Finite Group Databasebeta

← C11×#61973 #14639166

Subgroups — C11×#61973 #14639166

Order 2816.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3514C211yesmaximal, characteristic, complemented
2C11×#3482C211yesmaximal, characteristic, complemented
3C11×#3400C211yesmaximal, characteristic, complemented
4C11×#3398C211yesmaximal, characteristic, complemented
5C11×#3373C211yesmaximal, characteristic, complemented
6C11×#3367C211yesmaximal, characteristic, complemented
7C11×#3328C211yesmaximal, characteristic, complemented
8C11×#3324C211yesmaximal, characteristic, complemented
9C11×#3313C212yesmaximal, complemented
10C11×#3311C212yesmaximal, complemented
11C11×#3276C211yesmaximal, characteristic, complemented
12C11×#3272C211yesmaximal, characteristic, complemented
13C11×#3269C212yesmaximal, complemented
14C11×#3267C212yesmaximal, complemented
15C11×#3252C212yesmaximal, complemented
16C11×#3248C211yesmaximal, characteristic, complemented
17C11×#3215C212yesmaximal, complemented
18C11×#3210C211yesmaximal, characteristic, complemented
19C11×#3111C212yesmaximal, complemented
20C11×#3102C211yesmaximal, characteristic, complemented
21C11×#3040C212yesmaximal, complemented
22C11×#3035C211yesmaximal, characteristic, complemented
23C11×#2989C211yesmaximal, characteristic, complemented
24C2×C11×#137C2212yescomplemented
25C2×C11×AGL(1,ℤ/8)C2212yes—
26C2×C11×#135C2212yescomplemented
27C11×#559C2211yescharacteristic
28C11×#557C2211yescharacteristic, complemented
29C11×#556C2211yescharacteristic
30C11×#556C2211yescharacteristic
31C11×#556C2212yescomplemented
32C11×#555—21no—
33C11×#552—21no—
34C11×#552—22no—
35C11×#551—22no—
36D4×Q8×C11C2211yescharacteristic
37D4×Q8×C11C2211yescharacteristic, complemented
38C11×#548—21no—
39C11×#548C2212yes—
40C11×#547C2211yescharacteristic
41C11×#547C2212yescomplemented
42C11×#546—21no—
43C11×#546C2212yes—
44D42×C11C2211yescharacteristic
45C11×#542—21no—
46C11×#538—22no—
47C11×#533C2211yescharacteristic, complemented
48C11×#533C2212yescomplemented
49C11×#532C2211yescharacteristic
50C11×#529—21no—
51C11×#529—22no—
52C11×#529C2211yescharacteristic
53C11×#529C2212yes—
54C2×C11×#124C2212yes—
55C11×#518—21no—
56C4×C11×#41C2211yescharacteristic
57C4×C11×#41C2211yescharacteristic, complemented
58C4×C11×#41C2212yescomplemented
59C2×C4×Q8×C11—21no—
60C11×#497C2212yes—
61C11×#497C2212yescomplemented
62C11×#494C2211yescharacteristic, complemented
63C11×#492C2211yescharacteristic
64C11×#489C2212yes—
65C11×#489C2212yescomplemented
66C11×#487C2211yescharacteristic, complemented
67C11×#486C2211yescharacteristic
68C11×#485C2212yescomplemented
69C11×#485C2211yescharacteristic, complemented
70C11×#482C2211yescharacteristic
71C11×#482C2212yes—
72C11×#479C2212yescomplemented
73C11×#479C2211yescharacteristic, complemented
74C11×#478C2211yescharacteristic, complemented
75C11×#477C2212yescomplemented
76C11×#476C2212yescomplemented
77C11×#475C2211yescharacteristic, complemented
78C11×#474C2211yescharacteristic
79C11×#470C2212yescomplemented
80C11×#470C2212yescomplemented
81C11×#468C2212yes—
82C11×#468C2212yes—
83C11×#467C2212yescomplemented
84C11×#465C2212yes—
85C11×#464C2211yescharacteristic
86C11×#464C2212yes—
87C11×#464C2212yes—
88C11×#464C2212yescomplemented
89C11×#464C2212yescomplemented
90C11×#464C2212yescomplemented
91C11×#464C2212yescomplemented
92C11×#463C2212yes—
93C11×#463C2211yescharacteristic
94C11×#463C2212yescomplemented
95C11×#463C2212yescomplemented
96C11×#462C2211yescharacteristic, complemented
97C11×#462C2212yescomplemented
98C11×#462C2211yescharacteristic, complemented
99C11×#461C2211yescharacteristic
100C11×#461C2212yescomplemented
101C11×#461C2211yescharacteristic, complemented
102C11×#460C2211yescharacteristic
103C11×#459C2211yescharacteristic
104C11×#452C2212yescomplemented
105C11×#452C2212yescomplemented
106C11×#452C2212yescomplemented
107C11×#452C2211yescharacteristic, complemented
108C11×#451C2212yescomplemented
109C11×#451C2212yescomplemented
110C11×#450C2212yes—
111C11×#450C2212yes—
112C11×#449C2211yescharacteristic
113C11×#449C2212yes—
114C11×#446C2211yescharacteristic, complemented
115C11×#446C2211yescharacteristic, complemented
116C11×#442C2212yescomplemented
117C11×#441C2212yescomplemented
118C11×#440C2212yescomplemented
119C11×#440C2212yescomplemented
120C4×C11×Q16C2211yescharacteristic, complemented
121C4×C11×SD16C2211yescharacteristic
122C4×C11×SD16C2211yescharacteristic, complemented
123C4×C11×D8C2211yescharacteristic
124C11×#436C2211yescharacteristic
125C11×#436C2211yescharacteristic
126C11×#435C2212yescomplemented
127C11×#435C2212yescomplemented
128C11×#432C2212yescomplemented
129C11×#431C2211yescharacteristic, complemented
130C11×#423C2212yescomplemented
131C2×C11×C4⋊C8C2211yescharacteristic, complemented
132C11×#419C2212yescomplemented
133C11×#418C2212yes—
134C11×#416C2212yescomplemented
135C2×C11×#41D411yescharacteristic
136C2×C11×#41C2312yes—
137C2×C11×#41C2311yescharacteristic
138C2×C11×#41C2312yes—
139C22×Q8×C11—21no—
140C22×Q8×C11C2312yes—
141C22×D4×C11—21no—
142C22×D4×C11C2312yes—
143C11×#137—44no—
144C11×AGL(1,ℤ/8)—44no—
145C11×#135—44no—
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2312yes—
149C2×C11×Q16C2311yescharacteristic
150C2×C11×Q16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2311yescharacteristic
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2311yescharacteristic
156C2×C11×SD16C2312yes—
157C2×C11×SD16C2312yes—
158C2×C11×D8C2312yes—
159C2×C11×D8C2311yescharacteristic
160C2×C11×M16C2312yes—
161C2×C11×M16C2312yes—
162C22×C8×C11C2312yes—
163C11×C4⋊Q8—21no—
164C11×C4⋊Q8C2311yescharacteristic
165C11×C4⋊Q8C2311yescharacteristic
166C11×C4⋊Q8C2312yes—
167C11×C4⋊Q8C2312yes—
168C11×C4⋊Q8C2311yescharacteristic
169C11×#127C2311yescharacteristic
170C11×#126—22no—
171C11×#126—22no—
172C11×#126—22no—
173C11×#126—22no—
174C11×#126—22no—
175C11×#126—21no—
176C11×#125—21no—
177C11×#125—22no—
178C11×#125—22no—
179C11×#125—21no—
180C11×#125C2311yescharacteristic
181C11×#124—21no—
182C11×#124—21no—
183C11×#124—22no—
184C11×#124—22no—
185C11×#124—22no—
186C11×#124—22no—
187C11×#124C2312yes—
188C11×#124C2312yes—
189C11×#124C2311yescharacteristic
190C11×#124C2312yes—
191C11×#123—21no—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×#123—22no—
198C11×C22⋊Q8—21no—
199C11×C22⋊Q8—21no—
200C11×C22⋊Q8—22no—
201C11×C22⋊Q8—21no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8C2312yes—
206C11×C22⋊Q8C2311yescharacteristic
207C11×C22⋊Q8C2312yes—
208C11×C22⋊Q8C2312yes—
209C11×C22⋊Q8C2312yes—
210C11×#121—21no—
211C11×#121—22no—
212C11×#121—22no—
213C11×#121—21no—
214C11×#121—21no—
215C11×#121—21no—
216C11×#121—22no—
217C11×#121C2312yes—
218C11×#121C2311yescharacteristic
219C11×#120—22no—
220C11×#120—22no—
221C4×Q8×C11—21no—
222C4×Q8×C11—21no—
223C4×Q8×C11—22no—
224C4×Q8×C11—21no—
225C4×Q8×C11—22no—
226C4×Q8×C11D411yescharacteristic
227C4×Q8×C11C2311yescharacteristic
228C4×Q8×C11C2312yes—
229C4×Q8×C11C2311yescharacteristic
230C4×Q8×C11C2312yes—
231C4×Q8×C11C2312yes—
232C4×Q8×C11C2311yescharacteristic
233C4×Q8×C11C2311yescharacteristic
234C4×D4×C11—21no—
235C4×D4×C11—22no—
236C4×D4×C11—21no—
237C4×D4×C11—21no—
238C4×D4×C11—22no—
239C4×D4×C11—22no—
240C4×D4×C11—21no—
241C4×D4×C11—21no—
242C4×D4×C11—22no—
243C4×D4×C11—21no—
244C4×D4×C11—21no—
245C4×D4×C11D411yescharacteristic
246C4×D4×C11D412yes—
247C4×D4×C11C2311yescharacteristic
248C4×D4×C11C2311yescharacteristic
249C4×D4×C11C2312yes—
250C4×D4×C11C2311yescharacteristic
251C4×D4×C11C2312yes—
252C4×D4×C11C2311yescharacteristic
253C4×D4×C11C2312yes—
254C11×#117—22no—
255C11×#117—21no—
256C11×#117—21no—
257C11×#117—22no—
258C11×#117—21no—
259C11×#117—21no—
260C11×#117—22no—
261C11×#117D412yes—
262C11×#117D411yescharacteristic
263C11×#117C2311yescharacteristic
264C11×#117C2312yes—
265C2×C11×C4⋊C4—21no—
266C2×C11×C4⋊C4—22no—
267C2×C11×C22⋊C4—22no—
268C2×C11×C22⋊C4—22no—
269C2×C11×C22⋊C4—22no—
270C2×C42×C11—21no—
271C2×C42×C11—22no—
272C2×C42×C11C2312yes—
273C2×C42×C11C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#107C2311yescharacteristic
276C11×#107C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2311yescharacteristic
279C11×#106C2312yes—
280C11×C4⋊C8C2312yes—
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2311yescharacteristic
283C11×C4⋊C8C2311yescharacteristic
284C11×C4⋊C8C2312yes—
285C11×C4⋊C8C2312yes—
286C11×C4⋊C8C2311yescharacteristic
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2311yescharacteristic
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#103C2312yes—
297C11×#103C2312yes—
298C11×#102C2311yescharacteristic
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2311yescharacteristic
304C11×#102C2312yes—
305C11×#102C2311yescharacteristic
306C11×#102C2311yescharacteristic
307C11×C22⋊C8C2311yescharacteristic
308C11×C22⋊C8C2311yescharacteristic
309C11×C22⋊C8C2312yes—
310C11×C22⋊C8C2312yes—
311C11×#97C2312yes—
312C11×#97C2312yes—
313C4×C8×C11C2311yescharacteristic
314C4×C8×C11C2311yescharacteristic
315#61973C1111yesmaximal, characteristic, direct product factor, Sylow
316C24×C11—22no—
317C11×#41—22no—
318C11×#41—24no—
319C11×#41—42no—
320C11×#41—42no—
321C11×#41—41no—
322C11×#41—42no—
323C11×#41—42no—
324C2×Q8×C11—22no—
325C2×Q8×C11—21no—
326C2×Q8×C11—22no—
327C2×Q8×C11—42no—
328C2×Q8×C11—42no—
329C2×Q8×C11—44no—
330C2×Q8×C11C2×D411yescharacteristic
331C2×Q8×C11C2411yescharacteristic
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2412yes—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11—21no—
338C2×D4×C11—21no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—21no—
342C2×D4×C11—22no—
343C2×D4×C11—42no—
344C2×D4×C11—42no—
345C2×D4×C11—44no—
346C2×D4×C11C2×D411yescharacteristic
347C2×D4×C11C2×D412yes—
348C2×D4×C11C2411yescharacteristic
349C2×D4×C11C2412yes—
350C2×D4×C11C2411yescharacteristic
351C22×C4×C11—22no—
352C22×C4×C11—21no—
353C22×C4×C11—21no—
354C22×C4×C11—22no—
355C22×C4×C11—22no—
356C22×C4×C11—21no—
357C22×C4×C11—21no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11C2×D411yescharacteristic
361C22×C4×C11C2×D412yes—
362C22×C4×C11C2×D412yes—
363C22×C4×C11C2×D411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2412yes—
366C11×Q16—41no—
367C11×Q16—42no—
368C11×Q16—42no—
369C11×Q16—42no—
370C11×Q16—42no—
371C11×SD16—24no—
372C11×SD16—22no—
373C11×SD16—41no—
374C11×SD16—42no—
375C11×SD16—42no—
376C11×SD16—42no—
377C11×SD16—42no—
378C11×D8—24no—
379C11×D8—22no—
380C11×M16—42no—
381C11×M16—42no—
382C2×C8×C11—42no—
383C2×C8×C11C2411yescharacteristic
384C2×C8×C11C2411yescharacteristic
385C2×C8×C11C2411yescharacteristic
386C2×C8×C11C2411yescharacteristic
387C2×C8×C11C2412yes—
388C2×C8×C11C2412yes—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—21no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4C2×D411yescharacteristic
411C11×C4⋊C4C2×D412yes—
412C11×C4⋊C4C2×D411yescharacteristic
413C11×C4⋊C4C2×D412yes—
414C11×C4⋊C4C2411yescharacteristic
415C11×C4⋊C4C2411yescharacteristic
416C11×C4⋊C4C2412yes—
417C11×C4⋊C4C2411yescharacteristic
418C11×C4⋊C4C2411yescharacteristic
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—21no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—21no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4C2×D412yes—
442C11×C22⋊C4C2×D412yes—
443C11×C22⋊C4C2×D412yes—
444C42×C11—21no—
445C42×C11—22no—
446C42×C11—21no—
447C42×C11—22no—
448C42×C11—22no—
449C42×C11—21no—
450C42×C11—22no—
451C42×C11—21no—
452C42×C11C2×D411yescharacteristic
453C42×C11C2×D412yes—
454C42×C11C2×D412yes—
455C42×C11C2×D411yescharacteristic
456C42×C11C2411yescharacteristic
457C42×C11C2412yes—
458C42×C11C2411yescharacteristic
459#3514C2×C1111yescharacteristic, complemented
460#3482C2×C1111yescharacteristic, complemented
461#3400C2×C1111yescharacteristic, complemented
462#3398C2×C1111yescharacteristic, complemented
463#3373C2×C1111yescharacteristic, complemented
464#3367C2×C1111yescharacteristic, complemented
465#3328C2×C1111yescharacteristic, complemented
466#3324C2×C1111yescharacteristic, complemented
467#3313C2×C1112yescomplemented
468#3311C2×C1112yescomplemented
469#3276C2×C1111yescharacteristic, complemented
470#3272C2×C1111yescharacteristic, complemented
471#3269C2×C1112yescomplemented
472#3267C2×C1112yescomplemented
473#3252C2×C1112yescomplemented
474#3248C2×C1111yescharacteristic, complemented
475#3215C2×C1112yescomplemented
476#3210C2×C1111yescharacteristic, complemented
477#3111C2×C1112yescomplemented
478#3102C2×C1111yescharacteristic, complemented
479#3040C2×C1112yescomplemented
480#3035C2×C1111yescharacteristic, complemented
481#2989C2×C1111yescharacteristic, complemented
482C23×C11—21no—
483C23×C11—21no—
484C23×C11—22no—
485C23×C11—44no—
486C23×C11—82no—
487C23×C11—82no—
488C23×C11C22×D412yes—
489C23×C11C22×D411yescharacteristic
490Q8×C11—22no—
491Q8×C11—21no—
492Q8×C11—22no—
493Q8×C11—21no—
494Q8×C11—22no—
495Q8×C11—21no—
496Q8×C11—22no—
497Q8×C11—21no—
498Q8×C11—22no—
499Q8×C11—44no—
500Q8×C11—42no—
501Q8×C11—82no—
502D4×C11—22no—
503D4×C11—21no—
504D4×C11—22no—
505D4×C11—21no—
506D4×C11—21no—
507D4×C11—22no—
508D4×C11—42no—
509D4×C11—44no—
510D4×C11—42no—
511D4×C11—44no—
512D4×C11—42no—
513D4×C11—81no—
514D4×C11—82no—
515D4×C11—81no—
516D4×C11—82no—
517D4×C11H(5,𝔽2)12yes—
518C2×C4×C11—22no—
519C2×C4×C11—21no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—22no—
526C2×C4×C11—21no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—42no—
533C2×C4×C11—41no—
534C2×C4×C11—42no—
535C2×C4×C11—42no—
536C2×C4×C11—44no—
537C2×C4×C11—42no—
538C2×C4×C11—44no—
539C2×C4×C11—42no—
540C2×C4×C11—42no—
541C2×C4×C11—82no—
542C2×C4×C11—82no—
543C2×C4×C11—82no—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D412yes—
548C2×C4×C11C22×D412yes—
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C2511yescharacteristic
553C8×C11—22no—
554C8×C11—22no—
555C8×C11—21no—
556C8×C11—21no—
557C8×C11—21no—
558C8×C11—21no—
559C2×#137C22×C1112yescomplemented
560C2×AGL(1,ℤ/8)C22×C1112yes—
561C2×#135C22×C1112yescomplemented
562#559C22×C1111yescharacteristic
563#557C22×C1111yescharacteristic, complemented
564#556C22×C1111yescharacteristic
565#556C22×C1111yescharacteristic
566#556C22×C1112yescomplemented
567#555—21no—
568#552—21no—
569#552—22no—
570#551—22no—
571D4×Q8C22×C1111yescharacteristic
572D4×Q8C22×C1111yescharacteristic, complemented
573#548—21no—
574#548C22×C1112yes—
575#547C22×C1111yescharacteristic
576#547C22×C1112yescomplemented
577#546—21no—
578#546C22×C1112yes—
579D42C22×C1111yescharacteristic
580#542—21no—
581#538—22no—
582#533C22×C1111yescharacteristic, complemented
583#533C22×C1112yescomplemented
584#532C22×C1111yescharacteristic
585#529—21no—
586#529—22no—
587#529C22×C1111yescharacteristic
588#529C22×C1112yes—
589C2×#124C22×C1112yes—
590#518—21no—
591C4×#41C22×C1111yescharacteristic
592C4×#41C22×C1111yescharacteristic, complemented
593C4×#41C22×C1112yescomplemented
594C2×C4×Q8—21no—
595#497C22×C1112yes—
596#497C22×C1112yescomplemented
597#494C22×C1111yescharacteristic, complemented
598#492C22×C1111yescharacteristic
599#489C22×C1112yes—
600#489C22×C1112yescomplemented
601#487C22×C1111yescharacteristic, complemented
602#486C22×C1111yescharacteristic
603#485C22×C1112yescomplemented
604#485C22×C1111yescharacteristic, complemented
605#482C22×C1111yescharacteristic
606#482C22×C1112yes—
607#479C22×C1111yescharacteristic, complemented
608#479C22×C1112yescomplemented
609#478C22×C1111yescharacteristic, complemented
610#477C22×C1112yescomplemented
611#476C22×C1112yescomplemented
612#475C22×C1111yescharacteristic, complemented
613#474C22×C1111yescharacteristic
614#470C22×C1112yescomplemented
615#470C22×C1112yescomplemented
616#468C22×C1112yes—
617#468C22×C1112yes—
618#467C22×C1112yescomplemented
619#465C22×C1112yes—
620#464C22×C1111yescharacteristic
621#464C22×C1112yes—
622#464C22×C1112yes—
623#464C22×C1112yescomplemented
624#464C22×C1112yescomplemented
625#464C22×C1112yescomplemented
626#464C22×C1112yescomplemented
627#463C22×C1111yescharacteristic
628#463C22×C1112yes—
629#463C22×C1112yescomplemented
630#463C22×C1112yescomplemented
631#462C22×C1111yescharacteristic, complemented
632#462C22×C1112yescomplemented
633#462C22×C1111yescharacteristic, complemented
634#461C22×C1111yescharacteristic
635#461C22×C1111yescharacteristic, complemented
636#461C22×C1112yescomplemented
637#460C22×C1111yescharacteristic
638#459C22×C1111yescharacteristic
639#452C22×C1111yescharacteristic, complemented
640#452C22×C1112yescomplemented
641#452C22×C1112yescomplemented
642#452C22×C1112yescomplemented
643#451C22×C1112yescomplemented
644#451C22×C1112yescomplemented
645#450C22×C1112yes—
646#450C22×C1112yes—
647#449C22×C1111yescharacteristic
648#449C22×C1112yes—
649#446C22×C1111yescharacteristic, complemented
650#446C22×C1111yescharacteristic, complemented
651#442C22×C1112yescomplemented
652#441C22×C1112yescomplemented
653#440C22×C1112yescomplemented
654#440C22×C1112yescomplemented
655C4×Q16C22×C1111yescharacteristic, complemented
656C4×SD16C22×C1111yescharacteristic
657C4×SD16C22×C1111yescharacteristic, complemented
658C4×D8C22×C1111yescharacteristic
659#436C22×C1111yescharacteristic
660#436C22×C1111yescharacteristic
661#435C22×C1112yescomplemented
662#435C22×C1112yescomplemented
663#432C22×C1112yescomplemented
664#431C22×C1111yescharacteristic, complemented
665#423C22×C1112yescomplemented
666C2×C4⋊C8C22×C1111yescharacteristic, complemented
667#419C22×C1112yescomplemented
668#418C22×C1112yes—
669#416C22×C1112yescomplemented
670C22×C11—21no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—21no—
674C22×C11—22no—
675C22×C11—21no—
676C22×C11—22no—
677C22×C11—41no—
678C22×C11—41no—
679C22×C11—42no—
680C22×C11—41no—
681C22×C11—42no—
682C22×C11—41no—
683C22×C11—41no—
684C22×C11—42no—
685C22×C11—164no—
686C22×C11C23×D411yescharacteristic
687C4×C11—21no—
688C4×C11—22no—
689C4×C11—21no—
690C4×C11—21no—
691C4×C11—22no—
692C4×C11—21no—
693C4×C11—22no—
694C4×C11—41no—
695C4×C11—41no—
696C4×C11—41no—
697C4×C11—42no—
698C4×C11—42no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11—41no—
703C4×C11#57512yes—
704C4×C11C2×H(5,𝔽2)11yescharacteristic
705C4×C11#58511yescharacteristic
706C2×#41D4×C1111yescharacteristic
707C2×#41C23×C1112yes—
708C2×#41C23×C1111yescharacteristic
709C2×#41C23×C1112yes—
710C22×Q8—21no—
711C22×Q8C23×C1112yes—
712C22×D4—21no—
713C22×D4C23×C1112yes—
714#137—44no—
715AGL(1,ℤ/8)—44no—
716#135—44no—
717C2×Q16C23×C1112yes—
718C2×Q16C23×C1112yes—
719C2×Q16C23×C1112yes—
720C2×Q16C23×C1111yescharacteristic
721C2×Q16C23×C1112yes—
722C2×SD16C23×C1112yes—
723C2×SD16C23×C1111yescharacteristic
724C2×SD16C23×C1112yes—
725C2×SD16C23×C1112yes—
726C2×SD16C23×C1112yes—
727C2×SD16C23×C1111yescharacteristic
728C2×SD16C23×C1112yes—
729C2×D8C23×C1112yes—
730C2×D8C23×C1111yescharacteristic
731C2×M16C23×C1112yes—
732C2×M16C23×C1112yes—
733C22×C8C23×C1112yes—
734C4⋊Q8—21no—
735C4⋊Q8C23×C1111yescharacteristic
736C4⋊Q8C23×C1111yescharacteristic
737C4⋊Q8C23×C1112yes—
738C4⋊Q8C23×C1111yescharacteristic
739C4⋊Q8C23×C1112yes—
740#127C23×C1111yescharacteristic
741#126—22no—
742#126—22no—
743#126—22no—
744#126—22no—
745#126—22no—
746#126—21no—
747#125—21no—
748#125—22no—
749#125—22no—
750#125—21no—
751#125C23×C1111yescharacteristic
752#124—21no—
753#124—21no—
754#124—22no—
755#124—22no—
756#124—22no—
757#124—22no—
758#124C23×C1111yescharacteristic
759#124C23×C1112yes—
760#124C23×C1112yes—
761#124C23×C1112yes—
762#123—21no—
763#123—22no—
764#123—22no—
765#123—22no—
766#123—22no—
767#123—22no—
768#123—22no—
769C22⋊Q8—21no—
770C22⋊Q8—21no—
771C22⋊Q8—22no—
772C22⋊Q8—21no—
773C22⋊Q8—22no—
774C22⋊Q8—22no—
775C22⋊Q8—22no—
776C22⋊Q8C23×C1112yes—
777C22⋊Q8C23×C1111yescharacteristic
778C22⋊Q8C23×C1112yes—
779C22⋊Q8C23×C1112yes—
780C22⋊Q8C23×C1112yes—
781#121—21no—
782#121—22no—
783#121—22no—
784#121—21no—
785#121—21no—
786#121—21no—
787#121—22no—
788#121C23×C1112yes—
789#121C23×C1111yescharacteristic
790#120—22no—
791#120—22no—
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8—22no—
795C4×Q8—21no—
796C4×Q8—22no—
797C4×Q8D4×C1111yescharacteristic
798C4×Q8C23×C1111yescharacteristic
799C4×Q8C23×C1112yes—
800C4×Q8C23×C1111yescharacteristic
801C4×Q8C23×C1112yes—
802C4×Q8C23×C1112yes—
803C4×Q8C23×C1111yescharacteristic
804C4×Q8C23×C1111yescharacteristic
805C4×D4—21no—
806C4×D4—22no—
807C4×D4—21no—
808C4×D4—21no—
809C4×D4—22no—
810C4×D4—22no—
811C4×D4—21no—
812C4×D4—21no—
813C4×D4—22no—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4D4×C1111yescharacteristic
817C4×D4D4×C1112yes—
818C4×D4C23×C1111yescharacteristic
819C4×D4C23×C1111yescharacteristic
820C4×D4C23×C1112yes—
821C4×D4C23×C1111yescharacteristic
822C4×D4C23×C1112yes—
823C4×D4C23×C1111yescharacteristic
824C4×D4C23×C1112yes—
825#117—22no—
826#117—21no—
827#117—21no—
828#117—22no—
829#117—21no—
830#117—21no—
831#117—22no—
832#117D4×C1112yes—
833#117D4×C1111yescharacteristic
834#117C23×C1112yes—
835#117C23×C1111yescharacteristic
836C2×C4⋊C4—21no—
837C2×C4⋊C4—22no—
838C2×C22⋊C4—22no—
839C2×C22⋊C4—22no—
840C2×C22⋊C4—22no—
841C2×C42—21no—
842C2×C42—22no—
843C2×C42C23×C1112yes—
844C2×C42C23×C1111yescharacteristic
845#107C23×C1111yescharacteristic
846#107C23×C1111yescharacteristic
847#107C23×C1112yes—
848#106C23×C1111yescharacteristic
849#106C23×C1111yescharacteristic
850#106C23×C1112yes—
851C4⋊C8C23×C1112yes—
852C4⋊C8C23×C1111yescharacteristic
853C4⋊C8C23×C1111yescharacteristic
854C4⋊C8C23×C1111yescharacteristic
855C4⋊C8C23×C1112yes—
856C4⋊C8C23×C1112yes—
857C4⋊C8C23×C1111yescharacteristic
858#103C23×C1112yes—
859#103C23×C1112yes—
860#103C23×C1111yescharacteristic
861#103C23×C1112yes—
862#103C23×C1112yes—
863#103C23×C1111yescharacteristic
864#103C23×C1111yescharacteristic
865#103C23×C1111yescharacteristic
866#103C23×C1112yes—
867#103C23×C1112yes—
868#103C23×C1112yes—
869#102C23×C1112yes—
870#102C23×C1112yes—
871#102C23×C1111yescharacteristic
872#102C23×C1112yes—
873#102C23×C1112yes—
874#102C23×C1111yescharacteristic
875#102C23×C1111yescharacteristic
876#102C23×C1111yescharacteristic
877#102C23×C1112yes—
878C22⋊C8C23×C1111yescharacteristic
879C22⋊C8C23×C1111yescharacteristic
880C22⋊C8C23×C1112yes—
881C22⋊C8C23×C1112yes—
882#97C23×C1112yes—
883#97C23×C1112yes—
884C4×C8C23×C1111yescharacteristic
885C4×C8C23×C1111yescharacteristic
886C2×C11—41no—
887C2×C11—42no—
888C2×C11—42no—
889C2×C11—82no—
890C2×C11—81no—
891C2×C11#348811yescharacteristic
892C2×C11C2×#57511yescharacteristic
893C2×C11#358611yescharacteristic
894C24—22no—
895#41—22no—
896#41—24no—
897#41—42no—
898#41—42no—
899#41—41no—
900#41—42no—
901#41—42no—
902C2×Q8—22no—
903C2×Q8—21no—
904C2×Q8—22no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—44no—
908C2×Q8C2×D4×C1111yescharacteristic
909C2×Q8C24×C1111yescharacteristic
910C2×Q8C24×C1112yes—
911C2×Q8C24×C1111yescharacteristic
912C2×Q8C24×C1112yes—
913C2×D4—22no—
914C2×D4—22no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—22no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—22no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4C2×D4×C1111yescharacteristic
925C2×D4C2×D4×C1112yes—
926C2×D4C24×C1111yescharacteristic
927C2×D4C24×C1112yes—
928C2×D4C24×C1111yescharacteristic
929C22×C4—22no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4C2×D4×C1111yescharacteristic
939C22×C4C2×D4×C1112yes—
940C22×C4C2×D4×C1112yes—
941C22×C4C2×D4×C1111yescharacteristic
942C22×C4C24×C1111yescharacteristic
943C22×C4C24×C1112yes—
944Q16—42no—
945Q16—42no—
946Q16—42no—
947Q16—41no—
948Q16—42no—
949SD16—24no—
950SD16—22no—
951SD16—42no—
952SD16—42no—
953SD16—42no—
954SD16—42no—
955SD16—41no—
956D8—24no—
957D8—22no—
958M16—42no—
959M16—42no—
960C2×C8—42no—
961C2×C8C24×C1111yescharacteristic
962C2×C8C24×C1111yescharacteristic
963C2×C8C24×C1111yescharacteristic
964C2×C8C24×C1111yescharacteristic
965C2×C8C24×C1112yes—
966C2×C8C24×C1112yes—
967C4⋊C4—22no—
968C4⋊C4—21no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—22no—
977C4⋊C4—21no—
978C4⋊C4—22no—
979C4⋊C4—21no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—21no—
983C4⋊C4—22no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—22no—
987C4⋊C4—21no—
988C4⋊C4C2×D4×C1111yescharacteristic
989C4⋊C4C2×D4×C1112yes—
990C4⋊C4C2×D4×C1111yescharacteristic
991C4⋊C4C2×D4×C1112yes—
992C4⋊C4C24×C1111yescharacteristic
993C4⋊C4C24×C1111yescharacteristic
994C4⋊C4C24×C1112yes—
995C4⋊C4C24×C1111yescharacteristic
996C4⋊C4C24×C1111yescharacteristic
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—21no—
1003C22⋊C4—21no—
1004C22⋊C4—22no—
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—21no—
1014C22⋊C4—22no—
1015C22⋊C4—21no—
1016C22⋊C4—22no—
1017C22⋊C4—21no—
1018C22⋊C4—22no—
1019C22⋊C4C2×D4×C1112yes—
1020C22⋊C4C2×D4×C1112yes—
1021C22⋊C4C2×D4×C1112yes—
1022C42—21no—
1023C42—22no—
1024C42—21no—
1025C42—22no—
1026C42—22no—
1027C42—21no—
1028C42—22no—
1029C42—21no—
1030C42C2×D4×C1111yescharacteristic
1031C42C2×D4×C1112yes—
1032C42C2×D4×C1112yes—
1033C42C2×D4×C1111yescharacteristic
1034C42C24×C1111yescharacteristic
1035C42C24×C1112yes—
1036C42C24×C1111yescharacteristic
1037C11#6197311yescharacteristic, direct product factor, Sylow
1038C23—21no—
1039C23—21no—
1040C23—22no—
1041C23—44no—
1042C23—82no—
1043C23—82no—
1044C23C22×D4×C1112yes—
1045C23C22×D4×C1111yescharacteristic
1046Q8—22no—
1047Q8—21no—
1048Q8—22no—
1049Q8—21no—
1050Q8—22no—
1051Q8—22no—
1052Q8—21no—
1053Q8—21no—
1054Q8—22no—
1055Q8—44no—
1056Q8—42no—
1057Q8—82no—
1058D4—22no—
1059D4—21no—
1060D4—22no—
1061D4—21no—
1062D4—21no—
1063D4—22no—
1064D4—42no—
1065D4—44no—
1066D4—42no—
1067D4—44no—
1068D4—42no—
1069D4—81no—
1070D4—82no—
1071D4—81no—
1072D4—82no—
1073D4C11×H(5,𝔽2)12yes—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—42no—
1089C2×C4—41no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—44no—
1093C2×C4—42no—
1094C2×C4—44no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—82no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4C22×D4×C1111yescharacteristic
1101C2×C4C22×D4×C1111yescharacteristic
1102C2×C4C22×D4×C1112yes—
1103C2×C4C22×D4×C1112yes—
1104C2×C4C22×D4×C1112yes—
1105C2×C4C22×D4×C1111yescharacteristic
1106C2×C4C22×D4×C1111yescharacteristic
1107C2×C4C22×D4×C1111yescharacteristic
1108C2×C4C25×C1111yescharacteristic
1109C8—22no—
1110C8—22no—
1111C8—21no—
1112C8—21no—
1113C8—21no—
1114C8—21no—
1115C22—22no—
1116C22—21no—
1117C22—22no—
1118C22—21no—
1119C22—22no—
1120C22—21no—
1121C22—22no—
1122C22—41no—
1123C22—41no—
1124C22—42no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—42no—
1129C22—41no—
1130C22—164no—
1131C22C23×D4×C1111yescharacteristic
1132C4—21no—
1133C4—22no—
1134C4—21no—
1135C4—22no—
1136C4—21no—
1137C4—22no—
1138C4—21no—
1139C4—41no—
1140C4—42no—
1141C4—42no—
1142C4—41no—
1143C4—41no—
1144C4—42no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4C11×#57512yes—
1149C4C2×C11×H(5,𝔽2)11yescharacteristic
1150C4C11×#58511yescharacteristic
1151C2—42no—
1152C2—41no—
1153C2—42no—
1154C2—81no—
1155C2—82no—
1156C2C11×#348811yescharacteristic
1157C2C2×C11×#57511yescharacteristic
1158C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3514C2semidirect
2. C11×#3482C2semidirect
3. C11×#3400C2semidirect
4. C11×#3398C2semidirect
5. C11×#3373C2semidirect
6. C11×#3367C2semidirect
7. C11×#3328C2semidirect
8. C11×#3324C2semidirect
9. C11×#3313C2semidirect
10. C11×#3311C2semidirect
11. C11×#3276C2semidirect
12. C11×#3272C2semidirect
13. C11×#3269C2semidirect
14. C11×#3267C2semidirect
15. C11×#3252C2semidirect
16. C11×#3248C2semidirect
17. C11×#3215C2semidirect
18. C11×#3210C2semidirect
19. C11×#3111C2semidirect
20. C11×#3102C2semidirect
21. C11×#3040C2semidirect
22. C11×#3035C2semidirect
23. C11×#2989C2semidirect
24. C2×C11×#137C22semidirect
26. C2×C11×#135C22semidirect
28. C11×#557C22semidirect
31. C11×#556C22semidirect
37. D4×Q8×C11C22semidirect
41. C11×#547C22semidirect
47. C11×#533C22semidirect
48. C11×#533C22semidirect
57. C4×C11×#41C22semidirect
58. C4×C11×#41C22semidirect
61. C11×#497C22semidirect
62. C11×#494C22semidirect
65. C11×#489C22semidirect
66. C11×#487C22semidirect
68. C11×#485C22semidirect
69. C11×#485C22semidirect
72. C11×#479C22semidirect
73. C11×#479C22semidirect
74. C11×#478C22semidirect
75. C11×#477C22semidirect
76. C11×#476C22semidirect
77. C11×#475C22semidirect
79. C11×#470C22semidirect
80. C11×#470C22semidirect
83. C11×#467C22semidirect
88. C11×#464C22semidirect
89. C11×#464C22semidirect
90. C11×#464C22semidirect
91. C11×#464C22semidirect
94. C11×#463C22semidirect
95. C11×#463C22semidirect
96. C11×#462C22semidirect
97. C11×#462C22semidirect
98. C11×#462C22semidirect
100. C11×#461C22semidirect
101. C11×#461C22semidirect
104. C11×#452C22semidirect
105. C11×#452C22semidirect
106. C11×#452C22semidirect
107. C11×#452C22semidirect
108. C11×#451C22semidirect
109. C11×#451C22semidirect
114. C11×#446C22semidirect
115. C11×#446C22semidirect
116. C11×#442C22semidirect
117. C11×#441C22semidirect
118. C11×#440C22semidirect
119. C11×#440C22semidirect
120. C4×C11×Q16C22semidirect
122. C4×C11×SD16C22semidirect
126. C11×#435C22semidirect
127. C11×#435C22semidirect
128. C11×#432C22semidirect
129. C11×#431C22semidirect
130. C11×#423C22semidirect
131. C2×C11×C4⋊C8C22semidirect
132. C11×#419C22semidirect
134. C11×#416C22semidirect
315. #61973C11direct (N × H)
459. #3514C2×C11semidirect
460. #3482C2×C11semidirect
461. #3400C2×C11semidirect
462. #3398C2×C11semidirect
463. #3373C2×C11semidirect
464. #3367C2×C11semidirect
465. #3328C2×C11semidirect
466. #3324C2×C11semidirect
467. #3313C2×C11semidirect
468. #3311C2×C11semidirect
469. #3276C2×C11semidirect
470. #3272C2×C11semidirect
471. #3269C2×C11semidirect
472. #3267C2×C11semidirect
473. #3252C2×C11semidirect
474. #3248C2×C11semidirect
475. #3215C2×C11semidirect
476. #3210C2×C11semidirect
477. #3111C2×C11semidirect
478. #3102C2×C11semidirect
479. #3040C2×C11semidirect
480. #3035C2×C11semidirect
481. #2989C2×C11semidirect
559. C2×#137C22×C11semidirect
561. C2×#135C22×C11semidirect
563. #557C22×C11semidirect
566. #556C22×C11semidirect
572. D4×Q8C22×C11semidirect
576. #547C22×C11semidirect
582. #533C22×C11semidirect
583. #533C22×C11semidirect
592. C4×#41C22×C11semidirect
593. C4×#41C22×C11semidirect
596. #497C22×C11semidirect
597. #494C22×C11semidirect
600. #489C22×C11semidirect
601. #487C22×C11semidirect
603. #485C22×C11semidirect
604. #485C22×C11semidirect
607. #479C22×C11semidirect
608. #479C22×C11semidirect
609. #478C22×C11semidirect
610. #477C22×C11semidirect
611. #476C22×C11semidirect
612. #475C22×C11semidirect
614. #470C22×C11semidirect
615. #470C22×C11semidirect
618. #467C22×C11semidirect
623. #464C22×C11semidirect
624. #464C22×C11semidirect
625. #464C22×C11semidirect
626. #464C22×C11semidirect
629. #463C22×C11semidirect
630. #463C22×C11semidirect
631. #462C22×C11semidirect
632. #462C22×C11semidirect
633. #462C22×C11semidirect
635. #461C22×C11semidirect
636. #461C22×C11semidirect
639. #452C22×C11semidirect
640. #452C22×C11semidirect
641. #452C22×C11semidirect
642. #452C22×C11semidirect
643. #451C22×C11semidirect
644. #451C22×C11semidirect
649. #446C22×C11semidirect
650. #446C22×C11semidirect
651. #442C22×C11semidirect
652. #441C22×C11semidirect
653. #440C22×C11semidirect
654. #440C22×C11semidirect
655. C4×Q16C22×C11semidirect
657. C4×SD16C22×C11semidirect
661. #435C22×C11semidirect
662. #435C22×C11semidirect
663. #432C22×C11semidirect
664. #431C22×C11semidirect
665. #423C22×C11semidirect
666. C2×C4⋊C8C22×C11semidirect
667. #419C22×C11semidirect
669. #416C22×C11semidirect
1037. C11#61973direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35142
C11×#34822
C11×#34002
C11×#33982
C11×#33732
C11×#33672
C11×#33282
C11×#33242
C11×#33132
C11×#33112
C11×#32762
C11×#32722
C11×#32692
C11×#32672
C11×#32522
C11×#32482
C11×#32152
C11×#32102
C11×#31112
C11×#31022
C11×#30402
C11×#30352
C11×#29892
#6197311