Finite Group Databasebeta

← #14926684

Subgroups — #14926684

Order 2816.

2322 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C212yesmaximal, complemented
2#13076947C212yesmaximal, complemented
3#13076917C212yesmaximal, complemented
4#13074730C211yesmaximal, characteristic, complemented
5#13074718C211yesmaximal, characteristic
6#13074358C212yesmaximal, complemented
7#13073694C214yesmaximal, complemented
8#13073670C214yesmaximal, complemented
9#13073289C214yesmaximal, complemented
10#13072583C214yesmaximal, complemented
11#13071319C212yesmaximal, complemented
12C4×#66983C212yesmaximal, complemented
13C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66983C2212yes—
20C2×#66983C2212yes—
21C2×#66983C2212yes—
22C2×#66982C2214yes—
23C2×C4×C22⋊D11C2214yes—
24C2×#66977C2212yes—
25#10623046—216no—
26C2×#66951C2214yes—
27C2×#66949C2214yes—
28C2×#66947C2214yes—
29C2×#66942C2214yes—
30C2×#66928C2212yes—
31C2×C4×D44C2212yes—
32C4×C11×C4⋊C4C2214yes—
33C4×C11×C4⋊C4C2214yes—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622826C2214yes—
37#10622826C2214yes—
38#10622825C2212yes—
39#10622825C2212yes—
40#10622607C2214yes—
41#10622607C2214yes—
42#10622604C2214yes—
43#10622596C2214yes—
44#10622553C2214yes—
45#10622553C2214yes—
46#10622553C2214yes—
47#10622553C2214yes—
48#10622553C2214yes—
49#10622552C2212yes—
50#10622552C2212yes—
51#10622552C2212yes—
52#10622552C2212yes—
53C4×(C2×D11)⋊C4C2214yes—
54#10622549C2212yes—
55C4×C4⋊Dic11C2212yes—
56#10622542C2212yes—
57#10622541C2212yes—
58#10622541C2212yes—
59#10622541C2212yes—
60#10622290C2214yes—
61#10622284C2214yes—
62#10622283C2214yes—
63#10622281C2214yes—
64#10622278C2214yes—
65#10622274C2214yes—
66#10622269C2214yes—
67#10622266C2214yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11C2314yes—
76C22×D44C2312yes—
77C22×D44C2312yes—
78C22×D44C2312yes—
79C22×C4×D11C2314yes—
80C22×Dic22C2312yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4D418yescomplemented
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C42×C11—24no—
86C2×C42×C11—42no—
87C2×C42×C11—42no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2312yes—
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2312yes—
94C2×C22⋊Dic11C2314yes—
95#66983—28no—
96#66983—28no—
97#66983—28no—
98#66982—216no—
99C4×C22⋊D11—216no—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2312yes—
118#66977—28no—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×C4×Dic11C2314yes—
124#66951—216no—
125#66949—216no—
126#66947—216no—
127#66942—216no—
128#66928—44no—
129C4×D44—44no—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138#35004—111nomaximal, Sylow
139C24×C11C2411yescharacteristic
140C23×D11C2414yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11#4114yes—
161C22×C4×C11#4114yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—28no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—28no—
173C22×Dic11C2414yes—
174C22×Dic11C2414yes—
175C22×Dic11C2414yes—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44—24no—
179C2×D44—42no—
180C2×D44—42no—
181C2×D44—42no—
182C2×D44—42no—
183C2×D44—42no—
184C2×D44—42no—
185C2×C4×D11—28no—
186C2×C4×D11—44no—
187C2×C4×D11—44no—
188C2×Dic22—24no—
189C2×Dic22—42no—
190C2×Dic22—42no—
191C11×C4⋊C4—28no—
192C11×C4⋊C4C2×D4116yes—
193C42×C11—24no—
194C42×C11—24no—
195C42×C11—24no—
196C42×C11—24no—
197C42×C11—42no—
198C42×C11—42no—
199C22⋊Dic11—28no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—44no—
209(C2×D11)⋊C4—44no—
210C4⋊Dic11—24no—
211C4⋊Dic11—24no—
212C4⋊Dic11—24no—
213C4⋊Dic11—24no—
214C4⋊Dic11—42no—
215C4⋊Dic11—42no—
216C4⋊Dic11—42no—
217C4⋊Dic11—42no—
218Dic11⋊C4—28no—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221Dic11⋊C4—28no—
222C4×Dic11—28no—
223C2×#539—112no—
224#2854—112no—
225#2850—112no—
226#2659—111no—
227#2656—111no—
228#2618—112no—
229#2556—114no—
230#2554—114no—
231#2519—114no—
232#2461—114no—
233#2325—112no—
234C4×#121—112no—
235C2×C4×C4⋊C4D1111yescharacteristic, complemented
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11C22×D412yes—
241C23×C11C2×#4112yes—
242C23×C11C2×#4112yes—
243C23×C11C2511yescharacteristic
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C2×C4×C11—28no—
252C2×C4×C11—28no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—44no—
271C2×C4×C11—44no—
272C2×C4×C11—44no—
273C2×C4×C11—44no—
274C2×C4×C11—44no—
275C2×C4×C11C22×D414yes—
276C2×C4×C11C22×D414yes—
277C2×C4×C11C22×D414yes—
278C2×C4×C11C2×#4114yes—
279C2×C4×C11C2×#4114yes—
280C2×C4×C11H(5,𝔽2)12yes—
281C2×C4×C112−1+412yes—
282C22⋊D11—416no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292D44—48no—
293D44—84no—
294D44—84no—
295C4×D11—88no—
296Dic22—84no—
297#539—2216no—
298C2×#126—114no—
299C2×#125—114no—
300C2×#124—112no—
301C2×#123—114no—
302C2×#123—114no—
303C2×C22⋊Q8—112no—
304C2×C22⋊Q8—114no—
305C2×#121—112no—
306C2×#121—112no—
307C2×#121—112no—
308C2×C4×D4—114no—
309C2×C4×D4—112no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C4⋊C4C2×D1111yescharacteristic
312C22×C42C2×D1111yescharacteristic
313C22×C42C2×D1111yescharacteristic
314C22×C42C2×D1111yescharacteristic
315#399—114no—
316#398—114no—
317#398—114no—
318#396—114no—
319#396—114no—
320#395—114no—
321#394—114no—
322#392—114no—
323#391—112no—
324#390—112no—
325#390—112no—
326#390—112no—
327#390—112no—
328#389—112no—
329#389—112no—
330#389—112no—
331#388—114no—
332#388—114no—
333#388—114no—
334#388—114no—
335#388—114no—
336#388—114no—
337#387—114no—
338#386—114no—
339#386—114no—
340#386—114no—
341#385—114no—
342#382—112no—
343#380—112no—
344#380—112no—
345C4×C4⋊C4—112no—
346C4×C4⋊C4C2×D1114yes—
347C4×C4⋊C4C2×D1114yes—
348C4×C22⋊C4—114no—
349C2×#95C2×D1111yescharacteristic
350C2×#95C2×D1111yescharacteristic
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11#53214yes—
358C22×C11C23×D411yescharacteristic
359C22×C11C22×#4111yescharacteristic
360C22×C11C22×#4111yescharacteristic
361C22×C11C2×H(5,𝔽2)11yescharacteristic
362C22×C11C2×2−1+411yescharacteristic
363C22×C11#58511yescharacteristic
364C22×C11#58511yescharacteristic
365C2×D11—44no—
366C2×D11—44no—
367C2×D11—44no—
368C2×D11—44no—
369C2×D11—44no—
370C2×D11—44no—
371C2×D11—44no—
372C4×C11—24no—
373C4×C11—24no—
374C4×C11—24no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—24no—
378C4×C11—24no—
379C4×C11—42no—
380Dic11—44no—
381Dic11—44no—
382Dic11—44no—
383C22×Q8—112no—
384C22×D4—114no—
385C22×D4—112no—
386C22×D4—112no—
387C22×D4—112no—
388C23×C4—114no—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1111yescharacteristic
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1111yescharacteristic
396#126—2216no—
397#125—2216no—
398#124—444no—
399#123—2216no—
400#123—2216no—
401C22⋊Q8—228no—
402C22⋊Q8—2216no—
403#121—228no—
404#121—228no—
405#121—228no—
406C4×D4—2216no—
407C4×D4—444no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—112no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—114no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4D4418yescomplemented
422C2×C4⋊C4C22×D1114yes—
423C2×C4⋊C4C22×D1114yes—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—114no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4—114no—
435C2×C42—24no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—114no—
439C2×C42C22×D1112yes—
440C2×C42C22×D1112yes—
441C2×C42C22×D1112yes—
442C2×C42C22×D1112yes—
443C2×C42C22×D1112yes—
444C2×C42C22×D1112yes—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—114no—
450#95—114no—
451#95C22×D1114yes—
452#95C22×D1114yes—
453C2×C11—24no—
454C2×C11C2×#53211yescharacteristic
455C2×C11#345911yescharacteristic
456C2×C11#346111yescharacteristic
457C2×C11#349111yescharacteristic
458C2×C11#349211yescharacteristic
459C2×C11#349611yescharacteristic
460C2×C11#349711yescharacteristic
461D11—84no—
462C24—114no—
463C24C23×D1111yescharacteristic
464C2×Q8—224no—
465C2×Q8—442no—
466C2×Q8—442no—
467C2×D4—228no—
468C2×D4—228no—
469C2×D4—228no—
470C2×D4—224no—
471C2×D4—224no—
472C2×D4—224no—
473C2×D4—442no—
474C2×D4—442no—
475C2×D4—442no—
476C2×D4—442no—
477C2×D4—442no—
478C2×D4—442no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—114no—
498C22×C4—228no—
499C22×C4—444no—
500C22×C4—444no—
501C22×C4C2×D4414yes—
502C22×C4C2×D4414yes—
503C22×C4C2×D4414yes—
504C22×C4#433914yes—
505C22×C4#433914yes—
506C22×C4C23×D1112yes—
507C22×C4C23×D1112yes—
508C22×C4C23×D1112yes—
509C22×C4C23×D1112yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1111yescharacteristic
513C22×C4C23×D1111yescharacteristic
514C4⋊C4—28no—
515C4⋊C4—228no—
516C4⋊C4—224no—
517C4⋊C4—228no—
518C4⋊C4—228no—
519C4⋊C4—224no—
520C4⋊C4—228no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4C2×D44116yes—
528C22⋊C4—228no—
529C22⋊C4—228no—
530C22⋊C4—228no—
531C22⋊C4—228no—
532C22⋊C4—228no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—228no—
536C22⋊C4—228no—
537C22⋊C4—444no—
538C22⋊C4—444no—
539C42—24no—
540C42—24no—
541C42—24no—
542C42—24no—
543C42—42no—
544C42—42no—
545C42—228no—
546C11#3500411yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—224no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—224no—
558C23C22×D4412yes—
559C23C2×#433912yes—
560C23C2×#433912yes—
561C23C24×D1111yescharacteristic
562Q8—884no—
563D4—448no—
564D4—4416no—
565D4—884no—
566D4—884no—
567C2×C4—28no—
568C2×C4—28no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—888no—
601C2×C4C22×D4414yes—
602C2×C4C22×D4414yes—
603C2×C4C22×D4414yes—
604C2×C4C2×#433914yes—
605C2×C4C2×#433914yes—
606C2×C4#6703712yes—
607C2×C4#6704012yes—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22#1062300814yes—
622C22C23×D4411yescharacteristic
623C22C22×#433911yescharacteristic
624C22C22×#433911yescharacteristic
625C22C2×#6703711yescharacteristic
626C22C2×#6704011yescharacteristic
627C22#1062345311yescharacteristic
628C22#1062345311yescharacteristic
629C4—24no—
630C4—24no—
631C4—24no—
632C4—24no—
633C4—24no—
634C4—22no—
635C4—22no—
636C4—42no—
637C4—444no—
638C4—444no—
639C4—444no—
640C2—24no—
641C2—884no—
642C2C2×#1062300811yescharacteristic
643C2#1308202511yescharacteristic
644C2#1308204911yescharacteristic
645C2#1308231411yescharacteristic
646C2#1308232511yescharacteristic
647C2#1308238011yescharacteristic
648C2#1308238711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C4×C11×C4⋊C4C2
prime radical#13074718C2
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#35004
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10623046C2semidirect
2. #13076947C2semidirect
3. #13076917C2semidirect
4. #13074730C2semidirect
6. #13074358C2semidirect
7. #13073694C2semidirect
8. #13073670C2semidirect
9. #13073289C2semidirect
10. #13072583C2semidirect
11. #13071319C2semidirect
12. C4×#66983C2semidirect
13. C2×C4×C11×C4⋊C4C2semidirect
82. C2×C11×C4⋊C4D4semidirect
235. C2×C4×C4⋊C4D11semidirect
421. C2×C4⋊C4D44semidirect
546. C11#35004semidirect

Maximal subgroups

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

subgroupindex
C2×#106230462
#130769472
#130769172
#130747302
#130747182
#130743582
#130736942
#130736702
#130732892
#130725832
#130713192
C4×#669832
C2×C4×C11×C4⋊C42
#3500411