Finite Group Databasebeta

← C11×#62017 #14639210

Subgroups — C11×#62017 #14639210

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3561C211yesmaximal, characteristic, complemented
2C11×#3520C211yesmaximal, characteristic, complemented
3C11×#3402C212yesmaximal, complemented
4C11×#3367C212yesmaximal, complemented
5C11×#3314C212yesmaximal, complemented
6C11×#3308C212yesmaximal, complemented
7C11×#3299C212yesmaximal, complemented
8C11×#3280C212yesmaximal, complemented
9C11×#3269C212yesmaximal, complemented
10C11×#3266C212yesmaximal, complemented
11C11×#3262C212yesmaximal, complemented
12C11×#3249C211yesmaximal, characteristic, complemented
13C11×#3225C212yesmaximal, complemented
14C11×#3215C211yesmaximal, characteristic, complemented
15C11×#3124C212yesmaximal, complemented
16C11×#3110C211yesmaximal, characteristic, complemented
17C11×#3046C212yesmaximal, complemented
18C2×C11×#463C211yesmaximal, characteristic, complemented
19C11×#2992C211yesmaximal, characteristic, complemented
20C2×C11×#137C2212yescomplemented
21C2×C11×#135C2212yes—
22C22×C11×SD16C2211yescharacteristic
23C22×C11×D8C2211yescharacteristic
24C11×#563—21no—
25C11×#562—21no—
26C11×#556C2211yescharacteristic, complemented
27C11×#556C2212yescomplemented
28C11×#554C2212yes—
29C11×#552—21no—
30C11×#551—22no—
31C11×#551—22no—
32D4×Q8×C11C2212yes—
33D4×Q8×C11C2211yescharacteristic, complemented
34C11×#548—21no—
35C11×#548C2212yescomplemented
36C11×#547C2211yescharacteristic, complemented
37C11×#547C2211yescharacteristic, complemented
38C11×#546C2212yes—
39C11×#546C2212yes—
40C11×#543—21no—
41C11×#542—22no—
42C11×#542C2212yescomplemented
43C11×#542C2212yescomplemented
44C11×#539—22no—
45C11×#538—21no—
46C11×#536C2212yescomplemented
47C11×#533C2211yescharacteristic
48C11×#533C2211yescharacteristic
49C11×#529C2211yescharacteristic
50C2×C11×#124C2211yescharacteristic
51C11×#525—21no—
52C2×C11×C22⋊Q8—21no—
53C11×#520C2212yescomplemented
54C2×C4×D4×C11C2211yescharacteristic
55C11×#497C2212yescomplemented
56C11×#497C2212yescomplemented
57C11×#495C2212yes—
58C11×#489C2212yescomplemented
59C11×#489C2212yescomplemented
60C11×#487C2212yescomplemented
61C11×#484C2212yes—
62C11×#484C2212yescomplemented
63C11×#480C2212yescomplemented
64C11×#477C2212yescomplemented
65C11×#477C2212yescomplemented
66C11×#477C2212yescomplemented
67C11×#474C2211yescharacteristic, complemented
68C11×#474C2212yescomplemented
69C11×#474C2211yescharacteristic, complemented
70C11×#468C2212yescomplemented
71C11×#468C2212yescomplemented
72C11×#467C2212yes—
73C11×#467C2212yes—
74C11×#467C2212yescomplemented
75C11×#466C2212yes—
76C11×#464C2212yescomplemented
77C11×#464C2212yescomplemented
78C11×#464C2212yescomplemented
79C11×#464C2212yescomplemented
80C11×#463C2212yes—
81C11×#463C2212yes—
82C11×#463C2212yes—
83C11×#463C2212yes—
84C11×#463C2212yes—
85C11×#463C2212yes—
86C11×#462C2212yescomplemented
87C11×#462C2212yescomplemented
88C11×#462C2212yescomplemented
89C11×#461C2211yescharacteristic, complemented
90C11×#461C2212yescomplemented
91C11×#461C2211yescharacteristic, complemented
92C11×#452C2212yescomplemented
93C11×#452C2212yescomplemented
94C11×#451C2212yes—
95C11×#451C2212yescomplemented
96C11×#450C2212yes—
97C11×#450C2212yes—
98C11×#449C2212yes—
99C11×#449C2212yes—
100C11×#448C2212yescomplemented
101C11×#446C2212yescomplemented
102C11×#440C2212yescomplemented
103C11×#440C2212yescomplemented
104C11×#440C2212yescomplemented
105C11×#440C2212yescomplemented
106C4×C11×Q16C2212yescomplemented
107C4×C11×D8C2212yes—
108C11×#435C2212yes—
109C11×#435C2212yescomplemented
110C8×D4×C11C2212yes—
111C11×#433C2212yescomplemented
112C11×#432C2211yescharacteristic
113C11×#424C2212yescomplemented
114C2×C11×C4⋊C8C2211yescharacteristic
115C11×#417C2212yescomplemented
116C2×C11×#103C2211yescharacteristic
117C2×C11×#103C2212yescomplemented
118C2×C11×#102C2211yescharacteristic
119C2×C11×#41—21no—
120C2×C11×#41C2312yes—
121C2×C11×#41C2312yes—
122C22×Q8×C11—21no—
123C22×Q8×C11C2311yescharacteristic
124C22×Q8×C11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11—21no—
128C11×#137—44no—
129C11×#135—44no—
130C2×C11×Q16C2312yes—
131C2×C11×Q16C2312yes—
132C2×C11×Q16C2312yes—
133C2×C11×Q16C2312yes—
134C2×C11×SD16—42no—
135C2×C11×SD16C2312yes—
136C2×C11×SD16C2312yes—
137C2×C11×SD16C2312yes—
138C2×C11×SD16C2312yes—
139C2×C11×SD16C2312yes—
140C2×C11×SD16C2312yes—
141C2×C11×D8—42no—
142C2×C11×D8C2312yes—
143C2×C11×D8C2312yes—
144C2×C11×M16C2312yes—
145C22×C8×C11C2311yescharacteristic
146C22×C8×C11C2311yescharacteristic
147C22×C8×C11C2312yes—
148C11×C4⋊Q8—22no—
149C11×C4⋊Q8C2311yescharacteristic
150C11×C4⋊Q8C2312yes—
151C11×C4⋊Q8C2311yescharacteristic
152C11×C4⋊Q8C2311yescharacteristic
153C11×C4⋊Q8C2312yes—
154C11×C4⋊Q8C2311yescharacteristic
155C11×#126—22no—
156C11×#126—22no—
157C11×#126—22no—
158C11×#126—22no—
159C11×#126—22no—
160C11×#126D412yes—
161C11×#125—22no—
162C11×#125—21no—
163C11×#125—21no—
164C11×#125D411yescharacteristic
165C11×#124—22no—
166C11×#124—22no—
167C11×#124—22no—
168C11×#124—21no—
169C11×#124—21no—
170C11×#124D411yescharacteristic
171C11×#124C2312yes—
172C11×#124C2312yes—
173C11×#124C2312yes—
174C11×#124C2312yes—
175C11×#123—22no—
176C11×#123—22no—
177C11×#123—22no—
178C11×#123—22no—
179C11×#123—22no—
180C11×#123—22no—
181C11×#123—22no—
182C11×#123—22no—
183C11×#123D412yes—
184C11×C22⋊Q8—21no—
185C11×C22⋊Q8—22no—
186C11×C22⋊Q8—21no—
187C11×C22⋊Q8—21no—
188C11×C22⋊Q8—22no—
189C11×C22⋊Q8—21no—
190C11×C22⋊Q8—21no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—22no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8—22no—
200C11×C22⋊Q8D411yescharacteristic
201C11×C22⋊Q8C2312yes—
202C11×C22⋊Q8C2312yes—
203C11×C22⋊Q8C2312yes—
204C11×C22⋊Q8C2312yes—
205C11×#121—21no—
206C11×#121—22no—
207C11×#121—22no—
208C11×#121—22no—
209C11×#121D411yescharacteristic
210C11×#121C2312yes—
211C11×#121C2312yes—
212C11×#120—22no—
213C11×#120—22no—
214C4×Q8×C11—21no—
215C4×Q8×C11—21no—
216C4×Q8×C11C2312yes—
217C4×Q8×C11C2312yes—
218C4×Q8×C11C2312yes—
219C4×Q8×C11C2312yes—
220C4×Q8×C11C2311yescharacteristic
221C4×D4×C11—22no—
222C4×D4×C11—22no—
223C4×D4×C11—22no—
224C4×D4×C11—22no—
225C4×D4×C11—22no—
226C4×D4×C11—21no—
227C4×D4×C11—21no—
228C4×D4×C11C2311yescharacteristic
229C4×D4×C11C2311yescharacteristic
230C4×D4×C11C2311yescharacteristic
231C4×D4×C11C2311yescharacteristic
232C4×D4×C11C2312yes—
233C4×D4×C11C2312yes—
234C4×D4×C11C2312yes—
235C4×D4×C11C2311yescharacteristic
236C11×#117—21no—
237C11×#117—21no—
238C11×#117—22no—
239C11×#117—21no—
240C11×#117—22no—
241C11×#117C2312yes—
242C2×C11×C4⋊C4—22no—
243C2×C11×C4⋊C4—21no—
244C2×C11×C4⋊C4C2311yescharacteristic
245C2×C11×C4⋊C4C2312yes—
246C2×C11×C22⋊C4—21no—
247C2×C11×C22⋊C4—21no—
248C2×C11×C22⋊C4—21no—
249C2×C11×C22⋊C4—22no—
250C2×C11×C22⋊C4—22no—
251C2×C42×C11C2311yescharacteristic
252C11×#107C2312yes—
253C11×#107C2312yes—
254C11×#107C2312yes—
255C11×#107C2312yes—
256C11×C4⋊C8C2312yes—
257C11×C4⋊C8C2312yes—
258C11×C4⋊C8C2311yescharacteristic
259C11×C4⋊C8C2312yes—
260C11×C4⋊C8C2312yes—
261C11×C4⋊C8C2311yescharacteristic
262C11×#103C2312yes—
263C11×#103C2312yes—
264C11×#103C2312yes—
265C11×#103C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#103C2312yes—
269C11×#103C2312yes—
270C11×#103C2312yes—
271C11×#103C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×#102C2312yes—
277C11×#102C2312yes—
278C11×C22⋊C8C2312yes—
279C11×C22⋊C8C2312yes—
280C11×C22⋊C8C2312yes—
281C11×#97C2312yes—
282C11×#97C2312yes—
283C4×C8×C11C2312yes—
284#62017C1111yesmaximal, characteristic, direct product factor, Sylow
285C24×C11—21no—
286C24×C11—21no—
287C11×#41—24no—
288C11×#41—42no—
289C11×#41—42no—
290C11×#41—42no—
291C11×#41—82no—
292C2×Q8×C11—21no—
293C2×Q8×C11—21no—
294C2×Q8×C11—22no—
295C2×Q8×C11—22no—
296C2×Q8×C11—21no—
297C2×Q8×C11—41no—
298C2×Q8×C11—42no—
299C2×Q8×C11—41no—
300C2×Q8×C11—42no—
301C2×Q8×C11—82no—
302C2×Q8×C11C2×D411yescharacteristic
303C2×Q8×C11C2412yes—
304C2×Q8×C11C2412yes—
305C2×Q8×C11C2412yes—
306C2×D4×C11—22no—
307C2×D4×C11—22no—
308C2×D4×C11—22no—
309C2×D4×C11—22no—
310C2×D4×C11—22no—
311C2×D4×C11—21no—
312C2×D4×C11—21no—
313C2×D4×C11—41no—
314C2×D4×C11—41no—
315C2×D4×C11—41no—
316C2×D4×C11C2×D412yes—
317C2×D4×C11C2×D411yescharacteristic
318C2×D4×C11C2412yes—
319C2×D4×C11C2411yescharacteristic
320C2×D4×C11C2411yescharacteristic
321C22×C4×C11—21no—
322C22×C4×C11—21no—
323C22×C4×C11—22no—
324C22×C4×C11—22no—
325C22×C4×C11—22no—
326C22×C4×C11—21no—
327C22×C4×C11—21no—
328C22×C4×C11—22no—
329C22×C4×C11—22no—
330C22×C4×C11—22no—
331C22×C4×C11—21no—
332C22×C4×C11—21no—
333C22×C4×C11—82no—
334C22×C4×C11C2×D411yescharacteristic
335C22×C4×C11C2×D411yescharacteristic
336C22×C4×C11C2411yescharacteristic
337C22×C4×C11C2412yes—
338C11×Q16—42no—
339C11×Q16—42no—
340C11×Q16—42no—
341C11×Q16—42no—
342C11×SD16—24no—
343C11×SD16—24no—
344C11×SD16—42no—
345C11×SD16—42no—
346C11×SD16—42no—
347C11×SD16—42no—
348C11×D8—24no—
349C11×D8—42no—
350C11×M16—42no—
351C2×C8×C11—41no—
352C2×C8×C11—41no—
353C2×C8×C11—42no—
354C2×C8×C11C2412yes—
355C2×C8×C11C2412yes—
356C2×C8×C11C2412yes—
357C2×C8×C11C2412yes—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—21no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—21no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—21no—
366C11×C4⋊C4—21no—
367C11×C4⋊C4—21no—
368C11×C4⋊C4—21no—
369C11×C4⋊C4—22no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—22no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—22no—
374C11×C4⋊C4—21no—
375C11×C4⋊C4—22no—
376C11×C4⋊C4—22no—
377C11×C4⋊C4C2×D412yes—
378C11×C4⋊C4C2×D411yescharacteristic
379C11×C4⋊C4C2×D412yes—
380C11×C4⋊C4C2×D411yescharacteristic
381C11×C4⋊C4C2×D412yes—
382C11×C4⋊C4C2×D412yes—
383C11×C4⋊C4C2411yescharacteristic
384C11×C4⋊C4C2411yescharacteristic
385C11×C4⋊C4C2412yes—
386C11×C4⋊C4C2412yes—
387C11×C22⋊C4—22no—
388C11×C22⋊C4—22no—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4—21no—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—21no—
394C11×C22⋊C4—21no—
395C11×C22⋊C4—21no—
396C11×C22⋊C4—22no—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4—22no—
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⋊C4C2×D412yes—
408C11×C22⋊C4C2×D412yes—
409C11×C22⋊C4C2×D412yes—
410C11×C22⋊C4C2×D412yes—
411C11×C22⋊C4C2×D412yes—
412C42×C11—22no—
413C42×C11—22no—
414C42×C11—22no—
415C42×C11—22no—
416C42×C11C2×D411yescharacteristic
417C42×C11C2×D411yescharacteristic
418C42×C11C2412yes—
419C42×C11C2411yescharacteristic
420C42×C11C2411yescharacteristic
421#3561C2×C1111yescharacteristic, complemented
422#3520C2×C1111yescharacteristic, complemented
423#3402C2×C1112yescomplemented
424#3367C2×C1112yescomplemented
425#3314C2×C1112yescomplemented
426#3308C2×C1112yescomplemented
427#3299C2×C1112yescomplemented
428#3280C2×C1112yescomplemented
429#3269C2×C1112yescomplemented
430#3266C2×C1112yescomplemented
431#3262C2×C1112yescomplemented
432#3249C2×C1111yescharacteristic, complemented
433#3225C2×C1112yescomplemented
434#3215C2×C1111yescharacteristic, complemented
435#3124C2×C1112yescomplemented
436#3110C2×C1111yescharacteristic, complemented
437#3046C2×C1112yescomplemented
438C2×#463C2×C1111yescharacteristic, complemented
439#2992C2×C1111yescharacteristic, complemented
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—42no—
444C23×C11—42no—
445C23×C11—42no—
446C23×C11—81no—
447C23×C11—81no—
448C23×C11—81no—
449C23×C11C22×D412yes—
450C23×C11C22×D411yescharacteristic
451Q8×C11—22no—
452Q8×C11—22no—
453Q8×C11—22no—
454Q8×C11—22no—
455Q8×C11—22no—
456Q8×C11—22no—
457Q8×C11—41no—
458Q8×C11—42no—
459Q8×C11—81no—
460Q8×C11—82no—
461Q8×C11—81no—
462Q8×C11—82no—
463D4×C11—24no—
464D4×C11—22no—
465D4×C11—21no—
466D4×C11—21no—
467D4×C11—21no—
468D4×C11—22no—
469D4×C11—41no—
470D4×C11—42no—
471D4×C11—44no—
472D4×C11—81no—
473D4×C11—82no—
474D4×C11—82no—
475D4×C11—82no—
476D4×C11H(5,𝔽2)12yes—
477C2×C4×C11—22no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—41no—
490C2×C4×C11—44no—
491C2×C4×C11—42no—
492C2×C4×C11—42no—
493C2×C4×C11—82no—
494C2×C4×C11—81no—
495C2×C4×C11—81no—
496C2×C4×C11—82no—
497C2×C4×C11—82no—
498C2×C4×C11—81no—
499C2×C4×C11—82no—
500C2×C4×C11—81no—
501C2×C4×C11—82no—
502C2×C4×C11C22×D411yescharacteristic
503C2×C4×C11C22×D411yescharacteristic
504C2×C4×C11C22×D412yes—
505C2×C4×C11C22×D411yescharacteristic
506C2×C4×C11C22×D411yescharacteristic
507C2×C4×C11C22×D411yescharacteristic
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C2511yescharacteristic
511C8×C11—22no—
512C8×C11—22no—
513C8×C11—22no—
514C8×C11—22no—
515C2×#137C22×C1112yescomplemented
516C2×#135C22×C1112yes—
517C22×SD16C22×C1111yescharacteristic
518C22×D8C22×C1111yescharacteristic
519#563—21no—
520#562—21no—
521#556C22×C1112yescomplemented
522#556C22×C1111yescharacteristic, complemented
523#554C22×C1112yes—
524#552—21no—
525#551—22no—
526#551—22no—
527D4×Q8C22×C1112yes—
528D4×Q8C22×C1111yescharacteristic, complemented
529#548—21no—
530#548C22×C1112yescomplemented
531#547C22×C1111yescharacteristic, complemented
532#547C22×C1111yescharacteristic, complemented
533#546C22×C1112yes—
534#546C22×C1112yes—
535#543—21no—
536#542—22no—
537#542C22×C1112yescomplemented
538#542C22×C1112yescomplemented
539#539—22no—
540#538—21no—
541#536C22×C1112yescomplemented
542#533C22×C1111yescharacteristic
543#533C22×C1111yescharacteristic
544#529C22×C1111yescharacteristic
545C2×#124C22×C1111yescharacteristic
546#525—21no—
547C2×C22⋊Q8—21no—
548#520C22×C1112yescomplemented
549C2×C4×D4C22×C1111yescharacteristic
550#497C22×C1112yescomplemented
551#497C22×C1112yescomplemented
552#495C22×C1112yes—
553#489C22×C1112yescomplemented
554#489C22×C1112yescomplemented
555#487C22×C1112yescomplemented
556#484C22×C1112yes—
557#484C22×C1112yescomplemented
558#480C22×C1112yescomplemented
559#477C22×C1112yescomplemented
560#477C22×C1112yescomplemented
561#477C22×C1112yescomplemented
562#474C22×C1111yescharacteristic, complemented
563#474C22×C1111yescharacteristic, complemented
564#474C22×C1112yescomplemented
565#468C22×C1112yescomplemented
566#468C22×C1112yescomplemented
567#467C22×C1112yes—
568#467C22×C1112yes—
569#467C22×C1112yescomplemented
570#466C22×C1112yes—
571#464C22×C1112yescomplemented
572#464C22×C1112yescomplemented
573#464C22×C1112yescomplemented
574#464C22×C1112yescomplemented
575#463C22×C1112yes—
576#463C22×C1112yes—
577#463C22×C1112yes—
578#463C22×C1112yes—
579#463C22×C1112yes—
580#463C22×C1112yes—
581#462C22×C1112yescomplemented
582#462C22×C1112yescomplemented
583#462C22×C1112yescomplemented
584#461C22×C1111yescharacteristic, complemented
585#461C22×C1111yescharacteristic, complemented
586#461C22×C1112yescomplemented
587#452C22×C1112yescomplemented
588#452C22×C1112yescomplemented
589#451C22×C1112yes—
590#451C22×C1112yescomplemented
591#450C22×C1112yes—
592#450C22×C1112yes—
593#449C22×C1112yes—
594#449C22×C1112yes—
595#448C22×C1112yescomplemented
596#446C22×C1112yescomplemented
597#440C22×C1112yescomplemented
598#440C22×C1112yescomplemented
599#440C22×C1112yescomplemented
600#440C22×C1112yescomplemented
601C4×Q16C22×C1112yescomplemented
602C4×D8C22×C1112yes—
603#435C22×C1112yes—
604#435C22×C1112yescomplemented
605C8×D4C22×C1112yes—
606#433C22×C1112yescomplemented
607#432C22×C1111yescharacteristic
608#424C22×C1112yescomplemented
609C2×C4⋊C8C22×C1111yescharacteristic
610#417C22×C1112yescomplemented
611C2×#103C22×C1111yescharacteristic
612C2×#103C22×C1112yescomplemented
613C2×#102C22×C1111yescharacteristic
614C22×C11—21no—
615C22×C11—21no—
616C22×C11—22no—
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—22no—
620C22×C11—41no—
621C22×C11—41no—
622C22×C11—41no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—41no—
626C22×C11—41no—
627C22×C11—42no—
628C22×C11—84no—
629C22×C11—162no—
630C22×C11#57812yes—
631C22×C11C23×D411yescharacteristic
632C4×C11—21no—
633C4×C11—21no—
634C4×C11—22no—
635C4×C11—22no—
636C4×C11—21no—
637C4×C11—21no—
638C4×C11—21no—
639C4×C11—22no—
640C4×C11—41no—
641C4×C11—41no—
642C4×C11—42no—
643C4×C11—42no—
644C4×C11—42no—
645C4×C11—42no—
646C4×C11—42no—
647C4×C11C2×H(5,𝔽2)11yescharacteristic
648C4×C11#58511yescharacteristic
649C2×#41—21no—
650C2×#41C23×C1112yes—
651C2×#41C23×C1112yes—
652C22×Q8—21no—
653C22×Q8C23×C1111yescharacteristic
654C22×Q8C23×C1112yes—
655C22×D4C23×C1111yescharacteristic
656C22×D4C23×C1111yescharacteristic
657C23×C4—21no—
658#137—44no—
659#135—44no—
660C2×Q16C23×C1112yes—
661C2×Q16C23×C1112yes—
662C2×Q16C23×C1112yes—
663C2×Q16C23×C1112yes—
664C2×SD16—42no—
665C2×SD16C23×C1112yes—
666C2×SD16C23×C1112yes—
667C2×SD16C23×C1112yes—
668C2×SD16C23×C1112yes—
669C2×SD16C23×C1112yes—
670C2×SD16C23×C1112yes—
671C2×D8—42no—
672C2×D8C23×C1112yes—
673C2×D8C23×C1112yes—
674C2×M16C23×C1112yes—
675C22×C8C23×C1111yescharacteristic
676C22×C8C23×C1111yescharacteristic
677C22×C8C23×C1112yes—
678C4⋊Q8—22no—
679C4⋊Q8C23×C1111yescharacteristic
680C4⋊Q8C23×C1111yescharacteristic
681C4⋊Q8C23×C1112yes—
682C4⋊Q8C23×C1111yescharacteristic
683C4⋊Q8C23×C1111yescharacteristic
684C4⋊Q8C23×C1112yes—
685#126—22no—
686#126—22no—
687#126—22no—
688#126—22no—
689#126—22no—
690#126D4×C1112yes—
691#125—22no—
692#125—21no—
693#125—21no—
694#125D4×C1111yescharacteristic
695#124—22no—
696#124—22no—
697#124—22no—
698#124—21no—
699#124—21no—
700#124D4×C1111yescharacteristic
701#124C23×C1112yes—
702#124C23×C1112yes—
703#124C23×C1112yes—
704#124C23×C1112yes—
705#123—22no—
706#123—22no—
707#123—22no—
708#123—22no—
709#123—22no—
710#123—22no—
711#123—22no—
712#123—22no—
713#123D4×C1112yes—
714C22⋊Q8—21no—
715C22⋊Q8—22no—
716C22⋊Q8—21no—
717C22⋊Q8—21no—
718C22⋊Q8—22no—
719C22⋊Q8—21no—
720C22⋊Q8—21no—
721C22⋊Q8—22no—
722C22⋊Q8—22no—
723C22⋊Q8—22no—
724C22⋊Q8—22no—
725C22⋊Q8—22no—
726C22⋊Q8—22no—
727C22⋊Q8—22no—
728C22⋊Q8—22no—
729C22⋊Q8—22no—
730C22⋊Q8D4×C1111yescharacteristic
731C22⋊Q8C23×C1112yes—
732C22⋊Q8C23×C1112yes—
733C22⋊Q8C23×C1112yes—
734C22⋊Q8C23×C1112yes—
735#121—21no—
736#121—22no—
737#121—22no—
738#121—22no—
739#121D4×C1111yescharacteristic
740#121C23×C1112yes—
741#121C23×C1112yes—
742#120—22no—
743#120—22no—
744C4×Q8—21no—
745C4×Q8—21no—
746C4×Q8C23×C1112yes—
747C4×Q8C23×C1112yes—
748C4×Q8C23×C1112yes—
749C4×Q8C23×C1112yes—
750C4×Q8C23×C1111yescharacteristic
751C4×D4—22no—
752C4×D4—22no—
753C4×D4—22no—
754C4×D4—22no—
755C4×D4—22no—
756C4×D4—21no—
757C4×D4—21no—
758C4×D4C23×C1111yescharacteristic
759C4×D4C23×C1111yescharacteristic
760C4×D4C23×C1111yescharacteristic
761C4×D4C23×C1111yescharacteristic
762C4×D4C23×C1112yes—
763C4×D4C23×C1112yes—
764C4×D4C23×C1112yes—
765C4×D4C23×C1111yescharacteristic
766#117—21no—
767#117—21no—
768#117—22no—
769#117—21no—
770#117—22no—
771#117C23×C1112yes—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—21no—
774C2×C4⋊C4C23×C1111yescharacteristic
775C2×C4⋊C4C23×C1112yes—
776C2×C22⋊C4—21no—
777C2×C22⋊C4—21no—
778C2×C22⋊C4—21no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C42C23×C1111yescharacteristic
782#107C23×C1112yes—
783#107C23×C1112yes—
784#107C23×C1112yes—
785#107C23×C1112yes—
786C4⋊C8C23×C1112yes—
787C4⋊C8C23×C1112yes—
788C4⋊C8C23×C1111yescharacteristic
789C4⋊C8C23×C1112yes—
790C4⋊C8C23×C1112yes—
791C4⋊C8C23×C1111yescharacteristic
792#103C23×C1112yes—
793#103C23×C1112yes—
794#103C23×C1112yes—
795#103C23×C1112yes—
796#103C23×C1112yes—
797#103C23×C1112yes—
798#103C23×C1112yes—
799#103C23×C1112yes—
800#103C23×C1112yes—
801#103C23×C1112yes—
802#102C23×C1112yes—
803#102C23×C1112yes—
804#102C23×C1112yes—
805#102C23×C1112yes—
806#102C23×C1112yes—
807#102C23×C1112yes—
808C22⋊C8C23×C1112yes—
809C22⋊C8C23×C1112yes—
810C22⋊C8C23×C1112yes—
811#97C23×C1112yes—
812#97C23×C1112yes—
813C4×C8C23×C1112yes—
814C2×C11—22no—
815C2×C11—42no—
816C2×C11—42no—
817C2×C11—81no—
818C2×C11—82no—
819C2×C11#348811yescharacteristic
820C2×C11C2×#57811yescharacteristic
821C2×C11#358511yescharacteristic
822C24—21no—
823C24—21no—
824#41—24no—
825#41—42no—
826#41—42no—
827#41—42no—
828#41—82no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—21no—
834C2×Q8—41no—
835C2×Q8—42no—
836C2×Q8—41no—
837C2×Q8—42no—
838C2×Q8—82no—
839C2×Q8C2×D4×C1111yescharacteristic
840C2×Q8C24×C1112yes—
841C2×Q8C24×C1112yes—
842C2×Q8C24×C1112yes—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4C2×D4×C1112yes—
854C2×D4C2×D4×C1111yescharacteristic
855C2×D4C24×C1112yes—
856C2×D4C24×C1111yescharacteristic
857C2×D4C24×C1111yescharacteristic
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—82no—
871C22×C4C2×D4×C1111yescharacteristic
872C22×C4C2×D4×C1111yescharacteristic
873C22×C4C24×C1111yescharacteristic
874C22×C4C24×C1112yes—
875Q16—42no—
876Q16—42no—
877Q16—42no—
878Q16—42no—
879SD16—24no—
880SD16—24no—
881SD16—42no—
882SD16—42no—
883SD16—42no—
884SD16—42no—
885D8—24no—
886D8—42no—
887M16—42no—
888C2×C8—41no—
889C2×C8—41no—
890C2×C8—42no—
891C2×C8C24×C1112yes—
892C2×C8C24×C1112yes—
893C2×C8C24×C1112yes—
894C2×C8C24×C1112yes—
895C4⋊C4—22no—
896C4⋊C4—21no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—21no—
901C4⋊C4—22no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—21no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4C2×D4×C1112yes—
915C4⋊C4C2×D4×C1111yescharacteristic
916C4⋊C4C2×D4×C1112yes—
917C4⋊C4C2×D4×C1111yescharacteristic
918C4⋊C4C2×D4×C1112yes—
919C4⋊C4C2×D4×C1112yes—
920C4⋊C4C24×C1111yescharacteristic
921C4⋊C4C24×C1111yescharacteristic
922C4⋊C4C24×C1112yes—
923C4⋊C4C24×C1112yes—
924C22⋊C4—22no—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—21no—
929C22⋊C4—22no—
930C22⋊C4—21no—
931C22⋊C4—21no—
932C22⋊C4—21no—
933C22⋊C4—22no—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4C2×D4×C1112yes—
945C22⋊C4C2×D4×C1112yes—
946C22⋊C4C2×D4×C1112yes—
947C22⋊C4C2×D4×C1112yes—
948C22⋊C4C2×D4×C1112yes—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42C2×D4×C1111yescharacteristic
954C42C2×D4×C1111yescharacteristic
955C42C24×C1112yes—
956C42C24×C1111yescharacteristic
957C42C24×C1111yescharacteristic
958C11#6201711yescharacteristic, direct product factor, Sylow
959C23—21no—
960C23—22no—
961C23—21no—
962C23—42no—
963C23—42no—
964C23—42no—
965C23—81no—
966C23—81no—
967C23—81no—
968C23C22×D4×C1112yes—
969C23C22×D4×C1111yescharacteristic
970Q8—22no—
971Q8—22no—
972Q8—22no—
973Q8—22no—
974Q8—22no—
975Q8—22no—
976Q8—41no—
977Q8—42no—
978Q8—81no—
979Q8—82no—
980Q8—81no—
981Q8—82no—
982D4—24no—
983D4—22no—
984D4—21no—
985D4—21no—
986D4—21no—
987D4—22no—
988D4—41no—
989D4—42no—
990D4—44no—
991D4—81no—
992D4—82no—
993D4—82no—
994D4—82no—
995D4C11×H(5,𝔽2)12yes—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—41no—
1009C2×C4—44no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—82no—
1013C2×C4—81no—
1014C2×C4—81no—
1015C2×C4—82no—
1016C2×C4—82no—
1017C2×C4—81no—
1018C2×C4—82no—
1019C2×C4—81no—
1020C2×C4—82no—
1021C2×C4C22×D4×C1111yescharacteristic
1022C2×C4C22×D4×C1111yescharacteristic
1023C2×C4C22×D4×C1112yes—
1024C2×C4C22×D4×C1111yescharacteristic
1025C2×C4C22×D4×C1111yescharacteristic
1026C2×C4C22×D4×C1111yescharacteristic
1027C2×C4C22×D4×C1112yes—
1028C2×C4C22×D4×C1112yes—
1029C2×C4C25×C1111yescharacteristic
1030C8—22no—
1031C8—22no—
1032C8—22no—
1033C8—22no—
1034C22—21no—
1035C22—21no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—41no—
1041C22—41no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—42no—
1046C22—41no—
1047C22—42no—
1048C22—84no—
1049C22—162no—
1050C22C11×#57812yes—
1051C22C23×D4×C1111yescharacteristic
1052C4—22no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—22no—
1057C4—21no—
1058C4—21no—
1059C4—22no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—41no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4C2×C11×H(5,𝔽2)11yescharacteristic
1068C4C11×#58511yescharacteristic
1069C2—22no—
1070C2—42no—
1071C2—42no—
1072C2—81no—
1073C2—82no—
1074C2C11×#348811yescharacteristic
1075C2C2×C11×#57811yescharacteristic
1076C2C11×#358511yescharacteristic
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×#3561C2semidirect
2. C11×#3520C2semidirect
3. C11×#3402C2semidirect
4. C11×#3367C2semidirect
5. C11×#3314C2semidirect
6. C11×#3308C2semidirect
7. C11×#3299C2semidirect
8. C11×#3280C2semidirect
9. C11×#3269C2semidirect
10. C11×#3266C2semidirect
11. C11×#3262C2semidirect
12. C11×#3249C2semidirect
13. C11×#3225C2semidirect
14. C11×#3215C2semidirect
15. C11×#3124C2semidirect
16. C11×#3110C2semidirect
17. C11×#3046C2semidirect
18. C2×C11×#463C2semidirect
19. C11×#2992C2semidirect
20. C2×C11×#137C22semidirect
26. C11×#556C22semidirect
27. C11×#556C22semidirect
33. D4×Q8×C11C22semidirect
35. C11×#548C22semidirect
36. C11×#547C22semidirect
37. C11×#547C22semidirect
42. C11×#542C22semidirect
43. C11×#542C22semidirect
46. C11×#536C22semidirect
53. C11×#520C22semidirect
55. C11×#497C22semidirect
56. C11×#497C22semidirect
58. C11×#489C22semidirect
59. C11×#489C22semidirect
60. C11×#487C22semidirect
62. C11×#484C22semidirect
63. C11×#480C22semidirect
64. C11×#477C22semidirect
65. C11×#477C22semidirect
66. C11×#477C22semidirect
67. C11×#474C22semidirect
68. C11×#474C22semidirect
69. C11×#474C22semidirect
70. C11×#468C22semidirect
71. C11×#468C22semidirect
74. C11×#467C22semidirect
76. C11×#464C22semidirect
77. C11×#464C22semidirect
78. C11×#464C22semidirect
79. C11×#464C22semidirect
86. C11×#462C22semidirect
87. C11×#462C22semidirect
88. C11×#462C22semidirect
89. C11×#461C22semidirect
90. C11×#461C22semidirect
91. C11×#461C22semidirect
92. C11×#452C22semidirect
93. C11×#452C22semidirect
95. C11×#451C22semidirect
100. C11×#448C22semidirect
101. C11×#446C22semidirect
102. C11×#440C22semidirect
103. C11×#440C22semidirect
104. C11×#440C22semidirect
105. C11×#440C22semidirect
106. C4×C11×Q16C22semidirect
109. C11×#435C22semidirect
111. C11×#433C22semidirect
113. C11×#424C22semidirect
115. C11×#417C22semidirect
117. C2×C11×#103C22semidirect
284. #62017C11direct (N × H)
421. #3561C2×C11semidirect
422. #3520C2×C11semidirect
423. #3402C2×C11semidirect
424. #3367C2×C11semidirect
425. #3314C2×C11semidirect
426. #3308C2×C11semidirect
427. #3299C2×C11semidirect
428. #3280C2×C11semidirect
429. #3269C2×C11semidirect
430. #3266C2×C11semidirect
431. #3262C2×C11semidirect
432. #3249C2×C11semidirect
433. #3225C2×C11semidirect
434. #3215C2×C11semidirect
435. #3124C2×C11semidirect
436. #3110C2×C11semidirect
437. #3046C2×C11semidirect
438. C2×#463C2×C11semidirect
439. #2992C2×C11semidirect
515. C2×#137C22×C11semidirect
521. #556C22×C11semidirect
522. #556C22×C11semidirect
528. D4×Q8C22×C11semidirect
530. #548C22×C11semidirect
531. #547C22×C11semidirect
532. #547C22×C11semidirect
537. #542C22×C11semidirect
538. #542C22×C11semidirect
541. #536C22×C11semidirect
548. #520C22×C11semidirect
550. #497C22×C11semidirect
551. #497C22×C11semidirect
553. #489C22×C11semidirect
554. #489C22×C11semidirect
555. #487C22×C11semidirect
557. #484C22×C11semidirect
558. #480C22×C11semidirect
559. #477C22×C11semidirect
560. #477C22×C11semidirect
561. #477C22×C11semidirect
562. #474C22×C11semidirect
563. #474C22×C11semidirect
564. #474C22×C11semidirect
565. #468C22×C11semidirect
566. #468C22×C11semidirect
569. #467C22×C11semidirect
571. #464C22×C11semidirect
572. #464C22×C11semidirect
573. #464C22×C11semidirect
574. #464C22×C11semidirect
581. #462C22×C11semidirect
582. #462C22×C11semidirect
583. #462C22×C11semidirect
584. #461C22×C11semidirect
585. #461C22×C11semidirect
586. #461C22×C11semidirect
587. #452C22×C11semidirect
588. #452C22×C11semidirect
590. #451C22×C11semidirect
595. #448C22×C11semidirect
596. #446C22×C11semidirect
597. #440C22×C11semidirect
598. #440C22×C11semidirect
599. #440C22×C11semidirect
600. #440C22×C11semidirect
601. C4×Q16C22×C11semidirect
604. #435C22×C11semidirect
606. #433C22×C11semidirect
608. #424C22×C11semidirect
610. #417C22×C11semidirect
612. C2×#103C22×C11semidirect
958. C11#62017direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35612
C11×#35202
C11×#34022
C11×#33672
C11×#33142
C11×#33082
C11×#32992
C11×#32802
C11×#32692
C11×#32662
C11×#32622
C11×#32492
C11×#32252
C11×#32152
C11×#31242
C11×#31102
C11×#30462
C2×C11×#4632
C11×#29922
#6201711