Finite Group Databasebeta

← #14769242

Subgroups — #14769242

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
2C2×#10622846C212yesmaximal, complemented
3#13071565C211yesmaximal, characteristic, complemented
4#13069544C211yesmaximal, characteristic, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069045C212yesmaximal, complemented
7#13068939C212yesmaximal, complemented
8#13068621C211yesmaximal, characteristic, complemented
9#13068556C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#550—24no—
14C11×#550C418yescomplemented
15C2×C11×#127—21no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—22no—
18C2×C11×#121C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66979C2212yes—
23C23×C11⋊C8C2212yes—
24#10622846—28no—
25C2×#66899C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2211yescharacteristic
28#10622834—21no—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33#10622825C2212yes—
34C2×C22⋊(C11⋊C8)C2212yes—
35D4×C11⋊C8—24no—
36C4⋊C4×Dic11—21no—
37#10622564—22no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C2×C11×#41—42no—
50C2×C11×#41C2×C418yes—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2312yes—
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C11×#127—28no—
61C11×#127—22no—
62C11×#127C2×C414yes—
63C11×#121—24no—
64C11×#121—216no—
65C11×#121C2×C418yes—
66C4×Q8×C11—22no—
67C4×Q8×C11C2×C414yes—
68C4×D4×C11—28no—
69C4×D4×C11C2×C414yes—
70C4×D4×C11D414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80#66979—24no—
81#66979—42no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—22no—
89C22×C11⋊C8—24no—
90C22×C11⋊C8—24no—
91C22×C11⋊C8—42no—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95#66899—24no—
96#66899—22no—
97#66899D414yescomplemented
98#66896—24no—
99#66896—24no—
100#66896—42no—
101#66896—42no—
102C11⋊#95—21no—
103C11⋊#95—22no—
104C22⋊(C11⋊C8)—24no—
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#22418—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11C2×D412yes—
110C11×#41—216no—
111C11×#41—48no—
112C11×#41—48no—
113C11×#41—48no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C22×C412yes—
118C2×Q8×C11C2×D412yes—
119C2×Q8×C11#4112yes—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—81no—
136C2×D4×C11—81no—
137C2×D4×C11—82no—
138C2×D4×C11—82no—
139C2×D4×C11C22⋊C414yes—
140C2×D4×C11C22×C414yes—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—28no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11C22×C414yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4C22⋊C414yes—
162C11×C4⋊C4C22×C412yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4C22⋊C418yes—
165C42×C11—24no—
166C42×C11C22×C412yes—
167C42×C11C2×D412yes—
168C22⋊Dic11—44no—
169C22⋊Dic11—82no—
170C4⋊Dic11—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—42no—
176C4⋊Dic11—81no—
177C4⋊Dic11C2×D412yes—
178C4×Dic11—44no—
179C4×Dic11—42no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—48no—
189C2×C11⋊C8C2×D412yes—
190C2×#550D1111yescharacteristic
191C2×C8×D4—111no—
192C2×#416—112no—
193#2354—111no—
194#1982—111no—
195#1957—111no—
196#1893—112no—
197#1875—112no—
198#1803—111no—
199#1788—112no—
200C4×#103—111no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11C2×C22⋊C414yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11C4×D414yes—
220D4×C11—24no—
221D4×C11—24no—
222D4×C11—28no—
223D4×C11—416no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—48no—
227D4×C11—84no—
228D4×C11—88no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—416no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C2×C22⋊C412yes—
245C2×C4×C11C2×C22⋊C414yes—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11#13512yes—
248C2×C4×C11#13512yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—41no—
264C11⋊C8—22no—
265C11⋊C8—42no—
266C11⋊C8—41no—
267C22×#41C2×D1112yes—
268C23×C8—112no—
269#550—24no—
270#550Dic1118yescomplemented
271C2×#127—21no—
272C2×#127C2×D1111yescharacteristic
273C2×#121—22no—
274C2×#121C2×D1112yes—
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#117—112no—
279C8×D4—224no—
280C2×C4⋊C8—111no—
281#416—228no—
282C2×#103—111no—
283C2×#103—112no—
284C2×#103—111no—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102—112no—
289C2×C22⋊C8—112no—
290C2×C4×C8—111no—
291#390—221no—
292#388—222no—
293#384—111no—
294#380—112no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4—221no—
297#340—112no—
298#340—111no—
299#340—111no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11C22×C22⋊C411yescharacteristic
315C22×C11D4211yescharacteristic
316C22×C11#54611yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×#13511yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57711yescharacteristic
321C4×C11—24no—
322C4×C11—24no—
323C4×C11—22no—
324C4×C11—42no—
325C4×C11#41614yescomplemented
326C4×C11C2×C4×D411yescharacteristic
327C4×C11#51811yescharacteristic
328C4×C11D4211yescharacteristic
329C4×C11#54611yescharacteristic
330Dic11—42no—
331Dic11—82no—
332Dic11—81no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—24no—
336C2×#41—42no—
337C2×#41—42no—
338C2×#41C2×Dic1118yes—
339C22×Q8C22×D1111yescharacteristic
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4C22⋊D1111yescharacteristic
345C22×D4C22×D1112yes—
346C23×C4—22no—
347C23×C4C22×D1112yes—
348C22×C8—111no—
349C22×C8—112no—
350C22×C8—111no—
351C22×C8—224no—
352C22×C8—224no—
353C22×C8—442no—
354#127—28no—
355#127—22no—
356#127C2×Dic1114yes—
357#121—24no—
358#121—216no—
359#121C2×Dic1118yes—
360C4×Q8—22no—
361C4×Q8C2×Dic1114yes—
362C4×D4—28no—
363C4×D4C2×Dic1114yes—
364C4×D4C22⋊D1114yes—
365#117—224no—
366#117—442no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—22no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4C22⋊D1112yes—
379C2×C42—21no—
380C2×C42—222no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—222no—
384#103—114no—
385#103—224no—
386#103—222no—
387#102—224no—
388#102—224no—
389#102—442no—
390#102—442no—
391C22⋊C8—224no—
392C4×C8—222no—
393#95—221no—
394#95—222no—
395C2×C11—44no—
396C2×C11—84no—
397C2×C11D4×C22⋊C411yescharacteristic
398C2×C11C2×#41611yescharacteristic
399C2×C11#289711yescharacteristic
400C2×C11#328411yescharacteristic
401C2×C11#328711yescharacteristic
402C2×C11#330411yescharacteristic
403C2×C11#330511yescharacteristic
404C24—22no—
405C24C2×C22⋊D1112yes—
406#41—216no—
407#41—48no—
408#41—48no—
409#41—48no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8D4×D1112yes—
414C2×Q8#434112yes—
415C2×Q8C22×Dic1112yes—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—81no—
432C2×D4—81no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4C22⋊Dic1114yes—
436C2×D4C22×Dic1114yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—28no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4C22×Dic1114yes—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1114yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—222no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—222no—
462C2×C8—221no—
463C2×C8—222no—
464C2×C8—448no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—112no—
468C4⋊C4—221no—
469C4⋊C4—222no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—222no—
473C4⋊C4—442no—
474C4⋊C4—881no—
475C4⋊C4C22⋊Dic1114yes—
476C4⋊C4C22×Dic1112yes—
477C22⋊C4—28no—
478C22⋊C4—444no—
479C22⋊C4—882no—
480C22⋊C4C22⋊Dic1118yes—
481C42—24no—
482C42—444no—
483C42—442no—
484C42C22×Dic1112yes—
485C42C2×C22⋊D1112yes—
486C11#2241811yescharacteristic, complemented, Sylow
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23C2×C22⋊Dic1114yes—
501C23C22×C22⋊D1111yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—22no—
505Q8D4×Dic1114yes—
506D4—24no—
507D4—24no—
508D4—28no—
509D4—416no—
510D4—42no—
511D4—42no—
512D4—48no—
513D4—84no—
514D4—88no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—416no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—222no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—442no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—442no—
537C2×C4—441no—
538C2×C4—442no—
539C2×C4#6700312yes—
540C2×C4#6700312yes—
541C2×C4C2×C22⋊Dic1112yes—
542C2×C4C2×C22⋊Dic1114yes—
543C2×C4C2×C22⋊Dic1112yes—
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C2×#434111yescharacteristic
546C2×C4#6703711yescharacteristic
547C2×C4#6703711yescharacteristic
548C2×C4C23×Dic1111yescharacteristic
549C2×C4C22×C22⋊D1111yescharacteristic
550C8—222no—
551C8—442no—
552C8—441no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—44no—
561C22—44no—
562C22—44no—
563C22—82no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22D4×C22⋊D1111yescharacteristic
568C22#1062333711yescharacteristic
569C22C2×#6700311yescharacteristic
570C22C2×#6700311yescharacteristic
571C22#1062336611yescharacteristic
572C22#1062336711yescharacteristic
573C22C22×C22⋊Dic1111yescharacteristic
574C4—24no—
575C4—24no—
576C4—22no—
577C4—42no—
578C4—442no—
579C4—882no—
580C4—881no—
581C4#1062284614yescomplemented
582C4C2×D4×Dic1111yescharacteristic
583C4#1062332911yescharacteristic
584C4D4×C22⋊D1111yescharacteristic
585C4#1062333711yescharacteristic
586C2—44no—
587C2—84no—
588C2D4×C22⋊Dic1111yescharacteristic
589C2C2×#1062284611yescharacteristic
590C2#1307714211yescharacteristic
591C2#1308034611yescharacteristic
592C2#1308037211yescharacteristic
593C2#1308055511yescharacteristic
594C2#1308056611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#550D11
hypocenterC11#22418
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×D4×C11⋊C8C2semidirect
2. C2×#10622846C2semidirect
3. #13071565C2semidirect
4. #13069544C2semidirect
5. #13069423C2semidirect
6. #13069045C2semidirect
7. #13068939C2semidirect
8. #13068621C2semidirect
9. #13068556C2semidirect
10. C4×#66899C2semidirect
14. C11×#550C4semidirect
97. #66899D4semidirect
270. #550Dic11semidirect
325. C4×C11#416semidirect
486. C11#22418semidirect
581. C4#10622846semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C11⋊C82
C2×#106228462
#130715652
#130695442
#130694232
#130690452
#130689392
#130686212
#130685562
C4×#668992
C2×C11×#5502
#2241811