Finite Group Databasebeta

← #14757278

Subgroups — #14757278

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622494C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic
3C2×#10622452C211yesmaximal, characteristic
4#13071237C211yesmaximal, characteristic
5#13070970C211yesmaximal, characteristic
6#13069387C211yesmaximal, characteristic, complemented
7#13069386C211yesmaximal, characteristic, complemented
8#13069384C211yesmaximal, characteristic, complemented
9#13069381C211yesmaximal, characteristic, complemented
10#13069378C211yesmaximal, characteristic, complemented
11#13069377C211yesmaximal, characteristic, complemented
12#13069371C211yesmaximal, characteristic, complemented
13#13068334C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#1947C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622602—21no—
33#10622602—21no—
34#10622590C2211yescharacteristic
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622585—21no—
39#10622585—21no—
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C4×(C2×D11)⋊C4—21no—
45#10622549C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622494—24no—
50#10622493—24no—
51#10622452C418yescomplemented
52#10622279—21no—
53#10622262—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4D411yescharacteristic
78C2×(C2×D11)⋊C4D411yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313C2×C414yes—
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102C2×C8×D11C2×C414yes—
103#66945—22no—
104#66945—22no—
105#66945—22no—
106#66945D414yes—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—22no—
110C4⋊C4×D11Q814yes—
111#66925C2×C414yes—
112#66925Q814yes—
113C11×#107—22no—
114C11×#107—22no—
115C11×C4⋊C8C2×C414yescomplemented
116C11×#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66882—22no—
125#66881—22no—
126Dic11⋊C8C2×C414yescomplemented
127Dic11⋊C8C2×C414yescomplemented
128#66872—22no—
129#66872—22no—
130#66872—22no—
131#66871—22no—
132C4⋊(C11⋊C8)C2×C414yescomplemented
133#21175—111nomaximal, Sylow
134C23×D11C2×D411yescharacteristic
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×C4×D11—24no—
150C2×C4×D11—42no—
151C2×C4×D11—81no—
152C2×C4×D11—81no—
153C2×C4×D11—81no—
154C2×C4×D11—81no—
155C2×C4×D11C22×C412yes—
156C2×C4×D11C2×D412yes—
157C2×C4×D11C2×Q812yes—
158C2×C4×D11C2×Q812yes—
159C2×C4×D11#4112yes—
160C2×C4×D11#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11C22×C412yes—
166C2×C8×C11C22×C412yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×Q812yes—
177C42×C11—81no—
178C42×C11C22×C412yes—
179C42×C11C2×Q812yes—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4C4⋊C414yes—
183(C2×D11)⋊C4C4⋊C414yes—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2×D412yes—
191C4⋊Dic11C2×Q812yes—
192Dic11⋊C4—24no—
193Dic11⋊C4—42no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196Dic11⋊C4C4⋊C414yes—
197Dic11⋊C4C4⋊C414yes—
198C4×Dic11—24no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C4×Dic11—81no—
203C4×Dic11C22×C412yes—
204C4×Dic11C2×Q812yes—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C412yes—
210C2×C11⋊C8C22×C412yes—
211#4313—28no—
212C8×D11—28no—
213C2×#428—111no—
214C2×#427—111no—
215C2×#424—111no—
216#2317—111no—
217#2274—111no—
218#1949—111no—
219#1949—111no—
220#1949—111no—
221#1949—111no—
222#1948—111no—
223#1948—111no—
224#1947—111no—
225#1947D1111yescharacteristic, complemented
226#1736—111no—
227C2×#340—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11C2×C4⋊C412yes—
234C22×D11#12112yes—
235C22×D11C22⋊Q812yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
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×C11C2×C4⋊C412yes—
253C2×C4×C11C2×C4⋊C412yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—22no—
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×Dic11C2×C4⋊C412yes—
277C2×Dic11C2×C4⋊C412yes—
278C2×Dic11C2×C4⋊C412yes—
279C2×Dic11#12112yes—
280C2×Dic11C22⋊Q812yes—
281C4×D11—84no—
282C4×D11—84no—
283C4×D11C4×D414yes—
284C4×D11C4×Q814yes—
285C4×D11#12514yes—
286C4×D11C4⋊Q814yes—
287C8×C11—22no—
288C8×C11—22no—
289C11⋊C8—22no—
290C11⋊C8—22no—
291C22×M16—111no—
292C23×C8—111no—
293C2×#117—111no—
294C2×#117—111no—
295C2×#117—111no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—111no—
298#428—224no—
299#427—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#107C2×D1111yescharacteristic
303C2×#107C2×D1111yescharacteristic
304C2×#106—111no—
305C2×#106—111no—
306C2×#106—111no—
307C2×#106—111no—
308#424—118no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8C2×D1111yescharacteristic
313#389—221no—
314#389—221no—
315#385—221no—
316#385—221no—
317#384—111no—
318#384C2×D1111yescharacteristic
319#382—111no—
320#382—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C4⋊C4—221no—
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C22⋊C4—221no—
328C4×C22⋊C4—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
337C22×C11C22×C4⋊C411yescharacteristic
338C22×C11C2×#12111yescharacteristic
339C22×C11C2×C22⋊Q811yescharacteristic
340C22×C11#57611yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57811yescharacteristic
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—22no—
350C2×D11#38914yes—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11C2×C4×D411yescharacteristic
358C4×C11C2×C4×Q811yescharacteristic
359C4×C11C2×#12511yescharacteristic
360C4×C11C2×C4⋊Q811yescharacteristic
361Dic11—22no—
362Dic11—22no—
363Dic11—42no—
364Dic11—42no—
365Dic11—81no—
366Dic11—81no—
367Dic11#38914yes—
368C23×C4—111no—
369C23×C4—221no—
370C23×C4—221no—
371C2×M16—114no—
372C2×M16—222no—
373C2×M16—222no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—114no—
377C22×C8—222no—
378C22×C8—222no—
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381#117—114no—
382#117—114no—
383#117—114no—
384#117—222no—
385#117—222no—
386#117—222no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—114no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C42—21no—
412C2×C42—111no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—22no—
420#107—22no—
421#107—222no—
422#107—222no—
423#106—222no—
424#106—222no—
425#106—222no—
426#106—222no—
427C4⋊C8—114no—
428C4⋊C8—114no—
429C4⋊C8—114no—
430C4⋊C8C4×D1114yescomplemented
431#95—21no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11C2×#38911yescharacteristic
440C2×C11#291211yescharacteristic
441C2×C11#291311yescharacteristic
442C2×C11#304511yescharacteristic
443C2×C11#304611yescharacteristic
444C2×C11#308111yescharacteristic
445C2×C11#308211yescharacteristic
446D11—24no—
447C24—111no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—224no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—442no—
467C22×C4—881no—
468C22×C4—881no—
469C22×C4—881no—
470C22×C4—881no—
471C22×C4D4×D1111yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474M16—228no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—112no—
480C2×C8—112no—
481C2×C8—228no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8C2×C4×D1112yes—
487C2×C8C2×C4×D1112yes—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—114no—
497C4⋊C4—114no—
498C4⋊C4—112no—
499C4⋊C4—112no—
500C4⋊C4—224no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4D4×D1112yes—
511C4⋊C4Q8×D1112yes—
512C22⋊C4—114no—
513C22⋊C4—114no—
514C22⋊C4—224no—
515C22⋊C4—442no—
516C42—81no—
517C42—112no—
518C42—112no—
519C42—224no—
520C42—442no—
521C42—881no—
522C42—881no—
523C42—881no—
524C42C2×C4×D1112yes—
525C42Q8×D1112yes—
526C11#2117511yescharacteristic, complemented, Sylow
527C23—112no—
528C23—112no—
529C23—112no—
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23C2×D4×D1111yescharacteristic
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—114no—
555C2×C4—114no—
556C2×C4—114no—
557C2×C4—114no—
558C2×C4—112no—
559C2×C4—112no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—884no—
577C2×C4—884no—
578C2×C4C4⋊C4×D1112yes—
579C2×C4C4⋊C4×D1112yes—
580C2×C4C22×C4×D1111yescharacteristic
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4C2×Q8×D1111yescharacteristic
583C2×C4C2×Q8×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C8—22no—
587C8—22no—
588C8—222no—
589C8—222no—
590C22—114no—
591C22—222no—
592C22—222no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—222no—
597C22C2×C4⋊C4×D1111yescharacteristic
598C22D11×#12111yescharacteristic
599C22D11×C22⋊Q811yescharacteristic
600C22#1062328811yescharacteristic
601C22#1062329711yescharacteristic
602C22#1062330611yescharacteristic
603C22#1062330911yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—114no—
611C4—222no—
612C4—222no—
613C4—442no—
614C4—442no—
615C4—881no—
616C4—881no—
617C4C4×D4×D1111yescharacteristic
618C4C4×Q8×D1111yescharacteristic
619C4D11×#12511yescharacteristic
620C4D11×C4⋊Q811yescharacteristic
621C2—224no—
622C2D11×#38911yescharacteristic
623C2#1307721011yescharacteristic
624C2#1307721211yescharacteristic
625C2#1307815011yescharacteristic
626C2#1307816311yescharacteristic
627C2#1307844011yescharacteristic
628C2#1307845311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11#21175
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
6. #13069387C2semidirect
7. #13069386C2semidirect
8. #13069384C2semidirect
9. #13069381C2semidirect
10. #13069378C2semidirect
11. #13069377C2semidirect
12. #13069371C2semidirect
15. C11×#1947C2semidirect
51. #10622452C4semidirect
115. C11×C4⋊C8C2×C4semidirect
126. Dic11⋊C8C2×C4semidirect
127. Dic11⋊C8C2×C4semidirect
132. C4⋊(C11⋊C8)C2×C4semidirect
225. #1947D11semidirect
430. C4⋊C8C4×D11semidirect
526. C11#21175semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
C2×#106224932
C2×#106224522
#130712372
#130709702
#130693872
#130693862
#130693842
#130693812
#130693782
#130693772
#130693712
#130683342
D11×#3402
C11×#19472
#2117511