Finite Group Databasebeta

← C11×#62018 #14639211

Subgroups — C11×#62018 #14639211

Order 2816.

1902 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3558C211yesmaximal, characteristic, complemented
2C11×#3520C211yesmaximal, characteristic, complemented
3C11×#3401C212yesmaximal, complemented
4C11×#3373C212yesmaximal, complemented
5C11×#3316C212yesmaximal, complemented
6C11×#3306C212yesmaximal, complemented
7C11×#3295C212yesmaximal, complemented
8C11×#3282C212yesmaximal, complemented
9C11×#3267C212yesmaximal, complemented
10C11×#3264C212yesmaximal, complemented
11C11×#3263C212yesmaximal, complemented
12C11×#3246C211yesmaximal, characteristic, complemented
13C11×#3224C212yesmaximal, complemented
14C11×#3215C211yesmaximal, characteristic, complemented
15C11×#3125C212yesmaximal, complemented
16C11×#3109C211yesmaximal, characteristic, complemented
17C11×#3045C212yesmaximal, complemented
18C2×C11×#463C211yesmaximal, characteristic, complemented
19C11×#2992C211yesmaximal, characteristic, complemented
20C2×C11×AGL(1,ℤ/8)C2212yescomplemented
21C2×C11×#135C2212yescomplemented
22C22×C11×SD16C2211yescharacteristic, complemented
23C22×C11×D8C2211yescharacteristic
24C11×#562—21no—
25C11×H(3,𝔽4)—21no—
26C11×#559C2212yescomplemented
27C11×#556C2211yescharacteristic, complemented
28C11×#554C2212yescomplemented
29C11×#552—21no—
30C11×#551—22no—
31D4×Q8×C11C2211yescharacteristic, complemented
32C11×#548—21no—
33C11×#548C2212yes—
34C11×#547C2211yescharacteristic, complemented
35C11×#547C2211yescharacteristic, complemented
36C11×#546—22no—
37C11×#546C2212yescomplemented
38C11×#546C2212yescomplemented
39D42×C11C2212yes—
40C11×#542C2212yescomplemented
41C11×#542C2212yescomplemented
42C11×#539—22no—
43C11×#538—22no—
44C11×#538—21no—
45C11×#535C2212yescomplemented
46C11×#534—21no—
47C11×#533C2211yescharacteristic, complemented
48C11×#532C2211yescharacteristic
49C11×#529C2211yescharacteristic
50C2×C11×#124C2211yescharacteristic
51C11×#525—21no—
52C2×C11×C22⋊Q8—21no—
53C11×#520C2212yescomplemented
54C2×C4×D4×C11C2211yescharacteristic, complemented
55C11×#497C2212yescomplemented
56C11×#496C2212yes—
57C11×#495C2212yescomplemented
58C11×#489C2212yescomplemented
59C11×#489C2212yescomplemented
60C11×#486C2212yescomplemented
61C11×#483C2212yescomplemented
62C11×#481C2212yescomplemented
63C11×#481C2212yescomplemented
64C11×#476C2212yescomplemented
65C11×#476C2211yescharacteristic, complemented
66C11×#476C2212yescomplemented
67C11×#476C2211yescharacteristic, complemented
68C11×#475C2212yescomplemented
69C11×#475C2212yescomplemented
70C11×#470C2212yescomplemented
71C11×#469C2212yes—
72C11×#465C2212yescomplemented
73C11×#465C2212yescomplemented
74C11×#465C2212yescomplemented
75C11×#465C2212yescomplemented
76C11×#464C2212yescomplemented
77C11×#464C2212yescomplemented
78C11×#464C2212yescomplemented
79C11×#464C2212yescomplemented
80C11×#463C2212yescomplemented
81C11×#463C2212yescomplemented
82C11×#463C2212yescomplemented
83C11×#463C2212yescomplemented
84C11×#463C2212yescomplemented
85C11×#463C2212yescomplemented
86C11×#461C2212yescomplemented
87C11×#460C2212yescomplemented
88C11×#460C2212yescomplemented
89C11×#459C2212yes—
90C11×#459C2211yescharacteristic, complemented
91C11×#459C2211yescharacteristic, complemented
92C11×#452C2212yescomplemented
93C11×#452C2212yescomplemented
94C11×#451C2212yescomplemented
95C11×#450C2212yes—
96C11×#450C2212yescomplemented
97C11×#449C2212yes—
98C11×#449C2212yescomplemented
99C11×#447C2212yescomplemented
100C11×#447C2212yescomplemented
101C11×#446C2212yescomplemented
102C11×#442C2212yescomplemented
103C11×#442C2212yescomplemented
104C11×#442C2212yescomplemented
105C11×#441C2212yescomplemented
106C4×C11×SD16C2212yescomplemented
107C4×C11×SD16C2212yescomplemented
108C11×#435C2212yescomplemented
109C11×#435C2212yescomplemented
110C8×D4×C11C2212yescomplemented
111C11×#433C2212yescomplemented
112C11×#432C2211yescharacteristic, complemented
113C11×#424C2212yescomplemented
114C2×C11×C4⋊C8C2211yescharacteristic, complemented
115C11×#417C2212yescomplemented
116C2×C11×#103C2211yescharacteristic, complemented
117C2×C11×#102C2211yescharacteristic
118C2×C11×#102C2212yescomplemented
119C2×C11×#41—21no—
120C2×C11×#41—21no—
121C2×C11×#41C2312yes—
122C2×C11×#41C2312yes—
123C22×Q8×C11—21no—
124C22×Q8×C11C2311yescharacteristic
125C22×D4×C11—22no—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11—21no—
130C11×AGL(1,ℤ/8)—44no—
131C11×#135—44no—
132C2×C11×Q16C2312yes—
133C2×C11×Q16C2312yes—
134C2×C11×SD16—42no—
135C2×C11×SD16C2312yes—
136C2×C11×SD16C2312yes—
137C2×C11×SD16C2312yes—
138C2×C11×SD16C2312yes—
139C2×C11×SD16C2312yes—
140C2×C11×SD16C2312yes—
141C2×C11×D8—42no—
142C2×C11×D8C2312yes—
143C2×C11×D8C2312yes—
144C2×C11×D8C2312yes—
145C2×C11×D8C2312yes—
146C2×C11×M16C2312yes—
147C22×C8×C11C2311yescharacteristic
148C22×C8×C11C2312yes—
149C22×C8×C11C2311yescharacteristic
150C11×C4⋊Q8C2311yescharacteristic
151C11×C4⋊Q8C2311yescharacteristic
152C11×C4⋊Q8C2312yes—
153C11×C4⋊Q8C2311yescharacteristic
154C11×#127C2312yes—
155C11×#127C2311yescharacteristic
156C11×#126—22no—
157C11×#126—22no—
158C11×#126—22no—
159C11×#126D412yes—
160C11×#125—22no—
161C11×#125—21no—
162C11×#125D411yescharacteristic
163C11×#124—22no—
164C11×#124—22no—
165C11×#124—22no—
166C11×#124—22no—
167C11×#124—21no—
168C11×#124—21no—
169C11×#124—21no—
170C11×#124D411yescharacteristic
171C11×#124C2312yes—
172C11×#124C2312yes—
173C11×#124C2312yes—
174C11×#124C2312yes—
175C11×#123—22no—
176C11×#123—22no—
177C11×#123—22no—
178C11×#123—22no—
179C11×#123—22no—
180C11×#123—22no—
181C11×#123—22no—
182C11×#123—22no—
183C11×#123D412yes—
184C11×C22⋊Q8—21no—
185C11×C22⋊Q8—21no—
186C11×C22⋊Q8—22no—
187C11×C22⋊Q8—21no—
188C11×C22⋊Q8—21no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8—22no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8D411yescharacteristic
195C11×C22⋊Q8C2312yes—
196C11×C22⋊Q8C2312yes—
197C11×C22⋊Q8C2312yes—
198C11×#121—21no—
199C11×#121—22no—
200C11×#121—21no—
201C11×#121—22no—
202C11×#121—22no—
203C11×#121—22no—
204C11×#121—22no—
205C11×#121—22no—
206C11×#121D411yescharacteristic
207C11×#121C2312yes—
208C11×#121C2312yes—
209C11×#121C2312yes—
210C11×#120—22no—
211C11×#120—22no—
212C11×#120—22no—
213C11×#120—22no—
214C11×#120—22no—
215C11×#120—22no—
216C4×Q8×C11—21no—
217C4×Q8×C11C2312yes—
218C4×Q8×C11C2312yes—
219C4×Q8×C11C2312yes—
220C4×Q8×C11C2311yescharacteristic
221C4×D4×C11—22no—
222C4×D4×C11—22no—
223C4×D4×C11—22no—
224C4×D4×C11—22no—
225C4×D4×C11—22no—
226C4×D4×C11—21no—
227C4×D4×C11—21no—
228C4×D4×C11—21no—
229C4×D4×C11C2311yescharacteristic
230C4×D4×C11C2311yescharacteristic
231C4×D4×C11C2311yescharacteristic
232C4×D4×C11C2311yescharacteristic
233C4×D4×C11C2312yes—
234C4×D4×C11C2312yes—
235C4×D4×C11C2312yes—
236C4×D4×C11C2312yes—
237C4×D4×C11C2311yescharacteristic
238C11×#117—21no—
239C11×#117—22no—
240C11×#117—21no—
241C11×#117C2312yes—
242C2×C11×C4⋊C4—22no—
243C2×C11×C4⋊C4—21no—
244C2×C11×C4⋊C4C2311yescharacteristic
245C2×C11×C4⋊C4C2312yes—
246C2×C11×C22⋊C4—21no—
247C2×C11×C22⋊C4—21no—
248C2×C11×C22⋊C4—21no—
249C2×C11×C22⋊C4—22no—
250C2×C11×C22⋊C4—22no—
251C2×C42×C11C2311yescharacteristic
252C11×#106C2312yes—
253C11×#106C2312yes—
254C11×#106C2312yes—
255C11×#106C2312yes—
256C11×C4⋊C8C2312yes—
257C11×C4⋊C8C2312yes—
258C11×C4⋊C8C2311yescharacteristic
259C11×C4⋊C8C2312yes—
260C11×C4⋊C8C2312yes—
261C11×C4⋊C8C2311yescharacteristic
262C11×#103C2312yes—
263C11×#103C2312yes—
264C11×#103C2312yes—
265C11×#103C2312yes—
266C11×#103C2312yes—
267C11×#103C2312yes—
268C11×#102C2312yes—
269C11×#102C2312yes—
270C11×#102C2312yes—
271C11×#102C2312yes—
272C11×#102C2312yes—
273C11×#102C2312yes—
274C11×#102C2312yes—
275C11×#102C2312yes—
276C11×#102C2312yes—
277C11×#102C2312yes—
278C11×C22⋊C8C2312yes—
279C11×C22⋊C8C2312yes—
280C11×C22⋊C8C2312yes—
281C11×#97C2312yes—
282C11×#97C2312yes—
283C4×C8×C11C2312yes—
284#62018C1111yesmaximal, characteristic, direct product factor, Sylow
285C24×C11—21no—
286C24×C11—21no—
287C24×C11—22no—
288C11×#41—24no—
289C11×#41—42no—
290C11×#41—42no—
291C11×#41—42no—
292C11×#41—82no—
293C11×#41—82no—
294C2×Q8×C11—21no—
295C2×Q8×C11—22no—
296C2×Q8×C11—21no—
297C2×Q8×C11—21no—
298C2×Q8×C11—41no—
299C2×Q8×C11—41no—
300C2×Q8×C11—82no—
301C2×Q8×C11C2×D411yescharacteristic
302C2×Q8×C11C2412yes—
303C2×Q8×C11C2412yes—
304C2×D4×C11—22no—
305C2×D4×C11—22no—
306C2×D4×C11—22no—
307C2×D4×C11—22no—
308C2×D4×C11—22no—
309C2×D4×C11—22no—
310C2×D4×C11—21no—
311C2×D4×C11—22no—
312C2×D4×C11—21no—
313C2×D4×C11—21no—
314C2×D4×C11—21no—
315C2×D4×C11—22no—
316C2×D4×C11—22no—
317C2×D4×C11—41no—
318C2×D4×C11—41no—
319C2×D4×C11—42no—
320C2×D4×C11—41no—
321C2×D4×C11—42no—
322C2×D4×C11—84no—
323C2×D4×C11C2×D412yes—
324C2×D4×C11C2×D411yescharacteristic
325C2×D4×C11C2412yes—
326C2×D4×C11C2412yes—
327C2×D4×C11C2411yescharacteristic
328C2×D4×C11C2411yescharacteristic
329C22×C4×C11—21no—
330C22×C4×C11—21no—
331C22×C4×C11—22no—
332C22×C4×C11—22no—
333C22×C4×C11—21no—
334C22×C4×C11—21no—
335C22×C4×C11—22no—
336C22×C4×C11—22no—
337C22×C4×C11—22no—
338C22×C4×C11—21no—
339C22×C4×C11—22no—
340C22×C4×C11—21no—
341C22×C4×C11—82no—
342C22×C4×C11C2×D411yescharacteristic
343C22×C4×C11C2×D411yescharacteristic
344C22×C4×C11C2411yescharacteristic
345C22×C4×C11C2412yes—
346C11×Q16—42no—
347C11×Q16—42no—
348C11×SD16—24no—
349C11×SD16—42no—
350C11×SD16—42no—
351C11×SD16—42no—
352C11×SD16—42no—
353C11×SD16—42no—
354C11×D8—24no—
355C11×D8—24no—
356C11×D8—42no—
357C11×D8—42no—
358C11×M16—42no—
359C2×C8×C11—41no—
360C2×C8×C11—41no—
361C2×C8×C11—42no—
362C2×C8×C11C2412yes—
363C2×C8×C11C2412yes—
364C2×C8×C11C2412yes—
365C2×C8×C11C2412yes—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—21no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—22no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—21no—
372C11×C4⋊C4—21no—
373C11×C4⋊C4—21no—
374C11×C4⋊C4—22no—
375C11×C4⋊C4—21no—
376C11×C4⋊C4—22no—
377C11×C4⋊C4—22no—
378C11×C4⋊C4—22no—
379C11×C4⋊C4C2×D412yes—
380C11×C4⋊C4C2×D411yescharacteristic
381C11×C4⋊C4C2×D412yes—
382C11×C4⋊C4C2×D411yescharacteristic
383C11×C4⋊C4C2×D412yes—
384C11×C4⋊C4C2×D412yes—
385C11×C4⋊C4C2411yescharacteristic
386C11×C4⋊C4C2411yescharacteristic
387C11×C4⋊C4C2412yes—
388C11×C4⋊C4C2412yes—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4—22no—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—21no—
394C11×C22⋊C4—21no—
395C11×C22⋊C4—21no—
396C11×C22⋊C4—21no—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4—22no—
401C11×C22⋊C4—22no—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—22no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4C2×D412yes—
411C11×C22⋊C4C2×D412yes—
412C11×C22⋊C4C2×D412yes—
413C11×C22⋊C4C2×D412yes—
414C11×C22⋊C4C2×D412yes—
415C42×C11—22no—
416C42×C11—22no—
417C42×C11—22no—
418C42×C11C2×D411yescharacteristic
419C42×C11C2×D411yescharacteristic
420C42×C11C2412yes—
421C42×C11C2411yescharacteristic
422C42×C11C2411yescharacteristic
423#3558C2×C1111yescharacteristic, complemented
424#3520C2×C1111yescharacteristic, complemented
425#3401C2×C1112yescomplemented
426#3373C2×C1112yescomplemented
427#3316C2×C1112yescomplemented
428#3306C2×C1112yescomplemented
429#3295C2×C1112yescomplemented
430#3282C2×C1112yescomplemented
431#3267C2×C1112yescomplemented
432#3264C2×C1112yescomplemented
433#3263C2×C1112yescomplemented
434#3246C2×C1111yescharacteristic, complemented
435#3224C2×C1112yescomplemented
436#3215C2×C1111yescharacteristic, complemented
437#3125C2×C1112yescomplemented
438#3109C2×C1111yescharacteristic, complemented
439#3045C2×C1112yescomplemented
440C2×#463C2×C1111yescharacteristic, complemented
441#2992C2×C1111yescharacteristic, complemented
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—42no—
447C23×C11—42no—
448C23×C11—42no—
449C23×C11—81no—
450C23×C11—81no—
451C23×C11—82no—
452C23×C11—82no—
453C23×C11—81no—
454C23×C11—82no—
455C23×C11C22×D412yes—
456C23×C11C22×D411yescharacteristic
457Q8×C11—22no—
458Q8×C11—22no—
459Q8×C11—22no—
460Q8×C11—22no—
461Q8×C11—41no—
462Q8×C11—42no—
463Q8×C11—81no—
464Q8×C11—82no—
465Q8×C11—81no—
466D4×C11—24no—
467D4×C11—22no—
468D4×C11—22no—
469D4×C11—21no—
470D4×C11—21no—
471D4×C11—21no—
472D4×C11—22no—
473D4×C11—22no—
474D4×C11—41no—
475D4×C11—42no—
476D4×C11—44no—
477D4×C11—44no—
478D4×C11—81no—
479D4×C11—82no—
480D4×C11—82no—
481D4×C11—81no—
482D4×C11—82no—
483D4×C11—81no—
484D4×C11—82no—
485D4×C11—82no—
486D4×C11—82no—
487D4×C11H(5,𝔽2)12yes—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—41no—
500C2×C4×C11—44no—
501C2×C4×C11—42no—
502C2×C4×C11—42no—
503C2×C4×C11—81no—
504C2×C4×C11—81no—
505C2×C4×C11—82no—
506C2×C4×C11—82no—
507C2×C4×C11—82no—
508C2×C4×C11—82no—
509C2×C4×C11—81no—
510C2×C4×C11—81no—
511C2×C4×C11—82no—
512C2×C4×C11C22×D411yescharacteristic
513C2×C4×C11C22×D412yes—
514C2×C4×C11C22×D412yes—
515C2×C4×C11C22×D411yescharacteristic
516C2×C4×C11C22×D411yescharacteristic
517C2×C4×C11C22×D411yescharacteristic
518C2×C4×C11C22×D411yescharacteristic
519C2×C4×C11C22×D412yes—
520C2×C4×C11C2511yescharacteristic
521C8×C11—22no—
522C8×C11—22no—
523C8×C11—22no—
524C8×C11—22no—
525C2×AGL(1,ℤ/8)C22×C1112yescomplemented
526C2×#135C22×C1112yescomplemented
527C22×SD16C22×C1111yescharacteristic, complemented
528C22×D8C22×C1111yescharacteristic
529#562—21no—
530H(3,𝔽4)—21no—
531#559C22×C1112yescomplemented
532#556C22×C1111yescharacteristic, complemented
533#554C22×C1112yescomplemented
534#552—21no—
535#551—22no—
536D4×Q8C22×C1111yescharacteristic, complemented
537#548—21no—
538#548C22×C1112yes—
539#547C22×C1111yescharacteristic, complemented
540#547C22×C1111yescharacteristic, complemented
541#546—22no—
542#546C22×C1112yescomplemented
543#546C22×C1112yescomplemented
544D42C22×C1112yes—
545#542C22×C1112yescomplemented
546#542C22×C1112yescomplemented
547#539—22no—
548#538—22no—
549#538—21no—
550#535C22×C1112yescomplemented
551#534—21no—
552#533C22×C1111yescharacteristic, complemented
553#532C22×C1111yescharacteristic
554#529C22×C1111yescharacteristic
555C2×#124C22×C1111yescharacteristic
556#525—21no—
557C2×C22⋊Q8—21no—
558#520C22×C1112yescomplemented
559C2×C4×D4C22×C1111yescharacteristic, complemented
560#497C22×C1112yescomplemented
561#496C22×C1112yes—
562#495C22×C1112yescomplemented
563#489C22×C1112yescomplemented
564#489C22×C1112yescomplemented
565#486C22×C1112yescomplemented
566#483C22×C1112yescomplemented
567#481C22×C1112yescomplemented
568#481C22×C1112yescomplemented
569#476C22×C1111yescharacteristic, complemented
570#476C22×C1111yescharacteristic, complemented
571#476C22×C1112yescomplemented
572#476C22×C1112yescomplemented
573#475C22×C1112yescomplemented
574#475C22×C1112yescomplemented
575#470C22×C1112yescomplemented
576#469C22×C1112yes—
577#465C22×C1112yescomplemented
578#465C22×C1112yescomplemented
579#465C22×C1112yescomplemented
580#465C22×C1112yescomplemented
581#464C22×C1112yescomplemented
582#464C22×C1112yescomplemented
583#464C22×C1112yescomplemented
584#464C22×C1112yescomplemented
585#463C22×C1112yescomplemented
586#463C22×C1112yescomplemented
587#463C22×C1112yescomplemented
588#463C22×C1112yescomplemented
589#463C22×C1112yescomplemented
590#463C22×C1112yescomplemented
591#461C22×C1112yescomplemented
592#460C22×C1112yescomplemented
593#460C22×C1112yescomplemented
594#459C22×C1112yes—
595#459C22×C1111yescharacteristic, complemented
596#459C22×C1111yescharacteristic, complemented
597#452C22×C1112yescomplemented
598#452C22×C1112yescomplemented
599#451C22×C1112yescomplemented
600#450C22×C1112yes—
601#450C22×C1112yescomplemented
602#449C22×C1112yes—
603#449C22×C1112yescomplemented
604#447C22×C1112yescomplemented
605#447C22×C1112yescomplemented
606#446C22×C1112yescomplemented
607#442C22×C1112yescomplemented
608#442C22×C1112yescomplemented
609#442C22×C1112yescomplemented
610#441C22×C1112yescomplemented
611C4×SD16C22×C1112yescomplemented
612C4×SD16C22×C1112yescomplemented
613#435C22×C1112yescomplemented
614#435C22×C1112yescomplemented
615C8×D4C22×C1112yescomplemented
616#433C22×C1112yescomplemented
617#432C22×C1111yescharacteristic, complemented
618#424C22×C1112yescomplemented
619C2×C4⋊C8C22×C1111yescharacteristic, complemented
620#417C22×C1112yescomplemented
621C2×#103C22×C1111yescharacteristic, complemented
622C2×#102C22×C1111yescharacteristic
623C2×#102C22×C1112yescomplemented
624C22×C11—21no—
625C22×C11—21no—
626C22×C11—22no—
627C22×C11—22no—
628C22×C11—22no—
629C22×C11—22no—
630C22×C11—41no—
631C22×C11—41no—
632C22×C11—41no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—41no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—41no—
641C22×C11—84no—
642C22×C11—162no—
643C22×C11—164no—
644C22×C11#57712yes—
645C22×C11C23×D411yescharacteristic
646C4×C11—21no—
647C4×C11—21no—
648C4×C11—22no—
649C4×C11—22no—
650C4×C11—21no—
651C4×C11—21no—
652C4×C11—21no—
653C4×C11—22no—
654C4×C11—41no—
655C4×C11—41no—
656C4×C11—42no—
657C4×C11—42no—
658C4×C11—42no—
659C4×C11—42no—
660C4×C11C2×H(5,𝔽2)11yescharacteristic
661C4×C11#58511yescharacteristic
662C2×#41—21no—
663C2×#41—21no—
664C2×#41C23×C1112yes—
665C2×#41C23×C1112yes—
666C22×Q8—21no—
667C22×Q8C23×C1111yescharacteristic
668C22×D4—22no—
669C22×D4C23×C1111yescharacteristic
670C22×D4C23×C1111yescharacteristic
671C22×D4C23×C1112yes—
672C23×C4—21no—
673AGL(1,ℤ/8)—44no—
674#135—44no—
675C2×Q16C23×C1112yes—
676C2×Q16C23×C1112yes—
677C2×SD16—42no—
678C2×SD16C23×C1112yes—
679C2×SD16C23×C1112yes—
680C2×SD16C23×C1112yes—
681C2×SD16C23×C1112yes—
682C2×SD16C23×C1112yes—
683C2×SD16C23×C1112yes—
684C2×D8—42no—
685C2×D8C23×C1112yes—
686C2×D8C23×C1112yes—
687C2×D8C23×C1112yes—
688C2×D8C23×C1112yes—
689C2×M16C23×C1112yes—
690C22×C8C23×C1111yescharacteristic
691C22×C8C23×C1111yescharacteristic
692C22×C8C23×C1112yes—
693C4⋊Q8C23×C1111yescharacteristic
694C4⋊Q8C23×C1111yescharacteristic
695C4⋊Q8C23×C1111yescharacteristic
696C4⋊Q8C23×C1112yes—
697#127C23×C1111yescharacteristic
698#127C23×C1112yes—
699#126—22no—
700#126—22no—
701#126—22no—
702#126D4×C1112yes—
703#125—22no—
704#125—21no—
705#125D4×C1111yescharacteristic
706#124—22no—
707#124—22no—
708#124—22no—
709#124—22no—
710#124—21no—
711#124—21no—
712#124—21no—
713#124D4×C1111yescharacteristic
714#124C23×C1112yes—
715#124C23×C1112yes—
716#124C23×C1112yes—
717#124C23×C1112yes—
718#123—22no—
719#123—22no—
720#123—22no—
721#123—22no—
722#123—22no—
723#123—22no—
724#123—22no—
725#123—22no—
726#123D4×C1112yes—
727C22⋊Q8—21no—
728C22⋊Q8—21no—
729C22⋊Q8—22no—
730C22⋊Q8—21no—
731C22⋊Q8—21no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—22no—
735C22⋊Q8—22no—
736C22⋊Q8—22no—
737C22⋊Q8D4×C1111yescharacteristic
738C22⋊Q8C23×C1112yes—
739C22⋊Q8C23×C1112yes—
740C22⋊Q8C23×C1112yes—
741#121—21no—
742#121—22no—
743#121—21no—
744#121—22no—
745#121—22no—
746#121—22no—
747#121—22no—
748#121—22no—
749#121D4×C1111yescharacteristic
750#121C23×C1112yes—
751#121C23×C1112yes—
752#121C23×C1112yes—
753#120—22no—
754#120—22no—
755#120—22no—
756#120—22no—
757#120—22no—
758#120—22no—
759C4×Q8—21no—
760C4×Q8C23×C1112yes—
761C4×Q8C23×C1112yes—
762C4×Q8C23×C1112yes—
763C4×Q8C23×C1111yescharacteristic
764C4×D4—22no—
765C4×D4—22no—
766C4×D4—22no—
767C4×D4—22no—
768C4×D4—22no—
769C4×D4—21no—
770C4×D4—21no—
771C4×D4—21no—
772C4×D4C23×C1111yescharacteristic
773C4×D4C23×C1111yescharacteristic
774C4×D4C23×C1111yescharacteristic
775C4×D4C23×C1111yescharacteristic
776C4×D4C23×C1112yes—
777C4×D4C23×C1112yes—
778C4×D4C23×C1112yes—
779C4×D4C23×C1112yes—
780C4×D4C23×C1111yescharacteristic
781#117—21no—
782#117—22no—
783#117—21no—
784#117C23×C1112yes—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—21no—
787C2×C4⋊C4C23×C1111yescharacteristic
788C2×C4⋊C4C23×C1112yes—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—21no—
791C2×C22⋊C4—21no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C42C23×C1111yescharacteristic
795#106C23×C1112yes—
796#106C23×C1112yes—
797#106C23×C1112yes—
798#106C23×C1112yes—
799C4⋊C8C23×C1112yes—
800C4⋊C8C23×C1112yes—
801C4⋊C8C23×C1111yescharacteristic
802C4⋊C8C23×C1112yes—
803C4⋊C8C23×C1112yes—
804C4⋊C8C23×C1111yescharacteristic
805#103C23×C1112yes—
806#103C23×C1112yes—
807#103C23×C1112yes—
808#103C23×C1112yes—
809#103C23×C1112yes—
810#103C23×C1112yes—
811#102C23×C1112yes—
812#102C23×C1112yes—
813#102C23×C1112yes—
814#102C23×C1112yes—
815#102C23×C1112yes—
816#102C23×C1112yes—
817#102C23×C1112yes—
818#102C23×C1112yes—
819#102C23×C1112yes—
820#102C23×C1112yes—
821C22⋊C8C23×C1112yes—
822C22⋊C8C23×C1112yes—
823C22⋊C8C23×C1112yes—
824#97C23×C1112yes—
825#97C23×C1112yes—
826C4×C8C23×C1112yes—
827C2×C11—22no—
828C2×C11—42no—
829C2×C11—42no—
830C2×C11—81no—
831C2×C11—82no—
832C2×C11—82no—
833C2×C11#348811yescharacteristic
834C2×C11C2×#57711yescharacteristic
835C2×C11#358511yescharacteristic
836C24—21no—
837C24—21no—
838C24—22no—
839#41—24no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—82no—
844#41—82no—
845C2×Q8—21no—
846C2×Q8—22no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—41no—
850C2×Q8—41no—
851C2×Q8—82no—
852C2×Q8C2×D4×C1111yescharacteristic
853C2×Q8C24×C1112yes—
854C2×Q8C24×C1112yes—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—21no—
862C2×D4—22no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—42no—
871C2×D4—41no—
872C2×D4—42no—
873C2×D4—84no—
874C2×D4C2×D4×C1112yes—
875C2×D4C2×D4×C1111yescharacteristic
876C2×D4C24×C1112yes—
877C2×D4C24×C1112yes—
878C2×D4C24×C1111yescharacteristic
879C2×D4C24×C1111yescharacteristic
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—22no—
891C22×C4—21no—
892C22×C4—82no—
893C22×C4C2×D4×C1111yescharacteristic
894C22×C4C2×D4×C1111yescharacteristic
895C22×C4C24×C1111yescharacteristic
896C22×C4C24×C1112yes—
897Q16—42no—
898Q16—42no—
899SD16—24no—
900SD16—42no—
901SD16—42no—
902SD16—42no—
903SD16—42no—
904SD16—42no—
905D8—24no—
906D8—24no—
907D8—42no—
908D8—42no—
909M16—42no—
910C2×C8—41no—
911C2×C8—41no—
912C2×C8—42no—
913C2×C8C24×C1112yes—
914C2×C8C24×C1112yes—
915C2×C8C24×C1112yes—
916C2×C8C24×C1112yes—
917C4⋊C4—22no—
918C4⋊C4—21no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—22no—
926C4⋊C4—21no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4C2×D4×C1112yes—
931C4⋊C4C2×D4×C1111yescharacteristic
932C4⋊C4C2×D4×C1112yes—
933C4⋊C4C2×D4×C1111yescharacteristic
934C4⋊C4C2×D4×C1112yes—
935C4⋊C4C2×D4×C1112yes—
936C4⋊C4C24×C1111yescharacteristic
937C4⋊C4C24×C1111yescharacteristic
938C4⋊C4C24×C1112yes—
939C4⋊C4C24×C1112yes—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—21no—
945C22⋊C4—21no—
946C22⋊C4—21no—
947C22⋊C4—21no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4C2×D4×C1112yes—
962C22⋊C4C2×D4×C1112yes—
963C22⋊C4C2×D4×C1112yes—
964C22⋊C4C2×D4×C1112yes—
965C22⋊C4C2×D4×C1112yes—
966C42—22no—
967C42—22no—
968C42—22no—
969C42C2×D4×C1111yescharacteristic
970C42C2×D4×C1111yescharacteristic
971C42C24×C1112yes—
972C42C24×C1111yescharacteristic
973C42C24×C1111yescharacteristic
974C11#6201811yescharacteristic, direct product factor, Sylow
975C23—21no—
976C23—21no—
977C23—22no—
978C23—22no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—81no—
983C23—81no—
984C23—82no—
985C23—82no—
986C23—81no—
987C23—82no—
988C23C22×D4×C1112yes—
989C23C22×D4×C1111yescharacteristic
990Q8—22no—
991Q8—22no—
992Q8—22no—
993Q8—22no—
994Q8—41no—
995Q8—42no—
996Q8—81no—
997Q8—82no—
998Q8—81no—
999D4—24no—
1000D4—22no—
1001D4—22no—
1002D4—21no—
1003D4—21no—
1004D4—21no—
1005D4—22no—
1006D4—22no—
1007D4—41no—
1008D4—42no—
1009D4—44no—
1010D4—44no—
1011D4—81no—
1012D4—82no—
1013D4—82no—
1014D4—81no—
1015D4—82no—
1016D4—81no—
1017D4—82no—
1018D4—82no—
1019D4—82no—
1020D4C11×H(5,𝔽2)12yes—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—41no—
1033C2×C4—44no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—81no—
1037C2×C4—81no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—81no—
1043C2×C4—81no—
1044C2×C4—82no—
1045C2×C4C22×D4×C1111yescharacteristic
1046C2×C4C22×D4×C1112yes—
1047C2×C4C22×D4×C1112yes—
1048C2×C4C22×D4×C1111yescharacteristic
1049C2×C4C22×D4×C1111yescharacteristic
1050C2×C4C22×D4×C1111yescharacteristic
1051C2×C4C22×D4×C1111yescharacteristic
1052C2×C4C22×D4×C1112yes—
1053C2×C4C25×C1111yescharacteristic
1054C8—22no—
1055C8—22no—
1056C8—22no—
1057C8—22no—
1058C22—21no—
1059C22—21no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—41no—
1065C22—41no—
1066C22—42no—
1067C22—41no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—41no—
1072C22—41no—
1073C22—42no—
1074C22—42no—
1075C22—84no—
1076C22—162no—
1077C22—164no—
1078C22C11×#57712yes—
1079C22C23×D4×C1111yescharacteristic
1080C4—22no—
1081C4—21no—
1082C4—21no—
1083C4—21no—
1084C4—22no—
1085C4—21no—
1086C4—21no—
1087C4—22no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—41no—
1092C4—41no—
1093C4—42no—
1094C4C2×C11×H(5,𝔽2)11yescharacteristic
1095C4C11×#58511yescharacteristic
1096C2—22no—
1097C2—42no—
1098C2—42no—
1099C2—81no—
1100C2—82no—
1101C2—82no—
1102C2C11×#348811yescharacteristic
1103C2C2×C11×#57711yescharacteristic
1104C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#529 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3558C2semidirect
2. C11×#3520C2semidirect
3. C11×#3401C2semidirect
4. C11×#3373C2semidirect
5. C11×#3316C2semidirect
6. C11×#3306C2semidirect
7. C11×#3295C2semidirect
8. C11×#3282C2semidirect
9. C11×#3267C2semidirect
10. C11×#3264C2semidirect
11. C11×#3263C2semidirect
12. C11×#3246C2semidirect
13. C11×#3224C2semidirect
14. C11×#3215C2semidirect
15. C11×#3125C2semidirect
16. C11×#3109C2semidirect
17. C11×#3045C2semidirect
18. C2×C11×#463C2semidirect
19. C11×#2992C2semidirect
20. C2×C11×AGL(1,ℤ/8)C22semidirect
21. C2×C11×#135C22semidirect
22. C22×C11×SD16C22semidirect
26. C11×#559C22semidirect
27. C11×#556C22semidirect
28. C11×#554C22semidirect
31. D4×Q8×C11C22semidirect
34. C11×#547C22semidirect
35. C11×#547C22semidirect
37. C11×#546C22semidirect
38. C11×#546C22semidirect
40. C11×#542C22semidirect
41. C11×#542C22semidirect
45. C11×#535C22semidirect
47. C11×#533C22semidirect
53. C11×#520C22semidirect
54. C2×C4×D4×C11C22semidirect
55. C11×#497C22semidirect
57. C11×#495C22semidirect
58. C11×#489C22semidirect
59. C11×#489C22semidirect
60. C11×#486C22semidirect
61. C11×#483C22semidirect
62. C11×#481C22semidirect
63. C11×#481C22semidirect
64. C11×#476C22semidirect
65. C11×#476C22semidirect
66. C11×#476C22semidirect
67. C11×#476C22semidirect
68. C11×#475C22semidirect
69. C11×#475C22semidirect
70. C11×#470C22semidirect
72. C11×#465C22semidirect
73. C11×#465C22semidirect
74. C11×#465C22semidirect
75. C11×#465C22semidirect
76. C11×#464C22semidirect
77. C11×#464C22semidirect
78. C11×#464C22semidirect
79. C11×#464C22semidirect
80. C11×#463C22semidirect
81. C11×#463C22semidirect
82. C11×#463C22semidirect
83. C11×#463C22semidirect
84. C11×#463C22semidirect
85. C11×#463C22semidirect
86. C11×#461C22semidirect
87. C11×#460C22semidirect
88. C11×#460C22semidirect
90. C11×#459C22semidirect
91. C11×#459C22semidirect
92. C11×#452C22semidirect
93. C11×#452C22semidirect
94. C11×#451C22semidirect
96. C11×#450C22semidirect
98. C11×#449C22semidirect
99. C11×#447C22semidirect
100. C11×#447C22semidirect
101. C11×#446C22semidirect
102. C11×#442C22semidirect
103. C11×#442C22semidirect
104. C11×#442C22semidirect
105. C11×#441C22semidirect
106. C4×C11×SD16C22semidirect
107. C4×C11×SD16C22semidirect
108. C11×#435C22semidirect
109. C11×#435C22semidirect
110. C8×D4×C11C22semidirect
111. C11×#433C22semidirect
112. C11×#432C22semidirect
113. C11×#424C22semidirect
114. C2×C11×C4⋊C8C22semidirect
115. C11×#417C22semidirect
116. C2×C11×#103C22semidirect
118. C2×C11×#102C22semidirect
284. #62018C11direct (N × H)
423. #3558C2×C11semidirect
424. #3520C2×C11semidirect
425. #3401C2×C11semidirect
426. #3373C2×C11semidirect
427. #3316C2×C11semidirect
428. #3306C2×C11semidirect
429. #3295C2×C11semidirect
430. #3282C2×C11semidirect
431. #3267C2×C11semidirect
432. #3264C2×C11semidirect
433. #3263C2×C11semidirect
434. #3246C2×C11semidirect
435. #3224C2×C11semidirect
436. #3215C2×C11semidirect
437. #3125C2×C11semidirect
438. #3109C2×C11semidirect
439. #3045C2×C11semidirect
440. C2×#463C2×C11semidirect
441. #2992C2×C11semidirect
525. C2×AGL(1,ℤ/8)C22×C11semidirect
526. C2×#135C22×C11semidirect
527. C22×SD16C22×C11semidirect
531. #559C22×C11semidirect
532. #556C22×C11semidirect
533. #554C22×C11semidirect
536. D4×Q8C22×C11semidirect
539. #547C22×C11semidirect
540. #547C22×C11semidirect
542. #546C22×C11semidirect
543. #546C22×C11semidirect
545. #542C22×C11semidirect
546. #542C22×C11semidirect
550. #535C22×C11semidirect
552. #533C22×C11semidirect
558. #520C22×C11semidirect
559. C2×C4×D4C22×C11semidirect
560. #497C22×C11semidirect
562. #495C22×C11semidirect
563. #489C22×C11semidirect
564. #489C22×C11semidirect
565. #486C22×C11semidirect
566. #483C22×C11semidirect
567. #481C22×C11semidirect
568. #481C22×C11semidirect
569. #476C22×C11semidirect
570. #476C22×C11semidirect
571. #476C22×C11semidirect
572. #476C22×C11semidirect
573. #475C22×C11semidirect
574. #475C22×C11semidirect
575. #470C22×C11semidirect
577. #465C22×C11semidirect
578. #465C22×C11semidirect
579. #465C22×C11semidirect
580. #465C22×C11semidirect
581. #464C22×C11semidirect
582. #464C22×C11semidirect
583. #464C22×C11semidirect
584. #464C22×C11semidirect
585. #463C22×C11semidirect
586. #463C22×C11semidirect
587. #463C22×C11semidirect
588. #463C22×C11semidirect
589. #463C22×C11semidirect
590. #463C22×C11semidirect
591. #461C22×C11semidirect
592. #460C22×C11semidirect
593. #460C22×C11semidirect
595. #459C22×C11semidirect
596. #459C22×C11semidirect
597. #452C22×C11semidirect
598. #452C22×C11semidirect
599. #451C22×C11semidirect
601. #450C22×C11semidirect
603. #449C22×C11semidirect
604. #447C22×C11semidirect
605. #447C22×C11semidirect
606. #446C22×C11semidirect
607. #442C22×C11semidirect
608. #442C22×C11semidirect
609. #442C22×C11semidirect
610. #441C22×C11semidirect
611. C4×SD16C22×C11semidirect
612. C4×SD16C22×C11semidirect
613. #435C22×C11semidirect
614. #435C22×C11semidirect
615. C8×D4C22×C11semidirect
616. #433C22×C11semidirect
617. #432C22×C11semidirect
618. #424C22×C11semidirect
619. C2×C4⋊C8C22×C11semidirect
620. #417C22×C11semidirect
621. C2×#103C22×C11semidirect
623. C2×#102C22×C11semidirect
974. C11#62018direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35582
C11×#35202
C11×#34012
C11×#33732
C11×#33162
C11×#33062
C11×#32952
C11×#32822
C11×#32672
C11×#32642
C11×#32632
C11×#32462
C11×#32242
C11×#32152
C11×#31252
C11×#31092
C11×#30452
C2×C11×#4632
C11×#29922
#6201811