Finite Group Databasebeta

← C11×#61991 #14639184

Subgroups — C11×#61991 #14639184

Order 2816.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3514C211yesmaximal, characteristic
2Q8×C11×#41C211yesmaximal, characteristic, complemented
3C11×#3400C211yesmaximal, characteristic, complemented
4C11×#3398C211yesmaximal, characteristic, complemented
5C11×#3375C211yesmaximal, characteristic, complemented
6C11×#3369C211yesmaximal, characteristic, complemented
7C11×#3316C212yesmaximal, complemented
8C11×#3314C212yesmaximal, complemented
9C11×#3299C211yesmaximal, characteristic, complemented
10C11×#3295C211yesmaximal, characteristic, complemented
11D4×C11×Q16C211yesmaximal, characteristic, complemented
12D4×C11×SD16C211yesmaximal, characteristic, complemented
13C11×#3270C212yesmaximal, complemented
14C11×#3266C212yesmaximal, complemented
15C11×#3252C211yesmaximal, characteristic, complemented
16C11×#3248C212yesmaximal, complemented
17C11×#3215C212yesmaximal, complemented
18C11×#3210C211yesmaximal, characteristic, complemented
19C11×#3117C212yesmaximal, complemented
20C11×#3108C211yesmaximal, characteristic, complemented
21C11×#3037C211yesmaximal, characteristic, complemented
22C2×C11×#464C212yesmaximal, complemented
23C11×#2990C211yesmaximal, characteristic, complemented
24C2×C11×#137C2212yescomplemented
25C22×C11×Q16C2212yescomplemented
26C22×C11×SD16C2212yes—
27C11×#559C2211yescharacteristic
28Q82×C11C2211yescharacteristic, complemented
29C11×#557—21no—
30C11×#557C2211yescharacteristic, complemented
31C11×#556C2211yescharacteristic
32C11×#555—21no—
33C11×#554—21no—
34C11×#554—22no—
35C11×#554C2211yescharacteristic
36C11×#554C2212yescomplemented
37C11×#551—22no—
38D4×Q8×C11C2211yescharacteristic
39D4×Q8×C11C2211yescharacteristic
40D4×Q8×C11C2212yescomplemented
41C11×#548C2212yes—
42C11×#546—21no—
43C11×#546C2212yes—
44D42×C11C2211yescharacteristic
45C11×#542—21no—
46C11×#538—22no—
47C11×#533—22no—
48C11×#533—21no—
49C11×#533C2211yescharacteristic, complemented
50C11×#533C2212yescomplemented
51C11×#532C2211yescharacteristic
52C11×#529C2212yes—
53C11×#529C2211yescharacteristic
54C2×C11×#124C2212yes—
55C11×#518—21no—
56C4×C11×#41—21no—
57C4×C11×#41C2211yescharacteristic
58C2×C4×Q8×C11C2212yescomplemented
59C2×C4×Q8×C11C2211yescharacteristic, complemented
60C11×#497C2212yes—
61C11×#497C2212yescomplemented
62C11×#494C2211yescharacteristic, complemented
63C11×#492C2211yescharacteristic
64C11×#489C2212yes—
65C11×#489C2212yescomplemented
66C11×#487C2211yescharacteristic, complemented
67C11×#486C2211yescharacteristic
68C11×#484C2212yescomplemented
69C11×#483C2211yescharacteristic, complemented
70C11×#481C2212yes—
71C11×#480C2211yescharacteristic
72C11×#479C2211yescharacteristic, complemented
73C11×#479C2212yescomplemented
74C11×#479C2211yescharacteristic, complemented
75C11×#477C2211yescharacteristic, complemented
76C11×#476C2211yescharacteristic
77C11×#475C2212yescomplemented
78C11×#474C2212yescomplemented
79C11×#470C2212yescomplemented
80C11×#468C2212yes—
81C11×#467C2212yescomplemented
82C11×#467C2212yescomplemented
83C11×#465C2212yes—
84C11×#465C2212yes—
85C11×#464C2211yescharacteristic
86C11×#464C2212yes—
87C11×#464C2212yes—
88C11×#464C2211yescharacteristic
89C11×#464C2212yes—
90C11×#464C2212yescomplemented
91C11×#464C2212yescomplemented
92C11×#464C2212yescomplemented
93C11×#464C2212yescomplemented
94C11×#464C2212yescomplemented
95C11×#464C2212yescomplemented
96C11×#462C2212yescomplemented
97C11×#462C2211yescharacteristic, complemented
98C11×#462C2211yescharacteristic, complemented
99C11×#462C2211yescharacteristic, complemented
100C11×#461C2211yescharacteristic
101C11×#461C2212yescomplemented
102C11×#460C2211yescharacteristic
103C11×#460C2211yescharacteristic
104C11×#452C2212yescomplemented
105C11×#452C2212yescomplemented
106C11×#451C2212yescomplemented
107C11×#451C2212yescomplemented
108C11×#451C2212yescomplemented
109C11×#451C2211yescharacteristic, complemented
110C11×#450C2212yes—
111C11×#450C2212yes—
112C11×#448C2211yescharacteristic
113C11×#448C2212yes—
114C11×#446C2211yescharacteristic, complemented
115C11×#446C2211yescharacteristic, complemented
116C11×#441C2212yescomplemented
117C11×#441C2212yescomplemented
118C11×#440C2212yescomplemented
119C11×#440C2212yescomplemented
120C4×C11×Q16C2211yescharacteristic, complemented
121C4×C11×Q16C2211yescharacteristic, complemented
122C4×C11×SD16C2211yescharacteristic
123C4×C11×SD16C2211yescharacteristic
124C11×#435C2212yescomplemented
125C11×#435C2212yescomplemented
126C8×D4×C11C2211yescharacteristic
127C8×D4×C11C2211yescharacteristic
128C11×#432C2212yescomplemented
129C11×#431C2211yescharacteristic, complemented
130C11×#423C2211yescharacteristic, complemented
131C2×C11×C4⋊C8C2212yescomplemented
132C11×#417C2212yescomplemented
133C2×C11×#103C2212yescomplemented
134C2×C11×#102C2212yes—
135C2×C11×#41D411yescharacteristic
136C2×C11×#41C2312yes—
137C22×Q8×C11C2312yes—
138C22×Q8×C11C2311yescharacteristic
139C22×Q8×C11C2312yes—
140C22×D4×C11—21no—
141C22×D4×C11C2312yes—
142C11×#137—44no—
143C2×C11×Q16—44no—
144C2×C11×Q16C2311yescharacteristic
145C2×C11×Q16C2312yes—
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2312yes—
149C2×C11×Q16C2311yescharacteristic
150C2×C11×Q16C2312yes—
151C2×C11×SD16—44no—
152C2×C11×SD16C2311yescharacteristic
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2311yescharacteristic
157C2×C11×SD16C2312yes—
158C2×C11×SD16C2312yes—
159C2×C11×M16C2312yes—
160C22×C8×C11C2312yes—
161C22×C8×C11C2312yes—
162C11×C4⋊Q8—21no—
163C11×C4⋊Q8—22no—
164C11×C4⋊Q8—21no—
165C11×C4⋊Q8—22no—
166C11×C4⋊Q8—21no—
167C11×C4⋊Q8C2311yescharacteristic
168C11×C4⋊Q8C2311yescharacteristic
169C11×C4⋊Q8C2312yes—
170C11×C4⋊Q8C2312yes—
171C11×C4⋊Q8C2311yescharacteristic
172C11×#127C2311yescharacteristic
173C11×#126—22no—
174C11×#126—22no—
175C11×#126—21no—
176C11×#125—21no—
177C11×#125—22no—
178C11×#125—21no—
179C11×#125—22no—
180C11×#125—21no—
181C11×#125—22no—
182C11×#125C2311yescharacteristic
183C11×#124—21no—
184C11×#124—22no—
185C11×#124—22no—
186C11×#124—22no—
187C11×#124C2312yes—
188C11×#124C2312yes—
189C11×#124C2311yescharacteristic
190C11×#124C2312yes—
191C11×#123—21no—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×C22⋊Q8—21no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—21no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8—22no—
200C11×C22⋊Q8—22no—
201C11×C22⋊Q8—22no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—22no—
206C11×C22⋊Q8C2312yes—
207C11×C22⋊Q8C2311yescharacteristic
208C11×C22⋊Q8C2312yes—
209C11×C22⋊Q8C2312yes—
210C11×C22⋊Q8C2312yes—
211C11×#121—22no—
212C11×#121—21no—
213C11×#121—21no—
214C11×#121—21no—
215C11×#121—22no—
216C11×#121C2312yes—
217C11×#121C2311yescharacteristic
218C11×#120—22no—
219C11×#120—22no—
220C4×Q8×C11—21no—
221C4×Q8×C11—21no—
222C4×Q8×C11—22no—
223C4×Q8×C11—21no—
224C4×Q8×C11—21no—
225C4×Q8×C11—22no—
226C4×Q8×C11—22no—
227C4×Q8×C11—21no—
228C4×Q8×C11D411yescharacteristic
229C4×Q8×C11C2311yescharacteristic
230C4×Q8×C11C2312yes—
231C4×Q8×C11C2311yescharacteristic
232C4×Q8×C11C2311yescharacteristic
233C4×Q8×C11C2312yes—
234C4×Q8×C11C2311yescharacteristic
235C4×Q8×C11C2312yes—
236C4×Q8×C11C2312yes—
237C4×Q8×C11C2311yescharacteristic
238C4×Q8×C11C2311yescharacteristic
239C4×D4×C11—21no—
240C4×D4×C11—22no—
241C4×D4×C11—21no—
242C4×D4×C11—22no—
243C4×D4×C11—21no—
244C4×D4×C11—22no—
245C4×D4×C11—21no—
246C4×D4×C11—21no—
247C4×D4×C11—22no—
248C4×D4×C11—21no—
249C4×D4×C11—21no—
250C4×D4×C11D411yescharacteristic
251C4×D4×C11D412yes—
252C4×D4×C11C2311yescharacteristic
253C4×D4×C11C2312yes—
254C4×D4×C11C2311yescharacteristic
255C4×D4×C11C2312yes—
256C11×#117—22no—
257C11×#117—21no—
258C11×#117—21no—
259C11×#117—21no—
260C11×#117—22no—
261C11×#117D412yes—
262C11×#117D411yescharacteristic
263C2×C11×C4⋊C4—22no—
264C2×C11×C4⋊C4—21no—
265C2×C11×C4⋊C4C2312yes—
266C2×C11×C4⋊C4C2311yescharacteristic
267C2×C11×C22⋊C4—22no—
268C2×C11×C22⋊C4—22no—
269C2×C11×C22⋊C4—22no—
270C2×C42×C11—22no—
271C2×C42×C11—21no—
272C2×C42×C11C2312yes—
273C2×C42×C11C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#107C2311yescharacteristic
276C11×#107C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2311yescharacteristic
279C11×#106C2312yes—
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2312yes—
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×C4⋊C8C2311yescharacteristic
285C11×C4⋊C8C2311yescharacteristic
286C11×C4⋊C8C2311yescharacteristic
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2311yescharacteristic
290C11×#103C2312yes—
291C11×#103C2311yescharacteristic
292C11×#103C2312yes—
293C11×#103C2312yes—
294C11×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#103C2311yescharacteristic
297C11×#103C2311yescharacteristic
298C11×#103C2312yes—
299C11×#103C2312yes—
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2312yes—
304C11×#102C2311yescharacteristic
305C11×#102C2312yes—
306C11×#102C2312yes—
307C11×C22⋊C8C2311yescharacteristic
308C11×C22⋊C8C2311yescharacteristic
309C11×C22⋊C8C2312yes—
310C11×C22⋊C8C2312yes—
311C11×#97C2312yes—
312C11×#97C2312yes—
313C4×C8×C11C2311yescharacteristic
314C4×C8×C11C2311yescharacteristic
315#61991C1111yesmaximal, characteristic, direct product factor, Sylow
316C24×C11—22no—
317C11×#41—24no—
318C11×#41—42no—
319C11×#41—42no—
320C2×Q8×C11—21no—
321C2×Q8×C11—22no—
322C2×Q8×C11—22no—
323C2×Q8×C11—21no—
324C2×Q8×C11—22no—
325C2×Q8×C11—24no—
326C2×Q8×C11—22no—
327C2×Q8×C11—42no—
328C2×Q8×C11—41no—
329C2×Q8×C11—42no—
330C2×Q8×C11—42no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2411yescharacteristic
333C2×Q8×C11C2412yes—
334C2×Q8×C11C2411yescharacteristic
335C2×Q8×C11C2412yes—
336C2×Q8×C11C2411yescharacteristic
337C2×D4×C11—22no—
338C2×D4×C11—21no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—21no—
342C2×D4×C11—22no—
343C2×D4×C11—42no—
344C2×D4×C11—42no—
345C2×D4×C11—44no—
346C2×D4×C11C2×D412yes—
347C2×D4×C11C2×D411yescharacteristic
348C2×D4×C11C2411yescharacteristic
349C2×D4×C11C2412yes—
350C22×C4×C11—21no—
351C22×C4×C11—22no—
352C22×C4×C11—21no—
353C22×C4×C11—22no—
354C22×C4×C11—22no—
355C22×C4×C11—21no—
356C22×C4×C11—22no—
357C22×C4×C11—22no—
358C22×C4×C11C2×D412yes—
359C22×C4×C11C2×D411yescharacteristic
360C22×C4×C11C2×D412yes—
361C22×C4×C11C2×D411yescharacteristic
362C22×C4×C11C2412yes—
363C22×C4×C11C2411yescharacteristic
364C11×Q16—22no—
365C11×Q16—24no—
366C11×Q16—42no—
367C11×Q16—42no—
368C11×Q16—41no—
369C11×Q16—42no—
370C11×Q16—42no—
371C11×SD16—22no—
372C11×SD16—24no—
373C11×SD16—42no—
374C11×SD16—42no—
375C11×SD16—41no—
376C11×SD16—42no—
377C11×SD16—42no—
378C11×M16—42no—
379C2×C8×C11—42no—
380C2×C8×C11—42no—
381C2×C8×C11C2411yescharacteristic
382C2×C8×C11C2411yescharacteristic
383C2×C8×C11C2411yescharacteristic
384C2×C8×C11C2411yescharacteristic
385C2×C8×C11C2412yes—
386C2×C8×C11C2412yes—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—21no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
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⋊C4—21no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—21no—
413C11×C4⋊C4C2×D411yescharacteristic
414C11×C4⋊C4C2×D412yes—
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2×D412yes—
417C11×C4⋊C4C2411yescharacteristic
418C11×C4⋊C4C2411yescharacteristic
419C11×C4⋊C4C2412yes—
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2411yescharacteristic
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—21no—
429C11×C22⋊C4—21no—
430C11×C22⋊C4—21no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4C2×D412yes—
440C11×C22⋊C4C2×D412yes—
441C11×C22⋊C4C2×D412yes—
442C42×C11—21no—
443C42×C11—22no—
444C42×C11—21no—
445C42×C11—22no—
446C42×C11—21no—
447C42×C11—22no—
448C42×C11—21no—
449C42×C11—22no—
450C42×C11—21no—
451C42×C11C2×D412yes—
452C42×C11C2×D411yescharacteristic
453C42×C11C2×D411yescharacteristic
454C42×C11C2×D412yes—
455C42×C11C2411yescharacteristic
456C42×C11C2412yes—
457C42×C11C2411yescharacteristic
458#3514C2×C1111yescharacteristic
459Q8×#41C2×C1111yescharacteristic, complemented
460#3400C2×C1111yescharacteristic, complemented
461#3398C2×C1111yescharacteristic, complemented
462#3375C2×C1111yescharacteristic, complemented
463#3369C2×C1111yescharacteristic, complemented
464#3316C2×C1112yescomplemented
465#3314C2×C1112yescomplemented
466#3299C2×C1111yescharacteristic, complemented
467#3295C2×C1111yescharacteristic, complemented
468D4×Q16C2×C1111yescharacteristic, complemented
469D4×SD16C2×C1111yescharacteristic, complemented
470#3270C2×C1112yescomplemented
471#3266C2×C1112yescomplemented
472#3252C2×C1111yescharacteristic, complemented
473#3248C2×C1112yescomplemented
474#3215C2×C1112yescomplemented
475#3210C2×C1111yescharacteristic, complemented
476#3117C2×C1112yescomplemented
477#3108C2×C1111yescharacteristic, complemented
478#3037C2×C1111yescharacteristic, complemented
479C2×#464C2×C1112yescomplemented
480#2990C2×C1111yescharacteristic, complemented
481C23×C11—21no—
482C23×C11—22no—
483C23×C11—44no—
484C23×C11—82no—
485C23×C11—82no—
486C23×C11C22×D411yescharacteristic
487C23×C11C22×D412yes—
488Q8×C11—22no—
489Q8×C11—21no—
490Q8×C11—22no—
491Q8×C11—21no—
492Q8×C11—21no—
493Q8×C11—22no—
494Q8×C11—21no—
495Q8×C11—22no—
496Q8×C11—21no—
497Q8×C11—22no—
498Q8×C11—42no—
499Q8×C11—44no—
500Q8×C11—82no—
501Q8×C11—81no—
502Q8×C11—82no—
503Q8×C11H(5,𝔽2)12yes—
504D4×C11—24no—
505D4×C11—21no—
506D4×C11—22no—
507D4×C11—21no—
508D4×C11—22no—
509D4×C11—44no—
510D4×C11—42no—
511D4×C11—81no—
512D4×C11—82no—
513D4×C11—81no—
514D4×C11—82no—
515D4×C11#13714yescomplemented
516C2×C4×C11—24no—
517C2×C4×C11—21no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—21no—
521C2×C4×C11—22no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—22no—
526C2×C4×C11—21no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—42no—
533C2×C4×C11—41no—
534C2×C4×C11—44no—
535C2×C4×C11—42no—
536C2×C4×C11—42no—
537C2×C4×C11—82no—
538C2×C4×C11—82no—
539C2×C4×C11—82no—
540C2×C4×C11—81no—
541C2×C4×C11—82no—
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D412yes—
544C2×C4×C11C22×D412yes—
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D411yescharacteristic
547C2×C4×C11C22×D412yes—
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C2511yescharacteristic
551C8×C11—21no—
552C8×C11—21no—
553C8×C11—22no—
554C8×C11—22no—
555C8×C11—21no—
556C8×C11—21no—
557C2×#137C22×C1112yescomplemented
558C22×Q16C22×C1112yescomplemented
559C22×SD16C22×C1112yes—
560#559C22×C1111yescharacteristic
561Q82C22×C1111yescharacteristic, complemented
562#557—21no—
563#557C22×C1111yescharacteristic, complemented
564#556C22×C1111yescharacteristic
565#555—21no—
566#554—21no—
567#554—22no—
568#554C22×C1111yescharacteristic
569#554C22×C1112yescomplemented
570#551—22no—
571D4×Q8C22×C1111yescharacteristic
572D4×Q8C22×C1111yescharacteristic
573D4×Q8C22×C1112yescomplemented
574#548C22×C1112yes—
575#546—21no—
576#546C22×C1112yes—
577D42C22×C1111yescharacteristic
578#542—21no—
579#538—22no—
580#533—22no—
581#533—21no—
582#533C22×C1111yescharacteristic, complemented
583#533C22×C1112yescomplemented
584#532C22×C1111yescharacteristic
585#529C22×C1111yescharacteristic
586#529C22×C1112yes—
587C2×#124C22×C1112yes—
588#518—21no—
589C4×#41—21no—
590C4×#41C22×C1111yescharacteristic
591C2×C4×Q8C22×C1111yescharacteristic, complemented
592C2×C4×Q8C22×C1112yescomplemented
593#497C22×C1112yes—
594#497C22×C1112yescomplemented
595#494C22×C1111yescharacteristic, complemented
596#492C22×C1111yescharacteristic
597#489C22×C1112yes—
598#489C22×C1112yescomplemented
599#487C22×C1111yescharacteristic, complemented
600#486C22×C1111yescharacteristic
601#484C22×C1112yescomplemented
602#483C22×C1111yescharacteristic, complemented
603#481C22×C1112yes—
604#480C22×C1111yescharacteristic
605#479C22×C1111yescharacteristic, complemented
606#479C22×C1111yescharacteristic, complemented
607#479C22×C1112yescomplemented
608#477C22×C1111yescharacteristic, complemented
609#476C22×C1111yescharacteristic
610#475C22×C1112yescomplemented
611#474C22×C1112yescomplemented
612#470C22×C1112yescomplemented
613#468C22×C1112yes—
614#467C22×C1112yescomplemented
615#467C22×C1112yescomplemented
616#465C22×C1112yes—
617#465C22×C1112yes—
618#464C22×C1111yescharacteristic
619#464C22×C1111yescharacteristic
620#464C22×C1112yes—
621#464C22×C1112yes—
622#464C22×C1112yes—
623#464C22×C1112yescomplemented
624#464C22×C1112yescomplemented
625#464C22×C1112yescomplemented
626#464C22×C1112yescomplemented
627#464C22×C1112yescomplemented
628#464C22×C1112yescomplemented
629#462C22×C1111yescharacteristic, complemented
630#462C22×C1112yescomplemented
631#462C22×C1111yescharacteristic, complemented
632#462C22×C1111yescharacteristic, complemented
633#461C22×C1111yescharacteristic
634#461C22×C1112yescomplemented
635#460C22×C1111yescharacteristic
636#460C22×C1111yescharacteristic
637#452C22×C1112yescomplemented
638#452C22×C1112yescomplemented
639#451C22×C1111yescharacteristic, complemented
640#451C22×C1112yescomplemented
641#451C22×C1112yescomplemented
642#451C22×C1112yescomplemented
643#450C22×C1112yes—
644#450C22×C1112yes—
645#448C22×C1111yescharacteristic
646#448C22×C1112yes—
647#446C22×C1111yescharacteristic, complemented
648#446C22×C1111yescharacteristic, complemented
649#441C22×C1112yescomplemented
650#441C22×C1112yescomplemented
651#440C22×C1112yescomplemented
652#440C22×C1112yescomplemented
653C4×Q16C22×C1111yescharacteristic, complemented
654C4×Q16C22×C1111yescharacteristic, complemented
655C4×SD16C22×C1111yescharacteristic
656C4×SD16C22×C1111yescharacteristic
657#435C22×C1112yescomplemented
658#435C22×C1112yescomplemented
659C8×D4C22×C1111yescharacteristic
660C8×D4C22×C1111yescharacteristic
661#432C22×C1112yescomplemented
662#431C22×C1111yescharacteristic, complemented
663#423C22×C1111yescharacteristic, complemented
664C2×C4⋊C8C22×C1112yescomplemented
665#417C22×C1112yescomplemented
666C2×#103C22×C1112yescomplemented
667C2×#102C22×C1112yes—
668C22×C11—22no—
669C22×C11—22no—
670C22×C11—21no—
671C22×C11—21no—
672C22×C11—21no—
673C22×C11—42no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11—41no—
677C22×C11—41no—
678C22×C11—42no—
679C22×C11—164no—
680C22×C11C2×#13714yes—
681C22×C11C23×D411yescharacteristic
682C4×C11—21no—
683C4×C11—22no—
684C4×C11—21no—
685C4×C11—21no—
686C4×C11—22no—
687C4×C11—22no—
688C4×C11—21no—
689C4×C11—22no—
690C4×C11—41no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—41no—
694C4×C11—42no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11—41no—
698C4×C11—41no—
699C4×C11C2×#13712yes—
700C4×C11C2×H(5,𝔽2)11yescharacteristic
701C4×C11#58511yescharacteristic
702C2×#41D4×C1111yescharacteristic
703C2×#41C23×C1112yes—
704C22×Q8C23×C1112yes—
705C22×Q8C23×C1111yescharacteristic
706C22×Q8C23×C1112yes—
707C22×D4—21no—
708C22×D4C23×C1112yes—
709#137—44no—
710C2×Q16—44no—
711C2×Q16C23×C1111yescharacteristic
712C2×Q16C23×C1112yes—
713C2×Q16C23×C1112yes—
714C2×Q16C23×C1112yes—
715C2×Q16C23×C1112yes—
716C2×Q16C23×C1111yescharacteristic
717C2×Q16C23×C1112yes—
718C2×SD16—44no—
719C2×SD16C23×C1111yescharacteristic
720C2×SD16C23×C1112yes—
721C2×SD16C23×C1112yes—
722C2×SD16C23×C1112yes—
723C2×SD16C23×C1112yes—
724C2×SD16C23×C1111yescharacteristic
725C2×SD16C23×C1112yes—
726C2×M16C23×C1112yes—
727C22×C8C23×C1112yes—
728C22×C8C23×C1112yes—
729C4⋊Q8—21no—
730C4⋊Q8—22no—
731C4⋊Q8—21no—
732C4⋊Q8—22no—
733C4⋊Q8—21no—
734C4⋊Q8C23×C1111yescharacteristic
735C4⋊Q8C23×C1111yescharacteristic
736C4⋊Q8C23×C1112yes—
737C4⋊Q8C23×C1111yescharacteristic
738C4⋊Q8C23×C1112yes—
739#127C23×C1111yescharacteristic
740#126—22no—
741#126—22no—
742#126—21no—
743#125—21no—
744#125—22no—
745#125—21no—
746#125—22no—
747#125—21no—
748#125—22no—
749#125C23×C1111yescharacteristic
750#124—21no—
751#124—22no—
752#124—22no—
753#124—22no—
754#124C23×C1111yescharacteristic
755#124C23×C1112yes—
756#124C23×C1112yes—
757#124C23×C1112yes—
758#123—21no—
759#123—22no—
760#123—22no—
761#123—22no—
762C22⋊Q8—21no—
763C22⋊Q8—22no—
764C22⋊Q8—21no—
765C22⋊Q8—22no—
766C22⋊Q8—22no—
767C22⋊Q8—22no—
768C22⋊Q8—22no—
769C22⋊Q8—22no—
770C22⋊Q8—22no—
771C22⋊Q8—22no—
772C22⋊Q8—22no—
773C22⋊Q8C23×C1112yes—
774C22⋊Q8C23×C1111yescharacteristic
775C22⋊Q8C23×C1112yes—
776C22⋊Q8C23×C1112yes—
777C22⋊Q8C23×C1112yes—
778#121—22no—
779#121—21no—
780#121—21no—
781#121—21no—
782#121—22no—
783#121C23×C1112yes—
784#121C23×C1111yescharacteristic
785#120—22no—
786#120—22no—
787C4×Q8—21no—
788C4×Q8—21no—
789C4×Q8—22no—
790C4×Q8—21no—
791C4×Q8—21no—
792C4×Q8—22no—
793C4×Q8—22no—
794C4×Q8—21no—
795C4×Q8D4×C1111yescharacteristic
796C4×Q8C23×C1111yescharacteristic
797C4×Q8C23×C1111yescharacteristic
798C4×Q8C23×C1112yes—
799C4×Q8C23×C1111yescharacteristic
800C4×Q8C23×C1112yes—
801C4×Q8C23×C1111yescharacteristic
802C4×Q8C23×C1112yes—
803C4×Q8C23×C1112yes—
804C4×Q8C23×C1111yescharacteristic
805C4×Q8C23×C1111yescharacteristic
806C4×D4—21no—
807C4×D4—22no—
808C4×D4—21no—
809C4×D4—22no—
810C4×D4—21no—
811C4×D4—22no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—22no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4D4×C1111yescharacteristic
818C4×D4D4×C1112yes—
819C4×D4C23×C1111yescharacteristic
820C4×D4C23×C1112yes—
821C4×D4C23×C1111yescharacteristic
822C4×D4C23×C1112yes—
823#117—22no—
824#117—21no—
825#117—21no—
826#117—21no—
827#117—22no—
828#117D4×C1112yes—
829#117D4×C1111yescharacteristic
830C2×C4⋊C4—22no—
831C2×C4⋊C4—21no—
832C2×C4⋊C4C23×C1112yes—
833C2×C4⋊C4C23×C1111yescharacteristic
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C42—22no—
838C2×C42—21no—
839C2×C42C23×C1112yes—
840C2×C42C23×C1111yescharacteristic
841#107C23×C1111yescharacteristic
842#107C23×C1111yescharacteristic
843#107C23×C1112yes—
844#106C23×C1111yescharacteristic
845#106C23×C1111yescharacteristic
846#106C23×C1112yes—
847C4⋊C8C23×C1111yescharacteristic
848C4⋊C8C23×C1112yes—
849C4⋊C8C23×C1112yes—
850C4⋊C8C23×C1112yes—
851C4⋊C8C23×C1111yescharacteristic
852C4⋊C8C23×C1111yescharacteristic
853C4⋊C8C23×C1111yescharacteristic
854#103C23×C1111yescharacteristic
855#103C23×C1112yes—
856#103C23×C1112yes—
857#103C23×C1112yes—
858#103C23×C1112yes—
859#103C23×C1111yescharacteristic
860#103C23×C1111yescharacteristic
861#103C23×C1111yescharacteristic
862#103C23×C1111yescharacteristic
863#103C23×C1111yescharacteristic
864#103C23×C1112yes—
865#103C23×C1112yes—
866#103C23×C1112yes—
867#102C23×C1111yescharacteristic
868#102C23×C1112yes—
869#102C23×C1112yes—
870#102C23×C1112yes—
871#102C23×C1112yes—
872#102C23×C1111yescharacteristic
873#102C23×C1112yes—
874C22⋊C8C23×C1111yescharacteristic
875C22⋊C8C23×C1111yescharacteristic
876C22⋊C8C23×C1112yes—
877C22⋊C8C23×C1112yes—
878#97C23×C1112yes—
879#97C23×C1112yes—
880C4×C8C23×C1111yescharacteristic
881C4×C8C23×C1111yescharacteristic
882C2×C11—24no—
883C2×C11—41no—
884C2×C11—82no—
885C2×C11—81no—
886C2×C11#348811yescharacteristic
887C2×C11C22×#13711yescharacteristic
888C2×C11#358411yescharacteristic
889C24—22no—
890#41—24no—
891#41—42no—
892#41—42no—
893C2×Q8—21no—
894C2×Q8—22no—
895C2×Q8—22no—
896C2×Q8—21no—
897C2×Q8—22no—
898C2×Q8—24no—
899C2×Q8—22no—
900C2×Q8—42no—
901C2×Q8—41no—
902C2×Q8—42no—
903C2×Q8—42no—
904C2×Q8C2×D4×C1111yescharacteristic
905C2×Q8C24×C1111yescharacteristic
906C2×Q8C24×C1112yes—
907C2×Q8C24×C1111yescharacteristic
908C2×Q8C24×C1112yes—
909C2×Q8C24×C1111yescharacteristic
910C2×D4—22no—
911C2×D4—21no—
912C2×D4—22no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—22no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4C2×D4×C1112yes—
920C2×D4C2×D4×C1111yescharacteristic
921C2×D4C24×C1111yescharacteristic
922C2×D4C24×C1112yes—
923C22×C4—21no—
924C22×C4—22no—
925C22×C4—21no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—21no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4C2×D4×C1112yes—
932C22×C4C2×D4×C1111yescharacteristic
933C22×C4C2×D4×C1112yes—
934C22×C4C2×D4×C1111yescharacteristic
935C22×C4C24×C1112yes—
936C22×C4C24×C1111yescharacteristic
937Q16—22no—
938Q16—24no—
939Q16—42no—
940Q16—42no—
941Q16—42no—
942Q16—41no—
943Q16—42no—
944SD16—22no—
945SD16—24no—
946SD16—42no—
947SD16—42no—
948SD16—42no—
949SD16—42no—
950SD16—41no—
951M16—42no—
952C2×C8—42no—
953C2×C8—42no—
954C2×C8C24×C1111yescharacteristic
955C2×C8C24×C1111yescharacteristic
956C2×C8C24×C1111yescharacteristic
957C2×C8C24×C1111yescharacteristic
958C2×C8C24×C1112yes—
959C2×C8C24×C1112yes—
960C4⋊C4—21no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—22no—
974C4⋊C4—21no—
975C4⋊C4—22no—
976C4⋊C4—21no—
977C4⋊C4—22no—
978C4⋊C4—21no—
979C4⋊C4—22no—
980C4⋊C4—21no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4C2×D4×C1111yescharacteristic
987C4⋊C4C2×D4×C1112yes—
988C4⋊C4C2×D4×C1111yescharacteristic
989C4⋊C4C2×D4×C1112yes—
990C4⋊C4C24×C1111yescharacteristic
991C4⋊C4C24×C1112yes—
992C4⋊C4C24×C1111yescharacteristic
993C4⋊C4C24×C1111yescharacteristic
994C4⋊C4C24×C1111yescharacteristic
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—21no—
1000C22⋊C4—22no—
1001C22⋊C4—21no—
1002C22⋊C4—21no—
1003C22⋊C4—21no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—21no—
1011C22⋊C4—22no—
1012C22⋊C4C2×D4×C1112yes—
1013C22⋊C4C2×D4×C1112yes—
1014C22⋊C4C2×D4×C1112yes—
1015C42—21no—
1016C42—22no—
1017C42—21no—
1018C42—22no—
1019C42—21no—
1020C42—22no—
1021C42—21no—
1022C42—22no—
1023C42—21no—
1024C42C2×D4×C1112yes—
1025C42C2×D4×C1111yescharacteristic
1026C42C2×D4×C1111yescharacteristic
1027C42C2×D4×C1112yes—
1028C42C24×C1111yescharacteristic
1029C42C24×C1112yes—
1030C42C24×C1111yescharacteristic
1031C11#6199111yescharacteristic, direct product factor, Sylow
1032C23—21no—
1033C23—22no—
1034C23—44no—
1035C23—82no—
1036C23—82no—
1037C23C22×D4×C1111yescharacteristic
1038C23C22×D4×C1112yes—
1039Q8—22no—
1040Q8—21no—
1041Q8—22no—
1042Q8—21no—
1043Q8—21no—
1044Q8—22no—
1045Q8—22no—
1046Q8—21no—
1047Q8—21no—
1048Q8—22no—
1049Q8—42no—
1050Q8—44no—
1051Q8—82no—
1052Q8—81no—
1053Q8—82no—
1054Q8C11×H(5,𝔽2)12yes—
1055D4—24no—
1056D4—21no—
1057D4—22no—
1058D4—21no—
1059D4—22no—
1060D4—44no—
1061D4—42no—
1062D4—81no—
1063D4—82no—
1064D4—81no—
1065D4—82no—
1066D4C11×#13714yescomplemented
1067C2×C4—24no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—41no—
1085C2×C4—44no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4—81no—
1092C2×C4—82no—
1093C2×C4C22×D4×C1111yescharacteristic
1094C2×C4C22×D4×C1112yes—
1095C2×C4C22×D4×C1112yes—
1096C2×C4C22×D4×C1111yescharacteristic
1097C2×C4C22×D4×C1111yescharacteristic
1098C2×C4C22×D4×C1112yes—
1099C2×C4C22×D4×C1111yescharacteristic
1100C2×C4C22×D4×C1111yescharacteristic
1101C2×C4C25×C1111yescharacteristic
1102C8—21no—
1103C8—21no—
1104C8—22no—
1105C8—22no—
1106C8—21no—
1107C8—21no—
1108C22—22no—
1109C22—22no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—42no—
1114C22—41no—
1115C22—41no—
1116C22—42no—
1117C22—42no—
1118C22—41no—
1119C22—164no—
1120C22C2×C11×#13714yes—
1121C22C23×D4×C1111yescharacteristic
1122C4—21no—
1123C4—22no—
1124C4—22no—
1125C4—21no—
1126C4—22no—
1127C4—21no—
1128C4—22no—
1129C4—21no—
1130C4—42no—
1131C4—41no—
1132C4—42no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—42no—
1138C4—41no—
1139C4C2×C11×#13712yes—
1140C4C2×C11×H(5,𝔽2)11yescharacteristic
1141C4C11×#58511yescharacteristic
1142C2—24no—
1143C2—41no—
1144C2—81no—
1145C2—82no—
1146C2C11×#348811yescharacteristic
1147C2C22×C11×#13711yescharacteristic
1148C2C11×#358411yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3514C2
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
2. Q8×C11×#41C2semidirect
3. C11×#3400C2semidirect
4. C11×#3398C2semidirect
5. C11×#3375C2semidirect
6. C11×#3369C2semidirect
7. C11×#3316C2semidirect
8. C11×#3314C2semidirect
9. C11×#3299C2semidirect
10. C11×#3295C2semidirect
11. D4×C11×Q16C2semidirect
12. D4×C11×SD16C2semidirect
13. C11×#3270C2semidirect
14. C11×#3266C2semidirect
15. C11×#3252C2semidirect
16. C11×#3248C2semidirect
17. C11×#3215C2semidirect
18. C11×#3210C2semidirect
19. C11×#3117C2semidirect
20. C11×#3108C2semidirect
21. C11×#3037C2semidirect
22. C2×C11×#464C2semidirect
23. C11×#2990C2semidirect
24. C2×C11×#137C22semidirect
25. C22×C11×Q16C22semidirect
28. Q82×C11C22semidirect
30. C11×#557C22semidirect
36. C11×#554C22semidirect
40. D4×Q8×C11C22semidirect
49. C11×#533C22semidirect
50. C11×#533C22semidirect
58. C2×C4×Q8×C11C22semidirect
59. C2×C4×Q8×C11C22semidirect
61. C11×#497C22semidirect
62. C11×#494C22semidirect
65. C11×#489C22semidirect
66. C11×#487C22semidirect
68. C11×#484C22semidirect
69. C11×#483C22semidirect
72. C11×#479C22semidirect
73. C11×#479C22semidirect
74. C11×#479C22semidirect
75. C11×#477C22semidirect
77. C11×#475C22semidirect
78. C11×#474C22semidirect
79. C11×#470C22semidirect
81. C11×#467C22semidirect
82. C11×#467C22semidirect
90. C11×#464C22semidirect
91. C11×#464C22semidirect
92. C11×#464C22semidirect
93. C11×#464C22semidirect
94. C11×#464C22semidirect
95. C11×#464C22semidirect
96. C11×#462C22semidirect
97. C11×#462C22semidirect
98. C11×#462C22semidirect
99. C11×#462C22semidirect
101. C11×#461C22semidirect
104. C11×#452C22semidirect
105. C11×#452C22semidirect
106. C11×#451C22semidirect
107. C11×#451C22semidirect
108. C11×#451C22semidirect
109. C11×#451C22semidirect
114. C11×#446C22semidirect
115. C11×#446C22semidirect
116. C11×#441C22semidirect
117. C11×#441C22semidirect
118. C11×#440C22semidirect
119. C11×#440C22semidirect
120. C4×C11×Q16C22semidirect
121. C4×C11×Q16C22semidirect
124. C11×#435C22semidirect
125. C11×#435C22semidirect
128. C11×#432C22semidirect
129. C11×#431C22semidirect
130. C11×#423C22semidirect
131. C2×C11×C4⋊C8C22semidirect
132. C11×#417C22semidirect
133. C2×C11×#103C22semidirect
315. #61991C11direct (N × H)
459. Q8×#41C2×C11semidirect
460. #3400C2×C11semidirect
461. #3398C2×C11semidirect
462. #3375C2×C11semidirect
463. #3369C2×C11semidirect
464. #3316C2×C11semidirect
465. #3314C2×C11semidirect
466. #3299C2×C11semidirect
467. #3295C2×C11semidirect
468. D4×Q16C2×C11semidirect
469. D4×SD16C2×C11semidirect
470. #3270C2×C11semidirect
471. #3266C2×C11semidirect
472. #3252C2×C11semidirect
473. #3248C2×C11semidirect
474. #3215C2×C11semidirect
475. #3210C2×C11semidirect
476. #3117C2×C11semidirect
477. #3108C2×C11semidirect
478. #3037C2×C11semidirect
479. C2×#464C2×C11semidirect
480. #2990C2×C11semidirect
515. D4×C11#137semidirect
557. C2×#137C22×C11semidirect
558. C22×Q16C22×C11semidirect
561. Q82C22×C11semidirect
563. #557C22×C11semidirect
569. #554C22×C11semidirect
573. D4×Q8C22×C11semidirect
582. #533C22×C11semidirect
583. #533C22×C11semidirect
591. C2×C4×Q8C22×C11semidirect
592. C2×C4×Q8C22×C11semidirect
594. #497C22×C11semidirect
595. #494C22×C11semidirect
598. #489C22×C11semidirect
599. #487C22×C11semidirect
601. #484C22×C11semidirect
602. #483C22×C11semidirect
605. #479C22×C11semidirect
606. #479C22×C11semidirect
607. #479C22×C11semidirect
608. #477C22×C11semidirect
610. #475C22×C11semidirect
611. #474C22×C11semidirect
612. #470C22×C11semidirect
614. #467C22×C11semidirect
615. #467C22×C11semidirect
623. #464C22×C11semidirect
624. #464C22×C11semidirect
625. #464C22×C11semidirect
626. #464C22×C11semidirect
627. #464C22×C11semidirect
628. #464C22×C11semidirect
629. #462C22×C11semidirect
630. #462C22×C11semidirect
631. #462C22×C11semidirect
632. #462C22×C11semidirect
634. #461C22×C11semidirect
637. #452C22×C11semidirect
638. #452C22×C11semidirect
639. #451C22×C11semidirect
640. #451C22×C11semidirect
641. #451C22×C11semidirect
642. #451C22×C11semidirect
647. #446C22×C11semidirect
648. #446C22×C11semidirect
649. #441C22×C11semidirect
650. #441C22×C11semidirect
651. #440C22×C11semidirect
652. #440C22×C11semidirect
653. C4×Q16C22×C11semidirect
654. C4×Q16C22×C11semidirect
657. #435C22×C11semidirect
658. #435C22×C11semidirect
661. #432C22×C11semidirect
662. #431C22×C11semidirect
663. #423C22×C11semidirect
664. C2×C4⋊C8C22×C11semidirect
665. #417C22×C11semidirect
666. C2×#103C22×C11semidirect
1031. C11#61991direct (N × H)
1066. D4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#35142
Q8×C11×#412
C11×#34002
C11×#33982
C11×#33752
C11×#33692
C11×#33162
C11×#33142
C11×#32992
C11×#32952
D4×C11×Q162
D4×C11×SD162
C11×#32702
C11×#32662
C11×#32522
C11×#32482
C11×#32152
C11×#32102
C11×#31172
C11×#31082
C11×#30372
C2×C11×#4642
C11×#29902
#6199111