Finite Group Databasebeta

← C2×#13078971 #15623010

Subgroups — C2×#13078971 #15623010

Order 2816.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623220C211yesmaximal, characteristic, complemented
2C2×#10623246C211yesmaximal, characteristic
3#13078971C2116yesmaximal, direct product factor
4C2×#10622377C211yesmaximal, characteristic, complemented
5C2×#10622327C211yesmaximal, characteristic, complemented
6C2×#10622378C211yesmaximal, characteristic, complemented
7C2×#10622681C211yesmaximal, characteristic, complemented
8C2×#10622381C211yesmaximal, characteristic, complemented
9C2×#10622683C211yesmaximal, characteristic, complemented
10C2×#10622373C211yesmaximal, characteristic, complemented
11C2×#10622384C211yesmaximal, characteristic, complemented
12C2×#10622383C211yesmaximal, characteristic, complemented
13C2×#10622385C211yesmaximal, characteristic, complemented
14C2×D11×#102C211yesmaximal, characteristic, complemented
15C2×#10622321C211yesmaximal, characteristic, complemented
16C2×C11×#490C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic, complemented
21C2×#66993C2211yescharacteristic
22C2×#66992—21no—
23C2×#66992—21no—
24C2×#66990—21no—
25C2×#66990—21no—
26C2×#66989C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623246—24no—
30#10623246C2218yes—
31#10623220—24no—
32#10623220C2218yescomplemented
33C2×#66950—21no—
34C2×#66949—21no—
35C2×#66945C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66943C2211yescharacteristic, complemented
38C2×#66942—21no—
39C2×#66941—21no—
40C2×#66941C2211yescharacteristic, complemented
41C2×#66928C2211yescharacteristic
42C2×#66925C2211yescharacteristic
43C2×#66922C2211yescharacteristic, complemented
44C11×#490C2218yescomplemented
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×#97C2211yescharacteristic, complemented
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66880C2211yescharacteristic, complemented
57C2×#66880C2211yescharacteristic, complemented
58C2×#66879C2211yescharacteristic, complemented
59C2×C8×Dic11C2211yescharacteristic, complemented
60#10622683C2218yescomplemented
61#10622681C2218yescomplemented
62C2×#66874C2211yescharacteristic, complemented
63C2×#66874C2211yescharacteristic, complemented
64C2×#66873C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×C4×C11⋊C8C2211yescharacteristic, complemented
67#10622385C2218yescomplemented
68#10622384C2218yescomplemented
69#10622383C2218yescomplemented
70D11×#102C2218yescomplemented
71#10622381C2218yescomplemented
72#10622378C2218yescomplemented
73#10622377C2218yescomplemented
74#10622373C2218yescomplemented
75#10622327C2218yescomplemented
76#10622321C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C2×#4341—22no—
88C2×#4341—24no—
89C2×#4341—24no—
90C2×#4341C2314yes—
91C2×D4×D11—22no—
92C2×D4×D11—24no—
93C2×D4×D11—24no—
94C2×D4×D11C2314yes—
95C22×D44C2311yescharacteristic
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—21no—
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×#127—22no—
104C11×#127C2314yes—
105C11×#125—22no—
106C11×#125C2314yescomplemented
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114#66993—22no—
115#66993C2314yes—
116#66992—28no—
117#66992—28no—
118#66990—28no—
119#66990—28no—
120#66989—22no—
121#66989C2314yes—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4D411yescharacteristic
135C2×Dic11⋊C4D411yescharacteristic
136C2×C4×Dic11—21no—
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×#4313—24no—
141C2×#4313C2314yes—
142C2×C8×D11—24no—
143C2×C8×D11C2314yes—
144#66950—28no—
145#66949—28no—
146#66945—22no—
147#66945C2314yes—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150#66943—22no—
151#66943C2314yescomplemented
152#66942—28no—
153#66941—28no—
154#66941—22no—
155#66941C2314yescomplemented
156#66928—22no—
157#66928C2314yes—
158#66925D414yes—
159#66925C2314yes—
160#66922—22no—
161#66922C2314yescomplemented
162C11×#102C2314yes—
163C11×#102C2314yes—
164C11×#102C2314yescomplemented
165C11×#102C2314yescomplemented
166C11×#97C2314yescomplemented
167#66896C2314yes—
168#66896C2314yes—
169#66896C2314yescomplemented
170#66896C2314yescomplemented
171#66885C2314yes—
172#66885C2314yes—
173#66880C2314yescomplemented
174#66880C2314yescomplemented
175#66879C2314yescomplemented
176C8×Dic11C2314yescomplemented
177#66874C2314yescomplemented
178#66874C2314yescomplemented
179#66873C2314yes—
180#66873C2314yes—
181C4×C11⋊C8C2314yescomplemented
182C2×#3136—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C23×D11—21no—
186C23×D11—24no—
187C23×D11—44no—
188C23×D11—82no—
189C23×D11—82no—
190C23×D11C2×D411yescharacteristic
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—82no—
200C2×D4×C11—82no—
201C2×D4×C11C2412yes—
202C2×D4×C11C2412yes—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—82no—
215C2×C22⋊D11—82no—
216C22×Dic11—24no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—44no—
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224#4341—28no—
225#4341—28no—
226#4341—48no—
227D4×D11—28no—
228D4×D11—28no—
229D4×D11—48no—
230C2×D44—21no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44C2412yes—
234C2×C4×D11—24no—
235C2×C4×D11—82no—
236C2×C4×D11C2×D412yes—
237C2×C4×D11#4114yes—
238C2×C4×D11#4114yes—
239C2×C4×D11C2412yes—
240C2×Dic22—24no—
241C2×Dic22—21no—
242C2×Dic22—24no—
243C2×Dic22—22no—
244C2×Dic22—22no—
245C2×Dic22—82no—
246C2×Dic22—82no—
247C2×Dic22C2412yes—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11C2412yes—
251C2×C8×C11C2412yes—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C42×C11C2×D412yes—
259C42×C11C2412yes—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4C2×D414yes—
266(C2×D11)⋊C4C2×D414yes—
267C4⋊Dic11—24no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—24no—
271C4⋊Dic11C2412yes—
272C4⋊Dic11C2412yes—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4C2×D414yes—
277Dic11⋊C4C2×D414yes—
278C4×Dic11—24no—
279C4×Dic11C2×D412yes—
280C4×Dic11C2412yes—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8C2412yes—
284C2×C11⋊C8C2412yes—
285#4313—28no—
286C8×D11—28no—
287C2×#544—111no—
288C2×#535—111no—
289#3136—1116no—
290C2×#490—111no—
291C2×#490D1111yescharacteristic, complemented
292C2×#489—111no—
293C2×#489—111no—
294C2×#488—111no—
295C2×#488—111no—
296C2×#486—111no—
297C2×#486—111no—
298C2×#417—111no—
299C2×#418—111no—
300C2×#416—111no—
301C22×#102—111no—
302C2×#405—111no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—48no—
319C22×D11—84no—
320C22×D11—84no—
321C22×D11—816no—
322C22×D11#12414yes—
323C22×D11C22×D412yes—
324D4×C11—22no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—42no—
329D4×C11—42no—
330D4×C11—84no—
331D4×C11—84no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4112yes—
342C2×C4×C11C2×#4112yes—
343C2×C4×C11C2511yescharacteristic
344C22⋊D11—48no—
345C22⋊D11—48no—
346C22⋊D11—84no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—48no—
357C2×Dic11#12414yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×D412yes—
361D44—22no—
362D44—22no—
363D44—42no—
364C4×D11—84no—
365C4×D11#12418yes—
366C4×D11C2×#4114yes—
367C4×D11C2×#4114yes—
368Dic22—22no—
369Dic22—22no—
370Dic22—42no—
371Dic22—84no—
372Dic22—84no—
373C8×C11—22no—
374C8×C11—22no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C22×#41—111no—
378C23×D4—111no—
379C22×M16—111no—
380C23×C8—111no—
381#544—118no—
382#544—224no—
383#535—118no—
384#535—224no—
385C2×C4⋊Q8—111no—
386C2×C4⋊Q8—111no—
387C2×C4⋊Q8—221no—
388C2×#127—111no—
389C2×#127C2×D1111yescharacteristic
390C2×#125—111no—
391C2×#125—221no—
392C2×#125C2×D1111yescharacteristic, complemented
393C2×#124—111no—
394C2×#124—111no—
395C2×C22⋊Q8—221no—
396C2×C22⋊Q8—221no—
397C2×#121—221no—
398C2×#121—221no—
399C2×#120—221no—
400C2×#120—221no—
401C2×#117—111no—
402C2×#117—111no—
403C22×C4⋊C4—111no—
404#490—118no—
405#490C2×D1118yescomplemented
406#489—118no—
407#489—118no—
408#488—118no—
409#488—118no—
410#486—118no—
411#486—118no—
412#418—118no—
413#417—118no—
414#416—118no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—118no—
428C2×#102C2×D1111yescharacteristic
429C2×#102C2×D1111yescharacteristic
430C2×#102C2×D1111yescharacteristic, complemented
431C2×#102C2×D1111yescharacteristic, complemented
432#405—118no—
433C2×#97—111no—
434C2×#97C2×D1111yescharacteristic, complemented
435C2×C4×C8—111no—
436C2×C4×C8—111no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—84no—
444C22×C11—84no—
445C22×C11C2×#12412yes—
446C22×C11#57612yes—
447C22×C11#57712yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—28no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—816no—
456C2×D11—84no—
457C2×D11C2×#12414yes—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11C2×#12412yes—
463C4×C11C22×#4111yescharacteristic
464C4×C11C22×#4111yescharacteristic
465Dic11—22no—
466Dic11—22no—
467Dic11—42no—
468Dic11—42no—
469Dic11—42no—
470Dic11C2×#12414yes—
471C25—221no—
472C2×#41—114no—
473C2×#41—222no—
474C2×#41—224no—
475C2×#41—224no—
476C22×Q8—111no—
477C22×Q8—221no—
478C22×Q8—221no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—114no—
482C22×D4—111no—
483C22×D4—224no—
484C22×D4—224no—
485C22×D4—222no—
486C22×D4—221no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4C22×D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—111no—
493C23×C4—221no—
494C23×C4—221no—
495C2×M16—114no—
496C2×M16—224no—
497C22×C8—111no—
498C22×C8—111no—
499C22×C8—114no—
500C22×C8—224no—
501C22×C8C22×D1111yescharacteristic
502C22×C8C22×D1111yescharacteristic
503C4⋊Q8—114no—
504C4⋊Q8—114no—
505C4⋊Q8—222no—
506C4⋊Q8—228no—
507C4⋊Q8—222no—
508#127—22no—
509#127—114no—
510#127—222no—
511#127C22×D1114yes—
512#125—22no—
513#125—114no—
514#125—222no—
515#125—228no—
516#125C22×D1114yescomplemented
517#124—114no—
518#124—114no—
519#124—222no—
520#124—222no—
521C22⋊Q8—228no—
522C22⋊Q8—228no—
523#121—228no—
524#121—228no—
525#120—228no—
526#120—228no—
527#117—114no—
528#117—114no—
529#117—114no—
530#117—222no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—222no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C22⋊C4—111no—
547C2×C22⋊C4—111no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C42—111no—
554C2×C42—221no—
555C2×C42C22×D1111yescharacteristic
556#103—114no—
557#103—114no—
558#103—114no—
559#103—114no—
560#102—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564#102—114no—
565#102—114no—
566#102—114no—
567#102—114no—
568#102C22×D1114yes—
569#102C22×D1114yes—
570#102C22×D1114yescomplemented
571#102C22×D1114yescomplemented
572#97—114no—
573#97C22×D1114yescomplemented
574C4×C8—114no—
575C4×C8—114no—
576C2×C11—82no—
577C2×C11—82no—
578C2×C11#313614yescomplemented
579C2×C11C22×#12411yescharacteristic
580C2×C11C2×#57611yescharacteristic
581C2×C11C2×#57711yescharacteristic
582D11—24no—
583D11—82no—
584C24—21no—
585C24—21no—
586C24—111no—
587C24—224no—
588C24—221no—
589C24—444no—
590C24—882no—
591C24—882no—
592#41—228no—
593#41—228no—
594#41—448no—
595C2×Q8—112no—
596C2×Q8—224no—
597C2×Q8—221no—
598C2×Q8—224no—
599C2×Q8—222no—
600C2×Q8—222no—
601C2×Q8—882no—
602C2×Q8—882no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—112no—
614C2×D4—228no—
615C2×D4—228no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—221no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—448no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—882no—
627C2×D4—882no—
628C2×D4C23×D1112yes—
629C2×D4C23×D1112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—111no—
633C22×C4—112no—
634C22×C4—114no—
635C22×C4—114no—
636C22×C4—112no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—444no—
645C22×C4—882no—
646C22×C4D4×D1111yescharacteristic
647C22×C4D4×D1111yescharacteristic
648C22×C4C23×D1111yescharacteristic
649M16—228no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—112no—
653C2×C8—112no—
654C2×C8—228no—
655C2×C8—222no—
656C2×C8—222no—
657C2×C8C23×D1112yes—
658C2×C8C23×D1112yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—114no—
664C4⋊C4—114no—
665C4⋊C4—112no—
666C4⋊C4—112no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—224no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—224no—
674C4⋊C4C23×D1112yes—
675C4⋊C4C23×D1112yes—
676C22⋊C4—114no—
677C22⋊C4—114no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C42—112no—
684C42—112no—
685C42—224no—
686C42D4×D1112yes—
687C42C23×D1112yes—
688C11C2×#313611yescharacteristic, complemented, Sylow
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—112no—
698C23—114no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—448no—
703C23—442no—
704C23—442no—
705C23—442no—
706C23—884no—
707C23—884no—
708C23—8816no—
709C23C2×D4×D1111yescharacteristic
710Q8—222no—
711Q8—222no—
712Q8—442no—
713Q8—884no—
714Q8—884no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—222no—
724D4—222no—
725D4—448no—
726D4—448no—
727D4—442no—
728D4—884no—
729D4—884no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—112no—
737C2×C4—114no—
738C2×C4—114no—
739C2×C4—114no—
740C2×C4—118no—
741C2×C4—112no—
742C2×C4—112no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—448no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—884no—
753C2×C4C2×D4×D1112yes—
754C2×C4C2×D4×D1112yes—
755C2×C4C2×D4×D1111yescharacteristic
756C2×C4#41×D1112yes—
757C2×C4#41×D1112yes—
758C2×C4C24×D1111yescharacteristic
759C8—22no—
760C8—22no—
761C8—222no—
762C8—222no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—114no—
772C22—228no—
773C22—222no—
774C22—222no—
775C22—442no—
776C22—442no—
777C22—442no—
778C22—8816no—
779C22—884no—
780C22D11×#12412yes—
781C22#1062330512yes—
782C22#1062330612yes—
783C22C22×D4×D1111yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—114no—
789C4—222no—
790C4—222no—
791C4—442no—
792C4—442no—
793C4—442no—
794C4D11×#12412yes—
795C4C2×#41×D1111yescharacteristic
796C4C2×#41×D1111yescharacteristic
797C2—82no—
798C2—82no—
799C2—224no—
800C2—882no—
801C2#1307897114yesdirect product factor
802C2C2×D11×#12411yescharacteristic
803C2C2×#1062330511yescharacteristic
804C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
prime radicalC2×#10623246C2
hypercenterC2×#490D11
hypocenterC11C2×#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623220C2semidirect
3. #13078971C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622327C2semidirect
6. C2×#10622378C2semidirect
7. C2×#10622681C2semidirect
8. C2×#10622381C2semidirect
9. C2×#10622683C2semidirect
10. C2×#10622373C2semidirect
11. C2×#10622384C2semidirect
12. C2×#10622383C2semidirect
13. C2×#10622385C2semidirect
14. C2×D11×#102C2semidirect
15. C2×#10622321C2semidirect
16. C2×C11×#490C2semidirect
20. C2×C11×#125C22semidirect
32. #10623220C22semidirect
37. C2×#66943C22semidirect
40. C2×#66941C22semidirect
43. C2×#66922C22semidirect
44. C11×#490C22semidirect
47. C2×C11×#102C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×#97C22semidirect
52. C2×#66896C22semidirect
53. C2×#66896C22semidirect
56. C2×#66880C22semidirect
57. C2×#66880C22semidirect
58. C2×#66879C22semidirect
59. C2×C8×Dic11C22semidirect
60. #10622683C22semidirect
61. #10622681C22semidirect
62. C2×#66874C22semidirect
63. C2×#66874C22semidirect
66. C2×C4×C11⋊C8C22semidirect
67. #10622385C22semidirect
68. #10622384C22semidirect
69. #10622383C22semidirect
70. D11×#102C22semidirect
71. #10622381C22semidirect
72. #10622378C22semidirect
73. #10622377C22semidirect
74. #10622373C22semidirect
75. #10622327C22semidirect
76. #10622321C22semidirect
106. C11×#125C23semidirect
151. #66943C23semidirect
155. #66941C23semidirect
161. #66922C23semidirect
164. C11×#102C23semidirect
165. C11×#102C23semidirect
166. C11×#97C23semidirect
169. #66896C23semidirect
170. #66896C23semidirect
173. #66880C23semidirect
174. #66880C23semidirect
175. #66879C23semidirect
176. C8×Dic11C23semidirect
177. #66874C23semidirect
178. #66874C23semidirect
181. C4×C11⋊C8C23semidirect
291. C2×#490D11semidirect
392. C2×#125C2×D11semidirect
405. #490C2×D11semidirect
430. C2×#102C2×D11semidirect
431. C2×#102C2×D11semidirect
434. C2×#97C2×D11semidirect
516. #125C22×D11semidirect
570. #102C22×D11semidirect
571. #102C22×D11semidirect
573. #97C22×D11semidirect
578. C2×C11#3136semidirect
688. C11C2×#3136semidirect
801. C2#13078971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232202
C2×#106232462
#130789712
C2×#106223772
C2×#106223272
C2×#106223782
C2×#106226812
C2×#106223812
C2×#106226832
C2×#106223732
C2×#106223842
C2×#106223832
C2×#106223852
C2×D11×#1022
C2×#106223212
C2×C11×#4902
C2×#313611