Finite Group Databasebeta

← #14769553

Subgroups — #14769553

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622777C211yesmaximal, characteristic, complemented
2C2×SD16×Dic11C211yesmaximal, characteristic, complemented
3#13071457C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13069493C211yesmaximal, characteristic, complemented
6#13069483C211yesmaximal, characteristic, complemented
7#13068973C211yesmaximal, characteristic, complemented
8#13068973C211yesmaximal, characteristic, complemented
9#13068966C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068649C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)—24no—
19C2×C11×AGL(1,ℤ/8)—24no—
20C2×C11×AGL(1,ℤ/8)C418yescomplemented
21C22×C11×SD16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C22×C11×D8C2211yescharacteristic
24C22×C11×D8C2211yescharacteristic
25C22×C11×M16C2211yescharacteristic
26C22×C22⋊Dic11—21no—
27C2×Q8×Dic11C2211yescharacteristic, complemented
28C2×Q8×Dic11C2211yescharacteristic, complemented
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31#10622860—21no—
32C2×#66899C2211yescharacteristic, complemented
33C2×#66899C2211yescharacteristic, complemented
34#10622834—21no—
35#10622834—21no—
36#10622834C2211yescharacteristic
37#10622834C2211yescharacteristic
38#10622834C2211yescharacteristic, complemented
39#10622834C2211yescharacteristic, complemented
40#10622833—21no—
41#10622833—21no—
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic, complemented
47C2×#66896C2211yescharacteristic, complemented
48#10622825—21no—
49#10622825C2211yescharacteristic
50#10622825C2211yescharacteristic
51C4×C22⋊Dic11—21no—
52C4×C22⋊Dic11C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622777—24no—
55SD16×Dic11—24no—
56C2×#66882C2211yescharacteristic, complemented
57C2×#66881C2211yescharacteristic, complemented
58C2×#66879C2211yescharacteristic, complemented
59C2×C8×Dic11C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622188C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64C25×C11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—22no—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—22no—
77C22×D4×C11—41no—
78C22×D4×C11—41no—
79C22×D4×C11C2×C414yes—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C23×Dic11—21no—
86C23×Dic11—21no—
87C11×AGL(1,ℤ/8)—232no—
88C2×C11×SD16—22no—
89C2×C11×SD16—22no—
90C2×C11×SD16C2×C414yes—
91C2×C11×SD16C2×C414yescomplemented
92C2×C11×SD16D414yes—
93C2×C11×SD16D414yes—
94C2×C11×D8—22no—
95C2×C11×D8—22no—
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8C2×C414yes—
99C2×C11×D8C2×C414yescomplemented
100C2×C11×M16—22no—
101C2×C11×M16—22no—
102C2×C11×M16C2×C414yescomplemented
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—44no—
118C2×C22⋊Dic11D411yescharacteristic
119C2×C22⋊Dic11D411yescharacteristic
120Q8×Dic11—22no—
121Q8×Dic11—22no—
122Q8×Dic11—41no—
123Q8×Dic11—41no—
124D4×Dic11—22no—
125D4×Dic11—22no—
126D4×Dic11—41no—
127D4×Dic11—41no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140#66899—22no—
141#66899—22no—
142#66896—22no—
143#66896—22no—
144#66896—41no—
145#66896—41no—
146#66896—41no—
147#66896—41no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95D411yescharacteristic
151C11⋊#95D411yescharacteristic
152C22⋊(C11⋊C8)—22no—
153#66882—22no—
154#66881—22no—
155#66879—22no—
156C8×Dic11—22no—
157#22443—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—24no—
162C24×C11—42no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—81no—
167C24×C11—81no—
168C24×C11C2×D411yescharacteristic
169C11×#41—28no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11C22×C412yes—
177C2×Q8×C11C2×D412yes—
178C2×Q8×C11C2×D412yes—
179C2×D4×C11—28no—
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11—42no—
202C2×D4×C11C22×C412yes—
203C2×D4×C11C22×C412yes—
204C2×D4×C11C22×C412yes—
205C2×D4×C11C2×D412yes—
206C2×D4×C11C2×D412yes—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—24no—
213C22×C4×C11—42no—
214C22×C4×C11—42no—
215C22×C4×C11C22×C412yes—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11#4112yes—
218C22×C4×C11C2411yescharacteristic
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—42no—
224C22×Dic11—42no—
225C22×Dic11—42no—
226C22×Dic11—42no—
227C22×Dic11—81no—
228C22×Dic11—81no—
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C11×SD16—28no—
234C11×SD16C22⋊C4116yescomplemented
235C11×D8—28no—
236C11×D8—28no—
237C11×M16—28no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11C22×C412yes—
241C2×C8×C11C22×C412yes—
242C2×C8×C11C2×D412yes—
243C2×C8×C11C2×D412yes—
244C22⋊Dic11—22no—
245C22⋊Dic11—41no—
246C22⋊Dic11—42no—
247C22⋊Dic11—42no—
248C22⋊Dic11—42no—
249C22⋊Dic11—42no—
250C22⋊Dic11—42no—
251C22⋊Dic11—42no—
252C22⋊Dic11—42no—
253C22⋊Dic11—81no—
254C22⋊Dic11—81no—
255C22⋊Dic11—81no—
256C22⋊Dic11—81no—
257C22⋊Dic11—81no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—42no—
267C4⋊Dic11—42no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—21no—
272C4×Dic11—42no—
273C4×Dic11—42no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C22×AGL(1,ℤ/8)D1111yescharacteristic
281C2×#440—111no—
282C2×C4×SD16—111no—
283#2341—111no—
284D4×C22⋊C4—111no—
285#1972—111no—
286#1970—111no—
287#1880—111no—
288#1880—111no—
289#1879—111no—
290#1879—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753—111no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—48no—
307C23×C11—48no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—84no—
325C23×C11—84no—
326C23×C11—84no—
327C23×C11—84no—
328C23×C11—84no—
329C23×C11C4×D412yes—
330C23×C11C22×D411yescharacteristic
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11C2×C22⋊C414yescomplemented
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—48no—
343D4×C11—48no—
344D4×C11—41no—
345D4×C11—41no—
346D4×C11—41no—
347D4×C11—41no—
348D4×C11C2×C22⋊C414yes—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—48no—
359C2×C4×C11C4×D412yes—
360C2×C4×C11C23×C411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C2×#4111yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—21no—
376C2×Dic11—21no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—84no—
390C2×Dic11—84no—
391C2×Dic11AGL(1,ℤ/8)12yescomplemented
392C8×C11—22no—
393C8×C11C2×C22⋊C414yescomplemented
394C11⋊C8—41no—
395C11⋊C8—41no—
396C22×#41C2×D1111yescharacteristic
397C23×D4C2×D1111yescharacteristic
398C2×AGL(1,ℤ/8)—24no—
399C2×AGL(1,ℤ/8)—24no—
400C2×AGL(1,ℤ/8)Dic1118yescomplemented
401C22×SD16C2×D1111yescharacteristic
402C22×SD16C2×D1111yescharacteristic
403C22×D8C2×D1111yescharacteristic
404C22×D8C2×D1111yescharacteristic
405C22×M16C2×D1111yescharacteristic
406C2×C4×Q8—111no—
407C2×C4×Q8—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C22×C22⋊C4—221no—
411#440—224no—
412C4×SD16—224no—
413C2×#107—111no—
414C2×#106—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×C22⋊C8—111no—
424C2×#97—111no—
425C2×C4×C8—111no—
426#390—111no—
427#390—111no—
428#390—111no—
429#390—111no—
430#390—221no—
431#390—221no—
432#386—221no—
433#386—221no—
434#380—111no—
435#380—111no—
436#380—221no—
437#379—221no—
438C4×C22⋊C4—111no—
439C4×C22⋊C4—221no—
440#340—111no—
441#340—111no—
442#336—111no—
443#336—111no—
444C22×C11—22no—
445C22×C11—24no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—816no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11—81no—
471C22×C11—81no—
472C22×C11—81no—
473C22×C11C2×C4×D411yescharacteristic
474C22×C11D4211yescharacteristic
475C22×C11D4211yescharacteristic
476C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
477C22×C11#57511yescharacteristic
478C22×C11#57611yescharacteristic
479C22×C11#57711yescharacteristic
480C4×C11—22no—
481C4×C11—24no—
482C4×C11C22×C22⋊C411yescharacteristic
483C4×C11#51811yescharacteristic
484C4×C11#54611yescharacteristic
485C4×C11#54611yescharacteristic
486Dic11—22no—
487Dic11—41no—
488Dic11—41no—
489Dic11—41no—
490Dic11—81no—
491Dic11—81no—
492Dic11—81no—
493Dic11—81no—
494C25—21no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41C2×Dic1114yescomplemented
501C22×Q8C22×D1111yescharacteristic
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2×Dic1114yes—
510C22×D4C22×D1111yescharacteristic
511C22×D4C22×D1111yescharacteristic
512C22×D4C22×D1111yescharacteristic
513C23×C4—21no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4C22×D1111yescharacteristic
517AGL(1,ℤ/8)—232no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16C2×Dic1114yes—
521C2×SD16C2×Dic1114yescomplemented
522C2×SD16C22⋊D1114yes—
523C2×SD16C22⋊D1114yes—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—22no—
528C2×D8C2×Dic1114yes—
529C2×D8C2×Dic1114yescomplemented
530C2×M16—22no—
531C2×M16—22no—
532C2×M16C2×Dic1114yescomplemented
533C22×C8—111no—
534C22×C8—111no—
535C22×C8C22×D1111yescharacteristic
536C22×C8C22×D1111yescharacteristic
537C4×Q8—222no—
538C4×Q8—222no—
539C4×Q8—441no—
540C4×Q8—441no—
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—441no—
544C4×D4—441no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C22⋊C4—111no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—444no—
566C2×C42—111no—
567C2×C42—111no—
568C2×C42—221no—
569C2×C42—221no—
570#107—222no—
571#106—222no—
572#103—222no—
573#103—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—222no—
581#97—222no—
582C4×C8—222no—
583#95—111no—
584#95—111no—
585#95—221no—
586#95—221no—
587C2×C11—42no—
588C2×C11—44no—
589C2×C11—82no—
590C2×C11—82no—
591C2×C11D4×C22⋊C411yescharacteristic
592C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
593C2×C11#294611yescharacteristic
594C2×C11#326511yescharacteristic
595C2×C11#326811yescharacteristic
596C2×C11#327411yescharacteristic
597C2×C11#327511yescharacteristic
598C24—21no—
599C24—21no—
600C24—21no—
601C24—24no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—81no—
607C24—81no—
608C24D4×D1111yescharacteristic
609#41—28no—
610#41—44no—
611#41—44no—
612#41—44no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C22×Dic1112yes—
617C2×Q8C2×C22⋊D1112yes—
618C2×Q8C2×C22⋊D1112yes—
619C2×D4—28no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4C22×Dic1112yes—
643C2×D4C22×Dic1112yes—
644C2×D4C22×Dic1112yes—
645C2×D4C2×C22⋊D1112yes—
646C2×D4C2×C22⋊D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—111no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—881no—
668C22×C4—881no—
669C22×C4D4×D1111yescharacteristic
670C22×C4#434112yes—
671C22×C4C22×Dic1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—28no—
674SD16C22⋊Dic11116yescomplemented
675D8—28no—
676D8—28no—
677M16—28no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—221no—
681C2×C8—221no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8C22×Dic1112yes—
687C2×C8C22×Dic1112yes—
688C2×C8C2×C22⋊D1112yes—
689C2×C8C2×C22⋊D1112yes—
690C4⋊C4—221no—
691C4⋊C4—221no—
692C4⋊C4—221no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—442no—
699C4⋊C4—442no—
700C22⋊C4—222no—
701C22⋊C4—442no—
702C22⋊C4—442no—
703C22⋊C4—441no—
704C22⋊C4—442no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—881no—
710C22⋊C4—881no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—221no—
715C42—221no—
716C42—221no—
717C42—221no—
718C42—442no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—48no—
733C23—48no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23D4×Dic1112yes—
756C23C2×D4×D1111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C2×C22⋊Dic1114yescomplemented
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊Dic1114yes—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—112no—
786C2×C4—221no—
787C2×C4—221no—
788C2×C4—221no—
789C2×C4—221no—
790C2×C4—221no—
791C2×C4—221no—
792C2×C4—221no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—884no—
810C2×C4—884no—
811C2×C4D4×Dic1112yes—
812C2×C4C2×#434111yescharacteristic
813C2×C4#6703711yescharacteristic
814C2×C4#6703711yescharacteristic
815C2×C4C23×Dic1111yescharacteristic
816C2×C4C22×C22⋊D1111yescharacteristic
817C2×C4C22×C22⋊D1111yescharacteristic
818C8—22no—
819C8—441no—
820C8—441no—
821C8C2×C22⋊Dic1114yescomplemented
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22D11×AGL(1,ℤ/8)11yescharacteristic
852C22#1062330411yescharacteristic
853C22#1062330511yescharacteristic
854C22#1062330611yescharacteristic
855C22C2×D4×Dic1111yescharacteristic
856C22D4×C22⋊D1111yescharacteristic
857C22D4×C22⋊D1111yescharacteristic
858C4—22no—
859C4—24no—
860C4—222no—
861C4—441no—
862C4—441no—
863C4—441no—
864C4—881no—
865C4—881no—
866C4—881no—
867C4—881no—
868C4#1062332911yescharacteristic
869C4#1062333711yescharacteristic
870C4#1062333711yescharacteristic
871C4C22×C22⋊Dic1111yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—82no—
876C2D4×C22⋊Dic1111yescharacteristic
877C2AGL(1,ℤ/8)×Dic1111yescharacteristic
878C2#1307744911yescharacteristic
879C2#1308010511yescharacteristic
880C2#1308015011yescharacteristic
881C2#1308023011yescharacteristic
882C2#1308024711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#10622777C2semidirect
2. C2×SD16×Dic11C2semidirect
3. #13071457C2semidirect
4. D4×C22⋊Dic11C2semidirect
5. #13069493C2semidirect
6. #13069483C2semidirect
7. #13068973C2semidirect
8. #13068973C2semidirect
9. #13068966C2semidirect
10. #13068966C2semidirect
11. #13068649C2semidirect
12. #13068556C2semidirect
13. #13068547C2semidirect
14. #13068397C2semidirect
20. C2×C11×AGL(1,ℤ/8)C4semidirect
27. C2×Q8×Dic11C22semidirect
28. C2×Q8×Dic11C22semidirect
32. C2×#66899C22semidirect
33. C2×#66899C22semidirect
38. #10622834C22semidirect
39. #10622834C22semidirect
46. C2×#66896C22semidirect
47. C2×#66896C22semidirect
56. C2×#66882C22semidirect
57. C2×#66881C22semidirect
58. C2×#66879C22semidirect
59. C2×C8×Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622188C22semidirect
63. #10622188C22semidirect
70. C2×C11×#41C2×C4semidirect
91. C2×C11×SD16C2×C4semidirect
99. C2×C11×D8C2×C4semidirect
102. C2×C11×M16C2×C4semidirect
234. C11×SD16C22⋊C4semidirect
334. Q8×C11C2×C22⋊C4semidirect
391. C2×Dic11AGL(1,ℤ/8)semidirect
393. C8×C11C2×C22⋊C4semidirect
400. C2×AGL(1,ℤ/8)Dic11semidirect
500. C2×#41C2×Dic11semidirect
521. C2×SD16C2×Dic11semidirect
529. C2×D8C2×Dic11semidirect
532. C2×M16C2×Dic11semidirect
674. SD16C22⋊Dic11semidirect
720. C11#22443semidirect
760. Q8C2×C22⋊Dic11semidirect
821. C8C2×C22⋊Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
C2×SD16×Dic112
#130714572
D4×C22⋊Dic112
#130694932
#130694832
#130689732
#130689662
#130686492
#130685562
#130685472
#130683972
C22×C11×AGL(1,ℤ/8)2
#2244311