Finite Group Databasebeta

← #14775741

Subgroups — #14775741

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071676C211yesmaximal, characteristic, complemented
2#13071526C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic, complemented
4#13069386C211yesmaximal, characteristic, complemented
5#13069360C211yesmaximal, characteristic, complemented
6#13069345C211yesmaximal, characteristic, complemented
7#13069203C211yesmaximal, characteristic, complemented
8#13069196C211yesmaximal, characteristic, complemented
9#13068879C211yesmaximal, characteristic
10#13068865C211yesmaximal, characteristic
11#13068493C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic
13#13068441C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C2×C11×#476C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×Q8×Dic11—21no—
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C11×#476C418yescomplemented
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27#10622843—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825—21no—
31C2×C11⋊#95—21no—
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622594—21no—
41#10622594—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622563—21no—
45#10622563—21no—
46#10622549C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2×C414yescomplemented
69C4×D4×C11—22no—
70C4×D4×C11C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79Q8×Dic11—44no—
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11—41no—
83D4×Dic11—41no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C11×#106C2×C414yescomplemented
102C11×#106C2×C414yescomplemented
103C11×C4⋊C8C2×C414yescomplemented
104C11×#102C2×C414yes—
105C11×#102C2×C414yes—
106#66896—22no—
107#66896Q814yescomplemented
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66882—41no—
120#66881—41no—
121#66879—41no—
122C8×Dic11—41no—
123#66867—22no—
124#22975—111nomaximal, Sylow
125C24×C11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11—42no—
128C2×Q8×C11—42no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11C22×C412yes—
133C2×D4×C11C2×Q812yes—
134C2×D4×C11#4112yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—81no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—81no—
153C22×Dic11—81no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C22×C412yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C412yes—
169C11×C4⋊C4C22×C412yes—
170C11×C4⋊C4C22×C412yes—
171C11×C22⋊C4—24no—
172C42×C11C22×C412yes—
173C42×C11#4112yes—
174C22⋊Dic11—42no—
175C22⋊Dic11—42no—
176C4⋊Dic11—22no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—41no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—81no—
188C4⋊Dic11—81no—
189C4⋊Dic11C2×Q812yes—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—42no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C2×Q812yes—
203C2×#476D1111yescharacteristic
204#2365—111no—
205#2349—111no—
206#1993—111no—
207#1949—111no—
208#1944—111no—
209#1941—111no—
210#1920—111no—
211#1919—111no—
212#1864—111no—
213#1862—111no—
214#1771—111no—
215#1762—111no—
216#1762—111no—
217C4×#102—111no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11C22×D411yescharacteristic
226Q8×C11—48no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11C4×Q814yescomplemented
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—84no—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C4×D412yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
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×Dic11—84no—
277C2×Dic11—84no—
278C2×Dic11AGL(1,ℤ/8)12yes—
279C8×C11—22no—
280C8×C11—22no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C2×C4⋊Q8C2×D1111yescharacteristic
284C2×C4×Q8—221no—
285C2×C4×D4—111no—
286C2×C4×D4—111no—
287C2×C4×D4C2×D1111yescharacteristic
288#476Dic1118yescomplemented
289C2×#107—111no—
290C2×#106—111no—
291C2×#106C2×D1111yescharacteristic
292C2×#106C2×D1111yescharacteristic
293C2×C4⋊C8C2×D1111yescharacteristic
294C2×#102—111no—
295C2×#102—111no—
296C2×#102C2×D1111yescharacteristic
297C2×#102C2×D1111yescharacteristic
298C2×#97—111no—
299C2×#97—111no—
300C2×C4×C8—111no—
301#391—221no—
302#389—111no—
303#389—111no—
304#389—111no—
305#389—111no—
306#387—221no—
307#387—221no—
308#385—221no—
309#385—221no—
310#382—111no—
311#380—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C2×#95—221no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#336—111no—
326#336—111no—
327C22×C11—24no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11C2×C4×D411yescharacteristic
335C22×C11#54611yescharacteristic
336C22×C11D4×Q811yescharacteristic
337C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C11#57511yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C4×C11—22no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11C2×C4×Q811yescharacteristic
347C4×C11#52011yescharacteristic
348C4×C11#55211yescharacteristic
349C4×C11#55411yescharacteristic
350Dic11—22no—
351Dic11—42no—
352Dic11—41no—
353Dic11—41no—
354Dic11—41no—
355Dic11—81no—
356Dic11—81no—
357Dic11—81no—
358C22×Q8—21no—
359C22×D4C22×D1111yescharacteristic
360C23×C4—21no—
361C23×C4—221no—
362C23×C4—221no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8C2×Dic1114yescomplemented
369C4×Q8—444no—
370C4×D4—22no—
371C4×D4—222no—
372C4×D4—222no—
373C4×D4—441no—
374C4×D4—441no—
375C4×D4C2×Dic1114yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399#107—441no—
400#106—441no—
401#106C2×Dic1114yescomplemented
402#106C2×Dic1114yescomplemented
403C4⋊C8C2×Dic1114yescomplemented
404#102—114no—
405#102—222no—
406#102C2×Dic1114yes—
407#102C2×Dic1114yes—
408#97—222no—
409#97—441no—
410C4×C8—441no—
411#95—111no—
412#95—111no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422C2×C11—44no—
423C2×C11#236011yescharacteristic
424C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
425C2×C11#294911yescharacteristic
426C2×C11#330611yescharacteristic
427C2×C11#331111yescharacteristic
428C2×C11#338411yescharacteristic
429C2×C11#338811yescharacteristic
430C24—21no—
431C2×Q8—24no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4Q8×D1112yes—
438C2×D4#434312yes—
439C2×D4C22×Dic1112yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—81no—
445C22×C4—81no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—881no—
459C22×C4—881no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8C22×Dic1112yes—
474C2×C8C22×Dic1112yes—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—112no—
480C4⋊C4—222no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—441no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4C22×Dic1112yes—
494C4⋊C4C22×Dic1112yes—
495C4⋊C4C22×Dic1112yes—
496C22⋊C4—24no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42—221no—
503C42—442no—
504C42—442no—
505C42—442no—
506C42#434112yes—
507C42C22×Dic1112yes—
508C11#2297511yescharacteristic, complemented, Sylow
509C23—22no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23C2×D4×D1111yescharacteristic
517Q8—48no—
518D4—22no—
519D4—22no—
520D4—22no—
521D4Q8×Dic1114yescomplemented
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—84no—
536C2×C4—112no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—222no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—884no—
561C2×C4—884no—
562C2×C4D4×Dic1112yes—
563C2×C4D4×Dic1112yes—
564C2×C4C2×#434111yescharacteristic
565C2×C4C2×Q8×D1111yescharacteristic
566C2×C4C2×#434311yescharacteristic
567C2×C4#6704211yescharacteristic
568C2×C4#6704311yescharacteristic
569C2×C4C23×Dic1111yescharacteristic
570C8—22no—
571C8—22no—
572C8—222no—
573C8—441no—
574C22—24no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22#1062316111yescharacteristic
582C22#1062316311yescharacteristic
583C22#1062329311yescharacteristic
584C22#1062329311yescharacteristic
585C22D11×AGL(1,ℤ/8)11yescharacteristic
586C22#1062330411yescharacteristic
587C22C2×D4×Dic1111yescharacteristic
588C4—22no—
589C4—22no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—222no—
594C4—441no—
595C4—441no—
596C4—442no—
597C4—441no—
598C4—881no—
599C4—881no—
600C4—881no—
601C4#1062316611yescharacteristic
602C4#1062317311yescharacteristic
603C4C2×Q8×Dic1111yescharacteristic
604C4#1062335811yescharacteristic
605C2—44no—
606C2#1307162511yescharacteristic
607C2AGL(1,ℤ/8)×Dic1111yescharacteristic
608C2#1307747611yescharacteristic
609C2#1308057411yescharacteristic
610C2#1308064911yescharacteristic
611C2#1308151011yescharacteristic
612C2#1308155411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#476D11
hypocenterC11#22975
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13071676C2semidirect
3. #13069590C2semidirect
4. #13069386C2semidirect
5. #13069360C2semidirect
6. #13069345C2semidirect
7. #13069203C2semidirect
8. #13069196C2semidirect
11. #13068493C2semidirect
21. C11×#476C4semidirect
68. C11×C4⋊Q8C2×C4semidirect
101. C11×#106C2×C4semidirect
102. C11×#106C2×C4semidirect
103. C11×C4⋊C8C2×C4semidirect
107. #66896Q8semidirect
230. D4×C11C4×Q8semidirect
288. #476Dic11semidirect
368. C4⋊Q8C2×Dic11semidirect
401. #106C2×Dic11semidirect
402. #106C2×Dic11semidirect
403. C4⋊C8C2×Dic11semidirect
508. C11#22975semidirect
521. D4Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
#130716762
#130715262
#130695902
#130693862
#130693602
#130693452
#130692032
#130691962
#130688792
#130688652
#130684932
#130684432
#130684412
#102×Dic112
C2×C11×#4762
#2297511