Finite Group Databasebeta

← #14775362

Subgroups — #14775362

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622422C211yesmaximal, characteristic
2#13071648C211yesmaximal, characteristic
3#13071481C211yesmaximal, characteristic
4#13069352C211yesmaximal, characteristic, complemented
5#13069295C211yesmaximal, characteristic, complemented
6#13069206C211yesmaximal, characteristic, complemented
7#13069188C211yesmaximal, characteristic, complemented
8#13069046C211yesmaximal, characteristic
9#13068868C211yesmaximal, characteristic, complemented
10#13068814C211yesmaximal, characteristic
11C4×#66871C211yesmaximal, characteristic, complemented
12#13068448C211yesmaximal, characteristic, complemented
13#13068396C211yesmaximal, characteristic
14#13068334C211yesmaximal, characteristic
15C11×#1927C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66925—21no—
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622600C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622546—21no—
41#10622541C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622422C418yescomplemented
44#10622283—21no—
45#10622282—21no—
46#10622277—21no—
47#10622268—21no—
48#10622265—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70#66999—22no—
71#66999C2×C414yes—
72Q8×Dic11—22no—
73Q8×Dic11—41no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4D411yescharacteristic
78C2×(C2×D11)⋊C4D411yescharacteristic
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—41no—
99#66945—22no—
100#66945—41no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11C2×C414yes—
103#66925—44no—
104C11×#106—41no—
105C11×#103—41no—
106C11×#103C2×C414yes—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110#66899—22no—
111#66899C2×C414yes—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120(C2×D11)⋊C8C2×C414yes—
121#66882C2×C414yes—
122#66879—41no—
123#66871—22no—
124#66871C2×C414yes—
125C4×C11⋊C8—22no—
126#22947—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C22×C412yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×C4×D11—24no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11C22×C412yes—
156C2×C4×D11#4112yes—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C412yes—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—42no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—22no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—42no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—42no—
183C4⋊Dic11C22×C412yes—
184C4⋊Dic11C22×C412yes—
185C4⋊Dic11#4112yes—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—42no—
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⋊C8C22×C412yes—
202C2×C11⋊C8#4112yes—
203#4313—44no—
204C2×#484—111no—
205#2362—111no—
206#2344—111no—
207#1943—111no—
208#1933—111no—
209#1927D1111yescharacteristic, complemented
210#1921—111no—
211#1918—111no—
212#1894—111no—
213#1863—111no—
214#1854—111no—
215C4×#107—111no—
216#1763—111no—
217#1753—111no—
218#1736—111no—
219C23×C11C22×D411yescharacteristic
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11C4×D412yes—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
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—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11AGL(1,ℤ/8)12yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
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×Dic11C4×D412yes—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—48no—
281C8×C11—22no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C22×M16—111no—
286C2×C22⋊Q8—111no—
287C2×C4×Q8—111no—
288C2×#117—111no—
289C2×#117—221no—
290C22×C4⋊C4—111no—
291#484—118no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106C2×D1111yescharacteristic
296C2×#103—111no—
297C2×#103—111no—
298C2×#103C2×D1111yescharacteristic
299C2×#103C2×D1111yescharacteristic
300C2×C22⋊C8—111no—
301C2×#97—111no—
302C2×C4×C8—111no—
303#391C2×D1111yescharacteristic
304#389—111no—
305#389—111no—
306#389—111no—
307#388—221no—
308#388—221no—
309#387—221no—
310#387—221no—
311#387—221no—
312#381—221no—
313#380—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—221no—
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340C2×D1111yescharacteristic
327#336—111no—
328#336C2×D1111yescharacteristic
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#54611yescharacteristic
331C22×C11#54711yescharacteristic
332C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C11#57511yescharacteristic
334C22×C11#57811yescharacteristic
335C22×C11#57811yescharacteristic
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C4×C11—22no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C4×#4111yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#55111yescharacteristic
352C4×C11#55211yescharacteristic
353Dic11—22no—
354Dic11—41no—
355Dic11—42no—
356Dic11—42no—
357Dic11—42no—
358Dic11—41no—
359Dic11—81no—
360C22×Q8C22×D1111yescharacteristic
361C23×C4—111no—
362C23×C4—221no—
363C2×M16—222no—
364C2×M16—222no—
365C2×M16—441no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C22⋊Q8—114no—
371C22⋊Q8—222no—
372C4×Q8—222no—
373C4×Q8—441no—
374#117—222no—
375#117—444no—
376#117—441no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4—111no—
393C2×C22⋊C4—111no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—21no—
398C2×C42—111no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#107—114no—
405#107—114no—
406#107—222no—
407#106—41no—
408#103—41no—
409#103—114no—
410#103—222no—
411#103C4×D1114yes—
412C22⋊C8—114no—
413#97—441no—
414C4×C8—222no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426C2×C11#235911yescharacteristic
427C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
428C2×C11#295011yescharacteristic
429C2×C11#332711yescharacteristic
430C2×C11#333011yescharacteristic
431C2×C11#334311yescharacteristic
432C2×C11#334911yescharacteristic
433D11—42no—
434C24—111no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×C4×D1112yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—111no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—224no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464M16—444no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×C4×D1112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—112no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4C2×C4×D1112yes—
497C22⋊C4—224no—
498C22⋊C4—222no—
499C22⋊C4—441no—
500C22⋊C4—442no—
501C22⋊C4—442no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—221no—
506C42—221no—
507C42—442no—
508C42—442no—
509C42—442no—
510C42—442no—
511C11#2294711yescharacteristic, complemented, Sylow
512C23—112no—
513C23—221no—
514C23—221no—
515C23—221no—
516C23—221no—
517C23—221no—
518C23—221no—
519C23C2×D4×D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—112no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—448no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4#6696712yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4#6703711yescharacteristic
570C2×C4#41×D1111yescharacteristic
571C2×C4#41×D1111yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#6704311yescharacteristic
574C8—22no—
575C8—41no—
576C8—222no—
577C8—222no—
578C22—222no—
579C22—222no—
580C22—222no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22C4×D4×D1111yescharacteristic
586C22#1062314311yescharacteristic
587C22#1062318611yescharacteristic
588C22C2×#6696711yescharacteristic
589C22#1062329911yescharacteristic
590C22#1062331011yescharacteristic
591C22#1062331011yescharacteristic
592C4—22no—
593C4—41no—
594C4—42no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—222no—
599C4—441no—
600C4—441no—
601C4—442no—
602C4—442no—
603C4—442no—
604C4—881no—
605C4#1062305311yescharacteristic
606C4#1062307711yescharacteristic
607C4#1062321011yescharacteristic
608C4#1062323911yescharacteristic
609C2—442no—
610C2#1307160511yescharacteristic
611C2C4×#6696711yescharacteristic
612C2#1307748111yescharacteristic
613C2#1308089111yescharacteristic
614C2#1308092411yescharacteristic
615C2#1308105411yescharacteristic
616C2#1308115011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1927C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1927D11
hypocenterC11#22947
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
4. #13069352C2semidirect
5. #13069295C2semidirect
6. #13069206C2semidirect
7. #13069188C2semidirect
9. #13068868C2semidirect
11. C4×#66871C2semidirect
12. #13068448C2semidirect
15. C11×#1927C2semidirect
43. #10622422C4semidirect
209. #1927D11semidirect
511. C11#22947semidirect

Maximal subgroups

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

subgroupindex
C2×#106224222
#130716482
#130714812
#130693522
#130692952
#130692062
#130691882
#130690462
#130688682
#130688142
C4×#668712
#130684482
#130683962
#130683342
C11×#19272
#2294711