Finite Group Databasebeta

← #14769596

Subgroups — #14769596

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×D11C211yesmaximal, characteristic
2C2×C4×D88C211yesmaximal, characteristic, complemented
3C2×#10622485C211yesmaximal, characteristic, complemented
4#13071437C212yesmaximal, complemented
5#13069483C211yesmaximal, characteristic, complemented
6#13068967C212yesmaximal, complemented
7#13068961C212yesmaximal, complemented
8#13068642C211yesmaximal, characteristic, complemented
9#13068545C212yesmaximal, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11C11×#1970C211yesmaximal, characteristic, complemented
12C22×D4×D11C2212yes—
13C22×C11×D8C2211yescharacteristic
14C22×#4323C2212yes—
15C2×D8×D11—24no—
16C2×D8×D11—24no—
17C2×D8×D11C418yescomplemented
18C22×D88C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66946C2212yescomplemented
21C2×C22⋊C4×D11—22no—
22C2×C4×D44C2212yescomplemented
23C2×C11×#107C2211yescharacteristic, complemented
24C2×C11×#102C2212yescomplemented
25C2×C4×C8×C11C2211yescharacteristic, complemented
26C11×#390C2212yescomplemented
27#10622834C2212yescomplemented
28C2×#66896C2212yescomplemented
29C2×#66885C2212yescomplemented
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic, complemented
32C2×C8×Dic11C2211yescharacteristic, complemented
33#10622600C2212yes—
34C2×#66873C2212yescomplemented
35#10622569—22no—
36#10622569—22no—
37#10622568—22no—
38C4×(C2×D11)⋊C4C2211yescharacteristic
39#10622485—24no—
40C4×D88—24no—
41#10622188C2211yescharacteristic, complemented
42#10622167C2212yescomplemented
43#10622162C2211yescharacteristic, complemented
44C24×D11—22no—
45C22×D4×C11C2312yes—
46C22×C22⋊D11—22no—
47C2×D4×D11—24no—
48C2×D4×D11—24no—
49C2×D4×D11—24no—
50C2×D4×D11—42no—
51C2×D4×D11—42no—
52C2×D4×D11C2×C418yescomplemented
53C22×D44C2312yes—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11C2311yescharacteristic
57C2×C11×D8—22no—
58C2×C11×D8—22no—
59C2×C11×D8C2×C414yescomplemented
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×#4323—24no—
69C2×#4323—24no—
70C2×#4323C2×C418yescomplemented
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80D8×D11—232no—
81C2×D88C2×C414yes—
82C2×D88D414yes—
83C2×D88D414yes—
84C2×C8×D11—22no—
85C2×C8×D11—22no—
86C2×C8×D11C2×C414yescomplemented
87#66946—24no—
88#66946—42no—
89C22⋊C4×D11—48no—
90C4×D44—24no—
91C4×D44—42no—
92C11×#107—22no—
93C11×#102—42no—
94C4×C8×C11—22no—
95#66896—42no—
96C11⋊#95—22no—
97C11⋊#95D411yescharacteristic
98C11⋊#95D411yescharacteristic
99#66885—24no—
100(C2×D11)⋊C8—22no—
101#66882—22no—
102C8×Dic11—22no—
103#66873—24no—
104C22⋊C4×D8—111nomaximal, Sylow
105C24×C11—22no—
106C23×D11—22no—
107C23×D11—28no—
108C23×D11—44no—
109C23×D11—44no—
110C23×D11—44no—
111C23×D11—44no—
112C23×D11—82no—
113C23×D11—82no—
114C23×D11C2×D411yescharacteristic
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11C22×C414yes—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—28no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C22×Dic11—22no—
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132D4×D11—216no—
133D4×D11—48no—
134D4×D11—48no—
135D4×D11—48no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44C22×C414yes—
140C2×D44C2×D414yes—
141C2×D44C2×D414yes—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—44no—
147C2×C4×D11—44no—
148C2×C4×D11—44no—
149C2×C4×D11—44no—
150C2×C4×D11—82no—
151C2×C4×D11—82no—
152C2×C4×D11C22×C412yes—
153C2×C4×D11#4112yes—
154C11×D8—28no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C22×C412yes—
159C2×C8×C11C2×D412yes—
160C2×C8×C11C2×D412yes—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—82no—
165C42×C11—21no—
166C42×C11—21no—
167C22⋊Dic11—44no—
168C22⋊Dic11—82no—
169#4323—216no—
170(C2×D11)⋊C4—22no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4D814yescomplemented
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8C22×C412yes—
185D88C22⋊C4116yescomplemented
186C8×D11—28no—
187C23×D8—111no—
188C2×C4×D8—111no—
189C2×C4×D8—111no—
190D4×C22⋊C4—112no—
191#1970—111no—
192#1970D1111yescharacteristic, complemented
193#1879—112no—
194#1879—112no—
195#1808—111no—
196#1786—112no—
197C8×C22⋊C4—111no—
198C23×C11—24no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—416no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—416no—
219C22×D11—88no—
220C22×D11—88no—
221C22×D11—88no—
222C22×D11—88no—
223C22×D11—88no—
224C22×D11C4×D412yes—
225C22×D11C2×D812yes—
226C22×D11#13512yes—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—42no—
230D4×C11—42no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11C2×D812yescomplemented
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C22⋊D11—416no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11C4×D412yes—
258C2×Dic11C2×D812yescomplemented
259D44—24no—
260D44—24no—
261D44—24no—
262D44C2×C22⋊C418yescomplemented
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—88no—
268C4×D11—88no—
269C8×C11—41no—
270C8×C11C2×C22⋊C414yescomplemented
271C11⋊C8—22no—
272C11⋊C8—41no—
273C23×D4—112no—
274C22×D8—112no—
275C22×D8—118no—
276C22×D8—111no—
277C22×D8—224no—
278C22×D8—224no—
279C22×D8C2×D1111yescharacteristic
280C23×C8—111no—
281C2×C4×D4—112no—
282C2×C4×D4—112no—
283C22×C22⋊C4—222no—
284C4×D8—224no—
285C4×D8—224no—
286C2×#107—111no—
287C2×#107C2×D1111yescharacteristic, complemented
288C2×#102—112no—
289C2×#102—112no—
290C2×#102—112no—
291C2×#102C2×D1112yescomplemented
292C2×C22⋊C8—111no—
293C2×C4×C8—111no—
294C2×C4×C8C2×D1111yescharacteristic, complemented
295#390—112no—
296#390C2×D1112yescomplemented
297#386—222no—
298#386—222no—
299#380—112no—
300#379—222no—
301C4×C22⋊C4—111no—
302#340—112no—
303#336—111no—
304#336—111no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11C2×C4×D411yescharacteristic
313C22×C11D4211yescharacteristic
314C22×C11D4211yescharacteristic
315C22×C11C22×D811yescharacteristic
316C22×C11C2×#13511yescharacteristic
317C22×C11#57611yescharacteristic
318C22×C11#57611yescharacteristic
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—22no—
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—28no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—832no—
333C2×D11C4×D814yescomplemented
334C4×C11—22no—
335C4×C11—41no—
336C4×C11—82no—
337C4×C11C22×C22⋊C411yescharacteristic
338C4×C11#51811yescharacteristic
339C4×C11#54611yescharacteristic
340C4×C11#54611yescharacteristic
341Dic11—22no—
342Dic11—22no—
343Dic11—41no—
344Dic11—82no—
345C25—222no—
346C22×D4—118no—
347C22×D4—112no—
348C22×D4—224no—
349C22×D4—222no—
350C22×D4—224no—
351C22×D4—224no—
352C22×D4—442no—
353C22×D4—442no—
354C22×D4C22×D1112yes—
355C23×C4—111no—
356C23×C4—222no—
357C23×C4—222no—
358C2×D8—22no—
359C2×D8—22no—
360C2×D8—118no—
361C2×D8—114no—
362C2×D8—114no—
363C2×D8—114no—
364C2×D8—2232no—
365C2×D8—224no—
366C2×D8—224no—
367C2×D8C4×D1114yescomplemented
368C22×C8—111no—
369C22×C8—114no—
370C22×C8—111no—
371C22×C8—222no—
372C22×C8—222no—
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C4×D4—224no—
376C4×D4—224no—
377C4×D4—442no—
378C4×D4—442no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4C22×D1112yes—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—111no—
384C2×C22⋊C4—111no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—448no—
391C2×C42—111no—
392C2×C42C22×D1111yescharacteristic
393#107—22no—
394#107—222no—
395#102—42no—
396#102—224no—
397#102—224no—
398#102—442no—
399C22⋊C8—222no—
400C4×C8—22no—
401C4×C8—222no—
402#95—111no—
403#95—111no—
404#95—222no—
405C2×C11—84no—
406C2×C11D4×C22⋊C411yescharacteristic
407C2×C11C2×C4×D811yescharacteristic
408C2×C11#294811yescharacteristic
409C2×C11D4×D811yescharacteristic
410C2×C11D4×D811yescharacteristic
411C2×C11#328011yescharacteristic
412C2×C11#328011yescharacteristic
413D11—24no—
414D11—48no—
415C24—22no—
416C24—111no—
417C24—228no—
418C24—222no—
419C24—444no—
420C24—444no—
421C24—444no—
422C24—444no—
423C24—882no—
424C24—882no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—114no—
431C2×D4—114no—
432C2×D4—114no—
433C2×D4—228no—
434C2×D4—2216no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—448no—
439C2×D4—448no—
440C2×D4—448no—
441C2×D4—444no—
442C2×D4—444no—
443C2×D4C2×C4×D1114yes—
444C22×C4—22no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—111no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—222no—
455C22×C4—444no—
456C22×C4—444no—
457C22×C4—444no—
458C22×C4—444no—
459C22×C4—882no—
460C22×C4—882no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464D8—28no—
465D8—1116no—
466D8—2216no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—228no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8C2×C4×D1112yes—
478C2×C8D4×D1112yes—
479C2×C8D4×D1112yes—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C22⋊C4—44no—
485C22⋊C4—82no—
486C22⋊C4—114no—
487C22⋊C4—222no—
488C22⋊C4—444no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C22⋊C4—444no—
492C22⋊C4—882no—
493C42—21no—
494C42—21no—
495C42—221no—
496C42—221no—
497C11C22⋊C4×D811yescharacteristic, complemented, Sylow
498C23—24no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—112no—
506C23—112no—
507C23—112no—
508C23—221no—
509C23—221no—
510C23—221no—
511C23—221no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—4416no—
516C23—4416no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—888no—
522C23—888no—
523C23—888no—
524C23—888no—
525C23—888no—
526C23C2×D4×D1111yescharacteristic
527D4—24no—
528D4—24no—
529D4—42no—
530D4—42no—
531D4—118no—
532D4—224no—
533D4—224no—
534D4—224no—
535D4—4416no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—888no—
561C2×C4—888no—
562C2×C4D8×D1112yescomplemented
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4#6703711yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C2×C4#6704211yescharacteristic
569C8—41no—
570C8—222no—
571C8—441no—
572C8C22⋊C4×D1114yescomplemented
573C22—44no—
574C22—44no—
575C22—44no—
576C22—82no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—114no—
581C22—222no—
582C22—222no—
583C22—222no—
584C22—222no—
585C22—222no—
586C22—222no—
587C22—228no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—8832no—
595C22C4×D4×D1111yescharacteristic
596C22#1062314011yescharacteristic
597C22#1062324811yescharacteristic
598C22C2×D8×D1111yescharacteristic
599C22#1062328811yescharacteristic
600C22D11×#13511yescharacteristic
601C22#1062330011yescharacteristic
602C4—22no—
603C4—41no—
604C4—82no—
605C4—222no—
606C4—222no—
607C4—441no—
608C4—882no—
609C4C2×C22⋊C4×D1111yescharacteristic
610C4#1062307611yescharacteristic
611C4#1062314311yescharacteristic
612C4#1062320711yescharacteristic
613C2—84no—
614C2—224no—
615C2—448no—
616C2#1307143711yescharacteristic
617C2C4×D8×D1111yescharacteristic
618C2#1307746311yescharacteristic
619C2#1308029011yescharacteristic
620C2#1308029111yescharacteristic
621C2#1308030011yescharacteristic
622C2#1308030411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1970C2
socleC23×C11C22×D4
prime radicalC22×D8×D11C2
cosocleC22×C4×C11C24
hypercenter#1970D11
hypocenterC11C22⋊C4×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×C4×D88C2semidirect
3. C2×#10622485C2semidirect
4. #13071437C2semidirect
5. #13069483C2semidirect
6. #13068967C2semidirect
7. #13068961C2semidirect
8. #13068642C2semidirect
9. #13068545C2semidirect
10. C8×(C2×D11)⋊C4C2semidirect
11. C11×#1970C2semidirect
17. C2×D8×D11C4semidirect
20. C2×#66946C22semidirect
22. C2×C4×D44C22semidirect
23. C2×C11×#107C22semidirect
24. C2×C11×#102C22semidirect
25. C2×C4×C8×C11C22semidirect
26. C11×#390C22semidirect
27. #10622834C22semidirect
28. C2×#66896C22semidirect
29. C2×#66885C22semidirect
31. C2×#66882C22semidirect
32. C2×C8×Dic11C22semidirect
34. C2×#66873C22semidirect
41. #10622188C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
52. C2×D4×D11C2×C4semidirect
59. C2×C11×D8C2×C4semidirect
70. C2×#4323C2×C4semidirect
86. C2×C8×D11C2×C4semidirect
174. (C2×D11)⋊C4D8semidirect
185. D88C22⋊C4semidirect
192. #1970D11semidirect
239. C2×C4×C11C2×D8semidirect
258. C2×Dic11C2×D8semidirect
262. D44C2×C22⋊C4semidirect
270. C8×C11C2×C22⋊C4semidirect
287. C2×#107C2×D11semidirect
291. C2×#102C2×D11semidirect
294. C2×C4×C8C2×D11semidirect
296. #390C2×D11semidirect
333. C2×D11C4×D8semidirect
367. C2×D8C4×D11semidirect
497. C11C22⋊C4×D8semidirect
562. C2×C4D8×D11semidirect
572. C8C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×D8×D112
C2×C4×D882
C2×#106224852
#130714372
#130694832
#130689672
#130689612
#130686422
#130685452
C8×(C2×D11)⋊C42
C11×#19702
C22⋊C4×D811