Finite Group Databasebeta

← #14775182

Subgroups — #14775182

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622397C211yesmaximal, characteristic
2#13071659C211yesmaximal, characteristic
3#13071497C211yesmaximal, characteristic, complemented
4#13069352C211yesmaximal, characteristic, complemented
5#13069316C211yesmaximal, characteristic, complemented
6#13069192C211yesmaximal, characteristic, complemented
7#13069188C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic
9#13068861C211yesmaximal, characteristic, complemented
10#13068814C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068391C211yesmaximal, characteristic, complemented
14#13068331C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31#10622600C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34#10622586C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622571—21no—
38#10622570—21no—
39#10622558—21no—
40C22⋊C4×Dic11—21no—
41#10622553—21no—
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622545—21no—
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622397C418yescomplemented
48#10622282—21no—
49#10622263—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75#66991—22no—
76#66991C2×C414yes—
77D4×Dic11—22no—
78D4×Dic11—41no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C2×C8×D11—22no—
99C2×C8×D11—22no—
100C2×C8×D11—41no—
101#66945—22no—
102#66945—22no—
103#66945—41no—
104#66945C2×C414yescomplemented
105C11×#106—41no—
106C11×#102—41no—
107C11×#102C2×C414yes—
108C11×#95—21no—
109#66896—22no—
110#66896C2×C414yes—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119(C2×D11)⋊C8C2×C414yescomplemented
120#66882C2×C414yescomplemented
121#66879—41no—
122#66872C2×C414yescomplemented
123#66871—22no—
124#66867—22no—
125#22935—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11C2×D411yescharacteristic
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11C22×C412yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—24no—
141C2×C22⋊D11—81no—
142C2×C22⋊D11—81no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—81no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11C22×C412yes—
158C2×C4×D11#4112yes—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C412yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C412yes—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—81no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176C22⋊Dic11—24no—
177C22⋊Dic11—42no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C412yes—
189C4⋊Dic11C22×C412yes—
190C4⋊Dic11#4112yes—
191Dic11⋊C4—81no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194C4×Dic11—24no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C412yes—
205C2×C11⋊C8#4112yes—
206C8×D11—44no—
207C2×#482—111no—
208#2363—111no—
209#2346—111no—
210#1943—111no—
211#1936—111no—
212#1926D1111yescharacteristic, complemented
213#1919—111no—
214#1918—111no—
215#1893—111no—
216#1862—111no—
217#1854—111no—
218#1776—111no—
219#1762—111no—
220#1752—111no—
221#1735—111no—
222C23×C11—22no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11C22×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11C4×D412yes—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—41no—
240D4×C11—41no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C22⋊D11—84no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—84no—
284C2×Dic11C4×D412yes—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—22no—
288C4×D11—22no—
289C8×C11—22no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—22no—
293C23×C8—111no—
294C2×#121—111no—
295C2×C4×D4—111no—
296C2×#117—111no—
297C2×#117—111no—
298#482—118no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#106—111no—
302C2×#106C2×D1111yescharacteristic
303C2×#102—111no—
304C2×#102—111no—
305C2×#102C2×D1111yescharacteristic
306C2×#102C2×D1111yescharacteristic
307C2×C22⋊C8—111no—
308C2×#97—111no—
309C2×#97—111no—
310#390—221no—
311#390C2×D1111yescharacteristic
312#389—111no—
313#389—111no—
314#389—111no—
315#388—221no—
316#388—221no—
317#388—221no—
318#386—221no—
319#382—221no—
320#380—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4C2×D1111yescharacteristic
324C4×C22⋊C4—111no—
325C4×C22⋊C4—221no—
326#376—221no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#336—111no—
336#336C2×D1111yescharacteristic
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11C2×C4×D411yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#54711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57611yescharacteristic
350C22×C11#57711yescharacteristic
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11C4×#4111yescharacteristic
364C4×C11#52011yescharacteristic
365C4×C11#55111yescharacteristic
366C4×C11#55211yescharacteristic
367Dic11—22no—
368Dic11—42no—
369Dic11—42no—
370Dic11—41no—
371Dic11—41no—
372Dic11—42no—
373Dic11—81no—
374C22×D4—221no—
375C22×D4C22×D1111yescharacteristic
376C23×C4—111no—
377C23×C4—221no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—222no—
381C22×C8—222no—
382C22×C8—441no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385#121—114no—
386#121—222no—
387C4×D4—222no—
388C4×D4—441no—
389#117—114no—
390#117—222no—
391#117—222no—
392#117—441no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C42—21no—
413C2×C42—111no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—114no—
420#107—222no—
421#106—41no—
422#106—114no—
423#102—41no—
424#102—114no—
425#102—222no—
426#102C4×D1114yes—
427C22⋊C8—114no—
428#97—222no—
429#97—441no—
430#95—21no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11—82no—
440C2×C11#235911yescharacteristic
441C2×C11#294311yescharacteristic
442C2×C11#294611yescharacteristic
443C2×C11#331711yescharacteristic
444C2×C11#331911yescharacteristic
445C2×C11#334711yescharacteristic
446C2×C11#334811yescharacteristic
447D11—42no—
448C24—21no—
449C24—111no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—224no—
456C2×D4—881no—
457C2×D4—881no—
458C2×D4C2×C4×D1112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—881no—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—112no—
487C2×C8—112no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—444no—
493C2×C8C2×C4×D1112yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—112no—
500C4⋊C4—112no—
501C4⋊C4—112no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4C2×C4×D1112yes—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—224no—
514C22⋊C4—224no—
515C22⋊C4—441no—
516C22⋊C4—441no—
517C22⋊C4—442no—
518C22⋊C4—442no—
519C22⋊C4—881no—
520C42—21no—
521C42—21no—
522C42—42no—
523C42—224no—
524C42—221no—
525C42—221no—
526C42—442no—
527C42—442no—
528C42—881no—
529C11#2293511yescharacteristic, complemented, Sylow
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—112no—
538C23—221no—
539C23—221no—
540C23—221no—
541C23—221no—
542C23—221no—
543C23—221no—
544C23C2×D4×D1111yescharacteristic
545D4—22no—
546D4—22no—
547D4—41no—
548D4—41no—
549D4—884no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—112no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
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—884no—
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4#6703711yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C8—22no—
598C8—41no—
599C8—222no—
600C8—222no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—222no—
609C22—222no—
610C22—222no—
611C22—441no—
612C22—441no—
613C22—441no—
614C22—441no—
615C22C4×D4×D1111yescharacteristic
616C22#1062314311yescharacteristic
617C22#1062318611yescharacteristic
618C22#1062329311yescharacteristic
619C22#1062330011yescharacteristic
620C22#1062330411yescharacteristic
621C22#1062330411yescharacteristic
622C4—41no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—81no—
627C4—222no—
628C4—441no—
629C4—442no—
630C4—442no—
631C4—441no—
632C4—442no—
633C4—881no—
634C4#1062305311yescharacteristic
635C4#1062307711yescharacteristic
636C4#1062321011yescharacteristic
637C4#1062323911yescharacteristic
638C2—82no—
639C2—442no—
640C2#1307160511yescharacteristic
641C2#1307741311yescharacteristic
642C2#1307744311yescharacteristic
643C2#1308074911yescharacteristic
644C2#1308077911yescharacteristic
645C2#1308110911yescharacteristic
646C2#1308113411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1926C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1926D11
hypocenterC11#22935
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
3. #13071497C2semidirect
4. #13069352C2semidirect
5. #13069316C2semidirect
6. #13069192C2semidirect
7. #13069188C2semidirect
9. #13068861C2semidirect
10. #13068814C2semidirect
11. #13068514C2semidirect
12. #13068443C2semidirect
13. #13068391C2semidirect
14. #13068331C2semidirect
15. C11×#1926C2semidirect
47. #10622397C4semidirect
104. #66945C2×C4semidirect
119. (C2×D11)⋊C8C2×C4semidirect
120. #66882C2×C4semidirect
122. #66872C2×C4semidirect
212. #1926D11semidirect
529. C11#22935semidirect

Maximal subgroups

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

subgroupindex
C2×#106223972
#130716592
#130714972
#130693522
#130693162
#130691922
#130691882
#130690412
#130688612
#130688142
#130685142
#130684432
#130683912
#130683312
C11×#19262
#2293511