Finite Group Databasebeta

← #14775586

Subgroups — #14775586

Order 2816.

898 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×#10622483C211yesmaximal, characteristic
2#13071703C211yesmaximal, characteristic, complemented
3#13071517C211yesmaximal, characteristic
4#13069575C211yesmaximal, characteristic, complemented
5#13069378C211yesmaximal, characteristic, complemented
6#13069345C211yesmaximal, characteristic, complemented
7#13069341C211yesmaximal, characteristic, complemented
8#13069197C211yesmaximal, characteristic, complemented
9#13068880C211yesmaximal, characteristic
10#13068878C211yesmaximal, characteristic
11#13068477C211yesmaximal, characteristic, complemented
12C4×#66873C211yesmaximal, characteristic
13#13068430C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1919C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×C4⋊C4×D11—21no—
19C2×#66941C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622602—21no—
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C4×Dic11⋊C4—21no—
41C4×Dic11⋊C4C2211yescharacteristic
42#10622542—21no—
43#10622541C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622483C418yescomplemented
46#10622281—21no—
47#10622280—21no—
48#10622260—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4D411yescharacteristic
87C2×Dic11⋊C4D411yescharacteristic
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—22no—
95#66946—22no—
96#66946—41no—
97#66946C2×C414yes—
98C4⋊C4×D11—44no—
99#66941—22no—
100#66941C2×C414yescomplemented
101C4×D44—22no—
102C4×D44—41no—
103C11×#106C2×C414yescomplemented
104C11×#95—21no—
105C11×#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113#66885—22no—
114#66885C2×C414yes—
115#66881—41no—
116Dic11⋊C8C2×C414yescomplemented
117C8×Dic11—22no—
118C8×Dic11—41no—
119#66873C2×C414yes—
120#66873Q814yescomplemented
121#66872—41no—
122#66872C2×C414yescomplemented
123C4×C11⋊C8—41no—
124#22963—111nomaximal, Sylow
125C23×D11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44C22×C412yes—
144C2×D44C2×Q812yes—
145C2×D44#4112yes—
146C2×C4×D11—24no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—81no—
154C2×C4×D11—81no—
155C2×Dic22—24no—
156C2×Dic22—81no—
157C2×Dic22—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C412yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C22×C412yes—
171C11×C4⋊C4C22×C412yes—
172C11×C4⋊C4C2×Q812yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—81no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—42no—
185C4⋊Dic11—81no—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—22no—
189Dic11⋊C4—42no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192Dic11⋊C4SD1614yes—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196C4×Dic11—81no—
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⋊C8C2×Q812yes—
205C2×#476—111no—
206#2369—111no—
207D4×C4⋊C4—111no—
208#1990—111no—
209#1948—111no—
210#1941—111no—
211#1941—111no—
212#1919—111no—
213#1919D1111yescharacteristic, complemented
214#1864—111no—
215#1864—111no—
216C8×C4⋊C4—111no—
217C4×#102—111no—
218C4×#102—111no—
219C4×#102—111no—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
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—41no—
245C2×C4×C11C2×SD1612yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11C4×D412yes—
269C2×Dic11C4×D412yes—
270C2×Dic11C2×SD1612yes—
271C2×Dic11C2×SD1612yes—
272C2×Dic11#13512yes—
273D44—22no—
274D44—22no—
275D44—22no—
276D44C4×Q814yes—
277C4×D11—48no—
278C4×D11—84no—
279C4×D11—84no—
280Dic22—84no—
281C8×C11—22no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C2×C4⋊Q8—111no—
286C2×C4×D4—111no—
287C2×C4×D4—111no—
288C2×C4×D4—111no—
289C22×C4⋊C4—221no—
290#476—118no—
291C2×#106—111no—
292C2×#106—111no—
293C2×#106—111no—
294C2×#106C2×D1111yescharacteristic
295C2×C4⋊C8—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×C4×C8—111no—
301C2×C4×C8—111no—
302C2×C4×C8—111no—
303#391—221no—
304#391—221no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—221no—
309#389C2×D1111yescharacteristic
310#385—221no—
311#385—221no—
312#384—111no—
313#380—221no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—221no—
318C4×C4⋊C4C2×D1111yescharacteristic
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340C2×D1111yescharacteristic
325#340C2×D1111yescharacteristic
326#340C2×D1111yescharacteristic
327#336—111no—
328#336C2×D1111yescharacteristic
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#54611yescharacteristic
331C22×C11D4×Q811yescharacteristic
332C22×C11C22×SD1611yescharacteristic
333C22×C11C2×#13511yescharacteristic
334C22×C11#57611yescharacteristic
335C22×C11#57711yescharacteristic
336C2×D11—24no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C4×C11—22no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11C2×C4×Q811yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#55211yescharacteristic
352C4×C11#55411yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—42no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359Dic11C4×SD1614yes—
360C22×Q8—221no—
361C22×D4—111no—
362C23×C4—221no—
363C23×C4—221no—
364C23×C4—221no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C4⋊Q8—114no—
370C4⋊Q8—222no—
371C4×D4—114no—
372C4×D4—222no—
373C4×D4—222no—
374C4×D4—222no—
375C4×D4—441no—
376C4×D4—441no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—444no—
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—21no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42C22×D1111yescharacteristic
403#106—114no—
404#106—441no—
405#106—441no—
406#106C4×D1114yescomplemented
407C4⋊C8—114no—
408#102—114no—
409#102—114no—
410#102—114no—
411#102—222no—
412C4×C8—222no—
413C4×C8—441no—
414C4×C8—441no—
415#95—21no—
416#95—21no—
417#95—111no—
418#95—111no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424C2×C11#236011yescharacteristic
425C2×C11C2×C4×SD1611yescharacteristic
426C2×C11#294611yescharacteristic
427C2×C11#329511yescharacteristic
428C2×C11#330311yescharacteristic
429C2×C11Q8×SD1611yescharacteristic
430C2×C11#338011yescharacteristic
431D11—44no—
432C24—221no—
433C2×Q8—224no—
434C2×Q8—881no—
435C2×Q8—881no—
436C2×D4—112no—
437C2×D4—112no—
438C2×D4—112no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—224no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—881no—
461C22×C4—881no—
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
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—
476C2×C8C2×C4×D1112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—114no—
484C4⋊C4—112no—
485C4⋊C4—222no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4—881no—
497C4⋊C4C2×C4×D1112yes—
498C4⋊C4C2×C4×D1112yes—
499C4⋊C4Q8×D1112yes—
500C22⋊C4—224no—
501C22⋊C4—442no—
502C22⋊C4—442no—
503C42—21no—
504C42—21no—
505C42—81no—
506C42—112no—
507C42—112no—
508C42—221no—
509C42—221no—
510C42—442no—
511C42—881no—
512C11#2296311yescharacteristic, complemented, Sylow
513C23—222no—
514C23—222no—
515C23—222no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23C2×D4×D1111yescharacteristic
521Q8—884no—
522D4—114no—
523D4—222no—
524D4—222no—
525D4—222no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—41no—
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—112no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—221no—
556C2×C4—448no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—884no—
566C2×C4—884no—
567C2×C4SD16×D1112yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×Q8×D1111yescharacteristic
570C2×C4#41×D1111yescharacteristic
571C2×C4#41×D1111yescharacteristic
572C2×C4#6704211yescharacteristic
573C2×C4#6704311yescharacteristic
574C8—22no—
575C8—41no—
576C8—222no—
577C8—222no—
578C22—224no—
579C22—442no—
580C22—442no—
581C22—442no—
582C22—442no—
583C22—442no—
584C22—442no—
585C22C4×D4×D1111yescharacteristic
586C22#1062316311yescharacteristic
587C22#1062318511yescharacteristic
588C22C2×SD16×D1111yescharacteristic
589C22D11×#13511yescharacteristic
590C22#1062330511yescharacteristic
591C22#1062330911yescharacteristic
592C4—22no—
593C4—42no—
594C4—42no—
595C4—42no—
596C4—41no—
597C4—81no—
598C4—114no—
599C4—222no—
600C4—222no—
601C4—442no—
602C4—441no—
603C4—881no—
604C4—881no—
605C4#1062305411yescharacteristic
606C4C4×Q8×D1111yescharacteristic
607C4#1062322111yescharacteristic
608C4#1062323911yescharacteristic
609C2—444no—
610C2#1307162411yescharacteristic
611C2C4×SD16×D1111yescharacteristic
612C2#1307744711yescharacteristic
613C2#1308043811yescharacteristic
614C2#1308054211yescharacteristic
615C2#1308147511yescharacteristic
616C2#1308147811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1919C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1919D11
hypocenterC11#22963
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
2. #13071703C2semidirect
4. #13069575C2semidirect
5. #13069378C2semidirect
6. #13069345C2semidirect
7. #13069341C2semidirect
8. #13069197C2semidirect
11. #13068477C2semidirect
15. C11×#1919C2semidirect
45. #10622483C4semidirect
100. #66941C2×C4semidirect
103. C11×#106C2×C4semidirect
116. Dic11⋊C8C2×C4semidirect
120. #66873Q8semidirect
122. #66872C2×C4semidirect
213. #1919D11semidirect
406. #106C4×D11semidirect
512. C11#22963semidirect

Maximal subgroups

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

subgroupindex
C2×#106224832
#130717032
#130715172
#130695752
#130693782
#130693452
#130693412
#130691972
#130688802
#130688782
#130684772
C4×#668732
#130684302
C11×#19192
#2296311