Finite Group Databasebeta

← C11×#18416 #14595609

Subgroups — C11×#18416 #14595609

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3535C211yesmaximal, characteristic, complemented
2C11×#3194C211yesmaximal, characteristic, complemented
3C11×#3187C211yesmaximal, characteristic, complemented
4C11×#2661C211yesmaximal, characteristic, complemented
5C11×#1612C211yesmaximal, characteristic, complemented
6C11×#1611C211yesmaximal, characteristic, complemented
7C11×#1609C211yesmaximal, characteristic, complemented
8C11×#1608C211yesmaximal, characteristic, complemented
9C11×#1600C211yesmaximal, characteristic, complemented
10C11×#1599C211yesmaximal, characteristic, complemented
11C11×#1597C211yesmaximal, characteristic, complemented
12C11×#1596C211yesmaximal, characteristic, complemented
13C11×#1508C211yesmaximal, characteristic, complemented
14C11×#1501C211yesmaximal, characteristic, complemented
15C11×#1468C211yesmaximal, characteristic, complemented
16C11×#563—21no—
17C11×#562—21no—
18C11×#554—21no—
19C11×#552—21no—
20C11×#551—21no—
21C11×#551—21no—
22C11×#547—21no—
23C11×#546—21no—
24C11×#544C2211yescharacteristic
25C11×#543C2211yescharacteristic
26C11×#542—21no—
27C11×#539—21no—
28C11×#539—21no—
29C11×#539C2211yescharacteristic
30C11×#538C2211yescharacteristic
31C11×#536—21no—
32C11×#525C2211yescharacteristic
33C2×C11×#123C2211yescharacteristic
34C2×C11×C22⋊Q8C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic
36C11×#483C2211yescharacteristic
37C11×#483C2211yescharacteristic
38C11×#483C2211yescharacteristic
39C11×#482—21no—
40C11×#481—21no—
41C11×#480C2211yescharacteristic
42C11×#469—21no—
43C11×#468—21no—
44C11×#465—21no—
45C11×#465—21no—
46C11×#450C2211yescharacteristic
47C11×#450C2211yescharacteristic
48C11×#450C2211yescharacteristic
49C11×#449—21no—
50C11×#448—21no—
51C11×#447C2211yescharacteristic
52C11×#407C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#398C2211yescharacteristic
55C11×#397C2211yescharacteristic
56C11×#394—21no—
57C11×#394C2211yescharacteristic
58C11×#392—21no—
59C11×#392C2211yescharacteristic
60C11×#390—21no—
61C11×#388—21no—
62C4×C11×C22⋊C4C2211yescharacteristic
63C11×#328C2211yescharacteristic
64C11×#328C2211yescharacteristic
65C11×#328C2211yescharacteristic
66C11×#328C2211yescharacteristic
67C11×#328C2211yescharacteristic
68C11×#328C2211yescharacteristic
69C11×#327C2211yescharacteristic
70C11×#327C2211yescharacteristic
71C11×#324C2211yescharacteristic
72C11×#324C2211yescharacteristic
73C11×#323C2211yescharacteristic
74C11×#323C2211yescharacteristic
75C2×C11×#41—21no—
76C2×C11×#41D411yescharacteristic, complemented
77C22×Q8×C11D411yescharacteristic, complemented
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×SD16—21no—
86C2×C11×D8—21no—
87C2×C11×M16—21no—
88C22×C8×C11—21no—
89C11×C4⋊Q8—21no—
90C11×C4⋊Q8—21no—
91C11×C4⋊Q8—21no—
92C11×#126—21no—
93C11×#126—21no—
94C11×#126—21no—
95C11×#126—21no—
96C11×#126—21no—
97C11×#126—21no—
98C11×#125—21no—
99C11×#125—21no—
100C11×#125—21no—
101C11×#125—21no—
102C11×#125—21no—
103C11×#124—21no—
104C11×#124—21no—
105C11×#124—21no—
106C11×#124—21no—
107C11×#123—21no—
108C11×#123—21no—
109C11×#123—21no—
110C11×#123—21no—
111C11×#123—21no—
112C11×#123—21no—
113C11×#123—21no—
114C11×#123—21no—
115C11×#123—21no—
116C11×#123—21no—
117C11×#123—21no—
118C11×#123—21no—
119C11×#123—21no—
120C11×#123—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—21no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8—21no—
131C11×C22⋊Q8—21no—
132C11×C22⋊Q8—21no—
133C11×C22⋊Q8—21no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8D411yescharacteristic, complemented
136C11×C22⋊Q8D411yescharacteristic, complemented
137C11×C22⋊Q8D411yescharacteristic, complemented
138C11×C22⋊Q8C2311yescharacteristic
139C11×C22⋊Q8C2311yescharacteristic
140C11×C22⋊Q8C2311yescharacteristic
141C11×#121—21no—
142C11×#121—21no—
143C11×#121—21no—
144C11×#121—21no—
145C11×#121—21no—
146C11×#121—21no—
147C11×#121—21no—
148C11×#121—21no—
149C11×#121D411yescharacteristic, complemented
150C11×#121C2311yescharacteristic
151C11×#120—21no—
152C11×#120—21no—
153C4×Q8×C11—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—
161C11×#117—21no—
162C11×#117—21no—
163C11×#117—21no—
164C11×#117D411yescharacteristic, complemented
165C2×C11×C4⋊C4—21no—
166C2×C11×C4⋊C4—21no—
167C2×C11×C4⋊C4—21no—
168C2×C11×C4⋊C4D411yescharacteristic
169C2×C11×C4⋊C4D411yescharacteristic, complemented
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4D411yescharacteristic
181C2×C11×C22⋊C4D411yescharacteristic
182C2×C11×C22⋊C4C2311yescharacteristic
183C2×C42×C11—21no—
184C11×#107—21no—
185C11×#106—21no—
186C11×#106—21no—
187C11×#106—21no—
188C11×#103—21no—
189C11×#103—21no—
190C11×#103—21no—
191C11×#102—21no—
192C11×#102—21no—
193C11×#102—21no—
194C11×#102—21no—
195C11×#102—21no—
196C11×C22⋊C8—21no—
197C11×C22⋊C8—21no—
198C11×C22⋊C8C2311yescharacteristic
199C11×C22⋊C8C2311yescharacteristic
200C11×C22⋊C8C2311yescharacteristic
201C11×C22⋊C8C2311yescharacteristic
202C11×#95—21no—
203C11×#95—21no—
204C11×#95C2311yescharacteristic
205C11×#95C2311yescharacteristic
206#18416C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—21no—
208C24×C11C2×D411yescharacteristic
209C24×C11C2×D411yescharacteristic
210C11×#41—82no—
211C11×#41—81no—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—21no—
215C2×Q8×C11—81no—
216C2×Q8×C11C2×D411yescharacteristic
217C2×Q8×C11C2×D411yescharacteristic
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—42no—
229C2×D4×C11—41no—
230C2×D4×C11—41no—
231C2×D4×C11—81no—
232C2×D4×C11—81no—
233C2×D4×C11—81no—
234C2×D4×C11—81no—
235C2×D4×C11—81no—
236C2×D4×C11—81no—
237C2×D4×C11C2×D411yescharacteristic
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—81no—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C11×SD16—81no—
259C11×SD16—81no—
260C11×SD16—81no—
261C11×D8—81no—
262C11×M16—81no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—81no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
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—21no—
293C11×C4⋊C4—81no—
294C11×C4⋊C4C2×D411yescharacteristic
295C11×C4⋊C4C2×D411yescharacteristic
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
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—42no—
322C11×C22⋊C4—42no—
323C11×C22⋊C4—41no—
324C11×C22⋊C4—41no—
325C11×C22⋊C4—81no—
326C11×C22⋊C4—81no—
327C11×C22⋊C4—81no—
328C42×C11—21no—
329C42×C11—21no—
330C42×C11—21no—
331C42×C11—21no—
332C42×C11—21no—
333C42×C11—81no—
334#3535C2×C1111yescharacteristic, complemented
335#3194C2×C1111yescharacteristic, complemented
336#3187C2×C1111yescharacteristic, complemented
337#2661C2×C1111yescharacteristic, complemented
338#1612C2×C1111yescharacteristic, complemented
339#1611C2×C1111yescharacteristic, complemented
340#1609C2×C1111yescharacteristic, complemented
341#1608C2×C1111yescharacteristic, complemented
342#1600C2×C1111yescharacteristic, complemented
343#1599C2×C1111yescharacteristic, complemented
344#1597C2×C1111yescharacteristic, complemented
345#1596C2×C1111yescharacteristic, complemented
346#1508C2×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—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11#12011yescharacteristic
367C23×C11#12011yescharacteristic
368C23×C11C22×D411yescharacteristic
369Q8×C11—41no—
370Q8×C11—41no—
371Q8×C11—41no—
372Q8×C11—81no—
373Q8×C11—81no—
374Q8×C11—81no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—41no—
379D4×C11—41no—
380D4×C11—42no—
381D4×C11—42no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—81no—
385D4×C11—81no—
386D4×C11—81no—
387D4×C11—81no—
388D4×C11—84no—
389D4×C11—82no—
390D4×C11—82no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
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—42no—
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—81no—
422C2×C4×C11—81no—
423C2×C4×C11—81no—
424C2×C4×C11—81no—
425C2×C4×C11—81no—
426C2×C4×C11—81no—
427C2×C4×C11#12011yescharacteristic
428C2×C4×C11#12011yescharacteristic
429C2×C4×C11C22×D411yescharacteristic
430C2×C4×C11C22×D411yescharacteristic
431C8×C11—41no—
432C8×C11—41no—
433C8×C11—41no—
434C8×C11—41no—
435#563—21no—
436#562—21no—
437#554—21no—
438#552—21no—
439#551—21no—
440#551—21no—
441#547—21no—
442#546—21no—
443#544C22×C1111yescharacteristic
444#543C22×C1111yescharacteristic
445#542—21no—
446#539—21no—
447#539—21no—
448#539C22×C1111yescharacteristic
449#538C22×C1111yescharacteristic
450#536—21no—
451#525C22×C1111yescharacteristic
452C2×#123C22×C1111yescharacteristic
453C2×C22⋊Q8C22×C1111yescharacteristic
454C2×#121C22×C1111yescharacteristic
455#483C22×C1111yescharacteristic
456#483C22×C1111yescharacteristic
457#483C22×C1111yescharacteristic
458#482—21no—
459#481—21no—
460#480C22×C1111yescharacteristic
461#469—21no—
462#468—21no—
463#465—21no—
464#465—21no—
465#450C22×C1111yescharacteristic
466#450C22×C1111yescharacteristic
467#450C22×C1111yescharacteristic
468#449—21no—
469#448—21no—
470#447C22×C1111yescharacteristic
471#407C22×C1111yescharacteristic
472C2×C22⋊C8C22×C1111yescharacteristic
473#398C22×C1111yescharacteristic
474#397C22×C1111yescharacteristic
475#394—21no—
476#394C22×C1111yescharacteristic
477#392—21no—
478#392C22×C1111yescharacteristic
479#390—21no—
480#388—21no—
481C4×C22⋊C4C22×C1111yescharacteristic
482#328C22×C1111yescharacteristic
483#328C22×C1111yescharacteristic
484#328C22×C1111yescharacteristic
485#328C22×C1111yescharacteristic
486#328C22×C1111yescharacteristic
487#328C22×C1111yescharacteristic
488#327C22×C1111yescharacteristic
489#327C22×C1111yescharacteristic
490#324C22×C1111yescharacteristic
491#324C22×C1111yescharacteristic
492#323C22×C1111yescharacteristic
493#323C22×C1111yescharacteristic
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11—81no—
509C22×C11—81no—
510C22×C11—81no—
511C22×C11—81no—
512C22×C11—81no—
513C22×C11—81no—
514C22×C11—81no—
515C22×C11—81no—
516C22×C11—81no—
517C22×C11—81no—
518C22×C11—81no—
519C22×C11C2×#12011yescharacteristic
520C22×C11#57711yescharacteristic
521C22×C11#57711yescharacteristic
522C4×C11—21no—
523C4×C11—21no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—42no—
527C4×C11—41no—
528C4×C11—41no—
529C4×C11—41no—
530C4×C11—41no—
531C4×C11—41no—
532C4×C11—41no—
533C4×C11—41no—
534C4×C11—41no—
535C4×C11—41no—
536C4×C11—41no—
537C4×C11—81no—
538C4×C11—81no—
539C2×#41—21no—
540C2×#41D4×C1111yescharacteristic, complemented
541C22×Q8D4×C1111yescharacteristic, complemented
542C22×D4—21no—
543C22×D4—21no—
544C22×D4D4×C1111yescharacteristic
545C22×D4C23×C1111yescharacteristic
546C23×C4C23×C1111yescharacteristic
547C2×SD16—21no—
548C2×SD16—21no—
549C2×SD16—21no—
550C2×D8—21no—
551C2×M16—21no—
552C22×C8—21no—
553C4⋊Q8—21no—
554C4⋊Q8—21no—
555C4⋊Q8—21no—
556#126—21no—
557#126—21no—
558#126—21no—
559#126—21no—
560#126—21no—
561#126—21no—
562#125—21no—
563#125—21no—
564#125—21no—
565#125—21no—
566#125—21no—
567#124—21no—
568#124—21no—
569#124—21no—
570#124—21no—
571#123—21no—
572#123—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—
585C22⋊Q8—21no—
586C22⋊Q8—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⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8D4×C1111yescharacteristic, complemented
600C22⋊Q8D4×C1111yescharacteristic, complemented
601C22⋊Q8D4×C1111yescharacteristic, complemented
602C22⋊Q8C23×C1111yescharacteristic
603C22⋊Q8C23×C1111yescharacteristic
604C22⋊Q8C23×C1111yescharacteristic
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, complemented
614#121C23×C1111yescharacteristic
615#120—21no—
616#120—21no—
617C4×Q8—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—21no—
625#117—21no—
626#117—21no—
627#117—21no—
628#117D4×C1111yescharacteristic, complemented
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4D4×C1111yescharacteristic
633C2×C4⋊C4D4×C1111yescharacteristic, complemented
634C2×C4⋊C4C23×C1111yescharacteristic
635C2×C4⋊C4C23×C1111yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4D4×C1111yescharacteristic
645C2×C22⋊C4D4×C1111yescharacteristic
646C2×C22⋊C4C23×C1111yescharacteristic
647C2×C42—21no—
648#107—21no—
649#106—21no—
650#106—21no—
651#106—21no—
652#103—21no—
653#103—21no—
654#103—21no—
655#102—21no—
656#102—21no—
657#102—21no—
658#102—21no—
659#102—21no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8C23×C1111yescharacteristic
663C22⋊C8C23×C1111yescharacteristic
664C22⋊C8C23×C1111yescharacteristic
665C22⋊C8C23×C1111yescharacteristic
666#95—21no—
667#95—21no—
668#95C23×C1111yescharacteristic
669#95C23×C1111yescharacteristic
670C2×C11—21no—
671C2×C11—21no—
672C2×C11—41no—
673C2×C11—41no—
674C2×C11—81no—
675C2×C11—81no—
676C2×C11—161no—
677C2×C11#301011yescharacteristic
678C2×C11#301811yescharacteristic
679C2×C11#302611yescharacteristic
680C24—21no—
681C24C2×D4×C1111yescharacteristic
682C24C2×D4×C1111yescharacteristic
683#41—82no—
684#41—81no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—81no—
689C2×Q8C2×D4×C1111yescharacteristic
690C2×Q8C2×D4×C1111yescharacteristic
691C2×Q8C2×D4×C1111yescharacteristic
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—42no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4C2×D4×C1111yescharacteristic
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—81no—
722C22×C4C2×D4×C1111yescharacteristic
723C22×C4C2×D4×C1111yescharacteristic
724C22×C4C2×D4×C1111yescharacteristic
725C22×C4C2×D4×C1111yescharacteristic
726C22×C4C2×D4×C1111yescharacteristic
727C22×C4C2×D4×C1111yescharacteristic
728C22×C4C2×D4×C1111yescharacteristic
729C22×C4C2×D4×C1111yescharacteristic
730C22×C4C24×C1111yescharacteristic
731SD16—81no—
732SD16—81no—
733SD16—81no—
734D8—81no—
735M16—81no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—81no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—81no—
767C4⋊C4C2×D4×C1111yescharacteristic
768C4⋊C4C2×D4×C1111yescharacteristic
769C4⋊C4C2×D4×C1111yescharacteristic
770C4⋊C4C2×D4×C1111yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
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—42no—
795C22⋊C4—42no—
796C22⋊C4—41no—
797C22⋊C4—41no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C42—21no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—81no—
807C11#1841611yescharacteristic, direct product factor, Sylow
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C11×#12011yescharacteristic
826C23C11×#12011yescharacteristic
827C23C22×D4×C1111yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
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—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4C11×#12011yescharacteristic
887C2×C4C11×#12011yescharacteristic
888C2×C4C22×D4×C1111yescharacteristic
889C2×C4C22×D4×C1111yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×C11×#12011yescharacteristic
920C22C11×#57711yescharacteristic
921C22C11×#57711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C11×#301011yescharacteristic
947C2C11×#301811yescharacteristic
948C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C11×#3535C2semidirect
2. C11×#3194C2semidirect
3. C11×#3187C2semidirect
4. C11×#2661C2semidirect
5. C11×#1612C2semidirect
6. C11×#1611C2semidirect
7. C11×#1609C2semidirect
8. C11×#1608C2semidirect
9. C11×#1600C2semidirect
10. C11×#1599C2semidirect
11. C11×#1597C2semidirect
12. C11×#1596C2semidirect
13. C11×#1508C2semidirect
14. C11×#1501C2semidirect
15. C11×#1468C2semidirect
76. C2×C11×#41D4semidirect
77. C22×Q8×C11D4semidirect
135. C11×C22⋊Q8D4semidirect
136. C11×C22⋊Q8D4semidirect
137. C11×C22⋊Q8D4semidirect
149. C11×#121D4semidirect
164. C11×#117D4semidirect
169. C2×C11×C4⋊C4D4semidirect
206. #18416C11direct (N × H)
334. #3535C2×C11semidirect
335. #3194C2×C11semidirect
336. #3187C2×C11semidirect
337. #2661C2×C11semidirect
338. #1612C2×C11semidirect
339. #1611C2×C11semidirect
340. #1609C2×C11semidirect
341. #1608C2×C11semidirect
342. #1600C2×C11semidirect
343. #1599C2×C11semidirect
344. #1597C2×C11semidirect
345. #1596C2×C11semidirect
346. #1508C2×C11semidirect
347. #1501C2×C11semidirect
348. #1468C2×C11semidirect
540. C2×#41D4×C11semidirect
541. C22×Q8D4×C11semidirect
599. C22⋊Q8D4×C11semidirect
600. C22⋊Q8D4×C11semidirect
601. C22⋊Q8D4×C11semidirect
613. #121D4×C11semidirect
628. #117D4×C11semidirect
633. C2×C4⋊C4D4×C11semidirect
807. C11#18416direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35352
C11×#31942
C11×#31872
C11×#26612
C11×#16122
C11×#16112
C11×#16092
C11×#16082
C11×#16002
C11×#15992
C11×#15972
C11×#15962
C11×#15082
C11×#15012
C11×#14682
#1841611