊C8C2311yescharacteristic
198C11×C22⋊C8C2311yescharacteristic
199C11×C22⋊C8C2311yescharacteristic
200C11×#95—21no—
201C11×#95—21no—
202C11×#95—21no—
203C11×#95—21no—
204C11×#95C2311yescharacteristic
205C11×#95C2311yescharacteristic
206#18415C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—21no—
208C24×C11—21no—
209C24×C11C2×D411yescharacteristic
210C24×C11C2×D411yescharacteristic
211C11×#41—81no—
212C11×#41—81no—
213C11×#41—81no—
214C2×Q8×C11—21no—
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—81no—
218C2×Q8×C11C2×D411yescharacteristic
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—81no—
237C2×D4×C11—81no—
238C2×D4×C11—81no—
239C2×D4×C11—81no—
240C2×D4×C11—81no—
241C2×D4×C11—81no—
242C2×D4×C11—82no—
243C2×D4×C11C2×D411yescharacteristic
244C2×D4×C11C2×D411yescharacteristic
245C2×D4×C11C2×D411yescharacteristic
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—81no—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C11×Q16—81no—
268C11×SD16—81no—
269C11×SD16—81no—
270C11×SD16—81no—
271C11×M16—81no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—21no—
276C2×C8×C11—81no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—42no—
293C11×C4⋊C4—41no—
294C11×C4⋊C4—41no—
295C11×C4⋊C4—81no—
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D411yescharacteristic
299C11×C4⋊C4C2×D411yescharacteristic
300C11×C22⋊C4—21no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—21no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—21no—
316C11×C22⋊C4—21no—
317C11×C22⋊C4—21no—
318C11×C22⋊C4—21no—
319C11×C22⋊C4—21no—
320C11×C22⋊C4—21no—
321C11×C22⋊C4—21no—
322C11×C22⋊C4—21no—
323C11×C22⋊C4—21no—
324C11×C22⋊C4—21no—
325C11×C22⋊C4—42no—
326C11×C22⋊C4—42no—
327C11×C22⋊C4—41no—
328C11×C22⋊C4—41no—
329C11×C22⋊C4—81no—
330C42×C11—21no—
331C42×C11—21no—
332C42×C11—21no—
333C42×C11—81no—
334#3534C2×C1111yescharacteristic
335#3196C2×C1111yescharacteristic, complemented
336#3187C2×C1111yescharacteristic, complemented
337#2663C2×C1111yescharacteristic, complemented
338#1618C2×C1111yescharacteristic, complemented
339#1616C2×C1111yescharacteristic, complemented
340#1615C2×C1111yescharacteristic, complemented
341#1613C2×C1111yescharacteristic, complemented
342#1606C2×C1111yescharacteristic, complemented
343#1604C2×C1111yescharacteristic, complemented
344#1603C2×C1111yescharacteristic, complemented
345#1601C2×C1111yescharacteristic, complemented
346#1507C2×C1111yescharacteristic, complemented
347#1501C2×C1111yescharacteristic, complemented
348#1468C2×C1111yescharacteristic, complemented
349C23×C11—21no—
350C23×C11—21no—
351C23×C11—21no—
352C23×C11—21no—
353C23×C11—21no—
354C23×C11—21no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—42no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—81no—
363C23×C11—81no—
364C23×C11—81no—
365C23×C11—81no—
366C23×C11—81no—
367C23×C11#12011yescharacteristic
368C23×C11#12011yescharacteristic
369C23×C11C22×D411yescharacteristic
370Q8×C11—41no—
371Q8×C11—41no—
372Q8×C11—41no—
373Q8×C11—41no—
374Q8×C11—41no—
375Q8×C11—81no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—41no—
379D4×C11—42no—
380D4×C11—42no—
381D4×C11—41no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—41no—
386D4×C11—41no—
387D4×C11—81no—
388D4×C11—81no—
389D4×C11—81no—
390D4×C11—81no—
391D4×C11—81no—
392D4×C11—81no—
393D4×C11—81no—
394D4×C11—81no—
395D4×C11—81no—
396D4×C11—81no—
397D4×C11—81no—
398D4×C11—81no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
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—81no—
430C2×C4×C11—81no—
431C2×C4×C11—81no—
432C2×C4×C11—81no—
433C2×C4×C11—81no—
434C2×C4×C11—81no—
435C2×C4×C11—81no—
436C2×C4×C11#12011yescharacteristic
437C2×C4×C11#12011yescharacteristic
438C2×C4×C11C22×D411yescharacteristic
439C2×C4×C11C22×D411yescharacteristic
440C8×C11—41no—
441C8×C11—41no—
442C8×C11—41no—
443C8×C11—41no—
444#562—21no—
445#560—21no—
446#553—21no—
447#551—21no—
448#546—21no—
449#546—21no—
450#546—21no—
451D42—21no—
452#540—21no—
453#539—21no—
454#539C22×C1111yescharacteristic
455#538—21no—
456#538C22×C1111yescharacteristic
457#537C22×C1111yescharacteristic
458#534—21no—
459#534C22×C1111yescharacteristic
460#525C22×C1111yescharacteristic
461C2×#123C22×C1111yescharacteristic
462C2×C22⋊Q8C22×C1111yescharacteristic, complemented
463C2×#121C22×C1111yescharacteristic
464#485—21no—
465#484C22×C1111yescharacteristic, complemented
466#483—21no—
467#481C22×C1111yescharacteristic
468#481C22×C1111yescharacteristic, complemented
469#481C22×C1111yescharacteristic, complemented
470#470—21no—
471#468—21no—
472#465—21no—
473#465—21no—
474#452—21no—
475#451C22×C1111yescharacteristic, complemented
476#450—21no—
477#448C22×C1111yescharacteristic
478#448C22×C1111yescharacteristic, complemented
479#448C22×C1111yescharacteristic, complemented
480#407C22×C1111yescharacteristic, complemented
481C2×C22⋊C8C22×C1111yescharacteristic, complemented
482#400C22×C1111yescharacteristic, complemented
483#399C22×C1111yescharacteristic, complemented
484#397—21no—
485#395C22×C1111yescharacteristic, complemented
486#394—21no—
487#393C22×C1111yescharacteristic, complemented
488#389—21no—
489#388—21no—
490C4×C22⋊C4C22×C1111yescharacteristic, complemented
491#328C22×C1111yescharacteristic, complemented
492#328C22×C1111yescharacteristic, complemented
493#327C22×C1111yescharacteristic
494#327C22×C1111yescharacteristic
495#327C22×C1111yescharacteristic, complemented
496#327C22×C1111yescharacteristic, complemented
497#327C22×C1111yescharacteristic, complemented
498#327C22×C1111yescharacteristic, complemented
499#324C22×C1111yescharacteristic, complemented
500#324C22×C1111yescharacteristic, complemented
501#323C22×C1111yescharacteristic, complemented
502#323C22×C1111yescharacteristic, complemented
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—41no—
514C22×C11—41no—
515C22×C11—41no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—81no—
524C22×C11—81no—
525C22×C11—81no—
526C22×C11—81no—
527C22×C11—162no—
528C22×C11—162no—
529C22×C11C2×#12011yescharacteristic
530C22×C11#57711yescharacteristic
531C22×C11#57711yescharacteristic
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—42no—
537C4×C11—41no—
538C4×C11—41no—
539C4×C11—41no—
540C4×C11—41no—
541C4×C11—41no—
542C4×C11—41no—
543C4×C11—41no—
544C4×C11—41no—
545C4×C11—81no—
546C4×C11—81no—
547C4×C11—81no—
548C2×#41—21no—
549C2×#41D4×C1111yescharacteristic
550C22×Q8C23×C1111yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4D4×C1111yescharacteristic
555C22×D4D4×C1111yescharacteristic
556C23×C4C23×C1111yescharacteristic
557C2×Q16—21no—
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×M16—21no—
562C22×C8—21no—
563#127—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125—21no—
570#124—21no—
571#124—21no—
572#124—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8D4×C1111yescharacteristic
597C22⋊Q8C23×C1111yescharacteristic
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121D4×C1111yescharacteristic
614#121D4×C1111yescharacteristic
615#121D4×C1111yescharacteristic
616#121C23×C1111yescharacteristic
617#121C23×C1111yescharacteristic
618#121C23×C1111yescharacteristic
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624#120—21no—
625#120—21no—
626#120—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635#117—21no—
636#117D4×C1111yescharacteristic
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C1111yescharacteristic
641C2×C4⋊C4D4×C1111yescharacteristic
642C2×C4⋊C4C23×C1111yescharacteristic
643C2×C4⋊C4C23×C1111yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C1111yescharacteristic
652C2×C22⋊C4D4×C1111yescharacteristic
653C2×C22⋊C4C23×C1111yescharacteristic
654C2×C42—21no—
655#107—21no—
656#106—21no—
657#106—21no—
658#106—21no—
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#103—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8C23×C1111yescharacteristic
670C22⋊C8C23×C1111yescharacteristic
671C22⋊C8C23×C1111yescharacteristic
672C22⋊C8C23×C1111yescharacteristic
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95C23×C1111yescharacteristic
678#95C23×C1111yescharacteristic
679C2×C11—21no—
680C2×C11—21no—
681C2×C11—41no—
682C2×C11—41no—
683C2×C11—81no—
684C2×C11—81no—
685C2×C11—81no—
686C2×C11—81no—
687C2×C11#300911yescharacteristic
688C2×C11#301811yescharacteristic
689C2×C11#302611yescharacteristic
690C24—21no—
691C24—21no—
692C24C2×D4×C1111yescharacteristic
693C24C2×D4×C1111yescharacteristic
694#41—81no—
695#41—81no—
696#41—81no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—81no—
701C2×Q8C2×D4×C1111yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—82no—
726C2×D4C2×D4×C1111yescharacteristic
727C2×D4C2×D4×C1111yescharacteristic
728C2×D4C2×D4×C1111yescharacteristic
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—81no—
741C22×C4C2×D4×C1111yescharacteristic
742C22×C4C2×D4×C1111yescharacteristic
743C22×C4C2×D4×C1111yescharacteristic
744C22×C4C2×D4×C1111yescharacteristic
745C22×C4C2×D4×C1111yescharacteristic
746C22×C4C2×D4×C1111yescharacteristic
747C22×C4C2×D4×C1111yescharacteristic
748C22×C4C2×D4×C1111yescharacteristic
749C22×C4C24×C1111yescharacteristic
750Q16—81no—
751SD16—81no—
752SD16—81no—
753SD16—81no—
754M16—81no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—81no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—42no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4C2×D4×C1111yescharacteristic
780C4⋊C4C2×D4×C1111yescharacteristic
781C4⋊C4C2×D4×C1111yescharacteristic
782C4⋊C4C2×D4×C1111yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C42—21no—
814C42—21no—
815C42—21no—
816C42—81no—
817C11#1841511yescharacteristic, direct product factor, Sylow
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23C11×#12011yescharacteristic
837C23C11×#12011yescharacteristic
838C23C22×D4×C1111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
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—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4C11×#12011yescharacteristic
906C2×C4C11×#12011yescharacteristic
907C2×C4C22×D4×C1111yescharacteristic
908C2×C4C22×D4×C1111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×C11×#12011yescharacteristic
940C22C11×#57711yescharacteristic
941C22C11×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C11×#300911yescharacteristic
967C2C11×#301811yescharacteristic
968C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3196C2semidirect
3. C11×#3187C2semidirect
4. C11×#2663C2semidirect
5. C11×#1618C2semidirect
6. C11×#1616C2semidirect
7. C11×#1615C2semidirect
8. C11×#1613C2semidirect
9. C11×#1606C2semidirect
10. C11×#1604C2semidirect
11. C11×#1603C2semidirect
12. C11×#1601C2semidirect
13. C11×#1507C2semidirect
14. C11×#1501C2semidirect
15. C11×#1468C2semidirect
34. C2×C11×C22⋊Q8C22semidirect
37. C11×#484C22semidirect
40. C11×#481C22semidirect
41. C11×#481C22semidirect
47. C11×#451C22semidirect
50. C11×#448C22semidirect
51. C11×#448C22semidirect
52. C11×#407C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C11×#400C22semidirect
55. C11×#399C22semidirect
57. C11×#395C22semidirect
59. C11×#393C22semidirect
62. C4×C11×C22⋊C4C22semidirect
63. C11×#328C22semidirect
64. C11×#328C22semidirect
67. C11×#327C22semidirect
68. C11×#327C22semidirect
69. C11×#327C22semidirect
70. C11×#327C22semidirect
71. C11×#324C22semidirect
72. C11×#324C22semidirect
73. C11×#323C22semidirect
74. C11×#323C22semidirect
206. #18415C11direct (N × H)
335. #3196C2×C11semidirect
336. #3187C2×C11semidirect
337. #2663C2×C11semidirect
338. #1618C2×C11semidirect
339. #1616C2×C11semidirect
340. #1615C2×C11semidirect
341. #1613C2×C11semidirect
342. #1606C2×C11semidirect
343. #1604C2×C11semidirect
344. #1603C2×C11semidirect
345. #1601C2×C11semidirect
346. #1507C2×C11semidirect
347. #1501C2×C11semidirect
348. #1468C2×C11semidirect
462. C2×C22⋊Q8C22×C11semidirect
465. #484C22×C11semidirect
468. #481C22×C11semidirect
469. #481C22×C11semidirect
475. #451C22×C11semidirect
478. #448C22×C11semidirect
479. #448C22×C11semidirect
480. #407C22×C11semidirect
481. C2×C22⋊C8C22×C11semidirect
482. #400C22×C11semidirect
483. #399C22×C11semidirect
485. #395C22×C11semidirect
487. #393C22×C11semidirect
490. C4×C22⋊C4C22×C11semidirect
491. #328C22×C11semidirect
492. #328C22×C11semidirect
495. #327C22×C11semidirect
496. #327C22×C11semidirect
497. #327C22×C11semidirect
498. #327C22×C11semidirect
499. #324C22×C11semidirect
500. #324C22×C11semidirect
501. #323C22×C11semidirect
502. #323C22×C11semidirect
817. C11#18415direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35342
C11×#31962
C11×#31872
C11×#26632
C11×#16182
C11×#16162
C11×#16152
C11×#16132
C11×#16062
C11×#16042
C11×#16032
C11×#16012
C11×#15072
C11×#15012
C11×#14682
#1841511