Finite Group Databasebeta

← C11×#61928 #14639121

Subgroups — C11×#61928 #14639121

Order 2816.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3554C211yesmaximal, characteristic, complemented
2C11×#3507C211yesmaximal, characteristic, complemented
3C11×#3401C212yesmaximal, complemented
4C11×#3400C211yesmaximal, characteristic, complemented
5C11×#3399C211yesmaximal, characteristic, complemented
6C11×#3396C211yesmaximal, characteristic, complemented
7C11×#3394C212yesmaximal, complemented
8C11×#3392C211yesmaximal, characteristic, complemented
9C11×#3376C212yesmaximal, complemented
10C11×#3374C211yesmaximal, characteristic, complemented
11C11×#3373C211yesmaximal, characteristic, complemented
12C11×#3365C211yesmaximal, characteristic, complemented
13C11×#3360C212yesmaximal, complemented
14C11×#3359C211yesmaximal, characteristic, complemented
15C11×#3225C212yesmaximal, complemented
16C11×#3221C212yesmaximal, complemented
17C11×#3212C211yesmaximal, characteristic, complemented
18C11×#3207C211yesmaximal, characteristic, complemented
19C11×#3125C212yesmaximal, complemented
20C11×#3119C212yesmaximal, complemented
21C11×#3108C211yesmaximal, characteristic, complemented
22C11×#3103C211yesmaximal, characteristic, complemented
23C11×#2986C211yesmaximal, characteristic, complemented
24C11×#562—22no—
25C11×#559C2211yescharacteristic
26C11×#559C2211yescharacteristic
27C11×#559C2212yes—
28C11×#559C2211yescharacteristic
29C11×#557C2211yescharacteristic
30C11×#557C2211yescharacteristic
31C11×#557C2211yescharacteristic
32C11×#556—21no—
33C11×#556C2212yes—
34C11×#556C2212yes—
35C11×#554—21no—
36C11×#554C2212yes—
37C11×#552—22no—
38C11×#550C2211yescharacteristic
39D4×Q8×C11C2211yescharacteristic
40C11×#548—21no—
41C11×#547—21no—
42C11×#542—21no—
43C11×#542C2212yes—
44C11×#540C2212yes—
45C11×#539—22no—
46C11×#539—22no—
47C11×#536—21no—
48C11×#536C2212yes—
49C11×#533C2211yescharacteristic
50C11×#532C2211yescharacteristic
51C11×#532C2211yescharacteristic
52C11×#529—21no—
53C11×#529—21no—
54C11×#529C2211yescharacteristic
55C11×#520C2212yes—
56C2×C4×Q8×C11C2211yescharacteristic
57C11×#497C2212yes—
58C11×#496C2212yes—
59C11×#495C2212yes—
60C11×#495C2212yes—
61C11×#493C2211yescharacteristic
62C11×#492C2211yescharacteristic
63C11×#492C2212yes—
64C11×#491C2212yes—
65C11×#489C2212yes—
66C11×#488C2212yes—
67C11×#488C2212yes—
68C11×#487C2211yescharacteristic
69C11×#487C2212yes—
70C11×#486C2211yescharacteristic
71C11×#483C2211yescharacteristic
72C11×#481C2212yes—
73C11×#480C2211yescharacteristic
74C11×#479C2211yescharacteristic
75C11×#479C2212yes—
76C11×#479C2211yescharacteristic
77C11×#478C2212yes—
78C11×#476C2212yes—
79C11×#475C2211yescharacteristic
80C11×#475C2211yescharacteristic
81C11×#475C2212yes—
82C11×#464C2212yes—
83C11×#464C2211yescharacteristic
84C11×#464C2211yescharacteristic
85C11×#464C2212yes—
86C11×#463C2212yes—
87C11×#463C2212yes—
88C11×#463C2212yes—
89C11×#463C2212yes—
90C11×#463C2212yes—
91C11×#463C2212yes—
92C11×#462C2211yescharacteristic
93C11×#462C2212yes—
94C11×#461C2211yescharacteristic
95C11×#461C2212yes—
96C11×#461C2212yes—
97C11×#461C2212yes—
98C11×#460C2211yescharacteristic
99C11×#460C2211yescharacteristic
100C11×#460C2211yescharacteristic
101C11×#460C2212yes—
102C11×#459C2211yescharacteristic
103C11×#459C2212yes—
104C11×#452C2212yes—
105C11×#451C2211yescharacteristic
106C11×#449C2212yes—
107C11×#449C2212yes—
108C11×#449C2212yes—
109C11×#448C2211yescharacteristic
110C11×#448C2212yes—
111C11×#446C2211yescharacteristic
112C11×#446C2211yescharacteristic
113C11×#446C2212yes—
114C8×Q8×C11C2211yescharacteristic
115C8×Q8×C11C2212yes—
116C8×Q8×C11C2211yescharacteristic
117C11×#442C2212yes—
118C11×#442C2212yes—
119C11×#441C2212yes—
120C11×#440C2212yes—
121C4×C11×Q16C2211yescharacteristic
122C4×C11×Q16C2211yescharacteristic
123C4×C11×SD16C2212yes—
124C4×C11×SD16C2212yes—
125C4×C11×SD16C2211yescharacteristic
126C4×C11×SD16C2212yes—
127C4×C11×SD16C2212yes—
128C4×C11×SD16C2211yescharacteristic
129C4×C11×SD16C2212yes—
130C4×C11×D8C2212yes—
131C11×#433C2212yes—
132C11×#433C2212yes—
133C11×#431C2211yescharacteristic
134C11×#431C2211yescharacteristic
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41C2312yes—
138C22×Q8×C11—21no—
139C22×Q8×C11C2311yescharacteristic
140C2×C11×Q16C2311yescharacteristic
141C2×C11×Q16C2312yes—
142C2×C11×Q16C2311yescharacteristic
143C2×C11×SD16C2311yescharacteristic
144C2×C11×SD16C2312yes—
145C2×C11×SD16C2312yes—
146C2×C11×SD16C2312yes—
147C2×C11×SD16C2312yes—
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2311yescharacteristic
150C2×C11×SD16C2312yes—
151C2×C11×D8C2312yes—
152C2×C11×D8C2312yes—
153C2×C11×D8C2312yes—
154C11×C4⋊Q8—21no—
155C11×C4⋊Q8D411yescharacteristic
156C11×C4⋊Q8D411yescharacteristic
157C11×C4⋊Q8C2312yes—
158C11×C4⋊Q8C2311yescharacteristic
159C11×C4⋊Q8C2312yes—
160C11×C4⋊Q8C2312yes—
161C11×C4⋊Q8C2311yescharacteristic
162C11×#127C2311yescharacteristic
163C11×#127C2312yes—
164C11×#127C2311yescharacteristic
165C11×#126—22no—
166C11×#126—22no—
167C11×#126—22no—
168C11×#126—22no—
169C11×#126—22no—
170C11×#126—21no—
171C11×#125—21no—
172C11×#125—21no—
173C11×#125—22no—
174C11×#125—22no—
175C11×#125—22no—
176C11×#125D412yes—
177C11×#125C2312yes—
178C11×#125C2311yescharacteristic
179C11×#124—21no—
180C11×#124—21no—
181C11×#124—21no—
182C11×#124—22no—
183C11×#124—22no—
184C11×#124—21no—
185C11×#124C2312yes—
186C11×#124C2311yescharacteristic
187C11×#124C2312yes—
188C11×#124C2312yes—
189C11×#124C2312yes—
190C11×#123—21no—
191C11×#123—22no—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×#123—22no—
198C11×#123—22no—
199C11×#123—22no—
200C11×#123—22no—
201C11×C22⋊Q8—22no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—22no—
206C11×C22⋊Q8—22no—
207C11×C22⋊Q8—22no—
208C11×C22⋊Q8—22no—
209C11×C22⋊Q8—22no—
210C11×C22⋊Q8—21no—
211C11×C22⋊Q8D411yescharacteristic
212C11×C22⋊Q8D411yescharacteristic
213C11×C22⋊Q8D412yes—
214C11×C22⋊Q8C2311yescharacteristic
215C11×#121—21no—
216C11×#121—21no—
217C11×#121—21no—
218C11×#121—22no—
219C11×#121—21no—
220C11×#121—22no—
221C11×#121—22no—
222C11×#121C2311yescharacteristic
223C11×#121C2312yes—
224C4×Q8×C11—21no—
225C4×Q8×C11—21no—
226C4×Q8×C11—21no—
227C4×Q8×C11—21no—
228C4×Q8×C11—21no—
229C4×Q8×C11C2311yescharacteristic
230C4×Q8×C11C2311yescharacteristic
231C4×Q8×C11C2311yescharacteristic
232C4×Q8×C11C2311yescharacteristic
233C4×Q8×C11C2312yes—
234C4×Q8×C11C2312yes—
235C4×Q8×C11C2311yescharacteristic
236C4×Q8×C11C2312yes—
237C4×Q8×C11C2311yescharacteristic
238C4×Q8×C11C2311yescharacteristic
239C4×Q8×C11C2312yes—
240C4×D4×C11—21no—
241C4×D4×C11—21no—
242C4×D4×C11—21no—
243C4×D4×C11—22no—
244C4×D4×C11—21no—
245C4×D4×C11—22no—
246C4×D4×C11—22no—
247C4×D4×C11—21no—
248C4×D4×C11—21no—
249C4×D4×C11—21no—
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2311yescharacteristic
253C4×D4×C11C2312yes—
254C4×D4×C11C2312yes—
255C4×D4×C11C2312yes—
256C4×D4×C11C2312yes—
257C11×#117—22no—
258C11×#117—22no—
259C11×#117—22no—
260C11×#117—21no—
261C11×#117C2312yes—
262C2×C11×C4⋊C4—21no—
263C2×C11×C4⋊C4—22no—
264C2×C11×C4⋊C4—22no—
265C2×C11×C4⋊C4C2311yescharacteristic
266C2×C42×C11—21no—
267C2×C42×C11C2311yescharacteristic
268C11×#107C2311yescharacteristic
269C11×#107C2311yescharacteristic
270C11×#106C2312yes—
271C11×#106C2311yescharacteristic
272C11×#106C2312yes—
273C11×#106C2311yescharacteristic
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×#103C2311yescharacteristic
283C11×#103C2312yes—
284C11×#103C2311yescharacteristic
285C11×#103C2312yes—
286C11×#103C2312yes—
287C11×#103C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2311yescharacteristic
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2311yescharacteristic
294C11×#102C2312yes—
295C11×#102C2312yes—
296C11×#102C2312yes—
297C11×#102C2312yes—
298C11×#102C2311yescharacteristic
299C11×#102C2312yes—
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×C22⋊C8C2311yescharacteristic
303C11×C22⋊C8C2312yes—
304C11×C22⋊C8C2311yescharacteristic
305C11×#97C2312yes—
306C11×#97C2312yes—
307C4×C8×C11C2311yescharacteristic
308C4×C8×C11C2312yes—
309C4×C8×C11C2311yescharacteristic
310C4×C8×C11C2312yes—
311C4×C8×C11C2312yes—
312#61928C1111yesmaximal, characteristic, direct product factor, Sylow
313C11×#41—42no—
314C11×#41—42no—
315C11×#41—82no—
316C11×#41—82no—
317C2×Q8×C11—21no—
318C2×Q8×C11—21no—
319C2×Q8×C11—22no—
320C2×Q8×C11—41no—
321C2×Q8×C11—41no—
322C2×Q8×C11—82no—
323C2×Q8×C11C2×D411yescharacteristic
324C2×Q8×C11C2×D411yescharacteristic
325C2×Q8×C11C2×D412yes—
326C2×Q8×C11C2411yescharacteristic
327C2×Q8×C11C2411yescharacteristic
328C2×Q8×C11C2412yes—
329C2×Q8×C11C2411yescharacteristic
330C2×D4×C11—22no—
331C2×D4×C11—21no—
332C2×D4×C11—22no—
333C2×D4×C11—21no—
334C2×D4×C11—21no—
335C2×D4×C11—21no—
336C2×D4×C11—22no—
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11C2412yes—
340C2×D4×C11C2411yescharacteristic
341C2×D4×C11C2412yes—
342C22×C4×C11—21no—
343C22×C4×C11—21no—
344C22×C4×C11—22no—
345C22×C4×C11—21no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—22no—
349C22×C4×C11—22no—
350C22×C4×C11—22no—
351C22×C4×C11—22no—
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2×D411yescharacteristic
354C22×C4×C11C2411yescharacteristic
355C11×Q16—41no—
356C11×Q16—41no—
357C11×Q16—42no—
358C11×SD16—41no—
359C11×SD16—42no—
360C11×SD16—42no—
361C11×SD16—42no—
362C11×SD16—42no—
363C11×SD16—42no—
364C11×SD16—42no—
365C11×SD16—41no—
366C11×D8—42no—
367C11×D8—42no—
368C11×D8—42no—
369C2×C8×C11C2411yescharacteristic
370C2×C8×C11C2412yes—
371C2×C8×C11C2411yescharacteristic
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—21no—
380C11×C4⋊C4—21no—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—21no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—21no—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4C2×D412yes—
398C11×C4⋊C4C2×D412yes—
399C11×C4⋊C4C2×D412yes—
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D411yescharacteristic
402C11×C4⋊C4C2×D411yescharacteristic
403C11×C4⋊C4C2×D412yes—
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2412yes—
410C11×C4⋊C4C2411yescharacteristic
411C11×C22⋊C4—21no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—21no—
419C11×C22⋊C4—21no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
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—
433C42×C11—21no—
434C42×C11—21no—
435C42×C11—21no—
436C42×C11—21no—
437C42×C11—22no—
438C42×C11—22no—
439C42×C11—21no—
440C42×C11—22no—
441C42×C11C2×D411yescharacteristic
442C42×C11C2×D411yescharacteristic
443C42×C11C2411yescharacteristic
444C42×C11C2411yescharacteristic
445C42×C11C2412yes—
446C42×C11C2412yes—
447#3554C2×C1111yescharacteristic, complemented
448#3507C2×C1111yescharacteristic, complemented
449#3401C2×C1112yescomplemented
450#3400C2×C1111yescharacteristic, complemented
451#3399C2×C1111yescharacteristic, complemented
452#3396C2×C1111yescharacteristic, complemented
453#3394C2×C1112yescomplemented
454#3392C2×C1111yescharacteristic, complemented
455#3376C2×C1112yescomplemented
456#3374C2×C1111yescharacteristic, complemented
457#3373C2×C1111yescharacteristic, complemented
458#3365C2×C1111yescharacteristic, complemented
459#3360C2×C1112yescomplemented
460#3359C2×C1111yescharacteristic, complemented
461#3225C2×C1112yescomplemented
462#3221C2×C1112yescomplemented
463#3212C2×C1111yescharacteristic, complemented
464#3207C2×C1111yescharacteristic, complemented
465#3125C2×C1112yescomplemented
466#3119C2×C1112yescomplemented
467#3108C2×C1111yescharacteristic, complemented
468#3103C2×C1111yescharacteristic, complemented
469#2986C2×C1111yescharacteristic, complemented
470C23×C11—22no—
471C23×C11—22no—
472C23×C11—21no—
473C23×C11C22×D411yescharacteristic
474Q8×C11—22no—
475Q8×C11—22no—
476Q8×C11—21no—
477Q8×C11—21no—
478Q8×C11—21no—
479Q8×C11—22no—
480Q8×C11—21no—
481Q8×C11—21no—
482Q8×C11—22no—
483Q8×C11—21no—
484Q8×C11—42no—
485Q8×C11—42no—
486Q8×C11—42no—
487Q8×C11—82no—
488D4×C11—21no—
489D4×C11—22no—
490D4×C11—22no—
491D4×C11—22no—
492D4×C11—22no—
493D4×C11—21no—
494D4×C11—44no—
495D4×C11—42no—
496D4×C11—42no—
497D4×C11—81no—
498D4×C11—81no—
499D4×C11—82no—
500D4×C11—82no—
501D4×C11—81no—
502D4×C11—82no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—22no—
512C2×C4×C11—21no—
513C2×C4×C11—22no—
514C2×C4×C11—21no—
515C2×C4×C11—41no—
516C2×C4×C11—44no—
517C2×C4×C11—42no—
518C2×C4×C11—42no—
519C2×C4×C11—82no—
520C2×C4×C11—82no—
521C2×C4×C11—82no—
522C2×C4×C11—82no—
523C2×C4×C11—82no—
524C2×C4×C11—82no—
525C2×C4×C11—81no—
526C2×C4×C11C22×D411yescharacteristic
527C2×C4×C11C22×D412yes—
528C2×C4×C11C22×D412yes—
529C2×C4×C11C22×D412yes—
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C22×D411yescharacteristic
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C22×D412yes—
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C2511yescharacteristic
536C8×C11—21no—
537C8×C11—21no—
538C8×C11—22no—
539C8×C11—21no—
540C8×C11—22no—
541C8×C11—21no—
542#562—22no—
543#559C22×C1111yescharacteristic
544#559C22×C1111yescharacteristic
545#559C22×C1112yes—
546#559C22×C1111yescharacteristic
547#557C22×C1111yescharacteristic
548#557C22×C1111yescharacteristic
549#557C22×C1111yescharacteristic
550#556—21no—
551#556C22×C1112yes—
552#556C22×C1112yes—
553#554—21no—
554#554C22×C1112yes—
555#552—22no—
556#550C22×C1111yescharacteristic
557D4×Q8C22×C1111yescharacteristic
558#548—21no—
559#547—21no—
560#542—21no—
561#542C22×C1112yes—
562#540C22×C1112yes—
563#539—22no—
564#539—22no—
565#536—21no—
566#536C22×C1112yes—
567#533C22×C1111yescharacteristic
568#532C22×C1111yescharacteristic
569#532C22×C1111yescharacteristic
570#529—21no—
571#529—21no—
572#529C22×C1111yescharacteristic
573#520C22×C1112yes—
574C2×C4×Q8C22×C1111yescharacteristic
575#497C22×C1112yes—
576#496C22×C1112yes—
577#495C22×C1112yes—
578#495C22×C1112yes—
579#493C22×C1111yescharacteristic
580#492C22×C1112yes—
581#492C22×C1111yescharacteristic
582#491C22×C1112yes—
583#489C22×C1112yes—
584#488C22×C1112yes—
585#488C22×C1112yes—
586#487C22×C1112yes—
587#487C22×C1111yescharacteristic
588#486C22×C1111yescharacteristic
589#483C22×C1111yescharacteristic
590#481C22×C1112yes—
591#480C22×C1111yescharacteristic
592#479C22×C1111yescharacteristic
593#479C22×C1112yes—
594#479C22×C1111yescharacteristic
595#478C22×C1112yes—
596#476C22×C1112yes—
597#475C22×C1111yescharacteristic
598#475C22×C1111yescharacteristic
599#475C22×C1112yes—
600#464C22×C1111yescharacteristic
601#464C22×C1111yescharacteristic
602#464C22×C1112yes—
603#464C22×C1112yes—
604#463C22×C1112yes—
605#463C22×C1112yes—
606#463C22×C1112yes—
607#463C22×C1112yes—
608#463C22×C1112yes—
609#463C22×C1112yes—
610#462C22×C1112yes—
611#462C22×C1111yescharacteristic
612#461C22×C1111yescharacteristic
613#461C22×C1112yes—
614#461C22×C1112yes—
615#461C22×C1112yes—
616#460C22×C1111yescharacteristic
617#460C22×C1111yescharacteristic
618#460C22×C1111yescharacteristic
619#460C22×C1112yes—
620#459C22×C1111yescharacteristic
621#459C22×C1112yes—
622#452C22×C1112yes—
623#451C22×C1111yescharacteristic
624#449C22×C1112yes—
625#449C22×C1112yes—
626#449C22×C1112yes—
627#448C22×C1112yes—
628#448C22×C1111yescharacteristic
629#446C22×C1111yescharacteristic
630#446C22×C1111yescharacteristic
631#446C22×C1112yes—
632C8×Q8C22×C1111yescharacteristic
633C8×Q8C22×C1112yes—
634C8×Q8C22×C1111yescharacteristic
635#442C22×C1112yes—
636#442C22×C1112yes—
637#441C22×C1112yes—
638#440C22×C1112yes—
639C4×Q16C22×C1111yescharacteristic
640C4×Q16C22×C1111yescharacteristic
641C4×SD16C22×C1112yes—
642C4×SD16C22×C1112yes—
643C4×SD16C22×C1111yescharacteristic
644C4×SD16C22×C1112yes—
645C4×SD16C22×C1112yes—
646C4×SD16C22×C1111yescharacteristic
647C4×SD16C22×C1112yes—
648C4×D8C22×C1112yes—
649#433C22×C1112yes—
650#433C22×C1112yes—
651#431C22×C1111yescharacteristic
652#431C22×C1111yescharacteristic
653C22×C11—21no—
654C22×C11—21no—
655C22×C11—21no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—42no—
660C22×C11—41no—
661C22×C11—42no—
662C22×C11—41no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11C23×D411yescharacteristic
666C4×C11—21no—
667C4×C11—21no—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—21no—
671C4×C11—21no—
672C4×C11—22no—
673C4×C11—22no—
674C4×C11—41no—
675C4×C11—41no—
676C4×C11—41no—
677C4×C11—42no—
678C4×C11—41no—
679C4×C11—41no—
680C4×C11—41no—
681C4×C11—41no—
682C4×C11—42no—
683C4×C11#57712yes—
684C4×C11#58511yescharacteristic
685C4×C11#58511yescharacteristic
686C2×#41—21no—
687C2×#41—21no—
688C2×#41C23×C1112yes—
689C22×Q8—21no—
690C22×Q8C23×C1111yescharacteristic
691C2×Q16C23×C1111yescharacteristic
692C2×Q16C23×C1111yescharacteristic
693C2×Q16C23×C1112yes—
694C2×SD16C23×C1112yes—
695C2×SD16C23×C1112yes—
696C2×SD16C23×C1111yescharacteristic
697C2×SD16C23×C1111yescharacteristic
698C2×SD16C23×C1112yes—
699C2×SD16C23×C1112yes—
700C2×SD16C23×C1112yes—
701C2×SD16C23×C1112yes—
702C2×D8C23×C1112yes—
703C2×D8C23×C1112yes—
704C2×D8C23×C1112yes—
705C4⋊Q8—21no—
706C4⋊Q8D4×C1111yescharacteristic
707C4⋊Q8D4×C1111yescharacteristic
708C4⋊Q8C23×C1111yescharacteristic
709C4⋊Q8C23×C1112yes—
710C4⋊Q8C23×C1112yes—
711C4⋊Q8C23×C1111yescharacteristic
712C4⋊Q8C23×C1112yes—
713#127C23×C1111yescharacteristic
714#127C23×C1111yescharacteristic
715#127C23×C1112yes—
716#126—22no—
717#126—22no—
718#126—22no—
719#126—22no—
720#126—22no—
721#126—21no—
722#125—21no—
723#125—21no—
724#125—22no—
725#125—22no—
726#125—22no—
727#125D4×C1112yes—
728#125C23×C1111yescharacteristic
729#125C23×C1112yes—
730#124—21no—
731#124—21no—
732#124—21no—
733#124—22no—
734#124—22no—
735#124—21no—
736#124C23×C1111yescharacteristic
737#124C23×C1112yes—
738#124C23×C1112yes—
739#124C23×C1112yes—
740#124C23×C1112yes—
741#123—21no—
742#123—22no—
743#123—22no—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749#123—22no—
750#123—22no—
751#123—22no—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—22no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8—22no—
761C22⋊Q8—21no—
762C22⋊Q8D4×C1111yescharacteristic
763C22⋊Q8D4×C1111yescharacteristic
764C22⋊Q8D4×C1112yes—
765C22⋊Q8C23×C1111yescharacteristic
766#121—21no—
767#121—21no—
768#121—21no—
769#121—22no—
770#121—21no—
771#121—22no—
772#121—22no—
773#121C23×C1111yescharacteristic
774#121C23×C1112yes—
775C4×Q8—21no—
776C4×Q8—21no—
777C4×Q8—21no—
778C4×Q8—21no—
779C4×Q8—21no—
780C4×Q8C23×C1111yescharacteristic
781C4×Q8C23×C1111yescharacteristic
782C4×Q8C23×C1111yescharacteristic
783C4×Q8C23×C1111yescharacteristic
784C4×Q8C23×C1112yes—
785C4×Q8C23×C1112yes—
786C4×Q8C23×C1111yescharacteristic
787C4×Q8C23×C1112yes—
788C4×Q8C23×C1111yescharacteristic
789C4×Q8C23×C1111yescharacteristic
790C4×Q8C23×C1112yes—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—22no—
795C4×D4—21no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—21no—
799C4×D4—21no—
800C4×D4—21no—
801C4×D4C23×C1112yes—
802C4×D4C23×C1112yes—
803C4×D4C23×C1111yescharacteristic
804C4×D4C23×C1112yes—
805C4×D4C23×C1112yes—
806C4×D4C23×C1112yes—
807C4×D4C23×C1112yes—
808#117—22no—
809#117—22no—
810#117—22no—
811#117—21no—
812#117C23×C1112yes—
813C2×C4⋊C4—21no—
814C2×C4⋊C4—22no—
815C2×C4⋊C4—22no—
816C2×C4⋊C4C23×C1111yescharacteristic
817C2×C42—21no—
818C2×C42C23×C1111yescharacteristic
819#107C23×C1111yescharacteristic
820#107C23×C1111yescharacteristic
821#106C23×C1112yes—
822#106C23×C1111yescharacteristic
823#106C23×C1112yes—
824#106C23×C1111yescharacteristic
825C4⋊C8C23×C1111yescharacteristic
826C4⋊C8C23×C1111yescharacteristic
827C4⋊C8C23×C1111yescharacteristic
828C4⋊C8C23×C1111yescharacteristic
829C4⋊C8C23×C1112yes—
830C4⋊C8C23×C1112yes—
831C4⋊C8C23×C1112yes—
832C4⋊C8C23×C1112yes—
833#103C23×C1111yescharacteristic
834#103C23×C1112yes—
835#103C23×C1112yes—
836#103C23×C1112yes—
837#103C23×C1111yescharacteristic
838#103C23×C1111yescharacteristic
839#103C23×C1112yes—
840#103C23×C1111yescharacteristic
841#103C23×C1111yescharacteristic
842#103C23×C1111yescharacteristic
843#103C23×C1112yes—
844#103C23×C1112yes—
845#102C23×C1112yes—
846#102C23×C1112yes—
847#102C23×C1111yescharacteristic
848#102C23×C1112yes—
849#102C23×C1111yescharacteristic
850#102C23×C1112yes—
851#102C23×C1112yes—
852#102C23×C1112yes—
853C22⋊C8C23×C1111yescharacteristic
854C22⋊C8C23×C1112yes—
855C22⋊C8C23×C1111yescharacteristic
856#97C23×C1112yes—
857#97C23×C1112yes—
858C4×C8C23×C1112yes—
859C4×C8C23×C1111yescharacteristic
860C4×C8C23×C1111yescharacteristic
861C4×C8C23×C1112yes—
862C4×C8C23×C1112yes—
863C2×C11—41no—
864C2×C11—82no—
865C2×C11—82no—
866C2×C11—81no—
867C2×C11#348711yescharacteristic
868C2×C11C2×#57711yescharacteristic
869C2×C11#358411yescharacteristic
870#41—42no—
871#41—42no—
872#41—82no—
873#41—82no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—22no—
877C2×Q8—41no—
878C2×Q8—41no—
879C2×Q8—82no—
880C2×Q8C2×D4×C1111yescharacteristic
881C2×Q8C2×D4×C1111yescharacteristic
882C2×Q8C2×D4×C1112yes—
883C2×Q8C24×C1111yescharacteristic
884C2×Q8C24×C1111yescharacteristic
885C2×Q8C24×C1112yes—
886C2×Q8C24×C1111yescharacteristic
887C2×D4—22no—
888C2×D4—21no—
889C2×D4—22no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—22no—
894C2×D4—21no—
895C2×D4—22no—
896C2×D4C24×C1112yes—
897C2×D4C24×C1111yescharacteristic
898C2×D4C24×C1112yes—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4C2×D4×C1111yescharacteristic
910C22×C4C2×D4×C1111yescharacteristic
911C22×C4C24×C1111yescharacteristic
912Q16—41no—
913Q16—42no—
914Q16—41no—
915SD16—41no—
916SD16—42no—
917SD16—41no—
918SD16—42no—
919SD16—42no—
920SD16—42no—
921SD16—42no—
922SD16—42no—
923D8—42no—
924D8—42no—
925D8—42no—
926C2×C8C24×C1112yes—
927C2×C8C24×C1111yescharacteristic
928C2×C8C24×C1111yescharacteristic
929C2×C8C24×C1111yescharacteristic
930C2×C8C24×C1112yes—
931C2×C8C24×C1111yescharacteristic
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—21no—
954C4⋊C4C2×D4×C1112yes—
955C4⋊C4C2×D4×C1112yes—
956C4⋊C4C2×D4×C1112yes—
957C4⋊C4C2×D4×C1112yes—
958C4⋊C4C2×D4×C1111yescharacteristic
959C4⋊C4C2×D4×C1111yescharacteristic
960C4⋊C4C2×D4×C1112yes—
961C4⋊C4C2×D4×C1112yes—
962C4⋊C4C2×D4×C1112yes—
963C4⋊C4C24×C1111yescharacteristic
964C4⋊C4C24×C1111yescharacteristic
965C4⋊C4C24×C1111yescharacteristic
966C4⋊C4C24×C1112yes—
967C4⋊C4C24×C1111yescharacteristic
968C22⋊C4—21no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—21no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—21no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4C2×D4×C1112yes—
989C22⋊C4C2×D4×C1112yes—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—22no—
995C42—22no—
996C42—21no—
997C42—22no—
998C42C2×D4×C1111yescharacteristic
999C42C2×D4×C1111yescharacteristic
1000C42C24×C1111yescharacteristic
1001C42C24×C1111yescharacteristic
1002C42C24×C1112yes—
1003C42C24×C1112yes—
1004C11#6192811yescharacteristic, direct product factor, Sylow
1005C23—22no—
1006C23—21no—
1007C23—22no—
1008C23C22×D4×C1111yescharacteristic
1009Q8—22no—
1010Q8—22no—
1011Q8—21no—
1012Q8—21no—
1013Q8—21no—
1014Q8—22no—
1015Q8—21no—
1016Q8—21no—
1017Q8—22no—
1018Q8—21no—
1019Q8—42no—
1020Q8—42no—
1021Q8—42no—
1022Q8—82no—
1023D4—21no—
1024D4—22no—
1025D4—22no—
1026D4—22no—
1027D4—22no—
1028D4—21no—
1029D4—44no—
1030D4—42no—
1031D4—42no—
1032D4—81no—
1033D4—81no—
1034D4—82no—
1035D4—82no—
1036D4—81no—
1037D4—82no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—41no—
1051C2×C4—44no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—82no—
1055C2×C4—82no—
1056C2×C4—82no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—82no—
1060C2×C4—81no—
1061C2×C4C22×D4×C1111yescharacteristic
1062C2×C4C22×D4×C1112yes—
1063C2×C4C22×D4×C1112yes—
1064C2×C4C22×D4×C1112yes—
1065C2×C4C22×D4×C1111yescharacteristic
1066C2×C4C22×D4×C1111yescharacteristic
1067C2×C4C22×D4×C1111yescharacteristic
1068C2×C4C22×D4×C1112yes—
1069C2×C4C22×D4×C1111yescharacteristic
1070C2×C4C25×C1111yescharacteristic
1071C8—21no—
1072C8—21no—
1073C8—22no—
1074C8—22no—
1075C8—21no—
1076C8—21no—
1077C22—21no—
1078C22—21no—
1079C22—21no—
1080C22—42no—
1081C22—41no—
1082C22—42no—
1083C22—41no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—41no—
1089C22C23×D4×C1111yescharacteristic
1090C4—21no—
1091C4—21no—
1092C4—22no—
1093C4—22no—
1094C4—21no—
1095C4—21no—
1096C4—22no—
1097C4—22no—
1098C4—42no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—42no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4C11×#57712yes—
1108C4C11×#58511yescharacteristic
1109C4C11×#58511yescharacteristic
1110C2—41no—
1111C2—82no—
1112C2—81no—
1113C2—82no—
1114C2C11×#348711yescharacteristic
1115C2C2×C11×#57711yescharacteristic
1116C2C11×#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×#3554C2semidirect
2. C11×#3507C2semidirect
3. C11×#3401C2semidirect
4. C11×#3400C2semidirect
5. C11×#3399C2semidirect
6. C11×#3396C2semidirect
7. C11×#3394C2semidirect
8. C11×#3392C2semidirect
9. C11×#3376C2semidirect
10. C11×#3374C2semidirect
11. C11×#3373C2semidirect
12. C11×#3365C2semidirect
13. C11×#3360C2semidirect
14. C11×#3359C2semidirect
15. C11×#3225C2semidirect
16. C11×#3221C2semidirect
17. C11×#3212C2semidirect
18. C11×#3207C2semidirect
19. C11×#3125C2semidirect
20. C11×#3119C2semidirect
21. C11×#3108C2semidirect
22. C11×#3103C2semidirect
23. C11×#2986C2semidirect
312. #61928C11direct (N × H)
447. #3554C2×C11semidirect
448. #3507C2×C11semidirect
449. #3401C2×C11semidirect
450. #3400C2×C11semidirect
451. #3399C2×C11semidirect
452. #3396C2×C11semidirect
453. #3394C2×C11semidirect
454. #3392C2×C11semidirect
455. #3376C2×C11semidirect
456. #3374C2×C11semidirect
457. #3373C2×C11semidirect
458. #3365C2×C11semidirect
459. #3360C2×C11semidirect
460. #3359C2×C11semidirect
461. #3225C2×C11semidirect
462. #3221C2×C11semidirect
463. #3212C2×C11semidirect
464. #3207C2×C11semidirect
465. #3125C2×C11semidirect
466. #3119C2×C11semidirect
467. #3108C2×C11semidirect
468. #3103C2×C11semidirect
469. #2986C2×C11semidirect
1004. C11#61928direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35542
C11×#35072
C11×#34012
C11×#34002
C11×#33992
C11×#33962
C11×#33942
C11×#33922
C11×#33762
C11×#33742
C11×#33732
C11×#33652
C11×#33602
C11×#33592
C11×#32252
C11×#32212
C11×#32122
C11×#32072
C11×#31252
C11×#31192
C11×#31082
C11×#31032
C11×#29862
#6192811