Finite Group Databasebeta

← #15625268

Subgroups — #15625268

Order 2816.

2164 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×#10623008C211yesmaximal, characteristic
3#13079629C214yesmaximal, complemented
4#13079621C214yesmaximal, complemented
5#13079574C214yesmaximal, complemented
6#13079566C212yesmaximal, complemented
7#13079559C212yesmaximal, complemented
8#13079075C212yesmaximal, complemented
9#13079010C212yesmaximal, complemented
10#13078090C214yesmaximal, complemented
11#13077878C214yesmaximal, complemented
12C11×#2920C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
14C22×C42×C11C2211yescharacteristic
15C2×#66983—21no—
16C2×#66983—21no—
17C2×#66979—21no—
18C2×#66977—21no—
19C2×#66977C2212yes—
20C2×#66962C2218yescomplemented
21#10623008—21no—
22#10623008—21no—
23#10623008—21no—
24#10623008—21no—
25#10623008C2212yes—
26#10623008C2212yes—
27#10623008C2212yes—
28#10623008C2212yes—
29C2×#66928C2212yes—
30C2×#66927C2211yescharacteristic
31C2×C4×D44—21no—
32C2×C4×D44—21no—
33#10623001—21no—
34#10623001—21no—
35#10623001—21no—
36#10623001—21no—
37#10623001C2212yes—
38#10623001C2212yes—
39#10623001C2212yescomplemented
40#10623001C2212yescomplemented
41C2×#66923—21no—
42C2×#66922C2211yescharacteristic
43C2×#66922C2211yescharacteristic, complemented
44C2×#66922C2211yescharacteristic, complemented
45C2×C4×Dic22—21no—
46C2×C4×Dic22C2212yescomplemented
47C11×#432C2212yes—
48C11×#432C2212yescomplemented
49C11×#431C2212yes—
50C11×#431C2212yescomplemented
51C11×#423C2212yescomplemented
52C11×#407C2212yes—
53C4×C11×M16C2212yescomplemented
54#10622746C2218yescomplemented
55#10622462C2218yescomplemented
56#10622461C2218yescomplemented
57#10622458C22116yescomplemented
58#10622352C2218yes—
59#10622346C22116yescomplemented
60#10622344C2218yes—
61#10622328C2218yescomplemented
62#10622327C2218yescomplemented
63#10622312C2214yescomplemented
64#10622307C2214yescomplemented
65#10622306C2214yescomplemented
66#10622294C2214yescomplemented
67C23×C4×C11D411yescharacteristic
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—48no—
74C2×#4339C2314yes—
75C2×#4339C2314yes—
76C22×D44—21no—
77C22×D44—21no—
78C22×D44C2312yes—
79C22×C4×D11—22no—
80C22×Dic22—21no—
81C22×Dic22C2312yes—
82C22×Dic22C2312yes—
83C2×C11×M16C2314yes—
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D411yescharacteristic
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—22no—
97#66983—22no—
98#66983—22no—
99#66983—22no—
100#66983—22no—
101#66983—22no—
102#66983—22no—
103#66983—22no—
104#66983—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107#66979—22no—
108#66979—22no—
109#66979—22no—
110#66979—22no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2312yes—
117#66977—22no—
118#66977—22no—
119#66977—22no—
120#66977—22no—
121#66977—22no—
122#66977—22no—
123#66977C2314yes—
124#66977C2314yes—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×C4×Dic11—22no—
128#66962—416no—
129C2×Dic44C23116yes—
130C2×#4314C23116yes—
131#66928—22no—
132#66928—22no—
133#66928C2314yes—
134#66928C2314yes—
135#66927—21no—
136#66927—21no—
137#66927C2312yes—
138#66927C2312yes—
139C4×D44—22no—
140C4×D44—22no—
141C4×D44—22no—
142C4×D44—22no—
143C4×D44—22no—
144C4×D44—22no—
145C4×D44—22no—
146C4×D44—22no—
147#66923—22no—
148#66923—22no—
149#66923—22no—
150#66923—22no—
151#66922—21no—
152#66922—21no—
153#66922—21no—
154#66922—21no—
155#66922—21no—
156#66922—21no—
157#66922C2312yes—
158#66922C2312yes—
159#66922C2312yes—
160#66922C2312yes—
161#66922C2312yes—
162#66922C2312yes—
163C4×Dic22—22no—
164C4×Dic22—22no—
165C4×Dic22—22no—
166C4×Dic22—22no—
167C4×Dic22—22no—
168C4×Dic22—22no—
169C4×Dic22C2314yes—
170C4×Dic22C2314yes—
171C11×C4⋊C8C2314yes—
172C11×C4⋊C8C2314yes—
173C11×C22⋊C8C2314yes—
174C11×C22⋊C8C2314yes—
175C11×#97C2314yes—
176C4×C8×C11C2314yes—
177#66885C23116yes—
178#66880C23116yes—
179#60804—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C23×D11—22no—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—42no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—48no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209#4339—216no—
210#4339—48no—
211#4339—48no—
212#4339—48no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—44no—
219C2×D44—44no—
220C2×D44—44no—
221C2×D44C2414yes—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—48no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22—28no—
230C2×Dic22—44no—
231C2×Dic22—44no—
232C2×Dic22C2414yes—
233C2×Dic22C2414yes—
234C11×M16—28no—
235C2×C8×C11C2418yes—
236C42×C11C2×D411yescharacteristic
237C42×C11C2×D411yescharacteristic
238C42×C11C2×D411yescharacteristic
239C42×C11C2×D411yescharacteristic
240C42×C11C2×D411yescharacteristic
241C42×C11C2×D411yescharacteristic
242C42×C11C2×D411yescharacteristic
243C42×C11C2×D411yescharacteristic
244C42×C11C2×D411yescharacteristic
245C42×C11C2×D411yescharacteristic
246C42×C11C2×D411yescharacteristic
247C42×C11C2×D411yescharacteristic
248C42×C11C2411yescharacteristic
249C42×C11C2411yescharacteristic
250C42×C11C2411yescharacteristic
251C42×C11C2411yescharacteristic
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—22no—
259C4⋊Dic11—22no—
260C4⋊Dic11—22no—
261C4⋊Dic11—22no—
262C4⋊Dic11—22no—
263C4⋊Dic11—22no—
264C4⋊Dic11—22no—
265C4⋊Dic11—22no—
266C4⋊Dic11—22no—
267C4⋊Dic11—22no—
268C4⋊Dic11—22no—
269C4⋊Dic11C2414yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276Dic44—416no—
277#4314—416no—
278C2×#533—111no—
279C2×#532—111no—
280#3216—114no—
281#3215—114no—
282#3210—114no—
283#3209—112no—
284#3208—112no—
285#3152—112no—
286#3141—112no—
287#3037—114no—
288#3007—114no—
289#2920D1111yescharacteristic, complemented
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—41no—
293C23×C11C22×D411yescharacteristic
294C23×C11C22×D411yescharacteristic
295C23×C11C22×D411yescharacteristic
296C22×D11—24no—
297C22×D11—44no—
298C22×D11—44no—
299C22×D11—44no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11#13714yescomplemented
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11H(5,𝔽2)14yes—
329C2×C4×C11C2511yescharacteristic
330C22⋊D11—48no—
331C22⋊D11—48no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11—44no—
338D44—28no—
339D44—44no—
340D44—44no—
341D44—44no—
342D44—44no—
343D44—44no—
344C4×D11—48no—
345C4×D11—48no—
346Dic22—28no—
347Dic22—28no—
348Dic22—44no—
349Dic22—44no—
350Dic22—44no—
351Dic22—44no—
352C8×C11—28no—
353C22×#41—112no—
354C2×#137—118no—
355#533—112no—
356#533—112no—
357#533—112no—
358#533—112no—
359#533—221no—
360#533—221no—
361#533—221no—
362#533—221no—
363#532—112no—
364#532—112no—
365#532—112no—
366#532—112no—
367#532—221no—
368#532—221no—
369#532—221no—
370#532—221no—
371C2×C4⋊Q8—111no—
372C2×C4⋊Q8—111no—
373C2×C4⋊Q8—111no—
374C2×#127—111no—
375C2×#125—221no—
376C2×#124—112no—
377C2×C22⋊Q8—112no—
378C2×C22⋊Q8—221no—
379C2×#121—221no—
380C2×#121—221no—
381C2×C4×Q8—112no—
382C2×C4×Q8—221no—
383C2×C4×D4—221no—
384C2×C4×D4—221no—
385C2×#117—221no—
386C22×C42C2×D1111yescharacteristic
387#497—118no—
388#494—114no—
389#492—114no—
390#489—118no—
391#487—114no—
392#486—114no—
393#464—1116no—
394#462—118no—
395#460—118no—
396#452—1116no—
397#451—118no—
398#450—118no—
399#432C2×D1112yes—
400#432C2×D1112yescomplemented
401#431C2×D1112yes—
402#431C2×D1112yescomplemented
403#423C2×D1112yescomplemented
404#417—118no—
405#407C2×D1112yes—
406C4×M16C2×D1112yescomplemented
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—21no—
414C22×C11—44no—
415C22×C11#53512yes—
416C22×C11C2×#13712yes—
417C22×C11C23×D411yescharacteristic
418C2×D11—44no—
419C2×D11—44no—
420C2×D11—44no—
421C2×D11—88no—
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—21no—
425C4×C11—21no—
426C4×C11—21no—
427C4×C11—21no—
428C4×C11—21no—
429C4×C11#53512yes—
430C4×C11C2×#13712yes—
431C4×C11C2×#13712yes—
432C4×C11#57512yes—
433C4×C11C2×H(5,𝔽2)12yes—
434Dic11—44no—
435Dic11—44no—
436Dic11—44no—
437C2×#41—114no—
438C2×#41—114no—
439C2×#41—222no—
440C2×#41—222no—
441C2×#41—448no—
442C22×Q8—112no—
443C22×Q8—112no—
444C22×Q8—221no—
445C22×D4—112no—
446C22×D4—222no—
447C22×D4—221no—
448C22×D4—221no—
449C23×C4—222no—
450C23×C4D4411yescharacteristic
451C23×C4D4411yescharacteristic
452C23×C4C22×D1111yescharacteristic
453#137—4416no—
454C2×Q16—1116no—
455C2×SD16—1116no—
456C2×M16C22×D1114yes—
457C4⋊Q8—112no—
458C4⋊Q8—112no—
459C4⋊Q8—112no—
460C4⋊Q8—112no—
461C4⋊Q8—112no—
462C4⋊Q8—112no—
463C4⋊Q8—221no—
464C4⋊Q8—221no—
465C4⋊Q8—221no—
466C4⋊Q8—221no—
467C4⋊Q8—221no—
468C4⋊Q8—221no—
469#127—112no—
470#127—112no—
471#127—221no—
472#127—221no—
473#125—222no—
474#125—222no—
475#125—222no—
476#125—222no—
477#124—114no—
478#124—114no—
479#124—222no—
480#124—222no—
481C22⋊Q8—114no—
482C22⋊Q8—114no—
483C22⋊Q8—222no—
484C22⋊Q8—222no—
485C22⋊Q8—222no—
486C22⋊Q8—222no—
487C22⋊Q8—222no—
488C22⋊Q8—222no—
489#121—222no—
490#121—222no—
491#121—222no—
492#121—222no—
493#121—222no—
494#121—222no—
495#121—222no—
496#121—222no—
497C4×Q8—114no—
498C4×Q8—114no—
499C4×Q8—222no—
500C4×Q8—222no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×Q8—222no—
504C4×Q8—222no—
505C4×D4—222no—
506C4×D4—222no—
507C4×D4—222no—
508C4×D4—222no—
509C4×D4—222no—
510C4×D4—222no—
511C4×D4—222no—
512C4×D4—222no—
513#117—222no—
514#117—222no—
515#117—222no—
516#117—222no—
517C2×C4⋊C4—112no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—222no—
523C2×C4⋊C4—222no—
524C2×C4⋊C4—221no—
525C2×C22⋊C4—222no—
526C2×C22⋊C4—222no—
527C2×C22⋊C4—222no—
528C2×C42—222no—
529C2×C42D4411yescharacteristic
530C2×C42D4411yescharacteristic
531C2×C42D4411yescharacteristic
532C2×C42D4411yescharacteristic
533C2×C42D4411yescharacteristic
534C2×C42D4411yescharacteristic
535C2×C42C22×D1111yescharacteristic
536C2×C42C22×D1111yescharacteristic
537C2×C42C22×D1111yescharacteristic
538C2×C42C22×D1111yescharacteristic
539C2×C42C22×D1111yescharacteristic
540C2×C42C22×D1111yescharacteristic
541C4⋊C8C22×D1114yes—
542C4⋊C8C22×D1114yes—
543#103—1116no—
544#102—1116no—
545C22⋊C8C22×D1114yes—
546C22⋊C8C22×D1114yes—
547#97C22×D1114yes—
548C4×C8C22×D1114yes—
549C2×C11—22no—
550C2×C11—22no—
551C2×C11—41no—
552C2×C11C2×#53511yescharacteristic
553C2×C11C22×#13711yescharacteristic
554C2×C11C2×#57511yescharacteristic
555D11—84no—
556C24—222no—
557C24C2×D4411yescharacteristic
558#41—2216no—
559#41—448no—
560#41—448no—
561#41—448no—
562C2×Q8—114no—
563C2×Q8—114no—
564C2×Q8—222no—
565C2×Q8—222no—
566C2×Q8—222no—
567C2×Q8—222no—
568C2×Q8—228no—
569C2×Q8—444no—
570C2×Q8—444no—
571C2×D4—114no—
572C2×D4—224no—
573C2×D4—224no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—444no—
580C2×D4—444no—
581C2×D4—448no—
582C2×D4—444no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—42no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—448no—
592C22×C4C2×D4411yescharacteristic
593C22×C4C2×D4411yescharacteristic
594C22×C4C2×D4411yescharacteristic
595C22×C4C2×D4411yescharacteristic
596C22×C4C2×D4411yescharacteristic
597C22×C4C2×D4411yescharacteristic
598C22×C4C2×D4411yescharacteristic
599C22×C4C2×D4411yescharacteristic
600C22×C4C2×D4411yescharacteristic
601C22×C4C2×D4411yescharacteristic
602C22×C4C2×D4411yescharacteristic
603C22×C4C2×D4411yescharacteristic
604C22×C4C2×D4411yescharacteristic
605C22×C4C2×D4411yescharacteristic
606C22×C4C2×D4411yescharacteristic
607C22×C4C23×D1111yescharacteristic
608C22×C4C23×D1111yescharacteristic
609C22×C4C23×D1111yescharacteristic
610Q16—4416no—
611SD16—4416no—
612M16—28no—
613C2×C8C23×D1118yes—
614C4⋊C4—114no—
615C4⋊C4—222no—
616C4⋊C4—222no—
617C4⋊C4—222no—
618C4⋊C4—222no—
619C4⋊C4—222no—
620C4⋊C4—222no—
621C4⋊C4—222no—
622C4⋊C4—222no—
623C4⋊C4—222no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—222no—
629C4⋊C4—222no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C42—224no—
637C42—224no—
638C42C2×D4411yescharacteristic
639C42C2×D4411yescharacteristic
640C42C2×D4411yescharacteristic
641C42C2×D4411yescharacteristic
642C42C2×D4411yescharacteristic
643C42C2×D4411yescharacteristic
644C42C2×D4411yescharacteristic
645C42C2×D4411yescharacteristic
646C42C2×D4411yescharacteristic
647C42C2×D4411yescharacteristic
648C42C2×D4411yescharacteristic
649C42C2×D4411yescharacteristic
650C42C23×D1111yescharacteristic
651C42C23×D1111yescharacteristic
652C42C23×D1111yescharacteristic
653C42C23×D1111yescharacteristic
654C11#6080411yescharacteristic, complemented, Sylow
655C23—22no—
656C23—22no—
657C23—41no—
658C23—224no—
659C23—444no—
660C23—444no—
661C23—444no—
662C23C22×D4411yescharacteristic
663C23C22×D4411yescharacteristic
664C23C22×D4411yescharacteristic
665Q8—228no—
666Q8—228no—
667Q8—444no—
668Q8—444no—
669Q8—444no—
670Q8—444no—
671D4—228no—
672D4—444no—
673D4—444no—
674D4—448no—
675D4—448no—
676D4—444no—
677D4—444no—
678D4—444no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—448no—
699C2×C4—444no—
700C2×C4—444no—
701C2×C4—444no—
702C2×C4—448no—
703C2×C4#6696214yescomplemented
704C2×C4C22×D4411yescharacteristic
705C2×C4C22×D4411yescharacteristic
706C2×C4C22×D4411yescharacteristic
707C2×C4C22×D4411yescharacteristic
708C2×C4C22×D4411yescharacteristic
709C2×C4C22×D4411yescharacteristic
710C2×C4C22×D4411yescharacteristic
711C2×C4C22×D4411yescharacteristic
712C2×C4C22×D4411yescharacteristic
713C2×C4C22×D4411yescharacteristic
714C2×C4C22×D4411yescharacteristic
715C2×C4#6704214yes—
716C2×C4C24×D1111yescharacteristic
717C8—28no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—44no—
726C22—444no—
727C22—444no—
728C22—444no—
729C22—888no—
730C22#1062305612yes—
731C22C2×#6696212yes—
732C22C23×D4411yescharacteristic
733C4—21no—
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—444no—
741C4—444no—
742C4—444no—
743C4#1062305612yes—
744C4C2×#6696212yes—
745C4C2×#6696212yes—
746C4#1062327912yes—
747C4C2×#6704212yes—
748C2—22no—
749C2—22no—
750C2—41no—
751C2—884no—
752C2C2×#1062305611yescharacteristic
753C2C22×#6696211yescharacteristic
754C2C2×#1062327911yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2920C2
socleC22×C11C23×D4
prime radicalC2×#10623008C2
hypercenter#2920D11
hypocenterC11#60804
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
3. #13079629C2semidirect
4. #13079621C2semidirect
5. #13079574C2semidirect
6. #13079566C2semidirect
7. #13079559C2semidirect
8. #13079075C2semidirect
9. #13079010C2semidirect
10. #13078090C2semidirect
11. #13077878C2semidirect
12. C11×#2920C2semidirect
20. C2×#66962C22semidirect
39. #10623001C22semidirect
40. #10623001C22semidirect
43. C2×#66922C22semidirect
44. C2×#66922C22semidirect
46. C2×C4×Dic22C22semidirect
48. C11×#432C22semidirect
50. C11×#431C22semidirect
51. C11×#423C22semidirect
53. C4×C11×M16C22semidirect
54. #10622746C22semidirect
55. #10622462C22semidirect
56. #10622461C22semidirect
57. #10622458C22semidirect
59. #10622346C22semidirect
61. #10622328C22semidirect
62. #10622327C22semidirect
63. #10622312C22semidirect
64. #10622307C22semidirect
65. #10622306C22semidirect
66. #10622294C22semidirect
289. #2920D11semidirect
316. C2×C4×C11#137semidirect
400. #432C2×D11semidirect
402. #431C2×D11semidirect
403. #423C2×D11semidirect
406. C4×M16C2×D11semidirect
654. C11#60804semidirect
703. C2×C4#66962semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106230082
#130796292
#130796212
#130795742
#130795662
#130795592
#130790752
#130790102
#130780902
#130778782
C11×#29202
#6080411