Finite Group Databasebeta

← C11×#61927 #14639120

Subgroups — C11×#61927 #14639120

Order 2816.

1718 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3555C211yesmaximal, characteristic, complemented
2C11×#3506C211yesmaximal, characteristic, complemented
3C11×#3401C212yesmaximal, complemented
4C11×#3398C211yesmaximal, characteristic, complemented
5C11×#3397C211yesmaximal, characteristic, complemented
6C11×#3394C212yesmaximal, complemented
7C11×#3393C211yesmaximal, characteristic, complemented
8C11×#3392C211yesmaximal, characteristic, complemented
9C11×#3371C212yesmaximal, complemented
10C11×#3369C211yesmaximal, characteristic, complemented
11C11×#3366C211yesmaximal, characteristic, complemented
12C11×#3365C212yesmaximal, complemented
13C11×#3362C211yesmaximal, characteristic, complemented
14C11×#3360C211yesmaximal, characteristic, complemented
15C11×#3224C212yesmaximal, complemented
16C11×#3222C212yesmaximal, complemented
17C11×#3212C211yesmaximal, characteristic, complemented
18C11×#3210C211yesmaximal, characteristic, complemented
19C11×#3125C212yesmaximal, complemented
20C11×#3120C212yesmaximal, complemented
21C11×#3105C211yesmaximal, characteristic, complemented
22C11×#3101C211yesmaximal, characteristic, complemented
23C11×#2986C211yesmaximal, characteristic, complemented
24C11×#563—22no—
25C11×#559C2212yes—
26C11×#559C2212yes—
27Q82×C11C2211yescharacteristic, complemented
28C11×#557C2211yescharacteristic, complemented
29C11×#557C2212yescomplemented
30C11×#556—21no—
31C11×#556C2211yescharacteristic
32C11×#556C2211yescharacteristic
33C11×#556C2211yescharacteristic, complemented
34C11×#556C2212yescomplemented
35C11×#555—21no—
36C11×#554C2211yescharacteristic, complemented
37C11×#553—22no—
38C11×#552—21no—
39C11×#550C2211yescharacteristic
40C11×#550C2211yescharacteristic
41C11×#547—21no—
42C11×#544—21no—
43C11×#542C2212yes—
44C11×#541—21no—
45C11×#541—22no—
46C11×#541C2212yes—
47C11×#538—22no—
48C11×#535C2212yes—
49C11×#533C2211yescharacteristic
50C11×#533C2211yescharacteristic
51C11×#532C2211yescharacteristic
52C11×#529C2211yescharacteristic
53C11×#525—21no—
54C11×#525—21no—
55C11×#520C2212yes—
56C2×C4×D4×C11C2211yescharacteristic
57C11×#497C2212yes—
58C11×#496C2212yes—
59C11×#495C2212yes—
60C11×#495C2212yescomplemented
61C11×#494C2211yescharacteristic, complemented
62C11×#492C2212yes—
63C11×#492C2211yescharacteristic, complemented
64C11×#490C2212yes—
65C11×#489C2212yes—
66C11×#488C2212yes—
67C11×#488C2212yescomplemented
68C11×#487C2211yescharacteristic, complemented
69C11×#486C2212yes—
70C11×#486C2211yescharacteristic, complemented
71C11×#484C2211yescharacteristic
72C11×#483C2212yes—
73C11×#481C2211yescharacteristic
74C11×#479C2212yescomplemented
75C11×#478C2211yescharacteristic
76C11×#478C2211yescharacteristic
77C11×#478C2212yescomplemented
78C11×#476C2211yescharacteristic
79C11×#476C2211yescharacteristic
80C11×#476C2212yescomplemented
81C11×#475C2212yescomplemented
82C11×#464C2212yes—
83C11×#464C2212yes—
84C11×#464C2212yes—
85C11×#464C2212yescomplemented
86C11×#464C2212yescomplemented
87C11×#464C2212yescomplemented
88C11×#463C2212yes—
89C11×#463C2211yescharacteristic
90C11×#463C2211yescharacteristic
91C11×#463C2212yescomplemented
92C11×#462C2211yescharacteristic, complemented
93C11×#462C2212yescomplemented
94C11×#461C2211yescharacteristic
95C11×#461C2211yescharacteristic
96C11×#461C2211yescharacteristic, complemented
97C11×#461C2212yescomplemented
98C11×#460C2212yes—
99C11×#460C2212yes—
100C11×#460C2212yes—
101C11×#460C2211yescharacteristic, complemented
102C11×#459C2212yes—
103C11×#459C2211yescharacteristic, complemented
104C11×#452C2212yes—
105C11×#452C2212yes—
106C11×#452C2212yes—
107C11×#450C2211yescharacteristic
108C11×#450C2212yes—
109C11×#449C2212yes—
110C11×#447C2211yescharacteristic
111C11×#446C2211yescharacteristic, complemented
112C11×#446C2211yescharacteristic, complemented
113C11×#446C2212yescomplemented
114C8×Q8×C11C2211yescharacteristic, complemented
115C8×Q8×C11C2211yescharacteristic, complemented
116C8×Q8×C11C2212yescomplemented
117C11×#442C2212yescomplemented
118C11×#441C2212yescomplemented
119C11×#441C2212yescomplemented
120C11×#440C2212yescomplemented
121C4×C11×Q16C2212yescomplemented
122C4×C11×SD16C2212yes—
123C4×C11×SD16C2212yes—
124C4×C11×SD16C2211yescharacteristic
125C4×C11×SD16C2211yescharacteristic
126C4×C11×SD16C2212yescomplemented
127C4×C11×SD16C2212yescomplemented
128C4×C11×SD16C2212yescomplemented
129C4×C11×D8C2211yescharacteristic
130C4×C11×D8C2211yescharacteristic
131C11×#433C2212yes—
132C11×#433C2212yes—
133C11×#431C2211yescharacteristic
134C11×#431C2211yescharacteristic
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41C2312yes—
138C22×D4×C11C2311yescharacteristic
139C23×C4×C11—21no—
140C2×C11×Q16C2312yes—
141C2×C11×Q16C2312yes—
142C2×C11×Q16C2312yes—
143C2×C11×SD16C2311yescharacteristic
144C2×C11×SD16C2312yes—
145C2×C11×SD16C2312yes—
146C2×C11×SD16C2312yes—
147C2×C11×SD16C2312yes—
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2311yescharacteristic
151C2×C11×D8C2311yescharacteristic
152C2×C11×D8C2312yes—
153C2×C11×D8C2311yescharacteristic
154C11×C4⋊Q8—22no—
155C11×C4⋊Q8—22no—
156C11×C4⋊Q8—21no—
157C11×C4⋊Q8D411yescharacteristic
158C11×C4⋊Q8D411yescharacteristic
159C11×C4⋊Q8C2312yes—
160C11×C4⋊Q8C2311yescharacteristic
161C11×C4⋊Q8C2311yescharacteristic
162C11×C4⋊Q8C2312yes—
163C11×C4⋊Q8C2311yescharacteristic
164C11×#127C2312yes—
165C11×#127C2311yescharacteristic
166C11×#127C2312yes—
167C11×#126—22no—
168C11×#126—22no—
169C11×#126—22no—
170C11×#126—22no—
171C11×#126—22no—
172C11×#126—22no—
173C11×#126—22no—
174C11×#126—22no—
175C11×#126—21no—
176C11×#125—22no—
177C11×#125—22no—
178C11×#125—22no—
179C11×#125—22no—
180C11×#125—22no—
181C11×#125—21no—
182C11×#125—21no—
183C11×#125D412yes—
184C11×#125C2312yes—
185C11×#125C2311yescharacteristic
186C11×#124—22no—
187C11×#124—22no—
188C11×#124—22no—
189C11×#124C2312yes—
190C11×#124C2312yes—
191C11×#124C2311yescharacteristic
192C11×#124C2312yes—
193C11×#124C2312yes—
194C11×#123—21no—
195C11×#123—22no—
196C11×#123—22no—
197C11×#123—22no—
198C11×#123—22no—
199C11×#123—22no—
200C11×C22⋊Q8—21no—
201C11×C22⋊Q8—21no—
202C11×C22⋊Q8—21no—
203C11×C22⋊Q8—21no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—21no—
206C11×C22⋊Q8—22no—
207C11×C22⋊Q8—22no—
208C11×C22⋊Q8D411yescharacteristic
209C11×C22⋊Q8D411yescharacteristic
210C11×C22⋊Q8D412yes—
211C11×C22⋊Q8C2311yescharacteristic
212C11×C22⋊Q8C2312yes—
213C11×#121—21no—
214C11×#121—21no—
215C11×#121—21no—
216C11×#121—21no—
217C11×#121—22no—
218C11×#121—22no—
219C11×#121—22no—
220C11×#121—22no—
221C11×#121C2311yescharacteristic
222C11×#120—22no—
223C11×#120—22no—
224C4×Q8×C11—21no—
225C4×Q8×C11—21no—
226C4×Q8×C11—22no—
227C4×Q8×C11—21no—
228C4×Q8×C11C2312yes—
229C4×Q8×C11C2312yes—
230C4×Q8×C11C2311yescharacteristic
231C4×Q8×C11C2312yes—
232C4×Q8×C11C2312yes—
233C4×Q8×C11C2312yes—
234C4×Q8×C11C2312yes—
235C4×Q8×C11C2311yescharacteristic
236C4×Q8×C11C2311yescharacteristic
237C4×Q8×C11C2312yes—
238C4×D4×C11—21no—
239C4×D4×C11—22no—
240C4×D4×C11—22no—
241C4×D4×C11—22no—
242C4×D4×C11—22no—
243C4×D4×C11—21no—
244C4×D4×C11—21no—
245C4×D4×C11—21no—
246C4×D4×C11—21no—
247C4×D4×C11C2311yescharacteristic
248C4×D4×C11C2311yescharacteristic
249C4×D4×C11C2311yescharacteristic
250C4×D4×C11C2311yescharacteristic
251C4×D4×C11C2312yes—
252C4×D4×C11C2312yes—
253C4×D4×C11C2311yescharacteristic
254C4×D4×C11C2312yes—
255C11×#117—21no—
256C11×#117—22no—
257C11×#117—21no—
258C11×#117—21no—
259C11×#117—22no—
260C11×#117—21no—
261C11×#117—21no—
262C11×#117C2312yes—
263C2×C11×C4⋊C4—22no—
264C2×C11×C4⋊C4—21no—
265C2×C11×C4⋊C4C2311yescharacteristic
266C2×C11×C22⋊C4—21no—
267C2×C42×C11C2311yescharacteristic
268C11×#107C2311yescharacteristic
269C11×#107C2311yescharacteristic
270C11×#106C2311yescharacteristic
271C11×#106C2312yes—
272C11×#106C2311yescharacteristic
273C11×#106C2312yes—
274C11×C4⋊C8C2311yescharacteristic
275C11×C4⋊C8C2311yescharacteristic
276C11×C4⋊C8C2311yescharacteristic
277C11×C4⋊C8C2311yescharacteristic
278C11×C4⋊C8C2312yes—
279C11×C4⋊C8C2312yes—
280C11×C4⋊C8C2312yes—
281C11×C4⋊C8C2312yes—
282C11×#103C2312yes—
283C11×#103C2312yes—
284C11×#103C2311yescharacteristic
285C11×#103C2312yes—
286C11×#103C2312yes—
287C11×#103C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#102C2311yescharacteristic
291C11×#102C2312yes—
292C11×#102C2311yescharacteristic
293C11×#102C2312yes—
294C11×#102C2312yes—
295C11×#102C2311yescharacteristic
296C11×#102C2311yescharacteristic
297C11×#102C2311yescharacteristic
298C11×#102C2311yescharacteristic
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×C22⋊C8C2311yescharacteristic
303C11×C22⋊C8C2312yes—
304C11×C22⋊C8C2311yescharacteristic
305C11×#97C2312yes—
306C11×#97C2312yes—
307C4×C8×C11C2312yes—
308C4×C8×C11C2311yescharacteristic
309C4×C8×C11C2311yescharacteristic
310C4×C8×C11C2312yes—
311C4×C8×C11C2312yes—
312#61927C1111yesmaximal, characteristic, direct product factor, Sylow
313C24×C11—21no—
314C11×#41—42no—
315C11×#41—42no—
316C11×#41—82no—
317C11×#41—82no—
318C2×Q8×C11—21no—
319C2×Q8×C11—22no—
320C2×Q8×C11C2×D411yescharacteristic
321C2×Q8×C11C2×D411yescharacteristic
322C2×Q8×C11C2×D412yes—
323C2×Q8×C11C2412yes—
324C2×Q8×C11C2411yescharacteristic
325C2×Q8×C11C2412yes—
326C2×D4×C11—22no—
327C2×D4×C11—21no—
328C2×D4×C11—21no—
329C2×D4×C11—21no—
330C2×D4×C11—22no—
331C2×D4×C11—22no—
332C2×D4×C11—21no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—41no—
336C2×D4×C11—41no—
337C2×D4×C11C2411yescharacteristic
338C2×D4×C11C2411yescharacteristic
339C2×D4×C11C2412yes—
340C2×D4×C11C2411yescharacteristic
341C22×C4×C11—21no—
342C22×C4×C11—21no—
343C22×C4×C11—22no—
344C22×C4×C11—21no—
345C22×C4×C11—21no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—22no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11—82no—
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2×D411yescharacteristic
354C22×C4×C11C2411yescharacteristic
355C11×Q16—42no—
356C11×Q16—42no—
357C11×Q16—42no—
358C11×SD16—42no—
359C11×SD16—41no—
360C11×SD16—41no—
361C11×SD16—42no—
362C11×SD16—42no—
363C11×SD16—42no—
364C11×SD16—42no—
365C11×SD16—42no—
366C11×D8—41no—
367C11×D8—42no—
368C11×D8—41no—
369C2×C8×C11C2411yescharacteristic
370C2×C8×C11C2411yescharacteristic
371C2×C8×C11C2412yes—
372C2×C8×C11C2411yescharacteristic
373C2×C8×C11C2412yes—
374C2×C8×C11C2411yescharacteristic
375C11×C4⋊C4—21no—
376C11×C4⋊C4—21no—
377C11×C4⋊C4—22no—
378C11×C4⋊C4—22no—
379C11×C4⋊C4—22no—
380C11×C4⋊C4—21no—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4C2×D411yescharacteristic
398C11×C4⋊C4C2×D412yes—
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2×D412yes—
403C11×C4⋊C4C2×D412yes—
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2412yes—
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2411yescharacteristic
411C11×C22⋊C4—22no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—21no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—21no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—21no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4C2×D412yes—
433C11×C22⋊C4C2×D412yes—
434C42×C11—22no—
435C42×C11—22no—
436C42×C11—22no—
437C42×C11—21no—
438C42×C11—22no—
439C42×C11—22no—
440C42×C11—22no—
441C42×C11C2×D411yescharacteristic
442C42×C11C2×D411yescharacteristic
443C42×C11C2411yescharacteristic
444C42×C11C2411yescharacteristic
445C42×C11C2412yes—
446C42×C11C2412yes—
447#3555C2×C1111yescharacteristic, complemented
448#3506C2×C1111yescharacteristic, complemented
449#3401C2×C1112yescomplemented
450#3398C2×C1111yescharacteristic, complemented
451#3397C2×C1111yescharacteristic, complemented
452#3394C2×C1112yescomplemented
453#3393C2×C1111yescharacteristic, complemented
454#3392C2×C1111yescharacteristic, complemented
455#3371C2×C1112yescomplemented
456#3369C2×C1111yescharacteristic, complemented
457#3366C2×C1111yescharacteristic, complemented
458#3365C2×C1112yescomplemented
459#3362C2×C1111yescharacteristic, complemented
460#3360C2×C1111yescharacteristic, complemented
461#3224C2×C1112yescomplemented
462#3222C2×C1112yescomplemented
463#3212C2×C1111yescharacteristic, complemented
464#3210C2×C1111yescharacteristic, complemented
465#3125C2×C1112yescomplemented
466#3120C2×C1112yescomplemented
467#3105C2×C1111yescharacteristic, complemented
468#3101C2×C1111yescharacteristic, complemented
469#2986C2×C1111yescharacteristic, complemented
470C23×C11—21no—
471C23×C11—21no—
472C23×C11—21no—
473C23×C11—22no—
474C23×C11—42no—
475C23×C11—81no—
476C23×C11—81no—
477C23×C11C22×D411yescharacteristic
478Q8×C11—22no—
479Q8×C11—22no—
480Q8×C11—21no—
481Q8×C11—22no—
482Q8×C11—22no—
483Q8×C11—21no—
484Q8×C11—22no—
485Q8×C11—22no—
486Q8×C11—42no—
487Q8×C11—81no—
488Q8×C11—82no—
489D4×C11—21no—
490D4×C11—21no—
491D4×C11—21no—
492D4×C11—21no—
493D4×C11—22no—
494D4×C11—21no—
495D4×C11—21no—
496D4×C11—22no—
497D4×C11—42no—
498D4×C11—44no—
499D4×C11—42no—
500D4×C11—81no—
501D4×C11—82no—
502D4×C11—82no—
503D4×C11—82no—
504D4×C11—82no—
505D4×C11—81no—
506C2×C4×C11—22no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—22no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—22no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—22no—
517C2×C4×C11—41no—
518C2×C4×C11—44no—
519C2×C4×C11—42no—
520C2×C4×C11—42no—
521C2×C4×C11—42no—
522C2×C4×C11—82no—
523C2×C4×C11—81no—
524C2×C4×C11—81no—
525C2×C4×C11—82no—
526C2×C4×C11—82no—
527C2×C4×C11—81no—
528C2×C4×C11C22×D411yescharacteristic
529C2×C4×C11C22×D412yes—
530C2×C4×C11C22×D412yes—
531C2×C4×C11C22×D412yes—
532C2×C4×C11C22×D412yes—
533C2×C4×C11C22×D411yescharacteristic
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C2511yescharacteristic
538C8×C11—21no—
539C8×C11—22no—
540C8×C11—21no—
541C8×C11—21no—
542C8×C11—22no—
543C8×C11—21no—
544#563—22no—
545#559C22×C1112yes—
546#559C22×C1112yes—
547Q82C22×C1111yescharacteristic, complemented
548#557C22×C1111yescharacteristic, complemented
549#557C22×C1112yescomplemented
550#556—21no—
551#556C22×C1111yescharacteristic
552#556C22×C1111yescharacteristic
553#556C22×C1111yescharacteristic, complemented
554#556C22×C1112yescomplemented
555#555—21no—
556#554C22×C1111yescharacteristic, complemented
557#553—22no—
558#552—21no—
559#550C22×C1111yescharacteristic
560#550C22×C1111yescharacteristic
561#547—21no—
562#544—21no—
563#542C22×C1112yes—
564#541—21no—
565#541—22no—
566#541C22×C1112yes—
567#538—22no—
568#535C22×C1112yes—
569#533C22×C1111yescharacteristic
570#533C22×C1111yescharacteristic
571#532C22×C1111yescharacteristic
572#529C22×C1111yescharacteristic
573#525—21no—
574#525—21no—
575#520C22×C1112yes—
576C2×C4×D4C22×C1111yescharacteristic
577#497C22×C1112yes—
578#496C22×C1112yes—
579#495C22×C1112yes—
580#495C22×C1112yescomplemented
581#494C22×C1111yescharacteristic, complemented
582#492C22×C1112yes—
583#492C22×C1111yescharacteristic, complemented
584#490C22×C1112yes—
585#489C22×C1112yes—
586#488C22×C1112yes—
587#488C22×C1112yescomplemented
588#487C22×C1111yescharacteristic, complemented
589#486C22×C1112yes—
590#486C22×C1111yescharacteristic, complemented
591#484C22×C1111yescharacteristic
592#483C22×C1112yes—
593#481C22×C1111yescharacteristic
594#479C22×C1112yescomplemented
595#478C22×C1111yescharacteristic
596#478C22×C1111yescharacteristic
597#478C22×C1112yescomplemented
598#476C22×C1111yescharacteristic
599#476C22×C1111yescharacteristic
600#476C22×C1112yescomplemented
601#475C22×C1112yescomplemented
602#464C22×C1112yes—
603#464C22×C1112yes—
604#464C22×C1112yes—
605#464C22×C1112yescomplemented
606#464C22×C1112yescomplemented
607#464C22×C1112yescomplemented
608#463C22×C1112yes—
609#463C22×C1111yescharacteristic
610#463C22×C1111yescharacteristic
611#463C22×C1112yescomplemented
612#462C22×C1111yescharacteristic, complemented
613#462C22×C1112yescomplemented
614#461C22×C1111yescharacteristic
615#461C22×C1111yescharacteristic
616#461C22×C1111yescharacteristic, complemented
617#461C22×C1112yescomplemented
618#460C22×C1112yes—
619#460C22×C1112yes—
620#460C22×C1112yes—
621#460C22×C1111yescharacteristic, complemented
622#459C22×C1112yes—
623#459C22×C1111yescharacteristic, complemented
624#452C22×C1112yes—
625#452C22×C1112yes—
626#452C22×C1112yes—
627#450C22×C1112yes—
628#450C22×C1111yescharacteristic
629#449C22×C1112yes—
630#447C22×C1111yescharacteristic
631#446C22×C1111yescharacteristic, complemented
632#446C22×C1111yescharacteristic, complemented
633#446C22×C1112yescomplemented
634C8×Q8C22×C1111yescharacteristic, complemented
635C8×Q8C22×C1111yescharacteristic, complemented
636C8×Q8C22×C1112yescomplemented
637#442C22×C1112yescomplemented
638#441C22×C1112yescomplemented
639#441C22×C1112yescomplemented
640#440C22×C1112yescomplemented
641C4×Q16C22×C1112yescomplemented
642C4×SD16C22×C1112yes—
643C4×SD16C22×C1112yes—
644C4×SD16C22×C1111yescharacteristic
645C4×SD16C22×C1111yescharacteristic
646C4×SD16C22×C1112yescomplemented
647C4×SD16C22×C1112yescomplemented
648C4×SD16C22×C1112yescomplemented
649C4×D8C22×C1111yescharacteristic
650C4×D8C22×C1111yescharacteristic
651#433C22×C1112yes—
652#433C22×C1112yes—
653#431C22×C1111yescharacteristic
654#431C22×C1111yescharacteristic
655C22×C11—21no—
656C22×C11—21no—
657C22×C11—21no—
658C22×C11—41no—
659C22×C11—42no—
660C22×C11—41no—
661C22×C11—41no—
662C22×C11—42no—
663C22×C11—41no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—41no—
669C22×C11—42no—
670C22×C11—84no—
671C22×C11C23×D411yescharacteristic
672C4×C11—21no—
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—21no—
677C4×C11—21no—
678C4×C11—22no—
679C4×C11—22no—
680C4×C11—42no—
681C4×C11—41no—
682C4×C11—42no—
683C4×C11—41no—
684C4×C11—42no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11—41no—
688C4×C11#57712yes—
689C4×C11#58511yescharacteristic
690C4×C11#58511yescharacteristic
691C2×#41—21no—
692C2×#41—21no—
693C2×#41C23×C1112yes—
694C22×D4C23×C1111yescharacteristic
695C23×C4—21no—
696C2×Q16C23×C1112yes—
697C2×Q16C23×C1112yes—
698C2×Q16C23×C1112yes—
699C2×SD16C23×C1111yescharacteristic
700C2×SD16C23×C1112yes—
701C2×SD16C23×C1112yes—
702C2×SD16C23×C1111yescharacteristic
703C2×SD16C23×C1112yes—
704C2×SD16C23×C1112yes—
705C2×SD16C23×C1112yes—
706C2×SD16C23×C1112yes—
707C2×D8C23×C1111yescharacteristic
708C2×D8C23×C1111yescharacteristic
709C2×D8C23×C1112yes—
710C4⋊Q8—22no—
711C4⋊Q8—22no—
712C4⋊Q8—21no—
713C4⋊Q8D4×C1111yescharacteristic
714C4⋊Q8D4×C1111yescharacteristic
715C4⋊Q8C23×C1111yescharacteristic
716C4⋊Q8C23×C1111yescharacteristic
717C4⋊Q8C23×C1112yes—
718C4⋊Q8C23×C1111yescharacteristic
719C4⋊Q8C23×C1112yes—
720#127C23×C1111yescharacteristic
721#127C23×C1112yes—
722#127C23×C1112yes—
723#126—22no—
724#126—22no—
725#126—22no—
726#126—22no—
727#126—22no—
728#126—22no—
729#126—22no—
730#126—22no—
731#126—21no—
732#125—22no—
733#125—22no—
734#125—22no—
735#125—22no—
736#125—22no—
737#125—21no—
738#125—21no—
739#125D4×C1112yes—
740#125C23×C1111yescharacteristic
741#125C23×C1112yes—
742#124—22no—
743#124—22no—
744#124—22no—
745#124C23×C1111yescharacteristic
746#124C23×C1112yes—
747#124C23×C1112yes—
748#124C23×C1112yes—
749#124C23×C1112yes—
750#123—21no—
751#123—22no—
752#123—22no—
753#123—22no—
754#123—22no—
755#123—22no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—22no—
761C22⋊Q8—21no—
762C22⋊Q8—22no—
763C22⋊Q8—22no—
764C22⋊Q8D4×C1111yescharacteristic
765C22⋊Q8D4×C1111yescharacteristic
766C22⋊Q8D4×C1112yes—
767C22⋊Q8C23×C1111yescharacteristic
768C22⋊Q8C23×C1112yes—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—21no—
773#121—22no—
774#121—22no—
775#121—22no—
776#121—22no—
777#121C23×C1111yescharacteristic
778#120—22no—
779#120—22no—
780C4×Q8—21no—
781C4×Q8—21no—
782C4×Q8—22no—
783C4×Q8—21no—
784C4×Q8C23×C1112yes—
785C4×Q8C23×C1112yes—
786C4×Q8C23×C1111yescharacteristic
787C4×Q8C23×C1112yes—
788C4×Q8C23×C1112yes—
789C4×Q8C23×C1112yes—
790C4×Q8C23×C1112yes—
791C4×Q8C23×C1111yescharacteristic
792C4×Q8C23×C1111yescharacteristic
793C4×Q8C23×C1112yes—
794C4×D4—21no—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—22no—
799C4×D4—21no—
800C4×D4—21no—
801C4×D4—21no—
802C4×D4—21no—
803C4×D4C23×C1111yescharacteristic
804C4×D4C23×C1111yescharacteristic
805C4×D4C23×C1111yescharacteristic
806C4×D4C23×C1111yescharacteristic
807C4×D4C23×C1112yes—
808C4×D4C23×C1112yes—
809C4×D4C23×C1111yescharacteristic
810C4×D4C23×C1112yes—
811#117—21no—
812#117—22no—
813#117—21no—
814#117—21no—
815#117—22no—
816#117—21no—
817#117—21no—
818#117C23×C1112yes—
819C2×C4⋊C4—22no—
820C2×C4⋊C4—21no—
821C2×C4⋊C4C23×C1111yescharacteristic
822C2×C22⋊C4—21no—
823C2×C42C23×C1111yescharacteristic
824#107C23×C1111yescharacteristic
825#107C23×C1111yescharacteristic
826#106C23×C1111yescharacteristic
827#106C23×C1112yes—
828#106C23×C1111yescharacteristic
829#106C23×C1112yes—
830C4⋊C8C23×C1111yescharacteristic
831C4⋊C8C23×C1111yescharacteristic
832C4⋊C8C23×C1111yescharacteristic
833C4⋊C8C23×C1111yescharacteristic
834C4⋊C8C23×C1112yes—
835C4⋊C8C23×C1112yes—
836C4⋊C8C23×C1112yes—
837C4⋊C8C23×C1112yes—
838#103C23×C1111yescharacteristic
839#103C23×C1112yes—
840#103C23×C1112yes—
841#103C23×C1111yescharacteristic
842#103C23×C1112yes—
843#103C23×C1112yes—
844#103C23×C1112yes—
845#103C23×C1112yes—
846#102C23×C1111yescharacteristic
847#102C23×C1111yescharacteristic
848#102C23×C1111yescharacteristic
849#102C23×C1111yescharacteristic
850#102C23×C1111yescharacteristic
851#102C23×C1111yescharacteristic
852#102C23×C1112yes—
853#102C23×C1112yes—
854#102C23×C1112yes—
855#102C23×C1112yes—
856#102C23×C1112yes—
857#102C23×C1112yes—
858C22⋊C8C23×C1111yescharacteristic
859C22⋊C8C23×C1112yes—
860C22⋊C8C23×C1111yescharacteristic
861#97C23×C1112yes—
862#97C23×C1112yes—
863C4×C8C23×C1111yescharacteristic
864C4×C8C23×C1111yescharacteristic
865C4×C8C23×C1112yes—
866C4×C8C23×C1112yes—
867C4×C8C23×C1112yes—
868C2×C11—41no—
869C2×C11—81no—
870C2×C11—82no—
871C2×C11—81no—
872C2×C11—81no—
873C2×C11#348711yescharacteristic
874C2×C11C2×#57711yescharacteristic
875C2×C11#358411yescharacteristic
876C24—21no—
877#41—42no—
878#41—42no—
879#41—82no—
880#41—82no—
881C2×Q8—21no—
882C2×Q8—22no—
883C2×Q8C2×D4×C1111yescharacteristic
884C2×Q8C2×D4×C1111yescharacteristic
885C2×Q8C2×D4×C1112yes—
886C2×Q8C24×C1112yes—
887C2×Q8C24×C1111yescharacteristic
888C2×Q8C24×C1112yes—
889C2×D4—22no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—22no—
894C2×D4—22no—
895C2×D4—21no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4C24×C1111yescharacteristic
901C2×D4C24×C1111yescharacteristic
902C2×D4C24×C1112yes—
903C2×D4C24×C1111yescharacteristic
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—82no—
915C22×C4C2×D4×C1111yescharacteristic
916C22×C4C2×D4×C1111yescharacteristic
917C22×C4C24×C1111yescharacteristic
918Q16—42no—
919Q16—42no—
920Q16—42no—
921SD16—42no—
922SD16—42no—
923SD16—42no—
924SD16—41no—
925SD16—42no—
926SD16—42no—
927SD16—42no—
928SD16—41no—
929D8—41no—
930D8—42no—
931D8—41no—
932C2×C8C24×C1111yescharacteristic
933C2×C8C24×C1111yescharacteristic
934C2×C8C24×C1112yes—
935C2×C8C24×C1111yescharacteristic
936C2×C8C24×C1112yes—
937C2×C8C24×C1111yescharacteristic
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—21no—
960C4⋊C4C2×D4×C1111yescharacteristic
961C4⋊C4C2×D4×C1112yes—
962C4⋊C4C2×D4×C1111yescharacteristic
963C4⋊C4C2×D4×C1112yes—
964C4⋊C4C2×D4×C1112yes—
965C4⋊C4C2×D4×C1112yes—
966C4⋊C4C2×D4×C1112yes—
967C4⋊C4C2×D4×C1112yes—
968C4⋊C4C2×D4×C1112yes—
969C4⋊C4C24×C1112yes—
970C4⋊C4C24×C1111yescharacteristic
971C4⋊C4C24×C1111yescharacteristic
972C4⋊C4C24×C1111yescharacteristic
973C4⋊C4C24×C1111yescharacteristic
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—21no—
980C22⋊C4—21no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—21no—
986C22⋊C4—21no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—21no—
994C22⋊C4—22no—
995C22⋊C4C2×D4×C1112yes—
996C22⋊C4C2×D4×C1112yes—
997C42—22no—
998C42—22no—
999C42—22no—
1000C42—21no—
1001C42—22no—
1002C42—22no—
1003C42—22no—
1004C42C2×D4×C1111yescharacteristic
1005C42C2×D4×C1111yescharacteristic
1006C42C24×C1111yescharacteristic
1007C42C24×C1111yescharacteristic
1008C42C24×C1112yes—
1009C42C24×C1112yes—
1010C11#6192711yescharacteristic, direct product factor, Sylow
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—42no—
1016C23—81no—
1017C23—81no—
1018C23C22×D4×C1111yescharacteristic
1019Q8—22no—
1020Q8—22no—
1021Q8—21no—
1022Q8—22no—
1023Q8—22no—
1024Q8—21no—
1025Q8—22no—
1026Q8—22no—
1027Q8—42no—
1028Q8—81no—
1029Q8—82no—
1030D4—21no—
1031D4—21no—
1032D4—21no—
1033D4—21no—
1034D4—22no—
1035D4—21no—
1036D4—21no—
1037D4—22no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—81no—
1042D4—82no—
1043D4—82no—
1044D4—82no—
1045D4—82no—
1046D4—81no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—41no—
1059C2×C4—44no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—82no—
1064C2×C4—81no—
1065C2×C4—81no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—81no—
1069C2×C4C22×D4×C1111yescharacteristic
1070C2×C4C22×D4×C1112yes—
1071C2×C4C22×D4×C1112yes—
1072C2×C4C22×D4×C1112yes—
1073C2×C4C22×D4×C1112yes—
1074C2×C4C22×D4×C1111yescharacteristic
1075C2×C4C22×D4×C1111yescharacteristic
1076C2×C4C22×D4×C1111yescharacteristic
1077C2×C4C22×D4×C1111yescharacteristic
1078C2×C4C25×C1111yescharacteristic
1079C8—21no—
1080C8—22no—
1081C8—21no—
1082C8—22no—
1083C8—21no—
1084C8—21no—
1085C22—21no—
1086C22—21no—
1087C22—21no—
1088C22—42no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—42no—
1096C22—41no—
1097C22—42no—
1098C22—41no—
1099C22—41no—
1100C22—84no—
1101C22C23×D4×C1111yescharacteristic
1102C4—21no—
1103C4—21no—
1104C4—22no—
1105C4—22no—
1106C4—21no—
1107C4—21no—
1108C4—22no—
1109C4—22no—
1110C4—42no—
1111C4—41no—
1112C4—42no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4C11×#57712yes—
1119C4C11×#58511yescharacteristic
1120C4C11×#58511yescharacteristic
1121C2—41no—
1122C2—81no—
1123C2—81no—
1124C2—82no—
1125C2—81no—
1126C2C11×#348711yescharacteristic
1127C2C2×C11×#57711yescharacteristic
1128C2C11×#358411yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3555C2semidirect
2. C11×#3506C2semidirect
3. C11×#3401C2semidirect
4. C11×#3398C2semidirect
5. C11×#3397C2semidirect
6. C11×#3394C2semidirect
7. C11×#3393C2semidirect
8. C11×#3392C2semidirect
9. C11×#3371C2semidirect
10. C11×#3369C2semidirect
11. C11×#3366C2semidirect
12. C11×#3365C2semidirect
13. C11×#3362C2semidirect
14. C11×#3360C2semidirect
15. C11×#3224C2semidirect
16. C11×#3222C2semidirect
17. C11×#3212C2semidirect
18. C11×#3210C2semidirect
19. C11×#3125C2semidirect
20. C11×#3120C2semidirect
21. C11×#3105C2semidirect
22. C11×#3101C2semidirect
23. C11×#2986C2semidirect
27. Q82×C11C22semidirect
28. C11×#557C22semidirect
29. C11×#557C22semidirect
33. C11×#556C22semidirect
34. C11×#556C22semidirect
36. C11×#554C22semidirect
60. C11×#495C22semidirect
61. C11×#494C22semidirect
63. C11×#492C22semidirect
67. C11×#488C22semidirect
68. C11×#487C22semidirect
70. C11×#486C22semidirect
74. C11×#479C22semidirect
77. C11×#478C22semidirect
80. C11×#476C22semidirect
81. C11×#475C22semidirect
85. C11×#464C22semidirect
86. C11×#464C22semidirect
87. C11×#464C22semidirect
91. C11×#463C22semidirect
92. C11×#462C22semidirect
93. C11×#462C22semidirect
96. C11×#461C22semidirect
97. C11×#461C22semidirect
101. C11×#460C22semidirect
103. C11×#459C22semidirect
111. C11×#446C22semidirect
112. C11×#446C22semidirect
113. C11×#446C22semidirect
114. C8×Q8×C11C22semidirect
115. C8×Q8×C11C22semidirect
116. C8×Q8×C11C22semidirect
117. C11×#442C22semidirect
118. C11×#441C22semidirect
119. C11×#441C22semidirect
120. C11×#440C22semidirect
121. C4×C11×Q16C22semidirect
126. C4×C11×SD16C22semidirect
127. C4×C11×SD16C22semidirect
128. C4×C11×SD16C22semidirect
312. #61927C11direct (N × H)
447. #3555C2×C11semidirect
448. #3506C2×C11semidirect
449. #3401C2×C11semidirect
450. #3398C2×C11semidirect
451. #3397C2×C11semidirect
452. #3394C2×C11semidirect
453. #3393C2×C11semidirect
454. #3392C2×C11semidirect
455. #3371C2×C11semidirect
456. #3369C2×C11semidirect
457. #3366C2×C11semidirect
458. #3365C2×C11semidirect
459. #3362C2×C11semidirect
460. #3360C2×C11semidirect
461. #3224C2×C11semidirect
462. #3222C2×C11semidirect
463. #3212C2×C11semidirect
464. #3210C2×C11semidirect
465. #3125C2×C11semidirect
466. #3120C2×C11semidirect
467. #3105C2×C11semidirect
468. #3101C2×C11semidirect
469. #2986C2×C11semidirect
547. Q82C22×C11semidirect
548. #557C22×C11semidirect
549. #557C22×C11semidirect
553. #556C22×C11semidirect
554. #556C22×C11semidirect
556. #554C22×C11semidirect
580. #495C22×C11semidirect
581. #494C22×C11semidirect
583. #492C22×C11semidirect
587. #488C22×C11semidirect
588. #487C22×C11semidirect
590. #486C22×C11semidirect
594. #479C22×C11semidirect
597. #478C22×C11semidirect
600. #476C22×C11semidirect
601. #475C22×C11semidirect
605. #464C22×C11semidirect
606. #464C22×C11semidirect
607. #464C22×C11semidirect
611. #463C22×C11semidirect
612. #462C22×C11semidirect
613. #462C22×C11semidirect
616. #461C22×C11semidirect
617. #461C22×C11semidirect
621. #460C22×C11semidirect
623. #459C22×C11semidirect
631. #446C22×C11semidirect
632. #446C22×C11semidirect
633. #446C22×C11semidirect
634. C8×Q8C22×C11semidirect
635. C8×Q8C22×C11semidirect
636. C8×Q8C22×C11semidirect
637. #442C22×C11semidirect
638. #441C22×C11semidirect
639. #441C22×C11semidirect
640. #440C22×C11semidirect
641. C4×Q16C22×C11semidirect
646. C4×SD16C22×C11semidirect
647. C4×SD16C22×C11semidirect
648. C4×SD16C22×C11semidirect
1010. C11#61927direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35552
C11×#35062
C11×#34012
C11×#33982
C11×#33972
C11×#33942
C11×#33932
C11×#33922
C11×#33712
C11×#33692
C11×#33662
C11×#33652
C11×#33622
C11×#33602
C11×#32242
C11×#32222
C11×#32122
C11×#32102
C11×#31252
C11×#31202
C11×#31052
C11×#31012
C11×#29862
#6192711