Finite Group Databasebeta

← C11×#60709 #14637902

Subgroups — C11×#60709 #14637902

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3495C211yesmaximal, characteristic, complemented
2C11×#3494C211yesmaximal, characteristic, complemented
3C11×#3183C212yesmaximal, complemented
4C11×#3182C212yesmaximal, complemented
5C11×#3179C212yesmaximal, complemented
6C11×#3178C212yesmaximal, complemented
7C11×#3175C212yesmaximal, complemented
8C11×#3174C212yesmaximal, complemented
9C11×#3172C212yesmaximal, complemented
10C11×#3171C212yesmaximal, complemented
11C11×#3164C211yesmaximal, characteristic, complemented
12C11×#3154C211yesmaximal, characteristic, complemented
13C11×#3137C211yesmaximal, characteristic, complemented
14C11×#3136C211yesmaximal, characteristic, complemented
15C11×#3056C211yesmaximal, characteristic, complemented
16C11×#3055C211yesmaximal, characteristic, complemented
17C11×#3054C211yesmaximal, characteristic, complemented
18C2×C11×#468C211yesmaximal, characteristic, complemented
19C11×#2951C211yesmaximal, characteristic, complemented
20C11×#2949C211yesmaximal, characteristic, complemented
21C11×#2947C211yesmaximal, characteristic, complemented
22C11×#2946C211yesmaximal, characteristic, complemented
23C11×#2873C211yesmaximal, characteristic, complemented
24C2×C11×#137C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×#135C2211yescharacteristic
27C22×C11×SD16C2211yescharacteristic
28C22×C11×M16C2211yescharacteristic
29C22×C11×M16C2211yescharacteristic
30C11×#556—21no—
31C11×#555—21no—
32C11×#554—21no—
33C11×#553—21no—
34C11×#553—21no—
35C11×#552—22no—
36C11×#552—21no—
37C11×#552—21no—
38C11×#551—22no—
39C11×#551—22no—
40C11×#547—21no—
41C11×#546—22no—
42C11×#544C2211yescharacteristic
43C11×#544C2211yescharacteristic
44C11×#542C2212yes—
45C11×#542C2212yescomplemented
46C11×#541C2212yescomplemented
47C11×#540C2212yes—
48C11×#536C2211yescharacteristic
49C11×#535C2211yescharacteristic
50C11×#533C2212yescomplemented
51C11×#532C2212yes—
52C11×#529C2212yes—
53C11×#529C2212yescomplemented
54C11×#525C2211yescharacteristic
55C11×#525C2211yescharacteristic
56C2×C11×C22⋊Q8C2211yescharacteristic
57C2×C11×#121C2211yescharacteristic
58C11×#520C2211yescharacteristic
59C11×#520C2211yescharacteristic
60C11×#519C2211yescharacteristic
61C11×#518C2211yescharacteristic
62C2×C11×#117C2211yescharacteristic
63C11×#501C2212yescomplemented
64C11×#501C2212yescomplemented
65C11×#500C2212yescomplemented
66C11×#499C2212yescomplemented
67C11×#497C2212yescomplemented
68C11×#496C2212yescomplemented
69C11×#495C2212yescomplemented
70C11×#492C2212yescomplemented
71C11×#491C2212yescomplemented
72C11×#490C2212yescomplemented
73C11×#489C2212yescomplemented
74C11×#489C2212yescomplemented
75C11×#488C2212yescomplemented
76C11×#488C2212yescomplemented
77C11×#487C2212yescomplemented
78C11×#486C2212yescomplemented
79C11×#470C2211yescharacteristic, complemented
80C11×#470C2212yescomplemented
81C11×#470C2211yescharacteristic, complemented
82C11×#469C2212yes—
83C11×#469C2211yescharacteristic, complemented
84C11×#469C2211yescharacteristic, complemented
85C11×#468C2212yes—
86C11×#468C2212yes—
87C11×#468C2212yes—
88C11×#468C2212yes—
89C11×#468C2212yes—
90C11×#468C2212yescomplemented
91C11×#468C2211yescharacteristic, complemented
92C11×#468C2211yescharacteristic, complemented
93C11×#468C2211yescharacteristic, complemented
94C11×#468C2211yescharacteristic, complemented
95C11×#467C2212yescomplemented
96C11×#466C2212yes—
97C11×#465C2212yes—
98C11×#465C2212yescomplemented
99C11×#442C2212yescomplemented
100C11×#441C2212yescomplemented
101C11×#440C2212yescomplemented
102C11×#440C2212yescomplemented
103C11×#440C2212yescomplemented
104C11×#440C2212yescomplemented
105C11×#440C2212yescomplemented
106C11×#440C2212yescomplemented
107C4×C11×Q16C2212yescomplemented
108C4×C11×Q16C2212yescomplemented
109C4×C11×SD16C2212yescomplemented
110C4×C11×SD16C2212yescomplemented
111C4×C11×SD16C2212yescomplemented
112C4×C11×SD16C2212yescomplemented
113C4×C11×D8C2212yescomplemented
114C4×C11×D8C2212yescomplemented
115C11×#428C2211yescharacteristic
116C11×#428C2211yescharacteristic
117C11×#427C2211yescharacteristic
118C2×C11×#107C2211yescharacteristic
119C11×#419C2211yescharacteristic
120C11×#418C2211yescharacteristic
121C11×#417C2211yescharacteristic
122C11×#417C2211yescharacteristic
123C11×#416C2211yescharacteristic
124C11×#416C2211yescharacteristic
125C2×C11×#103C2211yescharacteristic
126C2×C11×#102C2211yescharacteristic
127C11×#405C2211yescharacteristic
128C11×#405C2211yescharacteristic
129C11×#405C2211yescharacteristic
130C11×#405C2211yescharacteristic
131C11×#405C2212yescomplemented
132C11×#405C2212yescomplemented
133C4×C11×M16C2212yescomplemented
134C4×C11×M16C2212yescomplemented
135C2×C11×#41—22no—
136C2×C11×#41C2311yescharacteristic
137C2×C11×#41C2311yescharacteristic
138C22×Q8×C11C2311yescharacteristic
139C22×D4×C11—21no—
140C22×D4×C11C2311yescharacteristic
141C23×C4×C11C2311yescharacteristic
142C11×#137—24no—
143C11×AGL(1,ℤ/8)—24no—
144C11×#135—24no—
145C2×C11×Q16C2312yes—
146C2×C11×Q16C2311yescharacteristic
147C2×C11×SD16—24no—
148C2×C11×SD16C2311yescharacteristic
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2311yescharacteristic
153C2×C11×SD16C2312yes—
154C2×C11×D8C2312yes—
155C2×C11×D8C2311yescharacteristic
156C2×C11×M16—24no—
157C2×C11×M16—24no—
158C2×C11×M16C2311yescharacteristic
159C2×C11×M16C2311yescharacteristic
160C2×C11×M16C2312yes—
161C2×C11×M16C2311yescharacteristic
162C2×C11×M16C2311yescharacteristic
163C2×C11×M16C2311yescharacteristic
164C2×C11×M16C2311yescharacteristic
165C22×C8×C11C2311yescharacteristic
166C22×C8×C11C2312yes—
167C22×C8×C11C2311yescharacteristic
168C11×C4⋊Q8—21no—
169C11×C4⋊Q8—21no—
170C11×C4⋊Q8C2312yes—
171C11×C4⋊Q8C2312yes—
172C11×C4⋊Q8C2312yes—
173C11×#127C2312yes—
174C11×#126—22no—
175C11×#126—22no—
176C11×#126—22no—
177C11×#126—22no—
178C11×#126—22no—
179C11×#126—22no—
180C11×#125—22no—
181C11×#125—22no—
182C11×#125—21no—
183C11×#125—21no—
184C11×#125—22no—
185C11×#125C2312yes—
186C11×#125C2312yes—
187C11×#124—22no—
188C11×#124—22no—
189C11×#124—22no—
190C11×#124C2312yes—
191C11×#124C2312yes—
192C11×#123—21no—
193C11×#123—21no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×#123—22no—
198C11×#123—22no—
199C11×#123—22no—
200C11×#123—22no—
201C11×C22⋊Q8—21no—
202C11×C22⋊Q8—21no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—21no—
205C11×C22⋊Q8—21no—
206C11×C22⋊Q8—22no—
207C11×C22⋊Q8—22no—
208C11×C22⋊Q8—22no—
209C11×C22⋊Q8—22no—
210C11×C22⋊Q8C2312yes—
211C11×C22⋊Q8C2312yes—
212C11×C22⋊Q8C2311yescharacteristic
213C11×C22⋊Q8C2311yescharacteristic
214C11×C22⋊Q8C2311yescharacteristic
215C11×C22⋊Q8C2311yescharacteristic
216C11×#121—21no—
217C11×#121—21no—
218C11×#121—22no—
219C11×#121—21no—
220C11×#121—21no—
221C11×#121—22no—
222C11×#121—22no—
223C11×#121C2312yes—
224C11×#121C2312yes—
225C11×#121C2311yescharacteristic
226C11×#121C2311yescharacteristic
227C11×#121C2311yescharacteristic
228C11×#121C2311yescharacteristic
229C11×#120—21no—
230C11×#120—21no—
231C11×#120—22no—
232C4×Q8×C11—21no—
233C4×Q8×C11—21no—
234C4×Q8×C11—22no—
235C4×Q8×C11C2312yes—
236C4×Q8×C11C2312yes—
237C4×Q8×C11C2312yes—
238C4×Q8×C11C2312yes—
239C4×D4×C11—21no—
240C4×D4×C11—21no—
241C4×D4×C11—21no—
242C4×D4×C11—21no—
243C4×D4×C11—22no—
244C4×D4×C11—22no—
245C4×D4×C11—21no—
246C4×D4×C11—21no—
247C4×D4×C11—22no—
248C4×D4×C11—22no—
249C4×D4×C11—22no—
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2312yes—
253C4×D4×C11C2312yes—
254C11×#117—22no—
255C11×#117—21no—
256C11×#117—21no—
257C11×#117—22no—
258C11×#117—22no—
259C11×#117—22no—
260C11×#117D412yes—
261C11×#117D411yescharacteristic
262C11×#117D411yescharacteristic
263C11×#117C2311yescharacteristic
264C11×#117C2311yescharacteristic
265C11×#117C2311yescharacteristic
266C11×#117C2311yescharacteristic
267C11×#117C2312yes—
268C2×C11×C4⋊C4—21no—
269C2×C11×C4⋊C4—21no—
270C2×C11×C4⋊C4—21no—
271C2×C11×C4⋊C4D411yescharacteristic
272C2×C11×C4⋊C4D411yescharacteristic
273C2×C11×C4⋊C4C2311yescharacteristic
274C2×C11×C4⋊C4C2311yescharacteristic
275C2×C11×C22⋊C4—21no—
276C2×C11×C22⋊C4—21no—
277C2×C11×C22⋊C4—22no—
278C2×C11×C22⋊C4D412yes—
279C2×C42×C11C2312yes—
280C11×#107C2311yescharacteristic
281C11×#107C2312yes—
282C11×#107C2311yescharacteristic
283C11×#107C2312yes—
284C11×#107C2312yes—
285C11×#107C2312yes—
286C11×#106C2312yes—
287C11×#106C2312yes—
288C11×#106C2311yescharacteristic
289C11×#106C2311yescharacteristic
290C11×#103C2311yescharacteristic
291C11×#103C2312yes—
292C11×#103C2312yes—
293C11×#103C2312yes—
294C11×#103C2311yescharacteristic
295C11×#103C2312yes—
296C11×#103C2312yes—
297C11×#103C2312yes—
298C11×#103C2311yescharacteristic
299C11×#103C2311yescharacteristic
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2312yes—
304C11×#102C2311yescharacteristic
305C11×#102C2312yes—
306C11×#102C2312yes—
307C11×#102C2312yes—
308C11×#102C2311yescharacteristic
309C11×#102C2311yescharacteristic
310C11×#97C2312yes—
311C11×#97C2312yes—
312C11×#97C2312yes—
313C11×#97C2312yes—
314C4×C8×C11C2312yes—
315C4×C8×C11C2312yes—
316C4×C8×C11C2312yes—
317C4×C8×C11C2312yes—
318#60709C1111yesmaximal, characteristic, direct product factor, Sylow
319C24×C11—21no—
320C24×C11C2×D411yescharacteristic
321C11×#41—22no—
322C11×#41—22no—
323C11×#41—22no—
324C11×#41—22no—
325C11×#41—84no—
326C2×Q8×C11—21no—
327C2×Q8×C11—22no—
328C2×Q8×C11—22no—
329C2×Q8×C11—22no—
330C2×Q8×C11—22no—
331C2×Q8×C11C2411yescharacteristic
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×D4×C11—21no—
335C2×D4×C11—21no—
336C2×D4×C11—21no—
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11—21no—
340C2×D4×C11—21no—
341C2×D4×C11—22no—
342C2×D4×C11—21no—
343C2×D4×C11—22no—
344C2×D4×C11—22no—
345C2×D4×C11—22no—
346C2×D4×C11—22no—
347C2×D4×C11—82no—
348C2×D4×C11C2411yescharacteristic
349C2×D4×C11C2412yes—
350C2×D4×C11C2411yescharacteristic
351C22×C4×C11—22no—
352C22×C4×C11—22no—
353C22×C4×C11—21no—
354C22×C4×C11—21no—
355C22×C4×C11—21no—
356C22×C4×C11—21no—
357C22×C4×C11—21no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11—22no—
362C22×C4×C11C2×D411yescharacteristic
363C22×C4×C11C2×D411yescharacteristic
364C22×C4×C11C2×D411yescharacteristic
365C22×C4×C11C2×D412yes—
366C22×C4×C11C2×D412yes—
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2411yescharacteristic
370C11×Q16—22no—
371C11×Q16—24no—
372C11×SD16—24no—
373C11×SD16—24no—
374C11×SD16—22no—
375C11×SD16—22no—
376C11×SD16—24no—
377C11×SD16—24no—
378C11×D8—22no—
379C11×D8—24no—
380C11×M16—24no—
381C11×M16—22no—
382C11×M16—22no—
383C11×M16—22no—
384C11×M16—22no—
385C11×M16—22no—
386C11×M16#4114yescomplemented
387C2×C8×C11—24no—
388C2×C8×C11—22no—
389C2×C8×C11#4114yescomplemented
390C2×C8×C11C2411yescharacteristic
391C2×C8×C11C2412yes—
392C2×C8×C11C2411yescharacteristic
393C2×C8×C11C2412yes—
394C2×C8×C11C2411yescharacteristic
395C2×C8×C11C2411yescharacteristic
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—21no—
413C11×C4⋊C4—22no—
414C11×C4⋊C4—21no—
415C11×C4⋊C4—22no—
416C11×C4⋊C4C2×D411yescharacteristic
417C11×C4⋊C4C2×D411yescharacteristic
418C11×C4⋊C4C2×D411yescharacteristic
419C11×C4⋊C4C2×D411yescharacteristic
420C11×C4⋊C4C2×D412yes—
421C11×C4⋊C4C2×D412yes—
422C11×C4⋊C4C2411yescharacteristic
423C11×C4⋊C4C2412yes—
424C11×C4⋊C4C2411yescharacteristic
425C11×C4⋊C4C2411yescharacteristic
426C11×C4⋊C4C2412yes—
427C11×C4⋊C4C2411yescharacteristic
428C11×C22⋊C4—21no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—21no—
432C11×C22⋊C4—21no—
433C11×C22⋊C4—21no—
434C11×C22⋊C4—21no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—22no—
440C11×C22⋊C4—21no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—22no—
443C11×C22⋊C4—22no—
444C11×C22⋊C4—22no—
445C11×C22⋊C4—21no—
446C11×C22⋊C4—22no—
447C11×C22⋊C4—21no—
448C11×C22⋊C4—21no—
449C11×C22⋊C4—22no—
450C11×C22⋊C4C2×D412yes—
451C11×C22⋊C4C2×D412yes—
452C11×C22⋊C4C2×D412yes—
453C11×C22⋊C4C2×D412yes—
454C42×C11—22no—
455C42×C11—22no—
456C42×C11—22no—
457C42×C11—22no—
458C42×C11—21no—
459C42×C11—21no—
460C42×C11C2×D412yes—
461C42×C11C2×D412yes—
462C42×C11C2412yes—
463C42×C11C2412yes—
464#3495C2×C1111yescharacteristic, complemented
465#3494C2×C1111yescharacteristic, complemented
466#3183C2×C1112yescomplemented
467#3182C2×C1112yescomplemented
468#3179C2×C1112yescomplemented
469#3178C2×C1112yescomplemented
470#3175C2×C1112yescomplemented
471#3174C2×C1112yescomplemented
472#3172C2×C1112yescomplemented
473#3171C2×C1112yescomplemented
474#3164C2×C1111yescharacteristic, complemented
475#3154C2×C1111yescharacteristic, complemented
476#3137C2×C1111yescharacteristic, complemented
477#3136C2×C1111yescharacteristic, complemented
478#3056C2×C1111yescharacteristic, complemented
479#3055C2×C1111yescharacteristic, complemented
480#3054C2×C1111yescharacteristic, complemented
481C2×#468C2×C1111yescharacteristic, complemented
482#2951C2×C1111yescharacteristic, complemented
483#2949C2×C1111yescharacteristic, complemented
484#2947C2×C1111yescharacteristic, complemented
485#2946C2×C1111yescharacteristic, complemented
486#2873C2×C1111yescharacteristic, complemented
487C23×C11—22no—
488C23×C11—21no—
489C23×C11—22no—
490C23×C11—21no—
491C23×C11—41no—
492C23×C11—41no—
493C23×C11—42no—
494C23×C11—81no—
495C23×C11—81no—
496C23×C11C22×D411yescharacteristic
497C23×C11C22×D411yescharacteristic
498C23×C11C22×D411yescharacteristic
499Q8×C11—22no—
500Q8×C11—21no—
501Q8×C11—22no—
502Q8×C11—21no—
503Q8×C11—21no—
504Q8×C11—21no—
505Q8×C11—42no—
506Q8×C11—82no—
507Q8×C11—82no—
508D4×C11—21no—
509D4×C11—22no—
510D4×C11—21no—
511D4×C11—21no—
512D4×C11—22no—
513D4×C11—21no—
514D4×C11—42no—
515D4×C11—44no—
516D4×C11—42no—
517D4×C11—42no—
518D4×C11—42no—
519D4×C11—42no—
520D4×C11—82no—
521D4×C11—82no—
522D4×C11—81no—
523D4×C11—81no—
524D4×C11—82no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—22no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—42no—
542C2×C4×C11—42no—
543C2×C4×C11—42no—
544C2×C4×C11—42no—
545C2×C4×C11—42no—
546C2×C4×C11—82no—
547C2×C4×C11—82no—
548C2×C4×C11—82no—
549C2×C4×C11—82no—
550C2×C4×C11—81no—
551C2×C4×C11—81no—
552C2×C4×C11C22×D412yes—
553C2×C4×C11C22×D412yes—
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C22×D412yes—
556C2×C4×C11C22×D412yes—
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11C2×#4112yes—
560C2×C4×C11C2×#4112yes—
561C2×C4×C11C2511yescharacteristic
562C8×C11—22no—
563C8×C11—21no—
564C8×C11—21no—
565C8×C11C2×#4114yes—
566C8×C11C2×#4112yes—
567C8×C11C2×#4112yes—
568C2×#137C22×C1111yescharacteristic
569C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
570C2×#135C22×C1111yescharacteristic
571C22×SD16C22×C1111yescharacteristic
572C22×M16C22×C1111yescharacteristic
573C22×M16C22×C1111yescharacteristic
574#556—21no—
575#555—21no—
576#554—21no—
577#553—21no—
578#553—21no—
579#552—22no—
580#552—21no—
581#552—21no—
582#551—22no—
583#551—22no—
584#547—21no—
585#546—22no—
586#544C22×C1111yescharacteristic
587#544C22×C1111yescharacteristic
588#542C22×C1112yes—
589#542C22×C1112yescomplemented
590#541C22×C1112yescomplemented
591#540C22×C1112yes—
592#536C22×C1111yescharacteristic
593#535C22×C1111yescharacteristic
594#533C22×C1112yescomplemented
595#532C22×C1112yes—
596#529C22×C1112yes—
597#529C22×C1112yescomplemented
598#525C22×C1111yescharacteristic
599#525C22×C1111yescharacteristic
600C2×C22⋊Q8C22×C1111yescharacteristic
601C2×#121C22×C1111yescharacteristic
602#520C22×C1111yescharacteristic
603#520C22×C1111yescharacteristic
604#519C22×C1111yescharacteristic
605#518C22×C1111yescharacteristic
606C2×#117C22×C1111yescharacteristic
607#501C22×C1112yescomplemented
608#501C22×C1112yescomplemented
609#500C22×C1112yescomplemented
610#499C22×C1112yescomplemented
611#497C22×C1112yescomplemented
612#496C22×C1112yescomplemented
613#495C22×C1112yescomplemented
614#492C22×C1112yescomplemented
615#491C22×C1112yescomplemented
616#490C22×C1112yescomplemented
617#489C22×C1112yescomplemented
618#489C22×C1112yescomplemented
619#488C22×C1112yescomplemented
620#488C22×C1112yescomplemented
621#487C22×C1112yescomplemented
622#486C22×C1112yescomplemented
623#470C22×C1111yescharacteristic, complemented
624#470C22×C1112yescomplemented
625#470C22×C1111yescharacteristic, complemented
626#469C22×C1112yes—
627#469C22×C1111yescharacteristic, complemented
628#469C22×C1111yescharacteristic, complemented
629#468C22×C1112yes—
630#468C22×C1112yes—
631#468C22×C1112yes—
632#468C22×C1112yes—
633#468C22×C1112yes—
634#468C22×C1112yescomplemented
635#468C22×C1111yescharacteristic, complemented
636#468C22×C1111yescharacteristic, complemented
637#468C22×C1111yescharacteristic, complemented
638#468C22×C1111yescharacteristic, complemented
639#467C22×C1112yescomplemented
640#466C22×C1112yes—
641#465C22×C1112yes—
642#465C22×C1112yescomplemented
643#442C22×C1112yescomplemented
644#441C22×C1112yescomplemented
645#440C22×C1112yescomplemented
646#440C22×C1112yescomplemented
647#440C22×C1112yescomplemented
648#440C22×C1112yescomplemented
649#440C22×C1112yescomplemented
650#440C22×C1112yescomplemented
651C4×Q16C22×C1112yescomplemented
652C4×Q16C22×C1112yescomplemented
653C4×SD16C22×C1112yescomplemented
654C4×SD16C22×C1112yescomplemented
655C4×SD16C22×C1112yescomplemented
656C4×SD16C22×C1112yescomplemented
657C4×D8C22×C1112yescomplemented
658C4×D8C22×C1112yescomplemented
659#428C22×C1111yescharacteristic
660#428C22×C1111yescharacteristic
661#427C22×C1111yescharacteristic
662C2×#107C22×C1111yescharacteristic
663#419C22×C1111yescharacteristic
664#418C22×C1111yescharacteristic
665#417C22×C1111yescharacteristic
666#417C22×C1111yescharacteristic
667#416C22×C1111yescharacteristic
668#416C22×C1111yescharacteristic
669C2×#103C22×C1111yescharacteristic
670C2×#102C22×C1111yescharacteristic
671#405C22×C1111yescharacteristic
672#405C22×C1111yescharacteristic
673#405C22×C1111yescharacteristic
674#405C22×C1111yescharacteristic
675#405C22×C1112yescomplemented
676#405C22×C1112yescomplemented
677C4×M16C22×C1112yescomplemented
678C4×M16C22×C1112yescomplemented
679C22×C11—21no—
680C22×C11—21no—
681C22×C11—21no—
682C22×C11—21no—
683C22×C11—21no—
684C22×C11—21no—
685C22×C11—21no—
686C22×C11—21no—
687C22×C11—41no—
688C22×C11—41no—
689C22×C11—42no—
690C22×C11—42no—
691C22×C11—41no—
692C22×C11—41no—
693C22×C11—41no—
694C22×C11—41no—
695C22×C11—42no—
696C22×C11—82no—
697C22×C11—162no—
698C22×C11#53212yes—
699C22×C11C23×D411yescharacteristic
700C4×C11—22no—
701C4×C11—22no—
702C4×C11—22no—
703C4×C11—22no—
704C4×C11—21no—
705C4×C11—21no—
706C4×C11—42no—
707C4×C11—41no—
708C4×C11—42no—
709C4×C11—41no—
710C4×C11—41no—
711C4×C11—41no—
712C4×C11—41no—
713C4×C11—41no—
714C4×C11—42no—
715C4×C11#53212yes—
716C4×C11C22×#4111yescharacteristic
717C4×C11C22×#4111yescharacteristic
718C2×#41—22no—
719C2×#41C23×C1111yescharacteristic
720C2×#41C23×C1111yescharacteristic
721C22×Q8C23×C1111yescharacteristic
722C22×D4—21no—
723C22×D4C23×C1111yescharacteristic
724C23×C4C23×C1111yescharacteristic
725#137—24no—
726AGL(1,ℤ/8)—24no—
727#135—24no—
728C2×Q16C23×C1111yescharacteristic
729C2×Q16C23×C1112yes—
730C2×SD16—24no—
731C2×SD16C23×C1112yes—
732C2×SD16C23×C1112yes—
733C2×SD16C23×C1111yescharacteristic
734C2×SD16C23×C1111yescharacteristic
735C2×SD16C23×C1112yes—
736C2×SD16C23×C1112yes—
737C2×D8C23×C1111yescharacteristic
738C2×D8C23×C1112yes—
739C2×M16—24no—
740C2×M16—24no—
741C2×M16C23×C1111yescharacteristic
742C2×M16C23×C1111yescharacteristic
743C2×M16C23×C1112yes—
744C2×M16C23×C1111yescharacteristic
745C2×M16C23×C1111yescharacteristic
746C2×M16C23×C1111yescharacteristic
747C2×M16C23×C1111yescharacteristic
748C22×C8C23×C1111yescharacteristic
749C22×C8C23×C1112yes—
750C22×C8C23×C1111yescharacteristic
751C4⋊Q8—21no—
752C4⋊Q8—21no—
753C4⋊Q8C23×C1112yes—
754C4⋊Q8C23×C1112yes—
755C4⋊Q8C23×C1112yes—
756#127C23×C1112yes—
757#126—22no—
758#126—22no—
759#126—22no—
760#126—22no—
761#126—22no—
762#126—22no—
763#125—22no—
764#125—22no—
765#125—21no—
766#125—21no—
767#125—22no—
768#125C23×C1112yes—
769#125C23×C1112yes—
770#124—22no—
771#124—22no—
772#124—22no—
773#124C23×C1112yes—
774#124C23×C1112yes—
775#123—21no—
776#123—21no—
777#123—22no—
778#123—22no—
779#123—22no—
780#123—22no—
781#123—22no—
782#123—22no—
783#123—22no—
784C22⋊Q8—21no—
785C22⋊Q8—21no—
786C22⋊Q8—22no—
787C22⋊Q8—21no—
788C22⋊Q8—21no—
789C22⋊Q8—22no—
790C22⋊Q8—22no—
791C22⋊Q8—22no—
792C22⋊Q8—22no—
793C22⋊Q8C23×C1112yes—
794C22⋊Q8C23×C1112yes—
795C22⋊Q8C23×C1111yescharacteristic
796C22⋊Q8C23×C1111yescharacteristic
797C22⋊Q8C23×C1111yescharacteristic
798C22⋊Q8C23×C1111yescharacteristic
799#121—21no—
800#121—21no—
801#121—22no—
802#121—21no—
803#121—21no—
804#121—22no—
805#121—22no—
806#121C23×C1112yes—
807#121C23×C1112yes—
808#121C23×C1111yescharacteristic
809#121C23×C1111yescharacteristic
810#121C23×C1111yescharacteristic
811#121C23×C1111yescharacteristic
812#120—21no—
813#120—21no—
814#120—22no—
815C4×Q8—21no—
816C4×Q8—21no—
817C4×Q8—22no—
818C4×Q8C23×C1112yes—
819C4×Q8C23×C1112yes—
820C4×Q8C23×C1112yes—
821C4×Q8C23×C1112yes—
822C4×D4—21no—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—21no—
826C4×D4—22no—
827C4×D4—22no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—22no—
831C4×D4—22no—
832C4×D4—22no—
833C4×D4C23×C1112yes—
834C4×D4C23×C1112yes—
835C4×D4C23×C1112yes—
836C4×D4C23×C1112yes—
837#117—22no—
838#117—21no—
839#117—21no—
840#117—22no—
841#117—22no—
842#117—22no—
843#117D4×C1112yes—
844#117D4×C1111yescharacteristic
845#117D4×C1111yescharacteristic
846#117C23×C1111yescharacteristic
847#117C23×C1111yescharacteristic
848#117C23×C1111yescharacteristic
849#117C23×C1111yescharacteristic
850#117C23×C1112yes—
851C2×C4⋊C4—21no—
852C2×C4⋊C4—21no—
853C2×C4⋊C4—21no—
854C2×C4⋊C4D4×C1111yescharacteristic
855C2×C4⋊C4D4×C1111yescharacteristic
856C2×C4⋊C4C23×C1111yescharacteristic
857C2×C4⋊C4C23×C1111yescharacteristic
858C2×C22⋊C4—21no—
859C2×C22⋊C4—21no—
860C2×C22⋊C4—22no—
861C2×C22⋊C4D4×C1112yes—
862C2×C42C23×C1112yes—
863#107C23×C1112yes—
864#107C23×C1112yes—
865#107C23×C1111yescharacteristic
866#107C23×C1111yescharacteristic
867#107C23×C1112yes—
868#107C23×C1112yes—
869#106C23×C1111yescharacteristic
870#106C23×C1111yescharacteristic
871#106C23×C1112yes—
872#106C23×C1112yes—
873#103C23×C1112yes—
874#103C23×C1112yes—
875#103C23×C1111yescharacteristic
876#103C23×C1111yescharacteristic
877#103C23×C1111yescharacteristic
878#103C23×C1111yescharacteristic
879#103C23×C1112yes—
880#103C23×C1112yes—
881#103C23×C1112yes—
882#103C23×C1112yes—
883#102C23×C1112yes—
884#102C23×C1112yes—
885#102C23×C1111yescharacteristic
886#102C23×C1111yescharacteristic
887#102C23×C1111yescharacteristic
888#102C23×C1111yescharacteristic
889#102C23×C1112yes—
890#102C23×C1112yes—
891#102C23×C1112yes—
892#102C23×C1112yes—
893#97C23×C1112yes—
894#97C23×C1112yes—
895#97C23×C1112yes—
896#97C23×C1112yes—
897C4×C8C23×C1112yes—
898C4×C8C23×C1112yes—
899C4×C8C23×C1112yes—
900C4×C8C23×C1112yes—
901C2×C11—22no—
902C2×C11—41no—
903C2×C11—41no—
904C2×C11—81no—
905C2×C11—81no—
906C2×C11—82no—
907C2×C11C2×#53211yescharacteristic
908C2×C11#358511yescharacteristic
909C2×C11#358611yescharacteristic
910C24—21no—
911C24C2×D4×C1111yescharacteristic
912#41—22no—
913#41—22no—
914#41—22no—
915#41—22no—
916#41—84no—
917C2×Q8—21no—
918C2×Q8—22no—
919C2×Q8—22no—
920C2×Q8—22no—
921C2×Q8—22no—
922C2×Q8C24×C1111yescharacteristic
923C2×Q8C24×C1112yes—
924C2×Q8C24×C1111yescharacteristic
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—22no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—22no—
933C2×D4—21no—
934C2×D4—22no—
935C2×D4—22no—
936C2×D4—22no—
937C2×D4—22no—
938C2×D4—82no—
939C2×D4C24×C1111yescharacteristic
940C2×D4C24×C1112yes—
941C2×D4C24×C1111yescharacteristic
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4C2×D4×C1111yescharacteristic
954C22×C4C2×D4×C1111yescharacteristic
955C22×C4C2×D4×C1111yescharacteristic
956C22×C4C2×D4×C1112yes—
957C22×C4C2×D4×C1112yes—
958C22×C4C24×C1111yescharacteristic
959C22×C4C24×C1111yescharacteristic
960C22×C4C24×C1111yescharacteristic
961Q16—22no—
962Q16—24no—
963SD16—24no—
964SD16—24no—
965SD16—22no—
966SD16—22no—
967SD16—24no—
968SD16—24no—
969D8—22no—
970D8—24no—
971M16—22no—
972M16—24no—
973M16—22no—
974M16—22no—
975M16—22no—
976M16—22no—
977M16C11×#4114yescomplemented
978C2×C8—22no—
979C2×C8—24no—
980C2×C8C11×#4114yescomplemented
981C2×C8C24×C1111yescharacteristic
982C2×C8C24×C1112yes—
983C2×C8C24×C1111yescharacteristic
984C2×C8C24×C1112yes—
985C2×C8C24×C1111yescharacteristic
986C2×C8C24×C1111yescharacteristic
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—21no—
1004C4⋊C4—22no—
1005C4⋊C4—21no—
1006C4⋊C4—22no—
1007C4⋊C4C2×D4×C1111yescharacteristic
1008C4⋊C4C2×D4×C1111yescharacteristic
1009C4⋊C4C2×D4×C1111yescharacteristic
1010C4⋊C4C2×D4×C1111yescharacteristic
1011C4⋊C4C2×D4×C1112yes—
1012C4⋊C4C2×D4×C1112yes—
1013C4⋊C4C24×C1111yescharacteristic
1014C4⋊C4C24×C1112yes—
1015C4⋊C4C24×C1111yescharacteristic
1016C4⋊C4C24×C1111yescharacteristic
1017C4⋊C4C24×C1112yes—
1018C4⋊C4C24×C1111yescharacteristic
1019C22⋊C4—21no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—21no—
1023C22⋊C4—21no—
1024C22⋊C4—21no—
1025C22⋊C4—21no—
1026C22⋊C4—21no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—21no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—21no—
1037C22⋊C4—22no—
1038C22⋊C4—21no—
1039C22⋊C4—21no—
1040C22⋊C4—22no—
1041C22⋊C4C2×D4×C1112yes—
1042C22⋊C4C2×D4×C1112yes—
1043C22⋊C4C2×D4×C1112yes—
1044C22⋊C4C2×D4×C1112yes—
1045C42—22no—
1046C42—22no—
1047C42—22no—
1048C42—22no—
1049C42—21no—
1050C42—21no—
1051C42C2×D4×C1112yes—
1052C42C2×D4×C1112yes—
1053C42C24×C1112yes—
1054C42C24×C1112yes—
1055C11#6070911yescharacteristic, direct product factor, Sylow
1056C23—22no—
1057C23—21no—
1058C23—22no—
1059C23—21no—
1060C23—41no—
1061C23—41no—
1062C23—42no—
1063C23—81no—
1064C23—81no—
1065C23C22×D4×C1111yescharacteristic
1066C23C22×D4×C1111yescharacteristic
1067C23C22×D4×C1111yescharacteristic
1068Q8—22no—
1069Q8—21no—
1070Q8—22no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—42no—
1075Q8—82no—
1076Q8—82no—
1077D4—21no—
1078D4—22no—
1079D4—21no—
1080D4—21no—
1081D4—22no—
1082D4—21no—
1083D4—42no—
1084D4—44no—
1085D4—42no—
1086D4—42no—
1087D4—42no—
1088D4—42no—
1089D4—82no—
1090D4—82no—
1091D4—81no—
1092D4—81no—
1093D4—82no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—82no—
1116C2×C4—82no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—81no—
1120C2×C4—81no—
1121C2×C4C22×D4×C1112yes—
1122C2×C4C22×D4×C1112yes—
1123C2×C4C22×D4×C1111yescharacteristic
1124C2×C4C22×D4×C1112yes—
1125C2×C4C22×D4×C1112yes—
1126C2×C4C22×D4×C1111yescharacteristic
1127C2×C4C22×D4×C1111yescharacteristic
1128C2×C4C2×C11×#4112yes—
1129C2×C4C2×C11×#4112yes—
1130C2×C4C25×C1111yescharacteristic
1131C8—21no—
1132C8—21no—
1133C8—22no—
1134C8C2×C11×#4114yes—
1135C8C2×C11×#4112yes—
1136C8C2×C11×#4112yes—
1137C22—21no—
1138C22—21no—
1139C22—21no—
1140C22—21no—
1141C22—21no—
1142C22—21no—
1143C22—21no—
1144C22—21no—
1145C22—41no—
1146C22—41no—
1147C22—42no—
1148C22—41no—
1149C22—41no—
1150C22—42no—
1151C22—42no—
1152C22—41no—
1153C22—41no—
1154C22—82no—
1155C22—162no—
1156C22C11×#53212yes—
1157C22C23×D4×C1111yescharacteristic
1158C4—21no—
1159C4—21no—
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—41no—
1165C4—41no—
1166C4—42no—
1167C4—42no—
1168C4—41no—
1169C4—42no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4C11×#53212yes—
1174C4C22×C11×#4111yescharacteristic
1175C4C22×C11×#4111yescharacteristic
1176C2—22no—
1177C2—41no—
1178C2—41no—
1179C2—82no—
1180C2—81no—
1181C2—81no—
1182C2C2×C11×#53211yescharacteristic
1183C2C11×#358511yescharacteristic
1184C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3495C2semidirect
2. C11×#3494C2semidirect
3. C11×#3183C2semidirect
4. C11×#3182C2semidirect
5. C11×#3179C2semidirect
6. C11×#3178C2semidirect
7. C11×#3175C2semidirect
8. C11×#3174C2semidirect
9. C11×#3172C2semidirect
10. C11×#3171C2semidirect
11. C11×#3164C2semidirect
12. C11×#3154C2semidirect
13. C11×#3137C2semidirect
14. C11×#3136C2semidirect
15. C11×#3056C2semidirect
16. C11×#3055C2semidirect
17. C11×#3054C2semidirect
18. C2×C11×#468C2semidirect
19. C11×#2951C2semidirect
20. C11×#2949C2semidirect
21. C11×#2947C2semidirect
22. C11×#2946C2semidirect
23. C11×#2873C2semidirect
45. C11×#542C22semidirect
46. C11×#541C22semidirect
50. C11×#533C22semidirect
53. C11×#529C22semidirect
63. C11×#501C22semidirect
64. C11×#501C22semidirect
65. C11×#500C22semidirect
66. C11×#499C22semidirect
67. C11×#497C22semidirect
68. C11×#496C22semidirect
69. C11×#495C22semidirect
70. C11×#492C22semidirect
71. C11×#491C22semidirect
72. C11×#490C22semidirect
73. C11×#489C22semidirect
74. C11×#489C22semidirect
75. C11×#488C22semidirect
76. C11×#488C22semidirect
77. C11×#487C22semidirect
78. C11×#486C22semidirect
79. C11×#470C22semidirect
80. C11×#470C22semidirect
81. C11×#470C22semidirect
83. C11×#469C22semidirect
84. C11×#469C22semidirect
90. C11×#468C22semidirect
91. C11×#468C22semidirect
92. C11×#468C22semidirect
93. C11×#468C22semidirect
94. C11×#468C22semidirect
95. C11×#467C22semidirect
98. C11×#465C22semidirect
99. C11×#442C22semidirect
100. C11×#441C22semidirect
101. C11×#440C22semidirect
102. C11×#440C22semidirect
103. C11×#440C22semidirect
104. C11×#440C22semidirect
105. C11×#440C22semidirect
106. C11×#440C22semidirect
107. C4×C11×Q16C22semidirect
108. C4×C11×Q16C22semidirect
109. C4×C11×SD16C22semidirect
110. C4×C11×SD16C22semidirect
111. C4×C11×SD16C22semidirect
112. C4×C11×SD16C22semidirect
113. C4×C11×D8C22semidirect
114. C4×C11×D8C22semidirect
131. C11×#405C22semidirect
132. C11×#405C22semidirect
133. C4×C11×M16C22semidirect
134. C4×C11×M16C22semidirect
318. #60709C11direct (N × H)
386. C11×M16#41semidirect
389. C2×C8×C11#41semidirect
464. #3495C2×C11semidirect
465. #3494C2×C11semidirect
466. #3183C2×C11semidirect
467. #3182C2×C11semidirect
468. #3179C2×C11semidirect
469. #3178C2×C11semidirect
470. #3175C2×C11semidirect
471. #3174C2×C11semidirect
472. #3172C2×C11semidirect
473. #3171C2×C11semidirect
474. #3164C2×C11semidirect
475. #3154C2×C11semidirect
476. #3137C2×C11semidirect
477. #3136C2×C11semidirect
478. #3056C2×C11semidirect
479. #3055C2×C11semidirect
480. #3054C2×C11semidirect
481. C2×#468C2×C11semidirect
482. #2951C2×C11semidirect
483. #2949C2×C11semidirect
484. #2947C2×C11semidirect
485. #2946C2×C11semidirect
486. #2873C2×C11semidirect
589. #542C22×C11semidirect
590. #541C22×C11semidirect
594. #533C22×C11semidirect
597. #529C22×C11semidirect
607. #501C22×C11semidirect
608. #501C22×C11semidirect
609. #500C22×C11semidirect
610. #499C22×C11semidirect
611. #497C22×C11semidirect
612. #496C22×C11semidirect
613. #495C22×C11semidirect
614. #492C22×C11semidirect
615. #491C22×C11semidirect
616. #490C22×C11semidirect
617. #489C22×C11semidirect
618. #489C22×C11semidirect
619. #488C22×C11semidirect
620. #488C22×C11semidirect
621. #487C22×C11semidirect
622. #486C22×C11semidirect
623. #470C22×C11semidirect
624. #470C22×C11semidirect
625. #470C22×C11semidirect
627. #469C22×C11semidirect
628. #469C22×C11semidirect
634. #468C22×C11semidirect
635. #468C22×C11semidirect
636. #468C22×C11semidirect
637. #468C22×C11semidirect
638. #468C22×C11semidirect
639. #467C22×C11semidirect
642. #465C22×C11semidirect
643. #442C22×C11semidirect
644. #441C22×C11semidirect
645. #440C22×C11semidirect
646. #440C22×C11semidirect
647. #440C22×C11semidirect
648. #440C22×C11semidirect
649. #440C22×C11semidirect
650. #440C22×C11semidirect
651. C4×Q16C22×C11semidirect
652. C4×Q16C22×C11semidirect
653. C4×SD16C22×C11semidirect
654. C4×SD16C22×C11semidirect
655. C4×SD16C22×C11semidirect
656. C4×SD16C22×C11semidirect
657. C4×D8C22×C11semidirect
658. C4×D8C22×C11semidirect
675. #405C22×C11semidirect
676. #405C22×C11semidirect
677. C4×M16C22×C11semidirect
678. C4×M16C22×C11semidirect
977. M16C11×#41semidirect
980. C2×C8C11×#41semidirect
1055. C11#60709direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34952
C11×#34942
C11×#31832
C11×#31822
C11×#31792
C11×#31782
C11×#31752
C11×#31742
C11×#31722
C11×#31712
C11×#31642
C11×#31542
C11×#31372
C11×#31362
C11×#30562
C11×#30552
C11×#30542
C2×C11×#4682
C11×#29512
C11×#29492
C11×#29472
C11×#29462
C11×#28732
#6070911