Finite Group Databasebeta

← #14769546

Subgroups — #14769546

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
1C22×#67002C211yesmaximal, characteristic
2C2×#10622430C211yesmaximal, characteristic, complemented
3C2×#10622401C211yesmaximal, characteristic, complemented
4#13071457C211yesmaximal, characteristic, complemented
5#13071436C211yesmaximal, characteristic, complemented
6#13069489C211yesmaximal, characteristic, complemented
7#13069479C211yesmaximal, characteristic, complemented
8#13068969C211yesmaximal, characteristic, complemented
9#13068969C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068961C211yesmaximal, characteristic, complemented
12#13068647C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×#67002—24no—
19C2×#67002—24no—
20C2×#67002C418yescomplemented
21C2×Q8×Dic11C2211yescharacteristic, complemented
22C2×Q8×Dic11C2211yescharacteristic, complemented
23C22×#4325C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×#4323C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×C22⋊C4×D11—21no—
31C2×C11×#103C2211yescharacteristic, complemented
32C2×C11×#103C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#380C2211yescharacteristic
37#10622834—21no—
38#10622834—21no—
39#10622834C2211yescharacteristic, complemented
40#10622834C2211yescharacteristic, complemented
41#10622825—21no—
42#10622825C2211yescharacteristic
43C4×C22⋊Dic11—21no—
44C4×C22⋊Dic11C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×#66879C2211yescharacteristic, complemented
50C2×C8×Dic11C2211yescharacteristic, complemented
51#10622601C2211yescharacteristic
52#10622601C2211yescharacteristic
53C2×#66872C2211yescharacteristic, complemented
54C2×#66871C2211yescharacteristic, complemented
55#10622568—21no—
56#10622430—24no—
57#10622401—24no—
58#10622278—21no—
59#10622278—21no—
60#10622188C2211yescharacteristic, complemented
61#10622188C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—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—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44C2×C414yes—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11D411yescharacteristic
98C2×C22⋊Dic11D411yescharacteristic
99#67002—232no—
100Q8×Dic11—22no—
101Q8×Dic11—22no—
102Q8×Dic11—41no—
103Q8×Dic11—41no—
104C2×#4325—22no—
105C2×#4325—22no—
106C2×#4325C2×C414yes—
107C2×#4325C2×C414yescomplemented
108C2×#4325D414yes—
109C2×#4325D414yes—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323—22no—
113C2×#4323—22no—
114C2×#4323C2×C414yes—
115C2×#4323C2×C414yescomplemented
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C2×#4318—22no—
131C2×#4318—22no—
132C2×#4318C2×C414yescomplemented
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135#66946—22no—
136#66946—22no—
137#66946—41no—
138#66946—41no—
139C22⋊C4×D11—44no—
140C11×#103—22no—
141C11×#103—22no—
142C11×#102—41no—
143C11×#102—41no—
144C11×C22⋊C8—22no—
145C11×#95—21no—
146C11⋊#95—21no—
147C11⋊#95D411yescharacteristic
148C11⋊#95D411yescharacteristic
149#66885—22no—
150#66885—22no—
151#66885—41no—
152#66885—41no—
153#66879—22no—
154C8×Dic11—22no—
155#66872—22no—
156#66871—22no—
157#22443—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11C2×D411yescharacteristic
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
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—24no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11C22×C412yes—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—24no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11#4112yes—
201C22×C4×C11C2411yescharacteristic
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C2×D44—28no—
209C2×D44—24no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—42no—
219C2×D44—42no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44—44no—
223C2×D44C22×C412yes—
224C2×D44C22×C412yes—
225C2×D44C2×D412yes—
226C2×D44C2×D412yes—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11—42no—
230C2×C4×D11—42no—
231C2×C4×D11—81no—
232C2×C4×D11—81no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C22⋊C4—42no—
244C22⋊Dic11—22no—
245C22⋊Dic11—41no—
246C22⋊Dic11—42no—
247C22⋊Dic11—42no—
248C22⋊Dic11—81no—
249C22⋊Dic11—81no—
250C22⋊Dic11—81no—
251#4325—28no—
252#4325C22⋊C4116yescomplemented
253#4323—28no—
254#4323—28no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—81no—
260(C2×D11)⋊C4—81no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—42no—
266C4⋊Dic11—42no—
267C4×Dic11—21no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—42no—
272C4×Dic11—42no—
273#4318—28no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8C22×C412yes—
277C2×C11⋊C8C22×C412yes—
278C2×C11⋊C8C2×D412yes—
279C2×C11⋊C8C2×D412yes—
280C22×AGL(1,ℤ/8)—111no—
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#1788D1111yescharacteristic, complemented
293#1786—111no—
294#1753—111no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—22no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11C4×D412yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—48no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—48no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11C2×C22⋊C414yescomplemented
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—41no—
339D4×C11—41no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—48no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11C4×D412yes—
357C2×C4×C11C23×C411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
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—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11AGL(1,ℤ/8)12yescomplemented
381D44—22no—
382D44—22no—
383D44—22no—
384D44—22no—
385D44—22no—
386D44—48no—
387D44—41no—
388D44—41no—
389D44C2×C22⋊C414yes—
390C4×D11—84no—
391C4×D11—84no—
392C8×C11—41no—
393C8×C11—41no—
394C11⋊C8—22no—
395C11⋊C8C2×C22⋊C414yescomplemented
396C22×#41C2×D1111yescharacteristic
397C23×D4—111no—
398C2×AGL(1,ℤ/8)—118no—
399C2×AGL(1,ℤ/8)—224no—
400C2×AGL(1,ℤ/8)—224no—
401C22×SD16—111no—
402C22×SD16—111no—
403C22×D8—111no—
404C22×D8—111no—
405C22×M16—111no—
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×#103C2×D1111yescharacteristic, complemented
416C2×#103C2×D1111yescharacteristic, complemented
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102C2×D1111yescharacteristic, complemented
422C2×#102C2×D1111yescharacteristic, complemented
423C2×C22⋊C8C2×D1111yescharacteristic
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—221no—
436#380C2×D1111yescharacteristic
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—22no—
446C22×C11—22no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11C2×C4×D411yescharacteristic
459C22×C11D4211yescharacteristic
460C22×C11D4211yescharacteristic
461C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C11#57511yescharacteristic
463C22×C11#57611yescharacteristic
464C22×C11#57711yescharacteristic
465C2×D11—24no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—816no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C4×C11—22no—
481C4×C11—24no—
482C4×C11—81no—
483C4×C11—81no—
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—
494C25—221no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41C4×D1114yescomplemented
501C22×Q8C22×D1111yescharacteristic
502C22×D4—21no—
503C22×D4—114no—
504C22×D4—111no—
505C22×D4—111no—
506C22×D4—222no—
507C22×D4—222no—
508C22×D4—221no—
509C22×D4—222no—
510C22×D4—441no—
511C22×D4—441no—
512C22×D4C22×D1111yescharacteristic
513C23×C4—21no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4C22×D1111yescharacteristic
517AGL(1,ℤ/8)—2232no—
518C2×SD16—114no—
519C2×SD16—114no—
520C2×SD16—114no—
521C2×SD16—114no—
522C2×SD16—222no—
523C2×SD16—222no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—222no—
527C2×D8—222no—
528C2×D8—222no—
529C2×D8—222no—
530C2×M16—114no—
531C2×M16—222no—
532C2×M16—222no—
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—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—111no—
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—22no—
573#103—22no—
574#102—41no—
575#102—41no—
576#102—222no—
577#102—222no—
578#102—441no—
579#102—441no—
580C22⋊C8—22no—
581#97—222no—
582C4×C8—222no—
583#95—21no—
584#95—111no—
585#95—111no—
586#95—221no—
587C2×C11—42no—
588C2×C11—82no—
589C2×C11D4×C22⋊C411yescharacteristic
590C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
591C2×C11#294611yescharacteristic
592C2×C11#326511yescharacteristic
593C2×C11#326811yescharacteristic
594C2×C11#327411yescharacteristic
595C2×C11#327511yescharacteristic
596D11—44no—
597D11—82no—
598C24—21no—
599C24—221no—
600C24—221no—
601C24—224no—
602C24—442no—
603C24—442no—
604C24—442no—
605C24—442no—
606C24—881no—
607C24—881no—
608C24D4×D1111yescharacteristic
609#41—28no—
610#41—44no—
611#41—44no—
612#41—44no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×C4×D1112yes—
617C2×Q8D4×D1112yes—
618C2×Q8D4×D1112yes—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4C2×C4×D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—21no—
654C22×C4—21no—
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—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—881no—
668C22×C4—881no—
669C22×C4C2×C4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4#434112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—228no—
676D8—228no—
677M16—228no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—112no—
685C2×C8—112no—
686C2×C8—112no—
687C2×C8—112no—
688C2×C8—221no—
689C2×C8—221no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—442no—
699C4⋊C4—442no—
700C22⋊C4—42no—
701C22⋊C4—222no—
702C22⋊C4—442no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—441no—
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—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—448no—
739C23—448no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—884no—
751C23—884no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23(C22⋊D11)⋊C412yes—
756C23C2×D4×D1111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C22⋊C4×D1114yescomplemented
761D4—22no—
762D4—22no—
763D4—48no—
764D4—41no—
765D4—41no—
766D4—114no—
767D4—222no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—448no—
773D4—441no—
774D4—441no—
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—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—112no—
792C2×C4—221no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
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×C4(C22⋊D11)⋊C412yes—
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×#434111yescharacteristic
816C2×C4#6703711yescharacteristic
817C2×C4#6703711yescharacteristic
818C8—41no—
819C8—41no—
820C8—114no—
821C8—222no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—224no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—8816no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C2×(C22⋊D11)⋊C411yescharacteristic
852C22#1062312111yescharacteristic
853C22#1062312111yescharacteristic
854C22#1062330011yescharacteristic
855C22#1062330111yescharacteristic
856C22D11×AGL(1,ℤ/8)11yescharacteristic
857C22#1062330811yescharacteristic
858C4—22no—
859C4—24no—
860C4—81no—
861C4—81no—
862C4—222no—
863C4—441no—
864C4—441no—
865C4—441no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062301711yescharacteristic
870C4#1062312211yescharacteristic
871C4#1062312211yescharacteristic
872C2—42no—
873C2—82no—
874C2—444no—
875C2—882no—
876C2#1307143211yescharacteristic
877C2#1307742911yescharacteristic
878C2#1307745111yescharacteristic
879C2#1308011411yescharacteristic
880C2#1308015911yescharacteristic
881C2#1308022911yescharacteristic
882C2#1308024011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622430C2semidirect
3. C2×#10622401C2semidirect
4. #13071457C2semidirect
5. #13071436C2semidirect
6. #13069489C2semidirect
7. #13069479C2semidirect
8. #13068969C2semidirect
9. #13068969C2semidirect
10. #13068961C2semidirect
11. #13068961C2semidirect
12. #13068647C2semidirect
13. #13068548C2semidirect
14. #13068402C2semidirect
15. C11×#1788C2semidirect
20. C2×#67002C4semidirect
21. C2×Q8×Dic11C22semidirect
22. C2×Q8×Dic11C22semidirect
31. C2×C11×#103C22semidirect
32. C2×C11×#103C22semidirect
33. C2×C11×#102C22semidirect
34. C2×C11×#102C22semidirect
39. #10622834C22semidirect
40. #10622834C22semidirect
49. C2×#66879C22semidirect
50. C2×C8×Dic11C22semidirect
53. C2×#66872C22semidirect
54. C2×#66871C22semidirect
60. #10622188C22semidirect
61. #10622188C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
70. C2×C11×#41C2×C4semidirect
107. C2×#4325C2×C4semidirect
115. C2×#4323C2×C4semidirect
132. C2×#4318C2×C4semidirect
252. #4325C22⋊C4semidirect
292. #1788D11semidirect
334. Q8×C11C2×C22⋊C4semidirect
380. C2×Dic11AGL(1,ℤ/8)semidirect
395. C11⋊C8C2×C22⋊C4semidirect
415. C2×#103C2×D11semidirect
416. C2×#103C2×D11semidirect
421. C2×#102C2×D11semidirect
422. C2×#102C2×D11semidirect
500. C2×#41C4×D11semidirect
720. C11#22443semidirect
760. Q8C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106224302
C2×#106224012
#130714572
#130714362
#130694892
#130694792
#130689692
#130689612
#130686472
#130685482
#130684022
C11×#17882
#2244311