Finite Group Databasebeta

← C11×#61670 #14638863

Subgroups — C11×#61670 #14638863

Order 2816.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3547C211yesmaximal, characteristic, complemented
2C11×#3496C211yesmaximal, characteristic, complemented
3C11×#3319C212yesmaximal, complemented
4C11×#3315C212yesmaximal, complemented
5C11×#3314C212yesmaximal, complemented
6C11×#3310C212yesmaximal, complemented
7C11×#3269C212yesmaximal, complemented
8C11×#3267C212yesmaximal, complemented
9C11×#3266C212yesmaximal, complemented
10C11×#3265C212yesmaximal, complemented
11C11×#3219C211yesmaximal, characteristic, complemented
12C11×#3216C211yesmaximal, characteristic, complemented
13C11×#3203C212yesmaximal, complemented
14C11×#3201C212yesmaximal, complemented
15C11×#3114C211yesmaximal, characteristic, complemented
16C11×#3110C211yesmaximal, characteristic, complemented
17C11×#3012C212yesmaximal, complemented
18C11×#3009C212yesmaximal, complemented
19C11×#2980C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2212yes—
21C2×C11×#137C2212yescomplemented
22C2×C11×AGL(1,ℤ/8)C2212yescomplemented
23C2×C11×#135C2212yescomplemented
24C22×C11×SD16C2212yescomplemented
25C11×#562—22no—
26C11×#555—21no—
27C11×#555C2211yescharacteristic, complemented
28C11×#554C2211yescharacteristic, complemented
29C11×#553—21no—
30C11×#552C2212yescomplemented
31D4×Q8×C11C2211yescharacteristic, complemented
32C11×#548C2212yescomplemented
33C11×#547—21no—
34C11×#547C2212yes—
35C11×#547C2211yescharacteristic, complemented
36C11×#546—22no—
37C11×#546C2212yes—
38C11×#546C2212yes—
39D42×C11—21no—
40D42×C11C2212yes—
41C11×#544—21no—
42C11×#542—22no—
43C11×#540—21no—
44C11×#537C2212yes—
45C11×#537C2212yescomplemented
46C11×#536C2212yescomplemented
47C11×#534—21no—
48C11×#534—21no—
49C11×#533C2211yescharacteristic, complemented
50C11×#532C2211yescharacteristic
51C11×#532C2211yescharacteristic
52C11×#529C2211yescharacteristic, complemented
53C2×C11×#121—22no—
54C2×C4×D4×C11C2211yescharacteristic
55C11×#497C2212yescomplemented
56C11×#497C2211yescharacteristic, complemented
57C11×#496C2211yescharacteristic, complemented
58C11×#491C2211yescharacteristic, complemented
59C11×#490C2211yescharacteristic, complemented
60C11×#489C2212yescomplemented
61C11×#485C2212yescomplemented
62C11×#484C2212yescomplemented
63C11×#484C2212yescomplemented
64C11×#483C2211yescharacteristic, complemented
65C11×#482C2212yescomplemented
66C11×#480C2211yescharacteristic, complemented
67C11×#480C2212yescomplemented
68C11×#478C2212yescomplemented
69C11×#474C2212yescomplemented
70C11×#470C2212yescomplemented
71C11×#468C2212yescomplemented
72C11×#468C2212yescomplemented
73C11×#468C2212yescomplemented
74C11×#467C2212yescomplemented
75C11×#467C2212yescomplemented
76C11×#466C2212yescomplemented
77C11×#465C2212yescomplemented
78C11×#464C2212yescomplemented
79C11×#463C2212yescomplemented
80C11×#463C2212yescomplemented
81C11×#462C2212yescomplemented
82C11×#461C2212yescomplemented
83C11×#460C2212yescomplemented
84C11×#452C2212yescomplemented
85C11×#452C2212yescomplemented
86C11×#452C2212yescomplemented
87C11×#452C2212yescomplemented
88C11×#452C2212yescomplemented
89C11×#452C2212yescomplemented
90C11×#452C2212yescomplemented
91C11×#451C2212yescomplemented
92C11×#450C2211yescharacteristic
93C11×#450C2212yes—
94C11×#450C2212yescomplemented
95C11×#450C2212yescomplemented
96C11×#450C2212yescomplemented
97C11×#449C2212yescomplemented
98C11×#449C2212yescomplemented
99C11×#449C2212yescomplemented
100C11×#448C2212yescomplemented
101C11×#447C2211yescharacteristic
102C11×#447C2212yescomplemented
103C11×#442C2212yescomplemented
104C11×#440C2212yescomplemented
105C11×#440C2212yescomplemented
106C11×#440C2212yescomplemented
107C11×#435C2212yescomplemented
108C11×#435C2212yescomplemented
109C11×#435C2212yescomplemented
110C11×#435C2212yescomplemented
111C11×#432C2211yescharacteristic, complemented
112C11×#432C2211yescharacteristic, complemented
113C11×#418C2212yescomplemented
114C11×#417C2212yescomplemented
115C11×#416C2212yescomplemented
116C2×C11×#102C2212yescomplemented
117C11×#408C2212yescomplemented
118C11×#408C2212yescomplemented
119C11×H(5,𝔽2)—44no—
120C11×H(5,𝔽2)—44no—
121C2×C11×#41—22no—
122C2×C11×#41C2312yes—
123C2×C11×#41C2312yes—
124C2×C11×#41C2312yes—
125C2×C11×#41C2312yes—
126C2×C11×#41C2312yes—
127C22×Q8×C11C2312yes—
128C22×D4×C11—22no—
129C22×D4×C11—22no—
130C22×D4×C11—22no—
131C22×D4×C11—22no—
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2312yes—
134C22×D4×C11C2312yes—
135C23×C4×C11—21no—
136C11×#137—44no—
137C11×AGL(1,ℤ/8)—44no—
138C11×#135—44no—
139C2×C11×Q16C2312yes—
140C2×C11×Q16C2312yes—
141C2×C11×Q16C2312yes—
142C2×C11×SD16—44no—
143C2×C11×SD16C2312yes—
144C2×C11×SD16C2312yes—
145C2×C11×SD16C2312yes—
146C2×C11×SD16C2312yes—
147C2×C11×SD16C2312yes—
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2312yes—
150C2×C11×D8C2312yes—
151C2×C11×D8C2312yes—
152C2×C11×M16C2312yes—
153C2×C11×M16C2312yes—
154C22×C8×C11C2312yes—
155C22×C8×C11C2312yes—
156C11×C4⋊Q8—22no—
157C11×C4⋊Q8—21no—
158C11×C4⋊Q8D411yescharacteristic
159C11×C4⋊Q8C2311yescharacteristic
160C11×C4⋊Q8C2311yescharacteristic
161C11×C4⋊Q8C2311yescharacteristic
162C11×#127D411yescharacteristic
163C11×#127C2311yescharacteristic
164C11×#126—22no—
165C11×#126—21no—
166C11×#125—22no—
167C11×#125—21no—
168C11×#125—21no—
169C11×#125C2311yescharacteristic
170C11×#124—22no—
171C11×#124—22no—
172C11×#124—22no—
173C11×#124D412yes—
174C11×#124C2312yes—
175C11×#124C2311yescharacteristic
176C11×#123—22no—
177C11×#123—22no—
178C11×#123—22no—
179C11×#123—21no—
180C11×#123—22no—
181C11×#123—22no—
182C11×#123—22no—
183C11×#123—22no—
184C11×#123—22no—
185C11×C22⋊Q8—22no—
186C11×C22⋊Q8—22no—
187C11×C22⋊Q8—21no—
188C11×C22⋊Q8—22no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8—22no—
191C11×C22⋊Q8C2311yescharacteristic
192C11×C22⋊Q8C2312yes—
193C11×C22⋊Q8C2312yes—
194C11×C22⋊Q8C2312yes—
195C11×C22⋊Q8C2312yes—
196C11×C22⋊Q8C2312yes—
197C11×C22⋊Q8C2312yes—
198C11×#121—22no—
199C11×#121—22no—
200C11×#121—22no—
201C11×#121—22no—
202C11×#121—22no—
203C11×#121—22no—
204C11×#121—22no—
205C11×#121—21no—
206C11×#121—22no—
207C11×#121—21no—
208C11×#121—21no—
209C11×#121—21no—
210C11×#121—22no—
211C11×#121—22no—
212C11×#121—22no—
213C11×#121D412yes—
214C11×#121D411yescharacteristic
215C11×#121D411yescharacteristic
216C11×#121C2311yescharacteristic
217C11×#121C2312yes—
218C11×#121C2312yes—
219C11×#121C2312yes—
220C11×#120—22no—
221C11×#120—22no—
222C11×#120—22no—
223C11×#120—22no—
224C4×Q8×C11—21no—
225C4×Q8×C11C2311yescharacteristic
226C4×Q8×C11C2312yes—
227C4×D4×C11—21no—
228C4×D4×C11—21no—
229C4×D4×C11—21no—
230C4×D4×C11—22no—
231C4×D4×C11—21no—
232C4×D4×C11—21no—
233C4×D4×C11—21no—
234C4×D4×C11—21no—
235C4×D4×C11C2312yes—
236C4×D4×C11C2312yes—
237C4×D4×C11C2311yescharacteristic
238C4×D4×C11C2312yes—
239C4×D4×C11C2311yescharacteristic
240C4×D4×C11C2311yescharacteristic
241C11×#117—21no—
242C11×#117—21no—
243C11×#117—22no—
244C11×#117—21no—
245C11×#117C2312yes—
246C2×C11×C4⋊C4—22no—
247C2×C11×C4⋊C4—21no—
248C2×C11×C4⋊C4C2311yescharacteristic
249C2×C11×C4⋊C4C2312yes—
250C2×C11×C22⋊C4—21no—
251C2×C11×C22⋊C4—22no—
252C2×C11×C22⋊C4—22no—
253C2×C42×C11C2311yescharacteristic
254C11×#107C2312yes—
255C11×#107C2312yes—
256C11×#107C2312yes—
257C11×#106C2312yes—
258C11×C4⋊C8C2312yes—
259C11×C4⋊C8C2312yes—
260C11×#103C2312yes—
261C11×#103C2312yes—
262C11×#103C2312yes—
263C11×#103C2312yes—
264C11×#103C2312yes—
265C11×#103C2312yes—
266C11×#103C2312yes—
267C11×#102C2312yes—
268C11×#102C2312yes—
269C11×#102C2312yes—
270C11×#102C2312yes—
271C11×#102C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×C22⋊C8C2311yescharacteristic
277C11×C22⋊C8C2312yes—
278C11×C22⋊C8C2311yescharacteristic
279C11×C22⋊C8C2312yes—
280C11×C22⋊C8C2312yes—
281C11×C22⋊C8C2312yes—
282C11×C22⋊C8C2312yes—
283C11×#97C2312yes—
284C11×#97C2311yescharacteristic
285C11×#97C2311yescharacteristic
286#61670C1111yesmaximal, characteristic, direct product factor, Sylow
287C24×C11—21no—
288C24×C11—22no—
289C24×C11—22no—
290C11×#41—24no—
291C11×#41—24no—
292C11×#41—42no—
293C11×#41—42no—
294C11×#41—42no—
295C11×#41—42no—
296C11×#41—42no—
297C11×#41—42no—
298C11×#41—42no—
299C11×#41—42no—
300C11×#41—48no—
301C2×Q8×C11—21no—
302C2×Q8×C11—22no—
303C2×Q8×C11—42no—
304C2×Q8×C11—42no—
305C2×Q8×C11C2×D412yes—
306C2×Q8×C11C2412yes—
307C2×Q8×C11C2411yescharacteristic
308C2×Q8×C11C2412yes—
309C2×D4×C11—24no—
310C2×D4×C11—24no—
311C2×D4×C11—24no—
312C2×D4×C11—22no—
313C2×D4×C11—22no—
314C2×D4×C11—22no—
315C2×D4×C11—21no—
316C2×D4×C11—22no—
317C2×D4×C11—22no—
318C2×D4×C11—22no—
319C2×D4×C11—22no—
320C2×D4×C11—21no—
321C2×D4×C11—21no—
322C2×D4×C11—22no—
323C2×D4×C11—22no—
324C2×D4×C11—21no—
325C2×D4×C11—42no—
326C2×D4×C11—42no—
327C2×D4×C11—48no—
328C2×D4×C11—48no—
329C2×D4×C11—48no—
330C2×D4×C11—84no—
331C2×D4×C11C2×D411yescharacteristic
332C2×D4×C11C2×D411yescharacteristic
333C2×D4×C11C2×D412yes—
334C2×D4×C11C2×D412yes—
335C2×D4×C11C2×D412yes—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2412yes—
338C2×D4×C11C2411yescharacteristic
339C2×D4×C11C2412yes—
340C22×C4×C11—21no—
341C22×C4×C11—22no—
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—21no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—22no—
349C22×C4×C11—22no—
350C22×C4×C11—82no—
351C22×C4×C11C2×D411yescharacteristic
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2411yescharacteristic
354C22×C4×C11C2412yes—
355C22×C4×C11C2412yes—
356C11×Q16—42no—
357C11×Q16—42no—
358C11×Q16—42no—
359C11×SD16—24no—
360C11×SD16—24no—
361C11×SD16—24no—
362C11×SD16—42no—
363C11×SD16—42no—
364C11×SD16—42no—
365C11×SD16—42no—
366C11×D8—24no—
367C11×D8—42no—
368C11×M16—42no—
369C11×M16—42no—
370C2×C8×C11—42no—
371C2×C8×C11—42no—
372C2×C8×C11C2412yes—
373C2×C8×C11C2412yes—
374C2×C8×C11C2412yes—
375C2×C8×C11C2412yes—
376C11×C4⋊C4—21no—
377C11×C4⋊C4—21no—
378C11×C4⋊C4—22no—
379C11×C4⋊C4—22no—
380C11×C4⋊C4—22no—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—21no—
394C11×C4⋊C4C2×D412yes—
395C11×C4⋊C4C2×D411yescharacteristic
396C11×C4⋊C4C2×D411yescharacteristic
397C11×C4⋊C4C2411yescharacteristic
398C11×C4⋊C4C2411yescharacteristic
399C11×C4⋊C4C2412yes—
400C11×C4⋊C4C2412yes—
401C11×C22⋊C4—22no—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—22no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—21no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4—22no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—21no—
420C11×C22⋊C4C2×D412yes—
421C11×C22⋊C4C2×D412yes—
422C11×C22⋊C4C2×D412yes—
423C11×C22⋊C4C2×D412yes—
424C42×C11—22no—
425C42×C11—22no—
426C42×C11—21no—
427C42×C11C2×D411yescharacteristic
428C42×C11C2×D411yescharacteristic
429C42×C11C2411yescharacteristic
430C42×C11C2411yescharacteristic
431#3547C2×C1111yescharacteristic, complemented
432#3496C2×C1111yescharacteristic, complemented
433#3319C2×C1112yescomplemented
434#3315C2×C1112yescomplemented
435#3314C2×C1112yescomplemented
436#3310C2×C1112yescomplemented
437#3269C2×C1112yescomplemented
438#3267C2×C1112yescomplemented
439#3266C2×C1112yescomplemented
440#3265C2×C1112yescomplemented
441#3219C2×C1111yescharacteristic, complemented
442#3216C2×C1111yescharacteristic, complemented
443#3203C2×C1112yescomplemented
444#3201C2×C1112yescomplemented
445#3114C2×C1111yescharacteristic, complemented
446#3110C2×C1111yescharacteristic, complemented
447#3012C2×C1112yescomplemented
448#3009C2×C1112yescomplemented
449#2980C2×C1111yescharacteristic, complemented
450C23×C11—24no—
451C23×C11—22no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—44no—
455C23×C11—44no—
456C23×C11—81no—
457C23×C11—81no—
458C23×C11—82no—
459C23×C11—82no—
460C23×C11—82no—
461C23×C11—82no—
462C23×C11C22×D412yes—
463C23×C11C22×D412yes—
464C23×C11C22×D411yescharacteristic
465Q8×C11—22no—
466Q8×C11—22no—
467Q8×C11—22no—
468Q8×C11—22no—
469Q8×C11—22no—
470Q8×C11—42no—
471Q8×C11—81no—
472Q8×C11—82no—
473D4×C11—24no—
474D4×C11—22no—
475D4×C11—22no—
476D4×C11—22no—
477D4×C11—22no—
478D4×C11—42no—
479D4×C11—42no—
480D4×C11—42no—
481D4×C11—42no—
482D4×C11—41no—
483D4×C11—41no—
484D4×C11—44no—
485D4×C11—44no—
486D4×C11—42no—
487D4×C11—44no—
488D4×C11—44no—
489D4×C11—44no—
490D4×C11—81no—
491D4×C11—81no—
492D4×C11—82no—
493D4×C11—82no—
494D4×C11—82no—
495D4×C11—82no—
496D4×C11H(5,𝔽2)14yes—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—44no—
512C2×C4×C11—44no—
513C2×C4×C11—42no—
514C2×C4×C11—44no—
515C2×C4×C11—44no—
516C2×C4×C11—82no—
517C2×C4×C11—82no—
518C2×C4×C11—82no—
519C2×C4×C11—81no—
520C2×C4×C11—82no—
521C2×C4×C11C22×D411yescharacteristic
522C2×C4×C11C22×D411yescharacteristic
523C2×C4×C11C22×D412yes—
524C2×C4×C11C22×D411yescharacteristic
525C2×C4×C11C22×D411yescharacteristic
526C2×C4×C11C22×D411yescharacteristic
527C2×C4×C11C22×D412yes—
528C2×C4×C11C2511yescharacteristic
529C8×C11—22no—
530C8×C11—22no—
531C8×C11—22no—
532C8×C11—22no—
533C2×H(5,𝔽2)C22×C1112yes—
534C2×#137C22×C1112yescomplemented
535C2×AGL(1,ℤ/8)C22×C1112yescomplemented
536C2×#135C22×C1112yescomplemented
537C22×SD16C22×C1112yescomplemented
538#562—22no—
539#555—21no—
540#555C22×C1111yescharacteristic, complemented
541#554C22×C1111yescharacteristic, complemented
542#553—21no—
543#552C22×C1112yescomplemented
544D4×Q8C22×C1111yescharacteristic, complemented
545#548C22×C1112yescomplemented
546#547—21no—
547#547C22×C1112yes—
548#547C22×C1111yescharacteristic, complemented
549#546—22no—
550#546C22×C1112yes—
551#546C22×C1112yes—
552D42—21no—
553D42C22×C1112yes—
554#544—21no—
555#542—22no—
556#540—21no—
557#537C22×C1112yes—
558#537C22×C1112yescomplemented
559#536C22×C1112yescomplemented
560#534—21no—
561#534—21no—
562#533C22×C1111yescharacteristic, complemented
563#532C22×C1111yescharacteristic
564#532C22×C1111yescharacteristic
565#529C22×C1111yescharacteristic, complemented
566C2×#121—22no—
567C2×C4×D4C22×C1111yescharacteristic
568#497C22×C1112yescomplemented
569#497C22×C1111yescharacteristic, complemented
570#496C22×C1111yescharacteristic, complemented
571#491C22×C1111yescharacteristic, complemented
572#490C22×C1111yescharacteristic, complemented
573#489C22×C1112yescomplemented
574#485C22×C1112yescomplemented
575#484C22×C1112yescomplemented
576#484C22×C1112yescomplemented
577#483C22×C1111yescharacteristic, complemented
578#482C22×C1112yescomplemented
579#480C22×C1111yescharacteristic, complemented
580#480C22×C1112yescomplemented
581#478C22×C1112yescomplemented
582#474C22×C1112yescomplemented
583#470C22×C1112yescomplemented
584#468C22×C1112yescomplemented
585#468C22×C1112yescomplemented
586#468C22×C1112yescomplemented
587#467C22×C1112yescomplemented
588#467C22×C1112yescomplemented
589#466C22×C1112yescomplemented
590#465C22×C1112yescomplemented
591#464C22×C1112yescomplemented
592#463C22×C1112yescomplemented
593#463C22×C1112yescomplemented
594#462C22×C1112yescomplemented
595#461C22×C1112yescomplemented
596#460C22×C1112yescomplemented
597#452C22×C1112yescomplemented
598#452C22×C1112yescomplemented
599#452C22×C1112yescomplemented
600#452C22×C1112yescomplemented
601#452C22×C1112yescomplemented
602#452C22×C1112yescomplemented
603#452C22×C1112yescomplemented
604#451C22×C1112yescomplemented
605#450C22×C1112yes—
606#450C22×C1111yescharacteristic
607#450C22×C1112yescomplemented
608#450C22×C1112yescomplemented
609#450C22×C1112yescomplemented
610#449C22×C1112yescomplemented
611#449C22×C1112yescomplemented
612#449C22×C1112yescomplemented
613#448C22×C1112yescomplemented
614#447C22×C1111yescharacteristic
615#447C22×C1112yescomplemented
616#442C22×C1112yescomplemented
617#440C22×C1112yescomplemented
618#440C22×C1112yescomplemented
619#440C22×C1112yescomplemented
620#435C22×C1112yescomplemented
621#435C22×C1112yescomplemented
622#435C22×C1112yescomplemented
623#435C22×C1112yescomplemented
624#432C22×C1111yescharacteristic, complemented
625#432C22×C1111yescharacteristic, complemented
626#418C22×C1112yescomplemented
627#417C22×C1112yescomplemented
628#416C22×C1112yescomplemented
629C2×#102C22×C1112yescomplemented
630#408C22×C1112yescomplemented
631#408C22×C1112yescomplemented
632C22×C11—21no—
633C22×C11—22no—
634C22×C11—22no—
635C22×C11—21no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—21no—
640C22×C11—22no—
641C22×C11—24no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—41no—
646C22×C11—41no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—41no—
650C22×C11—84no—
651C22×C11—164no—
652C22×C11—164no—
653C22×C11C23×D411yescharacteristic
654C4×C11—21no—
655C4×C11—21no—
656C4×C11—21no—
657C4×C11—21no—
658C4×C11—21no—
659C4×C11—22no—
660C4×C11—22no—
661C4×C11—42no—
662C4×C11—41no—
663C4×C11—42no—
664C4×C11—41no—
665C4×C11—42no—
666C4×C11—42no—
667C4×C11—41no—
668C4×C11C2×H(5,𝔽2)12yes—
669H(5,𝔽2)—44no—
670H(5,𝔽2)—44no—
671C2×#41—22no—
672C2×#41C23×C1112yes—
673C2×#41C23×C1112yes—
674C2×#41C23×C1112yes—
675C2×#41C23×C1112yes—
676C2×#41C23×C1112yes—
677C22×Q8C23×C1112yes—
678C22×D4—22no—
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4C23×C1111yescharacteristic
683C22×D4C23×C1112yes—
684C22×D4C23×C1112yes—
685C23×C4—21no—
686#137—44no—
687AGL(1,ℤ/8)—44no—
688#135—44no—
689C2×Q16C23×C1112yes—
690C2×Q16C23×C1112yes—
691C2×Q16C23×C1112yes—
692C2×SD16—44no—
693C2×SD16C23×C1112yes—
694C2×SD16C23×C1112yes—
695C2×SD16C23×C1112yes—
696C2×SD16C23×C1112yes—
697C2×SD16C23×C1112yes—
698C2×SD16C23×C1112yes—
699C2×SD16C23×C1112yes—
700C2×D8C23×C1112yes—
701C2×D8C23×C1112yes—
702C2×M16C23×C1112yes—
703C2×M16C23×C1112yes—
704C22×C8C23×C1112yes—
705C22×C8C23×C1112yes—
706C4⋊Q8—22no—
707C4⋊Q8—21no—
708C4⋊Q8D4×C1111yescharacteristic
709C4⋊Q8C23×C1111yescharacteristic
710C4⋊Q8C23×C1111yescharacteristic
711C4⋊Q8C23×C1111yescharacteristic
712#127D4×C1111yescharacteristic
713#127C23×C1111yescharacteristic
714#126—22no—
715#126—21no—
716#125—22no—
717#125—21no—
718#125—21no—
719#125C23×C1111yescharacteristic
720#124—22no—
721#124—22no—
722#124—22no—
723#124D4×C1112yes—
724#124C23×C1111yescharacteristic
725#124C23×C1112yes—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731#123—22no—
732#123—22no—
733#123—22no—
734#123—22no—
735C22⋊Q8—22no—
736C22⋊Q8—22no—
737C22⋊Q8—21no—
738C22⋊Q8—22no—
739C22⋊Q8—22no—
740C22⋊Q8—22no—
741C22⋊Q8C23×C1111yescharacteristic
742C22⋊Q8C23×C1112yes—
743C22⋊Q8C23×C1112yes—
744C22⋊Q8C23×C1112yes—
745C22⋊Q8C23×C1112yes—
746C22⋊Q8C23×C1112yes—
747C22⋊Q8C23×C1112yes—
748#121—22no—
749#121—22no—
750#121—22no—
751#121—22no—
752#121—22no—
753#121—22no—
754#121—22no—
755#121—21no—
756#121—22no—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—22no—
761#121—22no—
762#121—22no—
763#121D4×C1112yes—
764#121D4×C1111yescharacteristic
765#121D4×C1111yescharacteristic
766#121C23×C1111yescharacteristic
767#121C23×C1112yes—
768#121C23×C1112yes—
769#121C23×C1112yes—
770#120—22no—
771#120—22no—
772#120—22no—
773#120—22no—
774C4×Q8—21no—
775C4×Q8C23×C1111yescharacteristic
776C4×Q8C23×C1112yes—
777C4×D4—21no—
778C4×D4—21no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783C4×D4—21no—
784C4×D4—21no—
785C4×D4C23×C1112yes—
786C4×D4C23×C1112yes—
787C4×D4C23×C1111yescharacteristic
788C4×D4C23×C1112yes—
789C4×D4C23×C1111yescharacteristic
790C4×D4C23×C1111yescharacteristic
791#117—21no—
792#117—21no—
793#117—22no—
794#117—21no—
795#117C23×C1112yes—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—21no—
798C2×C4⋊C4C23×C1111yescharacteristic
799C2×C4⋊C4C23×C1112yes—
800C2×C22⋊C4—21no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C42C23×C1111yescharacteristic
804#107C23×C1112yes—
805#107C23×C1112yes—
806#107C23×C1112yes—
807#106C23×C1112yes—
808C4⋊C8C23×C1112yes—
809C4⋊C8C23×C1112yes—
810#103C23×C1112yes—
811#103C23×C1112yes—
812#103C23×C1112yes—
813#103C23×C1112yes—
814#103C23×C1112yes—
815#103C23×C1112yes—
816#103C23×C1112yes—
817#102C23×C1112yes—
818#102C23×C1112yes—
819#102C23×C1112yes—
820#102C23×C1112yes—
821#102C23×C1112yes—
822#102C23×C1112yes—
823#102C23×C1112yes—
824#102C23×C1112yes—
825#102C23×C1112yes—
826C22⋊C8C23×C1111yescharacteristic
827C22⋊C8C23×C1112yes—
828C22⋊C8C23×C1111yescharacteristic
829C22⋊C8C23×C1112yes—
830C22⋊C8C23×C1112yes—
831C22⋊C8C23×C1112yes—
832C22⋊C8C23×C1112yes—
833#97C23×C1111yescharacteristic
834#97C23×C1111yescharacteristic
835#97C23×C1112yes—
836C2×C11—41no—
837C2×C11—42no—
838C2×C11—42no—
839C2×C11—44no—
840C2×C11—81no—
841C2×C11—82no—
842C2×C11#348411yescharacteristic
843C2×C11#358511yescharacteristic
844C2×C11#358611yescharacteristic
845C24—21no—
846C24—22no—
847C24—22no—
848#41—24no—
849#41—24no—
850#41—42no—
851#41—42no—
852#41—42no—
853#41—42no—
854#41—42no—
855#41—42no—
856#41—42no—
857#41—42no—
858#41—48no—
859C2×Q8—21no—
860C2×Q8—22no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8C2×D4×C1112yes—
864C2×Q8C24×C1112yes—
865C2×Q8C24×C1111yescharacteristic
866C2×Q8C24×C1112yes—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—21no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—21no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—48no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—84no—
889C2×D4C2×D4×C1111yescharacteristic
890C2×D4C2×D4×C1111yescharacteristic
891C2×D4C2×D4×C1112yes—
892C2×D4C2×D4×C1112yes—
893C2×D4C2×D4×C1112yes—
894C2×D4C2×D4×C1112yes—
895C2×D4C24×C1112yes—
896C2×D4C24×C1111yescharacteristic
897C2×D4C24×C1112yes—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—21no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—82no—
909C22×C4C2×D4×C1111yescharacteristic
910C22×C4C2×D4×C1111yescharacteristic
911C22×C4C24×C1111yescharacteristic
912C22×C4C24×C1112yes—
913C22×C4C24×C1112yes—
914Q16—42no—
915Q16—42no—
916Q16—42no—
917SD16—24no—
918SD16—24no—
919SD16—24no—
920SD16—42no—
921SD16—42no—
922SD16—42no—
923SD16—42no—
924D8—24no—
925D8—42no—
926M16—42no—
927M16—42no—
928C2×C8—42no—
929C2×C8—42no—
930C2×C8C24×C1112yes—
931C2×C8C24×C1112yes—
932C2×C8C24×C1112yes—
933C2×C8C24×C1112yes—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—21no—
952C4⋊C4C2×D4×C1112yes—
953C4⋊C4C2×D4×C1111yescharacteristic
954C4⋊C4C2×D4×C1111yescharacteristic
955C4⋊C4C24×C1111yescharacteristic
956C4⋊C4C24×C1111yescharacteristic
957C4⋊C4C24×C1112yes—
958C4⋊C4C24×C1112yes—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—21no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—21no—
973C22⋊C4—21no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—22no—
977C22⋊C4—21no—
978C22⋊C4C2×D4×C1112yes—
979C22⋊C4C2×D4×C1112yes—
980C22⋊C4C2×D4×C1112yes—
981C22⋊C4C2×D4×C1112yes—
982C42—22no—
983C42—22no—
984C42—21no—
985C42C2×D4×C1111yescharacteristic
986C42C2×D4×C1111yescharacteristic
987C42C24×C1111yescharacteristic
988C42C24×C1111yescharacteristic
989C11#6167011yescharacteristic, direct product factor, Sylow
990C23—24no—
991C23—22no—
992C23—21no—
993C23—22no—
994C23—44no—
995C23—44no—
996C23—81no—
997C23—81no—
998C23—82no—
999C23—82no—
1000C23—82no—
1001C23—82no—
1002C23C22×D4×C1112yes—
1003C23C22×D4×C1112yes—
1004C23C22×D4×C1111yescharacteristic
1005Q8—22no—
1006Q8—22no—
1007Q8—22no—
1008Q8—22no—
1009Q8—22no—
1010Q8—42no—
1011Q8—81no—
1012Q8—82no—
1013D4—24no—
1014D4—22no—
1015D4—22no—
1016D4—22no—
1017D4—22no—
1018D4—42no—
1019D4—42no—
1020D4—42no—
1021D4—42no—
1022D4—41no—
1023D4—41no—
1024D4—44no—
1025D4—44no—
1026D4—42no—
1027D4—44no—
1028D4—44no—
1029D4—44no—
1030D4—81no—
1031D4—81no—
1032D4—82no—
1033D4—82no—
1034D4—82no—
1035D4—82no—
1036D4C11×H(5,𝔽2)14yes—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—42no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—82no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—81no—
1060C2×C4—82no—
1061C2×C4C22×D4×C1111yescharacteristic
1062C2×C4C22×D4×C1111yescharacteristic
1063C2×C4C22×D4×C1112yes—
1064C2×C4C22×D4×C1111yescharacteristic
1065C2×C4C22×D4×C1111yescharacteristic
1066C2×C4C22×D4×C1111yescharacteristic
1067C2×C4C22×D4×C1112yes—
1068C2×C4C25×C1111yescharacteristic
1069C8—22no—
1070C8—22no—
1071C8—22no—
1072C8—22no—
1073C22—22no—
1074C22—21no—
1075C22—22no—
1076C22—24no—
1077C22—21no—
1078C22—22no—
1079C22—22no—
1080C22—21no—
1081C22—22no—
1082C22—22no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—41no—
1087C22—42no—
1088C22—41no—
1089C22—41no—
1090C22—42no—
1091C22—84no—
1092C22—164no—
1093C22—164no—
1094C22C23×D4×C1111yescharacteristic
1095C4—21no—
1096C4—22no—
1097C4—22no—
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—21no—
1102C4—42no—
1103C4—42no—
1104C4—41no—
1105C4—42no—
1106C4—41no—
1107C4—42no—
1108C4—41no—
1109C4C2×C11×H(5,𝔽2)12yes—
1110C2—41no—
1111C2—42no—
1112C2—42no—
1113C2—44no—
1114C2—82no—
1115C2—81no—
1116C2C11×#348411yescharacteristic
1117C2C11×#358511yescharacteristic
1118C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3547C2semidirect
2. C11×#3496C2semidirect
3. C11×#3319C2semidirect
4. C11×#3315C2semidirect
5. C11×#3314C2semidirect
6. C11×#3310C2semidirect
7. C11×#3269C2semidirect
8. C11×#3267C2semidirect
9. C11×#3266C2semidirect
10. C11×#3265C2semidirect
11. C11×#3219C2semidirect
12. C11×#3216C2semidirect
13. C11×#3203C2semidirect
14. C11×#3201C2semidirect
15. C11×#3114C2semidirect
16. C11×#3110C2semidirect
17. C11×#3012C2semidirect
18. C11×#3009C2semidirect
19. C11×#2980C2semidirect
21. C2×C11×#137C22semidirect
22. C2×C11×AGL(1,ℤ/8)C22semidirect
23. C2×C11×#135C22semidirect
24. C22×C11×SD16C22semidirect
27. C11×#555C22semidirect
28. C11×#554C22semidirect
30. C11×#552C22semidirect
31. D4×Q8×C11C22semidirect
32. C11×#548C22semidirect
35. C11×#547C22semidirect
45. C11×#537C22semidirect
46. C11×#536C22semidirect
49. C11×#533C22semidirect
52. C11×#529C22semidirect
55. C11×#497C22semidirect
56. C11×#497C22semidirect
57. C11×#496C22semidirect
58. C11×#491C22semidirect
59. C11×#490C22semidirect
60. C11×#489C22semidirect
61. C11×#485C22semidirect
62. C11×#484C22semidirect
63. C11×#484C22semidirect
64. C11×#483C22semidirect
65. C11×#482C22semidirect
66. C11×#480C22semidirect
67. C11×#480C22semidirect
68. C11×#478C22semidirect
69. C11×#474C22semidirect
70. C11×#470C22semidirect
71. C11×#468C22semidirect
72. C11×#468C22semidirect
73. C11×#468C22semidirect
74. C11×#467C22semidirect
75. C11×#467C22semidirect
76. C11×#466C22semidirect
77. C11×#465C22semidirect
78. C11×#464C22semidirect
79. C11×#463C22semidirect
80. C11×#463C22semidirect
81. C11×#462C22semidirect
82. C11×#461C22semidirect
83. C11×#460C22semidirect
84. C11×#452C22semidirect
85. C11×#452C22semidirect
86. C11×#452C22semidirect
87. C11×#452C22semidirect
88. C11×#452C22semidirect
89. C11×#452C22semidirect
90. C11×#452C22semidirect
91. C11×#451C22semidirect
94. C11×#450C22semidirect
95. C11×#450C22semidirect
96. C11×#450C22semidirect
97. C11×#449C22semidirect
98. C11×#449C22semidirect
99. C11×#449C22semidirect
100. C11×#448C22semidirect
102. C11×#447C22semidirect
103. C11×#442C22semidirect
104. C11×#440C22semidirect
105. C11×#440C22semidirect
106. C11×#440C22semidirect
107. C11×#435C22semidirect
108. C11×#435C22semidirect
109. C11×#435C22semidirect
110. C11×#435C22semidirect
111. C11×#432C22semidirect
112. C11×#432C22semidirect
113. C11×#418C22semidirect
114. C11×#417C22semidirect
115. C11×#416C22semidirect
116. C2×C11×#102C22semidirect
117. C11×#408C22semidirect
118. C11×#408C22semidirect
286. #61670C11direct (N × H)
431. #3547C2×C11semidirect
432. #3496C2×C11semidirect
433. #3319C2×C11semidirect
434. #3315C2×C11semidirect
435. #3314C2×C11semidirect
436. #3310C2×C11semidirect
437. #3269C2×C11semidirect
438. #3267C2×C11semidirect
439. #3266C2×C11semidirect
440. #3265C2×C11semidirect
441. #3219C2×C11semidirect
442. #3216C2×C11semidirect
443. #3203C2×C11semidirect
444. #3201C2×C11semidirect
445. #3114C2×C11semidirect
446. #3110C2×C11semidirect
447. #3012C2×C11semidirect
448. #3009C2×C11semidirect
449. #2980C2×C11semidirect
534. C2×#137C22×C11semidirect
535. C2×AGL(1,ℤ/8)C22×C11semidirect
536. C2×#135C22×C11semidirect
537. C22×SD16C22×C11semidirect
540. #555C22×C11semidirect
541. #554C22×C11semidirect
543. #552C22×C11semidirect
544. D4×Q8C22×C11semidirect
545. #548C22×C11semidirect
548. #547C22×C11semidirect
558. #537C22×C11semidirect
559. #536C22×C11semidirect
562. #533C22×C11semidirect
565. #529C22×C11semidirect
568. #497C22×C11semidirect
569. #497C22×C11semidirect
570. #496C22×C11semidirect
571. #491C22×C11semidirect
572. #490C22×C11semidirect
573. #489C22×C11semidirect
574. #485C22×C11semidirect
575. #484C22×C11semidirect
576. #484C22×C11semidirect
577. #483C22×C11semidirect
578. #482C22×C11semidirect
579. #480C22×C11semidirect
580. #480C22×C11semidirect
581. #478C22×C11semidirect
582. #474C22×C11semidirect
583. #470C22×C11semidirect
584. #468C22×C11semidirect
585. #468C22×C11semidirect
586. #468C22×C11semidirect
587. #467C22×C11semidirect
588. #467C22×C11semidirect
589. #466C22×C11semidirect
590. #465C22×C11semidirect
591. #464C22×C11semidirect
592. #463C22×C11semidirect
593. #463C22×C11semidirect
594. #462C22×C11semidirect
595. #461C22×C11semidirect
596. #460C22×C11semidirect
597. #452C22×C11semidirect
598. #452C22×C11semidirect
599. #452C22×C11semidirect
600. #452C22×C11semidirect
601. #452C22×C11semidirect
602. #452C22×C11semidirect
603. #452C22×C11semidirect
604. #451C22×C11semidirect
607. #450C22×C11semidirect
608. #450C22×C11semidirect
609. #450C22×C11semidirect
610. #449C22×C11semidirect
611. #449C22×C11semidirect
612. #449C22×C11semidirect
613. #448C22×C11semidirect
615. #447C22×C11semidirect
616. #442C22×C11semidirect
617. #440C22×C11semidirect
618. #440C22×C11semidirect
619. #440C22×C11semidirect
620. #435C22×C11semidirect
621. #435C22×C11semidirect
622. #435C22×C11semidirect
623. #435C22×C11semidirect
624. #432C22×C11semidirect
625. #432C22×C11semidirect
626. #418C22×C11semidirect
627. #417C22×C11semidirect
628. #416C22×C11semidirect
629. C2×#102C22×C11semidirect
630. #408C22×C11semidirect
631. #408C22×C11semidirect
989. C11#61670direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35472
C11×#34962
C11×#33192
C11×#33152
C11×#33142
C11×#33102
C11×#32692
C11×#32672
C11×#32662
C11×#32652
C11×#32192
C11×#32162
C11×#32032
C11×#32012
C11×#31142
C11×#31102
C11×#30122
C11×#30092
C11×#29802
#6167011