Finite Group Databasebeta

← #14756906

Subgroups — #14756906

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic11C211yesmaximal, characteristic
2#13071253C211yesmaximal, characteristic, complemented
3#13070977C211yesmaximal, characteristic, complemented
4#13069239C211yesmaximal, characteristic, complemented
5#13069233C211yesmaximal, characteristic, complemented
6#13069209C211yesmaximal, characteristic, complemented
7#13069207C211yesmaximal, characteristic, complemented
8#13068966C211yesmaximal, characteristic
9#13068863C211yesmaximal, characteristic, complemented
10#13068861C211yesmaximal, characteristic, complemented
11#13068508C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#390C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C4×C22⋊Dic11—21no—
30C2×C11⋊#95—21no—
31D8×Dic11C418yescomplemented
32C2×#66882C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622558—21no—
42#10622557—21no—
43#10622556—21no—
44#10622555—21no—
45C22⋊C4×Dic11—21no—
46C22⋊C4×Dic11—21no—
47C4×C4⋊Dic11C2211yescharacteristic
48#10622545C2211yescharacteristic
49#10622541C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C2×C11×D8—22no—
67C2×C11×D8—22no—
68C2×C11×D8C2×C414yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84D4×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11—22no—
88D4×Dic11C2×C414yes—
89D4×Dic11C2×C414yescomplemented
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C11×#102—22no—
105C11×#102—22no—
106#66896—22no—
107#66896—22no—
108#66896C2×C414yes—
109#66896C2×C414yescomplemented
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120#66882C2×C414yescomplemented
121#66879—22no—
122C8×Dic11C2×C414yescomplemented
123#66871—22no—
124#66871—22no—
125#21129—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11C22×C412yes—
137C2×D4×C11C22×C412yes—
138C2×D4×C11#4112yes—
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—81no—
144C22×C4×C11—81no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—81no—
156C22×Dic11—81no—
157C22×Dic11—81no—
158C22×Dic11—81no—
159C22×Dic11—81no—
160C22×Dic11—81no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C11×D8—28no—
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#4112yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—81no—
178C11×C22⋊C4—81no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—24no—
182C22⋊Dic11—24no—
183C22⋊Dic11—24no—
184C22⋊Dic11—81no—
185C22⋊Dic11—81no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C412yes—
192C4⋊Dic11C22×C412yes—
193C4⋊Dic11#4112yes—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—81no—
199C4×Dic11—81no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C4×Dic11C22×C412yes—
203C4×Dic11#4112yes—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C412yes—
210C2×C4×D8—111no—
211#2319—111no—
212#2275—111no—
213#1925—111no—
214#1925—111no—
215#1921—111no—
216#1921—111no—
217#1879—111no—
218#1879D1111yescharacteristic
219#1862—111no—
220#1862—111no—
221C4×#107—111no—
222#1762—111no—
223#1762—111no—
224#1746—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11#11714yes—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
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—22no—
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—84no—
290C2×Dic11—84no—
291C2×Dic11—84no—
292C2×Dic11C4×D412yes—
293C2×Dic11C4×D412yes—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×D8C2×D1111yescharacteristic
299C2×C4×D4—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4C2×D1111yescharacteristic
303C4×D8—118no—
304C2×#107—111no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102C2×D1111yescharacteristic
312C2×#102C2×D1111yescharacteristic
313C2×#97—111no—
314C2×C4×C8—111no—
315#390—111no—
316#390C2×D1111yescharacteristic
317#389—111no—
318#389—111no—
319#388—221no—
320#388—221no—
321#381—221no—
322#380—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C22⋊C4—221no—
328C4×C22⋊C4—221no—
329C4×C22⋊C4—221no—
330#376—111no—
331C2×#95—221no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342C22×C11—24no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11C2×C4×D411yescharacteristic
357C22×C11#52511yescharacteristic
358C22×C11#52511yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57611yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57811yescharacteristic
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11C2×#11711yescharacteristic
368C4×C11C4×#4111yescharacteristic
369C4×C11#52911yescharacteristic
370C4×C11#52911yescharacteristic
371Dic11—22no—
372Dic11—22no—
373Dic11—41no—
374Dic11—42no—
375Dic11—41no—
376Dic11—42no—
377Dic11—42no—
378Dic11—81no—
379C22×D4C22×D1111yescharacteristic
380C22×D4C22×D1111yescharacteristic
381C23×C4—21no—
382C23×C4—221no—
383C23×C4—221no—
384C23×C4—221no—
385C2×D8—22no—
386C2×D8—22no—
387C2×D8C4×D1114yes—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—114no—
395C4×D4—114no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423#107—114no—
424#107—222no—
425#107—222no—
426#102—22no—
427#102—22no—
428#102—114no—
429#102—114no—
430#102—222no—
431#102—222no—
432#97—222no—
433C4×C8—114no—
434#95—111no—
435#95—111no—
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—44no—
445C2×C11—82no—
446C2×C11#229011yescharacteristic
447C2×C11#294811yescharacteristic
448C2×C11#295111yescharacteristic
449C2×C11#312211yescharacteristic
450C2×C11#312211yescharacteristic
451C2×C11#312411yescharacteristic
452C2×C11#312411yescharacteristic
453C24—21no—
454C24—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4C2×C4×D1112yes—
464C2×D4C2×C4×D1112yes—
465C2×D4#434112yes—
466C2×D4#434112yes—
467C22×C4—21no—
468C22×C4—24no—
469C22×C4—21no—
470C22×C4—81no—
471C22×C4—81no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—224no—
482C22×C4—221no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4—881no—
487C22×C4—881no—
488C22×C4—881no—
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492D8—28no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—112no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8C2×C4×D1112yes—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—112no—
509C4⋊C4—112no—
510C4⋊C4—112no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—881no—
517C4⋊C4—881no—
518C4⋊C4#434112yes—
519C22⋊C4—24no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C22⋊C4—224no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C42—21no—
528C42—21no—
529C42—112no—
530C42—112no—
531C42—221no—
532C42—221no—
533C42—881no—
534C42—881no—
535C42—881no—
536C42—881no—
537C11#2112911yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×D4×D1111yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4#6693014yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4—112no—
575C2×C4—112no—
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—222no—
585C2×C4—222no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—222no—
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×C4—884no—
600C2×C4—884no—
601C2×C4C22×C4×D1111yescharacteristic
602C2×C4C2×#434111yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4C2×#434111yescharacteristic
605C2×C4#41×D1111yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C8—22no—
608C8—41no—
609C8—222no—
610C8—441no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C4×D4×D1111yescharacteristic
626C22#1062311711yescharacteristic
627C22#1062313711yescharacteristic
628C22#1062328811yescharacteristic
629C22#1062330211yescharacteristic
630C22#1062330511yescharacteristic
631C22#1062330511yescharacteristic
632C4—41no—
633C4—42no—
634C4—41no—
635C4—81no—
636C4—222no—
637C4—222no—
638C4—441no—
639C4—442no—
640C4—441no—
641C4—442no—
642C4—442no—
643C4—881no—
644C4C2×#6693011yescharacteristic
645C4C4×#434111yescharacteristic
646C4#1062313111yescharacteristic
647C4#1062318011yescharacteristic
648C2—44no—
649C2—82no—
650C2#1307105611yescharacteristic
651C2#1307746511yescharacteristic
652C2#1307748611yescharacteristic
653C2#1307885311yescharacteristic
654C2#1307885711yescharacteristic
655C2#1307887111yescharacteristic
656C2#1307887511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
cosocleC22×C4×C11C24
hypercenter#1879D11
hypocenterC11#21129
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #13071253C2semidirect
3. #13070977C2semidirect
4. #13069239C2semidirect
5. #13069233C2semidirect
6. #13069209C2semidirect
7. #13069207C2semidirect
9. #13068863C2semidirect
10. #13068861C2semidirect
11. #13068508C2semidirect
12. #13068443C2semidirect
13. #13068443C2semidirect
14. #13068366C2semidirect
31. D8×Dic11C4semidirect
89. D4×Dic11C2×C4semidirect
109. #66896C2×C4semidirect
120. #66882C2×C4semidirect
122. C8×Dic11C2×C4semidirect
537. C11#21129semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic112
#130712532
#130709772
#130692392
#130692332
#130692092
#130692072
#130689662
#130688632
#130688612
#130685082
#130684432
#130683662
C11×#18792
#2112911