Finite Group Databasebeta

← #14770465

Subgroups — #14770465

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623216C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic
3#13071568C211yesmaximal, characteristic
4#13069587C211yesmaximal, characteristic
5#13069583C211yesmaximal, characteristic
6#13069574C211yesmaximal, characteristic
7#13069572C211yesmaximal, characteristic
8#13069562C211yesmaximal, characteristic
9#13068630C211yesmaximal, characteristic
10#13068628C211yesmaximal, characteristic
11#13068620C211yesmaximal, characteristic
12#13068445C211yesmaximal, characteristic
13#13068445C211yesmaximal, characteristic
14C4×#66880C211yesmaximal, characteristic
15C11×#1991C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17#10623216—24no—
18#10623216C418yescomplemented
19C2×#66943C2211yescharacteristic
20C2×#66942—21no—
21C2×#66942—21no—
22C2×#66941—21no—
23C2×#66941C2211yescharacteristic
24C2×#66940—21no—
25C2×#66940C2211yescharacteristic
26C2×#66940C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C11×#382C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622590C2211yescharacteristic
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622292—24no—
46#10622266—21no—
47#10622265—21no—
48#10622262—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Dic22—21no—
63C22×Dic22D411yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#125—22no—
68C11×#125C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4D411yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66943—22no—
101#66943C2×C414yes—
102#66942—28no—
103#66942—28no—
104#66941—28no—
105#66941—22no—
106#66941C2×C414yes—
107#66940—28no—
108#66940—22no—
109#66940—22no—
110#66940C2×C414yes—
111#66940C2×C414yes—
112C4×Dic22—22no—
113C4×Dic22C2×C414yes—
114C4×Dic22C2×C414yes—
115C4×Dic22D414yes—
116C4×C8×C11—22no—
117C11×#95—21no—
118C11×#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66880—22no—
125#66880Q814yescomplemented
126#66879—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—22no—
130#66874—22no—
131#66874—22no—
132C4⋊(C11⋊C8)—22no—
133#22527—111nomaximal, Sylow
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
148C22×Dic11C2×D411yescharacteristic
149C2×Dic22—24no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—41no—
154C2×Dic22—41no—
155C2×Dic22—42no—
156C2×Dic22—42no—
157C2×Dic22C22⋊C414yes—
158C2×Dic22C22×C412yes—
159C2×Dic22C2×Q812yes—
160C2×Dic22#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×Q812yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4C22×C412yes—
177C42×C11C22×C412yes—
178C42×C11C2×D412yes—
179C4⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22⋊C414yes—
185C4⋊Dic11C22×C412yes—
186C4⋊Dic11C2×Q812yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189Dic11⋊C4—24no—
190Dic11⋊C4—24no—
191Dic11⋊C4—24no—
192Dic11⋊C4—42no—
193Dic11⋊C4—81no—
194Dic11⋊C4C22⋊C414yes—
195Dic11⋊C4C22⋊C414yes—
196C4×Dic11—24no—
197C4×Dic11—24no—
198C4×Dic11—24no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C4×Dic11C22×C412yes—
203C4×Dic11C22×C412yes—
204C4×Dic11C2×D412yes—
205C4×Dic11C2×D412yes—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×#557—111no—
213C2×#446—111no—
214#2355—111no—
215#1993—111no—
216#1992—111no—
217#1991D1111yescharacteristic
218#1989—111no—
219#1989—111no—
220#1987—111no—
221#1805—111no—
222#1805—111no—
223#1803—111no—
224#1763—111no—
225#1763—111no—
226C4×#103—111no—
227C23×C11C22×D411yescharacteristic
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
245C2×C4×C11C2×C22⋊C412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11C2×C22⋊C412yes—
273C2×Dic11C2×C22⋊C412yes—
274C2×Dic11C2×C22⋊C412yes—
275C2×Dic11C2×C22⋊C412yes—
276Dic22—22no—
277Dic22—22no—
278Dic22—22no—
279Dic22—44no—
280Dic22—48no—
281Dic22C4×Q814yes—
282C8×C11—22no—
283C8×C11—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286#557—118no—
287#557—224no—
288C2×C4⋊Q8—111no—
289C2×C4⋊Q8—221no—
290C2×#125—111no—
291C2×#125—221no—
292C2×#125—221no—
293C2×#125C2×D1111yescharacteristic
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8—221no—
299#446—224no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#97—111no—
308C2×#97—111no—
309C2×C4×C8C2×D1111yescharacteristic
310#391—221no—
311#387—221no—
312#387—221no—
313#384—111no—
314#382—111no—
315#382C2×D1111yescharacteristic
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—221no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#340C2×D1111yescharacteristic
331#340C2×D1111yescharacteristic
332C22×C11C22×C22⋊C411yescharacteristic
333C22×C11#54811yescharacteristic
334C22×C11D4×Q811yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×C4×Q811yescharacteristic
346C4×C11#51911yescharacteristic
347C4×C11#54811yescharacteristic
348C4×C11D4×Q811yescharacteristic
349Dic11—24no—
350Dic11—22no—
351Dic11—22no—
352Dic11—22no—
353Dic11—22no—
354Dic11—42no—
355Dic11—42no—
356Dic11—81no—
357C22×Q8—111no—
358C22×Q8—111no—
359C22×Q8—221no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366C4⋊Q8—228no—
367#125—22no—
368#125—114no—
369#125—222no—
370#125—228no—
371#125—228no—
372#125C4×D1114yes—
373C4×Q8—114no—
374C4×Q8—114no—
375C4×Q8—114no—
376C4×Q8—114no—
377C4×Q8—114no—
378C4×Q8—222no—
379C4×Q8—222no—
380C4×Q8—228no—
381C4×Q8—222no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
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⋊C4—221no—
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411C4⋊C8—222no—
412C4⋊C8—222no—
413C4⋊C8—222no—
414#103—114no—
415#103—222no—
416#103—222no—
417#103—222no—
418#97—222no—
419#97—222no—
420C4×C8—22no—
421#95—21no—
422#95—21no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11Q8×C22⋊C411yescharacteristic
429C2×C11#289611yescharacteristic
430C2×C11#289811yescharacteristic
431C2×C11#337111yescharacteristic
432C2×C11#337711yescharacteristic
433C2×C11#338811yescharacteristic
434C2×C11#339011yescharacteristic
435C2×Q8—114no—
436C2×Q8—112no—
437C2×Q8—112no—
438C2×Q8—112no—
439C2×Q8—224no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×Q8—441no—
445C2×Q8—442no—
446C2×Q8—442no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8Q8×D1112yes—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—114no—
483C4⋊C4—114no—
484C4⋊C4—114no—
485C4⋊C4—112no—
486C4⋊C4—112no—
487C4⋊C4—224no—
488C4⋊C4—224no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—881no—
499C4⋊C4C2×C4×D1112yes—
500C4⋊C4C2×C4×D1112yes—
501C42—112no—
502C42—112no—
503C42—112no—
504C42—112no—
505C42—224no—
506C42—224no—
507C42—224no—
508C42—442no—
509C42—881no—
510C42—881no—
511C42C2×C4×D1112yes—
512C42D4×D1112yes—
513C11#2252711yescharacteristic, complemented, Sylow
514C23C2×D4×D1111yescharacteristic
515Q8—114no—
516Q8—222no—
517Q8—222no—
518Q8—222no—
519Q8—444no—
520Q8—448no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4C22⋊C4×D1112yes—
562C2×C4C22⋊C4×D1112yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×Q8×D1111yescharacteristic
566C2×C4#6704011yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C2×C4#6704311yescharacteristic
569C8—22no—
570C8—41no—
571C8—441no—
572C8—441no—
573C22C2×C22⋊C4×D1111yescharacteristic
574C22#1062320811yescharacteristic
575C22#1062325811yescharacteristic
576C22#1062329911yescharacteristic
577C22#1062329911yescharacteristic
578C22#1062330111yescharacteristic
579C22#1062330211yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—224no—
587C4—222no—
588C4—222no—
589C4—222no—
590C4—222no—
591C4—442no—
592C4—442no—
593C4—881no—
594C4C4×Q8×D1111yescharacteristic
595C4#1062310311yescharacteristic
596C4#1062316311yescharacteristic
597C4#1062316411yescharacteristic
598C2#1307145011yescharacteristic
599C2#1307713111yescharacteristic
600C2#1307714511yescharacteristic
601C2#1308139011yescharacteristic
602C2#1308146411yescharacteristic
603C2#1308156711yescharacteristic
604C2#1308158611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1991C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1991D11
hypocenterC11#22527
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1991

Complements

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

NH ≅ G/Ntype
18. #10623216C4semidirect
125. #66880Q8semidirect
513. C11#22527semidirect

Maximal subgroups

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

subgroupindex
C2×#106232162
C2×#106222922
#130715682
#130695872
#130695832
#130695742
#130695722
#130695622
#130686302
#130686282
#130686202
#130684452
C4×#668802
C11×#19912
#2252711