Finite Group Databasebeta

← D11×#1510 #14721001

Subgroups — D11×#1510 #14721001

Order 2816.

1790 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic, complemented
3D11×#381C211yesmaximal, characteristic, complemented
4#13067146C211yesmaximal, characteristic, complemented
5#13067145C211yesmaximal, characteristic, complemented
6#13067144C211yesmaximal, characteristic, complemented
7#13067143C214yesmaximal, complemented
8D11×#327C214yesmaximal, complemented
9C11×#1510C211yesmaximal, characteristic, complemented
10C22×D4×D11—21no—
11C22×D4×D11C411yescharacteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C2×#66992—21no—
15C2×#66991C411yescharacteristic, complemented
16C2×#66983C2211yescharacteristic
17C2×M16×D11—21no—
18D11×#121—21no—
19D11×#121—21no—
20D11×#121—21no—
21D11×#121—21no—
22D11×#121C412yescomplemented
23D11×#121C412yescomplemented
24D11×#121C2212yes—
25D11×#121C2212yes—
26C2×#66948C411yescharacteristic, complemented
27C2×C4⋊C4×D11C411yescharacteristic, complemented
28C2×#66937—21no—
29C2×C22⋊C4×D11—21no—
30C2×C22⋊C4×D11—21no—
31C11×#407C2211yescharacteristic, complemented
32C11×#381C2211yescharacteristic, complemented
33#10622824C2211yescharacteristic, complemented
34#10622820C2211yescharacteristic, complemented
35#10622739—21no—
36#10622556—21no—
37#10622339—21no—
38#10622339C2212yescomplemented
39D11×C22⋊C8—21no—
40D11×C22⋊C8C2212yescomplemented
41#10622277—21no—
42#10622277C2212yescomplemented
43D11×#95—21no—
44D11×#95C2212yescomplemented
45C11×#327C2214yescomplemented
46#10622175C2214yescomplemented
47#10622108C2214yescomplemented
48#10622089C2214yescomplemented
49C24×D11—21no—
50C24×D11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11C2×C411yescharacteristic, complemented
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—21no—
55C22×C22⋊D11—21no—
56C22×C22⋊D11—21no—
57C23×Dic11D411yescharacteristic
58C2×D4×D11—22no—
59C2×D4×D11—22no—
60C2×D4×D11—22no—
61C2×D4×D11—22no—
62C2×D4×D11—21no—
63C2×D4×D11—21no—
64C2×D4×D11—44no—
65C2×D4×D11—48no—
66C2×D4×D11C2×C412yes—
67C2×D4×D11C2×C412yescomplemented
68C22×D44—21no—
69C22×D44C2×C411yescharacteristic, complemented
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×C4×D11—44no—
73C22×C4×D11C2×C411yescharacteristic
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2×C411yescharacteristic
77C22×C4×D11D411yescharacteristic
78C22×C4×D11D411yescharacteristic
79C22×C4×D11D411yescharacteristic
80C22×C4×D11D411yescharacteristic
81C22×C4×D11D411yescharacteristic
82C22×C4×D11D411yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C2×C11×M16—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121C2×C412yescomplemented
89C11×#121C2312yes—
90C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95#66992—22no—
96#66992—22no—
97#66992—22no—
98#66992—22no—
99#66991—21no—
100#66991—21no—
101#66991C2×C412yes—
102#66991C2×C412yescomplemented
103#66983—21no—
104#66983—21no—
105#66983C2×C412yescomplemented
106#66983C2312yes—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—22no—
110C2×C4⋊Dic11C2×C411yescharacteristic, complemented
111C2×Dic11⋊C4—21no—
112C2×#4318—21no—
113M16×D11—44no—
114C2×#4313—22no—
115C2×C8×D11—22no—
116#66948—21no—
117#66948—21no—
118#66948C2×C412yes—
119#66948C2×C412yescomplemented
120C4⋊C4×D11—21no—
121C4⋊C4×D11—21no—
122C4⋊C4×D11C2×C412yes—
123C4⋊C4×D11C2×C412yescomplemented
124#66937—22no—
125#66937—22no—
126#66937—22no—
127#66937—22no—
128C22⋊C4×D11—22no—
129C22⋊C4×D11—22no—
130C22⋊C4×D11—22no—
131C22⋊C4×D11—22no—
132C22⋊C4×D11—44no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8C2312yescomplemented
135C11×#95—21no—
136C11×#95C2312yescomplemented
137C11⋊#95—21no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95C2312yescomplemented
141C22⋊(C11⋊C8)—21no—
142C22⋊(C11⋊C8)C2312yescomplemented
143(C2×D11)⋊C8—22no—
144(C2×D11)⋊C8—22no—
145C2×#1510—111nomaximal, Sylow
146C24×C11—21no—
147C24×C11C2×D411yescharacteristic
148C23×D11—24no—
149C23×D11—24no—
150C23×D11—21no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—42no—
154C23×D11—44no—
155C23×D11—44no—
156C23×D11—44no—
157C23×D11C22⋊C411yescharacteristic
158C23×D11C22⋊C411yescharacteristic
159C23×D11C22⋊C411yescharacteristic
160C23×D11C22⋊C411yescharacteristic
161C23×D11C2×D411yescharacteristic
162C23×D11C2×D411yescharacteristic
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—42no—
167C2×D4×C11—44no—
168C2×D4×C11C22×C412yes—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—42no—
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—22no—
181C2×C22⋊D11—22no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—44no—
185C2×C22⋊D11—44no—
186C2×C22⋊D11—44no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—42no—
190C22×Dic11C22⋊C411yescharacteristic
191C22×Dic11C22⋊C411yescharacteristic
192C22×Dic11C22⋊C411yescharacteristic
193C22×Dic11C22⋊C411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196D4×D11—48no—
197D4×D11—48no—
198D4×D11—48no—
199D4×D11—44no—
200D4×D11—44no—
201D4×D11—48no—
202D4×D11—44no—
203D4×D11—44no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—21no—
207C2×D44—42no—
208C2×D44—44no—
209C2×D44C22×C412yes—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×C4×D11—42no—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—42no—
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11C22⋊C411yescharacteristic
229C2×C4×D11C22⋊C411yescharacteristic
230C2×C4×D11C22⋊C411yescharacteristic
231C2×C4×D11C22⋊C411yescharacteristic
232C2×C4×D11C22⋊C411yescharacteristic
233C2×C4×D11C22⋊C411yescharacteristic
234C2×C4×D11C22⋊C411yescharacteristic
235C2×C4×D11C22⋊C411yescharacteristic
236C2×C4×D11C22×C411yescharacteristic
237C2×C4×D11C22×C411yescharacteristic
238C2×C4×D11C22×C411yescharacteristic
239C2×C4×D11C22×C411yescharacteristic
240C2×C4×D11C2×D411yescharacteristic
241C2×C4×D11C2×D411yescharacteristic
242C2×C4×D11C2×D411yescharacteristic
243C2×C4×D11C2×D411yescharacteristic
244C11×M16—42no—
245C2×C8×C11—22no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4C22×C412yes—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—42no—
251C22⋊Dic11—22no—
252C22⋊Dic11—22no—
253C22⋊Dic11—42no—
254(C2×D11)⋊C4—22no—
255(C2×D11)⋊C4—22no—
256(C2×D11)⋊C4—22no—
257(C2×D11)⋊C4—22no—
258(C2×D11)⋊C4—44no—
259C4⋊Dic11—21no—
260C4⋊Dic11C22×C412yes—
261Dic11⋊C4—22no—
262Dic11⋊C4—22no—
263#4318—42no—
264C2×C11⋊C8—22no—
265#4313—44no—
266C8×D11—44no—
267C22×#121—111no—
268C2×#407—111no—
269C2×#381—111no—
270#1510—111no—
271#1510—111no—
272#1510—114no—
273#1510—111no—
274#1510D1111yescharacteristic, direct product factor
275C2×#327—114no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—41no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—42no—
283C23×C11C2×C22⋊C411yescharacteristic
284C23×C11C2×C22⋊C411yescharacteristic
285C23×C11C22×D411yescharacteristic
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—416no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—44no—
310C22×D11—44no—
311C22×D11—44no—
312C22×D11—44no—
313C22×D11—816no—
314C22×D11#9914yes—
315C22×D11C2×C22⋊C411yescharacteristic
316C22×D11C2×C22⋊C411yescharacteristic
317C22×D11C2×C22⋊C411yescharacteristic
318C22×D11C2×C22⋊C411yescharacteristic
319C22×D11AGL(1,ℤ/8)14yes—
320D4×C11—42no—
321D4×C11—42no—
322D4×C11—44no—
323D4×C11—44no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11C2×C22⋊C411yescharacteristic
336C2×C4×C11C2×C22⋊C411yescharacteristic
337C2×C4×C11C23×C411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C22⋊D11—44no—
340C22⋊D11—44no—
341C22⋊D11—44no—
342C22⋊D11—44no—
343C22⋊D11—44no—
344C22⋊D11—44no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11C2×C22⋊C411yescharacteristic
357C2×Dic11C2×C22⋊C411yescharacteristic
358C2×Dic11C2×C22⋊C411yescharacteristic
359C2×Dic11C2×C22⋊C411yescharacteristic
360D44—42no—
361D44—42no—
362D44—44no—
363D44—44no—
364C4×D11—22no—
365C4×D11—22no—
366C4×D11—22no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—22no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—41no—
373C4×D11—41no—
374C4×D11—41no—
375C4×D11—41no—
376C4×D11—41no—
377C4×D11—41no—
378C4×D11—41no—
379C4×D11—41no—
380C4×D11—44no—
381C4×D11—44no—
382C4×D11—88no—
383C8×C11—42no—
384C11⋊C8—42no—
385C23×D4—111no—
386C23×D4—221no—
387C24×C4—111no—
388C22×M16—221no—
389C2×#121—111no—
390C2×#121—111no—
391C2×#121—112no—
392C2×#121—112no—
393C2×#121—112no—
394C2×#121—112no—
395C2×#121—111no—
396C2×#121—221no—
397C2×#121—221no—
398C2×#121—221no—
399C2×#121—221no—
400C2×#121—221no—
401C2×#121—221no—
402C2×#121C2×D1111yescharacteristic
403C22×C4⋊C4—111no—
404C22×C22⋊C4—221no—
405C22×C22⋊C4—221no—
406#407—111no—
407#407—112no—
408#407—221no—
409#407—221no—
410#407C2×D1111yescharacteristic, complemented
411C2×C22⋊C8—112no—
412C2×C22⋊C8—221no—
413#381—111no—
414#381—112no—
415#381—221no—
416#381—221no—
417#381C2×D1111yescharacteristic, complemented
418C2×#95—112no—
419C2×#95—221no—
420#327—114no—
421#327—114no—
422#327—114no—
423#327C2×D1114yescomplemented
424C22×C11—21no—
425C22×C11—21no—
426C22×C11—21no—
427C22×C11—21no—
428C22×C11—21no—
429C22×C11—21no—
430C22×C11—21no—
431C22×C11—44no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—84no—
436C22×C11C2×#9912yes—
437C22×C11C22×C22⋊C411yescharacteristic
438C22×C11C2×AGL(1,ℤ/8)12yes—
439C2×D11—21no—
440C2×D11—21no—
441C2×D11—21no—
442C2×D11—21no—
443C2×D11—28no—
444C2×D11—28no—
445C2×D11—21no—
446C2×D11—21no—
447C2×D11—21no—
448C2×D11—44no—
449C2×D11—44no—
450C2×D11—44no—
451C2×D11—44no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—88no—
456C2×D11—84no—
457C2×D11—88no—
458C2×D11C2×#9912yes—
459C2×D11C2×#9912yes—
460C2×D11#41812yes—
461C2×D11#41812yes—
462C2×D11#42112yes—
463C4×C11—21no—
464C4×C11—21no—
465C4×C11—21no—
466C4×C11—21no—
467C4×C11—42no—
468C4×C11—82no—
469Dic11—21no—
470Dic11—21no—
471Dic11—21no—
472Dic11—21no—
473Dic11—42no—
474Dic11—82no—
475C25—111no—
476C25—221no—
477C22×D4—21no—
478C22×D4—112no—
479C22×D4—112no—
480C22×D4—111no—
481C22×D4—221no—
482C22×D4—221no—
483C22×D4—221no—
484C22×D4—221no—
485C22×D4—222no—
486C22×D4—222no—
487C22×D4—222no—
488C22×D4—222no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4—444no—
492C22×D4—448no—
493C22×D4C4×D1111yescharacteristic, complemented
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—221no—
508C23×C4—222no—
509C23×C4—444no—
510C23×C4C22×D1111yescharacteristic
511C2×M16—21no—
512C2×M16—222no—
513C2×M16—221no—
514C2×M16—444no—
515C22×C8—222no—
516#121—21no—
517#121—21no—
518#121—112no—
519#121—112no—
520#121—112no—
521#121—112no—
522#121—112no—
523#121—112no—
524#121—222no—
525#121—222no—
526#121—222no—
527#121—222no—
528#121—221no—
529#121—221no—
530#121—221no—
531#121—221no—
532#121—222no—
533#121—222no—
534#121—222no—
535#121—222no—
536#121—221no—
537#121—221no—
538#121C4×D1112yescomplemented
539#121C22×D1112yes—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4C4×D1111yescharacteristic, complemented
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—222no—
550C2×C22⋊C4—222no—
551C2×C22⋊C4—222no—
552C2×C22⋊C4—222no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—222no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—444no—
559C22⋊C8—21no—
560C22⋊C8—112no—
561C22⋊C8—222no—
562C22⋊C8—222no—
563C22⋊C8—221no—
564C22⋊C8C22×D1112yescomplemented
565#95—21no—
566#95—112no—
567#95—222no—
568#95—222no—
569#95—221no—
570#95C22×D1112yescomplemented
571C2×C11—22no—
572C2×C11—22no—
573C2×C11—41no—
574C2×C11—82no—
575C2×C11C22×#9911yescharacteristic
576C2×C11C2×#41811yescharacteristic
577C2×C11C2×#42111yescharacteristic
578D11—22no—
579D11—22no—
580D11—41no—
581D11—82no—
582D11#151014yesdirect product factor
583C24—21no—
584C24—111no—
585C24—111no—
586C24—111no—
587C24—111no—
588C24—111no—
589C24—111no—
590C24—224no—
591C24—224no—
592C24—222no—
593C24—222no—
594C24—221no—
595C24—444no—
596C24—442no—
597C24—444no—
598C24—444no—
599C24D4×D1111yescharacteristic
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—42no—
604C2×D4—44no—
605C2×D4—112no—
606C2×D4—222no—
607C2×D4—222no—
608C2×D4—222no—
609C2×D4—222no—
610C2×D4—222no—
611C2×D4—222no—
612C2×D4—222no—
613C2×D4—222no—
614C2×D4—221no—
615C2×D4—442no—
616C2×D4—444no—
617C2×D4—444no—
618C2×D4—444no—
619C2×D4—444no—
620C2×D4—444no—
621C2×D4—444no—
622C2×D4—448no—
623C2×D4—448no—
624C2×D4—448no—
625C2×D4—448no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4C2×C4×D1112yes—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—42no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—111no—
644C22×C4—111no—
645C22×C4—111no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—111no—
649C22×C4—111no—
650C22×C4—111no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—224no—
655C22×C4—224no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—221no—
659C22×C4—222no—
660C22×C4—442no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—444no—
671C22×C4—444no—
672C22×C4—444no—
673C22×C4—444no—
674C22×C4—442no—
675C22×C4C2×C4×D1111yescharacteristic
676C22×C4C2×C4×D1111yescharacteristic
677C22×C4D4×D1111yescharacteristic
678C22×C4D4×D1111yescharacteristic
679C22×C4D4×D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681M16—42no—
682M16—444no—
683M16—442no—
684C2×C8—22no—
685C2×C8—222no—
686C2×C8—444no—
687C4⋊C4—21no—
688C4⋊C4—112no—
689C4⋊C4—222no—
690C4⋊C4—222no—
691C4⋊C4—221no—
692C4⋊C4C2×C4×D1112yes—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—222no—
697C22⋊C4—222no—
698C22⋊C4—222no—
699C22⋊C4—222no—
700C22⋊C4—222no—
701C22⋊C4—222no—
702C22⋊C4—444no—
703C22⋊C4—442no—
704C11C2×#151011yescharacteristic, complemented, Sylow
705C23—22no—
706C23—22no—
707C23—22no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—111no—
713C23—111no—
714C23—111no—
715C23—114no—
716C23—114no—
717C23—111no—
718C23—222no—
719C23—222no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—441no—
733C23—441no—
734C23—441no—
735C23—442no—
736C23—442no—
737C23—444no—
738C23—444no—
739C23—444no—
740C23—444no—
741C23—4416no—
742C23—444no—
743C23—444no—
744C23—442no—
745C23—8816no—
746C23C22⋊C4×D1111yescharacteristic
747C23C22⋊C4×D1111yescharacteristic
748C23C2×D4×D1111yescharacteristic
749D4—42no—
750D4—42no—
751D4—44no—
752D4—44no—
753D4—442no—
754D4—442no—
755D4—444no—
756D4—444no—
757D4—444no—
758D4—444no—
759D4—444no—
760D4—444no—
761D4—444no—
762D4—444no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—111no—
775C2×C4—111no—
776C2×C4—111no—
777C2×C4—111no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—441no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—444no—
798C2×C4—444no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—442no—
804C2×C4—442no—
805C2×C4—442no—
806C2×C4—442no—
807C2×C4—888no—
808C2×C4C22⋊C4×D1111yescharacteristic
809C2×C4C22⋊C4×D1111yescharacteristic
810C2×C4C22×C4×D1111yescharacteristic
811C2×C4C2×D4×D1111yescharacteristic
812C8—42no—
813C8—442no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—84no—
826C22—112no—
827C22—112no—
828C22—112no—
829C22—112no—
830C22—112no—
831C22—228no—
832C22—228no—
833C22—221no—
834C22—221no—
835C22—221no—
836C22—221no—
837C22—221no—
838C22—221no—
839C22—221no—
840C22—444no—
841C22—444no—
842C22—444no—
843C22—444no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—884no—
848C22—888no—
849C22—888no—
850C22D11×#9912yes—
851C22C2×C22⋊C4×D1111yescharacteristic
852C22D11×AGL(1,ℤ/8)12yes—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—42no—
858C4—82no—
859C4—221no—
860C4—221no—
861C4—221no—
862C4—221no—
863C4—442no—
864C4—882no—
865C2—22no—
866C2—22no—
867C2—41no—
868C2—82no—
869C2—114no—
870C2—222no—
871C2—222no—
872C2—441no—
873C2—882no—
874C2C2×D11×#9911yescharacteristic
875C2D11×#41811yescharacteristic
876C2D11×#42111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1510C2
socleC22×C11C22×C22⋊C4
prime radicalC2×D11×#121C2
cosocleC22×C4×C11C24
hypercenter#1510D11
hypocenterC11C2×#1510
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. D11×#381C2semidirect
4. #13067146C2semidirect
5. #13067145C2semidirect
6. #13067144C2semidirect
7. #13067143C2semidirect
8. D11×#327C2semidirect
9. C11×#1510C2semidirect
11. C22×D4×D11C4semidirect
15. C2×#66991C4semidirect
22. D11×#121C4semidirect
23. D11×#121C4semidirect
26. C2×#66948C4semidirect
27. C2×C4⋊C4×D11C4semidirect
31. C11×#407C22semidirect
32. C11×#381C22semidirect
33. #10622824C22semidirect
34. #10622820C22semidirect
38. #10622339C22semidirect
40. D11×C22⋊C8C22semidirect
42. #10622277C22semidirect
44. D11×#95C22semidirect
45. C11×#327C22semidirect
46. #10622175C22semidirect
47. #10622108C22semidirect
48. #10622089C22semidirect
52. C22×D4×C11C2×C4semidirect
67. C2×D4×D11C2×C4semidirect
69. C22×D44C2×C4semidirect
88. C11×#121C2×C4semidirect
90. C2×C11×C4⋊C4C2×C4semidirect
102. #66991C2×C4semidirect
105. #66983C2×C4semidirect
110. C2×C4⋊Dic11C2×C4semidirect
119. #66948C2×C4semidirect
123. C4⋊C4×D11C2×C4semidirect
134. C11×C22⋊C8C23semidirect
136. C11×#95C23semidirect
140. C11⋊#95C23semidirect
142. C22⋊(C11⋊C8)C23semidirect
274. #1510D11direct (N × H)
410. #407C2×D11semidirect
417. #381C2×D11semidirect
423. #327C2×D11semidirect
493. C22×D4C4×D11semidirect
538. #121C4×D11semidirect
546. C2×C4⋊C4C4×D11semidirect
564. C22⋊C8C22×D11semidirect
570. #95C22×D11semidirect
582. D11#1510direct (N × H)
704. C11C2×#1510semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
D11×#4072
D11×#3812
#130671462
#130671452
#130671442
#130671432
D11×#3272
C11×#15102
C2×#151011