Finite Group Databasebeta

← C11×#23402 #14600595

Subgroups — C11×#23402 #14600595

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic, complemented
3C2×C11×#535C211yesmaximal, characteristic, complemented
4C2×C11×#421C211yesmaximal, characteristic, complemented
5C11×#2896C211yesmaximal, characteristic, complemented
6C22×C11×#100C211yesmaximal, characteristic, complemented
7C11×#2004C214yesmaximal, complemented
8C11×#2002C214yesmaximal, complemented
9C11×#1733C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C23×D4×C11C2211yescharacteristic
13C11×#575—24no—
14C11×#575—24no—
15C2×C11×#137—21no—
16C2×C11×#137C2212yescomplemented
17C2×C11×AGL(1,ℤ/8)—21no—
18C2×C11×AGL(1,ℤ/8)C2212yescomplemented
19C2×C11×#135—22no—
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#535—22no—
23C11×#535—24no—
24C11×#535—22no—
25C11×#535—22no—
26C11×#535—24no—
27C11×#535C2214yes—
28C2×C11×#127—21no—
29C2×C11×#127C2212yescomplemented
30C2×C11×#124—21no—
31C2×C11×#124C2212yescomplemented
32C2×C11×#121—22no—
33C2×C11×#121—22no—
34C2×C11×#120—22no—
35C2×C11×#120—22no—
36C2×C11×#117C2211yescharacteristic
37C2×C11×#117C2211yescharacteristic
38C11×#421—24no—
39C2×C11×#104C2214yescomplemented
40C11×#419C2212yescomplemented
41C11×#418C2212yescomplemented
42C11×#417—22no—
43C11×#416—22no—
44C2×C11×#100—24no—
45C2×C11×#100C2214yescomplemented
46C11×#339C2214yescomplemented
47C25×C11D412yes—
48C2×C11×#41—21no—
49C2×C11×#41—22no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—22no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C2×C11×#41—22no—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41—22no—
61C2×C11×#41D412yescomplemented
62C2×C11×#41D414yescomplemented
63C2×C11×#41C2312yes—
64C22×Q8×C11D411yescharacteristic, complemented
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11—24no—
69C22×D4×C11—24no—
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11D412yes—
79C22×D4×C11D411yescharacteristic, complemented
80C22×D4×C11C2312yes—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C11×#137—28no—
86C11×#137—24no—
87C11×#137—24no—
88C11×AGL(1,ℤ/8)—28no—
89C11×AGL(1,ℤ/8)—24no—
90C11×AGL(1,ℤ/8)—24no—
91C11×#135—216no—
92C2×C11×Q16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×D8—22no—
96C2×C11×M16—21no—
97C2×C11×M16—22no—
98C2×C11×M16—21no—
99C2×C11×M16—22no—
100C2×C11×M16—22no—
101C2×C11×M16D414yescomplemented
102C2×C11×M16C2312yes—
103C2×C11×M16C2312yes—
104C22×C8×C11—21no—
105C22×C8×C11—21no—
106C11×#127—24no—
107C11×#127—24no—
108C11×#127—24no—
109C11×#127—24no—
110C11×#124—24no—
111C11×#124—24no—
112C11×#124—24no—
113C11×#124—24no—
114C11×#121—216no—
115C11×#121—28no—
116C11×#121—28no—
117C11×#120—216no—
118C11×#120—28no—
119C11×#120—28no—
120C11×#117—21no—
121C11×#117—21no—
122C11×#117—22no—
123C11×#117D412yescomplemented
124C11×#117D414yescomplemented
125C11×#117C2312yes—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4D412yescomplemented
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—24no—
132C2×C42×C11—21no—
133C2×C42×C11C2312yes—
134C11×#104—28no—
135C11×#103—24no—
136C11×#102—24no—
137C11×#100—28no—
138#23402C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—22no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—24no—
143C24×C11—22no—
144C24×C11—24no—
145C24×C11—84no—
146C24×C11C2×D414yes—
147C24×C11C2×D411yescharacteristic
148C11×#41—24no—
149C11×#41—24no—
150C11×#41—24no—
151C11×#41—24no—
152C11×#41—24no—
153C11×#41—24no—
154C11×#41—22no—
155C11×#41—22no—
156C11×#41—22no—
157C11×#41—22no—
158C11×#41—42no—
159C11×#41—42no—
160C11×#41—42no—
161C11×#41—42no—
162C11×#41—42no—
163C11×#41—42no—
164C11×#41—42no—
165C11×#41—42no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11C2×D412yes—
175C2×Q8×C11C2×D412yescomplemented
176C2×D4×C11—24no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—216no—
180C2×D4×C11—216no—
181C2×D4×C11—22no—
182C2×D4×C11—24no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—21no—
186C2×D4×C11—22no—
187C2×D4×C11—24no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—22no—
199C2×D4×C11—41no—
200C2×D4×C11—41no—
201C2×D4×C11—42no—
202C2×D4×C11—42no—
203C2×D4×C11—42no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—88no—
213C2×D4×C11—88no—
214C2×D4×C11C2×D412yes—
215C2×D4×C11C2×D412yescomplemented
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—22no—
219C22×C4×C11—21no—
220C22×C4×C11—24no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—41no—
224C22×C4×C11—41no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11#4112yes—
237C22×C4×C11C2411yescharacteristic
238C11×Q16—28no—
239C11×SD16—28no—
240C11×SD16—28no—
241C11×D8—28no—
242C11×M16—24no—
243C11×M16—22no—
244C11×M16—22no—
245C11×M16—22no—
246C11×M16—42no—
247C11×M16C2×D414yescomplemented
248C2×C8×C11—24no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11—42no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—22no—
254C11×C4⋊C4C2×D414yes—
255C11×C22⋊C4—216no—
256C11×C22⋊C4—216no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—22no—
260C42×C11—22no—
261C42×C11—22no—
262C42×C11—22no—
263C42×C11C2×D414yescomplemented
264C2×#575C2×C1111yescharacteristic, complemented
265C2×#535C2×C1111yescharacteristic, complemented
266C2×#535C2×C1111yescharacteristic, complemented
267C2×#421C2×C1111yescharacteristic, complemented
268#2896C2×C1111yescharacteristic, complemented
269C22×#100C2×C1111yescharacteristic, complemented
270#2004C2×C1114yescomplemented
271#2002C2×C1114yescomplemented
272#1733C2×C1111yescharacteristic, complemented
273C23×C11—24no—
274C23×C11—22no—
275C23×C11—24no—
276C23×C11—22no—
277C23×C11—24no—
278C23×C11—42no—
279C23×C11—48no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—48no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—42no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11—84no—
289C23×C11—88no—
290C23×C11—88no—
291C23×C11#12011yescharacteristic
292C23×C11#12011yescharacteristic
293C23×C11#12012yes—
294C23×C11#12112yes—
295C23×C11C22×D411yescharacteristic
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—41no—
301Q8×C11—41no—
302Q8×C11—42no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—42no—
308D4×C11—42no—
309D4×C11—44no—
310D4×C11—44no—
311D4×C11—44no—
312D4×C11—42no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—41no—
316D4×C11—42no—
317D4×C11—41no—
318D4×C11—44no—
319D4×C11—44no—
320D4×C11—42no—
321D4×C11—816no—
322D4×C11—816no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—22no—
327C2×C4×C11—44no—
328C2×C4×C11—44no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—44no—
335C2×C4×C11—44no—
336C2×C4×C11—44no—
337C2×C4×C11#12012yes—
338C2×C4×C11#12012yes—
339C2×C4×C11#12012yes—
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12011yescharacteristic
342C2×C4×C11#12112yes—
343C2×C4×C11#12112yes—
344C2×C4×C11#12112yes—
345C2×C4×C11#12112yes—
346C2×C4×C11#12112yes—
347C2×C4×C11#12712yes—
348C2×C4×C11#12712yes—
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4111yescharacteristic
355C8×C11—24no—
356C8×C11—42no—
357C22×#41C22×C1111yescharacteristic
358C22×#41C22×C1111yescharacteristic
359C23×D4C22×C1111yescharacteristic
360#575—24no—
361#575—24no—
362C2×#137—21no—
363C2×#137C22×C1112yescomplemented
364C2×AGL(1,ℤ/8)—21no—
365C2×AGL(1,ℤ/8)C22×C1112yescomplemented
366C2×#135—22no—
367C22×M16C22×C1111yescharacteristic
368C22×M16C22×C1111yescharacteristic
369#535—22no—
370#535—24no—
371#535—22no—
372#535—22no—
373#535—24no—
374#535C22×C1114yes—
375C2×#127—21no—
376C2×#127C22×C1112yescomplemented
377C2×#124—21no—
378C2×#124C22×C1112yescomplemented
379C2×#121—22no—
380C2×#121—22no—
381C2×#120—22no—
382C2×#120—22no—
383C2×#117C22×C1111yescharacteristic
384C2×#117C22×C1111yescharacteristic
385#421—24no—
386C2×#104C22×C1114yescomplemented
387#419C22×C1112yescomplemented
388#418C22×C1112yescomplemented
389#417—22no—
390#416—22no—
391C2×#100—24no—
392C2×#100C22×C1114yescomplemented
393#339C22×C1114yescomplemented
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—44no—
400C22×C11—48no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—44no—
404C22×C11—44no—
405C22×C11—48no—
406C22×C11—84no—
407C22×C11—82no—
408C22×C11—84no—
409C22×C11—88no—
410C22×C11—88no—
411C22×C11—82no—
412C22×C11#39212yes—
413C22×C11#39212yes—
414C22×C11C2×#12011yescharacteristic
415C22×C11C2×#12011yescharacteristic
416C22×C11C2×#12111yescharacteristic
417C4×C11—44no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11—44no—
421C4×C11#39212yes—
422C4×C11#39212yes—
423C4×C11C2×#12011yescharacteristic
424C4×C11C2×#12111yescharacteristic
425C4×C11C2×#12111yescharacteristic
426C4×C11C2×#12711yescharacteristic
427C25D4×C1112yes—
428C2×#41—21no—
429C2×#41—22no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41D4×C1112yescomplemented
442C2×#41D4×C1114yescomplemented
443C2×#41C23×C1112yes—
444C22×Q8D4×C1111yescharacteristic, complemented
445C22×Q8C23×C1111yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4D4×C1112yes—
459C22×D4D4×C1111yescharacteristic, complemented
460C22×D4C23×C1112yes—
461C22×D4C23×C1111yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C1111yescharacteristic
465#137—28no—
466#137—24no—
467#137—24no—
468AGL(1,ℤ/8)—28no—
469AGL(1,ℤ/8)—24no—
470AGL(1,ℤ/8)—24no—
471#135—216no—
472C2×Q16—22no—
473C2×SD16—22no—
474C2×SD16—22no—
475C2×D8—22no—
476C2×M16—21no—
477C2×M16—22no—
478C2×M16—21no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16D4×C1114yescomplemented
482C2×M16C23×C1112yes—
483C2×M16C23×C1112yes—
484C22×C8—21no—
485C22×C8—21no—
486#127—24no—
487#127—24no—
488#127—24no—
489#127—24no—
490#124—24no—
491#124—24no—
492#124—24no—
493#124—24no—
494#121—216no—
495#121—28no—
496#121—28no—
497#120—28no—
498#120—216no—
499#120—28no—
500#117—21no—
501#117—21no—
502#117—22no—
503#117D4×C1112yescomplemented
504#117D4×C1114yescomplemented
505#117C23×C1112yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4D4×C1112yescomplemented
508C2×C22⋊C4—24no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—24no—
512C2×C42—21no—
513C2×C42C23×C1112yes—
514#104—28no—
515#103—24no—
516#102—24no—
517#100—28no—
518C2×C11—21no—
519C2×C11—21no—
520C2×C11—22no—
521C2×C11—22no—
522C2×C11—84no—
523C2×C11—82no—
524C2×C11—82no—
525C2×C11C2×#39211yescharacteristic
526C2×C11#301912yes—
527C24—22no—
528C24—21no—
529C24—21no—
530C24—22no—
531C24—24no—
532C24—24no—
533C24—84no—
534C24C2×D4×C1114yes—
535C24C2×D4×C1111yescharacteristic
536#41—24no—
537#41—24no—
538#41—24no—
539#41—24no—
540#41—24no—
541#41—24no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—42no—
547#41—42no—
548#41—42no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8C2×D4×C1112yes—
563C2×Q8C2×D4×C1112yescomplemented
564C2×D4—22no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—216no—
568C2×D4—216no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—24no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—88no—
601C2×D4—88no—
602C2×D4C2×D4×C1112yes—
603C2×D4C2×D4×C1112yescomplemented
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—22no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4C2×D4×C1111yescharacteristic
617C22×C4C2×D4×C1111yescharacteristic
618C22×C4C2×D4×C1111yescharacteristic
619C22×C4C2×D4×C1112yes—
620C22×C4C2×D4×C1112yes—
621C22×C4C2×D4×C1111yescharacteristic
622C22×C4C2×D4×C1111yescharacteristic
623C22×C4C2×D4×C1112yes—
624C22×C4C11×#4112yes—
625C22×C4C24×C1111yescharacteristic
626Q16—28no—
627SD16—28no—
628SD16—28no—
629D8—28no—
630M16—24no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—42no—
635M16C2×D4×C1114yescomplemented
636C2×C8—24no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—42no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4C2×D4×C1114yes—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—22no—
646C22⋊C4—24no—
647C22⋊C4—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42C2×D4×C1114yescomplemented
652C11#2340211yescharacteristic, direct product factor, Sylow
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—42no—
659C23—48no—
660C23—44no—
661C23—44no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—44no—
667C23—44no—
668C23—84no—
669C23—88no—
670C23—88no—
671C23C11×#12011yescharacteristic
672C23C11×#12011yescharacteristic
673C23C11×#12012yes—
674C23C11×#12112yes—
675C23C22×D4×C1111yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—42no—
682Q8—41no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—44no—
697D4—44no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—816no—
702D4—816no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4C11×#12012yes—
718C2×C4C11×#12012yes—
719C2×C4C11×#12011yescharacteristic
720C2×C4C11×#12011yescharacteristic
721C2×C4C11×#12012yes—
722C2×C4C11×#12112yes—
723C2×C4C11×#12112yes—
724C2×C4C11×#12112yes—
725C2×C4C11×#12112yes—
726C2×C4C11×#12112yes—
727C2×C4C11×#12712yes—
728C2×C4C11×#12712yes—
729C2×C4C22×D4×C1111yescharacteristic
730C2×C4C22×D4×C1111yescharacteristic
731C2×C4C22×D4×C1111yescharacteristic
732C2×C4C22×D4×C1111yescharacteristic
733C2×C4C22×D4×C1111yescharacteristic
734C2×C4C2×C11×#4111yescharacteristic
735C8—24no—
736C8—42no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—48no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—44no—
748C22—48no—
749C22—84no—
750C22—88no—
751C22—82no—
752C22—84no—
753C22—88no—
754C22—82no—
755C22C11×#39212yes—
756C22C11×#39212yes—
757C22C2×C11×#12011yescharacteristic
758C22C2×C11×#12011yescharacteristic
759C22C2×C11×#12111yescharacteristic
760C4—44no—
761C4—42no—
762C4—42no—
763C4—44no—
764C4C11×#39212yes—
765C4C11×#39212yes—
766C4C2×C11×#12011yescharacteristic
767C4C2×C11×#12111yescharacteristic
768C4C2×C11×#12111yescharacteristic
769C4C2×C11×#12711yescharacteristic
770C2—21no—
771C2—21no—
772C2—22no—
773C2—22no—
774C2—84no—
775C2—82no—
776C2—82no—
777C2C2×C11×#39211yescharacteristic
778C2C11×#301912yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#575C2semidirect
2. C2×C11×#535C2semidirect
3. C2×C11×#535C2semidirect
4. C2×C11×#421C2semidirect
5. C11×#2896C2semidirect
6. C22×C11×#100C2semidirect
7. C11×#2004C2semidirect
8. C11×#2002C2semidirect
9. C11×#1733C2semidirect
16. C2×C11×#137C22semidirect
18. C2×C11×AGL(1,ℤ/8)C22semidirect
29. C2×C11×#127C22semidirect
31. C2×C11×#124C22semidirect
39. C2×C11×#104C22semidirect
40. C11×#419C22semidirect
41. C11×#418C22semidirect
45. C2×C11×#100C22semidirect
46. C11×#339C22semidirect
61. C2×C11×#41D4semidirect
62. C2×C11×#41D4semidirect
64. C22×Q8×C11D4semidirect
79. C22×D4×C11D4semidirect
101. C2×C11×M16D4semidirect
123. C11×#117D4semidirect
124. C11×#117D4semidirect
127. C2×C11×C4⋊C4D4semidirect
138. #23402C11direct (N × H)
175. C2×Q8×C11C2×D4semidirect
215. C2×D4×C11C2×D4semidirect
247. C11×M16C2×D4semidirect
263. C42×C11C2×D4semidirect
264. C2×#575C2×C11semidirect
265. C2×#535C2×C11semidirect
266. C2×#535C2×C11semidirect
267. C2×#421C2×C11semidirect
268. #2896C2×C11semidirect
269. C22×#100C2×C11semidirect
270. #2004C2×C11semidirect
271. #2002C2×C11semidirect
272. #1733C2×C11semidirect
363. C2×#137C22×C11semidirect
365. C2×AGL(1,ℤ/8)C22×C11semidirect
376. C2×#127C22×C11semidirect
378. C2×#124C22×C11semidirect
386. C2×#104C22×C11semidirect
387. #419C22×C11semidirect
388. #418C22×C11semidirect
392. C2×#100C22×C11semidirect
393. #339C22×C11semidirect
441. C2×#41D4×C11semidirect
442. C2×#41D4×C11semidirect
444. C22×Q8D4×C11semidirect
459. C22×D4D4×C11semidirect
481. C2×M16D4×C11semidirect
503. #117D4×C11semidirect
504. #117D4×C11semidirect
507. C2×C4⋊C4D4×C11semidirect
563. C2×Q8C2×D4×C11semidirect
603. C2×D4C2×D4×C11semidirect
635. M16C2×D4×C11semidirect
651. C42C2×D4×C11semidirect
652. C11#23402direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C2×C11×#5352
C2×C11×#4212
C11×#28962
C22×C11×#1002
C11×#20042
C11×#20022
C11×#17332
#2340211