Finite Group Databasebeta

← C11×#61336 #14638529

Subgroups — C11×#61336 #14638529

Order 2816.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3510C211yesmaximal, characteristic, complemented
2C11×#3503C211yesmaximal, characteristic, complemented
3C11×#3377C212yesmaximal, complemented
4C11×#3376C212yesmaximal, complemented
5C11×#3375C212yesmaximal, complemented
6C11×#3373C212yesmaximal, complemented
7C11×#3371C212yesmaximal, complemented
8C11×#3370C212yesmaximal, complemented
9C11×#3369C212yesmaximal, complemented
10C11×#3367C212yesmaximal, complemented
11C11×#3137C211yesmaximal, characteristic, complemented
12C11×#3136C211yesmaximal, characteristic, complemented
13C2×C11×#489C211yesmaximal, characteristic, complemented
14C11×#3082C211yesmaximal, characteristic, complemented
15C11×#3081C211yesmaximal, characteristic, complemented
16C11×#3079C211yesmaximal, characteristic, complemented
17C11×#3046C211yesmaximal, characteristic, complemented
18C11×#3045C211yesmaximal, characteristic
19C11×#3040C211yesmaximal, characteristic, complemented
20C11×#2961C211yesmaximal, characteristic, complemented
21C11×#2947C211yesmaximal, characteristic, complemented
22C11×#2946C211yesmaximal, characteristic, complemented
23C11×#2943C211yesmaximal, characteristic, complemented
24C2×C11×#137C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×#135C2211yescharacteristic
27C11×#559C2212yes—
28C11×#559C2212yes—
29Q82×C11C2212yescomplemented
30C11×#557C2212yescomplemented
31C11×#556C2212yes—
32C11×#556C2212yes—
33C11×#554—22no—
34C11×#554C2212yescomplemented
35C11×#551—22no—
36C11×#551—22no—
37D4×Q8×C11—22no—
38D4×Q8×C11C2212yescomplemented
39C11×#544—21no—
40C11×#544—21no—
41C11×#544C2211yescharacteristic
42C11×#544C2211yescharacteristic
43C11×#542—21no—
44C11×#542—21no—
45C11×#536C2211yescharacteristic
46C11×#535C2211yescharacteristic
47C11×#533—21no—
48C11×#533C2211yescharacteristic
49C2×C11×C4⋊Q8—21no—
50C2×C11×C4⋊Q8C2211yescharacteristic
51C11×#529—21no—
52C11×#529—21no—
53C2×C11×#124C2211yescharacteristic
54C11×#520C2211yescharacteristic
55C11×#520C2211yescharacteristic
56C11×#519C2211yescharacteristic
57C11×#518C2211yescharacteristic
58C4×C11×#41C2211yescharacteristic
59C4×C11×#41C2211yescharacteristic
60C11×#491C2212yescomplemented
61C11×#490C2212yes—
62C11×#489C2212yes—
63C11×#489C2212yes—
64C11×#489C2212yes—
65C11×#489C2212yes—
66C11×#489C2212yes—
67C11×#489C2212yescomplemented
68C11×#488C2212yes—
69C11×#488C2212yescomplemented
70C11×#487C2212yescomplemented
71C11×#486C2212yes—
72C11×#479C2212yescomplemented
73C11×#479C2212yescomplemented
74C11×#478C2212yes—
75C11×#478C2212yes—
76C11×#477C2212yescomplemented
77C11×#477C2212yescomplemented
78C11×#476C2212yes—
79C11×#476C2212yescomplemented
80C11×#475C2212yescomplemented
81C11×#475C2212yescomplemented
82C11×#474C2212yes—
83C11×#474C2212yescomplemented
84C11×#464C2212yes—
85C11×#464C2212yes—
86C11×#464C2212yes—
87C11×#464C2212yescomplemented
88C11×#463C2212yes—
89C11×#463C2212yes—
90C11×#463C2212yes—
91C11×#463C2212yescomplemented
92C11×#462C2212yescomplemented
93C11×#461C2212yescomplemented
94C11×#460C2212yes—
95C11×#459C2212yes—
96C11×#446C2212yescomplemented
97C11×#446C2212yescomplemented
98C11×#446C2212yescomplemented
99C11×#446C2212yescomplemented
100C11×#442C2212yes—
101C11×#442C2211yescharacteristic, complemented
102C11×#442C2211yescharacteristic, complemented
103C11×#441C2211yescharacteristic, complemented
104C11×#441C2211yescharacteristic, complemented
105C11×#441C2212yescomplemented
106C11×#440C2212yes—
107C11×#440C2211yescharacteristic, complemented
108C11×#440C2211yescharacteristic, complemented
109C11×#440C2211yescharacteristic, complemented
110C11×#440C2211yescharacteristic, complemented
111C11×#440C2212yescomplemented
112C4×C11×Q16C2212yescomplemented
113C4×C11×SD16C2212yes—
114C4×C11×SD16C2212yescomplemented
115C4×C11×D8C2212yes—
116C11×#428C2211yescharacteristic
117C11×#428C2211yescharacteristic
118C11×#427C2211yescharacteristic
119C11×#424C2211yescharacteristic
120C11×#424C2211yescharacteristic
121C11×#423C2211yescharacteristic
122C11×#419C2211yescharacteristic
123C11×#418C2211yescharacteristic
124C11×#417C2211yescharacteristic
125C11×#417C2211yescharacteristic
126C11×#416C2211yescharacteristic
127C11×#416C2211yescharacteristic
128C2×C11×#103C2211yescharacteristic
129C2×C11×#103C2211yescharacteristic
130C2×C11×#102C2211yescharacteristic
131C2×C11×#102C2211yescharacteristic
132C11×#405C2211yescharacteristic
133C11×#405C2211yescharacteristic
134C2×C11×#97C2211yescharacteristic
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C22×Q8×C11—22no—
138C22×Q8×C11—21no—
139C22×Q8×C11C2311yescharacteristic
140C22×D4×C11C2311yescharacteristic
141C11×#137—24no—
142C11×AGL(1,ℤ/8)—24no—
143C11×#135—24no—
144C2×C11×Q16C2311yescharacteristic
145C2×C11×Q16C2312yes—
146C2×C11×SD16C2311yescharacteristic
147C2×C11×SD16C2311yescharacteristic
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2312yes—
150C2×C11×D8C2311yescharacteristic
151C2×C11×D8C2312yes—
152C2×C11×M16C2311yescharacteristic
153C2×C11×M16C2311yescharacteristic
154C22×C8×C11C2311yescharacteristic
155C22×C8×C11C2311yescharacteristic
156C11×C4⋊Q8—22no—
157C11×C4⋊Q8—21no—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8—22no—
160C11×C4⋊Q8—22no—
161C11×C4⋊Q8—22no—
162C11×C4⋊Q8—21no—
163C11×C4⋊Q8—21no—
164C11×C4⋊Q8D411yescharacteristic
165C11×C4⋊Q8D411yescharacteristic
166C11×C4⋊Q8C2312yes—
167C11×C4⋊Q8C2312yes—
168C11×C4⋊Q8C2312yes—
169C11×C4⋊Q8C2312yes—
170C11×C4⋊Q8C2312yes—
171C11×#127C2312yes—
172C11×#126—22no—
173C11×#126—22no—
174C11×#126—22no—
175C11×#126—22no—
176C11×#125—21no—
177C11×#125—21no—
178C11×#125—22no—
179C11×#125—22no—
180C11×#125D411yescharacteristic
181C11×#125D411yescharacteristic
182C11×#125C2312yes—
183C11×#125C2312yes—
184C11×#124—22no—
185C11×#124—22no—
186C11×#124—21no—
187C11×#124—21no—
188C11×#124C2312yes—
189C11×#124C2312yes—
190C11×#124C2312yes—
191C11×#124C2312yes—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8—22no—
200C11×C22⋊Q8—21no—
201C11×C22⋊Q8—21no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—22no—
206C11×C22⋊Q8—22no—
207C11×C22⋊Q8—22no—
208C11×C22⋊Q8—22no—
209C11×C22⋊Q8D412yes—
210C11×C22⋊Q8D412yes—
211C11×#121—21no—
212C11×#121—21no—
213C11×#120—22no—
214C4×Q8×C11—22no—
215C4×Q8×C11—21no—
216C4×Q8×C11—21no—
217C4×Q8×C11—22no—
218C4×Q8×C11C2311yescharacteristic
219C4×Q8×C11C2311yescharacteristic
220C4×Q8×C11C2311yescharacteristic
221C4×Q8×C11C2311yescharacteristic
222C4×Q8×C11C2312yes—
223C4×Q8×C11C2312yes—
224C4×Q8×C11C2312yes—
225C4×Q8×C11C2312yes—
226C4×Q8×C11C2312yes—
227C4×Q8×C11C2312yes—
228C4×D4×C11—21no—
229C4×D4×C11—21no—
230C4×D4×C11—21no—
231C4×D4×C11—21no—
232C4×D4×C11—21no—
233C4×D4×C11—21no—
234C4×D4×C11—22no—
235C4×D4×C11—22no—
236C4×D4×C11—22no—
237C4×D4×C11—22no—
238C4×D4×C11C2311yescharacteristic
239C4×D4×C11C2311yescharacteristic
240C4×D4×C11C2311yescharacteristic
241C4×D4×C11C2311yescharacteristic
242C4×D4×C11C2312yes—
243C4×D4×C11C2312yes—
244C4×D4×C11C2312yes—
245C4×D4×C11C2312yes—
246C11×#117—21no—
247C11×#117—21no—
248C11×#117—22no—
249C11×#117—22no—
250C11×#117—22no—
251C11×#117—21no—
252C11×#117—21no—
253C11×#117C2311yescharacteristic
254C11×#117C2311yescharacteristic
255C11×#117C2311yescharacteristic
256C11×#117C2311yescharacteristic
257C2×C11×C4⋊C4—21no—
258C2×C11×C4⋊C4—21no—
259C2×C11×C4⋊C4—21no—
260C2×C11×C4⋊C4—22no—
261C2×C11×C4⋊C4C2311yescharacteristic
262C2×C11×C4⋊C4C2311yescharacteristic
263C2×C11×C22⋊C4—21no—
264C2×C11×C22⋊C4—21no—
265C2×C11×C22⋊C4—22no—
266C2×C42×C11—21no—
267C2×C42×C11—21no—
268C2×C42×C11C2311yescharacteristic
269C11×#107C2311yescharacteristic
270C11×#107C2311yescharacteristic
271C11×#107C2312yes—
272C11×#107C2312yes—
273C11×#106C2311yescharacteristic
274C11×#106C2311yescharacteristic
275C11×#106C2312yes—
276C11×#106C2312yes—
277C11×C4⋊C8C2312yes—
278C11×C4⋊C8C2312yes—
279C11×C4⋊C8C2312yes—
280C11×C4⋊C8C2312yes—
281C11×C4⋊C8C2312yes—
282C11×C4⋊C8C2312yes—
283C11×#103C2312yes—
284C11×#103C2312yes—
285C11×#103C2312yes—
286C11×#103C2312yes—
287C11×#103C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2311yescharacteristic
291C11×#103C2312yes—
292C11×#103C2312yes—
293C11×#103C2311yescharacteristic
294C11×#103C2311yescharacteristic
295C11×#102C2312yes—
296C11×#102C2312yes—
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2312yes—
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×#102C2311yescharacteristic
303C11×#102C2312yes—
304C11×#102C2312yes—
305C11×#102C2311yescharacteristic
306C11×#102C2311yescharacteristic
307C11×#97C2311yescharacteristic
308C11×#97C2311yescharacteristic
309C11×#97C2311yescharacteristic
310C11×#97C2311yescharacteristic
311C11×#97C2312yes—
312C11×#97C2312yes—
313C4×C8×C11C2312yes—
314C4×C8×C11C2312yes—
315#61336C1111yesmaximal, characteristic, direct product factor, Sylow
316C24×C11—21no—
317C11×#41—22no—
318C11×#41—22no—
319C11×#41—22no—
320C11×#41#4114yes—
321C2×Q8×C11—21no—
322C2×Q8×C11—22no—
323C2×Q8×C11—22no—
324C2×Q8×C11—22no—
325C2×Q8×C11—22no—
326C2×Q8×C11—22no—
327C2×Q8×C11—22no—
328C2×Q8×C11—82no—
329C2×Q8×C11—84no—
330C2×Q8×C11C2×D412yes—
331C2×Q8×C11C2×D412yes—
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2411yescharacteristic
335C2×D4×C11—21no—
336C2×D4×C11—21no—
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11C2412yes—
343C2×D4×C11C2411yescharacteristic
344C2×D4×C11C2411yescharacteristic
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11—21no—
348C22×C4×C11—21no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11—21no—
352C22×C4×C11—21no—
353C22×C4×C11—21no—
354C22×C4×C11—22no—
355C22×C4×C11—22no—
356C22×C4×C11—22no—
357C22×C4×C11—22no—
358C22×C4×C11C2×D411yescharacteristic
359C22×C4×C11C2×D411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C11×Q16—22no—
362C11×Q16—24no—
363C11×SD16—22no—
364C11×SD16—24no—
365C11×SD16—22no—
366C11×SD16—24no—
367C11×D8—22no—
368C11×D8—24no—
369C11×M16—22no—
370C11×M16—22no—
371C2×C8×C11—22no—
372C2×C8×C11—22no—
373C2×C8×C11C2411yescharacteristic
374C2×C8×C11C2411yescharacteristic
375C2×C8×C11C2412yes—
376C2×C8×C11C2412yes—
377C2×C8×C11C2411yescharacteristic
378C2×C8×C11C2411yescharacteristic
379C11×C4⋊C4—22no—
380C11×C4⋊C4—21no—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—21no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D411yescharacteristic
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2×D411yescharacteristic
403C11×C4⋊C4C2×D411yescharacteristic
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2×D412yes—
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2412yes—
410C11×C4⋊C4C2412yes—
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2411yescharacteristic
415C11×C22⋊C4—21no—
416C11×C22⋊C4—21no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—21no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4C2×D412yes—
434C11×C22⋊C4C2×D412yes—
435C42×C11—21no—
436C42×C11—21no—
437C42×C11—21no—
438C42×C11—21no—
439C42×C11—21no—
440C42×C11—21no—
441C42×C11—22no—
442C42×C11—22no—
443C42×C11—22no—
444C42×C11—22no—
445C42×C11C2×D411yescharacteristic
446C42×C11C2×D411yescharacteristic
447C42×C11C2412yes—
448C42×C11C2412yes—
449C42×C11C2411yescharacteristic
450C42×C11C2411yescharacteristic
451#3510C2×C1111yescharacteristic, complemented
452#3503C2×C1111yescharacteristic, complemented
453#3377C2×C1112yescomplemented
454#3376C2×C1112yescomplemented
455#3375C2×C1112yescomplemented
456#3373C2×C1112yescomplemented
457#3371C2×C1112yescomplemented
458#3370C2×C1112yescomplemented
459#3369C2×C1112yescomplemented
460#3367C2×C1112yescomplemented
461#3137C2×C1111yescharacteristic, complemented
462#3136C2×C1111yescharacteristic, complemented
463C2×#489C2×C1111yescharacteristic, complemented
464#3082C2×C1111yescharacteristic, complemented
465#3081C2×C1111yescharacteristic, complemented
466#3079C2×C1111yescharacteristic, complemented
467#3046C2×C1111yescharacteristic, complemented
468#3045C2×C1111yescharacteristic
469#3040C2×C1111yescharacteristic, complemented
470#2961C2×C1111yescharacteristic, complemented
471#2947C2×C1111yescharacteristic, complemented
472#2946C2×C1111yescharacteristic, complemented
473#2943C2×C1111yescharacteristic, complemented
474C23×C11—21no—
475C23×C11—22no—
476C23×C11—21no—
477C23×C11—42no—
478C23×C11—81no—
479C23×C11—81no—
480C23×C11C22×D411yescharacteristic
481Q8×C11—21no—
482Q8×C11—22no—
483Q8×C11—21no—
484Q8×C11—22no—
485Q8×C11—21no—
486Q8×C11—42no—
487Q8×C11—42no—
488Q8×C11—44no—
489Q8×C11—42no—
490Q8×C11—82no—
491Q8×C11—82no—
492Q8×C11—82no—
493Q8×C11C2×#4112yes—
494D4×C11—24no—
495D4×C11—22no—
496D4×C11—21no—
497D4×C11—21no—
498D4×C11—22no—
499D4×C11—21no—
500D4×C11—42no—
501D4×C11—42no—
502D4×C11—82no—
503D4×C11—82no—
504D4×C11C2×#4112yes—
505C2×C4×C11—21no—
506C2×C4×C11—24no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—22no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—42no—
518C2×C4×C11—42no—
519C2×C4×C11—42no—
520C2×C4×C11—42no—
521C2×C4×C11—81no—
522C2×C4×C11—82no—
523C2×C4×C11—81no—
524C2×C4×C11—82no—
525C2×C4×C11—82no—
526C2×C4×C11—82no—
527C2×C4×C11—81no—
528C2×C4×C11—81no—
529C2×C4×C11C22×D412yes—
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C22×D411yescharacteristic
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C22×D411yescharacteristic
534C2×C4×C11C22×D412yes—
535C2×C4×C11C22×D412yes—
536C2×C4×C11C22×D412yes—
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C2×#4112yes—
539C2×C4×C112−1+412yes—
540C2×C4×C11C2511yescharacteristic
541C8×C11—21no—
542C8×C11—21no—
543C8×C11—22no—
544C8×C11—22no—
545C8×C11—21no—
546C8×C11—21no—
547C2×#137C22×C1111yescharacteristic
548C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
549C2×#135C22×C1111yescharacteristic
550#559C22×C1112yes—
551#559C22×C1112yes—
552Q82C22×C1112yescomplemented
553#557C22×C1112yescomplemented
554#556C22×C1112yes—
555#556C22×C1112yes—
556#554—22no—
557#554C22×C1112yescomplemented
558#551—22no—
559#551—22no—
560D4×Q8—22no—
561D4×Q8C22×C1112yescomplemented
562#544—21no—
563#544—21no—
564#544C22×C1111yescharacteristic
565#544C22×C1111yescharacteristic
566#542—21no—
567#542—21no—
568#536C22×C1111yescharacteristic
569#535C22×C1111yescharacteristic
570#533—21no—
571#533C22×C1111yescharacteristic
572C2×C4⋊Q8—21no—
573C2×C4⋊Q8C22×C1111yescharacteristic
574#529—21no—
575#529—21no—
576C2×#124C22×C1111yescharacteristic
577#520C22×C1111yescharacteristic
578#520C22×C1111yescharacteristic
579#519C22×C1111yescharacteristic
580#518C22×C1111yescharacteristic
581C4×#41C22×C1111yescharacteristic
582C4×#41C22×C1111yescharacteristic
583#491C22×C1112yescomplemented
584#490C22×C1112yes—
585#489C22×C1112yes—
586#489C22×C1112yes—
587#489C22×C1112yes—
588#489C22×C1112yes—
589#489C22×C1112yes—
590#489C22×C1112yescomplemented
591#488C22×C1112yes—
592#488C22×C1112yescomplemented
593#487C22×C1112yescomplemented
594#486C22×C1112yes—
595#479C22×C1112yescomplemented
596#479C22×C1112yescomplemented
597#478C22×C1112yes—
598#478C22×C1112yes—
599#477C22×C1112yescomplemented
600#477C22×C1112yescomplemented
601#476C22×C1112yes—
602#476C22×C1112yescomplemented
603#475C22×C1112yescomplemented
604#475C22×C1112yescomplemented
605#474C22×C1112yes—
606#474C22×C1112yescomplemented
607#464C22×C1112yes—
608#464C22×C1112yes—
609#464C22×C1112yes—
610#464C22×C1112yescomplemented
611#463C22×C1112yes—
612#463C22×C1112yes—
613#463C22×C1112yes—
614#463C22×C1112yescomplemented
615#462C22×C1112yescomplemented
616#461C22×C1112yescomplemented
617#460C22×C1112yes—
618#459C22×C1112yes—
619#446C22×C1112yescomplemented
620#446C22×C1112yescomplemented
621#446C22×C1112yescomplemented
622#446C22×C1112yescomplemented
623#442C22×C1112yes—
624#442C22×C1111yescharacteristic, complemented
625#442C22×C1111yescharacteristic, complemented
626#441C22×C1111yescharacteristic, complemented
627#441C22×C1112yescomplemented
628#441C22×C1111yescharacteristic, complemented
629#440C22×C1112yes—
630#440C22×C1111yescharacteristic, complemented
631#440C22×C1112yescomplemented
632#440C22×C1111yescharacteristic, complemented
633#440C22×C1111yescharacteristic, complemented
634#440C22×C1111yescharacteristic, complemented
635C4×Q16C22×C1112yescomplemented
636C4×SD16C22×C1112yes—
637C4×SD16C22×C1112yescomplemented
638C4×D8C22×C1112yes—
639#428C22×C1111yescharacteristic
640#428C22×C1111yescharacteristic
641#427C22×C1111yescharacteristic
642#424C22×C1111yescharacteristic
643#424C22×C1111yescharacteristic
644#423C22×C1111yescharacteristic
645#419C22×C1111yescharacteristic
646#418C22×C1111yescharacteristic
647#417C22×C1111yescharacteristic
648#417C22×C1111yescharacteristic
649#416C22×C1111yescharacteristic
650#416C22×C1111yescharacteristic
651C2×#103C22×C1111yescharacteristic
652C2×#103C22×C1111yescharacteristic
653C2×#102C22×C1111yescharacteristic
654C2×#102C22×C1111yescharacteristic
655#405C22×C1111yescharacteristic
656#405C22×C1111yescharacteristic
657C2×#97C22×C1111yescharacteristic
658C22×C11—21no—
659C22×C11—21no—
660C22×C11—22no—
661C22×C11—41no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—42no—
665C22×C11—41no—
666C22×C11—42no—
667C22×C11—41no—
668C22×C11—42no—
669C22×C11—162no—
670C22×C11#54812yes—
671C22×C11C23×D411yescharacteristic
672C4×C11—21no—
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—21no—
677C4×C11—21no—
678C4×C11—22no—
679C4×C11—22no—
680C4×C11—22no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—42no—
684C4×C11—42no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11—41no—
688C4×C11—42no—
689C4×C11#54812yes—
690C4×C11C22×#4111yescharacteristic
691C4×C11C2×2−1+411yescharacteristic
692C2×#41C23×C1111yescharacteristic
693C2×#41C23×C1111yescharacteristic
694C22×Q8—22no—
695C22×Q8—21no—
696C22×Q8C23×C1111yescharacteristic
697C22×D4C23×C1111yescharacteristic
698#137—24no—
699AGL(1,ℤ/8)—24no—
700#135—24no—
701C2×Q16C23×C1111yescharacteristic
702C2×Q16C23×C1112yes—
703C2×SD16C23×C1111yescharacteristic
704C2×SD16C23×C1111yescharacteristic
705C2×SD16C23×C1112yes—
706C2×SD16C23×C1112yes—
707C2×D8C23×C1111yescharacteristic
708C2×D8C23×C1112yes—
709C2×M16C23×C1111yescharacteristic
710C2×M16C23×C1111yescharacteristic
711C22×C8C23×C1111yescharacteristic
712C22×C8C23×C1111yescharacteristic
713C4⋊Q8—22no—
714C4⋊Q8—21no—
715C4⋊Q8—21no—
716C4⋊Q8—22no—
717C4⋊Q8—22no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—21no—
721C4⋊Q8D4×C1111yescharacteristic
722C4⋊Q8D4×C1111yescharacteristic
723C4⋊Q8C23×C1112yes—
724C4⋊Q8C23×C1112yes—
725C4⋊Q8C23×C1112yes—
726C4⋊Q8C23×C1112yes—
727C4⋊Q8C23×C1112yes—
728#127C23×C1112yes—
729#126—22no—
730#126—22no—
731#126—22no—
732#126—22no—
733#125—21no—
734#125—21no—
735#125—22no—
736#125—22no—
737#125D4×C1111yescharacteristic
738#125D4×C1111yescharacteristic
739#125C23×C1112yes—
740#125C23×C1112yes—
741#124—22no—
742#124—22no—
743#124—21no—
744#124—21no—
745#124C23×C1112yes—
746#124C23×C1112yes—
747#124C23×C1112yes—
748#124C23×C1112yes—
749#123—22no—
750#123—22no—
751#123—22no—
752#123—22no—
753#123—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—22no—
760C22⋊Q8—22no—
761C22⋊Q8—22no—
762C22⋊Q8—22no—
763C22⋊Q8—22no—
764C22⋊Q8—22no—
765C22⋊Q8—22no—
766C22⋊Q8D4×C1112yes—
767C22⋊Q8D4×C1112yes—
768#121—21no—
769#121—21no—
770#120—22no—
771C4×Q8—22no—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8—22no—
775C4×Q8C23×C1111yescharacteristic
776C4×Q8C23×C1111yescharacteristic
777C4×Q8C23×C1111yescharacteristic
778C4×Q8C23×C1111yescharacteristic
779C4×Q8C23×C1112yes—
780C4×Q8C23×C1112yes—
781C4×Q8C23×C1112yes—
782C4×Q8C23×C1112yes—
783C4×Q8C23×C1112yes—
784C4×Q8C23×C1112yes—
785C4×D4—21no—
786C4×D4—21no—
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4—21no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—22no—
795C4×D4C23×C1111yescharacteristic
796C4×D4C23×C1111yescharacteristic
797C4×D4C23×C1111yescharacteristic
798C4×D4C23×C1111yescharacteristic
799C4×D4C23×C1112yes—
800C4×D4C23×C1112yes—
801C4×D4C23×C1112yes—
802C4×D4C23×C1112yes—
803#117—21no—
804#117—21no—
805#117—22no—
806#117—22no—
807#117—22no—
808#117—21no—
809#117—21no—
810#117C23×C1111yescharacteristic
811#117C23×C1111yescharacteristic
812#117C23×C1111yescharacteristic
813#117C23×C1111yescharacteristic
814C2×C4⋊C4—21no—
815C2×C4⋊C4—21no—
816C2×C4⋊C4—21no—
817C2×C4⋊C4—22no—
818C2×C4⋊C4C23×C1111yescharacteristic
819C2×C4⋊C4C23×C1111yescharacteristic
820C2×C22⋊C4—21no—
821C2×C22⋊C4—21no—
822C2×C22⋊C4—22no—
823C2×C42—21no—
824C2×C42—21no—
825C2×C42C23×C1111yescharacteristic
826#107C23×C1111yescharacteristic
827#107C23×C1111yescharacteristic
828#107C23×C1112yes—
829#107C23×C1112yes—
830#106C23×C1111yescharacteristic
831#106C23×C1111yescharacteristic
832#106C23×C1112yes—
833#106C23×C1112yes—
834C4⋊C8C23×C1112yes—
835C4⋊C8C23×C1112yes—
836C4⋊C8C23×C1112yes—
837C4⋊C8C23×C1112yes—
838C4⋊C8C23×C1112yes—
839C4⋊C8C23×C1112yes—
840#103C23×C1112yes—
841#103C23×C1112yes—
842#103C23×C1112yes—
843#103C23×C1112yes—
844#103C23×C1111yescharacteristic
845#103C23×C1111yescharacteristic
846#103C23×C1111yescharacteristic
847#103C23×C1111yescharacteristic
848#103C23×C1112yes—
849#103C23×C1112yes—
850#103C23×C1112yes—
851#103C23×C1112yes—
852#102C23×C1112yes—
853#102C23×C1112yes—
854#102C23×C1112yes—
855#102C23×C1112yes—
856#102C23×C1111yescharacteristic
857#102C23×C1111yescharacteristic
858#102C23×C1111yescharacteristic
859#102C23×C1111yescharacteristic
860#102C23×C1112yes—
861#102C23×C1112yes—
862#102C23×C1112yes—
863#102C23×C1112yes—
864#97C23×C1111yescharacteristic
865#97C23×C1111yescharacteristic
866#97C23×C1111yescharacteristic
867#97C23×C1111yescharacteristic
868#97C23×C1112yes—
869#97C23×C1112yes—
870C4×C8C23×C1112yes—
871C4×C8C23×C1112yes—
872C2×C11—22no—
873C2×C11—42no—
874C2×C11—81no—
875C2×C11—82no—
876C2×C11C2×#54811yescharacteristic
877C2×C11#358511yescharacteristic
878C2×C11#358611yescharacteristic
879C24—21no—
880#41—22no—
881#41—22no—
882#41—22no—
883#41C11×#4114yes—
884C2×Q8—21no—
885C2×Q8—22no—
886C2×Q8—22no—
887C2×Q8—22no—
888C2×Q8—22no—
889C2×Q8—22no—
890C2×Q8—22no—
891C2×Q8—82no—
892C2×Q8—84no—
893C2×Q8C2×D4×C1112yes—
894C2×Q8C2×D4×C1112yes—
895C2×Q8C24×C1112yes—
896C2×Q8C24×C1111yescharacteristic
897C2×Q8C24×C1111yescharacteristic
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4C24×C1112yes—
906C2×D4C24×C1111yescharacteristic
907C2×D4C24×C1111yescharacteristic
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4C2×D4×C1111yescharacteristic
922C22×C4C2×D4×C1111yescharacteristic
923C22×C4C24×C1111yescharacteristic
924Q16—22no—
925Q16—24no—
926SD16—22no—
927SD16—24no—
928SD16—22no—
929SD16—24no—
930D8—22no—
931D8—24no—
932M16—22no—
933M16—22no—
934C2×C8—22no—
935C2×C8—22no—
936C2×C8C24×C1111yescharacteristic
937C2×C8C24×C1111yescharacteristic
938C2×C8C24×C1112yes—
939C2×C8C24×C1112yes—
940C2×C8C24×C1111yescharacteristic
941C2×C8C24×C1111yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4C2×D4×C1111yescharacteristic
963C4⋊C4C2×D4×C1111yescharacteristic
964C4⋊C4C2×D4×C1112yes—
965C4⋊C4C2×D4×C1111yescharacteristic
966C4⋊C4C2×D4×C1111yescharacteristic
967C4⋊C4C2×D4×C1112yes—
968C4⋊C4C2×D4×C1112yes—
969C4⋊C4C2×D4×C1112yes—
970C4⋊C4C2×D4×C1112yes—
971C4⋊C4C2×D4×C1112yes—
972C4⋊C4C24×C1112yes—
973C4⋊C4C24×C1112yes—
974C4⋊C4C24×C1111yescharacteristic
975C4⋊C4C24×C1111yescharacteristic
976C4⋊C4C24×C1111yescharacteristic
977C4⋊C4C24×C1111yescharacteristic
978C22⋊C4—21no—
979C22⋊C4—21no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—21no—
987C22⋊C4—21no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—21no—
991C22⋊C4—21no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4C2×D4×C1112yes—
997C22⋊C4C2×D4×C1112yes—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—22no—
1008C42C2×D4×C1111yescharacteristic
1009C42C2×D4×C1111yescharacteristic
1010C42C24×C1112yes—
1011C42C24×C1112yes—
1012C42C24×C1111yescharacteristic
1013C42C24×C1111yescharacteristic
1014C11#6133611yescharacteristic, direct product factor, Sylow
1015C23—21no—
1016C23—22no—
1017C23—21no—
1018C23—42no—
1019C23—81no—
1020C23—81no—
1021C23C22×D4×C1111yescharacteristic
1022Q8—21no—
1023Q8—22no—
1024Q8—21no—
1025Q8—22no—
1026Q8—21no—
1027Q8—42no—
1028Q8—42no—
1029Q8—44no—
1030Q8—42no—
1031Q8—82no—
1032Q8—82no—
1033Q8—82no—
1034Q8C2×C11×#4112yes—
1035D4—24no—
1036D4—22no—
1037D4—21no—
1038D4—21no—
1039D4—22no—
1040D4—21no—
1041D4—42no—
1042D4—42no—
1043D4—82no—
1044D4—82no—
1045D4C2×C11×#4112yes—
1046C2×C4—21no—
1047C2×C4—24no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—81no—
1063C2×C4—82no—
1064C2×C4—81no—
1065C2×C4—82no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—81no—
1069C2×C4—81no—
1070C2×C4C22×D4×C1112yes—
1071C2×C4C22×D4×C1111yescharacteristic
1072C2×C4C22×D4×C1111yescharacteristic
1073C2×C4C22×D4×C1111yescharacteristic
1074C2×C4C22×D4×C1111yescharacteristic
1075C2×C4C22×D4×C1112yes—
1076C2×C4C22×D4×C1112yes—
1077C2×C4C22×D4×C1112yes—
1078C2×C4C22×D4×C1111yescharacteristic
1079C2×C4C2×C11×#4112yes—
1080C2×C4C11×2−1+412yes—
1081C2×C4C25×C1111yescharacteristic
1082C8—21no—
1083C8—21no—
1084C8—22no—
1085C8—22no—
1086C8—21no—
1087C8—21no—
1088C22—21no—
1089C22—21no—
1090C22—22no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—42no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—42no—
1099C22—162no—
1100C22C11×#54812yes—
1101C22C23×D4×C1111yescharacteristic
1102C4—22no—
1103C4—21no—
1104C4—21no—
1105C4—22no—
1106C4—22no—
1107C4—21no—
1108C4—21no—
1109C4—22no—
1110C4—22no—
1111C4—41no—
1112C4—42no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4—42no—
1117C4—41no—
1118C4—41no—
1119C4C11×#54812yes—
1120C4C22×C11×#4111yescharacteristic
1121C4C2×C11×2−1+411yescharacteristic
1122C2—22no—
1123C2—42no—
1124C2—82no—
1125C2—81no—
1126C2C2×C11×#54811yescharacteristic
1127C2C11×#358511yescharacteristic
1128C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3045C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3510C2semidirect
2. C11×#3503C2semidirect
3. C11×#3377C2semidirect
4. C11×#3376C2semidirect
5. C11×#3375C2semidirect
6. C11×#3373C2semidirect
7. C11×#3371C2semidirect
8. C11×#3370C2semidirect
9. C11×#3369C2semidirect
10. C11×#3367C2semidirect
11. C11×#3137C2semidirect
12. C11×#3136C2semidirect
13. C2×C11×#489C2semidirect
14. C11×#3082C2semidirect
15. C11×#3081C2semidirect
16. C11×#3079C2semidirect
17. C11×#3046C2semidirect
19. C11×#3040C2semidirect
20. C11×#2961C2semidirect
21. C11×#2947C2semidirect
22. C11×#2946C2semidirect
23. C11×#2943C2semidirect
29. Q82×C11C22semidirect
30. C11×#557C22semidirect
34. C11×#554C22semidirect
38. D4×Q8×C11C22semidirect
60. C11×#491C22semidirect
67. C11×#489C22semidirect
69. C11×#488C22semidirect
70. C11×#487C22semidirect
72. C11×#479C22semidirect
73. C11×#479C22semidirect
76. C11×#477C22semidirect
77. C11×#477C22semidirect
79. C11×#476C22semidirect
80. C11×#475C22semidirect
81. C11×#475C22semidirect
83. C11×#474C22semidirect
87. C11×#464C22semidirect
91. C11×#463C22semidirect
92. C11×#462C22semidirect
93. C11×#461C22semidirect
96. C11×#446C22semidirect
97. C11×#446C22semidirect
98. C11×#446C22semidirect
99. C11×#446C22semidirect
101. C11×#442C22semidirect
102. C11×#442C22semidirect
103. C11×#441C22semidirect
104. C11×#441C22semidirect
105. C11×#441C22semidirect
107. C11×#440C22semidirect
108. C11×#440C22semidirect
109. C11×#440C22semidirect
110. C11×#440C22semidirect
111. C11×#440C22semidirect
112. C4×C11×Q16C22semidirect
114. C4×C11×SD16C22semidirect
315. #61336C11direct (N × H)
451. #3510C2×C11semidirect
452. #3503C2×C11semidirect
453. #3377C2×C11semidirect
454. #3376C2×C11semidirect
455. #3375C2×C11semidirect
456. #3373C2×C11semidirect
457. #3371C2×C11semidirect
458. #3370C2×C11semidirect
459. #3369C2×C11semidirect
460. #3367C2×C11semidirect
461. #3137C2×C11semidirect
462. #3136C2×C11semidirect
463. C2×#489C2×C11semidirect
464. #3082C2×C11semidirect
465. #3081C2×C11semidirect
466. #3079C2×C11semidirect
467. #3046C2×C11semidirect
469. #3040C2×C11semidirect
470. #2961C2×C11semidirect
471. #2947C2×C11semidirect
472. #2946C2×C11semidirect
473. #2943C2×C11semidirect
552. Q82C22×C11semidirect
553. #557C22×C11semidirect
557. #554C22×C11semidirect
561. D4×Q8C22×C11semidirect
583. #491C22×C11semidirect
590. #489C22×C11semidirect
592. #488C22×C11semidirect
593. #487C22×C11semidirect
595. #479C22×C11semidirect
596. #479C22×C11semidirect
599. #477C22×C11semidirect
600. #477C22×C11semidirect
602. #476C22×C11semidirect
603. #475C22×C11semidirect
604. #475C22×C11semidirect
606. #474C22×C11semidirect
610. #464C22×C11semidirect
614. #463C22×C11semidirect
615. #462C22×C11semidirect
616. #461C22×C11semidirect
619. #446C22×C11semidirect
620. #446C22×C11semidirect
621. #446C22×C11semidirect
622. #446C22×C11semidirect
624. #442C22×C11semidirect
625. #442C22×C11semidirect
626. #441C22×C11semidirect
627. #441C22×C11semidirect
628. #441C22×C11semidirect
630. #440C22×C11semidirect
631. #440C22×C11semidirect
632. #440C22×C11semidirect
633. #440C22×C11semidirect
634. #440C22×C11semidirect
635. C4×Q16C22×C11semidirect
637. C4×SD16C22×C11semidirect
1014. C11#61336direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35102
C11×#35032
C11×#33772
C11×#33762
C11×#33752
C11×#33732
C11×#33712
C11×#33702
C11×#33692
C11×#33672
C11×#31372
C11×#31362
C2×C11×#4892
C11×#30822
C11×#30812
C11×#30792
C11×#30462
C11×#30452
C11×#30402
C11×#29612
C11×#29472
C11×#29462
C11×#29432
#6133611