Finite Group Databasebeta

← C11×#61632 #14638825

Subgroups — C11×#61632 #14638825

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3536C211yesmaximal, characteristic, complemented
2C11×#3486C211yesmaximal, characteristic, complemented
3C11×#3316C212yesmaximal, complemented
4C11×#3308C212yesmaximal, complemented
5C11×#3299C212yesmaximal, complemented
6C11×#3298C212yesmaximal, complemented
7C11×#3285C212yesmaximal, complemented
8C11×#3282C212yesmaximal, complemented
9C11×#3270C212yesmaximal, complemented
10C11×#3266C212yesmaximal, complemented
11C11×#3225C212yesmaximal, complemented
12C11×#3201C212yesmaximal, complemented
13C11×#3190C211yesmaximal, characteristic, complemented
14C11×#3188C211yesmaximal, characteristic, complemented
15C11×#3121C212yesmaximal, complemented
16C11×#3013C212yesmaximal, complemented
17C2×C11×#451C211yesmaximal, characteristic, complemented
18C2×C11×#448C211yesmaximal, characteristic, complemented
19C11×#2977C211yesmaximal, characteristic, complemented
20C2×C11×2−1+4C2211yescharacteristic, complemented
21C23×Q8×C11C2211yescharacteristic
22C2×C11×#137C2212yescomplemented
23C2×C11×#135C2212yescomplemented
24C22×C11×Q16C2212yescomplemented
25C22×C11×SD16C2212yes—
26C11×#562—22no—
27C11×#554C2212yes—
28D4×Q8×C11—21no—
29D4×Q8×C11—21no—
30D4×Q8×C11C2212yes—
31D4×Q8×C11C2212yescomplemented
32C11×#548—21no—
33C11×#548—21no—
34C11×#548C2212yes—
35C11×#548C2212yes—
36C11×#548C2212yescomplemented
37C11×#547C2212yes—
38C11×#546—22no—
39C11×#546C2212yes—
40C11×#543—21no—
41C11×#542C2212yes—
42C11×#539—21no—
43C11×#538—21no—
44C11×#537—21no—
45C11×#537C2212yes—
46C11×#536—22no—
47C11×#536C2211yescharacteristic, complemented
48C11×#536C2211yescharacteristic, complemented
49C11×#525—22no—
50C11×#525C2211yescharacteristic
51C11×#525C2211yescharacteristic
52C2×C11×C22⋊Q8C2211yescharacteristic
53C2×C11×#121C2211yescharacteristic
54C11×#519C2211yescharacteristic, complemented
55C11×#497C2212yescomplemented
56C11×#495C2212yescomplemented
57C11×#489C2212yescomplemented
58C11×#487C2212yescomplemented
59C11×#485C2212yescomplemented
60C11×#484C2211yescharacteristic
61C11×#484C2212yescomplemented
62C11×#483C2211yescharacteristic, complemented
63C11×#483C2212yescomplemented
64C11×#482C2212yes—
65C11×#481C2211yescharacteristic
66C11×#480C2211yescharacteristic, complemented
67C11×#477C2212yescomplemented
68C11×#475C2212yescomplemented
69C11×#470C2212yescomplemented
70C11×#468C2212yescomplemented
71C11×#467C2212yes—
72C11×#467C2212yescomplemented
73C11×#466C2212yes—
74C11×#465C2212yes—
75C11×#465C2212yes—
76C11×#465C2212yescomplemented
77C11×#464C2212yescomplemented
78C11×#464C2212yescomplemented
79C11×#464C2212yescomplemented
80C11×#463C2212yescomplemented
81C11×#462C2212yescomplemented
82C11×#461C2212yescomplemented
83C11×#452C2212yescomplemented
84C11×#452C2212yescomplemented
85C11×#452C2212yescomplemented
86C11×#452C2212yescomplemented
87C11×#451C2212yes—
88C11×#451C2212yes—
89C11×#451C2211yescharacteristic, complemented
90C11×#451C2212yescomplemented
91C11×#451C2212yescomplemented
92C11×#451C2212yescomplemented
93C11×#450C2211yescharacteristic
94C11×#449C2212yes—
95C11×#449C2212yescomplemented
96C11×#448C2212yes—
97C11×#448C2212yes—
98C11×#448C2212yes—
99C11×#448C2212yes—
100C11×#448C2211yescharacteristic, complemented
101C11×#448C2212yescomplemented
102C11×#447C2211yescharacteristic
103C11×#441C2212yescomplemented
104C11×#440C2212yescomplemented
105C4×C11×Q16C2212yescomplemented
106C4×C11×SD16C2212yescomplemented
107C11×#435C2212yes—
108C11×#435C2212yescomplemented
109C8×D4×C11C2212yes—
110C8×D4×C11C2212yescomplemented
111C11×#433C2212yescomplemented
112C11×#417C2212yescomplemented
113C2×C11×#103C2212yes—
114C2×C11×#103C2212yescomplemented
115C2×C11×#103C2212yescomplemented
116C11×#408C2212yescomplemented
117C2×C11×C22⋊C8C2211yescharacteristic
118C2×C11×C22⋊C8C2211yescharacteristic
119C11×2−1+4—44no—
120C2×C11×#41—22no—
121C2×C11×#41—21no—
122C2×C11×#41—22no—
123C2×C11×#41C2312yes—
124C2×C11×#41C2311yescharacteristic
125C2×C11×#41C2312yes—
126C2×C11×#41C2311yescharacteristic
127C22×Q8×C11—21no—
128C22×Q8×C11—21no—
129C22×Q8×C11—21no—
130C22×Q8×C11—21no—
131C22×Q8×C11—44no—
132C22×Q8×C11C2311yescharacteristic
133C22×Q8×C11C2312yes—
134C22×Q8×C11C2312yes—
135C22×Q8×C11C2312yes—
136C22×Q8×C11C2311yescharacteristic
137C22×Q8×C11C2311yescharacteristic
138C22×D4×C11—21no—
139C22×D4×C11C2311yescharacteristic
140C23×C4×C11—21no—
141C23×C4×C11C2311yescharacteristic
142C11×#137—44no—
143C11×#135—44no—
144C2×C11×Q16—44no—
145C2×C11×Q16C2312yes—
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2312yes—
149C2×C11×Q16C2312yes—
150C2×C11×SD16—44no—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2312yes—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2312yes—
157C2×C11×D8C2312yes—
158C2×C11×M16C2312yes—
159C22×C8×C11C2312yes—
160C22×C8×C11C2312yes—
161C22×C8×C11C2312yes—
162C11×C4⋊Q8—21no—
163C11×C4⋊Q8—22no—
164C11×C4⋊Q8—22no—
165C11×C4⋊Q8C2312yes—
166C11×C4⋊Q8C2312yes—
167C11×#126—22no—
168C11×#125—22no—
169C11×#124—21no—
170C11×#124—22no—
171C11×#124—22no—
172C11×#124—22no—
173C11×#124—22no—
174C11×#124C2312yes—
175C11×#124C2312yes—
176C11×#123—22no—
177C11×#123—21no—
178C11×#123—22no—
179C11×#123—22no—
180C11×#123—22no—
181C11×#123—22no—
182C11×#123—22no—
183C11×#123D412yes—
184C11×C22⋊Q8—22no—
185C11×C22⋊Q8—21no—
186C11×C22⋊Q8—21no—
187C11×C22⋊Q8—22no—
188C11×C22⋊Q8—22no—
189C11×C22⋊Q8—21no—
190C11×C22⋊Q8—21no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—22no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8—22no—
200C11×C22⋊Q8D411yescharacteristic
201C11×C22⋊Q8D411yescharacteristic
202C11×C22⋊Q8C2312yes—
203C11×C22⋊Q8C2312yes—
204C11×C22⋊Q8C2311yescharacteristic
205C11×C22⋊Q8C2311yescharacteristic
206C11×C22⋊Q8C2312yes—
207C11×C22⋊Q8C2312yes—
208C11×C22⋊Q8C2312yes—
209C11×#121—22no—
210C11×#121—22no—
211C11×#121—22no—
212C11×#121—22no—
213C11×#121—22no—
214C11×#121—22no—
215C11×#121—21no—
216C11×#121—21no—
217C11×#121—22no—
218C11×#121D411yescharacteristic
219C11×#121D411yescharacteristic
220C11×#121C2312yes—
221C11×#121C2312yes—
222C11×#121C2311yescharacteristic
223C11×#121C2311yescharacteristic
224C11×#121C2312yes—
225C11×#120—21no—
226C11×#120—22no—
227C11×#120D412yes—
228C4×Q8×C11—21no—
229C4×Q8×C11—21no—
230C4×Q8×C11C2312yes—
231C4×Q8×C11C2312yes—
232C4×Q8×C11C2312yes—
233C4×D4×C11—22no—
234C4×D4×C11—22no—
235C4×D4×C11—22no—
236C4×D4×C11—21no—
237C4×D4×C11—21no—
238C4×D4×C11—22no—
239C4×D4×C11—22no—
240C4×D4×C11—22no—
241C4×D4×C11C2312yes—
242C4×D4×C11C2312yes—
243C4×D4×C11C2312yes—
244C11×#117—22no—
245C11×#117C2311yescharacteristic
246C11×#117C2311yescharacteristic
247C2×C11×C4⋊C4—21no—
248C2×C11×C4⋊C4C2311yescharacteristic
249C2×C11×C4⋊C4C2311yescharacteristic
250C2×C11×C4⋊C4C2312yes—
251C2×C11×C22⋊C4—21no—
252C2×C11×C22⋊C4—21no—
253C2×C11×C22⋊C4—22no—
254C11×#107C2312yes—
255C11×#107C2312yes—
256C11×#106C2312yes—
257C11×#106C2312yes—
258C11×C4⋊C8C2312yes—
259C11×C4⋊C8C2312yes—
260C11×#103C2312yes—
261C11×#103C2312yes—
262C11×#103C2312yes—
263C11×#103C2312yes—
264C11×#103C2312yes—
265C11×#103C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#103C2312yes—
269C11×#103C2312yes—
270C11×#103C2312yes—
271C11×#103C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×C22⋊C8C2312yes—
277C11×C22⋊C8C2312yes—
278C11×C22⋊C8C2311yescharacteristic
279C11×C22⋊C8C2311yescharacteristic
280C11×C22⋊C8C2311yescharacteristic
281C11×C22⋊C8C2311yescharacteristic
282C11×C22⋊C8C2312yes—
283C11×C22⋊C8C2312yes—
284C11×#97C2312yes—
285C4×C8×C11C2312yes—
286#61632C1111yesmaximal, characteristic, direct product factor, Sylow
287C24×C11—21no—
288C24×C11C2×D411yescharacteristic
289C11×#41—24no—
290C11×#41—42no—
291C11×#41—42no—
292C11×#41—42no—
293C11×#41—48no—
294C11×#41—42no—
295C11×#41—42no—
296C11×#41—44no—
297C11×#41—84no—
298C2×Q8×C11—24no—
299C2×Q8×C11—21no—
300C2×Q8×C11—22no—
301C2×Q8×C11—22no—
302C2×Q8×C11—21no—
303C2×Q8×C11—22no—
304C2×Q8×C11—21no—
305C2×Q8×C11—22no—
306C2×Q8×C11—24no—
307C2×Q8×C11—24no—
308C2×Q8×C11—24no—
309C2×Q8×C11—42no—
310C2×Q8×C11—42no—
311C2×Q8×C11—42no—
312C2×Q8×C11—42no—
313C2×Q8×C11—44no—
314C2×Q8×C11—42no—
315C2×Q8×C11—44no—
316C2×Q8×C11—44no—
317C2×Q8×C11—44no—
318C2×Q8×C11C2×D411yescharacteristic
319C2×Q8×C11C2412yes—
320C2×Q8×C11C2411yescharacteristic
321C2×Q8×C11C2412yes—
322C2×Q8×C11C2412yes—
323C2×D4×C11—21no—
324C2×D4×C11—21no—
325C2×D4×C11—22no—
326C2×D4×C11—21no—
327C2×D4×C11—22no—
328C2×D4×C11—22no—
329C2×D4×C11—22no—
330C2×D4×C11—22no—
331C2×D4×C11—21no—
332C2×D4×C11—42no—
333C2×D4×C11—82no—
334C2×D4×C11C2×D412yes—
335C2×D4×C11C2×D412yes—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2×D411yescharacteristic
338C2×D4×C11C2411yescharacteristic
339C2×D4×C11C2412yes—
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11—21no—
348C22×C4×C11—22no—
349C22×C4×C11—22no—
350C22×C4×C11—21no—
351C22×C4×C11—22no—
352C22×C4×C11—22no—
353C22×C4×C11—42no—
354C22×C4×C11—44no—
355C22×C4×C11C2×D411yescharacteristic
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2412yes—
362C11×Q16—24no—
363C11×Q16—24no—
364C11×Q16—42no—
365C11×Q16—42no—
366C11×Q16—42no—
367C11×SD16—24no—
368C11×SD16—24no—
369C11×SD16—42no—
370C11×SD16—42no—
371C11×SD16—42no—
372C11×SD16—42no—
373C11×D8—42no—
374C11×M16—42no—
375C2×C8×C11—42no—
376C2×C8×C11—42no—
377C2×C8×C11—42no—
378C2×C8×C11C2412yes—
379C2×C8×C11C2412yes—
380C2×C8×C11C2412yes—
381C2×C8×C11C2412yes—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4C2×D411yescharacteristic
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2411yescharacteristic
403C11×C4⋊C4C2411yescharacteristic
404C11×C4⋊C4C2412yes—
405C11×C4⋊C4C2412yes—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—21no—
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—21no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4C2×D412yes—
425C11×C22⋊C4C2×D412yes—
426C11×C22⋊C4C2×D412yes—
427C11×C22⋊C4C2×D412yes—
428C11×C22⋊C4C2×D412yes—
429C42×C11—22no—
430C42×C11—22no—
431C42×C11—21no—
432C42×C11—22no—
433C42×C11C2412yes—
434#3536C2×C1111yescharacteristic, complemented
435#3486C2×C1111yescharacteristic, complemented
436#3316C2×C1112yescomplemented
437#3308C2×C1112yescomplemented
438#3299C2×C1112yescomplemented
439#3298C2×C1112yescomplemented
440#3285C2×C1112yescomplemented
441#3282C2×C1112yescomplemented
442#3270C2×C1112yescomplemented
443#3266C2×C1112yescomplemented
444#3225C2×C1112yescomplemented
445#3201C2×C1112yescomplemented
446#3190C2×C1111yescharacteristic, complemented
447#3188C2×C1111yescharacteristic, complemented
448#3121C2×C1112yescomplemented
449#3013C2×C1112yescomplemented
450C2×#451C2×C1111yescharacteristic, complemented
451C2×#448C2×C1111yescharacteristic, complemented
452#2977C2×C1111yescharacteristic, complemented
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11—41no—
458C23×C11—42no—
459C23×C11—81no—
460C23×C11—81no—
461C23×C11C22×D411yescharacteristic
462C23×C11C22×D412yes—
463C23×C11C22×D411yescharacteristic
464C23×C11C22×D411yescharacteristic
465Q8×C11—24no—
466Q8×C11—22no—
467Q8×C11—22no—
468Q8×C11—22no—
469Q8×C11—22no—
470Q8×C11—22no—
471Q8×C11—22no—
472Q8×C11—41no—
473Q8×C11—44no—
474Q8×C11—44no—
475Q8×C11—44no—
476Q8×C11—42no—
477Q8×C11—81no—
478Q8×C11—82no—
479Q8×C11H(5,𝔽2)14yes—
480D4×C11—24no—
481D4×C11—24no—
482D4×C11—22no—
483D4×C11—22no—
484D4×C11—22no—
485D4×C11—41no—
486D4×C11—42no—
487D4×C11—44no—
488D4×C11—42no—
489D4×C11—42no—
490D4×C11—44no—
491D4×C11—42no—
492D4×C11—81no—
493D4×C11—82no—
494D4×C11—82no—
495D4×C11—82no—
496C2×C4×C11—24no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—21no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—44no—
514C2×C4×C11—44no—
515C2×C4×C11—44no—
516C2×C4×C11—44no—
517C2×C4×C11—42no—
518C2×C4×C11—42no—
519C2×C4×C11—42no—
520C2×C4×C11—82no—
521C2×C4×C11—82no—
522C2×C4×C11—81no—
523C2×C4×C11—81no—
524C2×C4×C11—82no—
525C2×C4×C11C22×D412yes—
526C2×C4×C11C22×D412yes—
527C2×C4×C11C22×D411yescharacteristic
528C2×C4×C11C22×D411yescharacteristic
529C2×C4×C11C22×D412yes—
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C2511yescharacteristic
532C8×C11—22no—
533C8×C11—22no—
534C8×C11—22no—
535C8×C11—22no—
536C2×2−1+4C22×C1111yescharacteristic, complemented
537C23×Q8C22×C1111yescharacteristic
538C2×#137C22×C1112yescomplemented
539C2×#135C22×C1112yescomplemented
540C22×Q16C22×C1112yescomplemented
541C22×SD16C22×C1112yes—
542#562—22no—
543#554C22×C1112yes—
544D4×Q8—21no—
545D4×Q8—21no—
546D4×Q8C22×C1112yes—
547D4×Q8C22×C1112yescomplemented
548#548—21no—
549#548—21no—
550#548C22×C1112yes—
551#548C22×C1112yes—
552#548C22×C1112yescomplemented
553#547C22×C1112yes—
554#546—22no—
555#546C22×C1112yes—
556#543—21no—
557#542C22×C1112yes—
558#539—21no—
559#538—21no—
560#537—21no—
561#537C22×C1112yes—
562#536—22no—
563#536C22×C1111yescharacteristic, complemented
564#536C22×C1111yescharacteristic, complemented
565#525—22no—
566#525C22×C1111yescharacteristic
567#525C22×C1111yescharacteristic
568C2×C22⋊Q8C22×C1111yescharacteristic
569C2×#121C22×C1111yescharacteristic
570#519C22×C1111yescharacteristic, complemented
571#497C22×C1112yescomplemented
572#495C22×C1112yescomplemented
573#489C22×C1112yescomplemented
574#487C22×C1112yescomplemented
575#485C22×C1112yescomplemented
576#484C22×C1111yescharacteristic
577#484C22×C1112yescomplemented
578#483C22×C1111yescharacteristic, complemented
579#483C22×C1112yescomplemented
580#482C22×C1112yes—
581#481C22×C1111yescharacteristic
582#480C22×C1111yescharacteristic, complemented
583#477C22×C1112yescomplemented
584#475C22×C1112yescomplemented
585#470C22×C1112yescomplemented
586#468C22×C1112yescomplemented
587#467C22×C1112yes—
588#467C22×C1112yescomplemented
589#466C22×C1112yes—
590#465C22×C1112yes—
591#465C22×C1112yes—
592#465C22×C1112yescomplemented
593#464C22×C1112yescomplemented
594#464C22×C1112yescomplemented
595#464C22×C1112yescomplemented
596#463C22×C1112yescomplemented
597#462C22×C1112yescomplemented
598#461C22×C1112yescomplemented
599#452C22×C1112yescomplemented
600#452C22×C1112yescomplemented
601#452C22×C1112yescomplemented
602#452C22×C1112yescomplemented
603#451C22×C1112yes—
604#451C22×C1112yes—
605#451C22×C1112yescomplemented
606#451C22×C1111yescharacteristic, complemented
607#451C22×C1112yescomplemented
608#451C22×C1112yescomplemented
609#450C22×C1111yescharacteristic
610#449C22×C1112yes—
611#449C22×C1112yescomplemented
612#448C22×C1112yes—
613#448C22×C1112yes—
614#448C22×C1112yes—
615#448C22×C1112yes—
616#448C22×C1111yescharacteristic, complemented
617#448C22×C1112yescomplemented
618#447C22×C1111yescharacteristic
619#441C22×C1112yescomplemented
620#440C22×C1112yescomplemented
621C4×Q16C22×C1112yescomplemented
622C4×SD16C22×C1112yescomplemented
623#435C22×C1112yes—
624#435C22×C1112yescomplemented
625C8×D4C22×C1112yes—
626C8×D4C22×C1112yescomplemented
627#433C22×C1112yescomplemented
628#417C22×C1112yescomplemented
629C2×#103C22×C1112yes—
630C2×#103C22×C1112yescomplemented
631C2×#103C22×C1112yescomplemented
632#408C22×C1112yescomplemented
633C2×C22⋊C8C22×C1111yescharacteristic
634C2×C22⋊C8C22×C1111yescharacteristic
635C22×C11—21no—
636C22×C11—21no—
637C22×C11—21no—
638C22×C11—21no—
639C22×C11—21no—
640C22×C11—22no—
641C22×C11—22no—
642C22×C11—21no—
643C22×C11—22no—
644C22×C11—21no—
645C22×C11—44no—
646C22×C11—41no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—41no—
650C22×C11—41no—
651C22×C11—42no—
652C22×C11—162no—
653C22×C11#57712yes—
654C22×C11#57812yes—
655C22×C11C23×D411yescharacteristic
656C4×C11—24no—
657C4×C11—21no—
658C4×C11—22no—
659C4×C11—21no—
660C4×C11—21no—
661C4×C11—22no—
662C4×C11—22no—
663C4×C11—41no—
664C4×C11—42no—
665C4×C11—42no—
666C4×C11—42no—
667C4×C11—42no—
668C4×C11—41no—
669C4×C11—41no—
670C4×C11C2×H(5,𝔽2)12yes—
6712−1+4—44no—
672C2×#41—22no—
673C2×#41—21no—
674C2×#41—22no—
675C2×#41C23×C1112yes—
676C2×#41C23×C1111yescharacteristic
677C2×#41C23×C1112yes—
678C2×#41C23×C1111yescharacteristic
679C22×Q8—21no—
680C22×Q8—21no—
681C22×Q8—21no—
682C22×Q8—21no—
683C22×Q8—44no—
684C22×Q8C23×C1111yescharacteristic
685C22×Q8C23×C1112yes—
686C22×Q8C23×C1112yes—
687C22×Q8C23×C1112yes—
688C22×Q8C23×C1111yescharacteristic
689C22×Q8C23×C1111yescharacteristic
690C22×D4—21no—
691C22×D4C23×C1111yescharacteristic
692C23×C4—21no—
693C23×C4C23×C1111yescharacteristic
694#137—44no—
695#135—44no—
696C2×Q16—44no—
697C2×Q16C23×C1112yes—
698C2×Q16C23×C1112yes—
699C2×Q16C23×C1112yes—
700C2×Q16C23×C1112yes—
701C2×Q16C23×C1112yes—
702C2×SD16—44no—
703C2×SD16C23×C1112yes—
704C2×SD16C23×C1112yes—
705C2×SD16C23×C1112yes—
706C2×SD16C23×C1112yes—
707C2×SD16C23×C1112yes—
708C2×SD16C23×C1112yes—
709C2×D8C23×C1112yes—
710C2×M16C23×C1112yes—
711C22×C8C23×C1112yes—
712C22×C8C23×C1112yes—
713C22×C8C23×C1112yes—
714C4⋊Q8—21no—
715C4⋊Q8—22no—
716C4⋊Q8—22no—
717C4⋊Q8C23×C1112yes—
718C4⋊Q8C23×C1112yes—
719#126—22no—
720#125—22no—
721#124—21no—
722#124—22no—
723#124—22no—
724#124—22no—
725#124—22no—
726#124C23×C1112yes—
727#124C23×C1112yes—
728#123—22no—
729#123—21no—
730#123—22no—
731#123—22no—
732#123—22no—
733#123—22no—
734#123—22no—
735#123D4×C1112yes—
736C22⋊Q8—22no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—22no—
740C22⋊Q8—22no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—22no—
744C22⋊Q8—22no—
745C22⋊Q8—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—22no—
750C22⋊Q8—22no—
751C22⋊Q8—22no—
752C22⋊Q8D4×C1111yescharacteristic
753C22⋊Q8D4×C1111yescharacteristic
754C22⋊Q8C23×C1112yes—
755C22⋊Q8C23×C1112yes—
756C22⋊Q8C23×C1111yescharacteristic
757C22⋊Q8C23×C1111yescharacteristic
758C22⋊Q8C23×C1112yes—
759C22⋊Q8C23×C1112yes—
760C22⋊Q8C23×C1112yes—
761#121—22no—
762#121—22no—
763#121—22no—
764#121—22no—
765#121—22no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121—22no—
770#121D4×C1111yescharacteristic
771#121D4×C1111yescharacteristic
772#121C23×C1112yes—
773#121C23×C1112yes—
774#121C23×C1111yescharacteristic
775#121C23×C1111yescharacteristic
776#121C23×C1112yes—
777#120—21no—
778#120—22no—
779#120D4×C1112yes—
780C4×Q8—21no—
781C4×Q8—21no—
782C4×Q8C23×C1112yes—
783C4×Q8C23×C1112yes—
784C4×Q8C23×C1112yes—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—22no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4C23×C1112yes—
794C4×D4C23×C1112yes—
795C4×D4C23×C1112yes—
796#117—22no—
797#117C23×C1111yescharacteristic
798#117C23×C1111yescharacteristic
799C2×C4⋊C4—21no—
800C2×C4⋊C4C23×C1111yescharacteristic
801C2×C4⋊C4C23×C1111yescharacteristic
802C2×C4⋊C4C23×C1112yes—
803C2×C22⋊C4—21no—
804C2×C22⋊C4—21no—
805C2×C22⋊C4—22no—
806#107C23×C1112yes—
807#107C23×C1112yes—
808#106C23×C1112yes—
809#106C23×C1112yes—
810C4⋊C8C23×C1112yes—
811C4⋊C8C23×C1112yes—
812#103C23×C1112yes—
813#103C23×C1112yes—
814#103C23×C1112yes—
815#103C23×C1112yes—
816#103C23×C1112yes—
817#103C23×C1112yes—
818#103C23×C1112yes—
819#103C23×C1112yes—
820#103C23×C1112yes—
821#103C23×C1112yes—
822#103C23×C1112yes—
823#103C23×C1112yes—
824#102C23×C1112yes—
825#102C23×C1112yes—
826#102C23×C1112yes—
827#102C23×C1112yes—
828C22⋊C8C23×C1112yes—
829C22⋊C8C23×C1112yes—
830C22⋊C8C23×C1111yescharacteristic
831C22⋊C8C23×C1111yescharacteristic
832C22⋊C8C23×C1111yescharacteristic
833C22⋊C8C23×C1111yescharacteristic
834C22⋊C8C23×C1112yes—
835C22⋊C8C23×C1112yes—
836#97C23×C1112yes—
837C4×C8C23×C1112yes—
838C2×C11—22no—
839C2×C11—22no—
840C2×C11—42no—
841C2×C11—41no—
842C2×C11—81no—
843C2×C11—82no—
844C2×C11#348411yescharacteristic
845C2×C11C2×#57711yescharacteristic
846C2×C11C2×#57811yescharacteristic
847C24—21no—
848C24C2×D4×C1111yescharacteristic
849#41—24no—
850#41—42no—
851#41—42no—
852#41—42no—
853#41—48no—
854#41—42no—
855#41—42no—
856#41—44no—
857#41—84no—
858C2×Q8—24no—
859C2×Q8—21no—
860C2×Q8—22no—
861C2×Q8—22no—
862C2×Q8—21no—
863C2×Q8—22no—
864C2×Q8—21no—
865C2×Q8—22no—
866C2×Q8—24no—
867C2×Q8—24no—
868C2×Q8—24no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—44no—
874C2×Q8—42no—
875C2×Q8—44no—
876C2×Q8—44no—
877C2×Q8—44no—
878C2×Q8C2×D4×C1111yescharacteristic
879C2×Q8C24×C1112yes—
880C2×Q8C24×C1111yescharacteristic
881C2×Q8C24×C1112yes—
882C2×Q8C24×C1112yes—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—22no—
886C2×D4—21no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—21no—
892C2×D4—42no—
893C2×D4—82no—
894C2×D4C2×D4×C1112yes—
895C2×D4C2×D4×C1112yes—
896C2×D4C2×D4×C1112yes—
897C2×D4C2×D4×C1111yescharacteristic
898C2×D4C24×C1111yescharacteristic
899C2×D4C24×C1112yes—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—21no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—42no—
914C22×C4—44no—
915C22×C4C2×D4×C1111yescharacteristic
916C22×C4C2×D4×C1111yescharacteristic
917C22×C4C2×D4×C1111yescharacteristic
918C22×C4C24×C1111yescharacteristic
919C22×C4C24×C1111yescharacteristic
920C22×C4C24×C1111yescharacteristic
921C22×C4C24×C1112yes—
922Q16—24no—
923Q16—24no—
924Q16—42no—
925Q16—42no—
926Q16—42no—
927SD16—24no—
928SD16—24no—
929SD16—42no—
930SD16—42no—
931SD16—42no—
932SD16—42no—
933D8—42no—
934M16—42no—
935C2×C8—42no—
936C2×C8—42no—
937C2×C8—42no—
938C2×C8C24×C1112yes—
939C2×C8C24×C1112yes—
940C2×C8C24×C1112yes—
941C2×C8C24×C1112yes—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4C2×D4×C1111yescharacteristic
959C4⋊C4C2×D4×C1111yescharacteristic
960C4⋊C4C2×D4×C1112yes—
961C4⋊C4C2×D4×C1112yes—
962C4⋊C4C24×C1111yescharacteristic
963C4⋊C4C24×C1111yescharacteristic
964C4⋊C4C24×C1112yes—
965C4⋊C4C24×C1112yes—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—21no—
969C22⋊C4—21no—
970C22⋊C4—21no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—21no—
983C22⋊C4—22no—
984C22⋊C4C2×D4×C1112yes—
985C22⋊C4C2×D4×C1112yes—
986C22⋊C4C2×D4×C1112yes—
987C22⋊C4C2×D4×C1112yes—
988C22⋊C4C2×D4×C1112yes—
989C42—22no—
990C42—22no—
991C42—21no—
992C42—22no—
993C42C24×C1112yes—
994C11#6163211yescharacteristic, direct product factor, Sylow
995C23—22no—
996C23—22no—
997C23—21no—
998C23—22no—
999C23—41no—
1000C23—42no—
1001C23—81no—
1002C23—81no—
1003C23C22×D4×C1111yescharacteristic
1004C23C22×D4×C1112yes—
1005C23C22×D4×C1111yescharacteristic
1006C23C22×D4×C1111yescharacteristic
1007Q8—24no—
1008Q8—22no—
1009Q8—22no—
1010Q8—22no—
1011Q8—22no—
1012Q8—22no—
1013Q8—22no—
1014Q8—41no—
1015Q8—44no—
1016Q8—44no—
1017Q8—44no—
1018Q8—42no—
1019Q8—81no—
1020Q8—82no—
1021Q8C11×H(5,𝔽2)14yes—
1022D4—24no—
1023D4—24no—
1024D4—22no—
1025D4—22no—
1026D4—22no—
1027D4—41no—
1028D4—42no—
1029D4—44no—
1030D4—42no—
1031D4—42no—
1032D4—44no—
1033D4—42no—
1034D4—81no—
1035D4—82no—
1036D4—82no—
1037D4—82no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—82no—
1063C2×C4—82no—
1064C2×C4—81no—
1065C2×C4—81no—
1066C2×C4—82no—
1067C2×C4C22×D4×C1112yes—
1068C2×C4C22×D4×C1112yes—
1069C2×C4C22×D4×C1111yescharacteristic
1070C2×C4C22×D4×C1111yescharacteristic
1071C2×C4C22×D4×C1112yes—
1072C2×C4C22×D4×C1111yescharacteristic
1073C2×C4C25×C1111yescharacteristic
1074C8—22no—
1075C8—22no—
1076C8—22no—
1077C8—22no—
1078C22—21no—
1079C22—21no—
1080C22—21no—
1081C22—21no—
1082C22—21no—
1083C22—22no—
1084C22—22no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—44no—
1089C22—41no—
1090C22—42no—
1091C22—42no—
1092C22—41no—
1093C22—41no—
1094C22—42no—
1095C22—162no—
1096C22C11×#57712yes—
1097C22C11×#57812yes—
1098C22C23×D4×C1111yescharacteristic
1099C4—24no—
1100C4—21no—
1101C4—22no—
1102C4—21no—
1103C4—21no—
1104C4—22no—
1105C4—22no—
1106C4—41no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—41no—
1112C4—41no—
1113C4C2×C11×H(5,𝔽2)12yes—
1114C2—22no—
1115C2—22no—
1116C2—41no—
1117C2—42no—
1118C2—82no—
1119C2—81no—
1120C2C11×#348411yescharacteristic
1121C2C2×C11×#57711yescharacteristic
1122C2C2×C11×#57811yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#525 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3536C2semidirect
2. C11×#3486C2semidirect
3. C11×#3316C2semidirect
4. C11×#3308C2semidirect
5. C11×#3299C2semidirect
6. C11×#3298C2semidirect
7. C11×#3285C2semidirect
8. C11×#3282C2semidirect
9. C11×#3270C2semidirect
10. C11×#3266C2semidirect
11. C11×#3225C2semidirect
12. C11×#3201C2semidirect
13. C11×#3190C2semidirect
14. C11×#3188C2semidirect
15. C11×#3121C2semidirect
16. C11×#3013C2semidirect
17. C2×C11×#451C2semidirect
18. C2×C11×#448C2semidirect
19. C11×#2977C2semidirect
20. C2×C11×2−1+4C22semidirect
22. C2×C11×#137C22semidirect
23. C2×C11×#135C22semidirect
24. C22×C11×Q16C22semidirect
31. D4×Q8×C11C22semidirect
36. C11×#548C22semidirect
47. C11×#536C22semidirect
48. C11×#536C22semidirect
54. C11×#519C22semidirect
55. C11×#497C22semidirect
56. C11×#495C22semidirect
57. C11×#489C22semidirect
58. C11×#487C22semidirect
59. C11×#485C22semidirect
61. C11×#484C22semidirect
62. C11×#483C22semidirect
63. C11×#483C22semidirect
66. C11×#480C22semidirect
67. C11×#477C22semidirect
68. C11×#475C22semidirect
69. C11×#470C22semidirect
70. C11×#468C22semidirect
72. C11×#467C22semidirect
76. C11×#465C22semidirect
77. C11×#464C22semidirect
78. C11×#464C22semidirect
79. C11×#464C22semidirect
80. C11×#463C22semidirect
81. C11×#462C22semidirect
82. C11×#461C22semidirect
83. C11×#452C22semidirect
84. C11×#452C22semidirect
85. C11×#452C22semidirect
86. C11×#452C22semidirect
89. C11×#451C22semidirect
90. C11×#451C22semidirect
91. C11×#451C22semidirect
92. C11×#451C22semidirect
95. C11×#449C22semidirect
100. C11×#448C22semidirect
101. C11×#448C22semidirect
103. C11×#441C22semidirect
104. C11×#440C22semidirect
105. C4×C11×Q16C22semidirect
106. C4×C11×SD16C22semidirect
108. C11×#435C22semidirect
110. C8×D4×C11C22semidirect
111. C11×#433C22semidirect
112. C11×#417C22semidirect
114. C2×C11×#103C22semidirect
115. C2×C11×#103C22semidirect
116. C11×#408C22semidirect
286. #61632C11direct (N × H)
434. #3536C2×C11semidirect
435. #3486C2×C11semidirect
436. #3316C2×C11semidirect
437. #3308C2×C11semidirect
438. #3299C2×C11semidirect
439. #3298C2×C11semidirect
440. #3285C2×C11semidirect
441. #3282C2×C11semidirect
442. #3270C2×C11semidirect
443. #3266C2×C11semidirect
444. #3225C2×C11semidirect
445. #3201C2×C11semidirect
446. #3190C2×C11semidirect
447. #3188C2×C11semidirect
448. #3121C2×C11semidirect
449. #3013C2×C11semidirect
450. C2×#451C2×C11semidirect
451. C2×#448C2×C11semidirect
452. #2977C2×C11semidirect
536. C2×2−1+4C22×C11semidirect
538. C2×#137C22×C11semidirect
539. C2×#135C22×C11semidirect
540. C22×Q16C22×C11semidirect
547. D4×Q8C22×C11semidirect
552. #548C22×C11semidirect
563. #536C22×C11semidirect
564. #536C22×C11semidirect
570. #519C22×C11semidirect
571. #497C22×C11semidirect
572. #495C22×C11semidirect
573. #489C22×C11semidirect
574. #487C22×C11semidirect
575. #485C22×C11semidirect
577. #484C22×C11semidirect
578. #483C22×C11semidirect
579. #483C22×C11semidirect
582. #480C22×C11semidirect
583. #477C22×C11semidirect
584. #475C22×C11semidirect
585. #470C22×C11semidirect
586. #468C22×C11semidirect
588. #467C22×C11semidirect
592. #465C22×C11semidirect
593. #464C22×C11semidirect
594. #464C22×C11semidirect
595. #464C22×C11semidirect
596. #463C22×C11semidirect
597. #462C22×C11semidirect
598. #461C22×C11semidirect
599. #452C22×C11semidirect
600. #452C22×C11semidirect
601. #452C22×C11semidirect
602. #452C22×C11semidirect
605. #451C22×C11semidirect
606. #451C22×C11semidirect
607. #451C22×C11semidirect
608. #451C22×C11semidirect
611. #449C22×C11semidirect
616. #448C22×C11semidirect
617. #448C22×C11semidirect
619. #441C22×C11semidirect
620. #440C22×C11semidirect
621. C4×Q16C22×C11semidirect
622. C4×SD16C22×C11semidirect
624. #435C22×C11semidirect
626. C8×D4C22×C11semidirect
627. #433C22×C11semidirect
628. #417C22×C11semidirect
630. C2×#103C22×C11semidirect
631. C2×#103C22×C11semidirect
632. #408C22×C11semidirect
994. C11#61632direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35362
C11×#34862
C11×#33162
C11×#33082
C11×#32992
C11×#32982
C11×#32852
C11×#32822
C11×#32702
C11×#32662
C11×#32252
C11×#32012
C11×#31902
C11×#31882
C11×#31212
C11×#30132
C2×C11×#4512
C2×C11×#4482
C11×#29772
#6163211