Finite Group Databasebeta

← #14758678

Subgroups — #14758678

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622322C211yesmaximal, characteristic
2#13071221C211yesmaximal, characteristic
3#13070970C211yesmaximal, characteristic
4#13069383C211yesmaximal, characteristic, complemented
5#13069381C211yesmaximal, characteristic, complemented
6#13069376C211yesmaximal, characteristic, complemented
7#13069373C211yesmaximal, characteristic, complemented
8#13068818C211yesmaximal, characteristic
9#13068814C211yesmaximal, characteristic
10#13068810C211yesmaximal, characteristic
11#13068802C211yesmaximal, characteristic
12#13068513C211yesmaximal, characteristic, complemented
13C4×#66871C211yesmaximal, characteristic, complemented
14C4×#66872C211yesmaximal, characteristic, complemented
15C11×#1776C211yesmaximal, characteristic, complemented
16C2×#66945C2211yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622553—21no—
41C4×(C2×D11)⋊C4—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622546—21no—
45C4×Dic11⋊C4—21no—
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622322C418yescomplemented
48#10622282—21no—
49#10622279—21no—
50#10622265—21no—
51#10622262—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4D411yescharacteristic
84C2×Dic11⋊C4D411yescharacteristic
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66945—22no—
94#66945—22no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11—22no—
97#66925C2×C414yes—
98#66925Q814yes—
99C11×#107—22no—
100C11×#106—22no—
101C11×#97C2×C414yescomplemented
102C11×#95—21no—
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112(C2×D11)⋊C8C2×C414yes—
113(C2×D11)⋊C8C2×C414yes—
114#66882—22no—
115#66881—22no—
116Dic11⋊C8C2×C414yescomplemented
117Dic11⋊C8C2×C414yescomplemented
118#66872—22no—
119#66872—22no—
120#66871—22no—
121#66871—22no—
122C4×C11⋊C8C2×C414yescomplemented
123#21367—111nomaximal, Sylow
124C23×D11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×C4×D11—24no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—81no—
145C2×C4×D11—81no—
146C2×C4×D11C22×C412yes—
147C2×C4×D11C2×Q812yes—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C22×C412yes—
153C2×C8×C11C22×C412yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4#4112yes—
161C11×C4⋊C4#4112yes—
162C42×C11—81no—
163C42×C11—81no—
164C42×C11C22×C412yes—
165C42×C11C2×Q812yes—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—81no—
168(C2×D11)⋊C4—81no—
169(C2×D11)⋊C4C4⋊C414yes—
170(C2×D11)⋊C4C4⋊C414yes—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11#4112yes—
178C4⋊Dic11#4112yes—
179Dic11⋊C4—24no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182Dic11⋊C4C4⋊C414yes—
183Dic11⋊C4C4⋊C414yes—
184C4×Dic11—24no—
185C4×Dic11—81no—
186C4×Dic11—81no—
187C4×Dic11—81no—
188C4×Dic11—81no—
189C4×Dic11C22×C412yes—
190C4×Dic11C2×Q812yes—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8C22×C412yes—
196C2×C11⋊C8C22×C412yes—
197C2×#433—111no—
198#2314—111no—
199#2274—111no—
200#1949—111no—
201#1949—111no—
202#1948—111no—
203#1947—111no—
204#1854—111no—
205#1854—111no—
206#1853—111no—
207#1852—111no—
208#1776—111no—
209#1776D1111yescharacteristic, complemented
210C4×#107—111no—
211C4×#106—111no—
212C23×C11C22×D411yescharacteristic
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219C22×D11C2×C4⋊C412yes—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11C2×C4⋊C412yes—
237C2×C4×C11C2×C4⋊C412yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11C2×C4⋊C412yes—
263C2×Dic11C2×C4⋊C412yes—
264C2×Dic11C2×C4⋊C412yes—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—84no—
270C8×C11—22no—
271C8×C11—22no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C2×#117—111no—
275C2×#117—111no—
276C22×C4⋊C4—111no—
277#433—118no—
278C2×#107—111no—
279C2×#107—111no—
280C2×#107—111no—
281C2×#107C2×D1111yescharacteristic
282C2×#106—111no—
283C2×#106—111no—
284C2×#106—111no—
285C2×#106C2×D1111yescharacteristic
286C2×C4⋊C8—111no—
287C2×C4⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×#97C2×D1111yescharacteristic
291C2×C4×C8—111no—
292#388—221no—
293#388—221no—
294#387—221no—
295#387—221no—
296#384—111no—
297#382—111no—
298#380—111no—
299#380—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—221no—
305C4×C4⋊C4—221no—
306C4×C4⋊C4C2×D1111yescharacteristic
307C4×C4⋊C4C2×D1111yescharacteristic
308C4×C22⋊C4—221no—
309C4×C22⋊C4—221no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340C2×D1111yescharacteristic
317#340C2×D1111yescharacteristic
318C22×C11C22×C4⋊C411yescharacteristic
319C22×C11#52511yescharacteristic
320C22×C11#52511yescharacteristic
321C22×C11#57611yescharacteristic
322C22×C11#57711yescharacteristic
323C22×C11#57711yescharacteristic
324C22×C11#57811yescharacteristic
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11C4×#4111yescharacteristic
339C4×C11C4×#4111yescharacteristic
340C4×C11#53311yescharacteristic
341C4×C11#53311yescharacteristic
342Dic11—22no—
343Dic11—22no—
344Dic11—22no—
345Dic11—42no—
346Dic11—42no—
347Dic11—81no—
348Dic11—81no—
349C23×C4—111no—
350C23×C4—221no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355#117—114no—
356#117—114no—
357#117—222no—
358#117—222no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C22⋊C4—111no—
375C2×C22⋊C4—111no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—111no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388#107—22no—
389#107—222no—
390#107—222no—
391#107—222no—
392#106—22no—
393#106—222no—
394#106—222no—
395#106—222no—
396C4⋊C8—114no—
397C4⋊C8—114no—
398C22⋊C8—114no—
399C22⋊C8—114no—
400#97C4×D1114yescomplemented
401C4×C8—114no—
402#95—21no—
403#95—21no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412C2×C11#229611yescharacteristic
413C2×C11#291211yescharacteristic
414C2×C11#291311yescharacteristic
415C2×C11#311811yescharacteristic
416C2×C11#311911yescharacteristic
417C2×C11#312011yescharacteristic
418C2×C11#312111yescharacteristic
419D11—42no—
420C24—111no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—112no—
429C22×C4—112no—
430C22×C4—224no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—881no—
440C22×C4—881no—
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8C2×C4×D1112yes—
455C2×C8C2×C4×D1112yes—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—114no—
463C4⋊C4—114no—
464C4⋊C4—112no—
465C4⋊C4—112no—
466C4⋊C4—224no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4#433912yes—
476C4⋊C4#433912yes—
477C22⋊C4—114no—
478C22⋊C4—114no—
479C22⋊C4—224no—
480C22⋊C4—881no—
481C22⋊C4—881no—
482C42—81no—
483C42—81no—
484C42—112no—
485C42—112no—
486C42—224no—
487C42—881no—
488C42—881no—
489C42—881no—
490C42—881no—
491C42C2×C4×D1112yes—
492C42Q8×D1112yes—
493C11#2136711yescharacteristic, complemented, Sylow
494C23—112no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23C2×D4×D1111yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—112no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—884no—
544C2×C4C4⋊C4×D1112yes—
545C2×C4C4⋊C4×D1112yes—
546C2×C4C22×C4×D1111yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C2×#433911yescharacteristic
549C2×C4C2×Q8×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—22no—
553C8—22no—
554C8—222no—
555C8—222no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22C2×C4⋊C4×D1111yescharacteristic
564C22#1062307811yescharacteristic
565C22#1062307811yescharacteristic
566C22#1062330511yescharacteristic
567C22#1062330611yescharacteristic
568C22#1062330911yescharacteristic
569C22#1062331011yescharacteristic
570C4—22no—
571C4—22no—
572C4—42no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—222no—
577C4—222no—
578C4—222no—
579C4—442no—
580C4—442no—
581C4—881no—
582C4—881no—
583C4C4×#433911yescharacteristic
584C4#1062305311yescharacteristic
585C4#1062310911yescharacteristic
586C4#1062310911yescharacteristic
587C2—442no—
588C2#1307109611yescharacteristic
589C2#1307721011yescharacteristic
590C2#1307721511yescharacteristic
591C2#1307879811yescharacteristic
592C2#1307881311yescharacteristic
593C2#1307883411yescharacteristic
594C2#1307884911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1776C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1776D11
hypocenterC11#21367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
4. #13069383C2semidirect
5. #13069381C2semidirect
6. #13069376C2semidirect
7. #13069373C2semidirect
12. #13068513C2semidirect
13. C4×#66871C2semidirect
14. C4×#66872C2semidirect
15. C11×#1776C2semidirect
47. #10622322C4semidirect
101. C11×#97C2×C4semidirect
116. Dic11⋊C8C2×C4semidirect
117. Dic11⋊C8C2×C4semidirect
122. C4×C11⋊C8C2×C4semidirect
209. #1776D11semidirect
400. #97C4×D11semidirect
493. C11#21367semidirect

Maximal subgroups

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

subgroupindex
C2×#106223222
#130712212
#130709702
#130693832
#130693812
#130693762
#130693732
#130688182
#130688142
#130688102
#130688022
#130685132
C4×#668712
C4×#668722
C11×#17762
#2136711