Finite Group Databasebeta

← #14795092

Subgroups — #14795092

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622407C211yesmaximal, characteristic, complemented
2C2×#10622332C211yesmaximal, characteristic
3#13076966C211yesmaximal, characteristic
4C22⋊Q8×Dic11C211yesmaximal, characteristic
5#13070042C211yesmaximal, characteristic
6#13070039C211yesmaximal, characteristic
7#13069809C211yesmaximal, characteristic
8#13069562C211yesmaximal, characteristic, complemented
9#13069376C211yesmaximal, characteristic, complemented
10#13069360C211yesmaximal, characteristic, complemented
11#13069358C211yesmaximal, characteristic, complemented
12#13069308C211yesmaximal, characteristic, complemented
13#13069303C211yesmaximal, characteristic, complemented
14#13068619C211yesmaximal, characteristic, complemented
15C11×#2035C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×#66931—21no—
21C2×C11×#106C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622594—21no—
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622563—21no—
47#10622555—21no—
48C22⋊C4×Dic11—21no—
49#10622407—24no—
50#10622332—24no—
51#10622260—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11D411yescharacteristic
64C23×Dic11D411yescharacteristic
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66941—22no—
102#66941—22no—
103#66931—44no—
104C11×#106—22no—
105C11×#103—22no—
106C11×#103—22no—
107C11×C22⋊C8—22no—
108C11×#95—21no—
109#66899—22no—
110#66899—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)—22no—
120#66882—22no—
121#66879—22no—
122#66879—22no—
123Dic11⋊C8—22no—
124Dic11⋊C8D414yes—
125#66872—22no—
126#66871—22no—
127#24711—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11#4112yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—41no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×Dic22—42no—
162C2×Dic22—42no—
163C2×Dic22—42no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C2×D412yes—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4#4112yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—42no—
179C22⋊Dic11—42no—
180C22⋊Dic11—42no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—42no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196C4×Dic11—22no—
197C4×Dic11—22no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11C2×D412yes—
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⋊C8C2×D412yes—
210C2×#477—111no—
211C2×#432—111no—
212#2857—111no—
213C4×C22⋊Q8—111no—
214#2075—111no—
215#2075—111no—
216#2035—111no—
217#2035D1111yescharacteristic
218#1987—111no—
219#1948—111no—
220#1944—111no—
221#1944—111no—
222#1935—111no—
223#1935—111no—
224#1803—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11AGL(1,ℤ/8)12yes—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
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×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×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—41no—
273C2×Dic11—41no—
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—41no—
284C2×Dic11#12112yes—
285C2×Dic11#12112yes—
286C2×Dic11#13712yes—
287C2×Dic11#13712yes—
288Dic22—84no—
289C8×C11—22no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—41no—
293C2×C4⋊Q8—111no—
294C2×C22⋊Q8—221no—
295C2×C22⋊Q8C2×D1111yescharacteristic
296C2×C4×Q8—111no—
297C22×C42—111no—
298#477—224no—
299#432—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106C2×D1111yescharacteristic
304C2×C4⋊C8—111no—
305C2×C4⋊C8—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103C2×D1111yescharacteristic
309C2×#103C2×D1111yescharacteristic
310C2×C22⋊C8—111no—
311C2×C22⋊C8C2×D1111yescharacteristic
312C2×#97—111no—
313C2×#97—111no—
314#391—111no—
315#391—221no—
316#389—111no—
317#389—111no—
318#389—111no—
319#389—221no—
320#387—221no—
321#385—221no—
322#384—111no—
323#380—111no—
324#380—111no—
325#380—221no—
326#380C2×D1111yescharacteristic
327C4×C4⋊C4—111no—
328C4×C4⋊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
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11C2×#12111yescharacteristic
346C22×C11#52511yescharacteristic
347C22×C11#53611yescharacteristic
348C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C11C2×#13711yescharacteristic
350C22×C11C2×#13711yescharacteristic
351C22×C11#57511yescharacteristic
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#54711yescharacteristic
358C4×C11#54811yescharacteristic
359C4×C11#55211yescharacteristic
360C4×C11#55611yescharacteristic
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368Dic11#47014yes—
369C22×Q8—221no—
370C22×Q8C22×D1111yescharacteristic
371C23×C4—111no—
372C23×C4—111no—
373C23×C4C22×D1111yescharacteristic
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378C4⋊Q8—222no—
379C4⋊Q8—222no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—444no—
383C4×Q8—222no—
384C4×Q8—222no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—222no—
409C2×C42—222no—
410C2×C42—221no—
411C2×C42—221no—
412#107—222no—
413#107—222no—
414#106—22no—
415#106—222no—
416C4⋊C8—114no—
417C4⋊C8—222no—
418#103—22no—
419#103—22no—
420#103—222no—
421#103—222no—
422C22⋊C8—22no—
423C22⋊C8—222no—
424#97—222no—
425#97—222no—
426#95—21no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435C2×C11—42no—
436C2×C11#241511yescharacteristic
437C2×C11C2×#47011yescharacteristic
438C2×C11#305511yescharacteristic
439C2×C11#311211yescharacteristic
440C2×C11#311611yescharacteristic
441C2×C11#323711yescharacteristic
442C2×C11#323811yescharacteristic
443C24D4×D1111yescharacteristic
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—442no—
450C2×Q8—442no—
451C2×Q8—442no—
452C2×Q8#434112yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—441no—
477C22×C4D4×D1111yescharacteristic
478C22×C4C23×D1111yescharacteristic
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—112no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8D4×D1112yes—
491C4⋊C4—24no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4#434112yes—
513C22⋊C4—24no—
514C22⋊C4—42no—
515C22⋊C4—442no—
516C22⋊C4—442no—
517C42—112no—
518C42—112no—
519C42—222no—
520C42—222no—
521C42—221no—
522C42—221no—
523C42—442no—
524C42—442no—
525C11#2471111yescharacteristic, complemented, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23#6696712yes—
533C23C2×D4×D1111yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538Q8—884no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—112no—
559C2×C4—112no—
560C2×C4—112no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—444no—
571C2×C4—444no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×#434111yescharacteristic
586C2×C4C2×#434111yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#6704311yescharacteristic
589C2×C4#6704311yescharacteristic
590C8—22no—
591C8—41no—
592C8—222no—
593C8—441no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22#1062311711yescharacteristic
602C22D11×#12111yescharacteristic
603C22#1062317911yescharacteristic
604C22C2×#6696711yescharacteristic
605C22#1062329911yescharacteristic
606C22D11×#13711yescharacteristic
607C22D11×#13711yescharacteristic
608C4—41no—
609C4—42no—
610C4—42no—
611C4—81no—
612C4—81no—
613C4—114no—
614C4—222no—
615C4—441no—
616C4—441no—
617C4—881no—
618C4—881no—
619C4—881no—
620C4—881no—
621C4#1062312911yescharacteristic
622C4#1062314211yescharacteristic
623C4#1062318111yescharacteristic
624C4#1062320211yescharacteristic
625C2—42no—
626C2#1307203811yescharacteristic
627C2D11×#47011yescharacteristic
628C2#1307822811yescharacteristic
629C2#1307873311yescharacteristic
630C2#1307877111yescharacteristic
631C2#1307982711yescharacteristic
632C2#1307984011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2035C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2035D11
hypocenterC11#24711
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
1. C2×#10622407C2semidirect
8. #13069562C2semidirect
9. #13069376C2semidirect
10. #13069360C2semidirect
11. #13069358C2semidirect
12. #13069308C2semidirect
13. #13069303C2semidirect
14. #13068619C2semidirect
525. C11#24711semidirect

Maximal subgroups

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

subgroupindex
C2×#106224072
C2×#106223322
#130769662
C22⋊Q8×Dic112
#130700422
#130700392
#130698092
#130695622
#130693762
#130693602
#130693582
#130693082
#130693032
#130686192
C11×#20352
#2471111