Finite Group Databasebeta

← C2×#13078548 #15621561

Subgroups — C2×#13078548 #15621561

Order 2816.

2346 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13078548C2116yesmaximal, direct product factor
4C2×#10622427C211yesmaximal, characteristic, complemented
5C2×#10622428C211yesmaximal, characteristic, complemented
6C2×#10622658C211yesmaximal, characteristic, complemented
7C2×#10622498C211yesmaximal, characteristic, complemented
8C2×#10622479C211yesmaximal, characteristic, complemented
9C2×#10622350C211yesmaximal, characteristic, complemented
10C2×#10622616C211yesmaximal, characteristic, complemented
11C2×#10622494C211yesmaximal, characteristic, complemented
12C2×#10622474C211yesmaximal, characteristic, complemented
13C2×#10622416C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×#10622339C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26#10623158—24no—
27#10623158C2218yes—
28D11×#117—24no—
29D11×#117C2218yescomplemented
30C2×#66948C2211yescharacteristic
31C2×#66947—21no—
32C2×#66946—21no—
33C2×#66945C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×#66945C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66935—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C2×C22⋊C4×D11—21no—
41C2×#66930—21no—
42C2×#66925—21no—
43C2×C42×D11—21no—
44C11×#485C2218yescomplemented
45C2×C11×#107C2211yescharacteristic, complemented
46C2×C11×#106C2211yescharacteristic, complemented
47C2×C11×#103C2211yescharacteristic, complemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66885C2211yescharacteristic, complemented
54C2×#66885C2211yescharacteristic, complemented
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×#66882C2211yescharacteristic, complemented
58C2×#66881C2211yescharacteristic, complemented
59#10622658C2218yescomplemented
60#10622616C2218yescomplemented
61C2×#66873C2211yescharacteristic, complemented
62C2×#66873C2211yescharacteristic, complemented
63C2×#66872C2211yescharacteristic, complemented
64C2×#66872C2211yescharacteristic, complemented
65C2×#66871C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622498C2218yescomplemented
68#10622494C2218yescomplemented
69#10622479C2218yescomplemented
70#10622474C2218yescomplemented
71#10622428C2218yescomplemented
72#10622427C2218yescomplemented
73#10622416C2218yescomplemented
74#10622416C2218yescomplemented
75#10622350C2218yescomplemented
76#10622339C2218yescomplemented
77C24×D11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C23×Dic11D411yescharacteristic
82C2×#4343—22no—
83C2×#4343—24no—
84C2×#4343—24no—
85C2×#4343C2314yes—
86C22×D44—21no—
87C22×D44—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—24no—
90C22×C4×D11—24no—
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11D411yescharacteristic
95C22×C4×D11D411yescharacteristic
96C22×C4×D11D414yes—
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2314yes—
99C22×C4×D11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8C2314yes—
104C11×#117—22no—
105C11×#117C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C42×C11—21no—
113C2×C22⋊Dic11—21no—
114#66999—22no—
115#66999C2314yes—
116#66983—22no—
117#66983C2314yes—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124#66979—22no—
125#66979C2314yes—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×#4313—24no—
139C2×#4313—24no—
140C2×#4313C2314yes—
141C2×#4313C2314yes—
142#66948—22no—
143#66948C2314yes—
144#66947—28no—
145#66946—28no—
146#66945—22no—
147#66945—22no—
148#66945—22no—
149#66945C2314yes—
150#66945C2314yes—
151#66945C2314yes—
152C4⋊C4×D11—22no—
153C4⋊C4×D11—22no—
154C4⋊C4×D11C2314yes—
155C4⋊C4×D11C2314yes—
156#66935—28no—
157(C22⋊D11)⋊C4—28no—
158C22⋊C4×D11—28no—
159#66930—28no—
160#66925—28no—
161C42×D11—28no—
162C11×#107C2314yescomplemented
163C11×#106C2314yescomplemented
164C11×#103C2314yescomplemented
165C11×#103C2314yescomplemented
166C11×C22⋊C8C2314yes—
167#66899C2314yescomplemented
168#66899C2314yescomplemented
169C22⋊(C11⋊C8)C2314yes—
170#66885C2314yescomplemented
171#66885C2314yescomplemented
172(C2×D11)⋊C8C2314yes—
173(C2×D11)⋊C8C2314yes—
174#66882C2314yescomplemented
175#66881C2314yescomplemented
176#66873C2314yescomplemented
177#66873C2314yescomplemented
178#66872C2314yescomplemented
179#66872C2314yescomplemented
180#66871C2314yescomplemented
181#66871C2314yescomplemented
182C2×#3093—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—24no—
185C23×D11—21no—
186C23×D11—42no—
187C23×D11—42no—
188C23×D11C2×D411yescharacteristic
189C23×D11C2×D411yescharacteristic
190C23×D11C2×D414yes—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11C2412yes—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C22×Dic11—24no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214#4343—28no—
215#4343—28no—
216#4343—48no—
217C2×D44—24no—
218C2×D44—24no—
219C2×D44—21no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44—44no—
223C2×D44—44no—
224C2×D44C2412yes—
225C2×C4×D11—24no—
226C2×C4×D11—216no—
227C2×C4×D11—28no—
228C2×C4×D11—28no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—24no—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11—44no—
236C2×C4×D11—44no—
237C2×C4×D11—44no—
238C2×C4×D11C2×D414yes—
239C2×C4×D11C2×D414yes—
240C2×C4×D11C2×D412yes—
241C2×C4×D11C2×D412yes—
242C2×C4×D11#4114yes—
243C2×C4×D11#4114yes—
244C2×C4×D11C2412yes—
245C2×C4×D11C2412yes—
246C2×C8×C11—22no—
247C2×C8×C11—22no—
248C2×C8×C11C2412yes—
249C2×C8×C11C2412yes—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4C2412yes—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C42×C11—24no—
260C22⋊Dic11—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11C2412yes—
271C4⋊Dic11C2412yes—
272C4⋊Dic11C2412yes—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276C4×Dic11—24no—
277C4×Dic11—24no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284#4313—28no—
285#4313—28no—
286C2×#525—111no—
287C22×#117—111no—
288#3093—1116no—
289C2×#485—111no—
290C2×#485—111no—
291C2×#485—111no—
292C2×#485D1111yescharacteristic, complemented
293C2×#482—111no—
294C2×#482—111no—
295C2×#482—111no—
296C2×#482—111no—
297C2×#428—111no—
298C2×#428—111no—
299C2×#417—111no—
300C2×#417—111no—
301C2×#407—111no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11C22×D412yes—
306C23×C11C22×D411yescharacteristic
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—28no—
313C22×D11—22no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—416no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11#12314yes—
321C22×D11C22×D412yes—
322C22×D11C22×D412yes—
323Q8×C11—22no—
324Q8×C11—22no—
325Q8×C11—42no—
326C2×C4×C11—22no—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2×#4112yes—
341C2×C4×C11C2×#4112yes—
342C2×C4×C11C2511yescharacteristic
343C22⋊D11—48no—
344C2×Dic11—22no—
345C2×Dic11—28no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11#12314yes—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355D44—22no—
356D44—22no—
357D44—48no—
358D44—48no—
359D44—42no—
360C4×D11—28no—
361C4×D11—24no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—28no—
365C4×D11—48no—
366C4×D11—48no—
367C4×D11—48no—
368C4×D11#12318yes—
369C4×D11C2×#4114yes—
370C4×D11C2×#4114yes—
371C8×C11—22no—
372C8×C11—22no—
373C11⋊C8—22no—
374C11⋊C8—22no—
375C22×#41—111no—
376C24×C4—111no—
377C22×M16—111no—
378C22×M16—111no—
379#525—118no—
380#525—224no—
381C2×#123—221no—
382C2×C22⋊Q8—111no—
383C2×C22⋊Q8C2×D1111yescharacteristic
384C2×#121—111no—
385C2×#121—111no—
386C2×#120—221no—
387C2×C4×D4—221no—
388C2×C4×D4—221no—
389C2×#117—111no—
390C2×#117—118no—
391C2×#117—111no—
392C2×#117—111no—
393C2×#117—111no—
394C2×#117—221no—
395C2×#117—221no—
396C2×#117—224no—
397C2×#117C2×D1111yescharacteristic
398C22×C4⋊C4—111no—
399C22×C4⋊C4—111no—
400C22×C22⋊C4—221no—
401C22×C42—221no—
402#485—118no—
403#485—118no—
404#485—118no—
405#485C2×D1118yescomplemented
406#482—118no—
407#482—118no—
408#482—118no—
409#482—118no—
410#428—118no—
411#428—118no—
412C2×#107—111no—
413C2×#107—111no—
414C2×#107—111no—
415C2×#107C2×D1111yescharacteristic, complemented
416C2×#106—111no—
417C2×#106—111no—
418C2×#106—111no—
419C2×#106C2×D1111yescharacteristic, complemented
420#417—118no—
421#417—118no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103C2×D1111yescharacteristic, complemented
425C2×#103C2×D1111yescharacteristic, complemented
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430#407—118no—
431C2×C22⋊C8—111no—
432C2×C22⋊C8—111no—
433C2×C22⋊C8—111no—
434C2×C22⋊C8C2×D1111yescharacteristic
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—44no—
439C22×C11C2×#12312yes—
440C22×C11#57512yes—
441C22×C11#57512yes—
442C22×C11C23×D411yescharacteristic
443C2×D11—28no—
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—416no—
450C2×D11—44no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—84no—
455C2×D11C2×#12314yes—
456C4×C11—22no—
457C4×C11—42no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11C2×#12312yes—
462C4×C11C22×#4111yescharacteristic
463C4×C11C22×#4111yescharacteristic
464Dic11—22no—
465Dic11—42no—
466Dic11—42no—
467Dic11—42no—
468Dic11C2×#12314yes—
469C25—111no—
470C2×#41—114no—
471C2×#41—222no—
472C2×#41—224no—
473C2×#41—224no—
474C22×Q8C22×D1111yescharacteristic
475C22×D4—111no—
476C22×D4—221no—
477C22×D4—221no—
478C22×D4—221no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—114no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—114no—
486C23×C4—224no—
487C23×C4—224no—
488C23×C4—221no—
489C23×C4—221no—
490C23×C4—221no—
491C23×C4C22×D1111yescharacteristic
492C2×M16—114no—
493C2×M16—114no—
494C2×M16—224no—
495C2×M16—224no—
496C22×C8—111no—
497C22×C8—111no—
498C22×C8C22×D1111yescharacteristic
499C22×C8C22×D1111yescharacteristic
500#123—228no—
501C22⋊Q8—22no—
502C22⋊Q8—114no—
503C22⋊Q8—222no—
504C22⋊Q8C22×D1114yes—
505#121—114no—
506#121—114no—
507#121—222no—
508#121—222no—
509#120—228no—
510C4×D4—228no—
511C4×D4—228no—
512#117—22no—
513#117—114no—
514#117—114no—
515#117—114no—
516#117—114no—
517#117—228no—
518#117—228no—
519#117—222no—
520#117—222no—
521#117—222no—
522#117—222no—
523#117C22×D1114yes—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—222no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—228no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C42—21no—
549C2×C42—228no—
550C2×C42—221no—
551C2×C42—221no—
552C2×C42—221no—
553C2×C42—221no—
554#107—114no—
555#107—114no—
556#107—114no—
557#107C22×D1114yescomplemented
558#106—114no—
559#106—114no—
560#106—114no—
561#106C22×D1114yescomplemented
562#103—114no—
563#103—114no—
564#103C22×D1114yescomplemented
565#103C22×D1114yescomplemented
566#102—114no—
567#102—114no—
568#102—114no—
569#102—114no—
570C22⋊C8—114no—
571C22⋊C8—114no—
572C22⋊C8—114no—
573C22⋊C8C22×D1114yes—
574C2×C11—42no—
575C2×C11#309314yescomplemented
576C2×C11C22×#12311yescharacteristic
577C2×C11C2×#57511yescharacteristic
578C2×C11C2×#57511yescharacteristic
579D11—24no—
580D11—42no—
581D11—82no—
582C24—111no—
583C24—111no—
584C24—114no—
585C24—224no—
586C24—221no—
587C24—442no—
588C24—442no—
589C24D4×D1111yescharacteristic
590#41—228no—
591#41—228no—
592#41—448no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8C23×D1112yes—
597C2×D4—112no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—221no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—444no—
605C2×D4—444no—
606C2×D4—444no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—111no—
614C22×C4—112no—
615C22×C4—114no—
616C22×C4—114no—
617C22×C4—112no—
618C22×C4—114no—
619C22×C4—111no—
620C22×C4—114no—
621C22×C4—114no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—224no—
625C22×C4—2216no—
626C22×C4—228no—
627C22×C4—228no—
628C22×C4—224no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—224no—
632C22×C4—224no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—444no—
639C22×C4—444no—
640C22×C4—444no—
641C22×C4D4×D1112yes—
642C22×C4D4×D1111yescharacteristic
643C22×C4C23×D1112yes—
644C22×C4C23×D1111yescharacteristic
645M16—228no—
646M16—228no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—112no—
650C2×C8—112no—
651C2×C8—222no—
652C2×C8—222no—
653C2×C8C23×D1112yes—
654C2×C8C23×D1112yes—
655C4⋊C4—24no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—112no—
660C4⋊C4—112no—
661C4⋊C4—112no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—221no—
666C4⋊C4—221no—
667C4⋊C4—221no—
668C4⋊C4C23×D1112yes—
669C4⋊C4C23×D1112yes—
670C4⋊C4C23×D1112yes—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C42—24no—
681C42—224no—
682C42—224no—
683C42—224no—
684C42—224no—
685C11C2×#309311yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—22no—
689C23—114no—
690C23—112no—
691C23—112no—
692C23—228no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—444no—
700C23—444no—
701C23—4416no—
702C23—442no—
703C23—442no—
704C23—442no—
705C23C2×D4×D1112yes—
706C23C2×D4×D1111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710D4—222no—
711D4—222no—
712D4—448no—
713D4—448no—
714D4—448no—
715D4—442no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—114no—
729C2×C4—112no—
730C2×C4—118no—
731C2×C4—114no—
732C2×C4—114no—
733C2×C4—112no—
734C2×C4—228no—
735C2×C4—228no—
736C2×C4—228no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—448no—
745C2×C4—448no—
746C2×C4—448no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4C2×D4×D1112yes—
751C2×C4C2×D4×D1111yescharacteristic
752C2×C4#41×D1112yes—
753C2×C4#41×D1112yes—
754C2×C4C24×D1111yescharacteristic
755C8—22no—
756C8—22no—
757C8—222no—
758C8—222no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—114no—
764C22—228no—
765C22—222no—
766C22—222no—
767C22—222no—
768C22—222no—
769C22—222no—
770C22—4416no—
771C22—444no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22—884no—
776C22D11×#12312yes—
777C22#1062329912yes—
778C22#1062330812yes—
779C22C22×D4×D1111yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—114no—
786C4—222no—
787C4—442no—
788C4—442no—
789C4—442no—
790C4D11×#12312yes—
791C4C2×#41×D1111yescharacteristic
792C4C2×#41×D1111yescharacteristic
793C2—42no—
794C2—224no—
795C2—442no—
796C2—882no—
797C2#1307854814yesdirect product factor
798C2C2×D11×#12311yescharacteristic
799C2C2×#1062329911yescharacteristic
800C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC2×#10623158C2
hypercenterC2×#485D11
hypocenterC11C2×#3093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×D11×#117C2semidirect
3. #13078548C2direct (N × H)
4. C2×#10622427C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622658C2semidirect
7. C2×#10622498C2semidirect
8. C2×#10622479C2semidirect
9. C2×#10622350C2semidirect
10. C2×#10622616C2semidirect
11. C2×#10622494C2semidirect
12. C2×#10622474C2semidirect
13. C2×#10622416C2semidirect
14. C2×#10622416C2semidirect
15. C2×#10622339C2semidirect
16. C2×C11×#485C2semidirect
29. D11×#117C22semidirect
44. C11×#485C22semidirect
45. C2×C11×#107C22semidirect
46. C2×C11×#106C22semidirect
47. C2×C11×#103C22semidirect
48. C2×C11×#103C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
53. C2×#66885C22semidirect
54. C2×#66885C22semidirect
57. C2×#66882C22semidirect
58. C2×#66881C22semidirect
59. #10622658C22semidirect
60. #10622616C22semidirect
61. C2×#66873C22semidirect
62. C2×#66873C22semidirect
63. C2×#66872C22semidirect
64. C2×#66872C22semidirect
65. C2×#66871C22semidirect
66. C2×#66871C22semidirect
67. #10622498C22semidirect
68. #10622494C22semidirect
69. #10622479C22semidirect
70. #10622474C22semidirect
71. #10622428C22semidirect
72. #10622427C22semidirect
73. #10622416C22semidirect
74. #10622416C22semidirect
75. #10622350C22semidirect
76. #10622339C22semidirect
162. C11×#107C23semidirect
163. C11×#106C23semidirect
164. C11×#103C23semidirect
165. C11×#103C23semidirect
167. #66899C23semidirect
168. #66899C23semidirect
170. #66885C23semidirect
171. #66885C23semidirect
174. #66882C23semidirect
175. #66881C23semidirect
176. #66873C23semidirect
177. #66873C23semidirect
178. #66872C23semidirect
179. #66872C23semidirect
180. #66871C23semidirect
181. #66871C23semidirect
292. C2×#485D11semidirect
405. #485C2×D11semidirect
415. C2×#107C2×D11semidirect
419. C2×#106C2×D11semidirect
424. C2×#103C2×D11semidirect
425. C2×#103C2×D11semidirect
557. #107C22×D11semidirect
561. #106C22×D11semidirect
564. #103C22×D11semidirect
565. #103C22×D11semidirect
575. C2×C11#3093semidirect
685. C11C2×#3093semidirect
797. C2#13078548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×D11×#1172
#130785482
C2×#106224272
C2×#106224282
C2×#106226582
C2×#106224982
C2×#106224792
C2×#106223502
C2×#106226162
C2×#106224942
C2×#106224742
C2×#106224162
C2×#106223392
C2×C11×#4852
C2×#309311