Finite Group Databasebeta

← C11×#33347 #14610540

Subgroups — C11×#33347 #14610540

Order 2816.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3449C211yesmaximal, characteristic
2C2×C11×#413C211yesmaximal, characteristic, complemented
3C2×C11×#410C211yesmaximal, characteristic, complemented
4C11×#2123C212yesmaximal, complemented
5C11×#2122C212yesmaximal, complemented
6C11×#2121C214yesmaximal, complemented
7C11×#2120C214yesmaximal, complemented
8C22×C11×#41C411yescharacteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16—21no—
11C11×#537—21no—
12C11×#537—21no—
13C11×#536—21no—
14C11×#536C411yescharacteristic, complemented
15C11×#536C2211yescharacteristic
16C11×#535—21no—
17C11×#535C411yescharacteristic, complemented
18C11×#535C2211yescharacteristic
19C11×#534C412yescomplemented
20C11×#534C2212yes—
21C11×#532—21no—
22C11×#532—21no—
23C11×#525—21no—
24C11×#525—21no—
25C11×#525C412yescomplemented
26C11×#525C2212yes—
27C2×C11×#117—21no—
28C2×C11×#117C411yescharacteristic, complemented
29C11×#413—21no—
30C11×#413—21no—
31C11×#413C2212yes—
32C11×#413C2212yes—
33C2×C11×#101—21no—
34C2×C11×#100C2212yes—
35C11×#410—21no—
36C11×#410—21no—
37C11×#410C2212yes—
38C11×#410C2212yes—
39C2×C11×#99—21no—
40C2×C11×#99C2212yes—
41C11×#352C2218yescomplemented
42C11×AΣL(1,𝔽16)C2218yescomplemented
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—41no—
48C2×C11×#41—41no—
49C2×C11×#41—41no—
50C2×C11×#41—41no—
51C2×C11×#41—41no—
52C2×C11×#41—41no—
53C2×C11×#41—41no—
54C2×C11×#41—41no—
55C2×C11×#41C2×C411yescharacteristic
56C2×C11×#41C2×C411yescharacteristic
57C2×C11×#41D411yescharacteristic
58C2×C11×#41D411yescharacteristic
59C2×C11×#41D411yescharacteristic
60C2×C11×#41D411yescharacteristic
61C2×C11×#41C2311yescharacteristic
62C2×C11×#41C2311yescharacteristic
63C22×Q8×C11C2×C411yescharacteristic, complemented
64C22×Q8×C11D411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C22×D4×C11C2×C412yes—
67C22×D4×C11C2×C411yescharacteristic, complemented
68C22×D4×C11D411yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11C2×C411yescharacteristic
71C23×C4×C11C2×C412yescomplemented
72C23×C4×C11D411yescharacteristic
73C23×C4×C11D411yescharacteristic
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16—41no—
78C2×C11×M16—41no—
79C2×C11×M16—41no—
80C22×C8×C11—41no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×#127—21no—
84C11×#127—21no—
85C11×#124—21no—
86C11×#124—21no—
87C11×#124—21no—
88C11×#124—21no—
89C11×#123—22no—
90C11×#123—22no—
91C11×#123C2×C412yes—
92C11×#123C2×C412yescomplemented
93C11×#123C2×C412yescomplemented
94C11×#123C2312yes—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8—21no—
100C11×C22⋊Q8—21no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121—22no—
107C11×#121—21no—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121—21no—
111C11×#120—22no—
112C11×#120—22no—
113C11×#120C2×C412yes—
114C11×#120C2×C412yescomplemented
115C11×#120C2×C412yescomplemented
116C11×#120C2312yes—
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C11×#117—21no—
122C11×#117—21no—
123C11×#117—22no—
124C11×#117—22no—
125C11×#117—41no—
126C11×#117—41no—
127C11×#117C2×C412yescomplemented
128C11×#117C2×C411yescharacteristic, complemented
129C11×#117C2×C411yescharacteristic, complemented
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—41no—
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4C2×C412yes—
134C2×C42×C11—21no—
135C2×C42×C11—41no—
136C11×#101—22no—
137C11×#101—22no—
138C11×#100—22no—
139C11×#100C2314yes—
140C11×#99—22no—
141C11×#99—22no—
142C11×#99—22no—
143C11×#99C2314yes—
144#33347C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11C22⋊C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C412yes—
148C24×C11C2×D411yescharacteristic
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C11×#41—41no—
156C11×#41—41no—
157C11×#41—41no—
158C11×#41—41no—
159C11×#41—41no—
160C11×#41—41no—
161C11×#41—41no—
162C11×#41—41no—
163C11×#41—41no—
164C11×#41—41no—
165C11×#41—42no—
166C11×#41—42no—
167C11×#41—42no—
168C11×#41—42no—
169C11×#41—42no—
170C11×#41—42no—
171C11×#41—41no—
172C11×#41—41no—
173C11×#41—41no—
174C11×#41—41no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—41no—
178C2×Q8×C11—41no—
179C2×Q8×C11—41no—
180C2×Q8×C11—41no—
181C2×Q8×C11C22⋊C411yescharacteristic
182C2×Q8×C11C22⋊C411yescharacteristic
183C2×Q8×C11C2×D411yescharacteristic
184C2×Q8×C11C2×D411yescharacteristic
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—41no—
194C2×D4×C11—41no—
195C2×D4×C11—41no—
196C2×D4×C11—41no—
197C2×D4×C11—41no—
198C2×D4×C11—41no—
199C2×D4×C11—41no—
200C2×D4×C11—41no—
201C2×D4×C11—42no—
202C2×D4×C11—42no—
203C2×D4×C11C22⋊C411yescharacteristic
204C2×D4×C11C22⋊C411yescharacteristic
205C2×D4×C11C22⋊C411yescharacteristic
206C2×D4×C11C22⋊C411yescharacteristic
207C2×D4×C11C22×C411yescharacteristic
208C2×D4×C11C22×C411yescharacteristic
209C2×D4×C11C22×C411yescharacteristic
210C2×D4×C11C2×D411yescharacteristic
211C2×D4×C11C2×D411yescharacteristic
212C2×D4×C11C2×D411yescharacteristic
213C2×D4×C11C2×D411yescharacteristic
214C2×D4×C11C2411yescharacteristic
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—42no—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11C22⋊C411yescharacteristic
234C22×C4×C11C22⋊C411yescharacteristic
235C22×C4×C11C22⋊C411yescharacteristic
236C22×C4×C11C22⋊C411yescharacteristic
237C22×C4×C11C22⋊C411yescharacteristic
238C22×C4×C11C22⋊C411yescharacteristic
239C22×C4×C11C22⋊C411yescharacteristic
240C22×C4×C11C22⋊C411yescharacteristic
241C22×C4×C11C22⋊C411yescharacteristic
242C22×C4×C11C22×C411yescharacteristic
243C22×C4×C11C22×C411yescharacteristic
244C22×C4×C11C22×C412yes—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C11×M16—24no—
251C11×M16—42no—
252C11×M16—42no—
253C11×M16—42no—
254C2×C8×C11—42no—
255C2×C8×C11—42no—
256C2×C8×C11—42no—
257C11×C4⋊C4—22no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—22no—
261C11×C4⋊C4—22no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4—22no—
264C11×C4⋊C4—42no—
265C11×C4⋊C4—42no—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—22no—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—22no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—24no—
276C11×C22⋊C4—42no—
277C11×C22⋊C4C22×C412yes—
278C11×C22⋊C4C22×C412yes—
279C42×C11—22no—
280C42×C11—21no—
281C42×C11—21no—
282C42×C11—42no—
283C42×C11—42no—
284#3449C2×C1111yescharacteristic
285C2×#413C2×C1111yescharacteristic, complemented
286C2×#410C2×C1111yescharacteristic, complemented
287#2123C2×C1112yescomplemented
288#2122C2×C1112yescomplemented
289#2121C2×C1114yescomplemented
290#2120C2×C1114yescomplemented
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—81no—
300C23×C11—81no—
301C23×C11—81no—
302C23×C11—82no—
303C23×C11C2×C22⋊C411yescharacteristic
304C23×C11C2×C22⋊C411yescharacteristic
305C23×C11C2×C22⋊C411yescharacteristic
306C23×C11C2×C22⋊C411yescharacteristic
307C23×C11C2×C22⋊C411yescharacteristic
308C23×C11C23×C411yescharacteristic
309C23×C11C22×D411yescharacteristic
310Q8×C11—41no—
311Q8×C11—41no—
312Q8×C11—41no—
313Q8×C11—41no—
314Q8×C11—42no—
315Q8×C11—41no—
316Q8×C11—41no—
317D4×C11—41no—
318D4×C11—41no—
319D4×C11—41no—
320D4×C11—41no—
321D4×C11—41no—
322D4×C11—41no—
323D4×C11—41no—
324D4×C11—41no—
325D4×C11—41no—
326D4×C11—41no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—42no—
330D4×C11—44no—
331D4×C11—42no—
332D4×C11—42no—
333D4×C11—41no—
334D4×C11—41no—
335D4×C11—82no—
336D4×C11—82no—
337D4×C11—82no—
338D4×C11—82no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—44no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—44no—
377C2×C4×C11—82no—
378C2×C4×C11—84no—
379C2×C4×C11#9911yescharacteristic
380C2×C4×C11#9911yescharacteristic
381C2×C4×C11#9911yescharacteristic
382C2×C4×C11#9911yescharacteristic
383C2×C4×C11C2×C22⋊C411yescharacteristic
384C2×C4×C11C2×C22⋊C411yescharacteristic
385C2×C4×C11C2×C22⋊C411yescharacteristic
386C2×C4×C11C2×C22⋊C411yescharacteristic
387C2×C4×C11C2×C22⋊C411yescharacteristic
388C2×C4×C11C2×C22⋊C411yescharacteristic
389C2×C4×C11C2×C22⋊C411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C8×C11—44no—
392C22×#41C4×C1111yescharacteristic, complemented
393C22×#41C22×C1111yescharacteristic
394C22×M16—21no—
395#537—21no—
396#537—21no—
397#536—21no—
398#536C4×C1111yescharacteristic, complemented
399#536C22×C1111yescharacteristic
400#535—21no—
401#535C4×C1111yescharacteristic, complemented
402#535C22×C1111yescharacteristic
403#534C4×C1112yescomplemented
404#534C22×C1112yes—
405#532—21no—
406#532—21no—
407#525—21no—
408#525—21no—
409#525C4×C1112yescomplemented
410#525C22×C1112yes—
411C2×#117—21no—
412C2×#117C4×C1111yescharacteristic, complemented
413#413—21no—
414#413—21no—
415#413C22×C1112yes—
416#413C22×C1112yes—
417C2×#101—21no—
418C2×#100C22×C1112yes—
419#410—21no—
420#410—21no—
421#410C22×C1112yes—
422#410C22×C1112yes—
423C2×#99—21no—
424C2×#99C22×C1112yes—
425#352C22×C1118yescomplemented
426AΣL(1,𝔽16)C22×C1118yescomplemented
427C22×C11—21no—
428C22×C11—21no—
429C22×C11—21no—
430C22×C11—21no—
431C22×C11—21no—
432C22×C11—21no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—81no—
446C22×C11—81no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—84no—
450C22×C11C2×#9911yescharacteristic
451C22×C11C2×#9911yescharacteristic
452C22×C11C22×C22⋊C411yescharacteristic
453C4×C11—21no—
454C4×C11—21no—
455C4×C11—21no—
456C4×C11—21no—
457C4×C11—21no—
458C4×C11—21no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—84no—
463C4×C11C2×#9911yescharacteristic
464C4×C11C2×#9911yescharacteristic
465C4×C11C2×#9911yescharacteristic
466C4×C11C2×#9911yescharacteristic
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—41no—
472C2×#41—41no—
473C2×#41—41no—
474C2×#41—41no—
475C2×#41—41no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41C2×C4×C1111yescharacteristic
480C2×#41C2×C4×C1111yescharacteristic
481C2×#41D4×C1111yescharacteristic
482C2×#41D4×C1111yescharacteristic
483C2×#41D4×C1111yescharacteristic
484C2×#41D4×C1111yescharacteristic
485C2×#41C23×C1111yescharacteristic
486C2×#41C23×C1111yescharacteristic
487C22×Q8C2×C4×C1111yescharacteristic, complemented
488C22×Q8D4×C1111yescharacteristic
489C22×D4C2×C4×C1111yescharacteristic
490C22×D4C2×C4×C1112yes—
491C22×D4C2×C4×C1111yescharacteristic, complemented
492C22×D4D4×C1111yescharacteristic
493C22×D4C23×C1111yescharacteristic
494C23×C4C2×C4×C1111yescharacteristic
495C23×C4C2×C4×C1112yescomplemented
496C23×C4D4×C1111yescharacteristic
497C23×C4D4×C1111yescharacteristic
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C2×M16—41no—
503C2×M16—41no—
504C22×C8—41no—
505C4⋊Q8—21no—
506C4⋊Q8—21no—
507#127—21no—
508#127—21no—
509#124—21no—
510#124—21no—
511#124—21no—
512#124—21no—
513#123—22no—
514#123—22no—
515#123C2×C4×C1112yes—
516#123C2×C4×C1112yescomplemented
517#123C2×C4×C1112yescomplemented
518#123C23×C1112yes—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#120—22no—
536#120—22no—
537#120C2×C4×C1112yes—
538#120C2×C4×C1112yescomplemented
539#120C2×C4×C1112yescomplemented
540#120C23×C1112yes—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545#117—21no—
546#117—21no—
547#117—22no—
548#117—22no—
549#117—41no—
550#117—41no—
551#117C2×C4×C1112yescomplemented
552#117C2×C4×C1111yescharacteristic, complemented
553#117C2×C4×C1111yescharacteristic, complemented
554C2×C4⋊C4—21no—
555C2×C4⋊C4—41no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4C2×C4×C1112yes—
558C2×C42—21no—
559C2×C42—41no—
560#101—22no—
561#101—22no—
562#100—22no—
563#100C23×C1114yes—
564#99—22no—
565#99—22no—
566#99—22no—
567#99C23×C1114yes—
568C2×C11—21no—
569C2×C11—21no—
570C2×C11—21no—
571C2×C11—41no—
572C2×C11—41no—
573C2×C11—41no—
574C2×C11—41no—
575C2×C11—41no—
576C2×C11—41no—
577C2×C11—82no—
578C2×C11C22×#9911yescharacteristic
579C24C11×C22⋊C411yescharacteristic
580C24C22×C4×C1111yescharacteristic
581C24C22×C4×C1112yes—
582C24C2×D4×C1111yescharacteristic
583#41—41no—
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—42no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—41no—
606#41—41no—
607#41—41no—
608#41—41no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—41no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8C11×C22⋊C411yescharacteristic
616C2×Q8C11×C22⋊C411yescharacteristic
617C2×Q8C2×D4×C1111yescharacteristic
618C2×Q8C2×D4×C1111yescharacteristic
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4C11×C22⋊C411yescharacteristic
638C2×D4C11×C22⋊C411yescharacteristic
639C2×D4C11×C22⋊C411yescharacteristic
640C2×D4C11×C22⋊C411yescharacteristic
641C2×D4C22×C4×C1111yescharacteristic
642C2×D4C22×C4×C1111yescharacteristic
643C2×D4C22×C4×C1111yescharacteristic
644C2×D4C2×D4×C1111yescharacteristic
645C2×D4C2×D4×C1111yescharacteristic
646C2×D4C2×D4×C1111yescharacteristic
647C2×D4C2×D4×C1111yescharacteristic
648C2×D4C24×C1111yescharacteristic
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C11×C22⋊C411yescharacteristic
668C22×C4C11×C22⋊C411yescharacteristic
669C22×C4C11×C22⋊C411yescharacteristic
670C22×C4C11×C22⋊C411yescharacteristic
671C22×C4C11×C22⋊C411yescharacteristic
672C22×C4C11×C22⋊C411yescharacteristic
673C22×C4C11×C22⋊C411yescharacteristic
674C22×C4C11×C22⋊C411yescharacteristic
675C22×C4C11×C22⋊C411yescharacteristic
676C22×C4C22×C4×C1111yescharacteristic
677C22×C4C22×C4×C1111yescharacteristic
678C22×C4C22×C4×C1112yes—
679C22×C4C2×D4×C1111yescharacteristic
680C22×C4C2×D4×C1111yescharacteristic
681C22×C4C2×D4×C1111yescharacteristic
682C22×C4C2×D4×C1111yescharacteristic
683C22×C4C2×D4×C1111yescharacteristic
684M16—24no—
685M16—42no—
686M16—42no—
687M16—42no—
688C2×C8—42no—
689C2×C8—42no—
690C2×C8—42no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—24no—
710C22⋊C4—42no—
711C22⋊C4C22×C4×C1112yes—
712C22⋊C4C22×C4×C1112yes—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—42no—
717C42—42no—
718C11#3334711yescharacteristic, direct product factor, Sylow
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C11×C22⋊C411yescharacteristic
732C23C2×C11×C22⋊C411yescharacteristic
733C23C2×C11×C22⋊C411yescharacteristic
734C23C2×C11×C22⋊C411yescharacteristic
735C23C2×C11×C22⋊C411yescharacteristic
736C23C23×C4×C1111yescharacteristic
737C23C22×D4×C1111yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4C11×#9911yescharacteristic
808C2×C4C11×#9911yescharacteristic
809C2×C4C11×#9911yescharacteristic
810C2×C4C11×#9911yescharacteristic
811C2×C4C2×C11×C22⋊C411yescharacteristic
812C2×C4C2×C11×C22⋊C411yescharacteristic
813C2×C4C2×C11×C22⋊C411yescharacteristic
814C2×C4C2×C11×C22⋊C411yescharacteristic
815C2×C4C2×C11×C22⋊C411yescharacteristic
816C2×C4C2×C11×C22⋊C411yescharacteristic
817C2×C4C2×C11×C22⋊C411yescharacteristic
818C2×C4C22×D4×C1111yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×C11×#9911yescharacteristic
844C22C2×C11×#9911yescharacteristic
845C22C22×C11×C22⋊C411yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×C11×#9911yescharacteristic
857C4C2×C11×#9911yescharacteristic
858C4C2×C11×#9911yescharacteristic
859C4C2×C11×#9911yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×C11×#9911yescharacteristic
subgroupG/H
centerC4×C11C2×#99
commutatorC23C23×C4×C11
Frattini, cosocleC2×D4C24×C11
socleC2×C11C22×#99
prime radicalC11×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#413C2semidirect
3. C2×C11×#410C2semidirect
4. C11×#2123C2semidirect
5. C11×#2122C2semidirect
6. C11×#2121C2semidirect
7. C11×#2120C2semidirect
8. C22×C11×#41C4semidirect
14. C11×#536C4semidirect
17. C11×#535C4semidirect
19. C11×#534C4semidirect
25. C11×#525C4semidirect
28. C2×C11×#117C4semidirect
41. C11×#352C22semidirect
42. C11×AΣL(1,𝔽16)C22semidirect
63. C22×Q8×C11C2×C4semidirect
67. C22×D4×C11C2×C4semidirect
71. C23×C4×C11C2×C4semidirect
92. C11×#123C2×C4semidirect
93. C11×#123C2×C4semidirect
114. C11×#120C2×C4semidirect
115. C11×#120C2×C4semidirect
127. C11×#117C2×C4semidirect
128. C11×#117C2×C4semidirect
129. C11×#117C2×C4semidirect
144. #33347C11direct (N × H)
285. C2×#413C2×C11semidirect
286. C2×#410C2×C11semidirect
287. #2123C2×C11semidirect
288. #2122C2×C11semidirect
289. #2121C2×C11semidirect
290. #2120C2×C11semidirect
392. C22×#41C4×C11semidirect
398. #536C4×C11semidirect
401. #535C4×C11semidirect
403. #534C4×C11semidirect
409. #525C4×C11semidirect
412. C2×#117C4×C11semidirect
425. #352C22×C11semidirect
426. AΣL(1,𝔽16)C22×C11semidirect
487. C22×Q8C2×C4×C11semidirect
491. C22×D4C2×C4×C11semidirect
495. C23×C4C2×C4×C11semidirect
516. #123C2×C4×C11semidirect
517. #123C2×C4×C11semidirect
538. #120C2×C4×C11semidirect
539. #120C2×C4×C11semidirect
551. #117C2×C4×C11semidirect
552. #117C2×C4×C11semidirect
553. #117C2×C4×C11semidirect
718. C11#33347direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34492
C2×C11×#4132
C2×C11×#4102
C11×#21232
C11×#21222
C11×#21212
C11×#21202
#3334711