Finite Group Databasebeta

← #14775272

Subgroups — #14775272

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622387C211yesmaximal, characteristic
2#13071659C211yesmaximal, characteristic
3#13071489C211yesmaximal, characteristic, complemented
4#13069352C211yesmaximal, characteristic, complemented
5#13069302C211yesmaximal, characteristic, complemented
6#13069209C211yesmaximal, characteristic, complemented
7#13069185C211yesmaximal, characteristic, complemented
8#13069051C211yesmaximal, characteristic
9#13068861C211yesmaximal, characteristic, complemented
10#13068814C211yesmaximal, characteristic, complemented
11C4×#66871C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068396C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
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×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622571—21no—
38#10622570—21no—
39#10622558—21no—
40C22⋊C4×Dic11—21no—
41C4×(C2×D11)⋊C4—21no—
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622546—21no—
45#10622541C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622387C418yescomplemented
48#10622280—21no—
49#10622265—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×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66991—22no—
77#66991C2×C414yes—
78D4×Dic11—22no—
79D4×Dic11—41no—
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×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C2×#4313—22no—
99C2×#4313—22no—
100C2×#4313—41no—
101#66945—22no—
102#66945—41no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11C2×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#66871—22no—
123#66871C2×C414yescomplemented
124C4×C11⋊C8—22no—
125#22941—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—24no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×C4×D11C22×C412yes—
161C2×C4×D11#4112yes—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C412yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C412yes—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—81no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—81no—
179C22⋊Dic11—24no—
180C22⋊Dic11—42no—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C412yes—
191C4⋊Dic11C22×C412yes—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196Dic11⋊C4—81no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C22×C412yes—
207C2×C11⋊C8#4112yes—
208#4313—44no—
209C2×#480—111no—
210#2363—111no—
211#2345—111no—
212#1943—111no—
213#1934—111no—
214#1926D1111yescharacteristic, complemented
215#1921—111no—
216#1918—111no—
217#1895—111no—
218#1862—111no—
219#1854—111no—
220C4×#107—111no—
221#1762—111no—
222#1753—111no—
223#1736—111no—
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×D11C4×D412yes—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—41no—
242D4×C11—41no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
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—41no—
257C2×C4×C11#13712yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C22⋊D11—84no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
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—84no—
286C2×Dic11C4×D412yes—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—84no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C22×M16—111no—
297C2×#121—111no—
298C2×C4×D4—111no—
299C2×#117—111no—
300C22×C4⋊C4—111no—
301#480—118no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#106C2×D1111yescharacteristic
306C2×#102—111no—
307C2×#102—111no—
308C2×#102C2×D1111yescharacteristic
309C2×#102C2×D1111yescharacteristic
310C2×C22⋊C8—111no—
311C2×#97—111no—
312C2×C4×C8—111no—
313#390—221no—
314#390C2×D1111yescharacteristic
315#389—111no—
316#389—111no—
317#389—111no—
318#388—221no—
319#387—221no—
320#387—221no—
321#386—221no—
322#380—111no—
323#380—221no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C22⋊C4—111no—
328C4×C22⋊C4—221no—
329C4×C22⋊C4—221no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#336—111no—
339#336C2×D1111yescharacteristic
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11C2×C4×D411yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11#54711yescharacteristic
350C22×C11C2×#13711yescharacteristic
351C22×C11#57511yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57611yescharacteristic
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C4×C11—22no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C4×#4111yescharacteristic
367C4×C11#52011yescharacteristic
368C4×C11#55111yescharacteristic
369C4×C11#55211yescharacteristic
370Dic11—22no—
371Dic11—41no—
372Dic11—42no—
373Dic11—42no—
374Dic11—41no—
375Dic11—42no—
376Dic11—81no—
377C22×D4—221no—
378C22×D4C22×D1111yescharacteristic
379C23×C4—111no—
380C23×C4—221no—
381C23×C4—221no—
382C2×M16—222no—
383C2×M16—222no—
384C2×M16—441no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389#121—114no—
390#121—222no—
391C4×D4—222no—
392C4×D4—441no—
393#117—222no—
394#117—441no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
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×C42—21no—
417C2×C42—111no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42C22×D1111yescharacteristic
422#107—114no—
423#107—114no—
424#107—222no—
425#106—41no—
426#102—41no—
427#102—114no—
428#102—222no—
429#102C4×D1114yes—
430C22⋊C8—114no—
431#97—441no—
432C4×C8—222no—
433#95—21no—
434#95—111no—
435#95—111no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11—82no—
443C2×C11#235911yescharacteristic
444C2×C11C4×#13711yescharacteristic
445C2×C11#294811yescharacteristic
446C2×C11#332211yescharacteristic
447C2×C11#333311yescharacteristic
448C2×C11#334611yescharacteristic
449C2×C11#334711yescharacteristic
450D11—42no—
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×D4C2×C4×D1112yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—111no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—224no—
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—442no—
480C22×C4—442no—
481C22×C4—881no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487M16—444no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8C2×C4×D1112yes—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—112no—
506C4⋊C4—112no—
507C4⋊C4—112no—
508C4⋊C4—224no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—881no—
515C4⋊C4—881no—
516C4⋊C4—881no—
517C4⋊C4C2×C4×D1112yes—
518C22⋊C4—42no—
519C22⋊C4—81no—
520C22⋊C4—224no—
521C22⋊C4—222no—
522C22⋊C4—441no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C42—21no—
527C42—21no—
528C42—81no—
529C42—221no—
530C42—221no—
531C42—442no—
532C42—881no—
533C42—881no—
534C11#2294111yescharacteristic, complemented, Sylow
535C23—22no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—112no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23C2×D4×D1111yescharacteristic
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554D4—884no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—112no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
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—884no—
595C2×C4—884no—
596C2×C4#6696812yes—
597C2×C4C22×C4×D1111yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—22no—
604C8—41no—
605C8—222no—
606C8—222no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—222no—
615C22—222no—
616C22—222no—
617C22—441no—
618C22—441no—
619C22—441no—
620C22—441no—
621C22C4×D4×D1111yescharacteristic
622C22#1062314311yescharacteristic
623C22#1062318611yescharacteristic
624C22C2×#6696811yescharacteristic
625C22#1062329911yescharacteristic
626C22#1062330511yescharacteristic
627C22#1062330511yescharacteristic
628C4—22no—
629C4—41no—
630C4—42no—
631C4—81no—
632C4—81no—
633C4—222no—
634C4—441no—
635C4—442no—
636C4—442no—
637C4—441no—
638C4—442no—
639C4—881no—
640C4#1062305311yescharacteristic
641C4#1062307711yescharacteristic
642C4#1062321011yescharacteristic
643C4#1062323911yescharacteristic
644C2—82no—
645C2—442no—
646C2#1307160511yescharacteristic
647C2C4×#6696811yescharacteristic
648C2#1307746511yescharacteristic
649C2#1308082411yescharacteristic
650C2#1308095711yescharacteristic
651C2#1308109911yescharacteristic
652C2#1308111411yescharacteristic
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#22941
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. #13071489C2semidirect
4. #13069352C2semidirect
5. #13069302C2semidirect
6. #13069209C2semidirect
7. #13069185C2semidirect
9. #13068861C2semidirect
10. #13068814C2semidirect
11. C4×#66871C2semidirect
12. #13068443C2semidirect
13. #13068396C2semidirect
14. #13068334C2semidirect
15. C11×#1926C2semidirect
47. #10622387C4semidirect
104. C4⋊C4×D11C2×C4semidirect
119. (C2×D11)⋊C8C2×C4semidirect
120. #66882C2×C4semidirect
123. #66871C2×C4semidirect
214. #1926D11semidirect
534. C11#22941semidirect

Maximal subgroups

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

subgroupindex
C2×#106223872
#130716592
#130714892
#130693522
#130693022
#130692092
#130691852
#130690512
#130688612
#130688142
C4×#668712
#130684432
#130683962
#130683342
C11×#19262
#2294111