Finite Group Databasebeta

← #14758113

Subgroups — #14758113

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622777C211yesmaximal, characteristic
2#13071091C211yesmaximal, characteristic, complemented
3#13071078C211yesmaximal, characteristic
4#13069499C211yesmaximal, characteristic
5#13069352C211yesmaximal, characteristic, complemented
6#13069349C211yesmaximal, characteristic, complemented
7#13069310C211yesmaximal, characteristic
8#13069303C211yesmaximal, characteristic, complemented
9#13069302C211yesmaximal, characteristic
10#13069295C211yesmaximal, characteristic, complemented
11#13068516C211yesmaximal, characteristic, complemented
12#13068448C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic
14C4×#66879C211yesmaximal, characteristic, complemented
15C11×#1968C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66930—21no—
20C2×C11×#106C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#390C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622777C418yescomplemented
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622558—21no—
44#10622557—21no—
45C22⋊C4×Dic11—21no—
46C42×Dic11C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622267—21no—
51#10622266—21no—
52#10622262—21no—
53#10622261—21no—
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16C2×C414yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76Q8×Dic11—22no—
77Q8×Dic11C2×C414yes—
78D4×Dic11—22no—
79D4×Dic11C2×C414yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66930—44no—
101C11×#106—22no—
102C11×#103—22no—
103C11×#102—22no—
104C4×C8×C11—22no—
105C11×#95—21no—
106C11×#95—21no—
107#66899—22no—
108#66899C2×C414yes—
109#66896—22no—
110#66896C2×C414yes—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66882—22no—
120#66882C2×C414yes—
121#66879—22no—
122#66879—22no—
123#66879—22no—
124#66879C2×C414yes—
125C4×C11⋊C8—22no—
126#21288—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C22×C412yes—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C22×C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—24no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C11×SD16—28no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C22×C412yes—
161C2×C8×C11#4112yes—
162C2×C8×C11#4112yes—
163C2×C8×C11#4112yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C42×C11—21no—
171C42×C11—21no—
172C22⋊Dic11—24no—
173C22⋊Dic11—42no—
174C22⋊Dic11—42no—
175C4⋊Dic11—24no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C412yes—
183C4⋊Dic11C22×C412yes—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188C4×Dic11—24no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—41no—
194C4×Dic11—41no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C4×Dic11C22×C412yes—
198C4×Dic11#4112yes—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C412yes—
204C2×C11⋊C8#4112yes—
205C2×#440—111no—
206#2295—111no—
207#2293—111no—
208#1973—111no—
209#1968D1111yescharacteristic
210#1943—111no—
211#1942—111no—
212#1936—111no—
213#1935—111no—
214#1934—111no—
215#1933—111no—
216#1776—111no—
217#1763—111no—
218#1762—111no—
219C4×#97—111no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—41no—
231Q8×C11—41no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—41no—
235D4×C11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11#13712yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—48no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11C4×D412yes—
281C2×Dic11C4×D412yes—
282C8×C11—22no—
283C8×C11#11714yescomplemented
284C11⋊C8—22no—
285C11⋊C8—22no—
286C22×SD16C2×D1111yescharacteristic
287C2×C4×Q8—111no—
288C2×C4×D4—111no—
289C2×#117—221no—
290#440—118no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106C2×D1111yescharacteristic
294C2×#103—111no—
295C2×#103—111no—
296C2×#103C2×D1111yescharacteristic
297C2×#102—111no—
298C2×#102—111no—
299C2×#102C2×D1111yescharacteristic
300C2×#97—111no—
301C2×#97—111no—
302C2×#97—111no—
303C2×#97—111no—
304C2×C4×C8—111no—
305C2×C4×C8C2×D1111yescharacteristic
306#391—111no—
307#391C2×D1111yescharacteristic
308#390—111no—
309#390C2×D1111yescharacteristic
310#389—111no—
311#389—111no—
312#389—111no—
313#389—111no—
314#388—221no—
315#388—221no—
316#387—221no—
317#387—221no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—221no—
321C4×C22⋊C4—221no—
322#376—221no—
323C43—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#53211yescharacteristic
339C22×C11#53211yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57511yescharacteristic
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×#11711yescharacteristic
350C4×C11C4×#4111yescharacteristic
351C4×C11#52911yescharacteristic
352C4×C11#52911yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—41no—
356Dic11—41no—
357Dic11—42no—
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8C22×D1111yescharacteristic
362C22×D4C22×D1111yescharacteristic
363C23×C4—221no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16C4×D1114yes—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C4×Q8—114no—
372C4×Q8—222no—
373C4×D4—114no—
374C4×D4—222no—
375#117—444no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—114no—
403#107—222no—
404#106—22no—
405#103—22no—
406#103—114no—
407#103—222no—
408#102—22no—
409#102—114no—
410#102—222no—
411#97—114no—
412#97—222no—
413#97—222no—
414#97—222no—
415C4×C8—22no—
416C4×C8—222no—
417#95—21no—
418#95—21no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427C2×C11—82no—
428C2×C11#229311yescharacteristic
429C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
430C2×C11C4×#13711yescharacteristic
431C2×C11#318011yescharacteristic
432C2×C11#318111yescharacteristic
433C2×C11#318211yescharacteristic
434C2×C11#318311yescharacteristic
435C24—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C4×D1112yes—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4C2×C4×D1112yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—224no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465SD16—28no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—112no—
469C2×C8—112no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8C2×C4×D1112yes—
475C2×C8#434112yes—
476C2×C8#434112yes—
477C2×C8#434112yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—224no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—224no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—21no—
501C42—21no—
502C42—112no—
503C42—112no—
504C42—224no—
505C42—222no—
506C42—222no—
507C42—221no—
508C42—221no—
509C42—441no—
510C42—441no—
511C42—442no—
512C42—442no—
513C11#2128811yescharacteristic, complemented, Sylow
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D1111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—448no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4#6696712yes—
569C2×C4#6696812yes—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C2×#434111yescharacteristic
572C2×C4C2×#434111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C8—22no—
577C8—222no—
578C8—222no—
579C8#6693014yescomplemented
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C4×D4×D1111yescharacteristic
588C22#1062312711yescharacteristic
589C22#1062324711yescharacteristic
590C22C2×#6696711yescharacteristic
591C22C2×#6696811yescharacteristic
592C22#1062329911yescharacteristic
593C22#1062329911yescharacteristic
594C4—22no—
595C4—22no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—222no—
600C4—222no—
601C4—441no—
602C4—441no—
603C4—442no—
604C4—442no—
605C4—881no—
606C4—881no—
607C4C2×#6693011yescharacteristic
608C4C4×#434111yescharacteristic
609C4#1062313111yescharacteristic
610C4#1062321111yescharacteristic
611C2—82no—
612C2#1307107811yescharacteristic
613C2C4×#6696711yescharacteristic
614C2C4×#6696811yescharacteristic
615C2#1307930711yescharacteristic
616C2#1307931811yescharacteristic
617C2#1307933211yescharacteristic
618C2#1307934211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1968C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1968D11
hypocenterC11#21288
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
2. #13071091C2semidirect
5. #13069352C2semidirect
6. #13069349C2semidirect
8. #13069303C2semidirect
10. #13069295C2semidirect
11. #13068516C2semidirect
12. #13068448C2semidirect
14. C4×#66879C2semidirect
32. #10622777C4semidirect
283. C8×C11#117semidirect
513. C11#21288semidirect
579. C8#66930semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
#130710912
#130710782
#130694992
#130693522
#130693492
#130693102
#130693032
#130693022
#130692952
#130685162
#130684482
#130684432
C4×#668792
C11×#19682
#2128811