Finite Group Databasebeta

← #14775351

Subgroups — #14775351

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622392C211yesmaximal, characteristic
2#13071628C211yesmaximal, characteristic
3#13071497C211yesmaximal, characteristic, complemented
4#13069359C211yesmaximal, characteristic, complemented
5#13069296C211yesmaximal, characteristic, complemented
6#13069238C211yesmaximal, characteristic, complemented
7#13069208C211yesmaximal, characteristic, complemented
8#13069200C211yesmaximal, characteristic, complemented
9#13069051C211yesmaximal, characteristic
10#13068863C211yesmaximal, characteristic, complemented
11#13068805C211yesmaximal, characteristic, complemented
12#13068508C211yesmaximal, characteristic, complemented
13#13068401C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C22×#4313C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622823—21no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622600C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622569—21no—
41#10622558—21no—
42#10622553—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44#10622545—21no—
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622392C418yescomplemented
48#10622282—21no—
49#10622263—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C22⋊D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66991—22no—
79#66991C2×C414yes—
80C4×C22⋊D11—44no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—22no—
100C2×#4313—22no—
101C2×#4313—41no—
102#66945—22no—
103#66945C2×C414yescomplemented
104C4⋊C4×D11—22no—
105C4⋊C4×D11—41no—
106C11×#102—22no—
107C11×#102C2×C414yescomplemented
108C11×#97—41no—
109C11×#95—21no—
110#66896—41no—
111#66896C2×C414yescomplemented
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120(C2×D11)⋊C8C2×C414yescomplemented
121#66882—41no—
122#66881C2×C414yescomplemented
123C8×Dic11—22no—
124#66871—22no—
125#66871C2×C414yescomplemented
126#22946—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D411yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11C22×C412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C4×D11C22×C412yes—
162C2×C4×D11#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C412yes—
168C2×C8×C11#4112yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C412yes—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—42no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—42no—
179C22⋊Dic11—24no—
180C22⋊Dic11—42no—
181C22⋊Dic11—81no—
182(C2×D11)⋊C4—22no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—81no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C412yes—
193C4⋊Dic11C22×C412yes—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—81no—
197Dic11⋊C4—81no—
198C4×Dic11—24no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C22×C412yes—
209#4313—44no—
210C2×#482—111no—
211#2361—111no—
212#2346—111no—
213#1944—111no—
214#1934—111no—
215#1925—111no—
216#1921—111no—
217#1920—111no—
218#1895—111no—
219#1862—111no—
220#1852—111no—
221C4×#107—111no—
222#1762D1111yescharacteristic, complemented
223#1753—111no—
224#1736—111no—
225C23×C11—22no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11C22×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11C4×D412yes—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—84no—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C22⋊D11—48no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11C4×D412yes—
287C2×Dic11AGL(1,ℤ/8)12yes—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—84no—
293C8×C11—22no—
294C8×C11—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×M16—111no—
298C2×#121—111no—
299C2×C4×D4—221no—
300C2×C4×D4C2×D1111yescharacteristic
301C2×#117—111no—
302C22×C4⋊C4—111no—
303#482—118no—
304C2×#107—111no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#106—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102C2×D1111yescharacteristic
311C2×#102C2×D1111yescharacteristic
312C2×C22⋊C8—111no—
313C2×#97C2×D1111yescharacteristic
314C2×C4×C8—111no—
315#390—111no—
316#389—111no—
317#389—111no—
318#389—111no—
319#388—221no—
320#388—221no—
321#388—221no—
322#386—221no—
323#385—221no—
324#382—221no—
325#380—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4C2×D1111yescharacteristic
329C4×C22⋊C4—111no—
330#376—221no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#340C2×D1111yescharacteristic
339#336—111no—
340#336—111no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11C2×C4×D411yescharacteristic
349C22×C11#54611yescharacteristic
350C22×C11#54711yescharacteristic
351C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C11#57511yescharacteristic
353C22×C11#57611yescharacteristic
354C22×C11#57811yescharacteristic
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11C4×#4111yescharacteristic
368C4×C11#52011yescharacteristic
369C4×C11#55111yescharacteristic
370C4×C11#55211yescharacteristic
371Dic11—22no—
372Dic11—22no—
373Dic11—41no—
374Dic11—42no—
375Dic11—42no—
376Dic11—81no—
377Dic11—81no—
378C22×D4—221no—
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381C23×C4—111no—
382C23×C4—221no—
383C2×M16—222no—
384C2×M16—222no—
385C2×M16—441no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390#121—114no—
391#121—222no—
392C4×D4—22no—
393C4×D4—41no—
394C4×D4—444no—
395#117—114no—
396#117—222no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—441no—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42C22×D1111yescharacteristic
424#107—114no—
425#107—222no—
426#107—441no—
427#106—114no—
428#102—22no—
429#102—114no—
430#102—441no—
431#102C4×D1114yescomplemented
432C22⋊C8—114no—
433#97—41no—
434C4×C8—222no—
435#95—21no—
436#95—111no—
437#95—111no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11—82no—
445C2×C11#235911yescharacteristic
446C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C11#295111yescharacteristic
448C2×C11#332511yescharacteristic
449C2×C11#332711yescharacteristic
450C2×C11#334311yescharacteristic
451C2×C11#334711yescharacteristic
452D11—42no—
453C24—21no—
454C24—111no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—224no—
461C2×D4—442no—
462C2×D4—442no—
463C2×D4C2×C4×D1112yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—81no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—111no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—881no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—444no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—112no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8C2×C4×D1112yes—
501C2×C8#433912yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—112no—
507C4⋊C4—112no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—881no—
517C4⋊C4—881no—
518C4⋊C4C2×C4×D1112yes—
519C4⋊C4#433912yes—
520C22⋊C4—42no—
521C22⋊C4—222no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C22⋊C4—441no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—224no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—442no—
536C11#2294611yescharacteristic, complemented, Sylow
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—112no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23C2×D4×D1111yescharacteristic
552D4—22no—
553D4—22no—
554D4—41no—
555D4—41no—
556D4—448no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—112no—
574C2×C4—112no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—884no—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×#433911yescharacteristic
601C2×C4C2×#433911yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#6704311yescharacteristic
605C8—22no—
606C8—22no—
607C8—222no—
608C8—441no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—222no—
617C22—222no—
618C22—222no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22#1062302111yescharacteristic
624C22C4×D4×D1111yescharacteristic
625C22#1062308211yescharacteristic
626C22D11×AGL(1,ℤ/8)11yescharacteristic
627C22#1062330411yescharacteristic
628C22#1062330511yescharacteristic
629C22#1062331011yescharacteristic
630C4—41no—
631C4—42no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—222no—
636C4—222no—
637C4—441no—
638C4—442no—
639C4—442no—
640C4—881no—
641C4—881no—
642C4C4×#433911yescharacteristic
643C4#1062306011yescharacteristic
644C4#1062307711yescharacteristic
645C4#1062308711yescharacteristic
646C2—82no—
647C2—442no—
648C2#1307160911yescharacteristic
649C2#1307742711yescharacteristic
650C2#1307748811yescharacteristic
651C2#1308085411yescharacteristic
652C2#1308088511yescharacteristic
653C2#1308106111yescharacteristic
654C2#1308112111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#22946
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. #13071497C2semidirect
4. #13069359C2semidirect
5. #13069296C2semidirect
6. #13069238C2semidirect
7. #13069208C2semidirect
8. #13069200C2semidirect
10. #13068863C2semidirect
11. #13068805C2semidirect
12. #13068508C2semidirect
13. #13068401C2semidirect
14. #13068334C2semidirect
15. C11×#1762C2semidirect
47. #10622392C4semidirect
103. #66945C2×C4semidirect
107. C11×#102C2×C4semidirect
111. #66896C2×C4semidirect
120. (C2×D11)⋊C8C2×C4semidirect
122. #66881C2×C4semidirect
125. #66871C2×C4semidirect
222. #1762D11semidirect
431. #102C4×D11semidirect
536. C11#22946semidirect

Maximal subgroups

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

subgroupindex
C2×#106223922
#130716282
#130714972
#130693592
#130692962
#130692382
#130692082
#130692002
#130690512
#130688632
#130688052
#130685082
#130684012
#130683342
C11×#17622
#2294611