Finite Group Databasebeta

← #15618968

Subgroups — #15618968

Order 2816.

1864 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081911C211yesmaximal, characteristic
2#13077782C214yesmaximal, complemented
3#13077751C214yesmaximal, complemented
4#13077736C214yesmaximal, complemented
5#13077728C214yesmaximal, complemented
6#13077556C211yesmaximal, characteristic, complemented
7#13077553C211yesmaximal, characteristic, complemented
8#13077346C212yesmaximal, complemented
9#13077338C212yesmaximal, complemented
10#13077334C211yesmaximal, characteristic, complemented
11#13077278C212yesmaximal, complemented
12C2×#10622318C211yesmaximal, characteristic, complemented
13#13077182C212yesmaximal, complemented
14D11×#423C211yesmaximal, characteristic, complemented
15C11×#2932C211yesmaximal, characteristic, complemented
16C2×C11×#131C2212yes—
17C11×#532C2211yescharacteristic
18#10623359C2212yes—
19#41×Dic11C2212yes—
20C2×#67001C2212yes—
21C2×M16×D11C2212yes—
22#10623259C411yescharacteristic
23#10623259C411yescharacteristic
24#10623247C411yescharacteristic
25#10623247C411yescharacteristic
26#10623211C412yes—
27#10623211C412yes—
28#10623137C412yes—
29#10623137C412yes—
30#10623131C412yes—
31#10623131C412yes—
32#10623088C2212yes—
33#10623088C2212yes—
34C4×#4341C2212yes—
35C4×#4341C2212yes—
36C2×C42×D11C2211yescharacteristic
37#10623001C2211yescharacteristic
38C11×#435C2214yescomplemented
39C11×#435C2214yescomplemented
40C11×#423C2211yescharacteristic
41C11×#408C2212yes—
42C2×C11×#97C2211yescharacteristic
43#10622847C2212yes—
44#10622741C2214yes—
45#10622740C2214yes—
46#10622735C2212yes—
47#10622732C2212yes—
48#10622732C2214yescomplemented
49#10622731C2212yes—
50#10622731C2214yescomplemented
51#10622724C2214yes—
52C8×C22⋊D11C2214yes—
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55#10622715C2212yes—
56#10622715C2214yescomplemented
57#10622714C2212yes—
58C2×Dic11⋊C8C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2214yescomplemented
61#10622624C2214yescomplemented
62#10622624C2214yescomplemented
63#10622537C2211yescharacteristic
64C2×#66867C2211yescharacteristic
65#10622450C2212yes—
66#10622450C2212yes—
67D11×C4⋊C8C2212yes—
68D11×C4⋊C8C2212yes—
69#10622441C2214yescomplemented
70#10622441C2214yescomplemented
71#10622343C2214yes—
72#10622342C2214yes—
73#10622341C2214yes—
74(C22⋊D11)⋊C8C2214yes—
75#10622333C2214yescomplemented
76#10622333C2214yescomplemented
77#10622332C2214yescomplemented
78#10622331C2214yescomplemented
79#10622318C2212yes—
80#10622318C2212yes—
81#10622318C2212yes—
82#10622318C2212yes—
83#10622314C2214yescomplemented
84#10622314C2214yescomplemented
85C2×C11×#41C2312yes—
86C2×#4341C2×C412yes—
87C2×#4341C2×C412yes—
88C22×C4×D11C2×C411yescharacteristic
89C22×C4×D11C2×C411yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C11×#131—44no—
92C2×C11×M16C2312yes—
93C2×C11×M16C2314yes—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2314yes—
97C11×C4⋊Q8C2×C411yescharacteristic
98C11×#127C2×C411yescharacteristic
99C11×#124C2×C412yes—
100C11×#121C2×C412yes—
101C11×#121C2×C412yes—
102C4×D4×C11C2312yes—
103C4×D4×C11C2312yes—
104C2×C42×C11C2311yescharacteristic
105#67001—44no—
106#66999C2×C412yes—
107#66999C2×C412yes—
108Q8×Dic11C2×C412yes—
109Q8×Dic11C2×C412yes—
110#66991C2×C412yes—
111#66991C2×C412yes—
112#66991C2×C412yes—
113#66991C2×C412yes—
114#66990C2×C414yes—
115#66989C2×C412yes—
116#66989C2×C412yes—
117#66988C2×C414yes—
118D4×Dic11C2×C412yes—
119D4×Dic11C2×C412yes—
120D4×Dic11C2×C412yes—
121D4×Dic11C2×C412yes—
122D4×Dic11C2×C414yes—
123D4×Dic11C2×C414yes—
124C4×C22⋊D11C2314yes—
125C4×C22⋊D11C2314yes—
126#66979C2312yes—
127#66979C2314yes—
128#66977C2×C412yes—
129#66977C2×C412yes—
130C2×C4×Dic11C2×C411yescharacteristic
131C2×C4×Dic11C2×C411yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2314yes—
134C2×#4318C2312yes—
135C2×#4318C2314yes—
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2314yes—
139M16×D11—44no—
140C2×#4313C2314yes—
141C2×C8×D11C2314yes—
142#66950C2×C412yes—
143#66950C2×C412yes—
144#66945C2×C412yes—
145#66945C2×C412yes—
146#66943C2×C412yes—
147#66943C2×C412yes—
148#66940C2×C412yes—
149#66940C2×C412yes—
150#66936C2×C414yes—
151#66936C2×C414yes—
152(C22⋊D11)⋊C4C2×C414yes—
153(C22⋊D11)⋊C4C2×C414yes—
154#66932C2×C414yes—
155#66932C2×C414yes—
156#66930C2×C414yes—
157#66930C2×C414yes—
158C42×D11C2×C411yescharacteristic
159C42×D11C2×C411yescharacteristic
160C42×D11C2×C411yescharacteristic
161C42×D11C2×C411yescharacteristic
162C42×D11C2311yescharacteristic
163C42×D11C2311yescharacteristic
164C42×D11C2311yescharacteristic
165C42×D11C2311yescharacteristic
166#66923C2×C412yes—
167#66922C2×C411yescharacteristic
168#66922C2×C411yescharacteristic
169C4×Dic22C2312yes—
170C4×Dic22C2312yes—
171C11×C4⋊C8C2312yes—
172C11×C4⋊C8C2312yes—
173C11×C22⋊C8C2314yes—
174C11×C22⋊C8C2314yes—
175C11×#97C2312yes—
176C11×#97C2312yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179(C2×D11)⋊C8C2312yes—
180(C2×D11)⋊C8C2312yes—
181(C2×D11)⋊C8C2312yes—
182(C2×D11)⋊C8C2312yes—
183#66879C2314yes—
184#66879C2314yes—
185Dic11⋊C8C2314yes—
186Dic11⋊C8C2314yes—
187Dic11⋊C8C2314yes—
188Dic11⋊C8C2312yes—
189Dic11⋊C8C2314yes—
190Dic11⋊C8C2314yes—
191Dic11⋊C8C2312yes—
192Dic11⋊C8C2314yes—
193Dic11⋊C8C2312yes—
194Dic11⋊C8C2312yes—
195C8×Dic11C2314yes—
196C8×Dic11C2314yes—
197C4⋊(C11⋊C8)C2312yes—
198C4⋊(C11⋊C8)C2312yes—
199#66867C2312yes—
200#66867C2312yes—
201#60269—111nomaximal, Sylow
202C23×D11C22×C411yescharacteristic
203C11×#41—24no—
204C11×#41—24no—
205C2×Q8×C11C22×C412yes—
206C2×D4×C11C22×C414yes—
207C2×D4×C11C22×C412yes—
208C2×D4×C11C22×C412yes—
209C2×D4×C11C22×C412yes—
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C2414yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11C22×C414yes—
215C2×C22⋊D11C22×C414yes—
216C22×Dic11C22×C414yes—
217C22×Dic11C22×C411yescharacteristic
218C22×Dic11C22×C411yescharacteristic
219C22×Dic11C22×C414yes—
220C22×Dic11C22×C411yescharacteristic
221#4341—44no—
222#4341—44no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×C4×D11C22×C411yescharacteristic
228C2×C4×D11C22×C411yescharacteristic
229C2×C4×D11C22×C411yescharacteristic
230C2×C4×D11C22×C411yescharacteristic
231C2×C4×D11C22×C411yescharacteristic
232C2×C4×D11C22×C411yescharacteristic
233C2×C4×D11C22×C411yescharacteristic
234C2×C4×D11C22×C411yescharacteristic
235C2×C4×D11C22×C411yescharacteristic
236C2×C4×D11C22×C411yescharacteristic
237C2×C4×D11C2411yescharacteristic
238C2×C4×D11C2411yescharacteristic
239C2×Dic22C22×C412yes—
240C2×Dic22C22×C412yes—
241C11×M16—24no—
242C11×M16—44no—
243C2×C8×C11—22no—
244C2×C8×C11—22no—
245C2×C8×C11—44no—
246C2×C8×C11C2412yes—
247C2×C8×C11C2414yes—
248C2×C8×C11C2412yes—
249C11×C4⋊C4C22×C412yes—
250C11×C4⋊C4C22×C412yes—
251C11×C22⋊C4C22×C414yes—
252C11×C22⋊C4C22×C414yes—
253C42×C11C22×C411yescharacteristic
254C42×C11C22×C411yescharacteristic
255C42×C11C2411yescharacteristic
256C42×C11C2411yescharacteristic
257C22⋊Dic11C22×C414yes—
258C22⋊Dic11C22×C414yes—
259C22⋊Dic11C22×C414yes—
260C22⋊Dic11C22×C414yes—
261C22⋊Dic11C22×C414yes—
262(C2×D11)⋊C4C22×C414yes—
263(C2×D11)⋊C4C22×C414yes—
264C4⋊Dic11C22×C412yes—
265C4⋊Dic11C22×C412yes—
266C4⋊Dic11C22×C412yes—
267C4⋊Dic11C22×C412yes—
268C4⋊Dic11C22×C414yes—
269C4⋊Dic11C22×C414yes—
270Dic11⋊C4C22×C414yes—
271Dic11⋊C4C22×C414yes—
272Dic11⋊C4C22×C414yes—
273Dic11⋊C4C22×C414yes—
274C4×Dic11C22×C411yescharacteristic
275C4×Dic11C22×C411yescharacteristic
276C4×Dic11C22×C411yescharacteristic
277C4×Dic11C22×C411yescharacteristic
278C4×Dic11C22×C411yescharacteristic
279C4×Dic11C22×C411yescharacteristic
280C4×Dic11C22×C411yescharacteristic
281C4×Dic11C22×C411yescharacteristic
282C4×Dic11C22×C411yescharacteristic
283C4×Dic11C22×C411yescharacteristic
284C4×Dic11C22×C414yes—
285C4×Dic11C22×C414yes—
286C4×Dic11C2414yes—
287C4×Dic11C2411yescharacteristic
288C4×Dic11C2411yescharacteristic
289#4318—24no—
290#4318—44no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—44no—
294C2×C11⋊C8C2412yes—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2414yes—
297#4313—44no—
298C8×D11—44no—
299#3444—111no—
300#2995—114no—
301#2992—114no—
302#2990—114no—
303#2989—114no—
304#2961—111no—
305#2961—111no—
306#2933—112no—
307#2933—112no—
308#2932—111no—
309#2932D1111yescharacteristic, complemented
310#2925—112no—
311C2×#432—111no—
312#2906—112no—
313C2×#423—111no—
314C23×C11C23×C414yes—
315C23×C11C23×C411yescharacteristic
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—41no—
319C22×D11C23×C411yescharacteristic
320C22×D11C23×C411yescharacteristic
321Q8×C11—24no—
322D4×C11—28no—
323D4×C11—24no—
324D4×C11—42no—
325D4×C11—42no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11C23×C411yescharacteristic
331C2×C4×C11C23×C411yescharacteristic
332C2×C4×C11C23×C414yes—
333C2×C4×C11C23×C411yescharacteristic
334C2×C4×C11C23×C411yescharacteristic
335C2×C4×C11C23×C411yescharacteristic
336C2×C4×C11H(5,𝔽2)12yes—
337C2×C4×C112−1+412yes—
338C2×C4×C11C2511yescharacteristic
339C22⋊D11—28no—
340C22⋊D11—44no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—28no—
344C2×Dic11—41no—
345C2×Dic11—44no—
346C2×Dic11C23×C411yescharacteristic
347C2×Dic11C23×C411yescharacteristic
348C2×Dic11C23×C411yescharacteristic
349C2×Dic11C23×C411yescharacteristic
350C2×Dic11C23×C411yescharacteristic
351C2×Dic11C23×C414yes—
352C2×Dic11C23×C414yes—
353C2×Dic11C23×C411yescharacteristic
354C4×D11—22no—
355C4×D11—22no—
356C4×D11—22no—
357C4×D11—22no—
358C4×D11—21no—
359C4×D11—21no—
360C4×D11—21no—
361C4×D11—21no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—41no—
365C4×D11—41no—
366C4×D11—41no—
367C4×D11—41no—
368Dic22—42no—
369Dic22—42no—
370C8×C11—24no—
371C8×C11—22no—
372C8×C11—22no—
373C11⋊C8—24no—
374C11⋊C8—22no—
375C11⋊C8—22no—
376C2×#131—112no—
377C2×#131C2×D1112yes—
378C22×M16—112no—
379#533—111no—
380#533—111no—
381#533—111no—
382#532—111no—
383#532—111no—
384#532C2×D1111yescharacteristic
385#529—112no—
386#529—112no—
387#529—112no—
388#529—112no—
389#529—112no—
390#529—112no—
391#525—112no—
392#525—112no—
393#525—112no—
394C4×#41—112no—
395C4×#41—112no—
396C4×#41—112no—
397C22×C42—111no—
398#446—114no—
399#446—114no—
400#446—114no—
401#446—114no—
402#436—114no—
403#436—114no—
404#435—114no—
405#435—114no—
406#435—114no—
407#435—114no—
408#435—114no—
409#435—114no—
410#435C2×D1114yescomplemented
411#435C2×D1114yescomplemented
412C8×D4—114no—
413C8×D4—114no—
414#433—114no—
415#433—114no—
416#432—114no—
417#432—112no—
418#432—112no—
419#432—112no—
420#432—112no—
421#431—114no—
422#424—112no—
423#424—114no—
424#424—112no—
425#424—114no—
426#423—112no—
427#423—114no—
428#423—111no—
429#423—112no—
430#423—112no—
431#423C2×D1111yescharacteristic
432C2×C4⋊C8—111no—
433C2×C4⋊C8—114no—
434C2×C4⋊C8—111no—
435C2×C4⋊C8—112no—
436C2×C4⋊C8—112no—
437#408—112no—
438#408C2×D1112yes—
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441#405—112no—
442#405—112no—
443C2×#97—111no—
444C2×#97C2×D1111yescharacteristic
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11#52012yes—
451C22×C11C24×C411yescharacteristic
452C2×D11—21no—
453C2×D11—21no—
454C2×D11—21no—
455C2×D11—21no—
456C2×D11—21no—
457C2×D11—44no—
458C2×D11#56812yes—
459C4×C11—24no—
460C4×C11—21no—
461C4×C11—21no—
462C4×C11—21no—
463C4×C11—21no—
464C4×C11#52012yes—
465C4×C11C2×H(5,𝔽2)11yescharacteristic
466C4×C11C2×2−1+411yescharacteristic
467Dic11—21no—
468Dic11—21no—
469Dic11—24no—
470Dic11—24no—
471Dic11—21no—
472Dic11—21no—
473Dic11—21no—
474Dic11#56812yes—
475C2×#41—112no—
476C2×#41—112no—
477C2×#41C22×D1112yes—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481#131—44no—
482#131—444no—
483C2×M16—112no—
484C2×M16—114no—
485C2×M16—114no—
486C2×M16—444no—
487C2×M16C22×D1112yes—
488C2×M16C22×D1114yes—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—114no—
492C22×C8—114no—
493C22×C8C22×D1111yescharacteristic
494C22×C8C22×D1111yescharacteristic
495C22×C8C22×D1114yes—
496C4⋊Q8—111no—
497C4⋊Q8—111no—
498C4⋊Q8C4×D1111yescharacteristic
499#127C4×D1111yescharacteristic
500#126—114no—
501#126—114no—
502#125—112no—
503#125—112no—
504#125—112no—
505#124—112no—
506#124—112no—
507#124C4×D1112yes—
508#123—114no—
509#123—114no—
510#123—114no—
511C22⋊Q8—112no—
512C22⋊Q8—112no—
513C22⋊Q8—112no—
514C22⋊Q8—112no—
515C22⋊Q8—112no—
516C22⋊Q8—112no—
517#121—112no—
518#121—112no—
519#121—112no—
520#121—112no—
521#121C4×D1112yes—
522#121C4×D1112yes—
523#120—114no—
524C4×Q8—112no—
525C4×Q8—112no—
526C4×Q8—112no—
527C4×Q8—112no—
528C4×Q8—112no—
529C4×Q8—112no—
530C4×D4—114no—
531C4×D4—114no—
532C4×D4—112no—
533C4×D4—112no—
534C4×D4—112no—
535C4×D4—112no—
536C4×D4—114no—
537C4×D4—114no—
538C4×D4—114no—
539C4×D4—114no—
540C4×D4C22×D1112yes—
541C4×D4C22×D1112yes—
542#117—112no—
543#117—114no—
544#117—112no—
545#117—112no—
546#117—114no—
547#117—114no—
548C2×C42—111no—
549C2×C42—111no—
550C2×C42—114no—
551C2×C42—111no—
552C2×C42—111no—
553C2×C42—111no—
554C2×C42—111no—
555C2×C42—111no—
556C2×C42—111no—
557C2×C42—111no—
558C2×C42—111no—
559C2×C42—111no—
560C2×C42C22×D1111yescharacteristic
561C4⋊C8—112no—
562C4⋊C8—114no—
563C4⋊C8—114no—
564C4⋊C8—112no—
565C4⋊C8—114no—
566C4⋊C8—114no—
567C4⋊C8—112no—
568C4⋊C8—112no—
569C4⋊C8—114no—
570C4⋊C8—114no—
571C4⋊C8—112no—
572C4⋊C8—112no—
573C4⋊C8C22×D1112yes—
574C4⋊C8C22×D1112yes—
575C22⋊C8—114no—
576C22⋊C8—114no—
577C22⋊C8—112no—
578C22⋊C8—112no—
579C22⋊C8—112no—
580C22⋊C8—112no—
581C22⋊C8C22×D1114yes—
582C22⋊C8C22×D1114yes—
583#97—114no—
584#97—114no—
585#97—112no—
586#97—112no—
587#97C22×D1112yes—
588#97C22×D1112yes—
589C4×C8—114no—
590C4×C8—114no—
591C2×C11—22no—
592C2×C11—44no—
593C2×C11C2×#52011yescharacteristic
594C2×C11C2×#56811yescharacteristic
595C2×C11C2×#56811yescharacteristic
596D11—22no—
597D11—41no—
598C24—111no—
599#41—24no—
600#41—24no—
601#41—444no—
602#41—444no—
603C2×Q8—112no—
604C2×Q8—112no—
605C2×Q8C2×C4×D1112yes—
606C2×D4—114no—
607C2×D4—114no—
608C2×D4C2×C4×D1114yes—
609C2×D4C2×C4×D1112yes—
610C2×D4C2×C4×D1112yes—
611C2×D4C2×C4×D1112yes—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—114no—
615C22×C4—111no—
616C22×C4—114no—
617C22×C4—111no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—111no—
623C22×C4—111no—
624C22×C4—111no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—442no—
632C22×C4—442no—
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4C2×C4×D1111yescharacteristic
635C22×C4C23×D1114yes—
636C22×C4C23×D1111yescharacteristic
637M16—24no—
638M16—44no—
639M16—224no—
640M16—444no—
641M16—444no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—112no—
646C2×C8—114no—
647C2×C8—112no—
648C2×C8—222no—
649C2×C8—222no—
650C2×C8—444no—
651C2×C8—444no—
652C2×C8C23×D1112yes—
653C2×C8C23×D1114yes—
654C2×C8C23×D1112yes—
655C4⋊C4—112no—
656C4⋊C4—112no—
657C4⋊C4—112no—
658C4⋊C4—112no—
659C4⋊C4—114no—
660C4⋊C4—114no—
661C4⋊C4—114no—
662C4⋊C4—114no—
663C4⋊C4—114no—
664C4⋊C4—114no—
665C4⋊C4C2×C4×D1112yes—
666C4⋊C4C2×C4×D1112yes—
667C22⋊C4—114no—
668C22⋊C4—114no—
669C22⋊C4—114no—
670C22⋊C4—114no—
671C22⋊C4—114no—
672C22⋊C4—114no—
673C22⋊C4—114no—
674C22⋊C4C2×C4×D1114yes—
675C22⋊C4C2×C4×D1114yes—
676C42—111no—
677C42—111no—
678C42—111no—
679C42—111no—
680C42—111no—
681C42—111no—
682C42—111no—
683C42—111no—
684C42—111no—
685C42—111no—
686C42—114no—
687C42—114no—
688C42—114no—
689C42—111no—
690C42—111no—
691C42C2×C4×D1111yescharacteristic
692C42C2×C4×D1111yescharacteristic
693C42C23×D1111yescharacteristic
694C42C23×D1111yescharacteristic
695C11#6026911yescharacteristic, complemented, Sylow
696C23—111no—
697C23—111no—
698C23—222no—
699C23—222no—
700C23—441no—
701C23C22×C4×D1114yes—
702C23C22×C4×D1111yescharacteristic
703Q8—24no—
704Q8—442no—
705Q8—442no—
706D4—28no—
707D4—24no—
708D4—42no—
709D4—42no—
710D4—228no—
711D4—444no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—111no—
717C2×C4—111no—
718C2×C4—111no—
719C2×C4—111no—
720C2×C4—111no—
721C2×C4—111no—
722C2×C4—114no—
723C2×C4—114no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—228no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—444no—
743C2×C4C22×C4×D1111yescharacteristic
744C2×C4C22×C4×D1111yescharacteristic
745C2×C4C22×C4×D1111yescharacteristic
746C2×C4C22×C4×D1111yescharacteristic
747C2×C4C22×C4×D1114yes—
748C2×C4C22×C4×D1111yescharacteristic
749C2×C4#6703712yes—
750C2×C4#6704312yes—
751C2×C4C24×D1111yescharacteristic
752C8—22no—
753C8—24no—
754C8—22no—
755C8—222no—
756C8—224no—
757C8—222no—
758C22—21no—
759C22—21no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—112no—
764C22—221no—
765C22—221no—
766C22—221no—
767C22—221no—
768C22—221no—
769C22—444no—
770C22#1062307712yes—
771C22C23×C4×D1111yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—24no—
777C4—112no—
778C4—221no—
779C4—221no—
780C4—221no—
781C4—224no—
782C4—224no—
783C4—221no—
784C4—221no—
785C4#1062307712yes—
786C4C2×#6703711yescharacteristic
787C4C2×#6704311yescharacteristic
788C2—22no—
789C2—44no—
790C2—222no—
791C2—441no—
792C2C2×#1062307711yescharacteristic
793C2D11×#56811yescharacteristic
794C2D11×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2932C2
prime radical#13081911C2
cosocleC2×C4×C11C25
hypercenter#2932D11
hypocenterC11#60269
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #13077782C2semidirect
3. #13077751C2semidirect
4. #13077736C2semidirect
5. #13077728C2semidirect
6. #13077556C2semidirect
7. #13077553C2semidirect
8. #13077346C2semidirect
9. #13077338C2semidirect
10. #13077334C2semidirect
11. #13077278C2semidirect
12. C2×#10622318C2semidirect
13. #13077182C2semidirect
14. D11×#423C2semidirect
15. C11×#2932C2semidirect
38. C11×#435C22semidirect
39. C11×#435C22semidirect
48. #10622732C22semidirect
50. #10622731C22semidirect
56. #10622715C22semidirect
60. C2×Dic11⋊C8C22semidirect
61. #10622624C22semidirect
62. #10622624C22semidirect
69. #10622441C22semidirect
70. #10622441C22semidirect
75. #10622333C22semidirect
76. #10622333C22semidirect
77. #10622332C22semidirect
78. #10622331C22semidirect
83. #10622314C22semidirect
84. #10622314C22semidirect
309. #2932D11semidirect
410. #435C2×D11semidirect
411. #435C2×D11semidirect
695. C11#60269semidirect

Maximal subgroups

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

subgroupindex
#130819112
#130777822
#130777512
#130777362
#130777282
#130775562
#130775532
#130773462
#130773382
#130773342
#130772782
C2×#106223182
#130771822
D11×#4232
C11×#29322
#6026911