Finite Group Databasebeta

← C11×#61467 #14638660

Subgroups — C11×#61467 #14638660

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3482C211yesmaximal, characteristic, complemented
2C11×#3480C211yesmaximal, characteristic, complemented
3C11×#3394C211yesmaximal, characteristic, complemented
4C11×#3383C211yesmaximal, characteristic, complemented
5C11×#3365C211yesmaximal, characteristic, complemented
6C11×#3364C211yesmaximal, characteristic, complemented
7C11×#3353C211yesmaximal, characteristic, complemented
8C11×#3351C212yesmaximal, complemented
9C11×#3332C211yesmaximal, characteristic, complemented
10C11×#3328C211yesmaximal, characteristic, complemented
11C11×#3327C212yesmaximal, complemented
12C11×#3326C212yesmaximal, complemented
13C11×#3278C211yesmaximal, characteristic, complemented
14C11×#3277C212yesmaximal, complemented
15C11×#3183C212yesmaximal, complemented
16C11×#3182C211yesmaximal, characteristic, complemented
17C11×#3117C212yesmaximal, complemented
18C11×#3115C211yesmaximal, characteristic, complemented
19C11×#3113C211yesmaximal, characteristic, complemented
20C11×#3111C212yesmaximal, complemented
21C11×#2971C211yesmaximal, characteristic, complemented
22C4×C11×#137C211yesmaximal, characteristic, complemented
23C4×C11×#137C212yesmaximal, complemented
24C2×C11×#137C2211yescharacteristic
25C2×C11×#137C2212yes—
26C11×#559—21no—
27C11×#559C2211yescharacteristic
28C11×#557C2211yescharacteristic
29C11×#557C2211yescharacteristic
30C11×#556—21no—
31C11×#556—21no—
32C11×#556C2211yescharacteristic
33C11×#556C2211yescharacteristic
34C11×#553—22no—
35C11×#553C2212yes—
36C11×#552—22no—
37C11×#552C2212yes—
38C11×#550C2211yescharacteristic
39D4×Q8×C11C2211yescharacteristic
40C11×#548C2212yes—
41C11×#548C2212yes—
42C11×#547—21no—
43C11×#547C2211yescharacteristic
44C11×#533—21no—
45C11×#533C2211yescharacteristic
46C11×#532—21no—
47C11×#532C2211yescharacteristic
48C11×#529—22no—
49C11×#529—22no—
50C11×#529C2212yes—
51C11×#529C2212yes—
52C4×C11×#41—21no—
53C4×C11×#41—21no—
54C4×C11×#41C2212yes—
55C4×C11×#41C2211yescharacteristic
56C4×C11×#41C2211yescharacteristic
57C2×C4×Q8×C11C2211yescharacteristic
58C2×C4×Q8×C11C2212yes—
59C11×#500C2211yescharacteristic
60C11×#499C2212yes—
61C11×#495C2212yes—
62C11×#492C2211yescharacteristic
63C11×#488C2212yes—
64C11×#488C2212yes—
65C11×#487C2211yescharacteristic
66C11×#486C2211yescharacteristic
67C11×#485C2212yes—
68C11×#484C2212yes—
69C11×#483C2212yes—
70C11×#482C2212yes—
71C11×#482C2212yes—
72C11×#481C2212yes—
73C11×#479C2212yes—
74C11×#479C2212yes—
75C11×#479C2212yes—
76C11×#478C2212yes—
77C11×#475C2211yescharacteristic
78C11×#475C2211yescharacteristic
79C11×#475C2211yescharacteristic
80C11×#474C2211yescharacteristic
81C11×#470C2212yes—
82C11×#469C2212yes—
83C11×#468C2212yes—
84C11×#468C2212yes—
85C11×#468C2212yes—
86C11×#468C2212yes—
87C11×#464C2212yes—
88C11×#464C2212yes—
89C11×#464C2212yes—
90C11×#463C2212yes—
91C11×#462C2211yescharacteristic
92C11×#462C2211yescharacteristic
93C11×#460C2211yescharacteristic
94C11×#459C2211yescharacteristic
95C11×#452C2212yes—
96C11×#451C2212yes—
97C11×#451C2212yes—
98C11×#449C2212yes—
99C11×#449C2212yes—
100C11×#448C2212yes—
101C8×Q8×C11C2211yescharacteristic
102C8×Q8×C11C2211yescharacteristic
103C11×#442C2212yes—
104C11×#441C2212yes—
105C11×#441C2211yescharacteristic
106C11×#441C2212yes—
107C11×#441C2211yescharacteristic
108C11×#440C2212yes—
109C11×#440C2212yes—
110C11×#440C2211yescharacteristic
111C11×#440C2211yescharacteristic
112C11×#440C2212yes—
113C4×C11×Q16C2212yes—
114C4×C11×Q16C2211yescharacteristic
115C4×C11×Q16C2212yes—
116C4×C11×Q16C2211yescharacteristic
117C4×C11×SD16C2212yes—
118C4×C11×SD16C2211yescharacteristic
119C4×C11×SD16C2212yes—
120C4×C11×SD16C2211yescharacteristic
121C11×#436C2212yes—
122C11×#436C2211yescharacteristic
123C11×#436C2212yes—
124C11×#436C2211yescharacteristic
125C11×#432C2212yes—
126C11×#432C2211yescharacteristic
127C11×#428C2211yescharacteristic
128C11×#428C2212yes—
129C11×#419C2212yes—
130C11×#419C2211yescharacteristic
131C11×#417C2211yescharacteristic
132C11×#417C2212yes—
133C4×C11×M16C2211yescharacteristic
134C4×C11×M16C2212yes—
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41D411yescharacteristic
138C2×C11×#41C2311yescharacteristic
139C2×C11×#41C2312yes—
140C22×Q8×C11C2311yescharacteristic
141C22×Q8×C11C2312yes—
142C11×#137—24no—
143C11×#137—28no—
144C2×C11×Q16C2311yescharacteristic
145C2×C11×Q16C2312yes—
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2311yescharacteristic
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2311yescharacteristic
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2311yescharacteristic
152C2×C11×SD16C2312yes—
153C2×C11×D8C2312yes—
154C2×C11×M16C2311yescharacteristic
155C2×C11×M16C2312yes—
156C2×C11×M16C2311yescharacteristic
157C2×C11×M16C2312yes—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8—21no—
160C11×C4⋊Q8—21no—
161C11×C4⋊Q8C2311yescharacteristic
162C11×C4⋊Q8C2311yescharacteristic
163C11×C4⋊Q8C2311yescharacteristic
164C11×#127—21no—
165C11×#127C2311yescharacteristic
166C11×#126—22no—
167C11×#126—22no—
168C11×#126—22no—
169C11×#126—22no—
170C11×#126—22no—
171C11×#126—22no—
172C11×#125—22no—
173C11×#125—22no—
174C11×#125—22no—
175C11×#125—21no—
176C11×#125C2312yes—
177C11×#125C2312yes—
178C11×#124—21no—
179C11×#124—21no—
180C11×#124—22no—
181C11×#124—22no—
182C11×#124—21no—
183C11×#124C2312yes—
184C11×#124C2312yes—
185C11×#123—22no—
186C11×#123—22no—
187C11×#123—22no—
188C11×#123—22no—
189C11×#123—22no—
190C11×#123—22no—
191C11×C22⋊Q8—21no—
192C11×C22⋊Q8—21no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—21no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8C2312yes—
198C11×C22⋊Q8C2312yes—
199C11×C22⋊Q8C2312yes—
200C11×#121—22no—
201C11×#121—22no—
202C11×#121—22no—
203C11×#121—21no—
204C11×#121—22no—
205C11×#121C2312yes—
206C11×#121C2312yes—
207C11×#121C2312yes—
208C4×Q8×C11—21no—
209C4×Q8×C11—21no—
210C4×Q8×C11—21no—
211C4×Q8×C11—21no—
212C4×Q8×C11—22no—
213C4×Q8×C11—22no—
214C4×Q8×C11—21no—
215C4×Q8×C11—21no—
216C4×Q8×C11D411yescharacteristic
217C4×Q8×C11C2311yescharacteristic
218C4×Q8×C11C2311yescharacteristic
219C4×Q8×C11C2311yescharacteristic
220C4×Q8×C11C2312yes—
221C4×Q8×C11C2312yes—
222C4×Q8×C11C2311yescharacteristic
223C4×Q8×C11C2312yes—
224C4×Q8×C11C2311yescharacteristic
225C4×Q8×C11C2312yes—
226C4×Q8×C11C2311yescharacteristic
227C4×Q8×C11C2311yescharacteristic
228C4×D4×C11—21no—
229C4×D4×C11—22no—
230C4×D4×C11—21no—
231C4×D4×C11—22no—
232C4×D4×C11—21no—
233C4×D4×C11—22no—
234C4×D4×C11—22no—
235C4×D4×C11—21no—
236C4×D4×C11—21no—
237C4×D4×C11—22no—
238C4×D4×C11—22no—
239C4×D4×C11—22no—
240C4×D4×C11—21no—
241C4×D4×C11D411yescharacteristic
242C4×D4×C11D412yes—
243C4×D4×C11C2311yescharacteristic
244C4×D4×C11C2312yes—
245C4×D4×C11C2311yescharacteristic
246C4×D4×C11C2312yes—
247C4×D4×C11C2311yescharacteristic
248C4×D4×C11C2312yes—
249C11×#117—21no—
250C11×#117—21no—
251C11×#117—22no—
252C11×#117—22no—
253C11×#117—21no—
254C11×#117—22no—
255C11×#117—22no—
256C11×#117D411yescharacteristic
257C11×#117D412yes—
258C11×#117C2311yescharacteristic
259C11×#117C2312yes—
260C2×C11×C4⋊C4—22no—
261C2×C11×C4⋊C4—21no—
262C2×C11×C4⋊C4C2312yes—
263C2×C11×C4⋊C4C2311yescharacteristic
264C2×C42×C11—22no—
265C2×C42×C11—21no—
266C2×C42×C11—22no—
267C2×C42×C11—21no—
268C2×C42×C11C2312yes—
269C2×C42×C11C2311yescharacteristic
270C11×#107C2311yescharacteristic
271C11×#107C2312yes—
272C11×#107C2312yes—
273C11×#107C2312yes—
274C11×#107C2311yescharacteristic
275C11×#106C2312yes—
276C11×#106C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2312yes—
279C11×#106C2311yescharacteristic
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×#103C2311yescharacteristic
285C11×#103C2311yescharacteristic
286C11×#103C2311yescharacteristic
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2311yescharacteristic
290C11×#103C2312yes—
291C11×#103C2311yescharacteristic
292C11×#103C2312yes—
293C11×#103C2311yescharacteristic
294C11×#103C2312yes—
295C11×#103C2312yes—
296C11×#103C2312yes—
297C11×#102C2312yes—
298C11×#102C2311yescharacteristic
299C11×#102C2312yes—
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2312yes—
304C11×C22⋊C8C2312yes—
305C11×C22⋊C8C2312yes—
306C11×C22⋊C8C2312yes—
307C11×#97C2311yescharacteristic
308C11×#97C2311yescharacteristic
309C11×#97C2312yes—
310C4×C8×C11C2311yescharacteristic
311C4×C8×C11C2312yes—
312C4×C8×C11C2311yescharacteristic
313C4×C8×C11C2312yes—
314#61467C1111yesmaximal, characteristic, direct product factor, Sylow
315C11×#41—22no—
316C11×#41—24no—
317C11×#41—42no—
318C11×#41—41no—
319C11×#41—42no—
320C11×#41—44no—
321C11×#41—44no—
322C2×Q8×C11—21no—
323C2×Q8×C11—22no—
324C2×Q8×C11—21no—
325C2×Q8×C11—21no—
326C2×Q8×C11—24no—
327C2×Q8×C11—22no—
328C2×Q8×C11—42no—
329C2×Q8×C11—41no—
330C2×Q8×C11C2×D411yescharacteristic
331C2×Q8×C11C2411yescharacteristic
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2411yescharacteristic
335C2×D4×C11—22no—
336C2×D4×C11—21no—
337C2×D4×C11—22no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—21no—
342C2×D4×C11C2×D411yescharacteristic
343C2×D4×C11C2×D412yes—
344C2×D4×C11C2411yescharacteristic
345C2×D4×C11C2412yes—
346C22×C4×C11—22no—
347C22×C4×C11—21no—
348C22×C4×C11—22no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11—22no—
352C22×C4×C11—22no—
353C22×C4×C11—21no—
354C22×C4×C11—21no—
355C22×C4×C11—22no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D412yes—
358C22×C4×C11C2×D411yescharacteristic
359C22×C4×C11C2×D412yes—
360C22×C4×C11C2412yes—
361C22×C4×C11C2411yescharacteristic
362C11×Q16—22no—
363C11×Q16—24no—
364C11×Q16—42no—
365C11×Q16#4114yescomplemented
366C11×SD16—24no—
367C11×SD16—22no—
368C11×SD16—24no—
369C11×SD16—22no—
370C11×SD16—42no—
371C11×D8—42no—
372C11×M16—22no—
373C11×M16—24no—
374C11×M16—42no—
375C11×M16—41no—
376C2×C8×C11C2411yescharacteristic
377C2×C8×C11C2411yescharacteristic
378C2×C8×C11C2412yes—
379C2×C8×C11C2412yes—
380C2×C8×C11C2411yescharacteristic
381C2×C8×C11C2411yescharacteristic
382C11×C4⋊C4—21no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—21no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4C2×D411yescharacteristic
406C11×C4⋊C4C2×D411yescharacteristic
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2412yes—
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2412yes—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—21no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4C2×D412yes—
432C11×C22⋊C4C2×D412yes—
433C11×C22⋊C4C2×D412yes—
434C42×C11—21no—
435C42×C11—21no—
436C42×C11—21no—
437C42×C11—21no—
438C42×C11—22no—
439C42×C11—22no—
440C42×C11—22no—
441C42×C11—22no—
442C42×C11—21no—
443C42×C11—21no—
444C42×C11—22no—
445C42×C11—21no—
446C42×C11C2×D412yes—
447C42×C11C2×D411yescharacteristic
448C42×C11C2×D412yes—
449C42×C11C2×D411yescharacteristic
450C42×C11C2412yes—
451C42×C11C2411yescharacteristic
452C42×C11C2411yescharacteristic
453#3482C2×C1111yescharacteristic, complemented
454#3480C2×C1111yescharacteristic, complemented
455#3394C2×C1111yescharacteristic, complemented
456#3383C2×C1111yescharacteristic, complemented
457#3365C2×C1111yescharacteristic, complemented
458#3364C2×C1111yescharacteristic, complemented
459#3353C2×C1111yescharacteristic, complemented
460#3351C2×C1112yescomplemented
461#3332C2×C1111yescharacteristic, complemented
462#3328C2×C1111yescharacteristic, complemented
463#3327C2×C1112yescomplemented
464#3326C2×C1112yescomplemented
465#3278C2×C1111yescharacteristic, complemented
466#3277C2×C1112yescomplemented
467#3183C2×C1112yescomplemented
468#3182C2×C1111yescharacteristic, complemented
469#3117C2×C1112yescomplemented
470#3115C2×C1111yescharacteristic, complemented
471#3113C2×C1111yescharacteristic, complemented
472#3111C2×C1112yescomplemented
473#2971C2×C1111yescharacteristic, complemented
474C4×#137C2×C1111yescharacteristic, complemented
475C4×#137C2×C1112yescomplemented
476C23×C11—21no—
477C23×C11—22no—
478C23×C11C22×D411yescharacteristic
479C23×C11C22×D412yes—
480Q8×C11—22no—
481Q8×C11—21no—
482Q8×C11—21no—
483Q8×C11—21no—
484Q8×C11—22no—
485Q8×C11—22no—
486Q8×C11—21no—
487Q8×C11—42no—
488Q8×C11—44no—
489Q8×C11—42no—
490Q8×C11—42no—
491Q8×C11C2×#4112yes—
492Q8×C11C2×#4112yes—
493D4×C11—22no—
494D4×C11—21no—
495D4×C11—22no—
496D4×C11—21no—
497D4×C11—22no—
498D4×C11—42no—
499D4×C11—44no—
500D4×C11—42no—
501D4×C11—44no—
502D4×C11—44no—
503D4×C11—42no—
504D4×C11—81no—
505D4×C11—82no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—21no—
511C2×C4×C11—22no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—21no—
520C2×C4×C11—22no—
521C2×C4×C11—42no—
522C2×C4×C11—41no—
523C2×C4×C11—42no—
524C2×C4×C11—44no—
525C2×C4×C11—42no—
526C2×C4×C11—42no—
527C2×C4×C11—44no—
528C2×C4×C11—42no—
529C2×C4×C11—44no—
530C2×C4×C11—44no—
531C2×C4×C11—42no—
532C2×C4×C11—82no—
533C2×C4×C11—81no—
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D412yes—
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C22×D412yes—
539C2×C4×C11C22×D412yes—
540C2×C4×C11C22×D411yescharacteristic
541C2×C4×C11C22×D411yescharacteristic
542C2×C4×C11C2511yescharacteristic
543C8×C11—21no—
544C8×C11—22no—
545C8×C11—21no—
546C8×C11—22no—
547C8×C11—21no—
548C8×C11C2×#4112yes—
549C2×#137C22×C1111yescharacteristic
550C2×#137C22×C1112yes—
551#559—21no—
552#559C22×C1111yescharacteristic
553#557C22×C1111yescharacteristic
554#557C22×C1111yescharacteristic
555#556—21no—
556#556—21no—
557#556C22×C1111yescharacteristic
558#556C22×C1111yescharacteristic
559#553—22no—
560#553C22×C1112yes—
561#552—22no—
562#552C22×C1112yes—
563#550C22×C1111yescharacteristic
564D4×Q8C22×C1111yescharacteristic
565#548C22×C1112yes—
566#548C22×C1112yes—
567#547—21no—
568#547C22×C1111yescharacteristic
569#533—21no—
570#533C22×C1111yescharacteristic
571#532—21no—
572#532C22×C1111yescharacteristic
573#529—22no—
574#529—22no—
575#529C22×C1112yes—
576#529C22×C1112yes—
577C4×#41—21no—
578C4×#41—21no—
579C4×#41C22×C1112yes—
580C4×#41C22×C1111yescharacteristic
581C4×#41C22×C1111yescharacteristic
582C2×C4×Q8C22×C1111yescharacteristic
583C2×C4×Q8C22×C1112yes—
584#500C22×C1111yescharacteristic
585#499C22×C1112yes—
586#495C22×C1112yes—
587#492C22×C1111yescharacteristic
588#488C22×C1112yes—
589#488C22×C1112yes—
590#487C22×C1111yescharacteristic
591#486C22×C1111yescharacteristic
592#485C22×C1112yes—
593#484C22×C1112yes—
594#483C22×C1112yes—
595#482C22×C1112yes—
596#482C22×C1112yes—
597#481C22×C1112yes—
598#479C22×C1112yes—
599#479C22×C1112yes—
600#479C22×C1112yes—
601#478C22×C1112yes—
602#475C22×C1111yescharacteristic
603#475C22×C1111yescharacteristic
604#475C22×C1111yescharacteristic
605#474C22×C1111yescharacteristic
606#470C22×C1112yes—
607#469C22×C1112yes—
608#468C22×C1112yes—
609#468C22×C1112yes—
610#468C22×C1112yes—
611#468C22×C1112yes—
612#464C22×C1112yes—
613#464C22×C1112yes—
614#464C22×C1112yes—
615#463C22×C1112yes—
616#462C22×C1111yescharacteristic
617#462C22×C1111yescharacteristic
618#460C22×C1111yescharacteristic
619#459C22×C1111yescharacteristic
620#452C22×C1112yes—
621#451C22×C1112yes—
622#451C22×C1112yes—
623#449C22×C1112yes—
624#449C22×C1112yes—
625#448C22×C1112yes—
626C8×Q8C22×C1111yescharacteristic
627C8×Q8C22×C1111yescharacteristic
628#442C22×C1112yes—
629#441C22×C1112yes—
630#441C22×C1112yes—
631#441C22×C1111yescharacteristic
632#441C22×C1111yescharacteristic
633#440C22×C1111yescharacteristic
634#440C22×C1112yes—
635#440C22×C1112yes—
636#440C22×C1112yes—
637#440C22×C1111yescharacteristic
638C4×Q16C22×C1111yescharacteristic
639C4×Q16C22×C1112yes—
640C4×Q16C22×C1112yes—
641C4×Q16C22×C1111yescharacteristic
642C4×SD16C22×C1111yescharacteristic
643C4×SD16C22×C1112yes—
644C4×SD16C22×C1111yescharacteristic
645C4×SD16C22×C1112yes—
646#436C22×C1111yescharacteristic
647#436C22×C1112yes—
648#436C22×C1111yescharacteristic
649#436C22×C1112yes—
650#432C22×C1112yes—
651#432C22×C1111yescharacteristic
652#428C22×C1111yescharacteristic
653#428C22×C1112yes—
654#419C22×C1112yes—
655#419C22×C1111yescharacteristic
656#417C22×C1112yes—
657#417C22×C1111yescharacteristic
658C4×M16C22×C1111yescharacteristic
659C4×M16C22×C1112yes—
660C22×C11—21no—
661C22×C11—22no—
662C22×C11—21no—
663C22×C11—22no—
664C22×C11—21no—
665C22×C11—22no—
666C22×C11—41no—
667C22×C11—42no—
668C22×C11—41no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—41no—
672C22×C11C23×D411yescharacteristic
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—21no—
676C4×C11—22no—
677C4×C11—21no—
678C4×C11—22no—
679C4×C11—22no—
680C4×C11—21no—
681C4×C11—22no—
682C4×C11—41no—
683C4×C11—41no—
684C4×C11—41no—
685C4×C11—41no—
686C4×C11—42no—
687C4×C11—41no—
688C4×C11—42no—
689C4×C11—42no—
690C4×C11#57512yes—
691C4×C11C22×#4111yescharacteristic
692C4×C11#58511yescharacteristic
693C2×#41—21no—
694C2×#41—21no—
695C2×#41D4×C1111yescharacteristic
696C2×#41C23×C1111yescharacteristic
697C2×#41C23×C1112yes—
698C22×Q8C23×C1111yescharacteristic
699C22×Q8C23×C1112yes—
700#137—24no—
701#137—28no—
702C2×Q16C23×C1111yescharacteristic
703C2×Q16C23×C1112yes—
704C2×Q16C23×C1112yes—
705C2×Q16C23×C1111yescharacteristic
706C2×SD16C23×C1112yes—
707C2×SD16C23×C1111yescharacteristic
708C2×SD16C23×C1112yes—
709C2×SD16C23×C1111yescharacteristic
710C2×SD16C23×C1112yes—
711C2×D8C23×C1112yes—
712C2×M16C23×C1111yescharacteristic
713C2×M16C23×C1112yes—
714C2×M16C23×C1111yescharacteristic
715C2×M16C23×C1112yes—
716C4⋊Q8—21no—
717C4⋊Q8—21no—
718C4⋊Q8—21no—
719C4⋊Q8C23×C1111yescharacteristic
720C4⋊Q8C23×C1111yescharacteristic
721C4⋊Q8C23×C1111yescharacteristic
722#127—21no—
723#127C23×C1111yescharacteristic
724#126—22no—
725#126—22no—
726#126—22no—
727#126—22no—
728#126—22no—
729#126—22no—
730#125—22no—
731#125—22no—
732#125—22no—
733#125—21no—
734#125C23×C1112yes—
735#125C23×C1112yes—
736#124—21no—
737#124—21no—
738#124—22no—
739#124—22no—
740#124—21no—
741#124C23×C1112yes—
742#124C23×C1112yes—
743#123—22no—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—22no—
752C22⋊Q8—21no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8C23×C1112yes—
756C22⋊Q8C23×C1112yes—
757C22⋊Q8C23×C1112yes—
758#121—22no—
759#121—22no—
760#121—22no—
761#121—21no—
762#121—22no—
763#121C23×C1112yes—
764#121C23×C1112yes—
765#121C23×C1112yes—
766C4×Q8—21no—
767C4×Q8—21no—
768C4×Q8—21no—
769C4×Q8—21no—
770C4×Q8—22no—
771C4×Q8—22no—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8D4×C1111yescharacteristic
775C4×Q8C23×C1111yescharacteristic
776C4×Q8C23×C1111yescharacteristic
777C4×Q8C23×C1111yescharacteristic
778C4×Q8C23×C1112yes—
779C4×Q8C23×C1112yes—
780C4×Q8C23×C1111yescharacteristic
781C4×Q8C23×C1112yes—
782C4×Q8C23×C1111yescharacteristic
783C4×Q8C23×C1112yes—
784C4×Q8C23×C1111yescharacteristic
785C4×Q8C23×C1111yescharacteristic
786C4×D4—21no—
787C4×D4—22no—
788C4×D4—21no—
789C4×D4—22no—
790C4×D4—21no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—21no—
799C4×D4D4×C1111yescharacteristic
800C4×D4D4×C1112yes—
801C4×D4C23×C1111yescharacteristic
802C4×D4C23×C1112yes—
803C4×D4C23×C1111yescharacteristic
804C4×D4C23×C1112yes—
805C4×D4C23×C1111yescharacteristic
806C4×D4C23×C1112yes—
807#117—21no—
808#117—21no—
809#117—22no—
810#117—22no—
811#117—21no—
812#117—22no—
813#117—22no—
814#117D4×C1111yescharacteristic
815#117D4×C1112yes—
816#117C23×C1111yescharacteristic
817#117C23×C1112yes—
818C2×C4⋊C4—22no—
819C2×C4⋊C4—21no—
820C2×C4⋊C4C23×C1112yes—
821C2×C4⋊C4C23×C1111yescharacteristic
822C2×C42—22no—
823C2×C42—21no—
824C2×C42—22no—
825C2×C42—21no—
826C2×C42C23×C1112yes—
827C2×C42C23×C1111yescharacteristic
828#107C23×C1111yescharacteristic
829#107C23×C1112yes—
830#107C23×C1112yes—
831#107C23×C1111yescharacteristic
832#107C23×C1112yes—
833#106C23×C1111yescharacteristic
834#106C23×C1112yes—
835#106C23×C1111yescharacteristic
836#106C23×C1112yes—
837#106C23×C1112yes—
838C4⋊C8C23×C1111yescharacteristic
839C4⋊C8C23×C1111yescharacteristic
840C4⋊C8C23×C1112yes—
841C4⋊C8C23×C1112yes—
842#103C23×C1111yescharacteristic
843#103C23×C1111yescharacteristic
844#103C23×C1111yescharacteristic
845#103C23×C1112yes—
846#103C23×C1112yes—
847#103C23×C1111yescharacteristic
848#103C23×C1112yes—
849#103C23×C1111yescharacteristic
850#103C23×C1112yes—
851#103C23×C1111yescharacteristic
852#103C23×C1112yes—
853#103C23×C1112yes—
854#103C23×C1112yes—
855#102C23×C1112yes—
856#102C23×C1111yescharacteristic
857#102C23×C1112yes—
858#102C23×C1111yescharacteristic
859#102C23×C1112yes—
860#102C23×C1112yes—
861#102C23×C1112yes—
862C22⋊C8C23×C1112yes—
863C22⋊C8C23×C1112yes—
864C22⋊C8C23×C1112yes—
865#97C23×C1111yescharacteristic
866#97C23×C1111yescharacteristic
867#97C23×C1112yes—
868C4×C8C23×C1111yescharacteristic
869C4×C8C23×C1112yes—
870C4×C8C23×C1111yescharacteristic
871C4×C8C23×C1112yes—
872C2×C11—41no—
873C2×C11—42no—
874C2×C11—81no—
875C2×C11—82no—
876C2×C11D4×#4111yescharacteristic
877C2×C11C2×#57511yescharacteristic
878C2×C11#358611yescharacteristic
879#41—22no—
880#41—24no—
881#41—42no—
882#41—41no—
883#41—42no—
884#41—44no—
885#41—44no—
886C2×Q8—21no—
887C2×Q8—22no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—24no—
891C2×Q8—22no—
892C2×Q8—42no—
893C2×Q8—41no—
894C2×Q8C2×D4×C1111yescharacteristic
895C2×Q8C24×C1111yescharacteristic
896C2×Q8C24×C1112yes—
897C2×Q8C24×C1111yescharacteristic
898C2×Q8C24×C1111yescharacteristic
899C2×D4—22no—
900C2×D4—21no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4C2×D4×C1111yescharacteristic
907C2×D4C2×D4×C1112yes—
908C2×D4C24×C1111yescharacteristic
909C2×D4C24×C1112yes—
910C22×C4—22no—
911C22×C4—21no—
912C22×C4—22no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—22no—
920C22×C4C2×D4×C1111yescharacteristic
921C22×C4C2×D4×C1112yes—
922C22×C4C2×D4×C1111yescharacteristic
923C22×C4C2×D4×C1112yes—
924C22×C4C24×C1112yes—
925C22×C4C24×C1111yescharacteristic
926Q16—22no—
927Q16—24no—
928Q16—42no—
929Q16C11×#4114yescomplemented
930SD16—24no—
931SD16—22no—
932SD16—24no—
933SD16—22no—
934SD16—42no—
935D8—42no—
936M16—22no—
937M16—24no—
938M16—42no—
939M16—41no—
940C2×C8C24×C1111yescharacteristic
941C2×C8C24×C1111yescharacteristic
942C2×C8C24×C1112yes—
943C2×C8C24×C1112yes—
944C2×C8C24×C1111yescharacteristic
945C2×C8C24×C1111yescharacteristic
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—22no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—22no—
967C4⋊C4—21no—
968C4⋊C4—22no—
969C4⋊C4C2×D4×C1111yescharacteristic
970C4⋊C4C2×D4×C1111yescharacteristic
971C4⋊C4C2×D4×C1112yes—
972C4⋊C4C2×D4×C1112yes—
973C4⋊C4C24×C1111yescharacteristic
974C4⋊C4C24×C1112yes—
975C4⋊C4C24×C1111yescharacteristic
976C4⋊C4C24×C1111yescharacteristic
977C4⋊C4C24×C1111yescharacteristic
978C4⋊C4C24×C1112yes—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—21no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—21no—
990C22⋊C4—21no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4C2×D4×C1112yes—
996C22⋊C4C2×D4×C1112yes—
997C22⋊C4C2×D4×C1112yes—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—21no—
1007C42—21no—
1008C42—22no—
1009C42—21no—
1010C42C2×D4×C1112yes—
1011C42C2×D4×C1111yescharacteristic
1012C42C2×D4×C1112yes—
1013C42C2×D4×C1111yescharacteristic
1014C42C24×C1112yes—
1015C42C24×C1111yescharacteristic
1016C42C24×C1111yescharacteristic
1017C11#6146711yescharacteristic, direct product factor, Sylow
1018C23—21no—
1019C23—22no—
1020C23C22×D4×C1111yescharacteristic
1021C23C22×D4×C1112yes—
1022Q8—22no—
1023Q8—21no—
1024Q8—21no—
1025Q8—21no—
1026Q8—22no—
1027Q8—22no—
1028Q8—21no—
1029Q8—42no—
1030Q8—44no—
1031Q8—42no—
1032Q8—42no—
1033Q8C2×C11×#4112yes—
1034Q8C2×C11×#4112yes—
1035D4—22no—
1036D4—21no—
1037D4—22no—
1038D4—21no—
1039D4—22no—
1040D4—42no—
1041D4—44no—
1042D4—42no—
1043D4—44no—
1044D4—44no—
1045D4—42no—
1046D4—81no—
1047D4—82no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—42no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—44no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—44no—
1070C2×C4—42no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—42no—
1074C2×C4—82no—
1075C2×C4—81no—
1076C2×C4C22×D4×C1111yescharacteristic
1077C2×C4C22×D4×C1112yes—
1078C2×C4C22×D4×C1111yescharacteristic
1079C2×C4C22×D4×C1111yescharacteristic
1080C2×C4C22×D4×C1112yes—
1081C2×C4C22×D4×C1112yes—
1082C2×C4C22×D4×C1111yescharacteristic
1083C2×C4C22×D4×C1111yescharacteristic
1084C2×C4C25×C1111yescharacteristic
1085C8—21no—
1086C8—22no—
1087C8—21no—
1088C8—22no—
1089C8—21no—
1090C8C2×C11×#4112yes—
1091C22—21no—
1092C22—22no—
1093C22—21no—
1094C22—22no—
1095C22—21no—
1096C22—22no—
1097C22—41no—
1098C22—42no—
1099C22—42no—
1100C22—41no—
1101C22—41no—
1102C22—42no—
1103C22C23×D4×C1111yescharacteristic
1104C4—22no—
1105C4—21no—
1106C4—22no—
1107C4—22no—
1108C4—21no—
1109C4—22no—
1110C4—21no—
1111C4—22no—
1112C4—21no—
1113C4—41no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—42no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4C11×#57512yes—
1122C4C22×C11×#4111yescharacteristic
1123C4C11×#58511yescharacteristic
1124C2—41no—
1125C2—42no—
1126C2—81no—
1127C2—82no—
1128C2D4×C11×#4111yescharacteristic
1129C2C2×C11×#57511yescharacteristic
1130C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3482C2semidirect
2. C11×#3480C2semidirect
3. C11×#3394C2semidirect
4. C11×#3383C2semidirect
5. C11×#3365C2semidirect
6. C11×#3364C2semidirect
7. C11×#3353C2semidirect
8. C11×#3351C2semidirect
9. C11×#3332C2semidirect
10. C11×#3328C2semidirect
11. C11×#3327C2semidirect
12. C11×#3326C2semidirect
13. C11×#3278C2semidirect
14. C11×#3277C2semidirect
15. C11×#3183C2semidirect
16. C11×#3182C2semidirect
17. C11×#3117C2semidirect
18. C11×#3115C2semidirect
19. C11×#3113C2semidirect
20. C11×#3111C2semidirect
21. C11×#2971C2semidirect
22. C4×C11×#137C2semidirect
23. C4×C11×#137C2semidirect
314. #61467C11direct (N × H)
365. C11×Q16#41semidirect
453. #3482C2×C11semidirect
454. #3480C2×C11semidirect
455. #3394C2×C11semidirect
456. #3383C2×C11semidirect
457. #3365C2×C11semidirect
458. #3364C2×C11semidirect
459. #3353C2×C11semidirect
460. #3351C2×C11semidirect
461. #3332C2×C11semidirect
462. #3328C2×C11semidirect
463. #3327C2×C11semidirect
464. #3326C2×C11semidirect
465. #3278C2×C11semidirect
466. #3277C2×C11semidirect
467. #3183C2×C11semidirect
468. #3182C2×C11semidirect
469. #3117C2×C11semidirect
470. #3115C2×C11semidirect
471. #3113C2×C11semidirect
472. #3111C2×C11semidirect
473. #2971C2×C11semidirect
474. C4×#137C2×C11semidirect
475. C4×#137C2×C11semidirect
929. Q16C11×#41semidirect
1017. C11#61467direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34822
C11×#34802
C11×#33942
C11×#33832
C11×#33652
C11×#33642
C11×#33532
C11×#33512
C11×#33322
C11×#33282
C11×#33272
C11×#33262
C11×#32782
C11×#32772
C11×#31832
C11×#31822
C11×#31172
C11×#31152
C11×#31132
C11×#31112
C11×#29712
C4×C11×#1372
#6146711