Finite Group Databasebeta

← #14760964

Subgroups — #14760964

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622475C211yesmaximal, characteristic
2#13071146C211yesmaximal, characteristic
3C4×C4⋊C4×D11C211yesmaximal, characteristic
4#13069258C211yesmaximal, characteristic, complemented
5#13069257C211yesmaximal, characteristic, complemented
6#13069191C211yesmaximal, characteristic, complemented
7#13068922C211yesmaximal, characteristic
8#13068805C211yesmaximal, characteristic
9#13068701C211yesmaximal, characteristic
10#13068516C211yesmaximal, characteristic, complemented
11#13068512C211yesmaximal, characteristic, complemented
12#13068445C211yesmaximal, characteristic, complemented
13#13068445C211yesmaximal, characteristic, complemented
14#13068377C211yesmaximal, characteristic
15C11×#1919C211yesmaximal, characteristic, complemented
16C2×#66950C2211yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×C42×D11—21no—
21C2×C42×D11C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622602—21no—
33#10622600C2211yescharacteristic
34C4⋊C4×Dic11—21no—
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×Dic11⋊C4—21no—
44#10622542C2211yescharacteristic
45#10622475C418yescomplemented
46#10622279—21no—
47D11×#95—21no—
48#10622267—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66950—22no—
95#66950C2×C414yes—
96C4⋊C4×D11—22no—
97C4⋊C4×D11—22no—
98C4⋊C4×D11—22no—
99C4⋊C4×D11C2×C414yes—
100#66940—22no—
101#66940—22no—
102C42×D11—22no—
103C42×D11—22no—
104C42×D11—44no—
105C11×#106C2×C414yescomplemented
106C11×#95—21no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8C2×C414yes—
117#66882—22no—
118#66880—22no—
119#66880C2×C414yescomplemented
120#66879—22no—
121#66879—22no—
122#66874—22no—
123#66874C2×C414yescomplemented
124#66872C2×C414yescomplemented
125#66871—22no—
126#21579—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×C4×D11—22no—
143C2×C4×D11—24no—
144C2×C4×D11—22no—
145C2×C4×D11—24no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—41no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11C22×C412yes—
159C2×C4×D11#4112yes—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C22×C412yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4C22×C412yes—
180C11×C4⋊C4#4112yes—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—42no—
186C4⋊Dic11—24no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C412yes—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—42no—
196C4×Dic11—22no—
197C4×Dic11—22no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11#4112yes—
204C4×Dic11#4112yes—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C22×C412yes—
211C2×#483—111no—
212C4×C22⋊Q8—111no—
213C2×C4×C4⋊C4—111no—
214#1928—111no—
215#1928—111no—
216#1919—111no—
217#1919D1111yescharacteristic, complemented
218#1872—111no—
219#1852—111no—
220#1823—111no—
221#1776—111no—
222#1776—111no—
223#1763—111no—
224#1763—111no—
225#1749—111no—
226C23×C11C22×D411yescharacteristic
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11C4×D412yes—
232C22×D11AGL(1,ℤ/8)12yes—
233C22×D11#13712yes—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
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×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11#13712yes—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11C4×D412yes—
277C2×Dic11#12312yes—
278C2×Dic11#12312yes—
279C4×D11—28no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—44no—
285C4×D11—48no—
286C4×D11—48no—
287Dic22—22no—
288Dic22—22no—
289Dic22—41no—
290Dic22—41no—
291C8×C11—22no—
292C8×C11—41no—
293C11⋊C8—22no—
294C11⋊C8—41no—
295C2×C22⋊Q8—111no—
296C2×C4×Q8—111no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C42—111no—
300C22×C42—221no—
301#483—118no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#106—111no—
305C2×#106C2×D1111yescharacteristic
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
312C2×#97—111no—
313C2×#97—111no—
314#391—111no—
315#389C2×D1111yescharacteristic
316#387—221no—
317#385—221no—
318#380—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—221no—
324C4×C4⋊C4—221no—
325C4×C4⋊C4—221no—
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C22⋊C4—221no—
328C2×#95—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
337#336—111no—
338#336C2×D1111yescharacteristic
339C22×C11C2×C4×D411yescharacteristic
340C22×C11C2×#12311yescharacteristic
341C22×C11#52511yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11C2×#13711yescharacteristic
344C22×C11C2×#13711yescharacteristic
345C22×C11#57511yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11#44014yes—
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—81no—
359C4×C11C4×#4111yescharacteristic
360C4×C11C4×#4111yescharacteristic
361C4×C11#52911yescharacteristic
362C4×C11#52911yescharacteristic
363Dic11—22no—
364Dic11—22no—
365Dic11—22no—
366Dic11—42no—
367Dic11—42no—
368Dic11—42no—
369Dic11—81no—
370C22×Q8—111no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—221no—
375C23×C4—221no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22⋊Q8—114no—
381C22⋊Q8—222no—
382C4×Q8—222no—
383C4×Q8—222no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—222no—
407C2×C42—222no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—444no—
414C2×C42C22×D1111yescharacteristic
415#107—222no—
416#107—222no—
417#106—114no—
418#106C4×D1114yescomplemented
419#103—114no—
420#103—114no—
421#103—222no—
422#103—222no—
423C22⋊C8—114no—
424C22⋊C8—222no—
425#97—222no—
426#97—222no—
427#95—21no—
428#95—21no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11C4×#12311yescharacteristic
437C2×C11C2×#44011yescharacteristic
438C2×C11C4×#13711yescharacteristic
439C2×C11#309211yescharacteristic
440C2×C11#309511yescharacteristic
441C2×C11#311311yescharacteristic
442C2×C11#311411yescharacteristic
443D11—24no—
444C24—111no—
445C2×Q8—112no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—222no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—441no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—112no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8C2×C4×D1112yes—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—112no—
502C4⋊C4—112no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—224no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4C2×C4×D1112yes—
512C4⋊C4C2×C4×D1112yes—
513C4⋊C4#434312yes—
514C22⋊C4—224no—
515C22⋊C4—442no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—112no—
520C42—112no—
521C42—222no—
522C42—222no—
523C42—442no—
524C42—442no—
525C42—442no—
526C42—442no—
527C42—442no—
528C11#2157911yescharacteristic, complemented, Sylow
529C23—112no—
530C23—112no—
531C23—112no—
532C23—221no—
533C23—221no—
534C23—221no—
535C23—221no—
536C23C2×D4×D1111yescharacteristic
537Q8—222no—
538Q8—222no—
539Q8—441no—
540Q8—441no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—112no—
559C2×C4—112no—
560C2×C4—112no—
561C2×C4—228no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—444no—
576C2×C4—448no—
577C2×C4—448no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4#6696812yes—
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C2×#434311yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C8—22no—
595C8—41no—
596C8—222no—
597C8—441no—
598C22—114no—
599C22—222no—
600C22—222no—
601C22—222no—
602C22—222no—
603C22—222no—
604C22—222no—
605C22C4×D4×D1111yescharacteristic
606C22#1062315811yescharacteristic
607C22D11×#12311yescharacteristic
608C22C2×#6696811yescharacteristic
609C22#1062329911yescharacteristic
610C22D11×AGL(1,ℤ/8)11yescharacteristic
611C22D11×#13711yescharacteristic
612C4—22no—
613C4—41no—
614C4—42no—
615C4—42no—
616C4—42no—
617C4—81no—
618C4—222no—
619C4—222no—
620C4—222no—
621C4—442no—
622C4—442no—
623C4—442no—
624C4—881no—
625C4#1062305311yescharacteristic
626C4C4×#434311yescharacteristic
627C4#1062322211yescharacteristic
628C4#1062323711yescharacteristic
629C2—224no—
630C2#1307113711yescharacteristic
631C2D11×#44011yescharacteristic
632C2C4×#6696811yescharacteristic
633C2#1307853811yescharacteristic
634C2#1307856311yescharacteristic
635C2#1307874811yescharacteristic
636C2#1307875911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1919C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1919D11
hypocenterC11#21579
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
4. #13069258C2semidirect
5. #13069257C2semidirect
6. #13069191C2semidirect
10. #13068516C2semidirect
11. #13068512C2semidirect
12. #13068445C2semidirect
13. #13068445C2semidirect
15. C11×#1919C2semidirect
45. #10622475C4semidirect
105. C11×#106C2×C4semidirect
119. #66880C2×C4semidirect
123. #66874C2×C4semidirect
124. #66872C2×C4semidirect
217. #1919D11semidirect
418. #106C4×D11semidirect
528. C11#21579semidirect

Maximal subgroups

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

subgroupindex
C2×#106224752
#130711462
C4×C4⋊C4×D112
#130692582
#130692572
#130691912
#130689222
#130688052
#130687012
#130685162
#130685122
#130684452
#130683772
C11×#19192
#2157911