Finite Group Databasebeta

← #14795129

Subgroups — #14795129

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622622C211yesmaximal, characteristic, complemented
2C2×#10622453C211yesmaximal, characteristic, complemented
3#13074449C211yesmaximal, characteristic, complemented
4#13071303C211yesmaximal, characteristic
5#13070054C211yesmaximal, characteristic, complemented
6#13070048C211yesmaximal, characteristic, complemented
7#13069796C211yesmaximal, characteristic
8#13069796C211yesmaximal, characteristic
9#13069571C211yesmaximal, characteristic, complemented
10#13069372C211yesmaximal, characteristic, complemented
11#13069353C211yesmaximal, characteristic, complemented
12#13069348C211yesmaximal, characteristic, complemented
13#13069315C211yesmaximal, characteristic, complemented
14#13069301C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#384C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622826—21no—
28#10622823—21no—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622622—24no—
34#10622607—21no—
35#10622607—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622596—21no—
42#10622596—21no—
43#10622586C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622570—21no—
49#10622558—21no—
50C4×C4⋊Dic11C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52#10622453—24no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×C22⋊D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66991—22no—
80#66991—22no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4D411yescharacteristic
96C2×Dic11⋊C4D411yescharacteristic
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66925—22no—
102#66925—22no—
103#66923—22no—
104#66923—22no—
105C11×C4⋊C8—22no—
106C11×#102—22no—
107C11×#102—22no—
108#66896—22no—
109#66896—22no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117(C2×D11)⋊C8—22no—
118(C2×D11)⋊C8—22no—
119#66879—22no—
120C8×Dic11—22no—
121#66872—22no—
122#66871—22no—
123#66871—22no—
124#66871—22no—
125C4⋊(C11⋊C8)D414yescomplemented
126#24713—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×C11#4112yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—81no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—81no—
146C2×C22⋊D11—81no—
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—21no—
159C2×C4×D11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C22⋊C4—42no—
175C42×C11C2×D412yes—
176C42×C11#4112yes—
177C22⋊Dic11—24no—
178C22⋊Dic11—81no—
179C22⋊Dic11—81no—
180(C2×D11)⋊C4—22no—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—81no—
183(C2×D11)⋊C4—81no—
184(C2×D11)⋊C4—81no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—81no—
193C4⋊Dic11—81no—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—22no—
196Dic11⋊C4—22no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C2×D412yes—
208C2×C11⋊C8C2×D412yes—
209C2×#478—111no—
210C2×#433—111no—
211#2629—111no—
212#2324—111no—
213#2077—111no—
214#2076—111no—
215#2033—111no—
216#2033—111no—
217#1989—111no—
218#1947—111no—
219#1943—111no—
220#1942—111no—
221#1936—111no—
222#1934—111no—
223#1802D1111yescharacteristic, complemented
224C23×C11—22no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C22×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—41no—
242D4×C11—41no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—84no—
257C2×C4×C11#12112yes—
258C2×C4×C11#12112yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C22⋊D11—84no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
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×Dic11—41no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—22no—
294C11⋊C8—22no—
295C2×#125—111no—
296C2×#121—111no—
297C2×C4×D4C2×D1111yescharacteristic
298C2×#117—111no—
299#478—224no—
300#433—224no—
301C2×#107—111no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#106—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8C2×D1111yescharacteristic
307C2×#102—111no—
308C2×#102—111no—
309C2×#102C2×D1111yescharacteristic
310C2×#102C2×D1111yescharacteristic
311C2×C22⋊C8—111no—
312C2×C22⋊C8—111no—
313C2×#97—111no—
314C2×C4×C8—111no—
315#398—221no—
316#398—221no—
317#396—221no—
318#396—221no—
319#390—111no—
320#390—221no—
321#389—111no—
322#389—111no—
323#389—111no—
324#388—221no—
325#386—221no—
326#385—221no—
327#384C2×D1111yescharacteristic
328#380—111no—
329#380—111no—
330#380—111no—
331C4×C4⋊C4—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340C2×D1111yescharacteristic
339#340C2×D1111yescharacteristic
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11C2×#12111yescharacteristic
348C22×C11#52511yescharacteristic
349C22×C11#53611yescharacteristic
350C22×C11#57611yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57811yescharacteristic
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11#54711yescharacteristic
367C4×C11#54811yescharacteristic
368C4×C11#55211yescharacteristic
369C4×C11#55611yescharacteristic
370Dic11—42no—
371Dic11—41no—
372Dic11—41no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377C22×D4—221no—
378C22×D4C22×D1111yescharacteristic
379C23×C4—21no—
380C23×C4—111no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385#125—222no—
386#125—222no—
387#121—222no—
388#121—222no—
389C4×D4—22no—
390C4×D4—22no—
391#117—222no—
392#117—222no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—111no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#107—222no—
423#107—222no—
424#106—222no—
425C4⋊C8—22no—
426C4⋊C8—114no—
427#102—22no—
428#102—22no—
429#102—222no—
430#102—222no—
431C22⋊C8—222no—
432C22⋊C8—222no—
433#97—222no—
434C4×C8—222no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11—82no—
443C2×C11#241511yescharacteristic
444C2×C11#306111yescharacteristic
445C2×C11#306211yescharacteristic
446C2×C11#312011yescharacteristic
447C2×C11#312211yescharacteristic
448C2×C11#324111yescharacteristic
449C2×C11#324311yescharacteristic
450D11—81no—
451C24—21no—
452C24—111no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—224no—
459C2×D4—881no—
460C2×D4—881no—
461C2×D4#434112yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—81no—
467C22×C4—81no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4D4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—112no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—81no—
503C4⋊C4—81no—
504C4⋊C4—112no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—221no—
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⋊C4—881no—
519C22⋊C4—42no—
520C22⋊C4—224no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C42—221no—
529C42—221no—
530C42—881no—
531C42#433912yes—
532C42D4×D1112yes—
533C11#2471311yescharacteristic, complemented, Sylow
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—221no—
542C23—221no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23C2×D4×D1111yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—884no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—221no—
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—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4#6693712yes—
594C2×C4#6693712yes—
595C2×C4C2×#433911yescharacteristic
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4#6704011yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#6704311yescharacteristic
601C8—41no—
602C8—41no—
603C8—222no—
604C8—222no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—441no—
613C22—441no—
614C22—441no—
615C22—441no—
616C22—441no—
617C22—441no—
618C22—441no—
619C22C2×#6693711yescharacteristic
620C22#1062313711yescharacteristic
621C22#1062315911yescharacteristic
622C22#1062328811yescharacteristic
623C22#1062329311yescharacteristic
624C22#1062330511yescharacteristic
625C22#1062331011yescharacteristic
626C4—22no—
627C4—22no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—441no—
632C4—441no—
633C4—442no—
634C4—441no—
635C4—881no—
636C4—881no—
637C4—881no—
638C4#1062304411yescharacteristic
639C4#1062306411yescharacteristic
640C4#1062312911yescharacteristic
641C4#1062316211yescharacteristic
642C2—82no—
643C2—881no—
644C2#1307204711yescharacteristic
645C2#1307828511yescharacteristic
646C2#1307829411yescharacteristic
647C2#1307882711yescharacteristic
648C2#1307885711yescharacteristic
649C2#1307986811yescharacteristic
650C2#1307989611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#1802D11
hypocenterC11#24713
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#10622622C2semidirect
2. C2×#10622453C2semidirect
3. #13074449C2semidirect
5. #13070054C2semidirect
6. #13070048C2semidirect
9. #13069571C2semidirect
10. #13069372C2semidirect
11. #13069353C2semidirect
12. #13069348C2semidirect
13. #13069315C2semidirect
14. #13069301C2semidirect
15. C11×#1802C2semidirect
125. C4⋊(C11⋊C8)D4semidirect
223. #1802D11semidirect
533. C11#24713semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
C2×#106224532
#130744492
#130713032
#130700542
#130700482
#130697962
#130695712
#130693722
#130693532
#130693482
#130693152
#130693012
C11×#18022
#2471311