Finite Group Databasebeta

← #14790064

Subgroups — #14790064

Order 2816.

1092 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic, complemented
2C4×#67002C211yesmaximal, characteristic
3#13073570C211yesmaximal, characteristic, complemented
4#13069958C212yesmaximal, complemented
5#13069769C212yesmaximal, complemented
6#13069606C211yesmaximal, characteristic, complemented
7#13069561C211yesmaximal, characteristic, complemented
8#13068992C212yesmaximal
9#13068842C212yesmaximal, complemented
10#13068636C211yesmaximal, characteristic, complemented
11C11×#3503C211yesmaximal, characteristic, complemented
12Q82×C11—21no—
13C11×#557—21no—
14C11×#554—21no—
15C11×#554—22no—
16D4×Q8×C11—22no—
17D4×Q8×C11—21no—
18C11×#544—22no—
19C11×#544C2212yes—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520C2212yes—
25C4×C11×#41C2211yescharacteristic
26C2×#67002C2211yescharacteristic
27C2×#66999—22no—
28C2×C4×D44C2211yescharacteristic
29C2×#66901C2212yes—
30#10622845C2211yescharacteristic
31#10622700—21no—
32#10622697—21no—
33#10622679—22no—
34#10622639—21no—
35C4×#4325—21no—
36#10622627—21no—
37C4×#4323—21no—
38#10622614C2212yes—
39#10622614C2211yescharacteristic
40#10622608C2212yes—
41#10622608C2211yescharacteristic
42#10622605—22no—
43#10622601C2212yes—
44#10622589C2212yes—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622537C2211yescharacteristic
47C4×#4318C2211yescharacteristic
48#10622170C2212yes—
49#10622170C2212yes—
50#10622170C2212yes—
51#10622168C2212yes—
52#10622168C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8D411yescharacteristic
69C11×#125—24no—
70C11×#125—22no—
71C11×#125—22no—
72C11×#125D412yes—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—24no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11D411yescharacteristic
86C4×Q8×C11D411yescharacteristic
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—24no—
91C4×D4×C11D411yescharacteristic
92C4×D4×C11D411yescharacteristic
93C11×#117—22no—
94C11×#117—21no—
95C11×#117C2311yescharacteristic
96C11×#117C2312yes—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4D412yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103#67002—22no—
104#67002Q814yescomplemented
105#66999—48no—
106C2×#4325—21no—
107C2×#4323—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—24no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4—24no—
113C2×C4×Dic11C2312yes—
114C2×#4318C2311yescharacteristic
115C2×#4318C2312yes—
116C2×#4318C2311yescharacteristic
117C4×D44—21no—
118C4×D44—21no—
119C4×D44—21no—
120C4×D44—21no—
121#66901—24no—
122#66899—21no—
123#66896—21no—
124C11⋊#95—21no—
125#66873—21no—
126#66873—21no—
127#66873—22no—
128#66873—22no—
129#66872—21no—
130#66872—22no—
131#66871—21no—
132#66871—22no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—21no—
135#66867—21no—
136C4×C11⋊C8—21no—
137#24320—111nomaximal, Sylow
138C23×D11—21no—
139C11×#41—21no—
140C11×#41—21no—
141C11×#41C2×Q812yes—
142C11×#41#4112yes—
143C2×Q8×C11—24no—
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—44no—
149C2×Q8×C11—84no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—22no—
162C22×Dic11—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44C2×Q812yescomplemented
169C2×C4×D11—44no—
170C2×C4×D11—41no—
171C2×C4×D11—41no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2×D412yes—
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D412yes—
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C22⋊C4—24no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C42×C11—24no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—22no—
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C42×C11C2×D411yescharacteristic
203C42×C11C2×D411yescharacteristic
204#4325—24no—
205#4323—24no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—41no—
208(C2×D11)⋊C4—41no—
209C4⋊Dic11—24no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212Dic11⋊C4—48no—
213C4×Dic11—22no—
214C4×Dic11—22no—
215#4318—21no—
216#4318—22no—
217#4318—21no—
218#4318—22no—
219#4318—21no—
220#4318C2×Q812yescomplemented
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—22no—
224#3503D1111yescharacteristic, complemented
225#3077—111no—
226C4×AGL(1,ℤ/8)—111no—
227#2542—111no—
228#2060—112no—
229#2027—112no—
230#1997—111no—
231#1986—111no—
232#1883—112no—
233#1859—112no—
234#1806—111no—
235C23×C11—21no—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—41no—
241C22×D11—41no—
242Q8×C11—21no—
243Q8×C11—42no—
244Q8×C11—44no—
245Q8×C11—42no—
246Q8×C11—82no—
247Q8×C11—84no—
248Q8×C11C22⋊Q812yescomplemented
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—21no—
252D4×C11C22⋊Q812yescomplemented
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—44no—
266C2×C4×C11—84no—
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—24no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—41no—
282D44—22no—
283D44—22no—
284D44—41no—
285D44—41no—
286C4×D11—82no—
287C4×D11—82no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C11⋊C8—42no—
291C2×AGL(1,ℤ/8)—111no—
292Q82—21no—
293#557—21no—
294#554—21no—
295#554—22no—
296D4×Q8—22no—
297D4×Q8—21no—
298#544—22no—
299#544C2×D1112yes—
300#533—21no—
301#533C2×D1111yescharacteristic
302C2×C4⋊Q8—21no—
303C2×C4⋊Q8C2×D1111yescharacteristic
304C2×C22⋊Q8—222no—
305#520C2×D1112yes—
306C4×#41C2×D1111yescharacteristic
307C2×C4×D4—111no—
308#478—222no—
309#476—221no—
310#474—221no—
311#442—221no—
312#440—221no—
313C4×SD16—221no—
314C4×D8—221no—
315#428—112no—
316#428—111no—
317#423—111no—
318C2×#104—112no—
319#418—112no—
320#418—111no—
321#417—111no—
322C4×M16—111no—
323#399—222no—
324#390—112no—
325#384—112no—
326C4×C4⋊C4—111no—
327#343—112no—
328#343—112no—
329#339—112no—
330#339—112no—
331#339—112no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×#12011yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11D4×Q811yescharacteristic
340C2×D11—44no—
341C2×D11—42no—
342C2×D11—82no—
343C2×D11—81no—
344C2×D11—81no—
345C4×C11—22no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11#45312yes—
355C4×C11C2×C22⋊Q811yescharacteristic
356C4×C11#53611yescharacteristic
357C4×C11#54811yescharacteristic
358C4×C11D4×Q811yescharacteristic
359Dic11—44no—
360Dic11—81no—
361C2×#41C22×D1111yescharacteristic
362C22×Q8—22no—
363C22×Q8C22⋊D1112yes—
364C22×D4—111no—
365C23×C4—221no—
366AGL(1,ℤ/8)—114no—
367AGL(1,ℤ/8)—222no—
368C2×SD16—221no—
369C2×D8—221no—
370C2×M16—111no—
371C2×M16—111no—
372C2×M16—112no—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—24no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8C22⋊D1111yescharacteristic
383C4⋊Q8C22⋊D1111yescharacteristic
384#125—24no—
385#125—22no—
386#125—22no—
387#125C22⋊D1112yes—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—24no—
391C22⋊Q8—24no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—24no—
395C22⋊Q8—448no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8C22⋊D1111yescharacteristic
402C4×Q8C22⋊D1111yescharacteristic
403C4×D4—22no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—24no—
407C4×D4—221no—
408C4×D4—221no—
409C4×D4—221no—
410C4×D4—221no—
411C4×D4C22⋊D1111yescharacteristic
412C4×D4C22⋊D1111yescharacteristic
413#117—22no—
414#117—21no—
415#117C22×D1111yescharacteristic
416#117C22×D1112yes—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—224no—
422C2×C4⋊C4C22⋊D1112yes—
423C2×C4⋊C4C22×D1112yes—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—224no—
426C2×C42—21no—
427C2×C42—112no—
428C2×C42C22×D1111yescharacteristic
429#107—221no—
430#107—222no—
431#106—221no—
432#106—222no—
433C4⋊C8—221no—
434C4⋊C8—221no—
435#104—224no—
436#103—221no—
437#102—221no—
438#102—221no—
439#102—221no—
440#102—222no—
441#102—222no—
442#97—221no—
443C4×C8—221no—
444#95—221no—
445C2×C11—21no—
446C2×C11—21no—
447C2×C11—42no—
448C2×C11#240911yescharacteristic
449C2×C11C2×#45311yescharacteristic
450C2×C11#302011yescharacteristic
451D11—82no—
452C24—221no—
453#41—21no—
454#41—21no—
455#41Q8×D1112yes—
456#41#434312yes—
457C2×Q8—24no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—44no—
463C2×Q8—84no—
464C2×Q8C2×C22⋊D1111yescharacteristic
465C2×D4—21no—
466C2×D4—112no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4C2×C22⋊D1111yescharacteristic
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—444no—
480C22×C4—441no—
481C22×C4—441no—
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1114yes—
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486SD16—224no—
487D8—224no—
488M16—112no—
489M16—221no—
490M16—222no—
491M16—221no—
492M16—221no—
493M16—222no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—222no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—224no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—448no—
515C4⋊C4C2×C22⋊D1112yes—
516C4⋊C4C2×C22⋊D1111yescharacteristic
517C4⋊C4C2×C22⋊D1112yes—
518C4⋊C4C2×C22⋊D1111yescharacteristic
519C22⋊C4—24no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—448no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C42—24no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—22no—
532C42—222no—
533C42—222no—
534C42C2×C22⋊D1111yescharacteristic
535C42C2×C22⋊D1111yescharacteristic
536C42C2×C22⋊D1111yescharacteristic
537C42C2×C22⋊D1111yescharacteristic
538C11#2432011yescharacteristic, complemented, Sylow
539C23—21no—
540C23—222no—
541C23—442no—
542C23—442no—
543C23—441no—
544C23—441no—
545C23C22×C22⋊D1111yescharacteristic
546Q8—21no—
547Q8—42no—
548Q8—44no—
549Q8—42no—
550Q8—82no—
551Q8—84no—
552Q8#6699912yescomplemented
553D4—22no—
554D4—22no—
555D4—21no—
556D4—222no—
557D4—222no—
558D4—441no—
559D4—441no—
560D4#6699912yescomplemented
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—84no—
575C2×C4—224no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—441no—
580C2×C4—882no—
581C2×C4—882no—
582C2×C4#6700611yescharacteristic
583C2×C4#6700611yescharacteristic
584C2×C4#6700611yescharacteristic
585C2×C4#6700611yescharacteristic
586C2×C4C2×Q8×D1111yescharacteristic
587C2×C4C2×#434311yescharacteristic
588C2×C4#6704011yescharacteristic
589C2×C4#6704011yescharacteristic
590C2×C4C22×C22⋊D1111yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C8—222no—
593C8—441no—
594C8—442no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22—444no—
601C22—442no—
602C22—882no—
603C22—881no—
604C22—881no—
605C22Q8×C22⋊D1111yescharacteristic
606C22#1062334811yescharacteristic
607C22C2×#6700611yescharacteristic
608C4—22no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—41no—
613C4—44no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4—444no—
618C4—881no—
619C4#1062285412yes—
620C4C2×#6699911yescharacteristic
621C4Q8×C22⋊D1111yescharacteristic
622C4#1062334711yescharacteristic
623C4#1062334811yescharacteristic
624C2—21no—
625C2—21no—
626C2—42no—
627C2—882no—
628C2#1307197511yescharacteristic
629C2C2×#1062285411yescharacteristic
630C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×#67002C22
hypercenter#3503D11
hypocenterC11#24320
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13073570C2semidirect
4. #13069958C2semidirect
5. #13069769C2semidirect
6. #13069606C2semidirect
7. #13069561C2semidirect
9. #13068842C2semidirect
10. #13068636C2semidirect
11. C11×#3503C2semidirect
104. #67002Q8semidirect
168. C2×D44C2×Q8semidirect
220. #4318C2×Q8semidirect
224. #3503D11semidirect
248. Q8×C11C22⋊Q8semidirect
252. D4×C11C22⋊Q8semidirect
538. C11#24320semidirect
552. Q8#66999semidirect
560. D4#66999semidirect

Maximal subgroups

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

subgroupindex
#130784092
C4×#670022
#130735702
#130699582
#130697692
#130696062
#130695612
#130689922
#130688422
#130686362
C11×#35032
#2432011