Finite Group Databasebeta

← #14764980

Subgroups — #14764980

Order 2816.

1296 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×#10622345C211yesmaximal, characteristic
2C4×#66983C211yesmaximal, characteristic, complemented
3C2×#10622552C211yesmaximal, characteristic, complemented
4#13069492C212yesmaximal, complemented
5#13069313C212yesmaximal, complemented
6#13069244C212yesmaximal, complemented
7#13068963C212yesmaximal, complemented
8#13068931C211yesmaximal, characteristic, complemented
9#13068811C211yesmaximal, characteristic, complemented
10#13068548C211yesmaximal, characteristic, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C2×C4×C22⋊D11—21no—
16C22×(C2×D11)⋊C4—21no—
17C22×(C2×D11)⋊C4—21no—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×D88C2212yes—
20C2×C4×D44C2211yescharacteristic, complemented
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×#97C2212yescomplemented
24#10622826—21no—
25#10622825C2211yescharacteristic
26C2×#66885C2212yes—
27C2×#66885C2212yes—
28C2×#66885C2212yes—
29C2×#66885C2212yescomplemented
30C2×#66881C2212yescomplemented
31#10622553—21no—
32#10622552—21no—
33#10622552—21no—
34#10622552C2212yes—
35#10622552C2212yes—
36#10622552C2211yescharacteristic, complemented
37C4×(C2×D11)⋊C4—21no—
38C4×C4⋊Dic11C2211yescharacteristic, complemented
39#10622541C2211yescharacteristic, complemented
40#10622345C418yescomplemented
41C11×#336C2212yescomplemented
42#10622189C2212yescomplemented
43#10622189C2212yescomplemented
44C24×D11—21no—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C22×D44—21no—
51C22×D44—22no—
52C22×D44—42no—
53C22×D44—42no—
54C22×D44C2×C414yescomplemented
55C22×D44C2312yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2312yes—
60C2×C42×C11—42no—
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—21no—
66#66983—22no—
67#66983C2×C414yes—
68C4×C22⋊D11—44no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—44no—
78C2×(C2×D11)⋊C4—44no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—42no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×D88—42no—
88C2×D88—42no—
89C2×D88C2×C418yescomplemented
90C4×D44—42no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8C2×C414yescomplemented
93C11×#97—42no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97#66885—42no—
98#66885—42no—
99#66885—42no—
100#66885C2×C418yescomplemented
101#66881—42no—
102#22046—111nomaximal, Sylow
103C24×C11C2×D411yescharacteristic
104C23×D11—24no—
105C23×D11—21no—
106C23×D11—22no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—42no—
111C23×D11—42no—
112C23×D11—42no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4112yes—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—24no—
130C2×C22⋊D11—42no—
131C2×C22⋊D11—42no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C2×D44—24no—
140C2×D44—21no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—48no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—48no—
152C2×D44C22×C414yes—
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—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11C22×C414yes—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—41no—
166C42×C11—41no—
167C22⋊Dic11—42no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—44no—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—42no—
182C4⋊Dic11C22×C412yes—
183Dic11⋊C4—42no—
184C4×Dic11—42no—
185D88—48no—
186C2×#447—111no—
187C4×#121—111no—
188C2×#390—111no—
189#1972—112no—
190#1936—112no—
191#1926—112no—
192#1879—112no—
193#1874—111no—
194#1853—111no—
195#1786—111no—
196#1749D1111yescharacteristic, complemented
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11C4×D412yes—
202C23×C11AGL(1,ℤ/8)12yes—
203C23×C11AGL(1,ℤ/8)12yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—24no—
207C22×D11—48no—
208C22×D11—48no—
209C22×D11—41no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—41no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—42no—
219C22×D11—41no—
220C22×D11—42no—
221C22×D11—48no—
222C22×D11—84no—
223C22×D11—84no—
224C22×D11—84no—
225C22×D11—84no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11C4×D412yes—
244C2×C4×C11AGL(1,ℤ/8)12yes—
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)12yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C22⋊D11—48no—
250C2×Dic11—22no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—84no—
263D44—24no—
264D44—24no—
265D44—24no—
266D44—48no—
267D44—42no—
268D44—42no—
269D44—42no—
270C4×D11—84no—
271C8×C11—24no—
272C8×C11—42no—
273C23×D4—111no—
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×C42C2×D1111yescharacteristic
282#447—118no—
283C2×#106—112no—
284C2×#102—112no—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102—112no—
288C2×C22⋊C8C2×D1111yescharacteristic
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×#97C2×D1112yescomplemented
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#336C2×D1112yescomplemented
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11#44214yes—
312C22×C11C2×C4×D411yescharacteristic
313C22×C11#53411yescharacteristic
314C22×C11#53511yescharacteristic
315C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11#57511yescharacteristic
319C2×D11—44no—
320C2×D11—42no—
321C2×D11—44no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—44no—
325C2×D11—816no—
326C2×D11—82no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—82no—
330C2×D11—81no—
331C2×D11—82no—
332C2×D11—81no—
333C2×D11—82no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11#51812yes—
340C4×C11#53812yes—
341Dic11—42no—
342Dic11—81no—
343Dic11—81no—
344Dic11—82no—
345C25—221no—
346C22×D4—114no—
347C22×D4—111no—
348C22×D4—112no—
349C22×D4—221no—
350C22×D4—221no—
351C22×D4—222no—
352C22×D4—442no—
353C22×D4—442no—
354C23×C4—221no—
355C23×C4—221no—
356C23×C4D4411yescharacteristic
357C23×C4D4411yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C2×D8—118no—
360C2×D8—442no—
361C2×D8—442no—
362C22×C8C22×D1112yes—
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—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—442no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—444no—
386C2×C42—42no—
387C2×C42—221no—
388C2×C42D4411yescharacteristic
389C2×C42D4411yescharacteristic
390C2×C42C22×D1111yescharacteristic
391C2×C42C22×D1111yescharacteristic
392#106—442no—
393#102—118no—
394#102—442no—
395#102—442no—
396#102—442no—
397C22⋊C8—22no—
398C22⋊C8C4×D1114yescomplemented
399#97—42no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11—24no—
404C2×C11#232111yescharacteristic
405C2×C11C2×#44211yescharacteristic
406C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
407C2×C11#319211yescharacteristic
408C2×C11#319411yescharacteristic
409C2×C11#321311yescharacteristic
410C2×C11#321711yescharacteristic
411D11—82no—
412D11—84no—
413C24—224no—
414C24—221no—
415C24—222no—
416C24—442no—
417C24—442no—
418C24—442no—
419C24—442no—
420C24—442no—
421C24—442no—
422C24C2×D4411yescharacteristic
423C2×D4—114no—
424C2×D4—112no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—221no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—448no—
436C2×D4—442no—
437C2×D4—442no—
438C2×D4—448no—
439C2×D4—442no—
440C2×D4—442no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4C2×C4×D1112yes—
460C22×C4C2×D4411yescharacteristic
461C22×C4C2×D4411yescharacteristic
462C22×C4C2×D4411yescharacteristic
463C22×C4C2×D4411yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4#433912yes—
466C22×C4C23×D1111yescharacteristic
467D8—448no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8C2×C4×D1114yes—
474C4⋊C4—112no—
475C4⋊C4—221no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—442no—
481C4⋊C4—442no—
482C22⋊C4—224no—
483C22⋊C4—444no—
484C22⋊C4—444no—
485C22⋊C4—444no—
486C22⋊C4—442no—
487C22⋊C4—442no—
488C22⋊C4—442no—
489C22⋊C4—442no—
490C22⋊C4—444no—
491C42—22no—
492C42—22no—
493C42—41no—
494C42—41no—
495C42—442no—
496C11#2204611yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—222no—
502C23—224no—
503C23—448no—
504C23—448no—
505C23—442no—
506C23—442no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23—442no—
511C23—441no—
512C23—442no—
513C23—441no—
514C23—442no—
515C23—442no—
516C23—441no—
517C23—448no—
518C23—884no—
519C23—884no—
520C23—884no—
521C23—884no—
522C23C4×D4412yes—
523C23#6696112yes—
524C23#6696112yes—
525C23C22×D4411yescharacteristic
526D4—224no—
527D4—224no—
528D4—224no—
529D4—448no—
530D4—448no—
531D4—442no—
532D4—442no—
533D4—442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—222no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—442no—
562C2×C4—441no—
563C2×C4—884no—
564C2×C4—884no—
565C2×C4C4×D4412yes—
566C2×C4#6696112yes—
567C2×C4C22×C4×D1111yescharacteristic
568C2×C4C2×#433911yescharacteristic
569C2×C4#6703712yes—
570C2×C4#6704212yes—
571C8—24no—
572C8—42no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—442no—
580C22—444no—
581C22—444no—
582C22—442no—
583C22—444no—
584C22—442no—
585C22—8816no—
586C22—882no—
587C22—881no—
588C22—882no—
589C22—881no—
590C22—881no—
591C22—882no—
592C22—882no—
593C22—881no—
594C22#1062232414yes—
595C22C2×C4×D4411yescharacteristic
596C22#1062302411yescharacteristic
597C22#1062305611yescharacteristic
598C22C2×#6696111yescharacteristic
599C22C2×#6696111yescharacteristic
600C22C2×#6696111yescharacteristic
601C22#1062327911yescharacteristic
602C4—22no—
603C4—22no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—442no—
608C4—881no—
609C4—882no—
610C4—881no—
611C4#1062307612yes—
612C4#1062309112yes—
613C2—24no—
614C2—884no—
615C2—882no—
616C2#1307127611yescharacteristic
617C2C2×#1062232411yescharacteristic
618C2C4×#6696111yescharacteristic
619C2#1307941611yescharacteristic
620C2#1307943211yescharacteristic
621C2#1307960511yescharacteristic
622C2#1307963611yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1749C2
socleC23×C11C22×D4
prime radicalC2×#10622345C2
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C4×#66983C2semidirect
3. C2×#10622552C2semidirect
4. #13069492C2semidirect
5. #13069313C2semidirect
6. #13069244C2semidirect
7. #13068963C2semidirect
8. #13068931C2semidirect
9. #13068811C2semidirect
10. #13068548C2semidirect
11. C11×#1749C2semidirect
20. C2×C4×D44C22semidirect
23. C2×C11×#97C22semidirect
29. C2×#66885C22semidirect
30. C2×#66881C22semidirect
36. #10622552C22semidirect
38. C4×C4⋊Dic11C22semidirect
39. #10622541C22semidirect
40. #10622345C4semidirect
41. C11×#336C22semidirect
42. #10622189C22semidirect
43. #10622189C22semidirect
54. C22×D44C2×C4semidirect
89. C2×D88C2×C4semidirect
92. C11×C22⋊C8C2×C4semidirect
100. #66885C2×C4semidirect
196. #1749D11semidirect
290. C2×#97C2×D11semidirect
304. #336C2×D11semidirect
398. C22⋊C8C4×D11semidirect
496. C11#22046semidirect

Maximal subgroups

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

subgroupindex
C2×#106223452
C4×#669832
C2×#106225522
#130694922
#130693132
#130692442
#130689632
#130689312
#130688112
#130685482
C11×#17492
#2204611