Finite Group Databasebeta

← #14764907

Subgroups — #14764907

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
1#121×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622834C211yesmaximal, characteristic, complemented
3#13069483C212yesmaximal, complemented
4#13069301C212yesmaximal, complemented
5#13069238C212yesmaximal, complemented
6#13068966C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic, complemented
8#13068806C211yesmaximal, characteristic, complemented
9#13068547C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#447C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2212yes—
14C2×C11×#121C2211yescharacteristic
15C22×C22⋊Dic11—21no—
16C22×C22⋊Dic11—21no—
17C2×D4×Dic11—21no—
18C2×D4×Dic11C2211yescharacteristic, complemented
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C11×#447C418yescomplemented
22C2×C11×#102C2212yes—
23C2×C11×C22⋊C8C2211yescharacteristic
24#10622834—21no—
25#10622834—21no—
26#10622834C2212yes—
27#10622834C2212yes—
28#10622834C2211yescharacteristic, complemented
29#10622833—21no—
30C2×#66896C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yescomplemented
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66882C2212yescomplemented
36C2×C8×Dic11C2212yescomplemented
37#10622598C2211yescharacteristic, complemented
38C4⋊C4×Dic11C2211yescharacteristic, complemented
39#10622564—21no—
40C22⋊C4×Dic11—21no—
41#10622189C2212yescomplemented
42#10622188C2212yescomplemented
43#10622167C2212yescomplemented
44C25×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11—42no—
50C22×D4×C11C2×C414yescomplemented
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C23×Dic11—21no—
56C23×Dic11D411yescharacteristic
57C23×Dic11D411yescharacteristic
58C2×C11×D8—42no—
59C2×C11×D8—42no—
60C2×C11×D8C2×C418yescomplemented
61C22×C8×C11C2312yes—
62C11×#121—22no—
63C11×#121C2×C414yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—44no—
75C2×C22⋊Dic11—44no—
76D4×Dic11—42no—
77D4×Dic11—44no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—42no—
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—21no—
85C2×C4×Dic11—42no—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2312yes—
91C11×#102C2×C418yescomplemented
92C11×C22⋊C8C2×C414yescomplemented
93#66896—42no—
94#66896—42no—
95#66896—42no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C22⋊(C11⋊C8)—22no—
100#66882—42no—
101C8×Dic11—42no—
102#22040—111nomaximal, Sylow
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—21no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11C2×D411yescharacteristic
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—48no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—48no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11C22×C414yes—
130C2×D4×C11C22×C412yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—41no—
144C22×Dic11—41no—
145C22×Dic11—41no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11D814yescomplemented
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C11×D8—48no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11C22×C414yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C22×C412yes—
163C11×C22⋊C4—24no—
164C22⋊Dic11—42no—
165C22⋊Dic11—44no—
166C22⋊Dic11—42no—
167C22⋊Dic11—44no—
168C22⋊Dic11—44no—
169C22⋊Dic11—42no—
170C22⋊Dic11—44no—
171C22⋊Dic11—42no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—42no—
177C4⋊Dic11—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⋊C8—22no—
186C2×#447D1111yescharacteristic
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#1786—111no—
196C4×C22⋊C8—111no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—42no—
217C23×C11—48no—
218C23×C11—84no—
219C23×C11—84no—
220C23×C11—84no—
221C23×C11—84no—
222C23×C11C4×D412yes—
223C23×C11C2×D812yes—
224C23×C11#13512yes—
225C23×C11C22×D411yescharacteristic
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—48no—
230D4×C11—48no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
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—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—84no—
267C2×Dic11—84no—
268C2×Dic11C2×D812yes—
269C2×Dic11C2×D812yes—
270C2×Dic11AGL(1,ℤ/8)12yes—
271C8×C11—24no—
272C11⋊C8—42no—
273C23×D4C2×D1111yescharacteristic
274C22×D8C2×D1112yes—
275C2×#121C2×D1111yescharacteristic
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C22×C4⋊C4—111no—
279C22×C22⋊C4—221no—
280C22×C22⋊C4—221no—
281C22×C42—111no—
282#447Dic1118yescomplemented
283C2×#107—112no—
284C2×#102—112no—
285C2×#102—112no—
286C2×#102—112no—
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#380—111no—
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—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—42no—
316C22×C11—44no—
317C22×C11—816no—
318C22×C11—82no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—82no—
322C22×C11—81no—
323C22×C11—82no—
324C22×C11—81no—
325C22×C11—82no—
326C22×C11C4×D814yes—
327C22×C11C2×C4×D411yescharacteristic
328C22×C11#53411yescharacteristic
329C22×C11#53511yescharacteristic
330C22×C11C22×D811yescharacteristic
331C22×C11C2×#13511yescharacteristic
332C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C11#57511yescharacteristic
334C4×C11—22no—
335C4×C11—42no—
336C4×C11#51812yes—
337C4×C11#53812yes—
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—41no—
342Dic11—81no—
343Dic11—81no—
344Dic11—82no—
345C25—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—22no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4C2×Dic1114yescomplemented
352C22×D4C22×D1111yescharacteristic
353C22×D4C22×D1112yes—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—221no—
357C23×C4—221no—
358C23×C4C22×D1111yescharacteristic
359C2×D8—42no—
360C2×D8—42no—
361C2×D8C2×Dic1118yescomplemented
362C22×C8—112no—
363C22×C8C22×D1112yes—
364#121—22no—
365#121C2×Dic1114yes—
366C4×D4—442no—
367C4×D4—444no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—442no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
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—442no—
394#102—442no—
395#102—442no—
396#102C2×Dic1118yescomplemented
397C22⋊C8—222no—
398C22⋊C8C2×Dic1114yescomplemented
399C4×C8—442no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11—24no—
404C2×C11—82no—
405C2×C11—84no—
406C2×C11#232111yescharacteristic
407C2×C11C2×C4×D811yescharacteristic
408C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
409C2×C11#318611yescharacteristic
410C2×C11#318811yescharacteristic
411C2×C11#320511yescharacteristic
412C2×C11#321111yescharacteristic
413C24—24no—
414C24—21no—
415C24—22no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24D4×D1111yescharacteristic
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—48no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—48no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4C22×Dic1114yes—
440C2×D4C22×Dic1112yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—114no—
448C22×C4—111no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—442no—
455C22×C4—441no—
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4D4×D1111yescharacteristic
464C22×C4#434112yes—
465C22×C4C22×Dic1112yes—
466C22×C4C23×D1111yescharacteristic
467D8—48no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—222no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8C22×Dic1114yes—
474C4⋊C4—21no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C4⋊C4—442no—
480C4⋊C4—442no—
481C4⋊C4C22×Dic1112yes—
482C22⋊C4—24no—
483C22⋊C4—444no—
484C22⋊C4—444no—
485C22⋊C4—444no—
486C22⋊C4—442no—
487C22⋊C4—442no—
488C22⋊C4—444no—
489C22⋊C4—442no—
490C22⋊C4—442no—
491C42—222no—
492C42—222no—
493C42—441no—
494C42—441no—
495C42—442no—
496C11#2204011yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—22no—
502C23—24no—
503C23—48no—
504C23—48no—
505C23—48no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23D8×D1112yes—
523C23#6696512yes—
524C23D4×Dic1112yes—
525C23C2×D4×D1111yescharacteristic
526D4—24no—
527D4—24no—
528D4—24no—
529D4—48no—
530D4—48no—
531D4—42no—
532D4—42no—
533D4—42no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—441no—
556C2×C4—442no—
557C2×C4—441no—
558C2×C4—442no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—442no—
563C2×C4—441no—
564C2×C4—884no—
565C2×C4—884no—
566C2×C4D4×Dic1112yes—
567C2×C4C2×#434111yescharacteristic
568C2×C4#6703712yes—
569C2×C4#6703712yes—
570C2×C4C23×Dic1111yescharacteristic
571C8—24no—
572C8—442no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—44no—
581C22—44no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—816no—
586C22—82no—
587C22—81no—
588C22—81no—
589C22—82no—
590C22—82no—
591C22—81no—
592C22—82no—
593C22—81no—
594C22D8×Dic1114yes—
595C22#1062312011yescharacteristic
596C22#1062312311yescharacteristic
597C22C2×D8×D1111yescharacteristic
598C22C2×#6696511yescharacteristic
599C22D11×AGL(1,ℤ/8)11yescharacteristic
600C22#1062330411yescharacteristic
601C22C2×D4×Dic1111yescharacteristic
602C4—22no—
603C4—42no—
604C4—222no—
605C4—222no—
606C4—222no—
607C4—441no—
608C4—881no—
609C4—882no—
610C4—881no—
611C4#1062312412yes—
612C4#1062332912yes—
613C2—24no—
614C2—84no—
615C2—82no—
616C2#1307127711yescharacteristic
617C2C2×D8×Dic1111yescharacteristic
618C2AGL(1,ℤ/8)×Dic1111yescharacteristic
619C2#1307936511yescharacteristic
620C2#1307937811yescharacteristic
621C2#1307953211yescharacteristic
622C2#1307957811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#447C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#447D11
hypocenterC11#22040
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #121×Dic11C2semidirect
2. C2×#10622834C2semidirect
3. #13069483C2semidirect
4. #13069301C2semidirect
5. #13069238C2semidirect
6. #13068966C2semidirect
7. #13068934C2semidirect
8. #13068806C2semidirect
9. #13068547C2semidirect
10. C22⋊C8×Dic11C2semidirect
18. C2×D4×Dic11C22semidirect
21. C11×#447C4semidirect
28. #10622834C22semidirect
32. C2×#66896C22semidirect
35. C2×#66882C22semidirect
36. C2×C8×Dic11C22semidirect
37. #10622598C22semidirect
38. C4⋊C4×Dic11C22semidirect
41. #10622189C22semidirect
42. #10622188C22semidirect
43. #10622167C22semidirect
50. C22×D4×C11C2×C4semidirect
60. C2×C11×D8C2×C4semidirect
91. C11×#102C2×C4semidirect
92. C11×C22⋊C8C2×C4semidirect
152. C22×Dic11D8semidirect
282. #447Dic11semidirect
351. C22×D4C2×Dic11semidirect
361. C2×D8C2×Dic11semidirect
396. #102C2×Dic11semidirect
398. C22⋊C8C2×Dic11semidirect
496. C11#22040semidirect

Maximal subgroups

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

subgroupindex
#121×Dic112
C2×#106228342
#130694832
#130693012
#130692382
#130689662
#130689342
#130688062
#130685472
C22⋊C8×Dic112
C2×C11×#4472
#2204011