Finite Group Databasebeta

← #14755198

Subgroups — #14755198

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4#13071198C211yesmaximal, characteristic, complemented
5#13068973C214yesmaximal, complemented
6#13068966C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068314C211yesmaximal, characteristic, complemented
9C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C2×C11×AGL(1,ℤ/8)—24no—
13C2×C11×AGL(1,ℤ/8)—24no—
14C2×C11×AGL(1,ℤ/8)C418yescomplemented
15C22×C11×SD16C2212yes—
16C22×C11×D8C2212yes—
17C22×C11×M16C2211yescharacteristic
18#10623358—24no—
19#10623358—24no—
20C2×Q8×Dic11C2212yescomplemented
21C2×D4×Dic11—22no—
22C2×D4×Dic11C2212yescomplemented
23C2×#66979—21no—
24C2×#66979C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C22×C4⋊Dic11—21no—
27C22×C4⋊Dic11C2211yescharacteristic
28C23×C11⋊C8C2211yescharacteristic
29#10622860—22no—
30#10622846—24no—
31C2×#66899C2212yescomplemented
32#10622834—21no—
33#10622834—21no—
34#10622834C2214yes—
35C2×#66896—24no—
36C2×#66896C2214yes—
37C2×#66896C2212yescomplemented
38#10622189C2214yescomplemented
39#10622188C2214yescomplemented
40C25×C11—21no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C2×C11×#41D414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11C2×C414yescomplemented
56C22×D4×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C23×Dic11—22no—
62C11×AGL(1,ℤ/8)—232no—
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16C2×C418yescomplemented
66C2×C11×D8—24no—
67C2×C11×D8—24no—
68C2×C11×D8C2×C418yescomplemented
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16C2×C414yescomplemented
72C22×C8×C11C2312yes—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11D412yes—
78Q8×Dic11—24no—
79Q8×Dic11—24no—
80D4×Dic11—216no—
81D4×Dic11—24no—
82D4×Dic11—24no—
83#66979—28no—
84#66979—22no—
85#66979—22no—
86#66979—22no—
87#66979—22no—
88C2×C4⋊Dic11—28no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11D414yes—
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2312yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2312yes—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8C2312yes—
104#66899—24no—
105#66896—24no—
106#66896—28no—
107#20932—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—42no—
112C24×C11—42no—
113C24×C11—82no—
114C24×C11—82no—
115C24×C11C2×D411yescharacteristic
116C11×#41—28no—
117C11×#41—28no—
118C11×#41—28no—
119C11×#41C22⋊C4116yescomplemented
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11C22×C412yes—
124C2×Q8×C11C2×D412yes—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—42no—
141C2×D4×C11—44no—
142C2×D4×C11—42no—
143C2×D4×C11—44no—
144C2×D4×C11C22×C414yes—
145C2×D4×C11C22×C412yes—
146C2×D4×C11C2×D412yes—
147C2×D4×C11C2×D412yes—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—28no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—82no—
165C22×Dic11—84no—
166C22×Dic11C2×D412yes—
167C22×Dic11C2×D412yes—
168C11×SD16—216no—
169C11×D8—216no—
170C11×M16—28no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11C22×C414yes—
174C22⋊Dic11—28no—
175C22⋊Dic11—24no—
176C22⋊Dic11—42no—
177C22⋊Dic11—84no—
178C22⋊Dic11—84no—
179C4⋊Dic11—28no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11C2×D414yes—
187C4×Dic11—28no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190C4×Dic11—42no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—44no—
195C22×AGL(1,ℤ/8)D1111yescharacteristic
196C2×#520—111no—
197C2×#416—111no—
198C22×#102—111no—
199#2309—111no—
200#1880—114no—
201#1879—114no—
202#1736—111no—
203#1729—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—48no—
217C23×C11—88no—
218C23×C11—84no—
219C23×C11—84no—
220C23×C11—88no—
221C23×C11C4×D412yes—
222C23×C11#12012yes—
223C23×C11#12112yes—
224C23×C11C22×D411yescharacteristic
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11C2×C22⋊C414yes—
229D4×C11—216no—
230D4×C11—24no—
231D4×C11—22no—
232D4×C11—24no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—48no—
238D4×C11C2×C22⋊C414yes—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—216no—
243C2×C4×C11C2×C22⋊C414yes—
244C2×C4×C11C4×D414yes—
245C2×C4×C11C4×D412yes—
246C2×C4×C11#12012yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12112yes—
249C2×C4×C11#12314yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—44no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—84no—
266C2×Dic11—88no—
267C8×C11—24no—
268C11⋊C8—42no—
269C22×#41C2×D1111yescharacteristic
270C23×D4C2×D1111yescharacteristic
271C2×AGL(1,ℤ/8)—24no—
272C2×AGL(1,ℤ/8)—24no—
273C2×AGL(1,ℤ/8)Dic1118yescomplemented
274C22×SD16C2×D1112yes—
275C22×D8C2×D1112yes—
276C22×M16C2×D1111yescharacteristic
277C23×C8—111no—
278#520—224no—
279#520—224no—
280C2×C4×Q8—112no—
281C2×C4×D4—112no—
282C2×C4×D4—222no—
283C2×#117—111no—
284C2×#117—111no—
285C2×#117—221no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—221no—
288#416—224no—
289C2×#103—112no—
290C2×#102—114no—
291C2×#102—112no—
292C2×#102—224no—
293#390—114no—
294#390—221no—
295#390—221no—
296#379—222no—
297#340—114no—
298#336—114no—
299C22×C11—24no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11—48no—
309C22×C11—44no—
310C22×C11—816no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—84no—
314C22×C11#38614yes—
315C22×C11C2×C4×D411yescharacteristic
316C22×C11C2×#12011yescharacteristic
317C22×C11C2×#12111yescharacteristic
318C22×C11#57612yes—
319C22×C11#57712yes—
320C4×C11—24no—
321C4×C11#38614yes—
322C4×C11C22×C22⋊C411yescharacteristic
323C4×C11C2×C4×D411yescharacteristic
324C4×C11C2×#12111yescharacteristic
325C4×C11C2×#12311yescharacteristic
326Dic11—42no—
327Dic11—44no—
328Dic11—42no—
329Dic11—82no—
330C25—21no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41C2×Dic1114yes—
335C2×#41C22⋊D1114yes—
336C2×#41C22⋊D1114yes—
337C22×Q8C22×D1111yescharacteristic
338C22×D4—21no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4C2×Dic1114yescomplemented
346C22×D4C22×D1112yes—
347C22×D4C22×D1111yescharacteristic
348C23×C4—21no—
349C23×C4—222no—
350C23×C4—221no—
351C23×C4C22×D1111yescharacteristic
352AGL(1,ℤ/8)—232no—
353C2×SD16—24no—
354C2×SD16—24no—
355C2×SD16C2×Dic1118yescomplemented
356C2×D8—24no—
357C2×D8—24no—
358C2×D8C2×Dic1118yescomplemented
359C2×M16—22no—
360C2×M16—22no—
361C2×M16C2×Dic1114yescomplemented
362C22×C8—112no—
363C22×C8—222no—
364C22×C8—222no—
365C22×C8—222no—
366C22×C8C22×D1112yes—
367C4×Q8—224no—
368C4×Q8—224no—
369C4×D4—224no—
370C4×D4—2216no—
371C4×D4—224no—
372#117—228no—
373#117—222no—
374#117—222no—
375#117—222no—
376#117—222no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—228no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—222no—
386C2×C22⋊C4—112no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C42—112no—
392C2×C42—222no—
393C2×C42—221no—
394#103—224no—
395#102—228no—
396#102—224no—
397C2×C11—24no—
398C2×C11—44no—
399C2×C11—84no—
400C2×C11C2×#38611yescharacteristic
401C2×C11#294612yes—
402C2×C11#300811yescharacteristic
403C2×C11#301011yescharacteristic
404C2×C11#304512yes—
405C24—21no—
406C24—22no—
407C24—24no—
408C24—42no—
409C24—42no—
410C24—82no—
411C24—82no—
412C24D4×D1111yescharacteristic
413#41—28no—
414#41—28no—
415#41—28no—
416#41C22⋊Dic11116yescomplemented
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C22×Dic1112yes—
421C2×Q8C2×C22⋊D1112yes—
422C2×Q8C2×C22⋊D1112yes—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—28no—
427C2×D4—24no—
428C2×D4—28no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—44no—
438C2×D4—42no—
439C2×D4—44no—
440C2×D4—42no—
441C2×D4C22×Dic1114yes—
442C2×D4C22×Dic1112yes—
443C2×D4C2×C22⋊D1112yes—
444C2×D4C2×C22⋊D1112yes—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—222no—
452C22×C4—228no—
453C22×C4—224no—
454C22×C4—222no—
455C22×C4—884no—
456C22×C4—882no—
457C22×C4D4×D1111yescharacteristic
458C22×C4D4×D1112yes—
459C22×C4#434112yes—
460C22×C4#434112yes—
461C22×C4C22×Dic1112yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C23×D1111yescharacteristic
465SD16—216no—
466D8—216no—
467M16—28no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—222no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8—444no—
474C2×C8C22×Dic1114yes—
475C4⋊C4—114no—
476C4⋊C4—228no—
477C4⋊C4—224no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C22⋊C4—228no—
484C22⋊C4—224no—
485C22⋊C4—442no—
486C22⋊C4—884no—
487C22⋊C4—884no—
488C42—228no—
489C42—222no—
490C42—222no—
491C42—442no—
492C11#2093211yescharacteristic, complemented, Sylow
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—42no—
500C23—42no—
501C23—44no—
502C23—44no—
503C23—42no—
504C23—42no—
505C23—48no—
506C23—88no—
507C23—84no—
508C23—84no—
509C23—88no—
510C23D4×Dic1112yes—
511C23#6699012yes—
512C23#6699212yes—
513C23C2×D4×D1111yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—22no—
517Q8C2×C22⋊Dic1114yes—
518D4—216no—
519D4—22no—
520D4—24no—
521D4—22no—
522D4—22no—
523D4—24no—
524D4—42no—
525D4—42no—
526D4—48no—
527D4C2×C22⋊Dic1114yes—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—216no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—222no—
537C2×C4—444no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—884no—
542C2×C4—888no—
543C2×C4D4×Dic1114yes—
544C2×C4D4×Dic1112yes—
545C2×C4#6698814yes—
546C2×C4#6699012yes—
547C2×C4#6699214yes—
548C2×C4#6699212yes—
549C2×C4C2×C22⋊Dic1114yes—
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434111yescharacteristic
552C2×C4C2×#434111yescharacteristic
553C2×C4C23×Dic1111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—24no—
557C8—442no—
558C22—22no—
559C22—22no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—48no—
569C22—816no—
570C22—82no—
571C22—82no—
572C22—84no—
573C22#1062283314yes—
574C22#1062330512yes—
575C22#1062330612yes—
576C22C2×D4×Dic1111yescharacteristic
577C22C2×#6699011yescharacteristic
578C22C2×#6699211yescharacteristic
579C4—24no—
580C4—442no—
581C4—444no—
582C4—442no—
583C4—882no—
584C4#1062283314yes—
585C4C2×D4×Dic1111yescharacteristic
586C4C2×#6698811yescharacteristic
587C4C2×#6699211yescharacteristic
588C4C22×C22⋊Dic1111yescharacteristic
589C2—24no—
590C2—44no—
591C2—84no—
592C2C2×#1062283311yescharacteristic
593C2#1307744912yes—
594C2#1307788311yescharacteristic
595C2#1307790111yescharacteristic
596C2#1307815912yes—
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#20932
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×#10623358C2semidirect
2. C2×#10622846C2semidirect
3. C22×#66896C2semidirect
4. #13071198C2semidirect
5. #13068973C2semidirect
6. #13068966C2semidirect
7. #13068336C2semidirect
8. #13068314C2semidirect
14. C2×C11×AGL(1,ℤ/8)C4semidirect
20. C2×Q8×Dic11C22semidirect
22. C2×D4×Dic11C22semidirect
31. C2×#66899C22semidirect
37. C2×#66896C22semidirect
38. #10622189C22semidirect
39. #10622188C22semidirect
55. C22×D4×C11C2×C4semidirect
65. C2×C11×SD16C2×C4semidirect
68. C2×C11×D8C2×C4semidirect
71. C2×C11×M16C2×C4semidirect
119. C11×#41C22⋊C4semidirect
273. C2×AGL(1,ℤ/8)Dic11semidirect
345. C22×D4C2×Dic11semidirect
355. C2×SD16C2×Dic11semidirect
358. C2×D8C2×Dic11semidirect
361. C2×M16C2×Dic11semidirect
416. #41C22⋊Dic11semidirect
492. C11#20932semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106228462
C22×#668962
#130711982
#130689732
#130689662
#130683362
#130683142
C22×C11×AGL(1,ℤ/8)2
#2093211