Finite Group Databasebeta

← C2×#13078861 #15622069

Subgroups — C2×#13078861 #15622069

Order 2816.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623229C211yesmaximal, characteristic, complemented
2C2×#10623076C211yesmaximal, characteristic, complemented
3#13078861C2116yesmaximal, direct product factor
4C2×#10622498C211yesmaximal, characteristic, complemented
5C2×#10622479C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622456C211yesmaximal, characteristic, complemented
8C2×#10622628C211yesmaximal, characteristic, complemented
9C2×#10622386C211yesmaximal, characteristic, complemented
10C2×#10622386C211yesmaximal, characteristic, complemented
11C2×#10622482C211yesmaximal, characteristic, complemented
12C2×#10622398C211yesmaximal, characteristic, complemented
13C2×#10622485C211yesmaximal, characteristic, complemented
14C2×#10622369C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#478C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×C4×C22⋊D11—21no—
24C22×(C2×D11)⋊C4—21no—
25C22×D88C2211yescharacteristic
26C22×D88C2211yescharacteristic
27#10623229—24no—
28#10623229C2218yescomplemented
29#10623076—24no—
30#10623076C2218yescomplemented
31C2×#66948—21no—
32C2×#66948—21no—
33C2×#66948C2211yescharacteristic
34C2×#66948C2211yescharacteristic
35C2×#66947—21no—
36C2×#66947—21no—
37C2×#66946C2211yescharacteristic
38C2×#66946C2211yescharacteristic, complemented
39C2×#66946C2211yescharacteristic, complemented
40C2×#66945C2211yescharacteristic
41C2×(C22⋊D11)⋊C4—21no—
42C2×C22⋊C4×D11—21no—
43C2×#66927C2211yescharacteristic, complemented
44C2×C4×D44C2211yescharacteristic
45C2×#66925C2211yescharacteristic
46C11×#478C2218yescomplemented
47C2×C11×#107C2211yescharacteristic, complemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×C4⋊C8C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66885C2211yescharacteristic, complemented
53C2×#66885C2211yescharacteristic, complemented
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×#66879C2211yescharacteristic, complemented
57C2×C8×Dic11C2211yescharacteristic, complemented
58#10622679C2218yescomplemented
59#10622628C2218yescomplemented
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic, complemented
63C2×#66873C2211yescharacteristic, complemented
64C2×#66872C2211yescharacteristic, complemented
65C2×#66871C2211yescharacteristic, complemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622498C2218yescomplemented
68#10622485C2218yescomplemented
69#10622482C2218yescomplemented
70#10622479C2218yescomplemented
71#10622456C2218yescomplemented
72#10622453C2218yescomplemented
73#10622398C2218yescomplemented
74#10622386C2218yescomplemented
75#10622386C2218yescomplemented
76#10622369C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C2×D4×D11—24no—
83C2×D4×D11—24no—
84C2×D4×D11—22no—
85C2×D4×D11C2314yes—
86C22×D44—21no—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44—21no—
90C22×D44C2311yescharacteristic
91C22×D44C2311yescharacteristic
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#125—22no—
101C11×#125C2314yescomplemented
102C4×D4×C11—22no—
103C4×D4×C11C2314yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112D4×Dic11—22no—
113D4×Dic11C2314yes—
114C2×#4323—24no—
115C2×#4323—24no—
116C2×#4323C2314yes—
117C2×#4323C2314yes—
118C4×C22⋊D11—28no—
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—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—28no—
127C2×(C2×D11)⋊C4D411yescharacteristic
128C2×(C2×D11)⋊C4D411yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4D411yescharacteristic
131C2×Dic11⋊C4D411yescharacteristic
132C2×C4×Dic11—21no—
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×D88—24no—
137C2×D88—24no—
138C2×D88C2314yes—
139C2×D88C2314yes—
140#66948—22no—
141#66948—22no—
142#66948—28no—
143#66948—28no—
144#66948C2314yes—
145#66948C2314yes—
146#66947—28no—
147#66947—28no—
148#66946—22no—
149#66946—22no—
150#66946—22no—
151#66946C2314yes—
152#66946C2314yescomplemented
153#66946C2314yescomplemented
154#66945—22no—
155#66945C2314yes—
156(C22⋊D11)⋊C4—28no—
157C22⋊C4×D11—28no—
158#66927—22no—
159#66927C2314yescomplemented
160C4×D44—22no—
161C4×D44C2314yes—
162#66925D414yes—
163#66925C2314yes—
164C11×#107C2314yescomplemented
165C11×#106C2314yescomplemented
166C11×C4⋊C8C2314yescomplemented
167C11×#102C2314yes—
168C11×#102C2314yes—
169#66885C2314yescomplemented
170#66885C2314yescomplemented
171(C2×D11)⋊C8C2314yes—
172(C2×D11)⋊C8C2314yes—
173#66879C2314yescomplemented
174C8×Dic11C2314yescomplemented
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yescomplemented
178#66873C2314yescomplemented
179#66872C2314yescomplemented
180#66871C2314yescomplemented
181C4⋊(C11⋊C8)C2314yescomplemented
182C2×#3122—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11—28no—
186C23×D11—24no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—82no—
190C23×D11—82no—
191C23×D11C2×D411yescharacteristic
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11#4114yes—
195C2×D4×C11C2412yes—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—24no—
200C22×C4×C11—82no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—28no—
205C2×C22⋊D11—24no—
206C22×Dic11—24no—
207C22×Dic11—21no—
208C22×Dic11—82no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212D4×D11—216no—
213D4×D11—28no—
214D4×D11—28no—
215C2×D44—24no—
216C2×D44—24no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—24no—
221C2×D44—24no—
222C2×D44—22no—
223C2×D44—22no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—82no—
228C2×D44—82no—
229C2×D44—82no—
230C2×D44—82no—
231C2×D44#4114yes—
232C2×D44C2412yes—
233C2×D44C2412yes—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—82no—
242C2×C4×D11—82no—
243C2×C4×D11—82no—
244C2×C4×D11—82no—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2412yes—
247C2×C8×C11—22no—
248C2×C8×C11—22no—
249C2×C8×C11C2412yes—
250C2×C8×C11C2412yes—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—24no—
260C42×C11C2×D412yes—
261C42×C11C2412yes—
262C22⋊Dic11—24no—
263#4323—28no—
264#4323—28no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4C2×D414yes—
273(C2×D11)⋊C4C2×D414yes—
274C4⋊Dic11—21no—
275C4⋊Dic11C2412yes—
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—
285D88—28no—
286D88—28no—
287C2×#540—111no—
288C2×#518—111no—
289#3122—1116no—
290C2×#482—111no—
291C2×#482—111no—
292C2×#478—111no—
293C2×#478D1111yescharacteristic, complemented
294C2×#459—111no—
295C2×#459—111no—
296C2×#447—111no—
297C2×#447—111no—
298C2×#442—111no—
299C2×#442—111no—
300C2×C4×D8—111no—
301C2×C4×D8—111no—
302C2×#433—111no—
303C23×C11—24no—
304C23×C11—22no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11C22×D411yescharacteristic
308C22×D11—22no—
309C22×D11—24no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—216no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—84no—
325C22×D11—84no—
326C22×D11—816no—
327C22×D11C22×D412yes—
328D4×C11—24no—
329D4×C11—22no—
330D4×C11C2×#4114yes—
331C2×C4×C11—22no—
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×C11—42no—
339C2×C4×C11—84no—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C2×#4112yes—
344C2×C4×C11C2×#4112yes—
345C2×C4×C11C2511yescharacteristic
346C22⋊D11—216no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—42no—
352C2×Dic11—84no—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356D44—24no—
357D44—22no—
358D44—22no—
359D44—22no—
360D44—22no—
361D44—22no—
362D44—42no—
363D44—42no—
364D44—84no—
365D44—84no—
366D44—84no—
367D44—84no—
368D44C2×#4114yes—
369C4×D11—24no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—84no—
373C4×D11—84no—
374C4×D11—84no—
375C4×D11—84no—
376C8×C11—22no—
377C8×C11—22no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C23×D4—111no—
381C22×D8—111no—
382C22×D8—111no—
383C22×D8—111no—
384C22×D8—111no—
385#540—118no—
386#540—224no—
387C2×#127—111no—
388C2×#125C2×D1111yescharacteristic, complemented
389C2×#123—221no—
390C2×#123—221no—
391C2×#121—111no—
392C2×#121—111no—
393C2×#121—221no—
394C2×#121—221no—
395#518—118no—
396#518—224no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×C4×D4—111no—
400C2×C4×D4—111no—
401C2×C4×D4—111no—
402C2×C4×D4—221no—
403C2×C4×D4—221no—
404C2×C4×D4C2×D1111yescharacteristic
405C2×#117—111no—
406C2×#117—111no—
407C22×C22⋊C4—221no—
408C22×C22⋊C4—221no—
409#482—118no—
410#482—118no—
411#478—118no—
412#478C2×D1118yescomplemented
413#459—118no—
414#459—118no—
415#447—118no—
416#447—118no—
417#442—118no—
418#442—118no—
419C4×D8—118no—
420C4×D8—118no—
421#433—118no—
422C2×#107—111no—
423C2×#107C2×D1111yescharacteristic, complemented
424C2×#106—111no—
425C2×#106C2×D1111yescharacteristic, complemented
426C2×C4⋊C8—111no—
427C2×C4⋊C8C2×D1111yescharacteristic, complemented
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102C2×D1111yescharacteristic
435C2×#102C2×D1111yescharacteristic
436C2×C22⋊C8—111no—
437C2×C22⋊C8—111no—
438C2×#97—111no—
439C2×C4×C8—111no—
440C22×C11—24no—
441C22×C11—48no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11#52512yes—
445C22×C11#57612yes—
446C22×C11#57612yes—
447C22×C11C23×D411yescharacteristic
448C2×D11—22no—
449C2×D11—24no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—44no—
453C2×D11—48no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—816no—
463C2×D11—84no—
464C2×D11—84no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11#52512yes—
471C4×C11C22×#4111yescharacteristic
472C4×C11C22×#4111yescharacteristic
473Dic11—22no—
474Dic11—22no—
475Dic11—22no—
476Dic11—42no—
477C25—221no—
478C22×D4—114no—
479C22×D4—111no—
480C22×D4—111no—
481C22×D4—111no—
482C22×D4—221no—
483C22×D4—221no—
484C22×D4—222no—
485C22×D4—221no—
486C22×D4—224no—
487C22×D4—224no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4C22×D1111yescharacteristic
491C23×C4—21no—
492C23×C4—111no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4—221no—
498C2×D8—114no—
499C2×D8—114no—
500C2×D8—114no—
501C2×D8—114no—
502C2×D8—224no—
503C2×D8—224no—
504C2×D8—224no—
505C2×D8—224no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8C22×D1111yescharacteristic
509C22×C8C22×D1111yescharacteristic
510#127—114no—
511#127—222no—
512#125—22no—
513#125C22×D1114yescomplemented
514#123—228no—
515#123—228no—
516#121—114no—
517#121—114no—
518#121—228no—
519#121—228no—
520#121—222no—
521#121—222no—
522C4×D4—22no—
523C4×D4—114no—
524C4×D4—114no—
525C4×D4—114no—
526C4×D4—114no—
527C4×D4—114no—
528C4×D4—222no—
529C4×D4—222no—
530C4×D4—222no—
531C4×D4—222no—
532C4×D4—228no—
533C4×D4—228no—
534C4×D4—222no—
535C4×D4C22×D1114yes—
536#117—114no—
537#117—114no—
538#117—114no—
539#117—222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C4⋊C4C22×D1111yescharacteristic
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—111no—
551C2×C22⋊C4—228no—
552C2×C22⋊C4—228no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C42—111no—
562C2×C42—221no—
563C2×C42C22×D1111yescharacteristic
564#107—114no—
565#107C22×D1114yescomplemented
566#106—114no—
567#106C22×D1114yescomplemented
568C4⋊C8—114no—
569C4⋊C8C22×D1114yescomplemented
570#102—114no—
571#102—114no—
572#102—114no—
573#102—114no—
574#102—114no—
575#102—114no—
576#102C22×D1114yes—
577#102C22×D1114yes—
578C22⋊C8—114no—
579C22⋊C8—114no—
580#97—114no—
581C4×C8—114no—
582C2×C11—44no—
583C2×C11#312214yescomplemented
584C2×C11C2×#52511yescharacteristic
585C2×C11C2×#57611yescharacteristic
586C2×C11C2×#57611yescharacteristic
587D11—42no—
588D11—44no—
589D11—82no—
590D11—82no—
591C24—21no—
592C24—111no—
593C24—224no—
594C24—228no—
595C24—221no—
596C24—221no—
597C24—221no—
598C24—882no—
599C24—882no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—114no—
603C2×D4—112no—
604C2×D4—112no—
605C2×D4—112no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—228no—
610C2×D4—2216no—
611C2×D4—228no—
612C2×D4—228no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—222no—
619C2×D4—222no—
620C2×D4—222no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—882no—
624C2×D4—882no—
625C2×D4—882no—
626C2×D4—882no—
627C2×D4#434314yes—
628C2×D4C23×D1112yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—82no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—221no—
646C22×C4—224no—
647C22×C4—882no—
648C22×C4—882no—
649C22×C4—882no—
650C22×C4—882no—
651C22×C4—882no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655D8—228no—
656D8—228no—
657D8—228no—
658D8—228no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8C23×D1112yes—
666C2×C8C23×D1112yes—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—114no—
673C4⋊C4—114no—
674C4⋊C4—112no—
675C4⋊C4—221no—
676C4⋊C4C23×D1112yes—
677C4⋊C4C23×D1112yes—
678C4⋊C4C23×D1112yes—
679C22⋊C4—24no—
680C22⋊C4—114no—
681C22⋊C4—114no—
682C22⋊C4—224no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C42—112no—
691C42—112no—
692C42—224no—
693C42D4×D1112yes—
694C42C23×D1112yes—
695C11C2×#312211yescharacteristic, complemented, Sylow
696C23—24no—
697C23—22no—
698C23—42no—
699C23—42no—
700C23—112no—
701C23—2216no—
702C23—222no—
703C23—222no—
704C23—222no—
705C23—224no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—442no—
710C23—442no—
711C23—442no—
712C23—442no—
713C23—442no—
714C23—442no—
715C23—442no—
716C23—442no—
717C23—884no—
718C23—884no—
719C23—8816no—
720C23C2×D4×D1111yescharacteristic
721D4—24no—
722D4—22no—
723D4—114no—
724D4—2216no—
725D4—224no—
726D4—222no—
727D4—222no—
728D4—222no—
729D4—222no—
730D4—222no—
731D4—442no—
732D4—442no—
733D4—884no—
734D4—884no—
735D4—884no—
736D4—884no—
737D4C2×#434314yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—84no—
747C2×C4—112no—
748C2×C4—112no—
749C2×C4—112no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—224no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—442no—
758C2×C4—884no—
759C2×C4—884no—
760C2×C4—884no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4C2×#434312yes—
767C2×C4#41×D1112yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—24no—
774C22—48no—
775C22—42no—
776C22—42no—
777C22—222no—
778C22—224no—
779C22—222no—
780C22—222no—
781C22—444no—
782C22—448no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—442no—
790C22—442no—
791C22—8816no—
792C22—884no—
793C22—884no—
794C22#1062315812yes—
795C22#1062330012yes—
796C22#1062330512yes—
797C22C22×D4×D1111yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—222no—
804C4—222no—
805C4—222no—
806C4—442no—
807C4#1062315812yes—
808C4C22×#434311yescharacteristic
809C4C2×#41×D1111yescharacteristic
810C2—44no—
811C2—442no—
812C2—444no—
813C2—882no—
814C2—882no—
815C2#1307886114yesdirect product factor
816C2C2×#1062315811yescharacteristic
817C2C2×#1062330011yescharacteristic
818C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
hypercenterC2×#478D11
hypocenterC11C2×#3122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10623229C2semidirect
2. C2×#10623076C2semidirect
3. #13078861C2direct (N × H)
4. C2×#10622498C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622456C2semidirect
8. C2×#10622628C2semidirect
9. C2×#10622386C2semidirect
10. C2×#10622386C2semidirect
11. C2×#10622482C2semidirect
12. C2×#10622398C2semidirect
13. C2×#10622485C2semidirect
14. C2×#10622369C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#478C2semidirect
18. C2×C11×#125C22semidirect
28. #10623229C22semidirect
30. #10623076C22semidirect
38. C2×#66946C22semidirect
39. C2×#66946C22semidirect
43. C2×#66927C22semidirect
46. C11×#478C22semidirect
47. C2×C11×#107C22semidirect
48. C2×C11×#106C22semidirect
49. C2×C11×C4⋊C8C22semidirect
52. C2×#66885C22semidirect
53. C2×#66885C22semidirect
56. C2×#66879C22semidirect
57. C2×C8×Dic11C22semidirect
58. #10622679C22semidirect
59. #10622628C22semidirect
62. C2×#66873C22semidirect
63. C2×#66873C22semidirect
64. C2×#66872C22semidirect
65. C2×#66871C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622498C22semidirect
68. #10622485C22semidirect
69. #10622482C22semidirect
70. #10622479C22semidirect
71. #10622456C22semidirect
72. #10622453C22semidirect
73. #10622398C22semidirect
74. #10622386C22semidirect
75. #10622386C22semidirect
76. #10622369C22semidirect
101. C11×#125C23semidirect
152. #66946C23semidirect
153. #66946C23semidirect
159. #66927C23semidirect
164. C11×#107C23semidirect
165. C11×#106C23semidirect
166. C11×C4⋊C8C23semidirect
169. #66885C23semidirect
170. #66885C23semidirect
173. #66879C23semidirect
174. C8×Dic11C23semidirect
177. #66873C23semidirect
178. #66873C23semidirect
179. #66872C23semidirect
180. #66871C23semidirect
181. C4⋊(C11⋊C8)C23semidirect
293. C2×#478D11semidirect
388. C2×#125C2×D11semidirect
412. #478C2×D11semidirect
423. C2×#107C2×D11semidirect
425. C2×#106C2×D11semidirect
427. C2×C4⋊C8C2×D11semidirect
513. #125C22×D11semidirect
565. #107C22×D11semidirect
567. #106C22×D11semidirect
569. C4⋊C8C22×D11semidirect
583. C2×C11#3122semidirect
695. C11C2×#3122semidirect
815. C2#13078861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232292
C2×#106230762
#130788612
C2×#106224982
C2×#106224792
C2×#106226792
C2×#106224562
C2×#106226282
C2×#106223862
C2×#106224822
C2×#106223982
C2×#106224852
C2×#106223692
C2×#106224532
C2×C11×#4782
C2×#312211