Finite Group Databasebeta

← #14913516

Subgroups — #14913516

Order 2816.

2954 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2#13071746C214yesmaximal, complemented
3#13071698C214yesmaximal, complemented
4#13071662C214yesmaximal, complemented
5#13071594C214yesmaximal, complemented
6#13071114C211yesmaximal, characteristic, complemented
7#13071102C212yesmaximal, complemented
8#13071060C212yesmaximal, complemented
9#13071057C212yesmaximal, complemented
10C42×D44C212yesmaximal, complemented
11C4×#66946C212yesmaximal, complemented
12C4×C22⋊C4×D11C212yesmaximal, complemented
13C11×#2298C211yesmaximal, characteristic, complemented
14C22×#4339C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623055C4116yescomplemented
18C2×#66950C2212yes—
19C2×#66948C2212yes—
20C2×#66946C2214yes—
21C2×#66939C2212yes—
22C2×#66935C2212yes—
23C2×C22⋊C4×D11C2214yes—
24C2×C4×D44C2214yes—
25C2×C4×D44C2212yes—
26C2×C4×D44C2212yes—
27C2×#66925C2212yescomplemented
28C2×C42×D11C2212yes—
29C2×C42×D11C2212yes—
30C2×C42×D11C2212yescomplemented
31C11×#388C2214yes—
32C11×#387C2214yescomplemented
33C4×C11×C4⋊C4C2212yescomplemented
34C4×C11×C22⋊C4C2212yes—
35C11×#376C2211yescharacteristic, complemented
36C43×C11C2211yescharacteristic, complemented
37C4×C22⋊Dic11C2212yes—
38#10622603C2214yescomplemented
39#10622602C2214yes—
40#10622594C2214yescomplemented
41C4⋊C4×Dic11C2214yescomplemented
42#10622570C2214yes—
43#10622569C2214yes—
44#10622564C2214yes—
45C22⋊C4×Dic11C2214yes—
46C4×(C2×D11)⋊C4C2214yes—
47C4×(C2×D11)⋊C4C2212yes—
48C4×(C2×D11)⋊C4C2212yes—
49C4×(C2×D11)⋊C4C2214yescomplemented
50C4×(C2×D11)⋊C4C2212yescomplemented
51C4×(C2×D11)⋊C4C2212yescomplemented
52C4×C4⋊Dic11C2212yescomplemented
53C4×C4⋊Dic11C2214yescomplemented
54#10622545C2211yescharacteristic, complemented
55C42×Dic11C2211yescharacteristic, complemented
56#10622283C2214yescomplemented
57#10622281C2214yes—
58#10622279C2214yes—
59#10622279C2214yes—
60#10622279C2214yescomplemented
61#10622278C2214yes—
62#10622278C2214yes—
63#10622278C2214yescomplemented
64D11×#95C2214yes—
65#10622267C2214yescomplemented
66#10622266C2214yescomplemented
67#10622259C2214yescomplemented
68C24×D11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11C2312yes—
71C23×Dic11C2311yescharacteristic
72C2×#4339—44no—
73C2×#4339C2×C418yescomplemented
74C22×D44C2312yes—
75C22×D44C2312yes—
76C22×D44C2311yescharacteristic
77C22×C4×D11—44no—
78C22×C4×D11C2×C418yescomplemented
79C22×C4×D11C2314yes—
80C22×C4×D11C2314yes—
81C22×C4×D11C2314yes—
82C22×C4×D11C2312yes—
83C22×C4×D11C2312yes—
84C22×C4×D11C2312yes—
85C22×Dic22C2311yescharacteristic
86C11×#117C2×C418yescomplemented
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2314yes—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2312yes—
102C2×(C2×D11)⋊C4C2312yes—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2312yes—
109C2×Dic11⋊C4C2314yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2314yes—
116#66950C2×C4116yescomplemented
117#66948C2×C4116yescomplemented
118#66946—216no—
119#66939C2×C4116yescomplemented
120#66935C2×C4116yescomplemented
121C22⋊C4×D11—216no—
122C4×D44—216no—
123C4×D44C2×C4116yescomplemented
124C4×D44C2×C4116yescomplemented
125#66925—44no—
126C42×D11—44no—
127C42×D11—44no—
128C42×D11—44no—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139#34152—111nomaximal, Sylow
140C24×C11C2411yescharacteristic
141C23×D11—28no—
142C23×D11—42no—
143C23×D11C22×C414yes—
144C23×D11C2412yes—
145C23×D11C2412yes—
146C22×C4×C11—24no—
147C22×C4×C11C22×C414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—42no—
155C2×C22⋊D11—42no—
156C2×C22⋊D11C22×C418yes—
157C22×Dic11—42no—
158C22×Dic11C22×C414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2414yes—
163#4339—416no—
164C2×D44—28no—
165C2×D44—28no—
166C2×D44—42no—
167C2×D44C22×C418yes—
168C2×D44C22×C418yes—
169C2×D44C22×C414yes—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C2×C4×D11—28no—
173C2×C4×D11—28no—
174C2×C4×D11—28no—
175C2×C4×D11—28no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—44no—
181C2×C4×D11—44no—
182C2×C4×D11—44no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×C4×D11—416no—
186C2×C4×D11C22×C418yes—
187C2×C4×D11C22×C418yes—
188C2×C4×D11C22×C418yes—
189C2×Dic22—42no—
190C2×Dic22C22×C414yes—
191C11×C4⋊C4—28no—
192C11×C4⋊C4C22×C418yes—
193C11×C22⋊C4—28no—
194C11×C22⋊C4C22×C418yes—
195C42×C11—28no—
196C42×C11—24no—
197C42×C11—24no—
198C42×C11C22×C414yes—
199C42×C11C22×C414yes—
200C22⋊Dic11—28no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—44no—
205(C2×D11)⋊C4C22×C418yes—
206(C2×D11)⋊C4C22×C418yes—
207(C2×D11)⋊C4C22×C418yes—
208(C2×D11)⋊C4C22×C418yes—
209(C2×D11)⋊C4#41116yescomplemented
210C4⋊Dic11—28no—
211C4⋊Dic11C22×C418yes—
212C4⋊Dic11C22×C418yes—
213Dic11⋊C4—44no—
214C4×Dic11—28no—
215C4×Dic11—24no—
216C4×Dic11—24no—
217C4×Dic11—44no—
218C4×Dic11—44no—
219C4×Dic11—44no—
220C2×#525—111no—
221#2374—114no—
222#2368—114no—
223#2364—114no—
224#2358—114no—
225#2298—111no—
226#2298D1111yescharacteristic, complemented
227#2297—112no—
228#2290—112no—
229#2290—112no—
230C42×D4—112no—
231C42×D4—112no—
232C2×C4×C22⋊C4—112no—
233C23×C11—24no—
234C23×C11—22no—
235C23×C11C23×C412yes—
236C23×C11C2511yescharacteristic
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—216no—
245C22×D11—44no—
246C22×D11—416no—
247C22×D11C23×C414yes—
248C22×D11C23×C414yes—
249C22×D11C2×#4118yes—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—28no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11C23×C414yes—
260C2×C4×C11C23×C414yes—
261C2×C4×C11C23×C412yes—
262C2×C4×C11C23×C412yes—
263C2×C4×C11C2×#4118yes—
264C2×C4×C11H(5,𝔽2)14yes—
265C22⋊D11—48no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—44no—
276C2×Dic11C23×C414yes—
277C2×Dic11C23×C414yes—
278C2×Dic11C2×#4118yes—
279D44—216no—
280D44—216no—
281D44—44no—
282C4×D11—216no—
283C4×D11—216no—
284C4×D11—48no—
285C4×D11—416no—
286C4×D11—416no—
287C4×D11—416no—
288Dic22—44no—
289C22×#41—111no—
290C24×C4—111no—
291#525—1116no—
292C2×#123—112no—
293C2×C22⋊Q8—112no—
294C2×#121—112no—
295C2×#120—112no—
296C2×C4×D4—114no—
297C2×C4×D4—112no—
298C2×C4×D4—112no—
299C2×C4×D4—114no—
300C2×#117—112no—
301C2×#117C2×D1111yescharacteristic
302C22×C22⋊C4—114no—
303C22×C42—112no—
304C22×C42—112no—
305C22×C42—112no—
306#391—114no—
307#390—114no—
308#388—114no—
309#388—114no—
310#388—114no—
311#388C2×D1114yes—
312#387—114no—
313#387—114no—
314#387—114no—
315#387C2×D1114yescomplemented
316#386—114no—
317#386—114no—
318#386—114no—
319#386—114no—
320#385—114no—
321#385—114no—
322C4×C4⋊C4—114no—
323C4×C4⋊C4—114no—
324C4×C4⋊C4—112no—
325C4×C4⋊C4C2×D1112yescomplemented
326C4×C22⋊C4—112no—
327C4×C22⋊C4—114no—
328C4×C22⋊C4—114no—
329C4×C22⋊C4—114no—
330C4×C22⋊C4—112no—
331C4×C22⋊C4—112no—
332C4×C22⋊C4—112no—
333C4×C22⋊C4—112no—
334C4×C22⋊C4—114no—
335C4×C22⋊C4—114no—
336C4×C22⋊C4—114no—
337C4×C22⋊C4C2×D1112yes—
338#376—111no—
339#376C2×D1111yescharacteristic, complemented
340C2×#95—114no—
341C43—111no—
342C43C2×D1111yescharacteristic, complemented
343C22×C11—24no—
344C22×C11—22no—
345C22×C11—44no—
346C22×C11C24×C411yescharacteristic
347C22×C11C22×#4114yes—
348C22×C11C2×H(5,𝔽2)12yes—
349C2×D11—24no—
350C2×D11—24no—
351C2×D11—28no—
352C2×D11—28no—
353C2×D11—24no—
354C2×D11—24no—
355C2×D11—24no—
356C2×D11—416no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11C4×#4118yes—
360C4×C11—24no—
361C4×C11—24no—
362C4×C11—22no—
363C4×C11—28no—
364C4×C11—44no—
365C4×C11#51814yes—
366Dic11—24no—
367Dic11—24no—
368Dic11—28no—
369Dic11—44no—
370C25—111no—
371C2×#41—118no—
372C2×#41—444no—
373C22×Q8—111no—
374C22×D4—112no—
375C22×D4—112no—
376C22×D4—112no—
377C22×D4—111no—
378C23×C4—111no—
379C23×C4—112no—
380C23×C4—112no—
381C23×C4—118no—
382C23×C4—112no—
383C23×C4—114no—
384C23×C4—114no—
385C23×C4—114no—
386C23×C4—444no—
387C23×C4C22×D1111yescharacteristic
388#123—1116no—
389C22⋊Q8—1116no—
390#121—1116no—
391#120—1116no—
392C4×D4—1116no—
393C4×D4—1116no—
394C4×D4—2216no—
395C4×D4—2216no—
396#117—444no—
397#117C4×D1118yescomplemented
398C2×C4⋊C4—112no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4C22×D1114yes—
403C2×C4⋊C4C22×D1112yes—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—112no—
406C2×C22⋊C4—112no—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—112no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—2216no—
415C2×C22⋊C4C22×D1114yes—
416C2×C22⋊C4C22×D1112yes—
417C2×C42—114no—
418C2×C42—112no—
419C2×C42—112no—
420C2×C42—114no—
421C2×C42—114no—
422C2×C42—114no—
423C2×C42—444no—
424C2×C42—444no—
425C2×C42—444no—
426C2×C42C22×D1114yes—
427C2×C42C22×D1112yes—
428C2×C42C22×D1112yes—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431#95—114no—
432#95—114no—
433#95—114no—
434#95—114no—
435#95—114no—
436#95—114no—
437#95—114no—
438#95C22×D1114yes—
439#95C22×D1114yes—
440#95C22×D1114yes—
441C2×C11—42no—
442C2×C11C2×C4×#4112yes—
443C2×C11C2×#51811yescharacteristic
444C2×C11#348114yes—
445D11—28no—
446D11—44no—
447C24—112no—
448C24—112no—
449C24—114no—
450C24—228no—
451C24—442no—
452C24C23×D1111yescharacteristic
453#41—4416no—
454C2×Q8—114no—
455C2×Q8—442no—
456C2×D4—118no—
457C2×D4—118no—
458C2×D4—118no—
459C2×D4—114no—
460C2×D4—228no—
461C2×D4—228no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4—442no—
465C22×C4—24no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—114no—
470C22×C4—118no—
471C22×C4—118no—
472C22×C4—118no—
473C22×C4—114no—
474C22×C4—228no—
475C22×C4—228no—
476C22×C4—228no—
477C22×C4—228no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—228no—
483C22×C4—228no—
484C22×C4—4416no—
485C22×C4—444no—
486C22×C4—444no—
487C22×C4—444no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4C2×C4×D1114yes—
492C22×C4C23×D1114yes—
493C22×C4C23×D1111yescharacteristic
494C22×C4C23×D1112yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1114yes—
497C22×C4C23×D1111yescharacteristic
498C4⋊C4—28no—
499C4⋊C4—118no—
500C4⋊C4—118no—
501C4⋊C4—228no—
502C4⋊C4—444no—
503C4⋊C4C2×C4×D1118yes—
504C22⋊C4—28no—
505C22⋊C4—118no—
506C22⋊C4—118no—
507C22⋊C4—118no—
508C22⋊C4—118no—
509C22⋊C4—1116no—
510C22⋊C4—228no—
511C22⋊C4—228no—
512C22⋊C4—228no—
513C22⋊C4—228no—
514C22⋊C4—444no—
515C22⋊C4C2×C4×D1118yes—
516C42—28no—
517C42—24no—
518C42—24no—
519C42—228no—
520C42—224no—
521C42—224no—
522C42—444no—
523C42—444no—
524C42—444no—
525C42C2×C4×D1114yes—
526C42C2×C4×D1114yes—
527C11#3415211yescharacteristic, complemented, Sylow
528C23—24no—
529C23—22no—
530C23—114no—
531C23—118no—
532C23—114no—
533C23—2216no—
534C23—224no—
535C23—222no—
536C23—222no—
537C23—224no—
538C23—224no—
539C23—222no—
540C23—222no—
541C23—444no—
542C23—4416no—
543C23C22×C4×D1112yes—
544C23C24×D1111yescharacteristic
545Q8—444no—
546D4—2216no—
547D4—2216no—
548D4—444no—
549D4—448no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—28no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—114no—
560C2×C4—114no—
561C2×C4—118no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—2216no—
569C2×C4—2216no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—448no—
574C2×C4—4416no—
575C2×C4—4416no—
576C2×C4—4416no—
577C2×C4—444no—
578C2×C4C22×C4×D1114yes—
579C2×C4C22×C4×D1114yes—
580C2×C4C22×C4×D1112yes—
581C2×C4C22×C4×D1112yes—
582C2×C4#41×D1118yes—
583C2×C4#6704214yes—
584C22—24no—
585C22—22no—
586C22—44no—
587C22—118no—
588C22—228no—
589C22—228no—
590C22—224no—
591C22—224no—
592C22—224no—
593C22—224no—
594C22—224no—
595C22—4416no—
596C22—444no—
597C22—444no—
598C22C23×C4×D1111yescharacteristic
599C22C2×#41×D1114yes—
600C22C2×#6704212yes—
601C4—28no—
602C4—24no—
603C4—24no—
604C4—22no—
605C4—44no—
606C4—228no—
607C4—224no—
608C4—224no—
609C4—444no—
610C4#1062305214yes—
611C2—42no—
612C2—228no—
613C2—444no—
614C2C4×#41×D1112yes—
615C2C2×#1062305211yescharacteristic
616C2#1308222214yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2298C2
socle, cosocleC23×C11C25
prime radicalC2×#10623055C2
hypercenter#2298D11
hypocenterC11#34152
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #13071746C2semidirect
3. #13071698C2semidirect
4. #13071662C2semidirect
5. #13071594C2semidirect
6. #13071114C2semidirect
7. #13071102C2semidirect
8. #13071060C2semidirect
9. #13071057C2semidirect
10. C42×D44C2semidirect
11. C4×#66946C2semidirect
12. C4×C22⋊C4×D11C2semidirect
13. C11×#2298C2semidirect
17. #10623055C4semidirect
27. C2×#66925C22semidirect
30. C2×C42×D11C22semidirect
32. C11×#387C22semidirect
33. C4×C11×C4⋊C4C22semidirect
35. C11×#376C22semidirect
36. C43×C11C22semidirect
38. #10622603C22semidirect
40. #10622594C22semidirect
41. C4⋊C4×Dic11C22semidirect
49. C4×(C2×D11)⋊C4C22semidirect
50. C4×(C2×D11)⋊C4C22semidirect
51. C4×(C2×D11)⋊C4C22semidirect
52. C4×C4⋊Dic11C22semidirect
53. C4×C4⋊Dic11C22semidirect
54. #10622545C22semidirect
55. C42×Dic11C22semidirect
56. #10622283C22semidirect
60. #10622279C22semidirect
63. #10622278C22semidirect
65. #10622267C22semidirect
66. #10622266C22semidirect
67. #10622259C22semidirect
73. C2×#4339C2×C4semidirect
78. C22×C4×D11C2×C4semidirect
86. C11×#117C2×C4semidirect
116. #66950C2×C4semidirect
117. #66948C2×C4semidirect
119. #66939C2×C4semidirect
120. #66935C2×C4semidirect
123. C4×D44C2×C4semidirect
124. C4×D44C2×C4semidirect
209. (C2×D11)⋊C4#41semidirect
226. #2298D11semidirect
315. #387C2×D11semidirect
325. C4×C4⋊C4C2×D11semidirect
339. #376C2×D11semidirect
342. C43C2×D11semidirect
397. #117C4×D11semidirect
527. C11#34152semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
#130717462
#130716982
#130716622
#130715942
#130711142
#130711022
#130710602
#130710572
C42×D442
C4×#669462
C4×C22⋊C4×D112
C11×#22982
#3415211