Finite Group Databasebeta

← #14769538

Subgroups — #14769538

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622765C211yesmaximal, characteristic, complemented
2C2×D8×Dic11C211yesmaximal, characteristic, complemented
3#13071446C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13069499C211yesmaximal, characteristic, complemented
6#13069472C211yesmaximal, characteristic, complemented
7#13068966C211yesmaximal, characteristic, complemented
8#13068966C211yesmaximal, characteristic, complemented
9#13068952C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, 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×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic, complemented
31#10622860—21no—
32#10622843C2211yescharacteristic, complemented
33#10622843C2211yescharacteristic, complemented
34C2×#66899C2211yescharacteristic, complemented
35C2×#66899C2211yescharacteristic, complemented
36#10622834C2211yescharacteristic
37#10622834C2211yescharacteristic
38#10622833—21no—
39#10622833—21no—
40#10622833—21no—
41#10622833—21no—
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic, complemented
47C2×#66896C2211yescharacteristic, complemented
48#10622825C2211yescharacteristic
49#10622825C2211yescharacteristic
50#10622824—21no—
51C4×C22⋊Dic11C2211yescharacteristic
52C2×C11⋊#95—21no—
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622765—24no—
55D8×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×C414yescomplemented
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C23×Dic11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C23×Dic11—21no—
89C11×AGL(1,ℤ/8)—232no—
90C2×C11×SD16—22no—
91C2×C11×SD16—22no—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16C2×C414yescomplemented
95C2×C11×SD16C2×C414yescomplemented
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8C2×C414yes—
99C2×C11×D8C2×C414yescomplemented
100C2×C11×D8D414yes—
101C2×C11×D8D414yes—
102C2×C11×M16—22no—
103C2×C11×M16—22no—
104C2×C11×M16C2×C414yescomplemented
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
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
120D4×Dic11—22no—
121D4×Dic11—22no—
122D4×Dic11—22no—
123D4×Dic11—22no—
124D4×Dic11—41no—
125D4×Dic11—41no—
126D4×Dic11—41no—
127D4×Dic11—41no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136#66899—41no—
137#66899—41no—
138#66896—22no—
139#66896—22no—
140#66896—22no—
141#66896—22no—
142#66896—41no—
143#66896—41no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
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#22442—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×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11C22×C412yes—
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—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11C22×C412yes—
201C2×D4×C11C22×C412yes—
202C2×D4×C11C22×C412yes—
203C2×D4×C11C2×D412yes—
204C2×D4×C11C2×D412yes—
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—42no—
228C22×Dic11—42no—
229C22×Dic11—42no—
230C22×Dic11—42no—
231C22×Dic11—81no—
232C22×Dic11—81no—
233C22×Dic11—81no—
234C22×Dic11—81no—
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238C22×Dic11C2×D411yescharacteristic
239C11×SD16—28no—
240C11×SD16—28no—
241C11×D8—28no—
242C11×D8C22⋊C4116yescomplemented
243C11×M16—28no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11C22×C412yes—
247C2×C8×C11C22×C412yes—
248C2×C8×C11C2×D412yes—
249C2×C8×C11C2×D412yes—
250C22⋊Dic11—22no—
251C22⋊Dic11—41no—
252C22⋊Dic11—42no—
253C22⋊Dic11—42no—
254C22⋊Dic11—42no—
255C22⋊Dic11—42no—
256C22⋊Dic11—42no—
257C22⋊Dic11—42no—
258C22⋊Dic11—42no—
259C22⋊Dic11—81no—
260C22⋊Dic11—81no—
261C22⋊Dic11—81no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—21no—
272C4×Dic11—21no—
273C4×Dic11—21no—
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×#442—111no—
282C2×C4×D8—111no—
283#2339—111no—
284D4×C22⋊C4—111no—
285#1973—111no—
286#1968—111no—
287#1879—111no—
288#1879—111no—
289#1877—111no—
290#1877—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753—111no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—22no—
308C23×C11—48no—
309C23×C11—48no—
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—41no—
334Q8×C11—41no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—48no—
344D4×C11—48no—
345D4×C11—41no—
346D4×C11—41no—
347D4×C11C2×C22⋊C414yes—
348D4×C11C2×C22⋊C414yescomplemented
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—48no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
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×Dic11—84no—
392C2×Dic11—84no—
393C2×Dic11AGL(1,ℤ/8)12yescomplemented
394C8×C11—22no—
395C8×C11C2×C22⋊C414yescomplemented
396C11⋊C8—41no—
397C11⋊C8—41no—
398C22×#41C2×D1111yescharacteristic
399C23×D4C2×D1111yescharacteristic
400C2×AGL(1,ℤ/8)—24no—
401C2×AGL(1,ℤ/8)—24no—
402C2×AGL(1,ℤ/8)Dic1118yescomplemented
403C22×SD16C2×D1111yescharacteristic
404C22×SD16C2×D1111yescharacteristic
405C22×D8C2×D1111yescharacteristic
406C22×D8C2×D1111yescharacteristic
407C22×M16C2×D1111yescharacteristic
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4—111no—
411C2×C4×D4—111no—
412C22×C22⋊C4—221no—
413#442—224no—
414C4×D8—224no—
415C2×#107—111no—
416C2×#106—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×C22⋊C8—111no—
426C2×#97—111no—
427C2×C4×C8—111no—
428#391—111no—
429#391—111no—
430#390—111no—
431#390—111no—
432#386—221no—
433#386—221no—
434#386—221no—
435#386—221no—
436#381—221no—
437#380—111no—
438#380—111no—
439#379—221no—
440C4×C22⋊C4—111no—
441C2×#95—221no—
442#340—111no—
443#340—111no—
444#336—111no—
445#336—111no—
446C22×C11—22no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—41no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—41no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—41no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—816no—
471C22×C11—81no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11C2×C4×D411yescharacteristic
476C22×C11D4211yescharacteristic
477C22×C11D4211yescharacteristic
478C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
479C22×C11#57511yescharacteristic
480C22×C11#57611yescharacteristic
481C22×C11#57711yescharacteristic
482C4×C11—22no—
483C4×C11—42no—
484C4×C11C22×C22⋊C411yescharacteristic
485C4×C11#51811yescharacteristic
486C4×C11#54611yescharacteristic
487C4×C11#54611yescharacteristic
488Dic11—22no—
489Dic11—41no—
490Dic11—41no—
491Dic11—41no—
492Dic11—81no—
493Dic11—81no—
494Dic11—81no—
495Dic11—81no—
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41C2×Dic1114yescomplemented
503C22×Q8C22×D1111yescharacteristic
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×Dic1114yescomplemented
512C22×D4C22×D1111yescharacteristic
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521AGL(1,ℤ/8)—232no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16C2×Dic1114yescomplemented
527C2×SD16C2×Dic1114yescomplemented
528C2×D8—22no—
529C2×D8—22no—
530C2×D8C2×Dic1114yes—
531C2×D8C2×Dic1114yescomplemented
532C2×D8C22⋊D1114yes—
533C2×D8C22⋊D1114yes—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16C2×Dic1114yescomplemented
537C22×C8—111no—
538C22×C8—111no—
539C22×C8C22×D1111yescharacteristic
540C22×C8C22×D1111yescharacteristic
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—222no—
544C4×D4—222no—
545C4×D4—441no—
546C4×D4—441no—
547C4×D4—441no—
548C4×D4—441no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
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—
568#107—222no—
569#106—222no—
570#103—441no—
571#103—441no—
572#102—222no—
573#102—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578C22⋊C8—222no—
579#97—222no—
580C4×C8—222no—
581#95—111no—
582#95—111no—
583#95—221no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95—221no—
588#95—221no—
589C2×C11—42no—
590C2×C11—44no—
591C2×C11—44no—
592C2×C11—82no—
593C2×C11D4×C22⋊C411yescharacteristic
594C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
595C2×C11#294611yescharacteristic
596C2×C11#326411yescharacteristic
597C2×C11#326711yescharacteristic
598C2×C11#327211yescharacteristic
599C2×C11#327311yescharacteristic
600C24—21no—
601C24—21no—
602C24—21no—
603C24—24no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—81no—
609C24—81no—
610C24D4×D1111yescharacteristic
611#41—28no—
612#41—44no—
613#41—44no—
614#41—44no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8C22×Dic1112yes—
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—24no—
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—
647C2×D4C2×C22⋊D1112yes—
648C2×D4C2×C22⋊D1112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—442no—
673C22×C4—881no—
674C22×C4—881no—
675C22×C4—881no—
676C22×C4—881no—
677C22×C4D4×D1111yescharacteristic
678C22×C4#434112yes—
679C22×C4C22×Dic1112yes—
680C22×C4C23×D1111yescharacteristic
681SD16—28no—
682SD16—28no—
683D8—28no—
684D8C22⋊Dic11116yescomplemented
685M16—28no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8C22×Dic1112yes—
695C2×C8C22×Dic1112yes—
696C2×C8C2×C22⋊D1112yes—
697C2×C8C2×C22⋊D1112yes—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C22⋊C4—222no—
707C22⋊C4—442no—
708C22⋊C4—441no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—881no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C42—221no—
719C42—221no—
720C42—221no—
721C42—221no—
722C11#2244211yescharacteristic, complemented, Sylow
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—48no—
737C23—48no—
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—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23D4×Dic1112yes—
758C23C2×D4×D1111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4C2×C22⋊Dic1114yes—
776D4C2×C22⋊Dic1114yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—112no—
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—221no—
798C2×C4—221no—
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—441no—
810C2×C4—441no—
811C2×C4—884no—
812C2×C4—884no—
813C2×C4—884no—
814C2×C4—884no—
815C2×C4D4×Dic1112yes—
816C2×C4C2×#434111yescharacteristic
817C2×C4#6703711yescharacteristic
818C2×C4#6703711yescharacteristic
819C2×C4C23×Dic1111yescharacteristic
820C2×C4C22×C22⋊D1111yescharacteristic
821C2×C4C22×C22⋊D1111yescharacteristic
822C8—22no—
823C8—441no—
824C8—441no—
825C8C2×C22⋊Dic1114yescomplemented
826C22—22no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22D11×AGL(1,ℤ/8)11yescharacteristic
856C22#1062330411yescharacteristic
857C22#1062330511yescharacteristic
858C22#1062330611yescharacteristic
859C22C2×D4×Dic1111yescharacteristic
860C22D4×C22⋊D1111yescharacteristic
861C22D4×C22⋊D1111yescharacteristic
862C4—22no—
863C4—42no—
864C4—222no—
865C4—441no—
866C4—441no—
867C4—441no—
868C4—881no—
869C4—881no—
870C4—881no—
871C4—881no—
872C4#1062332911yescharacteristic
873C4#1062333711yescharacteristic
874C4#1062333711yescharacteristic
875C4C22×C22⋊Dic1111yescharacteristic
876C2—42no—
877C2—44no—
878C2—44no—
879C2—82no—
880C2D4×C22⋊Dic1111yescharacteristic
881C2AGL(1,ℤ/8)×Dic1111yescharacteristic
882C2#1307744911yescharacteristic
883C2#1308009011yescharacteristic
884C2#1308013511yescharacteristic
885C2#1308021011yescharacteristic
886C2#1308022111yescharacteristic
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#22442
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×#10622765C2semidirect
2. C2×D8×Dic11C2semidirect
3. #13071446C2semidirect
4. D4×C22⋊Dic11C2semidirect
5. #13069499C2semidirect
6. #13069472C2semidirect
7. #13068966C2semidirect
8. #13068966C2semidirect
9. #13068952C2semidirect
10. #13068952C2semidirect
11. #13068649C2semidirect
12. #13068556C2semidirect
13. #13068547C2semidirect
14. #13068397C2semidirect
20. C2×C11×AGL(1,ℤ/8)C4semidirect
29. C2×D4×Dic11C22semidirect
30. C2×D4×Dic11C22semidirect
32. #10622843C22semidirect
33. #10622843C22semidirect
34. C2×#66899C22semidirect
35. C2×#66899C22semidirect
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
79. C22×D4×C11C2×C4semidirect
94. C2×C11×SD16C2×C4semidirect
95. C2×C11×SD16C2×C4semidirect
99. C2×C11×D8C2×C4semidirect
104. C2×C11×M16C2×C4semidirect
242. C11×D8C22⋊C4semidirect
348. D4×C11C2×C22⋊C4semidirect
393. C2×Dic11AGL(1,ℤ/8)semidirect
395. C8×C11C2×C22⋊C4semidirect
402. C2×AGL(1,ℤ/8)Dic11semidirect
502. C2×#41C2×Dic11semidirect
511. C22×D4C2×Dic11semidirect
526. C2×SD16C2×Dic11semidirect
527. C2×SD16C2×Dic11semidirect
531. C2×D8C2×Dic11semidirect
536. C2×M16C2×Dic11semidirect
684. D8C22⋊Dic11semidirect
722. C11#22442semidirect
776. D4C2×C22⋊Dic11semidirect
825. C8C2×C22⋊Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×#106227652
C2×D8×Dic112
#130714462
D4×C22⋊Dic112
#130694992
#130694722
#130689662
#130689522
#130686492
#130685562
#130685472
#130683972
C22×C11×AGL(1,ℤ/8)2
#2244211