Finite Group Databasebeta

← C2×#13078857 #15622065

Subgroups — C2×#13078857 #15622065

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×#10623250C211yesmaximal, characteristic, complemented
2C2×#10623076C211yesmaximal, characteristic, complemented
3#13078857C2116yesmaximal, direct product factor
4C2×#10622392C211yesmaximal, characteristic, complemented
5C2×#10622397C211yesmaximal, characteristic, complemented
6C2×#10622460C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622685C211yesmaximal, characteristic, complemented
9C2×#10622769C211yesmaximal, characteristic, complemented
10C2×#10622769C211yesmaximal, characteristic, complemented
11C2×#10622765C211yesmaximal, characteristic, complemented
12C2×#10622398C211yesmaximal, characteristic, complemented
13C2×D8×Dic11C211yesmaximal, characteristic, complemented
14C2×#10622369C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#459C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C2×C11×#127C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66992—21no—
23C2×#66992—21no—
24C2×#66991C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×#66988—21no—
27C2×#66988—21no—
28C2×D4×Dic11C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic, complemented
31C22×#4323C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×C4×C22⋊D11—21no—
34C22×(C2×D11)⋊C4—21no—
35#10623250—24no—
36#10623250C2218yescomplemented
37#10623076—24no—
38#10623076C2218yescomplemented
39C2×#66946C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×(C22⋊D11)⋊C4—21no—
42C2×C22⋊C4×D11—21no—
43C2×C4×D44C2211yescharacteristic
44C2×#66925C2211yescharacteristic
45C2×#66923C2211yescharacteristic, complemented
46C11×#459C2218yescomplemented
47C2×C11×C4⋊C8C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54#10622769C2218yescomplemented
55#10622769C2218yescomplemented
56#10622765C2218yescomplemented
57D8×Dic11C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×C8×Dic11C2211yescharacteristic, complemented
66#10622685C2218yescomplemented
67#10622622C2218yescomplemented
68C2×#66872C2211yescharacteristic, complemented
69C2×#66871C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622460C2218yescomplemented
72#10622453C2218yescomplemented
73#10622398C2218yescomplemented
74#10622397C2218yescomplemented
75#10622392C2218yescomplemented
76#10622369C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C23×Dic11—21no—
88C23×Dic11—21no—
89C23×Dic11—21no—
90C2×D4×D11—24no—
91C2×D4×D11—24no—
92C2×D4×D11—22no—
93C2×D4×D11C2314yes—
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C2×C11×D8—24no—
99C2×C11×D8—24no—
100C2×C11×D8C2314yes—
101C2×C11×D8C2314yes—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C11×#127—22no—
105C11×#127C2314yescomplemented
106C4×D4×C11—22no—
107C4×D4×C11C2314yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66992—28no—
117#66992—28no—
118#66991—22no—
119#66991—22no—
120#66991C2314yes—
121#66991C2314yes—
122#66988—28no—
123#66988—28no—
124D4×Dic11—22no—
125D4×Dic11—22no—
126D4×Dic11—22no—
127D4×Dic11C2314yes—
128D4×Dic11C2314yescomplemented
129D4×Dic11C2314yescomplemented
130C2×#4323—24no—
131C2×#4323—24no—
132C2×#4323C2314yes—
133C2×#4323C2314yes—
134C4×C22⋊D11—28no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—28no—
139C2×(C2×D11)⋊C4D411yescharacteristic
140C2×(C2×D11)⋊C4D411yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×Dic11⋊C4D411yescharacteristic
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152#66946—22no—
153#66946C2314yes—
154#66945—22no—
155#66945C2314yes—
156(C22⋊D11)⋊C4—28no—
157C22⋊C4×D11—28no—
158C4×D44—22no—
159C4×D44C2314yes—
160#66925D414yes—
161#66925C2314yes—
162#66923—22no—
163#66923C2314yescomplemented
164C11×C4⋊C8C2314yescomplemented
165C11×#102C2314yescomplemented
166C11×#102C2314yescomplemented
167#66896C2314yes—
168#66896C2314yes—
169#66896C2314yescomplemented
170#66896C2314yescomplemented
171#66885C2314yes—
172#66885C2314yes—
173(C2×D11)⋊C8C2314yes—
174(C2×D11)⋊C8C2314yes—
175#66882C2314yescomplemented
176#66881C2314yescomplemented
177#66879C2314yescomplemented
178C8×Dic11C2314yescomplemented
179#66872C2314yescomplemented
180#66871C2314yescomplemented
181C4⋊(C11⋊C8)C2314yescomplemented
182C2×#3122—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C23×D11—21no—
187C23×D11—28no—
188C23×D11—24no—
189C23×D11—82no—
190C23×D11—82no—
191C23×D11C2×D411yescharacteristic
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—82no—
203C2×D4×C11—82no—
204C2×D4×C11#4114yes—
205C2×D4×C11C2412yes—
206C2×D4×C11C2412yes—
207C2×D4×C11C2412yes—
208C22×C4×C11—21no—
209C22×C4×C11—24no—
210C22×C4×C11—82no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—28no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—82no—
219C2×C22⋊D11—82no—
220C22×Dic11—24no—
221C22×Dic11—24no—
222C22×Dic11—24no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—82no—
227C22×Dic11—82no—
228C22×Dic11—82no—
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232D4×D11—216no—
233D4×D11—28no—
234D4×D11—28no—
235C2×D44—21no—
236C2×D44—22no—
237C2×D44#4114yes—
238C2×D44C2412yes—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—82no—
244C2×C4×D11—82no—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2412yes—
247C11×D8—28no—
248C11×D8—28no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—24no—
256C42×C11C2×D412yes—
257C42×C11C2412yes—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
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)⋊C4C2×D414yes—
269(C2×D11)⋊C4C2×D414yes—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4C2×D414yes—
279Dic11⋊C4C2×D414yes—
280C4×Dic11—24no—
281C4×Dic11C2×D412yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×#540—111no—
288C2×#518—111no—
289#3122—1116no—
290C2×#482—111no—
291C2×#482—111no—
292C2×#478—111no—
293C2×#478—111no—
294C2×#459—111no—
295C2×#459D1111yescharacteristic, complemented
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—22no—
306C23×C11—22no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11C22×D411yescharacteristic
316C22×D11—22no—
317C22×D11—24no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—216no—
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×C11—22no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—42no—
335D4×C11—42no—
336D4×C11—84no—
337D4×C11—84no—
338D4×C11C2×#4114yes—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—42no—
343C2×C4×C11—84no—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4112yes—
348C2×C4×C11C2×#4112yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—216no—
351C22⋊D11—84no—
352C22⋊D11—84no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—84no—
363C2×Dic11—84no—
364C2×Dic11—84no—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368D44—24no—
369D44—22no—
370D44C2×#4114yes—
371C4×D11—24no—
372C4×D11—22no—
373C4×D11—22no—
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×D8C2×D1111yescharacteristic
384C22×D8C2×D1111yescharacteristic
385#540—118no—
386#540—224no—
387C2×#127C2×D1111yescharacteristic, complemented
388C2×#125—111no—
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#478—118no—
413#459—118no—
414#459C2×D1118yescomplemented
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×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
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, complemented
435C2×#102C2×D1111yescharacteristic, complemented
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—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—84no—
451C22×C11—84no—
452C22×C11#52512yes—
453C22×C11#57612yes—
454C22×C11#57612yes—
455C22×C11C23×D411yescharacteristic
456C2×D11—22no—
457C2×D11—24no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—44no—
461C2×D11—48no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—816no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—42no—
468C4×C11#52512yes—
469C4×C11C22×#4111yescharacteristic
470C4×C11C22×#4111yescharacteristic
471Dic11—22no—
472Dic11—22no—
473Dic11—22no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477C25—221no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—114no—
481C22×D4—111no—
482C22×D4—222no—
483C22×D4—221no—
484C22×D4—224no—
485C22×D4—224no—
486C22×D4—221no—
487C22×D4—221no—
488C22×D4C22×D1111yescharacteristic
489C22×D4C22×D1111yescharacteristic
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—24no—
499C2×D8—24no—
500C2×D8—114no—
501C2×D8—114no—
502C2×D8—224no—
503C2×D8—224no—
504C2×D8C22×D1114yes—
505C2×D8C22×D1114yes—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8C22×D1111yescharacteristic
509C22×C8C22×D1111yescharacteristic
510#127—22no—
511#127C22×D1114yescomplemented
512#125—114no—
513#125—222no—
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—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
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#107—114no—
566#106—114no—
567#106—114no—
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×D1114yescomplemented
577#102C22×D1114yescomplemented
578C22⋊C8—114no—
579C22⋊C8—114no—
580#97—114no—
581C4×C8—114no—
582C2×C11—44no—
583C2×C11—82no—
584C2×C11—82no—
585C2×C11#312214yescomplemented
586C2×C11C2×#52511yescharacteristic
587C2×C11C2×#57611yescharacteristic
588C2×C11C2×#57611yescharacteristic
589D11—42no—
590D11—44no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—111no—
595C24—224no—
596C24—228no—
597C24—221no—
598C24—882no—
599C24—882no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—114no—
613C2×D4—112no—
614C2×D4—224no—
615C2×D4—228no—
616C2×D4—2216no—
617C2×D4—228no—
618C2×D4—228no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—221no—
622C2×D4—222no—
623C2×D4—882no—
624C2×D4—882no—
625C2×D4#434114yes—
626C2×D4C23×D1112yes—
627C2×D4C23×D1112yes—
628C2×D4C23×D1112yes—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—82no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—224no—
638C22×C4—224no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—221no—
644C22×C4—221no—
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—28no—
656D8—28no—
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—21no—
668C4⋊C4—114no—
669C4⋊C4—114no—
670C4⋊C4—112no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—224no—
677C4⋊C4—224no—
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—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—112no—
709C23—2216no—
710C23—222no—
711C23—222no—
712C23—222no—
713C23—224no—
714C23—222no—
715C23—442no—
716C23—442no—
717C23—884no—
718C23—884no—
719C23—8816no—
720C23C2×D4×D1111yescharacteristic
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—42no—
728D4—42no—
729D4—84no—
730D4—84no—
731D4—114no—
732D4—2216no—
733D4—224no—
734D4—222no—
735D4—884no—
736D4—884no—
737D4C2×#434114yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—84no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—224no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—442no—
756C2×C4—442no—
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×#434112yes—
767C2×C4#41×D1112yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—24no—
774C22—48no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—84no—
784C22—84no—
785C22—222no—
786C22—224no—
787C22—222no—
788C22—222no—
789C22—444no—
790C22—448no—
791C22—442no—
792C22—442no—
793C22—8816no—
794C22#1062313712yes—
795C22#1062328812yes—
796C22#1062330512yes—
797C22C22×D4×D1111yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—222no—
802C4—222no—
803C4—222no—
804C4—442no—
805C4—442no—
806C4—442no—
807C4#1062313712yes—
808C4C22×#434111yescharacteristic
809C4C2×#41×D1111yescharacteristic
810C2—44no—
811C2—82no—
812C2—82no—
813C2—442no—
814C2—444no—
815C2#1307885714yesdirect product factor
816C2C2×#1062313711yescharacteristic
817C2C2×#1062328811yescharacteristic
818C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623250C2semidirect
2. C2×#10623076C2semidirect
3. #13078857C2direct (N × H)
4. C2×#10622392C2semidirect
5. C2×#10622397C2semidirect
6. C2×#10622460C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622685C2semidirect
9. C2×#10622769C2semidirect
10. C2×#10622769C2semidirect
11. C2×#10622765C2semidirect
12. C2×#10622398C2semidirect
13. C2×D8×Dic11C2semidirect
14. C2×#10622369C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#459C2semidirect
20. C2×C11×#127C22semidirect
29. C2×D4×Dic11C22semidirect
30. C2×D4×Dic11C22semidirect
36. #10623250C22semidirect
38. #10623076C22semidirect
45. C2×#66923C22semidirect
46. C11×#459C22semidirect
47. C2×C11×C4⋊C8C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×#102C22semidirect
52. C2×#66896C22semidirect
53. C2×#66896C22semidirect
54. #10622769C22semidirect
55. #10622769C22semidirect
56. #10622765C22semidirect
57. D8×Dic11C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66879C22semidirect
65. C2×C8×Dic11C22semidirect
66. #10622685C22semidirect
67. #10622622C22semidirect
68. C2×#66872C22semidirect
69. C2×#66871C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622460C22semidirect
72. #10622453C22semidirect
73. #10622398C22semidirect
74. #10622397C22semidirect
75. #10622392C22semidirect
76. #10622369C22semidirect
105. C11×#127C23semidirect
128. D4×Dic11C23semidirect
129. D4×Dic11C23semidirect
163. #66923C23semidirect
164. C11×C4⋊C8C23semidirect
165. C11×#102C23semidirect
166. C11×#102C23semidirect
169. #66896C23semidirect
170. #66896C23semidirect
175. #66882C23semidirect
176. #66881C23semidirect
177. #66879C23semidirect
178. C8×Dic11C23semidirect
179. #66872C23semidirect
180. #66871C23semidirect
181. C4⋊(C11⋊C8)C23semidirect
295. C2×#459D11semidirect
387. C2×#127C2×D11semidirect
414. #459C2×D11semidirect
427. C2×C4⋊C8C2×D11semidirect
434. C2×#102C2×D11semidirect
435. C2×#102C2×D11semidirect
511. #127C22×D11semidirect
569. C4⋊C8C22×D11semidirect
576. #102C22×D11semidirect
577. #102C22×D11semidirect
585. C2×C11#3122semidirect
695. C11C2×#3122semidirect
815. C2#13078857direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232502
C2×#106230762
#130788572
C2×#106223922
C2×#106223972
C2×#106224602
C2×#106226222
C2×#106226852
C2×#106227692
C2×#106227652
C2×#106223982
C2×D8×Dic112
C2×#106223692
C2×#106224532
C2×C11×#4592
C2×#312211