Finite Group Databasebeta

← C2×#13069119 #14755682

Subgroups — C2×#13069119 #14755682

Order 2816.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic, complemented
3C22×#66901C211yesmaximal, characteristic, complemented
4C2×#10622853C211yesmaximal, characteristic, complemented
5#13069119C218yesmaximal, direct product factor
6C2×#10622197C211yesmaximal, characteristic, complemented
7C2×#10622193C211yesmaximal, characteristic, complemented
8C2×C11×#575C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C22×C11×#41C2211yescharacteristic
11C11×#575—22no—
12C11×#575—22no—
13C11×#575C414yescomplemented
14C11×#575C2214yes—
15C2×C11×#137—21no—
16C2×C11×#137C412yescomplemented
17C2×C11×AGL(1,ℤ/8)—21no—
18C2×C11×AGL(1,ℤ/8)C412yescomplemented
19C2×C11×#135—22no—
20C22×C11×M16C2211yescharacteristic
21#41×Dic11—22no—
22#41×Dic11—22no—
23#41×Dic11—22no—
24#41×Dic11C2214yescomplemented
25C2×Q8×Dic11—21no—
26C2×D4×Dic11—21no—
27C2×D4×Dic11—22no—
28C2×#66979—21no—
29C2×#66979C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C22×C4×Dic11—21no—
32C22×C4×Dic11C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34#10622853—22no—
35#10622853C2214yescomplemented
36#10622849—22no—
37#10622849C2214yescomplemented
38C2×#66901—22no—
39C2×#66901—21no—
40C2×#66901—21no—
41C2×#66901—22no—
42C2×#66901C2214yescomplemented
43C2×#66898—22no—
44#10622197C2214yescomplemented
45#10622193C2214yescomplemented
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C2×C11×#41—21no—
62C2×C11×#41C2×C412yes—
63C2×C11×#41C2×C412yes—
64C2×C11×#41C2×C412yescomplemented
65C2×C11×#41D412yes—
66C2×C11×#41D412yes—
67C2×C11×#41D412yes—
68C2×C11×#41C2312yes—
69C2×C11×#41C2312yes—
70C22×Q8×C11C2×C411yescharacteristic, complemented
71C22×Q8×C11D411yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11—21no—
74C22×D4×C11C2×C411yescharacteristic, complemented
75C22×D4×C11D411yescharacteristic
76C23×C4×C11—21no—
77C23×C4×C11—21no—
78C23×C4×C11C2311yescharacteristic
79C23×Dic11—22no—
80C23×Dic11—21no—
81C11×#137—24no—
82C11×#137—24no—
83C11×#137—24no—
84C11×#137C2×C418yescomplemented
85C11×AGL(1,ℤ/8)—24no—
86C11×AGL(1,ℤ/8)—24no—
87C11×AGL(1,ℤ/8)—24no—
88C11×AGL(1,ℤ/8)C2×C418yescomplemented
89C11×#135—28no—
90C11×#135—28no—
91C2×C11×Q16—22no—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×D8—22no—
95C2×C11×M16—21no—
96C2×C11×M16—21no—
97C2×C11×M16—21no—
98C2×C11×M16C2×C412yescomplemented
99C2×C11×M16C2×C412yescomplemented
100C2×C11×M16C2312yes—
101C22×C8×C11—21no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11D412yes—
105Q8×Dic11—24no—
106Q8×Dic11—24no—
107D4×Dic11—28no—
108D4×Dic11—24no—
109D4×Dic11—24no—
110D4×Dic11—28no—
111#66979—24no—
112#66979—21no—
113#66979—21no—
114#66979—21no—
115#66979—24no—
116#66979—21no—
117#66979—21no—
118#66979D412yes—
119#66979C2312yes—
120#66979C2312yes—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—24no—
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—24no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11D411yescharacteristic
133C2×C4×Dic11D411yescharacteristic
134C2×C4×Dic11D412yes—
135C2×C4×Dic11C2312yes—
136C2×#4318—21no—
137C2×#4318—21no—
138C2×#4318—21no—
139C2×#4318—21no—
140C2×#4318—21no—
141C2×#4318C2312yes—
142C22×C11⋊C8—21no—
143#66901—28no—
144#66901—24no—
145#66901—24no—
146#66898—28no—
147C2×#1906—111nomaximal, Sylow
148C24×C11—21no—
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C11×#41—22no—
152C11×#41—22no—
153C11×#41—22no—
154C11×#41—22no—
155C11×#41—22no—
156C11×#41—22no—
157C11×#41—22no—
158C11×#41—22no—
159C11×#41—22no—
160C11×#41—22no—
161C11×#41—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—22no—
166C11×#41—22no—
167C11×#41—22no—
168C11×#41—22no—
169C11×#41—22no—
170C11×#41—22no—
171C11×#41—41no—
172C11×#41—41no—
173C11×#41—41no—
174C11×#41—41no—
175C11×#41—41no—
176C11×#41—41no—
177C11×#41—41no—
178C11×#41—41no—
179C11×#41C22⋊C414yes—
180C11×#41C22⋊C414yes—
181C11×#41C22×C414yes—
182C11×#41C2×D414yes—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11C22⋊C412yes—
192C2×Q8×C11C22⋊C412yes—
193C2×Q8×C11C22×C412yescomplemented
194C2×Q8×C11C2×D412yes—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—41no—
212C2×D4×C11—41no—
213C2×D4×C11—41no—
214C2×D4×C11—41no—
215C2×D4×C11C22⋊C412yes—
216C2×D4×C11C22⋊C412yes—
217C2×D4×C11C22×C412yescomplemented
218C2×D4×C11C2×D412yes—
219C22×C4×C11—21no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—21no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—41no—
230C22×C4×C11—41no—
231C22×C4×C11—41no—
232C22×C4×C11—41no—
233C22×C4×C11C22×C411yescharacteristic
234C22×C4×C11C22×C411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11#4111yescharacteristic
243C22×C4×C11#4111yescharacteristic
244C22×C4×C11#4111yescharacteristic
245C22×C4×C11#4111yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×Dic11—28no—
248C22×Dic11—21no—
249C22×Dic11—22no—
250C22×Dic11—21no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—44no—
254C22×Dic11—48no—
255C22×Dic11—41no—
256C11×Q16—28no—
257C11×SD16—28no—
258C11×SD16—28no—
259C11×D8—28no—
260C11×M16—22no—
261C11×M16—22no—
262C11×M16—22no—
263C11×M16C22×C414yescomplemented
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C22⋊Dic11—28no—
268C22⋊Dic11—22no—
269C22⋊Dic11—22no—
270C22⋊Dic11—41no—
271C22⋊Dic11C2×D414yes—
272C4⋊Dic11—28no—
273C4⋊Dic11—22no—
274C4⋊Dic11—22no—
275C4⋊Dic11—22no—
276C4⋊Dic11—41no—
277C4×Dic11—28no—
278C4×Dic11—21no—
279C4×Dic11—22no—
280C4×Dic11—21no—
281C4×Dic11—22no—
282C4×Dic11—22no—
283C4×Dic11—22no—
284C4×Dic11—22no—
285C4×Dic11—41no—
286C4×Dic11C2×D412yes—
287C4×Dic11C2×D412yes—
288#4318—22no—
289#4318—22no—
290#4318—41no—
291#4318—41no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—41no—
294C2×C11⋊C8—41no—
295C2×#575D1111yescharacteristic
296C2×C4×#41—111no—
297C2×#421—111no—
298C22×#104—111no—
299C2×#410—111no—
300#1906—118no—
301C2×#344—111no—
302C2×#339—111no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—42no—
308C23×C11—44no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—82no—
312C23×C11C4×D411yescharacteristic
313C23×C11C4×D411yescharacteristic
314C23×C11#12011yescharacteristic
315C23×C11#12011yescharacteristic
316C23×C11#12111yescharacteristic
317C23×C11#12111yescharacteristic
318C23×C11C22×D411yescharacteristic
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—41no—
325Q8×C11—41no—
326Q8×C11C2×C22⋊C414yes—
327D4×C11—24no—
328D4×C11—24no—
329D4×C11—24no—
330D4×C11—24no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—42no—
337D4×C11—42no—
338D4×C11—42no—
339D4×C11—42no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11C2×C22⋊C414yes—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—24no—
349C2×C4×C11—24no—
350C2×C4×C11—22no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11C2×C22⋊C411yescharacteristic
358C2×C4×C11C2×C22⋊C411yescharacteristic
359C2×C4×C11C2×C22⋊C411yescharacteristic
360C2×C4×C11C2×C22⋊C411yescharacteristic
361C2×C4×C11C4×D411yescharacteristic
362C2×C4×C11C4×D411yescharacteristic
363C2×C4×C11C4×D411yescharacteristic
364C2×C4×C11C4×D411yescharacteristic
365C2×C4×C11C4×D411yescharacteristic
366C2×C4×C11C4×D411yescharacteristic
367C2×C4×C11#12011yescharacteristic
368C2×C4×C11#12011yescharacteristic
369C2×C4×C11#12111yescharacteristic
370C2×C4×C11#12111yescharacteristic
371C2×C4×C11#12111yescharacteristic
372C2×C4×C11#12111yescharacteristic
373C2×C4×C11#12111yescharacteristic
374C2×C4×C11#12111yescharacteristic
375C2×C4×C11#12311yescharacteristic
376C2×C4×C11#12311yescharacteristic
377C2×C4×C11#12311yescharacteristic
378C2×C4×C11#12311yescharacteristic
379C2×C4×C11C23×C411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C2×#4111yescharacteristic
384C2×C4×C11C2×#4111yescharacteristic
385C2×Dic11—24no—
386C2×Dic11—22no—
387C2×Dic11—24no—
388C2×Dic11—22no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11—416no—
392C2×Dic11—44no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—82no—
396C8×C11—24no—
397C11⋊C8—42no—
398C22×#41C2×D1111yescharacteristic
399C22×#41C2×D1111yescharacteristic
400#575—22no—
401#575—22no—
402#575Dic1114yescomplemented
403#575C2×D1114yes—
404C2×#137—21no—
405C2×#137Dic1112yescomplemented
406C2×AGL(1,ℤ/8)—21no—
407C2×AGL(1,ℤ/8)Dic1112yescomplemented
408C2×#135—22no—
409C22×M16—111no—
410C22×M16C2×D1111yescharacteristic
411C4×#41—114no—
412C4×#41—222no—
413C4×#41—222no—
414C4×#41—222no—
415C2×C4×Q8—221no—
416C2×C4×D4—222no—
417C2×C4×D4—221no—
418C2×#117—111no—
419C2×#117—111no—
420C2×#117—221no—
421C22×C42—111no—
422C22×C42—221no—
423#421—114no—
424#421—222no—
425C2×#104—114no—
426C2×#104—221no—
427C2×#104—222no—
428C2×#104—221no—
429C2×#104—222no—
430#410—114no—
431#410—222no—
432C2×#99—222no—
433#344—114no—
434#339—114no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—24no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—44no—
444C22×C11—44no—
445C22×C11—44no—
446C22×C11—42no—
447C22×C11—82no—
448C22×C11—82no—
449C22×C11—82no—
450C22×C11#38611yescharacteristic
451C22×C11#38611yescharacteristic
452C22×C11#38611yescharacteristic
453C22×C11#38611yescharacteristic
454C22×C11C2×C4×D411yescharacteristic
455C22×C11C2×#12011yescharacteristic
456C22×C11C2×#12111yescharacteristic
457C4×C11—24no—
458C4×C11—42no—
459C4×C11#38611yescharacteristic
460C4×C11#38611yescharacteristic
461C4×C11#38611yescharacteristic
462C4×C11#38611yescharacteristic
463C4×C11C22×C22⋊C411yescharacteristic
464C4×C11C2×C4×D411yescharacteristic
465C4×C11C2×#12111yescharacteristic
466C4×C11C2×#12311yescharacteristic
467Dic11—24no—
468Dic11—44no—
469Dic11—42no—
470Dic11—82no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41C2×Dic1112yes—
488C2×#41C2×Dic1112yes—
489C2×#41C2×Dic1112yescomplemented
490C2×#41C22⋊D1112yes—
491C2×#41C22⋊D1112yes—
492C2×#41C22⋊D1112yes—
493C2×#41C22×D1112yes—
494C2×#41C22×D1112yes—
495C22×Q8C2×Dic1111yescharacteristic, complemented
496C22×Q8C22⋊D1111yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2×Dic1111yescharacteristic, complemented
500C22×D4C22⋊D1111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—222no—
504C23×C4—221no—
505C23×C4C22×D1111yescharacteristic
506#137—24no—
507#137—24no—
508#137—24no—
509#137C2×Dic1118yescomplemented
510AGL(1,ℤ/8)—24no—
511AGL(1,ℤ/8)—24no—
512AGL(1,ℤ/8)—24no—
513AGL(1,ℤ/8)C2×Dic1118yescomplemented
514#135—28no—
515#135—28no—
516C2×Q16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×D8—22no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—112no—
524C2×M16—221no—
525C2×M16—221no—
526C2×M16—221no—
527C2×M16—221no—
528C2×M16—221no—
529C2×M16C2×Dic1112yescomplemented
530C2×M16C2×Dic1112yescomplemented
531C2×M16C22×D1112yes—
532C22×C8—21no—
533C22×C8—221no—
534C4×Q8—224no—
535C4×Q8—224no—
536C4×D4—228no—
537C4×D4—228no—
538C4×D4—224no—
539C4×D4—224no—
540#117—112no—
541#117—112no—
542#117—112no—
543#117—224no—
544#117—224no—
545#117—221no—
546#117—221no—
547#117—221no—
548#117—221no—
549#117—221no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—222no—
555C2×C22⋊C4—221no—
556C2×C42—111no—
557C2×C42—112no—
558C2×C42—111no—
559C2×C42—112no—
560C2×C42—224no—
561C2×C42—222no—
562C2×C42—224no—
563C2×C42—221no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42—221no—
567C2×C42—221no—
568#104—224no—
569#104—224no—
570#104—228no—
571#99—228no—
572C2×C11—21no—
573C2×C11—21no—
574C2×C11—21no—
575C2×C11—21no—
576C2×C11—21no—
577C2×C11—21no—
578C2×C11—44no—
579C2×C11—82no—
580C2×C11#190612yescomplemented
581C2×C11C2×#38611yescharacteristic
582C24—21no—
583C24—21no—
584C24D4×D1111yescharacteristic
585#41—22no—
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—22no—
605#41—41no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—41no—
611#41—41no—
612#41—41no—
613#41C22⋊Dic1114yes—
614#41C22⋊Dic1114yes—
615#41C22×Dic1114yes—
616#41C2×C22⋊D1114yes—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22⋊Dic1112yes—
626C2×Q8C22⋊Dic1112yes—
627C2×Q8C22×Dic1112yescomplemented
628C2×Q8C2×C22⋊D1112yes—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4C22⋊Dic1112yes—
650C2×D4C22⋊Dic1112yes—
651C2×D4C22×Dic1112yescomplemented
652C2×D4C2×C22⋊D1112yes—
653C22×C4—21no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—221no—
668C22×C4—228no—
669C22×C4—221no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—444no—
674C22×C4—448no—
675C22×C4—441no—
676C22×C4D4×D1111yescharacteristic
677C22×C4D4×D1111yescharacteristic
678C22×C4D4×D1111yescharacteristic
679C22×C4#434111yescharacteristic
680C22×C4#434111yescharacteristic
681C22×C4#434111yescharacteristic
682C22×C4#434111yescharacteristic
683C22×C4C22×Dic1111yescharacteristic
684C22×C4C22×Dic1111yescharacteristic
685C22×C4C2×C22⋊D1111yescharacteristic
686C22×C4C2×C22⋊D1111yescharacteristic
687C22×C4C2×C22⋊D1111yescharacteristic
688C22×C4C2×C22⋊D1111yescharacteristic
689C22×C4C23×D1111yescharacteristic
690Q16—28no—
691SD16—28no—
692SD16—28no—
693D8—28no—
694M16—22no—
695M16—22no—
696M16—22no—
697M16—222no—
698M16—222no—
699M16—441no—
700M16—441no—
701M16C22×Dic1114yescomplemented
702C2×C8—22no—
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—222no—
706C2×C8—441no—
707C2×C8—441no—
708C4⋊C4—228no—
709C4⋊C4—222no—
710C4⋊C4—222no—
711C4⋊C4—222no—
712C4⋊C4—441no—
713C22⋊C4—114no—
714C22⋊C4—228no—
715C22⋊C4—222no—
716C22⋊C4—222no—
717C22⋊C4—441no—
718C42—112no—
719C42—112no—
720C42—228no—
721C42—221no—
722C42—221no—
723C42—222no—
724C42—222no—
725C42—222no—
726C42—222no—
727C42—222no—
728C42—441no—
729C11C2×#190611yescharacteristic, complemented, Sylow
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—42no—
735C23—44no—
736C23—41no—
737C23—41no—
738C23—82no—
739C23D4×Dic1111yescharacteristic
740C23D4×Dic1111yescharacteristic
741C23#6699011yescharacteristic
742C23#6699011yescharacteristic
743C23#6699211yescharacteristic
744C23#6699211yescharacteristic
745C23C2×D4×D1111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—41no—
752Q8—41no—
753Q8C2×C22⋊Dic1114yes—
754D4—24no—
755D4—24no—
756D4—24no—
757D4—24no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—41no—
768D4—41no—
769D4C2×C22⋊Dic1114yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—224no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—224no—
788C2×C4—444no—
789C2×C4—444no—
790C2×C4—4416no—
791C2×C4—442no—
792C2×C4—444no—
793C2×C4—442no—
794C2×C4—882no—
795C2×C4D4×Dic1111yescharacteristic
796C2×C4D4×Dic1111yescharacteristic
797C2×C4D4×Dic1111yescharacteristic
798C2×C4D4×Dic1111yescharacteristic
799C2×C4D4×Dic1111yescharacteristic
800C2×C4D4×Dic1111yescharacteristic
801C2×C4#6698811yescharacteristic
802C2×C4#6698811yescharacteristic
803C2×C4#6698811yescharacteristic
804C2×C4#6698811yescharacteristic
805C2×C4#6699011yescharacteristic
806C2×C4#6699011yescharacteristic
807C2×C4#6699211yescharacteristic
808C2×C4#6699211yescharacteristic
809C2×C4#6699211yescharacteristic
810C2×C4#6699211yescharacteristic
811C2×C4#6699211yescharacteristic
812C2×C4#6699211yescharacteristic
813C2×C4C2×C22⋊Dic1111yescharacteristic
814C2×C4C2×C22⋊Dic1111yescharacteristic
815C2×C4C2×C22⋊Dic1111yescharacteristic
816C2×C4C2×C22⋊Dic1111yescharacteristic
817C2×C4C2×D4×D1111yescharacteristic
818C2×C4C2×#434111yescharacteristic
819C2×C4C2×#434111yescharacteristic
820C2×C4C23×Dic1111yescharacteristic
821C2×C4C22×C22⋊D1111yescharacteristic
822C2×C4C22×C22⋊D1111yescharacteristic
823C8—24no—
824C8—442no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22#1062283311yescharacteristic
841C22#1062283311yescharacteristic
842C22#1062283311yescharacteristic
843C22#1062283311yescharacteristic
844C22C2×D4×Dic1111yescharacteristic
845C22C2×#6699011yescharacteristic
846C22C2×#6699211yescharacteristic
847C4—24no—
848C4—42no—
849C4—224no—
850C4—442no—
851C4—444no—
852C4—882no—
853C4#1062283311yescharacteristic
854C4#1062283311yescharacteristic
855C4#1062283311yescharacteristic
856C4#1062283311yescharacteristic
857C4C2×D4×Dic1111yescharacteristic
858C4C2×#6698811yescharacteristic
859C4C2×#6699211yescharacteristic
860C4C22×C22⋊Dic1111yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—44no—
868C2—82no—
869C2#1306911912yesdirect product factor
870C2C2×#1062283311yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#575C2
socleC22×C11#386
cosocleC22×C4×C11C24
hypercenterC2×#575D11
hypocenterC11C2×#1906
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#41×Dic11C2semidirect
2. C2×#10622849C2semidirect
3. C22×#66901C2semidirect
4. C2×#10622853C2semidirect
5. #13069119C2direct (N × H)
6. C2×#10622197C2semidirect
7. C2×#10622193C2semidirect
13. C11×#575C4semidirect
16. C2×C11×#137C4semidirect
18. C2×C11×AGL(1,ℤ/8)C4semidirect
24. #41×Dic11C22semidirect
35. #10622853C22semidirect
37. #10622849C22semidirect
42. C2×#66901C22semidirect
44. #10622197C22semidirect
45. #10622193C22semidirect
64. C2×C11×#41C2×C4semidirect
70. C22×Q8×C11C2×C4semidirect
74. C22×D4×C11C2×C4semidirect
84. C11×#137C2×C4semidirect
88. C11×AGL(1,ℤ/8)C2×C4semidirect
98. C2×C11×M16C2×C4semidirect
99. C2×C11×M16C2×C4semidirect
193. C2×Q8×C11C22×C4semidirect
217. C2×D4×C11C22×C4semidirect
263. C11×M16C22×C4semidirect
402. #575Dic11semidirect
405. C2×#137Dic11semidirect
407. C2×AGL(1,ℤ/8)Dic11semidirect
489. C2×#41C2×Dic11semidirect
495. C22×Q8C2×Dic11semidirect
499. C22×D4C2×Dic11semidirect
509. #137C2×Dic11semidirect
513. AGL(1,ℤ/8)C2×Dic11semidirect
529. C2×M16C2×Dic11semidirect
530. C2×M16C2×Dic11semidirect
580. C2×C11#1906semidirect
627. C2×Q8C22×Dic11semidirect
651. C2×D4C22×Dic11semidirect
701. M16C22×Dic11semidirect
729. C11C2×#1906semidirect
869. C2#13069119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×Dic112
C2×#106228492
C22×#669012
C2×#106228532
#130691192
C2×#106221972
C2×#106221932
C2×C11×#5752
C2×#190611