Finite Group Databasebeta

← #14764901

Subgroups — #14764901

Order 2816.

1308 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
1C2×#10622830C211yesmaximal, characteristic
2#13071122C211yesmaximal, characteristic, complemented
3C2×#10622834C211yesmaximal, characteristic, complemented
4#13069479C212yesmaximal, complemented
5#13069296C212yesmaximal, complemented
6#13069239C212yesmaximal, complemented
7#13068961C212yesmaximal, complemented
8#13068931C211yesmaximal, characteristic, complemented
9#13068803C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C22⋊Dic11—21no—
14C22×C22⋊Dic11—21no—
15C22×#4323C2212yes—
16C2×#66983C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×#66946C2211yescharacteristic, complemented
20C2×(C22⋊D11)⋊C4—21no—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C11×C22⋊C8C2211yescharacteristic
24C11×#380C2211yescharacteristic
25#10622834—21no—
26#10622834—21no—
27#10622834C2212yes—
28#10622834C2212yes—
29#10622830C418yescomplemented
30C2×#66896C2212yes—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66885C2212yescomplemented
33C2×C8×Dic11C2212yescomplemented
34#10622601C2211yescharacteristic, complemented
35C4⋊C4×Dic11C2211yescharacteristic, complemented
36#10622586C2211yescharacteristic, complemented
37C2×#66871C2212yescomplemented
38#10622571—21no—
39#10622282—21no—
40#10622279—21no—
41#10622189C2212yescomplemented
42#10622188C2212yescomplemented
43#10622167C2212yescomplemented
44C25×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—42no—
48C22×D4×C11—42no—
49C22×D4×C11C2×C414yescomplemented
50C22×D4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—21no—
53C23×Dic11—21no—
54C23×Dic11D411yescharacteristic
55C23×Dic11D411yescharacteristic
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×C8×C11C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—44no—
67C2×C22⋊Dic11—44no—
68C2×#4323—42no—
69C2×#4323—42no—
70C2×#4323C2×C418yescomplemented
71#66983—22no—
72#66983C2×C414yes—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—42no—
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—42no—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89#66946—42no—
90(C22⋊D11)⋊C4—44no—
91C11×#102—42no—
92C11×#102—42no—
93C11×C22⋊C8—22no—
94C11×#95—21no—
95#66896C2×C418yescomplemented
96C11⋊#95—21no—
97C11⋊#95—21no—
98C22⋊(C11⋊C8)C2×C414yescomplemented
99#66885—42no—
100C8×Dic11—42no—
101#66871—42no—
102#22040—111nomaximal, Sylow
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11—42no—
111C24×C11C2×D411yescharacteristic
112C23×D11—21no—
113C2×D4×C11—24no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—48no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—48no—
123C2×D4×C11C22×C414yes—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—24no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—42no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11—41no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11D814yescomplemented
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—21no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44C22×C412yes—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C22⋊C4—42no—
163C22⋊Dic11—44no—
164C22⋊Dic11—44no—
165C22⋊Dic11—44no—
166C22⋊Dic11—44no—
167#4323—48no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—42no—
176C4⋊Dic11C22×C412yes—
177Dic11⋊C4—42no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—41no—
181C4×Dic11—41no—
182C4×Dic11—42no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8C22×C414yes—
186C2×#447—111no—
187C4×#121—111no—
188C2×#390—111no—
189#1970—112no—
190#1934—112no—
191#1925—112no—
192#1879—112no—
193#1874—111no—
194#1852—111no—
195#1786D1111yescharacteristic, complemented
196C4×C22⋊C8—111no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—24no—
202C23×C11—48no—
203C23×C11—48no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—48no—
211C23×C11—84no—
212C23×C11—84no—
213C23×C11—84no—
214C23×C11—84no—
215C23×C11C4×D412yes—
216C23×C11C2×D812yes—
217C23×C11#13512yes—
218C23×C11C22×D411yescharacteristic
219C22×D11—22no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—48no—
229D4×C11—42no—
230D4×C11—42no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
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×C11C4×D412yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C11H(5,𝔽2)12yes—
246C22⋊D11—48no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—84no—
265C2×Dic11C2×D812yes—
266C2×Dic11C2×D812yes—
267C2×Dic11AGL(1,ℤ/8)12yes—
268D44—24no—
269D44—42no—
270C4×D11—84no—
271C8×C11—42no—
272C11⋊C8—24no—
273C23×D4C2×D1111yescharacteristic
274C22×D8—112no—
275C2×#121—111no—
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C22×C4⋊C4—111no—
279C22×C22⋊C4—221no—
280C22×C22⋊C4—221no—
281C22×C42—111no—
282#447—118no—
283C2×#107—112no—
284C2×#102—112no—
285C2×#102—112no—
286C2×#102C2×D1112yes—
287C2×#102C2×D1112yes—
288C2×C22⋊C8—111no—
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×C4×C8—112no—
291#390—112no—
292#390—112no—
293#390—111no—
294#390—221no—
295#390—221no—
296#389—111no—
297#388—221no—
298#386—221no—
299#380C2×D1111yescharacteristic
300C4×C4⋊C4—111no—
301C4×C22⋊C4—221no—
302#340—112no—
303#340—112no—
304#336—112no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—816no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11C4×D814yes—
320C22×C11C2×C4×D411yescharacteristic
321C22×C11#53411yescharacteristic
322C22×C11#53511yescharacteristic
323C22×C11C22×D811yescharacteristic
324C22×C11C2×#13511yescharacteristic
325C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C11#57511yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—22no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#51812yes—
338C4×C11#53812yes—
339Dic11—22no—
340Dic11—22no—
341Dic11—22no—
342Dic11—41no—
343Dic11—42no—
344Dic11—82no—
345C25—21no—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—111no—
351C22×D4—221no—
352C22×D4C4×D1114yescomplemented
353C22×D4C22×D1112yes—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—221no—
357C23×C4—221no—
358C23×C4C22×D1111yescharacteristic
359C2×D8—118no—
360C2×D8—442no—
361C2×D8—442no—
362C22×C8—112no—
363C22×C8C22×D1112yes—
364#121—114no—
365#121—222no—
366C4×D4—442no—
367C4×D4—444no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—442no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—444no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—221no—
391C2×C42—442no—
392#107—442no—
393#102—42no—
394#102—42no—
395#102—118no—
396#102—442no—
397C22⋊C8—22no—
398C22⋊C8—114no—
399C4×C8—442no—
400#95—21no—
401#95—221no—
402#95—221no—
403C2×C11—24no—
404C2×C11—84no—
405C2×C11#232111yescharacteristic
406C2×C11C2×C4×D811yescharacteristic
407C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C11#318611yescharacteristic
409C2×C11#318811yescharacteristic
410C2×C11#320511yescharacteristic
411C2×C11#321111yescharacteristic
412D11—82no—
413C24—24no—
414C24—22no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—221no—
422C24D4×D1111yescharacteristic
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—48no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—48no—
433C2×D4—112no—
434C2×D4—224no—
435C2×D4—221no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—442no—
439C2×D4—442no—
440C2×D4C2×C4×D1114yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—114no—
449C22×C4—111no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4C2×C4×D1112yes—
464C22×C4D4×D1111yescharacteristic
465C22×C4#434112yes—
466C22×C4C23×D1111yescharacteristic
467D8—448no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—114no—
472C2×C8—222no—
473C2×C8—222no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—112no—
477C4⋊C4—221no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—442no—
481C4⋊C4—442no—
482C22⋊C4—42no—
483C22⋊C4—224no—
484C22⋊C4—442no—
485C22⋊C4—442no—
486C22⋊C4—442no—
487C22⋊C4—444no—
488C22⋊C4—444no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C42—222no—
492C42—222no—
493C42—441no—
494C42—441no—
495C42—442no—
496C11#2204011yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—24no—
502C23—48no—
503C23—48no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—48no—
511C23—84no—
512C23—84no—
513C23—84no—
514C23—84no—
515C23—222no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23(C22⋊D11)⋊C412yes—
523C23D8×D1112yes—
524C23#6696912yes—
525C23C2×D4×D1111yescharacteristic
526D4—24no—
527D4—24no—
528D4—48no—
529D4—42no—
530D4—42no—
531D4—224no—
532D4—448no—
533D4—442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—222no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—444no—
558C2×C4—444no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—884no—
565C2×C4—884no—
566C2×C4(C22⋊D11)⋊C412yes—
567C2×C4C22×C4×D1111yescharacteristic
568C2×C4C2×#434111yescharacteristic
569C2×C4#6703712yes—
570C2×C4#6703712yes—
571C8—42no—
572C8—224no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—816no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—82no—
587C22—442no—
588C22—442no—
589C22—442no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22#1062236914yes—
595C22C2×(C22⋊D11)⋊C411yescharacteristic
596C22#1062312011yescharacteristic
597C22#1062312311yescharacteristic
598C22C2×D8×D1111yescharacteristic
599C22C2×#6696911yescharacteristic
600C22D11×AGL(1,ℤ/8)11yescharacteristic
601C22#1062330411yescharacteristic
602C4—22no—
603C4—81no—
604C4—81no—
605C4—222no—
606C4—222no—
607C4—222no—
608C4—441no—
609C4—442no—
610C4—882no—
611C4#1062301712yes—
612C4#1062312412yes—
613C2—24no—
614C2—84no—
615C2—882no—
616C2#1307127111yescharacteristic
617C2C2×#1062236911yescharacteristic
618C2#1307742011yescharacteristic
619C2#1307936511yescharacteristic
620C2#1307938411yescharacteristic
621C2#1307953211yescharacteristic
622C2#1307958411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
cosocleC22×C4×C11C24
hypercenter#1786D11
hypocenterC11#22040
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #13071122C2semidirect
3. C2×#10622834C2semidirect
4. #13069479C2semidirect
5. #13069296C2semidirect
6. #13069239C2semidirect
7. #13068961C2semidirect
8. #13068931C2semidirect
9. #13068803C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C11×#1786C2semidirect
19. C2×#66946C22semidirect
29. #10622830C4semidirect
32. C2×#66885C22semidirect
33. C2×C8×Dic11C22semidirect
34. #10622601C22semidirect
35. C4⋊C4×Dic11C22semidirect
36. #10622586C22semidirect
37. C2×#66871C22semidirect
41. #10622189C22semidirect
42. #10622188C22semidirect
43. #10622167C22semidirect
49. C22×D4×C11C2×C4semidirect
70. C2×#4323C2×C4semidirect
95. #66896C2×C4semidirect
98. C22⋊(C11⋊C8)C2×C4semidirect
145. C22×Dic11D8semidirect
195. #1786D11semidirect
352. C22×D4C4×D11semidirect
496. C11#22040semidirect

Maximal subgroups

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

subgroupindex
C2×#106228302
#130711222
C2×#106228342
#130694792
#130692962
#130692392
#130689612
#130689312
#130688032
C22⋊C8×Dic112
C11×#17862
#2204011