Finite Group Databasebeta

← C11×#61494 #14638687

Subgroups — C11×#61494 #14638687

Order 2816.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3514C211yesmaximal, characteristic, complemented
3C11×#3399C211yesmaximal, characteristic, complemented
4C11×#3386C211yesmaximal, characteristic, complemented
5C11×#3365C211yesmaximal, characteristic, complemented
6C11×#3358C211yesmaximal, characteristic, complemented
7C11×#3353C211yesmaximal, characteristic, complemented
8C11×#3347C212yesmaximal, complemented
9C11×#3305C212yesmaximal, complemented
10C11×#3304C211yesmaximal, characteristic, complemented
11C11×#3297C212yesmaximal, complemented
12C11×#3294C211yesmaximal, characteristic, complemented
13C11×#3274C211yesmaximal, characteristic, complemented
14C11×#3268C212yesmaximal, complemented
15C11×#3179C212yesmaximal, complemented
16C11×#3169C211yesmaximal, characteristic, complemented
17C11×#3124C212yesmaximal, complemented
18C11×#3122C212yesmaximal, complemented
19C11×#3115C211yesmaximal, characteristic, complemented
20C11×#3115C211yesmaximal, characteristic, complemented
21C11×#2966C211yesmaximal, characteristic, complemented
22C11×#2946C212yesmaximal, complemented
23C4×C11×#135C211yesmaximal, characteristic, complemented
24C2×C11×AGL(1,ℤ/8)C2212yes—
25C2×C11×#135C2211yescharacteristic
26C11×#559C2211yescharacteristic
27C11×#557C2211yescharacteristic, complemented
28C11×#556C2211yescharacteristic
29C11×#555C2212yes—
30C11×#553—22no—
31C11×#553C2212yescomplemented
32C11×#551—22no—
33C11×#550—21no—
34C11×#550C2211yescharacteristic
35C11×#550C2212yescomplemented
36C11×#550C2211yescharacteristic, complemented
37D4×Q8×C11C2211yescharacteristic
38C11×#548—21no—
39C11×#547—21no—
40C11×#547C2211yescharacteristic
41C11×#546—21no—
42C11×#546C2212yes—
43D42×C11C2211yescharacteristic
44C11×#542C2212yes—
45C11×#540—22no—
46C11×#540C2212yescomplemented
47C11×#538—22no—
48C11×#532—21no—
49C11×#532C2211yescharacteristic
50C11×#532C2211yescharacteristic, complemented
51C11×#529—21no—
52C11×#529—21no—
53C11×#529C2211yescharacteristic
54C2×C11×#124—21no—
55C11×#520C2212yescomplemented
56C11×#518C2212yes—
57C4×C11×#41C2211yescharacteristic
58C4×C11×#41C2211yescharacteristic, complemented
59C11×#501C2212yescomplemented
60C11×#500C2211yescharacteristic, complemented
61C11×#496C2212yescomplemented
62C11×#493C2211yescharacteristic
63C11×#488C2212yescomplemented
64C11×#486C2211yescharacteristic
65C11×#486C2211yescharacteristic, complemented
66C11×#486C2212yescomplemented
67C11×#484C2212yescomplemented
68C11×#482C2212yescomplemented
69C11×#482C2212yescomplemented
70C11×#482C2212yescomplemented
71C11×#482C2212yescomplemented
72C11×#480C2212yes—
73C11×#478C2212yes—
74C11×#478C2212yescomplemented
75C11×#477C2212yescomplemented
76C11×#475C2211yescharacteristic, complemented
77C11×#475C2211yescharacteristic, complemented
78C11×#474C2211yescharacteristic
79C11×#474C2212yescomplemented
80C11×#474C2211yescharacteristic, complemented
81C11×#469C2212yes—
82C11×#468C2212yescomplemented
83C11×#466C2212yes—
84C11×#466C2212yescomplemented
85C11×#466C2212yescomplemented
86C11×#465C2212yescomplemented
87C11×#464C2212yescomplemented
88C11×#463C2212yescomplemented
89C11×#460C2211yescharacteristic
90C11×#460C2211yescharacteristic, complemented
91C11×#459C2212yes—
92C11×#459C2211yescharacteristic
93C11×#459C2211yescharacteristic
94C11×#459C2212yescomplemented
95C11×#452C2212yescomplemented
96C11×#449C2212yes—
97C11×#449C2212yes—
98C11×#449C2212yescomplemented
99C11×#447C2212yes—
100C11×#447C2212yes—
101C11×#446C2211yescharacteristic, complemented
102C8×Q8×C11C2211yescharacteristic, complemented
103C11×#442C2212yes—
104C11×#442C2212yescomplemented
105C11×#442C2212yescomplemented
106C11×#440C2212yes—
107C11×#440C2212yescomplemented
108C11×#440C2212yescomplemented
109C4×C11×Q16C2211yescharacteristic, complemented
110C4×C11×Q16C2211yescharacteristic, complemented
111C4×C11×SD16C2211yescharacteristic
112C4×C11×SD16C2211yescharacteristic
113C4×C11×SD16C2211yescharacteristic, complemented
114C4×C11×SD16C2211yescharacteristic, complemented
115C4×C11×SD16C2212yescomplemented
116C4×C11×D8C2211yescharacteristic
117C4×C11×D8C2211yescharacteristic
118C4×C11×D8C2212yes—
119C4×C11×D8C2212yescomplemented
120C4×C11×D8C2212yescomplemented
121C11×#436C2211yescharacteristic
122C11×#435C2212yescomplemented
123C8×D4×C11C2211yescharacteristic
124C8×D4×C11C2212yescomplemented
125C11×#433C2212yescomplemented
126C11×#432C2211yescharacteristic, complemented
127C11×#428C2212yescomplemented
128C11×#427C2211yescharacteristic, complemented
129C11×#416C2211yescharacteristic
130C11×#416C2211yescharacteristic, complemented
131C11×#416C2212yescomplemented
132C2×C11×#102C2212yes—
133C11×#405C2212yescomplemented
134C2×C4×C8×C11C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41—21no—
138C2×C11×#41—21no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2312yes—
142C22×Q8×C11—21no—
143C22×D4×C11—21no—
144C22×D4×C11C2312yes—
145C11×AGL(1,ℤ/8)—28no—
146C11×#135—24no—
147C2×C11×Q16C2311yescharacteristic
148C2×C11×SD16C2311yescharacteristic
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2311yescharacteristic
152C2×C11×D8C2312yes—
153C2×C11×D8C2311yescharacteristic
154C2×C11×D8C2312yes—
155C2×C11×D8C2312yes—
156C2×C11×D8C2312yes—
157C2×C11×M16C2312yes—
158C22×C8×C11C2311yescharacteristic
159C22×C8×C11C2311yescharacteristic
160C22×C8×C11C2312yes—
161C11×C4⋊Q8—21no—
162C11×C4⋊Q8C2311yescharacteristic
163C11×C4⋊Q8C2311yescharacteristic
164C11×C4⋊Q8C2312yes—
165C11×#127—21no—
166C11×#127—22no—
167C11×#127C2311yescharacteristic
168C11×#127C2311yescharacteristic
169C11×#127C2312yes—
170C11×#126—22no—
171C11×#126—22no—
172C11×#126—22no—
173C11×#126D412yes—
174C11×#125—22no—
175C11×#125D411yescharacteristic
176C11×#125C2312yes—
177C11×#124—21no—
178C11×#124—21no—
179C11×#124—22no—
180C11×#124—22no—
181C11×#124—22no—
182C11×#124—21no—
183C11×#124—21no—
184C11×#124D411yescharacteristic
185C11×#124C2312yes—
186C11×#123—22no—
187C11×#123—22no—
188C11×#123—22no—
189C11×#123—22no—
190C11×#123—22no—
191C11×#123—22no—
192C11×#123—22no—
193C11×#123D412yes—
194C11×C22⋊Q8—21no—
195C11×C22⋊Q8—21no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8D411yescharacteristic
199C11×C22⋊Q8C2312yes—
200C11×#121—22no—
201C11×#121—22no—
202C11×#121—21no—
203C11×#121—21no—
204C11×#121—21no—
205C11×#121—21no—
206C11×#121—22no—
207C11×#121—22no—
208C11×#121—22no—
209C11×#121—22no—
210C11×#121—22no—
211C11×#121—22no—
212C11×#121—22no—
213C11×#121D411yescharacteristic
214C11×#121C2312yes—
215C11×#121C2312yes—
216C11×#121C2312yes—
217C11×#121C2312yes—
218C11×#121C2312yes—
219C11×#120—22no—
220C11×#120—22no—
221C4×Q8×C11—21no—
222C4×Q8×C11—21no—
223C4×Q8×C11C2311yescharacteristic
224C4×Q8×C11C2311yescharacteristic
225C4×Q8×C11C2311yescharacteristic
226C4×Q8×C11C2311yescharacteristic
227C4×Q8×C11C2312yes—
228C4×Q8×C11C2311yescharacteristic
229C4×D4×C11—21no—
230C4×D4×C11—21no—
231C4×D4×C11—21no—
232C4×D4×C11—21no—
233C4×D4×C11—22no—
234C4×D4×C11—22no—
235C4×D4×C11—21no—
236C4×D4×C11—21no—
237C4×D4×C11—22no—
238C4×D4×C11—22no—
239C4×D4×C11—22no—
240C4×D4×C11—22no—
241C4×D4×C11—21no—
242C4×D4×C11—21no—
243C4×D4×C11C2311yescharacteristic
244C4×D4×C11C2311yescharacteristic
245C4×D4×C11C2311yescharacteristic
246C4×D4×C11C2311yescharacteristic
247C4×D4×C11C2312yes—
248C4×D4×C11C2312yes—
249C4×D4×C11C2312yes—
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2311yescharacteristic
253C4×D4×C11C2312yes—
254C11×#117—22no—
255C11×#117—22no—
256C11×#117—21no—
257C11×#117—21no—
258C11×#117C2311yescharacteristic
259C11×#117C2311yescharacteristic
260C11×#117C2312yes—
261C11×#117C2312yes—
262C2×C11×C4⋊C4—22no—
263C2×C11×C4⋊C4C2312yes—
264C2×C11×C22⋊C4—22no—
265C2×C11×C22⋊C4—22no—
266C2×C11×C22⋊C4—22no—
267C2×C42×C11—21no—
268C2×C42×C11—21no—
269C2×C42×C11C2311yescharacteristic
270C11×#107C2312yes—
271C11×#107C2312yes—
272C11×#107C2312yes—
273C11×#107C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#107C2312yes—
276C11×#106C2311yescharacteristic
277C11×#106C2312yes—
278C11×#106C2311yescharacteristic
279C11×#106C2312yes—
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×#103C2311yescharacteristic
285C11×#103C2311yescharacteristic
286C11×#103C2311yescharacteristic
287C11×#103C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#102C2311yescharacteristic
291C11×#102C2312yes—
292C11×#102C2312yes—
293C11×#102C2312yes—
294C11×#102C2311yescharacteristic
295C11×#102C2312yes—
296C11×#102C2311yescharacteristic
297C11×#102C2311yescharacteristic
298C11×#102C2312yes—
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2312yes—
304C11×C22⋊C8C2312yes—
305C11×C22⋊C8C2312yes—
306C11×C22⋊C8C2312yes—
307C11×#97C2312yes—
308C11×#97C2312yes—
309C4×C8×C11C2311yescharacteristic
310C4×C8×C11C2311yescharacteristic
311C4×C8×C11C2311yescharacteristic
312C4×C8×C11C2311yescharacteristic
313C4×C8×C11C2312yes—
314#61494C1111yesmaximal, characteristic, direct product factor, Sylow
315C24×C11—22no—
316C11×#41—22no—
317C11×#41—24no—
318C11×#41—22no—
319C11×#41—42no—
320C11×#41—41no—
321C11×#41—41no—
322C11×#41—82no—
323C11×#41—82no—
324C11×#41—82no—
325C11×#41—82no—
326C2×Q8×C11—21no—
327C2×Q8×C11—21no—
328C2×Q8×C11—22no—
329C2×Q8×C11—82no—
330C2×Q8×C11C2×D411yescharacteristic
331C2×Q8×C11C2411yescharacteristic
332C2×Q8×C11C2411yescharacteristic
333C2×D4×C11—24no—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11—21no—
337C2×D4×C11—22no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—21no—
344C2×D4×C11—21no—
345C2×D4×C11—21no—
346C2×D4×C11—21no—
347C2×D4×C11—22no—
348C2×D4×C11—22no—
349C2×D4×C11—42no—
350C2×D4×C11—82no—
351C2×D4×C11C2×D411yescharacteristic
352C2×D4×C11C2×D412yes—
353C2×D4×C11C2412yes—
354C2×D4×C11C2412yes—
355C2×D4×C11C2411yescharacteristic
356C2×D4×C11C2411yescharacteristic
357C22×C4×C11—22no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—21no—
361C22×C4×C11—21no—
362C22×C4×C11—22no—
363C22×C4×C11—21no—
364C22×C4×C11—21no—
365C22×C4×C11—22no—
366C22×C4×C11—22no—
367C22×C4×C11—22no—
368C22×C4×C11—22no—
369C22×C4×C11—22no—
370C22×C4×C11C2×D411yescharacteristic
371C22×C4×C11C2×D411yescharacteristic
372C22×C4×C11C2411yescharacteristic
373C22×C4×C11C2412yes—
374C11×Q16—22no—
375C11×SD16—22no—
376C11×SD16—24no—
377C11×SD16—42no—
378C11×SD16#4114yescomplemented
379C11×D8—24no—
380C11×D8—22no—
381C11×D8—24no—
382C11×D8—42no—
383C11×D8—42no—
384C11×M16—24no—
385C2×C8×C11—22no—
386C2×C8×C11—42no—
387C2×C8×C11—41no—
388C2×C8×C11C2411yescharacteristic
389C2×C8×C11C2411yescharacteristic
390C2×C8×C11C2411yescharacteristic
391C2×C8×C11C2412yes—
392C2×C8×C11C2412yes—
393C2×C8×C11C2411yescharacteristic
394C11×C4⋊C4—21no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4C2×D412yes—
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2×D411yescharacteristic
410C11×C4⋊C4C2×D411yescharacteristic
411C11×C4⋊C4C2×D412yes—
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2411yescharacteristic
415C11×C4⋊C4C2412yes—
416C11×C4⋊C4C2412yes—
417C11×C4⋊C4C2411yescharacteristic
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—21no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—21no—
431C11×C22⋊C4—21no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4C2×D412yes—
439C11×C22⋊C4C2×D412yes—
440C11×C22⋊C4C2×D412yes—
441C11×C22⋊C4C2×D412yes—
442C11×C22⋊C4C2×D412yes—
443C42×C11—21no—
444C42×C11—21no—
445C42×C11—21no—
446C42×C11—21no—
447C42×C11—21no—
448C42×C11—21no—
449C42×C11—22no—
450C42×C11—22no—
451C42×C11C2×D411yescharacteristic
452C42×C11C2×D411yescharacteristic
453C42×C11C2411yescharacteristic
454C42×C11C2411yescharacteristic
455C42×C11C2412yes—
456#3517C2×C1111yescharacteristic, complemented
457#3514C2×C1111yescharacteristic, complemented
458#3399C2×C1111yescharacteristic, complemented
459#3386C2×C1111yescharacteristic, complemented
460#3365C2×C1111yescharacteristic, complemented
461#3358C2×C1111yescharacteristic, complemented
462#3353C2×C1111yescharacteristic, complemented
463#3347C2×C1112yescomplemented
464#3305C2×C1112yescomplemented
465#3304C2×C1111yescharacteristic, complemented
466#3297C2×C1112yescomplemented
467#3294C2×C1111yescharacteristic, complemented
468#3274C2×C1111yescharacteristic, complemented
469#3268C2×C1112yescomplemented
470#3179C2×C1112yescomplemented
471#3169C2×C1111yescharacteristic, complemented
472#3124C2×C1112yescomplemented
473#3122C2×C1112yescomplemented
474#3115C2×C1111yescharacteristic, complemented
475#3115C2×C1111yescharacteristic, complemented
476#2966C2×C1111yescharacteristic, complemented
477#2946C2×C1112yescomplemented
478C4×#135C2×C1111yescharacteristic, complemented
479C23×C11—21no—
480C23×C11—22no—
481C23×C11—21no—
482C23×C11—22no—
483C23×C11—44no—
484C23×C11—82no—
485C23×C11—82no—
486C23×C11C22×D412yes—
487C23×C11C22×D411yescharacteristic
488Q8×C11—22no—
489Q8×C11—21no—
490Q8×C11—21no—
491Q8×C11—21no—
492Q8×C11—42no—
493Q8×C11—42no—
494Q8×C11—82no—
495Q8×C11C2×#4112yes—
496D4×C11—22no—
497D4×C11—22no—
498D4×C11—22no—
499D4×C11—21no—
500D4×C11—21no—
501D4×C11—22no—
502D4×C11—21no—
503D4×C11—22no—
504D4×C11—42no—
505D4×C11—44no—
506D4×C11—42no—
507D4×C11—44no—
508D4×C11—42no—
509D4×C11—42no—
510D4×C11—42no—
511D4×C11—81no—
512D4×C11—81no—
513D4×C11—82no—
514D4×C11—82no—
515D4×C11—82no—
516D4×C11—82no—
517D4×C11—82no—
518D4×C11—82no—
519D4×C11—82no—
520D4×C11C2×#4112yes—
521C2×C4×C11—21no—
522C2×C4×C11—22no—
523C2×C4×C11—21no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—41no—
535C2×C4×C11—42no—
536C2×C4×C11—44no—
537C2×C4×C11—42no—
538C2×C4×C11—42no—
539C2×C4×C11—42no—
540C2×C4×C11—81no—
541C2×C4×C11—81no—
542C2×C4×C11—82no—
543C2×C4×C11—82no—
544C2×C4×C11—82no—
545C2×C4×C11—82no—
546C2×C4×C11—82no—
547C2×C4×C11—82no—
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D412yes—
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C22×D412yes—
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C2511yescharacteristic
557C8×C11—21no—
558C8×C11—22no—
559C8×C11—21no—
560C8×C11—21no—
561C8×C11—22no—
562C8×C11C2×#4112yes—
563C2×AGL(1,ℤ/8)C22×C1112yes—
564C2×#135C22×C1111yescharacteristic
565#559C22×C1111yescharacteristic
566#557C22×C1111yescharacteristic, complemented
567#556C22×C1111yescharacteristic
568#555C22×C1112yes—
569#553—22no—
570#553C22×C1112yescomplemented
571#551—22no—
572#550—21no—
573#550C22×C1111yescharacteristic
574#550C22×C1112yescomplemented
575#550C22×C1111yescharacteristic, complemented
576D4×Q8C22×C1111yescharacteristic
577#548—21no—
578#547—21no—
579#547C22×C1111yescharacteristic
580#546—21no—
581#546C22×C1112yes—
582D42C22×C1111yescharacteristic
583#542C22×C1112yes—
584#540—22no—
585#540C22×C1112yescomplemented
586#538—22no—
587#532—21no—
588#532C22×C1111yescharacteristic
589#532C22×C1111yescharacteristic, complemented
590#529—21no—
591#529—21no—
592#529C22×C1111yescharacteristic
593C2×#124—21no—
594#520C22×C1112yescomplemented
595#518C22×C1112yes—
596C4×#41C22×C1111yescharacteristic
597C4×#41C22×C1111yescharacteristic, complemented
598#501C22×C1112yescomplemented
599#500C22×C1111yescharacteristic, complemented
600#496C22×C1112yescomplemented
601#493C22×C1111yescharacteristic
602#488C22×C1112yescomplemented
603#486C22×C1111yescharacteristic
604#486C22×C1111yescharacteristic, complemented
605#486C22×C1112yescomplemented
606#484C22×C1112yescomplemented
607#482C22×C1112yescomplemented
608#482C22×C1112yescomplemented
609#482C22×C1112yescomplemented
610#482C22×C1112yescomplemented
611#480C22×C1112yes—
612#478C22×C1112yes—
613#478C22×C1112yescomplemented
614#477C22×C1112yescomplemented
615#475C22×C1111yescharacteristic, complemented
616#475C22×C1111yescharacteristic, complemented
617#474C22×C1111yescharacteristic
618#474C22×C1112yescomplemented
619#474C22×C1111yescharacteristic, complemented
620#469C22×C1112yes—
621#468C22×C1112yescomplemented
622#466C22×C1112yes—
623#466C22×C1112yescomplemented
624#466C22×C1112yescomplemented
625#465C22×C1112yescomplemented
626#464C22×C1112yescomplemented
627#463C22×C1112yescomplemented
628#460C22×C1111yescharacteristic
629#460C22×C1111yescharacteristic, complemented
630#459C22×C1111yescharacteristic
631#459C22×C1112yes—
632#459C22×C1111yescharacteristic
633#459C22×C1112yescomplemented
634#452C22×C1112yescomplemented
635#449C22×C1112yes—
636#449C22×C1112yes—
637#449C22×C1112yescomplemented
638#447C22×C1112yes—
639#447C22×C1112yes—
640#446C22×C1111yescharacteristic, complemented
641C8×Q8C22×C1111yescharacteristic, complemented
642#442C22×C1112yes—
643#442C22×C1112yescomplemented
644#442C22×C1112yescomplemented
645#440C22×C1112yes—
646#440C22×C1112yescomplemented
647#440C22×C1112yescomplemented
648C4×Q16C22×C1111yescharacteristic, complemented
649C4×Q16C22×C1111yescharacteristic, complemented
650C4×SD16C22×C1111yescharacteristic
651C4×SD16C22×C1111yescharacteristic
652C4×SD16C22×C1111yescharacteristic, complemented
653C4×SD16C22×C1112yescomplemented
654C4×SD16C22×C1111yescharacteristic, complemented
655C4×D8C22×C1111yescharacteristic
656C4×D8C22×C1112yes—
657C4×D8C22×C1111yescharacteristic
658C4×D8C22×C1112yescomplemented
659C4×D8C22×C1112yescomplemented
660#436C22×C1111yescharacteristic
661#435C22×C1112yescomplemented
662C8×D4C22×C1111yescharacteristic
663C8×D4C22×C1112yescomplemented
664#433C22×C1112yescomplemented
665#432C22×C1111yescharacteristic, complemented
666#428C22×C1112yescomplemented
667#427C22×C1111yescharacteristic, complemented
668#416C22×C1111yescharacteristic
669#416C22×C1111yescharacteristic, complemented
670#416C22×C1112yescomplemented
671C2×#102C22×C1112yes—
672#405C22×C1112yescomplemented
673C2×C4×C8C22×C1111yescharacteristic, complemented
674C22×C11—21no—
675C22×C11—22no—
676C22×C11—21no—
677C22×C11—22no—
678C22×C11—22no—
679C22×C11—21no—
680C22×C11—22no—
681C22×C11—41no—
682C22×C11—41no—
683C22×C11—41no—
684C22×C11—42no—
685C22×C11—42no—
686C22×C11—42no—
687C22×C11—41no—
688C22×C11—42no—
689C22×C11—41no—
690C22×C11—42no—
691C22×C11—42no—
692C22×C11—164no—
693C22×C11C23×D411yescharacteristic
694C4×C11—21no—
695C4×C11—21no—
696C4×C11—22no—
697C4×C11—21no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—21no—
701C4×C11—22no—
702C4×C11—41no—
703C4×C11—41no—
704C4×C11—41no—
705C4×C11—41no—
706C4×C11—41no—
707C4×C11—42no—
708C4×C11—42no—
709C4×C11#57612yes—
710C4×C11C22×#4111yescharacteristic
711C4×C11#58511yescharacteristic
712C2×#41—21no—
713C2×#41—21no—
714C2×#41—21no—
715C2×#41—21no—
716C2×#41C23×C1111yescharacteristic
717C2×#41C23×C1111yescharacteristic
718C2×#41C23×C1112yes—
719C22×Q8—21no—
720C22×D4—21no—
721C22×D4C23×C1112yes—
722AGL(1,ℤ/8)—28no—
723#135—24no—
724C2×Q16C23×C1111yescharacteristic
725C2×SD16C23×C1111yescharacteristic
726C2×SD16C23×C1112yes—
727C2×SD16C23×C1112yes—
728C2×SD16C23×C1111yescharacteristic
729C2×D8C23×C1111yescharacteristic
730C2×D8C23×C1112yes—
731C2×D8C23×C1112yes—
732C2×D8C23×C1112yes—
733C2×D8C23×C1112yes—
734C2×M16C23×C1112yes—
735C22×C8C23×C1111yescharacteristic
736C22×C8C23×C1111yescharacteristic
737C22×C8C23×C1112yes—
738C4⋊Q8—21no—
739C4⋊Q8C23×C1111yescharacteristic
740C4⋊Q8C23×C1111yescharacteristic
741C4⋊Q8C23×C1112yes—
742#127—21no—
743#127—22no—
744#127C23×C1111yescharacteristic
745#127C23×C1111yescharacteristic
746#127C23×C1112yes—
747#126—22no—
748#126—22no—
749#126—22no—
750#126D4×C1112yes—
751#125—22no—
752#125D4×C1111yescharacteristic
753#125C23×C1112yes—
754#124—21no—
755#124—21no—
756#124—22no—
757#124—22no—
758#124—22no—
759#124—21no—
760#124—21no—
761#124D4×C1111yescharacteristic
762#124C23×C1112yes—
763#123—22no—
764#123—22no—
765#123—22no—
766#123—22no—
767#123—22no—
768#123—22no—
769#123—22no—
770#123D4×C1112yes—
771C22⋊Q8—21no—
772C22⋊Q8—21no—
773C22⋊Q8—22no—
774C22⋊Q8—22no—
775C22⋊Q8D4×C1111yescharacteristic
776C22⋊Q8C23×C1112yes—
777#121—22no—
778#121—22no—
779#121—21no—
780#121—21no—
781#121—21no—
782#121—21no—
783#121—22no—
784#121—22no—
785#121—22no—
786#121—22no—
787#121—22no—
788#121—22no—
789#121—22no—
790#121D4×C1111yescharacteristic
791#121C23×C1112yes—
792#121C23×C1112yes—
793#121C23×C1112yes—
794#121C23×C1112yes—
795#121C23×C1112yes—
796#120—22no—
797#120—22no—
798C4×Q8—21no—
799C4×Q8—21no—
800C4×Q8C23×C1111yescharacteristic
801C4×Q8C23×C1111yescharacteristic
802C4×Q8C23×C1111yescharacteristic
803C4×Q8C23×C1111yescharacteristic
804C4×Q8C23×C1112yes—
805C4×Q8C23×C1111yescharacteristic
806C4×D4—21no—
807C4×D4—21no—
808C4×D4—21no—
809C4×D4—21no—
810C4×D4—22no—
811C4×D4—22no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—22no—
815C4×D4—22no—
816C4×D4—22no—
817C4×D4—22no—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4C23×C1111yescharacteristic
821C4×D4C23×C1111yescharacteristic
822C4×D4C23×C1111yescharacteristic
823C4×D4C23×C1111yescharacteristic
824C4×D4C23×C1112yes—
825C4×D4C23×C1112yes—
826C4×D4C23×C1112yes—
827C4×D4C23×C1112yes—
828C4×D4C23×C1112yes—
829C4×D4C23×C1111yescharacteristic
830C4×D4C23×C1112yes—
831#117—22no—
832#117—22no—
833#117—21no—
834#117—21no—
835#117C23×C1111yescharacteristic
836#117C23×C1111yescharacteristic
837#117C23×C1112yes—
838#117C23×C1112yes—
839C2×C4⋊C4—22no—
840C2×C4⋊C4C23×C1112yes—
841C2×C22⋊C4—22no—
842C2×C22⋊C4—22no—
843C2×C22⋊C4—22no—
844C2×C42—21no—
845C2×C42—21no—
846C2×C42C23×C1111yescharacteristic
847#107C23×C1111yescharacteristic
848#107C23×C1111yescharacteristic
849#107C23×C1112yes—
850#107C23×C1112yes—
851#107C23×C1112yes—
852#107C23×C1112yes—
853#106C23×C1111yescharacteristic
854#106C23×C1111yescharacteristic
855#106C23×C1112yes—
856#106C23×C1112yes—
857C4⋊C8C23×C1111yescharacteristic
858C4⋊C8C23×C1111yescharacteristic
859C4⋊C8C23×C1112yes—
860C4⋊C8C23×C1112yes—
861#103C23×C1111yescharacteristic
862#103C23×C1111yescharacteristic
863#103C23×C1111yescharacteristic
864#103C23×C1111yescharacteristic
865#103C23×C1112yes—
866#103C23×C1112yes—
867#102C23×C1111yescharacteristic
868#102C23×C1112yes—
869#102C23×C1112yes—
870#102C23×C1112yes—
871#102C23×C1111yescharacteristic
872#102C23×C1112yes—
873#102C23×C1111yescharacteristic
874#102C23×C1111yescharacteristic
875#102C23×C1112yes—
876#102C23×C1112yes—
877#102C23×C1112yes—
878#102C23×C1112yes—
879#102C23×C1112yes—
880#102C23×C1112yes—
881C22⋊C8C23×C1112yes—
882C22⋊C8C23×C1112yes—
883C22⋊C8C23×C1112yes—
884#97C23×C1112yes—
885#97C23×C1112yes—
886C4×C8C23×C1111yescharacteristic
887C4×C8C23×C1111yescharacteristic
888C4×C8C23×C1111yescharacteristic
889C4×C8C23×C1111yescharacteristic
890C4×C8C23×C1112yes—
891C2×C11—41no—
892C2×C11—42no—
893C2×C11—42no—
894C2×C11—81no—
895C2×C11—82no—
896C2×C11—82no—
897C2×C11D4×#4111yescharacteristic
898C2×C11C2×#57611yescharacteristic
899C2×C11#358411yescharacteristic
900C24—22no—
901#41—22no—
902#41—24no—
903#41—22no—
904#41—42no—
905#41—41no—
906#41—41no—
907#41—82no—
908#41—82no—
909#41—82no—
910#41—82no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—22no—
914C2×Q8—82no—
915C2×Q8C2×D4×C1111yescharacteristic
916C2×Q8C24×C1111yescharacteristic
917C2×Q8C24×C1111yescharacteristic
918C2×D4—24no—
919C2×D4—21no—
920C2×D4—22no—
921C2×D4—21no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—22no—
927C2×D4—22no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—42no—
935C2×D4—82no—
936C2×D4C2×D4×C1111yescharacteristic
937C2×D4C2×D4×C1112yes—
938C2×D4C24×C1112yes—
939C2×D4C24×C1112yes—
940C2×D4C24×C1111yescharacteristic
941C2×D4C24×C1111yescharacteristic
942C22×C4—22no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—22no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4C2×D4×C1111yescharacteristic
956C22×C4C2×D4×C1111yescharacteristic
957C22×C4C24×C1111yescharacteristic
958C22×C4C24×C1112yes—
959Q16—22no—
960SD16—24no—
961SD16—22no—
962SD16—42no—
963SD16C11×#4114yescomplemented
964D8—22no—
965D8—24no—
966D8—24no—
967D8—42no—
968D8—42no—
969M16—24no—
970C2×C8—22no—
971C2×C8—41no—
972C2×C8—42no—
973C2×C8C24×C1111yescharacteristic
974C2×C8C24×C1111yescharacteristic
975C2×C8C24×C1111yescharacteristic
976C2×C8C24×C1112yes—
977C2×C8C24×C1112yes—
978C2×C8C24×C1111yescharacteristic
979C4⋊C4—21no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—22no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4C2×D4×C1112yes—
992C4⋊C4C2×D4×C1112yes—
993C4⋊C4C2×D4×C1112yes—
994C4⋊C4C2×D4×C1111yescharacteristic
995C4⋊C4C2×D4×C1111yescharacteristic
996C4⋊C4C2×D4×C1112yes—
997C4⋊C4C24×C1111yescharacteristic
998C4⋊C4C24×C1111yescharacteristic
999C4⋊C4C24×C1111yescharacteristic
1000C4⋊C4C24×C1112yes—
1001C4⋊C4C24×C1112yes—
1002C4⋊C4C24×C1111yescharacteristic
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—21no—
1014C22⋊C4—22no—
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4C2×D4×C1112yes—
1024C22⋊C4C2×D4×C1112yes—
1025C22⋊C4C2×D4×C1112yes—
1026C22⋊C4C2×D4×C1112yes—
1027C22⋊C4C2×D4×C1112yes—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—22no—
1035C42—22no—
1036C42C2×D4×C1111yescharacteristic
1037C42C2×D4×C1111yescharacteristic
1038C42C24×C1111yescharacteristic
1039C42C24×C1111yescharacteristic
1040C42C24×C1112yes—
1041C11#6149411yescharacteristic, direct product factor, Sylow
1042C23—21no—
1043C23—22no—
1044C23—21no—
1045C23—22no—
1046C23—44no—
1047C23—82no—
1048C23—82no—
1049C23C22×D4×C1112yes—
1050C23C22×D4×C1111yescharacteristic
1051Q8—22no—
1052Q8—21no—
1053Q8—21no—
1054Q8—21no—
1055Q8—42no—
1056Q8—42no—
1057Q8—82no—
1058Q8C2×C11×#4112yes—
1059D4—22no—
1060D4—22no—
1061D4—22no—
1062D4—21no—
1063D4—21no—
1064D4—22no—
1065D4—21no—
1066D4—22no—
1067D4—42no—
1068D4—44no—
1069D4—42no—
1070D4—44no—
1071D4—42no—
1072D4—42no—
1073D4—42no—
1074D4—81no—
1075D4—81no—
1076D4—82no—
1077D4—82no—
1078D4—82no—
1079D4—82no—
1080D4—82no—
1081D4—82no—
1082D4—82no—
1083D4C2×C11×#4112yes—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—41no—
1098C2×C4—42no—
1099C2×C4—44no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—81no—
1104C2×C4—81no—
1105C2×C4—82no—
1106C2×C4—82no—
1107C2×C4—82no—
1108C2×C4—82no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4C22×D4×C1111yescharacteristic
1112C2×C4C22×D4×C1111yescharacteristic
1113C2×C4C22×D4×C1112yes—
1114C2×C4C22×D4×C1112yes—
1115C2×C4C22×D4×C1111yescharacteristic
1116C2×C4C22×D4×C1111yescharacteristic
1117C2×C4C22×D4×C1112yes—
1118C2×C4C22×D4×C1111yescharacteristic
1119C2×C4C25×C1111yescharacteristic
1120C8—21no—
1121C8—22no—
1122C8—21no—
1123C8—21no—
1124C8—22no—
1125C8C2×C11×#4112yes—
1126C22—21no—
1127C22—22no—
1128C22—22no—
1129C22—21no—
1130C22—22no—
1131C22—21no—
1132C22—22no—
1133C22—41no—
1134C22—41no—
1135C22—42no—
1136C22—41no—
1137C22—42no—
1138C22—41no—
1139C22—42no—
1140C22—42no—
1141C22—41no—
1142C22—42no—
1143C22—42no—
1144C22—164no—
1145C22C23×D4×C1111yescharacteristic
1146C4—21no—
1147C4—22no—
1148C4—22no—
1149C4—21no—
1150C4—22no—
1151C4—21no—
1152C4—21no—
1153C4—22no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—42no—
1159C4—41no—
1160C4—41no—
1161C4C11×#57612yes—
1162C4C22×C11×#4111yescharacteristic
1163C4C11×#58511yescharacteristic
1164C2—42no—
1165C2—41no—
1166C2—42no—
1167C2—82no—
1168C2—81no—
1169C2—82no—
1170C2D4×C11×#4111yescharacteristic
1171C2C2×C11×#57611yescharacteristic
1172C2C11×#358411yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#529 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3517C2semidirect
2. C11×#3514C2semidirect
3. C11×#3399C2semidirect
4. C11×#3386C2semidirect
5. C11×#3365C2semidirect
6. C11×#3358C2semidirect
7. C11×#3353C2semidirect
8. C11×#3347C2semidirect
9. C11×#3305C2semidirect
10. C11×#3304C2semidirect
11. C11×#3297C2semidirect
12. C11×#3294C2semidirect
13. C11×#3274C2semidirect
14. C11×#3268C2semidirect
15. C11×#3179C2semidirect
16. C11×#3169C2semidirect
17. C11×#3124C2semidirect
18. C11×#3122C2semidirect
19. C11×#3115C2semidirect
20. C11×#3115C2semidirect
21. C11×#2966C2semidirect
22. C11×#2946C2semidirect
23. C4×C11×#135C2semidirect
27. C11×#557C22semidirect
31. C11×#553C22semidirect
35. C11×#550C22semidirect
36. C11×#550C22semidirect
46. C11×#540C22semidirect
50. C11×#532C22semidirect
55. C11×#520C22semidirect
58. C4×C11×#41C22semidirect
59. C11×#501C22semidirect
60. C11×#500C22semidirect
61. C11×#496C22semidirect
63. C11×#488C22semidirect
65. C11×#486C22semidirect
66. C11×#486C22semidirect
67. C11×#484C22semidirect
68. C11×#482C22semidirect
69. C11×#482C22semidirect
70. C11×#482C22semidirect
71. C11×#482C22semidirect
74. C11×#478C22semidirect
75. C11×#477C22semidirect
76. C11×#475C22semidirect
77. C11×#475C22semidirect
79. C11×#474C22semidirect
80. C11×#474C22semidirect
82. C11×#468C22semidirect
84. C11×#466C22semidirect
85. C11×#466C22semidirect
86. C11×#465C22semidirect
87. C11×#464C22semidirect
88. C11×#463C22semidirect
90. C11×#460C22semidirect
94. C11×#459C22semidirect
95. C11×#452C22semidirect
98. C11×#449C22semidirect
101. C11×#446C22semidirect
102. C8×Q8×C11C22semidirect
104. C11×#442C22semidirect
105. C11×#442C22semidirect
107. C11×#440C22semidirect
108. C11×#440C22semidirect
109. C4×C11×Q16C22semidirect
110. C4×C11×Q16C22semidirect
113. C4×C11×SD16C22semidirect
114. C4×C11×SD16C22semidirect
115. C4×C11×SD16C22semidirect
119. C4×C11×D8C22semidirect
120. C4×C11×D8C22semidirect
122. C11×#435C22semidirect
124. C8×D4×C11C22semidirect
125. C11×#433C22semidirect
126. C11×#432C22semidirect
127. C11×#428C22semidirect
128. C11×#427C22semidirect
130. C11×#416C22semidirect
131. C11×#416C22semidirect
133. C11×#405C22semidirect
134. C2×C4×C8×C11C22semidirect
314. #61494C11direct (N × H)
378. C11×SD16#41semidirect
456. #3517C2×C11semidirect
457. #3514C2×C11semidirect
458. #3399C2×C11semidirect
459. #3386C2×C11semidirect
460. #3365C2×C11semidirect
461. #3358C2×C11semidirect
462. #3353C2×C11semidirect
463. #3347C2×C11semidirect
464. #3305C2×C11semidirect
465. #3304C2×C11semidirect
466. #3297C2×C11semidirect
467. #3294C2×C11semidirect
468. #3274C2×C11semidirect
469. #3268C2×C11semidirect
470. #3179C2×C11semidirect
471. #3169C2×C11semidirect
472. #3124C2×C11semidirect
473. #3122C2×C11semidirect
474. #3115C2×C11semidirect
475. #3115C2×C11semidirect
476. #2966C2×C11semidirect
477. #2946C2×C11semidirect
478. C4×#135C2×C11semidirect
566. #557C22×C11semidirect
570. #553C22×C11semidirect
574. #550C22×C11semidirect
575. #550C22×C11semidirect
585. #540C22×C11semidirect
589. #532C22×C11semidirect
594. #520C22×C11semidirect
597. C4×#41C22×C11semidirect
598. #501C22×C11semidirect
599. #500C22×C11semidirect
600. #496C22×C11semidirect
602. #488C22×C11semidirect
604. #486C22×C11semidirect
605. #486C22×C11semidirect
606. #484C22×C11semidirect
607. #482C22×C11semidirect
608. #482C22×C11semidirect
609. #482C22×C11semidirect
610. #482C22×C11semidirect
613. #478C22×C11semidirect
614. #477C22×C11semidirect
615. #475C22×C11semidirect
616. #475C22×C11semidirect
618. #474C22×C11semidirect
619. #474C22×C11semidirect
621. #468C22×C11semidirect
623. #466C22×C11semidirect
624. #466C22×C11semidirect
625. #465C22×C11semidirect
626. #464C22×C11semidirect
627. #463C22×C11semidirect
629. #460C22×C11semidirect
633. #459C22×C11semidirect
634. #452C22×C11semidirect
637. #449C22×C11semidirect
640. #446C22×C11semidirect
641. C8×Q8C22×C11semidirect
643. #442C22×C11semidirect
644. #442C22×C11semidirect
646. #440C22×C11semidirect
647. #440C22×C11semidirect
648. C4×Q16C22×C11semidirect
649. C4×Q16C22×C11semidirect
652. C4×SD16C22×C11semidirect
653. C4×SD16C22×C11semidirect
654. C4×SD16C22×C11semidirect
658. C4×D8C22×C11semidirect
659. C4×D8C22×C11semidirect
661. #435C22×C11semidirect
663. C8×D4C22×C11semidirect
664. #433C22×C11semidirect
665. #432C22×C11semidirect
666. #428C22×C11semidirect
667. #427C22×C11semidirect
669. #416C22×C11semidirect
670. #416C22×C11semidirect
672. #405C22×C11semidirect
673. C2×C4×C8C22×C11semidirect
963. SD16C11×#41semidirect
1041. C11#61494direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35172
C11×#35142
C11×#33992
C11×#33862
C11×#33652
C11×#33582
C11×#33532
C11×#33472
C11×#33052
C11×#33042
C11×#32972
C11×#32942
C11×#32742
C11×#32682
C11×#31792
C11×#31692
C11×#31242
C11×#31222
C11×#31152
C11×#29662
C11×#29462
C4×C11×#1352
#6149411