Finite Group Databasebeta

← #14756900

Subgroups — #14756900

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622631C211yesmaximal, characteristic
2#13071259C211yesmaximal, characteristic
3#13070980C211yesmaximal, characteristic, complemented
4#13069246C211yesmaximal, characteristic
5#13069239C211yesmaximal, characteristic
6#13069211C211yesmaximal, characteristic, complemented
7#13069190C211yesmaximal, characteristic, complemented
8#13068968C211yesmaximal, characteristic
9#13068968C211yesmaximal, characteristic
10#13068885C211yesmaximal, characteristic, complemented
11#13068871C211yesmaximal, characteristic, complemented
12#13068514C211yesmaximal, characteristic, complemented
13C4×#66880C211yesmaximal, characteristic, complemented
14#13068367C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622834C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622825—21no—
29#10622824—21no—
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32#10622631C418yescomplemented
33#10622598C2211yescharacteristic
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622564—21no—
42#10622564—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44#10622545C2211yescharacteristic
45C4×Dic11⋊C4—21no—
46C4×Dic11⋊C4—21no—
47C2×#66867C2211yescharacteristic
48#10622262—21no—
49#10622261—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11C2×C414yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×#4324—22no—
78C2×#4324—22no—
79C2×#4324C2×C414yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66940—22no—
99#66940—22no—
100#66940—22no—
101#66940—22no—
102C4×Dic22—22no—
103C4×Dic22C2×C414yes—
104C11×#102—22no—
105C11×#102—22no—
106C4×C8×C11—22no—
107C11×#95—21no—
108#66896C2×C414yes—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66880—22no—
119#66880—22no—
120#66874C2×C414yes—
121#66872—22no—
122#66871—22no—
123#66871C2×C414yes—
124#66867C2×C414yes—
125#21128—111nomaximal, Sylow
126C24×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—81no—
138C22×C4×C11—81no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22C22×C412yes—
154C2×Dic22#4112yes—
155C2×Dic22#4112yes—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C412yes—
166C11×C4⋊C4#4112yes—
167C11×C4⋊C4#4112yes—
168C11×C22⋊C4—24no—
169C42×C11—81no—
170C42×C11C22×C412yes—
171C42×C11#4112yes—
172C22⋊Dic11—81no—
173C22⋊Dic11—81no—
174C22⋊Dic11—81no—
175C22⋊Dic11—81no—
176#4324—28no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—81no—
183C4⋊Dic11—81no—
184C4⋊Dic11C22×C412yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188C4×Dic11—24no—
189C4×Dic11—24no—
190C4×Dic11—24no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—81no—
196C4×Dic11—81no—
197C4×Dic11—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C412yes—
204C2×#440—111no—
205#2319—111no—
206#2276—111no—
207#1926—111no—
208#1925—111no—
209#1921—111no—
210#1918—111no—
211#1880—111no—
212#1880—111no—
213#1865—111no—
214#1863—111no—
215#1776—111no—
216C4×#103—111no—
217C4×#102D1111yescharacteristic
218#1746—111no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11C22×D411yescharacteristic
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—41no—
230D4×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—84no—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C4×D412yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277Dic22—22no—
278Dic22—22no—
279Dic22—22no—
280Dic22#11714yes—
281C8×C11—41no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C22×SD16—111no—
286C2×C4×Q8—111no—
287C2×C4×Q8—111no—
288C2×C4×Q8—111no—
289C2×C4×D4C2×D1111yescharacteristic
290#440—118no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#102—111no—
298C2×#102C2×D1111yescharacteristic
299C2×#102C2×D1111yescharacteristic
300C2×#97—111no—
301C2×C4×C8C2×D1111yescharacteristic
302#390—111no—
303#390—111no—
304#389—111no—
305#389—111no—
306#388—221no—
307#388—221no—
308#381—221no—
309#380—221no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—221no—
314C4×C4⋊C4—221no—
315C4×C4⋊C4—221no—
316C4×C4⋊C4C2×D1111yescharacteristic
317#376—111no—
318#376—221no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340C2×D1111yescharacteristic
324#340C2×D1111yescharacteristic
325#336—111no—
326#336—111no—
327#336—111no—
328#336—111no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11#52511yescharacteristic
339C22×C11#57611yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11C2×#11711yescharacteristic
349C4×C11C4×#4111yescharacteristic
350C4×C11#52911yescharacteristic
351C4×C11#52911yescharacteristic
352Dic11—24no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356Dic11—41no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8—111no—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C2×SD16—114no—
364C2×SD16—222no—
365C2×SD16—222no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4×Q8—114no—
371C4×Q8—222no—
372C4×Q8—222no—
373C4×Q8—222no—
374C4×Q8—222no—
375C4×Q8—222no—
376C4×D4—22no—
377C4×D4C4×D1114yes—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#107—114no—
405#107—222no—
406#106—222no—
407#103—114no—
408#103—222no—
409#103—222no—
410#102—22no—
411#102—22no—
412#102—114no—
413#97—114no—
414C4×C8—22no—
415#95—21no—
416#95—111no—
417#95—111no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—82no—
426C2×C11#229011yescharacteristic
427C2×C11#294611yescharacteristic
428C2×C11#294711yescharacteristic
429C2×C11#311911yescharacteristic
430C2×C11#312111yescharacteristic
431C2×C11#312411yescharacteristic
432C2×C11#312611yescharacteristic
433C24—21no—
434C2×Q8—112no—
435C2×Q8—112no—
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×C4×D1112yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463SD16—228no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—112no—
480C4⋊C4—224no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—881no—
489C4⋊C4—881no—
490C4⋊C4C2×C4×D1112yes—
491C4⋊C4#433912yes—
492C4⋊C4#433912yes—
493C22⋊C4—24no—
494C22⋊C4—881no—
495C22⋊C4—881no—
496C22⋊C4—881no—
497C22⋊C4—881no—
498C42—81no—
499C42—224no—
500C42—224no—
501C42—224no—
502C42—221no—
503C42—221no—
504C42—221no—
505C42—221no—
506C42—881no—
507C42—881no—
508C42—881no—
509C42C2×C4×D1112yes—
510C42#434112yes—
511C11#2112811yescharacteristic, complemented, Sylow
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C2×D4×D1111yescharacteristic
520Q8—114no—
521Q8—222no—
522Q8—222no—
523Q8—222no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
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—221no—
556C2×C4—221no—
557C2×C4—221no—
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(C22⋊D11)⋊C412yes—
567C2×C4(C22⋊D11)⋊C412yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×#433911yescharacteristic
570C2×C4C2×#433911yescharacteristic
571C2×C4C2×#434111yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C8—41no—
575C8—41no—
576C8—222no—
577C8—222no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×(C22⋊D11)⋊C411yescharacteristic
586C22#1062307811yescharacteristic
587C22#1062307811yescharacteristic
588C22#1062328811yescharacteristic
589C22#1062329311yescharacteristic
590C22#1062330111yescharacteristic
591C22#1062330211yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—224no—
598C4—441no—
599C4—441no—
600C4—441no—
601C4—441no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4C4×#433911yescharacteristic
606C4D11×#11711yescharacteristic
607C4#1062308811yescharacteristic
608C4#1062308811yescharacteristic
609C2—82no—
610C2#1307106211yescharacteristic
611C2#1307744211yescharacteristic
612C2#1307746211yescharacteristic
613C2#1307881111yescharacteristic
614C2#1307884111yescharacteristic
615C2#1307887411yescharacteristic
616C2#1307890411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#21128
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. #13070980C2semidirect
6. #13069211C2semidirect
7. #13069190C2semidirect
10. #13068885C2semidirect
11. #13068871C2semidirect
12. #13068514C2semidirect
13. C4×#66880C2semidirect
14. #13068367C2semidirect
32. #10622631C4semidirect
511. C11#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#106226312
#130712592
#130709802
#130692462
#130692392
#130692112
#130691902
#130689682
#130688852
#130688712
#130685142
C4×#668802
#130683672
C4×C11×#1022
#2112811