Finite Group Databasebeta

← #14765601

Subgroups — #14765601

Order 2816.

836 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
1#13071311C211yesmaximal, characteristic
2#13071234C211yesmaximal, characteristic, complemented
3#13069355C211yesmaximal, characteristic, complemented
4#13069350C211yesmaximal, characteristic, complemented
5#13069315C211yesmaximal, characteristic, complemented
6#13069301C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069189C211yesmaximal, characteristic, complemented
9#13068939C211yesmaximal, characteristic
10#13068879C211yesmaximal, characteristic, complemented
11#13068865C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068706C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C2×C11×#480C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C11×#480C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622834—21no—
28#10622834C2211yescharacteristic
29#10622833—21no—
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622825—21no—
33#10622825—21no—
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622598—21no—
41#10622598—21no—
42#10622598C2211yescharacteristic
43#10622598C2211yescharacteristic
44#10622598C2211yescharacteristic
45#10622598C2211yescharacteristic
46#10622598C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48#10622564—21no—
49#10622563—21no—
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—22no—
68C11×#121C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2×C414yescomplemented
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83D4×Dic11—41no—
84D4×Dic11—41no—
85#66979—41no—
86#66979—41no—
87#66979—41no—
88#66979—41no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#107C2×C414yescomplemented
107C11×#107C2×C414yescomplemented
108C11×#102C2×C414yes—
109C11×#102C2×C414yes—
110C11×C22⋊C8C2×C414yescomplemented
111#66896—41no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C22⋊(C11⋊C8)—22no—
121#66882—41no—
122#66881—41no—
123#66879—41no—
124C8×Dic11—41no—
125#22093—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D411yescharacteristic
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—81no—
135C2×D4×C11—81no—
136C2×D4×C11C22×C412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—81no—
146C22×C4×C11—81no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—42no—
156C22×Dic11—81no—
157C22×Dic11—81no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C22×C412yes—
167C2×C8×C11C22×C412yes—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C412yes—
173C11×C4⋊C4C22×C412yes—
174C11×C4⋊C4C22×C412yes—
175C11×C22⋊C4—24no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—42no—
179C22⋊Dic11—42no—
180C22⋊Dic11—81no—
181C22⋊Dic11—81no—
182C22⋊Dic11—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—41no—
192C4⋊Dic11—41no—
193C4⋊Dic11—81no—
194C4⋊Dic11—81no—
195C4⋊Dic11—81no—
196C4⋊Dic11—81no—
197C4⋊Dic11—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×#480D1111yescharacteristic
211#2324—111no—
212#2316—111no—
213#1943—111no—
214#1942—111no—
215#1936—111no—
216#1934—111no—
217#1921—111no—
218#1918—111no—
219#1875—111no—
220#1864—111no—
221#1862—111no—
222#1854—111no—
223#1824—111no—
224#1750—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C4×D412yes—
239C23×C11C22×D411yescharacteristic
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—84no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—84no—
261C2×C4×C11C4×D412yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—84no—
293C8×C11—22no—
294C8×C11—22no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C2×#121C2×D1111yescharacteristic
298C2×C4×D4—111no—
299C2×#117—111no—
300C2×#117—111no—
301C22×C4⋊C4C2×D1111yescharacteristic
302#480Dic1118yescomplemented
303C2×#107—111no—
304C2×#107C2×D1111yescharacteristic
305C2×#107C2×D1111yescharacteristic
306C2×#106—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102C2×D1111yescharacteristic
310C2×#102C2×D1111yescharacteristic
311C2×C22⋊C8—111no—
312C2×C22⋊C8C2×D1111yescharacteristic
313C2×#97—111no—
314C2×C4×C8—111no—
315#390—111no—
316#390—221no—
317#389—111no—
318#389—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#389—221no—
323#389—221no—
324#388—221no—
325#386—221no—
326#385—221no—
327#380—111no—
328#380—221no—
329#380—221no—
330C4×C4⋊C4—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#336—111no—
340#336—111no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#53411yescharacteristic
357C22×C11#53611yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C4×C11—22no—
363C4×C11—42no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11#52011yescharacteristic
367C4×C11#52011yescharacteristic
368C4×C11#53911yescharacteristic
369C4×C11#53911yescharacteristic
370Dic11—41no—
371Dic11—41no—
372Dic11—41no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×D4—21no—
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C22×C8—111no—
384C22×C8—111no—
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387#121—22no—
388#121C2×Dic1114yes—
389C4×D4—441no—
390C4×D4—441no—
391#117—441no—
392#117—441no—
393#117—441no—
394#117—441no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C2×Dic1114yescomplemented
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—111no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—221no—
423C2×C42—221no—
424#107—441no—
425#107C2×Dic1114yescomplemented
426#107C2×Dic1114yescomplemented
427#106—441no—
428#102—441no—
429#102—441no—
430#102C2×Dic1114yes—
431#102C2×Dic1114yes—
432C22⋊C8—222no—
433C22⋊C8C2×Dic1114yescomplemented
434#97—441no—
435C4×C8—441no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443C2×C11—42no—
444C2×C11—82no—
445C2×C11#232211yescharacteristic
446C2×C11#294711yescharacteristic
447C2×C11#294811yescharacteristic
448C2×C11#319811yescharacteristic
449C2×C11#320311yescharacteristic
450C2×C11#324111yescharacteristic
451C2×C11#324311yescharacteristic
452C24—21no—
453C24D4×D1111yescharacteristic
454C2×D4—24no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4C22×Dic1112yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4D4×D1111yescharacteristic
485C22×C4#434112yes—
486C22×C4C22×Dic1112yes—
487C22×C4C23×D1111yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8C22×Dic1112yes—
499C2×C8C22×Dic1112yes—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—441no—
513C4⋊C4—441no—
514C4⋊C4—881no—
515C4⋊C4—881no—
516C4⋊C4—881no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4C22×Dic1112yes—
520C4⋊C4C22×Dic1112yes—
521C4⋊C4C22×Dic1112yes—
522C22⋊C4—24no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—881no—
536C11#2209311yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23D4×Dic1112yes—
551C23C2×D4×D1111yescharacteristic
552D4—22no—
553D4—22no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
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—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—884no—
598C2×C4D4×Dic1112yes—
599C2×C4C2×#434111yescharacteristic
600C2×C4#6704211yescharacteristic
601C2×C4#6704211yescharacteristic
602C2×C4#6704311yescharacteristic
603C2×C4#6704311yescharacteristic
604C2×C4C23×Dic1111yescharacteristic
605C8—22no—
606C8—22no—
607C8—441no—
608C8—441no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22#1062317911yescharacteristic
624C22#1062318411yescharacteristic
625C22#1062328811yescharacteristic
626C22#1062328811yescharacteristic
627C22#1062330911yescharacteristic
628C22#1062331011yescharacteristic
629C22C2×D4×Dic1111yescharacteristic
630C4—22no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—441no—
635C4—441no—
636C4—441no—
637C4—441no—
638C4—881no—
639C4—881no—
640C4—881no—
641C4—881no—
642C4#1062319611yescharacteristic
643C4#1062319611yescharacteristic
644C4#1062335811yescharacteristic
645C4#1062335811yescharacteristic
646C2—42no—
647C2—82no—
648C2#1307128811yescharacteristic
649C2#1307746011yescharacteristic
650C2#1307746811yescharacteristic
651C2#1307947511yescharacteristic
652C2#1307951611yescharacteristic
653C2#1307986511yescharacteristic
654C2#1307989511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#480C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#480D11
hypocenterC11#22093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. #13071234C2semidirect
3. #13069355C2semidirect
4. #13069350C2semidirect
5. #13069315C2semidirect
6. #13069301C2semidirect
7. #13069210C2semidirect
8. #13069189C2semidirect
10. #13068879C2semidirect
11. #13068865C2semidirect
12. #13068817C2semidirect
13. #13068706C2semidirect
14. #13068384C2semidirect
21. C11×#480C4semidirect
71. C2×C11×C4⋊C4C2×C4semidirect
106. C11×#107C2×C4semidirect
107. C11×#107C2×C4semidirect
110. C11×C22⋊C8C2×C4semidirect
302. #480Dic11semidirect
408. C2×C4⋊C4C2×Dic11semidirect
425. #107C2×Dic11semidirect
426. #107C2×Dic11semidirect
433. C22⋊C8C2×Dic11semidirect
536. C11#22093semidirect

Maximal subgroups

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

subgroupindex
#130713112
#130712342
#130693552
#130693502
#130693152
#130693012
#130692102
#130691892
#130689392
#130688792
#130688652
#130688172
#130687062
#130683842
C2×C11×#4802
#2209311