Finite Group Databasebeta

← C2×#13078752 #15621883

Subgroups — C2×#13078752 #15621883

Order 2816.

2582 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13078752C2116yesmaximal, direct product factor
4C2×#10622475C211yesmaximal, characteristic, complemented
5C2×#10622387C211yesmaximal, characteristic, complemented
6C2×#10622484C211yesmaximal, characteristic, complemented
7C2×#10622379C211yesmaximal, characteristic, complemented
8C2×#10622400C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622389C211yesmaximal, characteristic, complemented
11C2×#10622769C211yesmaximal, characteristic
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622631C211yesmaximal, characteristic, complemented
15C2×#10622318C211yesmaximal, characteristic, complemented
16C2×C11×#442C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C23×C4×D11—21no—
19C22×C11×D8C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic, complemented
22C2×#66991C2211yescharacteristic
23C2×#66989C2211yescharacteristic, complemented
24C2×D4×Dic11C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C2×C4×C22⋊D11—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66979—21no—
30C22×#4314C2211yescharacteristic
31#10623088—24no—
32#10623088C2218yescomplemented
33C4×D4×D11—24no—
34C4×D4×D11C2218yescomplemented
35C2×#66950C2211yescharacteristic
36C2×#66946C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66943C2211yescharacteristic, complemented
39C2×#66936—21no—
40C2×(C22⋊D11)⋊C4—21no—
41C2×C22⋊C4×D11—21no—
42C2×#66932—21no—
43C2×C4×D44C2211yescharacteristic
44C2×C42×D11C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic, complemented
46C11×#442C2218yescomplemented
47C2×C11×#106C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic, complemented
50C2×C11×#97C2211yescharacteristic, complemented
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic, complemented
53#10622769C2218yes—
54#10622766C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic, complemented
59C2×#66880C2211yescharacteristic, complemented
60C2×Dic11⋊C8C2211yescharacteristic, complemented
61C2×Dic11⋊C8C2211yescharacteristic, complemented
62#10622631C2218yescomplemented
63#10622627C2218yescomplemented
64C2×#66874C2211yescharacteristic, complemented
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic, complemented
67C2×#66871C2211yescharacteristic, complemented
68C2×#66867C2211yescharacteristic, complemented
69#10622484C2218yescomplemented
70#10622475C2218yescomplemented
71#10622400C2218yescomplemented
72#10622389C2218yescomplemented
73#10622387C2218yescomplemented
74#10622379C2218yescomplemented
75#10622323C2218yescomplemented
76#10622318C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C2×D4×D11—24no—
86C2×D4×D11—24no—
87C2×D4×D11—22no—
88C2×D4×D11C2314yes—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—28no—
94C22×C4×D11—48no—
95C22×C4×D11D411yescharacteristic
96C22×C4×D11D411yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×Dic22C2311yescharacteristic
99C2×C11×D8—24no—
100C2×C11×D8C2314yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11C2314yes—
106C4×D4×C11C2314yescomplemented
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66991—22no—
117#66991C2314yes—
118#66989—22no—
119#66989C2314yescomplemented
120D4×Dic11—22no—
121D4×Dic11C2314yes—
122C2×#4324—24no—
123C2×#4324C2314yes—
124C2×#4323—24no—
125C2×#4323C2314yes—
126C4×C22⋊D11—28no—
127C4×C22⋊D11—28no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131#66979—28no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11D411yescharacteristic
141C2×C4×Dic11D411yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C2×#4314—24no—
146C2×#4314C2314yes—
147#66950—22no—
148#66950C2314yes—
149#66946—22no—
150#66946C2314yes—
151C4⋊C4×D11—22no—
152C4⋊C4×D11C2314yes—
153#66943—22no—
154#66943C2314yescomplemented
155#66936—28no—
156(C22⋊D11)⋊C4—28no—
157C22⋊C4×D11—28no—
158#66932—28no—
159C4×D44—22no—
160C4×D44C2314yes—
161C42×D11D414yes—
162C42×D11C2314yes—
163C4×Dic22—22no—
164C4×Dic22C2314yescomplemented
165C11×#106C2314yescomplemented
166C11×#102C2314yes—
167C11×#102C2314yescomplemented
168C11×#97C2314yescomplemented
169#66896C2314yes—
170#66896C2314yescomplemented
171#66885C2314yes—
172(C2×D11)⋊C8C2314yes—
173(C2×D11)⋊C8C2314yes—
174#66882C2314yescomplemented
175#66880C2314yescomplemented
176Dic11⋊C8C2314yescomplemented
177Dic11⋊C8C2314yescomplemented
178#66874C2314yescomplemented
179#66873C2314yes—
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182#66867C2314yescomplemented
183C2×#3114—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11—21no—
186C23×D11—28no—
187C23×D11—21no—
188C23×D11—24no—
189C23×D11—44no—
190C23×D11—44no—
191C23×D11C2×D411yescharacteristic
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11#4114yes—
198C2×D4×C11C2412yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—44no—
205C22×C4×C11—44no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—28no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C22×Dic11—24no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—44no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221D4×D11—216no—
222D4×D11—28no—
223D4×D11—28no—
224C2×D44—21no—
225C2×D44—22no—
226C2×D44#4114yes—
227C2×D44C2412yes—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—42no—
235C2×C4×D11—44no—
236C2×C4×D11—432no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C2×C4×D11C2×D412yes—
240C2×C4×D11C2×D414yes—
241C2×C4×D11C2×D414yes—
242C2×C4×D11C2412yes—
243C2×Dic22—21no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22C2412yes—
247C11×D8—28no—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11C2412yes—
251C2×C8×C11C2412yes—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2412yes—
255C11×C4⋊C4C2412yes—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C42×C11C2×D412yes—
259C42×C11C2412yes—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264#4324—28no—
265#4323—28no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269C4⋊Dic11—24no—
270C4⋊Dic11—24no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278C4×Dic11—24no—
279C4×Dic11C2×D412yes—
280C4×Dic11C2×D414yes—
281C4×Dic11C2×D414yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287#4314—28no—
288C2×#529—111no—
289C22×C4×D4—111no—
290#3114—1116no—
291C2×#483—111no—
292C2×#480—111no—
293C2×#478—111no—
294C2×#478—111no—
295C2×#463—111no—
296C2×#463—111no—
297C2×#450—111no—
298C2×#447—111no—
299C2×#442—111no—
300C2×#442D1111yescharacteristic, complemented
301C2×#440—111no—
302C2×#440—111no—
303C2×#432—111no—
304C23×C11—24no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—216no—
316C22×D11—24no—
317C22×D11—22no—
318C22×D11—432no—
319C22×D11—48no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—48no—
323C22×D11AGL(1,ℤ/8)14yes—
324C22×D11C22×D412yes—
325D4×C11—24no—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—22no—
329D4×C11—42no—
330D4×C11C2×#4114yes—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—48no—
336C2×C4×C11—48no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4112yes—
343C2×C4×C11C2×#4112yes—
344C2×C4×C11C2511yescharacteristic
345C22⋊D11—216no—
346C22⋊D11—48no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—48no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360D44—24no—
361D44—22no—
362D44C2×#4114yes—
363C4×D11—28no—
364C4×D11—24no—
365C4×D11—22no—
366C4×D11—22no—
367C4×D11—44no—
368C4×D11—48no—
369C4×D11—48no—
370C4×D11—48no—
371Dic22—22no—
372Dic22—22no—
373Dic22—42no—
374C8×C11—22no—
375C8×C11—22no—
376C11⋊C8—22no—
377C11⋊C8—22no—
378C23×D4—111no—
379C24×C4—221no—
380C22×SD16—111no—
381C22×SD16—111no—
382C22×D8—111no—
383C22×D8C2×D1111yescharacteristic
384#529—118no—
385#529—224no—
386C2×#126—221no—
387C2×#125—111no—
388C2×#124—111no—
389C2×#123—221no—
390C2×C22⋊Q8—111no—
391C2×#121—111no—
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4—118no—
395C2×C4×D4—111no—
396C2×C4×D4—111no—
397C2×C4×D4—221no—
398C2×C4×D4—224no—
399C2×C4×D4—221no—
400C2×C4×D4—221no—
401C2×C4×D4C2×D1111yescharacteristic
402C2×C4×D4C2×D1111yescharacteristic, complemented
403C2×#117—221no—
404C22×C4⋊C4—111no—
405C22×C22⋊C4—221no—
406C22×C42—111no—
407#483—118no—
408#480—118no—
409#478—118no—
410#478—118no—
411#463—118no—
412#463—118no—
413#450—118no—
414#447—118no—
415#442—118no—
416#442C2×D1118yescomplemented
417#440—118no—
418#440—118no—
419#432—118no—
420C2×#107—111no—
421C2×#107—111no—
422C2×#106—111no—
423C2×#106C2×D1111yescharacteristic, complemented
424C2×C4⋊C8—111no—
425C2×C4⋊C8—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102C2×D1111yescharacteristic
433C2×#102C2×D1111yescharacteristic, complemented
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×#97—111no—
437C2×#97C2×D1111yescharacteristic, complemented
438C22×C11—24no—
439C22×C11—48no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—84no—
446C22×C11#52512yes—
447C22×C11C2×AGL(1,ℤ/8)12yes—
448C22×C11#57512yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—28no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—24no—
454C2×D11—432no—
455C2×D11—48no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11C2×AGL(1,ℤ/8)14yes—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11#52512yes—
464C4×C11C22×#4111yescharacteristic
465C4×C11C22×#4111yescharacteristic
466Dic11—22no—
467Dic11—22no—
468Dic11—22no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472C25—221no—
473C22×Q8—111no—
474C22×D4—114no—
475C22×D4—111no—
476C22×D4—222no—
477C22×D4—221no—
478C22×D4—224no—
479C22×D4—224no—
480C22×D4—221no—
481C22×D4C22×D1111yescharacteristic
482C22×D4C22×D1111yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—221no—
489C23×C4—228no—
490C23×C4—221no—
491C23×C4—221no—
492C23×C4—221no—
493C23×C4—448no—
494C2×SD16—114no—
495C2×SD16—114no—
496C2×SD16—224no—
497C2×SD16—224no—
498C2×D8—24no—
499C2×D8—114no—
500C2×D8—224no—
501C2×D8C22×D1114yes—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8C22×D1111yescharacteristic
505C22×C8C22×D1111yescharacteristic
506#126—228no—
507#125—114no—
508#125—222no—
509#124—114no—
510#124—222no—
511#123—228no—
512C22⋊Q8—114no—
513C22⋊Q8—222no—
514#121—114no—
515#121—222no—
516C4×Q8—114no—
517C4×Q8—222no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—114no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—228no—
524C4×D4—222no—
525C4×D4—228no—
526C4×D4—222no—
527C4×D4—228no—
528C4×D4—222no—
529C4×D4C22×D1114yes—
530C4×D4C22×D1114yescomplemented
531#117—228no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—222no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4C22×D1111yescharacteristic
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—228no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
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—111no—
555C2×C42—111no—
556C2×C42—114no—
557C2×C42—114no—
558C2×C42—221no—
559C2×C42C22×D1111yescharacteristic
560#107—114no—
561#107—114no—
562#106—114no—
563#106C22×D1114yescomplemented
564C4⋊C8—114no—
565C4⋊C8—114no—
566#103—114no—
567#103—114no—
568#102—114no—
569#102—114no—
570#102—114no—
571#102—114no—
572#102C22×D1114yes—
573#102C22×D1114yescomplemented
574C22⋊C8—114no—
575C22⋊C8—114no—
576#97—114no—
577#97C22×D1114yescomplemented
578C2×C11—44no—
579C2×C11—82no—
580C2×C11#311414yescomplemented
581C2×C11C2×#52511yescharacteristic
582C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
583C2×C11C2×#57511yescharacteristic
584D11—24no—
585D11—44no—
586C24—21no—
587C24—21no—
588C24—111no—
589C24—224no—
590C24—228no—
591C24—221no—
592C24—444no—
593C24—444no—
594C2×Q8—112no—
595C2×Q8—221no—
596C2×Q8—222no—
597C2×Q8—222no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—114no—
604C2×D4—112no—
605C2×D4—224no—
606C2×D4—228no—
607C2×D4—2216no—
608C2×D4—228no—
609C2×D4—228no—
610C2×D4—224no—
611C2×D4—222no—
612C2×D4—221no—
613C2×D4—444no—
614C2×D4#433914yes—
615C2×D4C23×D1112yes—
616C2×D4C23×D1112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—111no—
624C22×C4—111no—
625C22×C4—111no—
626C22×C4—112no—
627C22×C4—114no—
628C22×C4—112no—
629C22×C4—114no—
630C22×C4—224no—
631C22×C4—224no—
632C22×C4—224no—
633C22×C4—224no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—224no—
640C22×C4—442no—
641C22×C4—444no—
642C22×C4—4432no—
643C22×C4—444no—
644C22×C4—444no—
645C22×C4—444no—
646C22×C4D4×D1111yescharacteristic
647C22×C4D4×D1111yescharacteristic
648C22×C4C23×D1111yescharacteristic
649SD16—228no—
650SD16—228no—
651D8—28no—
652D8—228no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—112no—
656C2×C8—112no—
657C2×C8—222no—
658C2×C8—222no—
659C2×C8C23×D1112yes—
660C2×C8C23×D1112yes—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—112no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—221no—
670C4⋊C4—221no—
671C4⋊C4—224no—
672C4⋊C4C23×D1112yes—
673C4⋊C4C23×D1112yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C42—114no—
684C42—112no—
685C42—114no—
686C42—112no—
687C42—224no—
688C42D4×D1112yes—
689C42C23×D1112yes—
690C11C2×#311411yescharacteristic, complemented, Sylow
691C23—24no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—114no—
700C23—112no—
701C23—2216no—
702C23—222no—
703C23—222no—
704C23—224no—
705C23—222no—
706C23—448no—
707C23—448no—
708C23—4432no—
709C23—442no—
710C23—442no—
711C23C2×D4×D1111yescharacteristic
712Q8—222no—
713Q8—222no—
714Q8—442no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—114no—
721D4—2216no—
722D4—224no—
723D4—222no—
724D4—448no—
725D4C2×#433914yes—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—228no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—224no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—444no—
748C2×C4—448no—
749C2×C4—448no—
750C2×C4—448no—
751C2×C4—448no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4C2×#433912yes—
756C2×C4C2×D4×D1112yes—
757C2×C4C2×D4×D1112yes—
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4#41×D1112yes—
760C2×C4C24×D1111yescharacteristic
761C8—22no—
762C8—22no—
763C8—222no—
764C8—222no—
765C22—24no—
766C22—42no—
767C22—42no—
768C22—48no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—84no—
773C22—114no—
774C22—222no—
775C22—222no—
776C22—228no—
777C22—224no—
778C22—4432no—
779C22—442no—
780C22—442no—
781C22—448no—
782C22#1062307812yes—
783C22D11×AGL(1,ℤ/8)12yes—
784C22#1062330412yes—
785C22C22×D4×D1111yescharacteristic
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—222no—
791C4—222no—
792C4—222no—
793C4—442no—
794C4—442no—
795C4—442no—
796C4#1062307812yes—
797C4C22×#433911yescharacteristic
798C4C2×#41×D1111yescharacteristic
799C2—44no—
800C2—82no—
801C2—224no—
802C2—444no—
803C2#1307875214yesdirect product factor
804C2C2×#1062307811yescharacteristic
805C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
806C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
hypercenterC2×#442D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#10623088C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13078752C2direct (N × H)
4. C2×#10622475C2semidirect
5. C2×#10622387C2semidirect
6. C2×#10622484C2semidirect
7. C2×#10622379C2semidirect
8. C2×#10622400C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622389C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622631C2semidirect
15. C2×#10622318C2semidirect
16. C2×C11×#442C2semidirect
21. C2×C4×D4×C11C22semidirect
23. C2×#66989C22semidirect
32. #10623088C22semidirect
34. C4×D4×D11C22semidirect
38. C2×#66943C22semidirect
45. C2×C4×Dic22C22semidirect
46. C11×#442C22semidirect
47. C2×C11×#106C22semidirect
49. C2×C11×#102C22semidirect
50. C2×C11×#97C22semidirect
52. C2×#66896C22semidirect
54. #10622766C22semidirect
58. C2×#66882C22semidirect
59. C2×#66880C22semidirect
60. C2×Dic11⋊C8C22semidirect
61. C2×Dic11⋊C8C22semidirect
62. #10622631C22semidirect
63. #10622627C22semidirect
64. C2×#66874C22semidirect
66. C2×#66872C22semidirect
67. C2×#66871C22semidirect
68. C2×#66867C22semidirect
69. #10622484C22semidirect
70. #10622475C22semidirect
71. #10622400C22semidirect
72. #10622389C22semidirect
73. #10622387C22semidirect
74. #10622379C22semidirect
75. #10622323C22semidirect
76. #10622318C22semidirect
106. C4×D4×C11C23semidirect
119. #66989C23semidirect
154. #66943C23semidirect
164. C4×Dic22C23semidirect
165. C11×#106C23semidirect
167. C11×#102C23semidirect
168. C11×#97C23semidirect
170. #66896C23semidirect
174. #66882C23semidirect
175. #66880C23semidirect
176. Dic11⋊C8C23semidirect
177. Dic11⋊C8C23semidirect
178. #66874C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
182. #66867C23semidirect
300. C2×#442D11semidirect
402. C2×C4×D4C2×D11semidirect
416. #442C2×D11semidirect
423. C2×#106C2×D11semidirect
433. C2×#102C2×D11semidirect
437. C2×#97C2×D11semidirect
530. C4×D4C22×D11semidirect
563. #106C22×D11semidirect
573. #102C22×D11semidirect
577. #97C22×D11semidirect
580. C2×C11#3114semidirect
690. C11C2×#3114semidirect
803. C2#13078752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×C4×D4×D112
#130787522
C2×#106224752
C2×#106223872
C2×#106224842
C2×#106223792
C2×#106224002
C2×#106227662
C2×#106223892
C2×#106227692
C2×#106226272
C2×#106223232
C2×#106226312
C2×#106223182
C2×C11×#4422
C2×#311411