Finite Group Databasebeta

← C2×#19135081 #25098478

Subgroups — C2×#19135081 #25098478

Order 11008.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063353C211yesmaximal, characteristic
2C2×#14583373C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4C2×#14582905C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19135081C218yesmaximal, direct product factor
7C2×#14582656C211yesmaximal, characteristic, complemented
8C2×C43×#344C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×D172C2211yescharacteristic
11C2×#13063353—22no—
12C2×#13063353—22no—
13C2×#13063353—22no—
14C2×#13063353—22no—
15C2×#13063353C414yescomplemented
16C2×#13063353C2214yes—
17C22×#10621873C412yescomplemented
18C22×D344C412yescomplemented
19#14583373—22no—
20#14583373—22no—
21#14583373—22no—
22#14583373C2214yescomplemented
23C2×C4×D172—22no—
24C2×#13063287—22no—
25C2×#13063284C2211yescharacteristic
26C2×#13063284C2211yescharacteristic
27C2×C22⋊C4×D43—22no—
28#14582915—22no—
29#14582915C2214yescomplemented
30C2×#13063251—22no—
31#14582905—22no—
32#14582905C2214yescomplemented
33C2×#13063247—22no—
34#14582872—22no—
35#14582872C2214yescomplemented
36C2×#13063239—22no—
37#14582656C2214yescomplemented
38C22×M16×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×#344C2214yescomplemented
42C24×D43—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898—21no—
53C2×#10621898C2×C412yescomplemented
54C2×#10621898C2312yes—
55C22×Dic86C2×C411yescharacteristic, complemented
56C22×D172—21no—
57C22×D172—21no—
58C22×D172—21no—
59C22×D172—21no—
60C22×D172—21no—
61C22×D172—21no—
62C22×D172—21no—
63C22×D172C2×C412yes—
64C22×D172C2×C412yes—
65C22×D172C2×C411yescharacteristic, complemented
66C22×D172D412yes—
67C22×D172D412yes—
68C22×D172D412yes—
69C22×D172D412yes—
70C22×D172C2312yes—
71C22×C22⋊D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—24no—
74#13063353—28no—
75#13063353—28no—
76#13063353—28no—
77#13063353—28no—
78C2×#10621873—24no—
79C2×#10621873—24no—
80C2×#10621873C2×C418yescomplemented
81C2×D344—24no—
82C2×D344—24no—
83C2×D344C2×C418yescomplemented
84C4×D172—28no—
85C4×D172—28no—
86#13063287—28no—
87#13063287—28no—
88#13063284—21no—
89#13063284—21no—
90#13063284—21no—
91#13063284—21no—
92#13063284—21no—
93#13063284D412yes—
94#13063284C2312yes—
95#13063284C2312yes—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×(C2×D43)⋊C4—24no—
101C22⋊C4×D43—28no—
102C22⋊C4×D43—28no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43D412yes—
105#13063251—28no—
106#13063247—28no—
107#13063239—28no—
108C23×C4×C43C2311yescharacteristic
109C2×M16×C43—21no—
110C2×M16×C43—21no—
111C2×M16×C43—21no—
112C2×M16×C43—21no—
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43C2×C412yescomplemented
119C2×M16×C43C2312yes—
120C2×M16×C43C2312yes—
121C22×C8×C43—21no—
122C22×C8×C43C2×C412yescomplemented
123#117×C43—21no—
124#117×C43—21no—
125#117×C43D412yes—
126#117×C43C2312yes—
127C2×C4⋊C4×C43—21no—
128C2×C22⋊C4×C43D412yes—
129C2×C42×C43—21no—
130C24×C43C2×D411yescharacteristic
131C23×D43—22no—
132C23×D43—22no—
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—21no—
139C23×D43—84no—
140C22×C4×C43—22no—
141C22×C4×C43C22×C411yescharacteristic
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C2×C22⋊D43—41no—
161C22×Dic43—21no—
162C22×Dic43—22no—
163C22×Dic43—41no—
164#10621898—22no—
165#10621898—22no—
166#10621898—22no—
167#10621898—22no—
168#10621898—22no—
169#10621898—22no—
170#10621898—22no—
171#10621898—22no—
172#10621898—41no—
173#10621898—41no—
174#10621898—41no—
175#10621898—41no—
176#10621898—41no—
177#10621898—41no—
178#10621898—41no—
179#10621898—41no—
180C2×D172—22no—
181C2×D172—22no—
182C2×D172—22no—
183C2×D172—22no—
184C2×D172—22no—
185C2×D172—22no—
186C2×D172—22no—
187C2×D172—22no—
188C2×D172—22no—
189C2×D172—22no—
190C2×D172—22no—
191C2×D172—22no—
192C2×D172—22no—
193C2×D172—22no—
194C2×D172—22no—
195C2×D172—22no—
196C2×D172—22no—
197C2×D172—22no—
198C2×D172—22no—
199C2×D172—22no—
200C2×D172—22no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172C22⋊C414yes—
207C2×D172C22⋊C414yes—
208C2×D172C22⋊C414yes—
209C2×D172C22⋊C414yes—
210C2×D172C22×C414yes—
211C2×D172C22×C412yescomplemented
212C2×D172C2×D414yes—
213C2×D172C2×D414yes—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—216no—
217C2×C4×D43—41no—
218C2×C4×D43—41no—
219C2×C4×D43—41no—
220C2×C4×D43—41no—
221C2×C4×D43—88no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86C22×C412yescomplemented
228M16×C43—22no—
229M16×C43—22no—
230M16×C43—22no—
231M16×C43—22no—
232M16×C43—22no—
233M16×C43—22no—
234M16×C43—41no—
235M16×C43—41no—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43—41no—
240C2×C8×C43—41no—
241C2×C8×C43C22×C414yescomplemented
242C4⋊C4×C43—22no—
243C4⋊C4×C43—22no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43C2×D414yes—
246C42×C43—22no—
247C42×C43—22no—
248C22⋊Dic43—22no—
249C22⋊Dic43—22no—
250C22⋊Dic43—22no—
251C22⋊Dic43—41no—
252(C2×D43)⋊C4—216no—
253C4⋊Dic43—22no—
254C4⋊Dic43—22no—
255C4⋊Dic43—22no—
256C4⋊Dic43—41no—
257C4×Dic43—22no—
258C4×Dic43—22no—
259C4×Dic43—41no—
260C4×Dic43C2×D414yes—
261D344—216no—
262#10621873—216no—
263C23×C43—42no—
264C23×C43C4×D411yescharacteristic
265C23×C43C4×D411yescharacteristic
266C23×C43#12011yescharacteristic
267C23×C43#12011yescharacteristic
268C23×C43#12111yescharacteristic
269C23×C43#12111yescharacteristic
270C23×C43C22×D411yescharacteristic
271C22×D43—24no—
272C22×D43—24no—
273C22×D43—24no—
274C22×D43—24no—
275C22×D43—24no—
276C22×D43—24no—
277C22×D43—24no—
278C22×D43—22no—
279C22×D43—48no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—84no—
283C22×D43—84no—
284C22×D43—84no—
285C22×D43—84no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—82no—
289C2×C4×C43—24no—
290C2×C4×C43—44no—
291C2×C4×C43C2×C22⋊C411yescharacteristic
292C2×C4×C43C2×C22⋊C411yescharacteristic
293C2×C4×C43C2×C22⋊C411yescharacteristic
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C4×D411yescharacteristic
296C2×C4×C43C4×D411yescharacteristic
297C2×C4×C43C4×D411yescharacteristic
298C2×C4×C43C4×D411yescharacteristic
299C2×C4×C43C4×D411yescharacteristic
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43#12011yescharacteristic
302C2×C4×C43#12011yescharacteristic
303C2×C4×C43#12111yescharacteristic
304C2×C4×C43#12111yescharacteristic
305C2×C4×C43#12111yescharacteristic
306C2×C4×C43#12111yescharacteristic
307C2×C4×C43#12111yescharacteristic
308C2×C4×C43#12111yescharacteristic
309C2×C4×C43#12311yescharacteristic
310C2×C4×C43#12311yescharacteristic
311C2×C4×C43#12311yescharacteristic
312C2×C4×C43#12311yescharacteristic
313C2×C4×C43C23×C411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C22⋊D43—42no—
320C22⋊D43—42no—
321C22⋊D43—42no—
322C22⋊D43—42no—
323C2×Dic43—22no—
324C2×Dic43—24no—
325C2×Dic43—44no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—42no—
329C2×Dic43—82no—
330D172—22no—
331D172—24no—
332D172—22no—
333D172—24no—
334D172—24no—
335D172—24no—
336D172—24no—
337D172—24no—
338D172—24no—
339D172—41no—
340D172—41no—
341D172C2×C22⋊C418yes—
342C4×D43—42no—
343C4×D43—42no—
344C4×D43—42no—
345C4×D43—42no—
346C4×D43—816no—
347Dic86—22no—
348Dic86—22no—
349Dic86—41no—
350Dic86—41no—
351C8×C43—24no—
352C8×C43—42no—
353C2×#1904—431nomaximal, Sylow
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43#38611yescharacteristic
362C22×C43#38611yescharacteristic
363C22×C43#38611yescharacteristic
364C22×C43#38611yescharacteristic
365C22×C43C2×C4×D411yescharacteristic
366C22×C43C2×#12011yescharacteristic
367C22×C43C2×#12111yescharacteristic
368C2×D43—28no—
369C2×D43—48no—
370C2×D43—48no—
371C2×D43—48no—
372C2×D43—42no—
373C2×D43—84no—
374C2×D43—84no—
375C2×D43—84no—
376C2×D43—84no—
377C2×D43—82no—
378C2×D43—82no—
379C2×D43—82no—
380C4×C43—44no—
381C4×C43#38611yescharacteristic
382C4×C43#38611yescharacteristic
383C4×C43#38611yescharacteristic
384C4×C43#38611yescharacteristic
385C4×C43C22×C22⋊C411yescharacteristic
386C4×C43C2×C4×D411yescharacteristic
387C4×C43C2×#12111yescharacteristic
388C4×C43C2×#12311yescharacteristic
389Dic43—44no—
390Dic43—42no—
391Dic43—82no—
392C22×AGL(1,ℤ/8)—431no—
393C2×#518—431no—
394C2×#421—431no—
395C2×#418—431no—
396C2×#410—431no—
397#1904—438no—
398C2×#344D4311yescharacteristic, complemented
399C2×H(3,ℤ/4)—431no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43#190412yescomplemented
407C2×C43C2×#38611yescharacteristic
408D43—48no—
409D43—82no—
410C22×#41—431no—
411C23×D4—431no—
412C2×AGL(1,ℤ/8)—434no—
413C2×AGL(1,ℤ/8)—434no—
414C2×AGL(1,ℤ/8)—862no—
415C2×AGL(1,ℤ/8)—862no—
416C2×AGL(1,ℤ/8)—862no—
417C2×AGL(1,ℤ/8)—862no—
418C22×SD16—432no—
419C22×D8—432no—
420C22×M16C2×D4311yescharacteristic
421C22×M16C2×D4311yescharacteristic
422#518—434no—
423#518—862no—
424#518—862no—
425#518—862no—
426C2×C4×D4—862no—
427C2×C4×D4—862no—
428C2×#117—431no—
429C2×#117—431no—
430C2×#117C2×D4311yescharacteristic
431C22×C22⋊C4—862no—
432#421—434no—
433#421—862no—
434C2×#104—862no—
435#418—434no—
436#418—862no—
437C2×#102—862no—
438#410—434no—
439#410—862no—
440C2×#99—862no—
441#344C2×D4314yescomplemented
442H(3,ℤ/4)—434no—
443C43C2×#190411yescharacteristic, complemented, Sylow
444C25—861no—
445C2×#41—432no—
446C2×#41—432no—
447C2×#41—861no—
448C2×#41—861no—
449C2×#41—861no—
450C2×#41—861no—
451C2×#41—861no—
452C2×#41—861no—
453C2×#41—861no—
454C2×#41—861no—
455C2×#41—861no—
456C2×#41—861no—
457C22×Q8—431no—
458C22×D4—432no—
459C22×D4—432no—
460C22×D4—431no—
461C22×D4—432no—
462C22×D4—432no—
463C22×D4—432no—
464C22×D4—432no—
465C22×D4—432no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4—861no—
474C23×C4—864no—
475C23×C4—861no—
476C23×C4C22×D4311yescharacteristic
477AGL(1,ℤ/8)—868no—
478AGL(1,ℤ/8)—868no—
479AGL(1,ℤ/8)—868no—
480AGL(1,ℤ/8)—868no—
481C2×SD16—438no—
482C2×SD16—864no—
483C2×SD16—864no—
484C2×D8—438no—
485C2×D8—864no—
486C2×D8—864no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16C4×D4312yescomplemented
497C2×M16C22×D4312yes—
498C2×M16C22×D4312yes—
499C22×C8—21no—
500C22×C8C4×D4312yescomplemented
501C4×D4—868no—
502C4×D4—868no—
503C4×D4—868no—
504C4×D4—868no—
505#117—21no—
506#117—21no—
507#117—432no—
508#117—432no—
509#117—432no—
510#117—861no—
511#117—861no—
512#117—861no—
513#117—861no—
514#117—861no—
515#117D17212yes—
516#117C22×D4312yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C22⋊C4—868no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—868no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4D17212yes—
526C2×C42—21no—
527C2×C42—432no—
528C2×C42—861no—
529#104—868no—
530#102—868no—
531#99—868no—
532C24—862no—
533C24—862no—
534C24—862no—
535C24—862no—
536C24—862no—
537C24—862no—
538C24—862no—
539C24—861no—
540C24—3444no—
541C24C2×D17211yescharacteristic
542#41—862no—
543#41—862no—
544#41—862no—
545#41—862no—
546#41—862no—
547#41—862no—
548#41—862no—
549#41—862no—
550#41—1721no—
551#41—1721no—
552#41—1721no—
553#41—1721no—
554#41—1721no—
555#41—1721no—
556#41—1721no—
557#41—1721no—
558C2×Q8—432no—
559C2×Q8—861no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×D4—434no—
565C2×D4—434no—
566C2×D4—434no—
567C2×D4—434no—
568C2×D4—434no—
569C2×D4—432no—
570C2×D4—434no—
571C2×D4—434no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—862no—
583C2×D4—862no—
584C2×D4—861no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—862no—
594C2×D4—862no—
595C2×D4—862no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—1721no—
601C2×D4—1721no—
602C2×D4—1721no—
603C2×D4—1721no—
604C22×C4—22no—
605C22×C4—8616no—
606C22×C4—861no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—3448no—
611C22×C4—1721no—
612C22×C4—1721no—
613C22×C4—1721no—
614C22×C4—1721no—
615C22×C4—1721no—
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×C4×D4311yescharacteristic
618C22×C4C2×D17211yescharacteristic
619C22×C4#1062189811yescharacteristic
620C22×C4#1062189811yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4D4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4#1062190211yescharacteristic
628C22×C4#1062190211yescharacteristic
629C22×C4C23×D4311yescharacteristic
630SD16—8616no—
631D8—8616no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—41no—
639M16—41no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8C2×C4×D4314yescomplemented
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—862no—
649C4⋊C4—862no—
650C4⋊C4—862no—
651C4⋊C4—1721no—
652C22⋊C4—22no—
653C22⋊C4—8616no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—1721no—
658C22⋊C4C2×D17214yes—
659C42—22no—
660C42—22no—
661C42—434no—
662C42—862no—
663C42—862no—
664C42—1721no—
665C23—42no—
666C23—864no—
667C23—864no—
668C23—864no—
669C23—864no—
670C23—864no—
671C23—864no—
672C23—864no—
673C23—862no—
674C23—3442no—
675C23—3444no—
676C23—3444no—
677C23—3444no—
678C23—3444no—
679C23—3444no—
680C23—3444no—
681C23—1728no—
682C23—1721no—
683C23—1721no—
684C23C4×D17211yescharacteristic
685C23C4×D17211yescharacteristic
686C23#1306329511yescharacteristic
687C23#1306329511yescharacteristic
688C23#1306330011yescharacteristic
689C23#1306330011yescharacteristic
690C23C22×D17211yescharacteristic
691Q8—862no—
692Q8—862no—
693Q8—1721no—
694Q8—1721no—
695D4—438no—
696D4—862no—
697D4—864no—
698D4—862no—
699D4—864no—
700D4—864no—
701D4—864no—
702D4—864no—
703D4—864no—
704D4—864no—
705D4—1722no—
706D4—1722no—
707D4—1722no—
708D4—1722no—
709D4—1721no—
710D4—1721no—
711C2×C4—24no—
712C2×C4—44no—
713C2×C4—862no—
714C2×C4—864no—
715C2×C4—34416no—
716C2×C4—3442no—
717C2×C4—1722no—
718C2×C4—1724no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4C22⋊C4×D4311yescharacteristic
726C2×C4C22⋊C4×D4311yescharacteristic
727C2×C4C22⋊C4×D4311yescharacteristic
728C2×C4C22⋊C4×D4311yescharacteristic
729C2×C4#1306328711yescharacteristic
730C2×C4#1306328711yescharacteristic
731C2×C4#1306328711yescharacteristic
732C2×C4#1306328711yescharacteristic
733C2×C4C4×D17211yescharacteristic
734C2×C4C4×D17211yescharacteristic
735C2×C4#1306329511yescharacteristic
736C2×C4#1306329511yescharacteristic
737C2×C4#1306329811yescharacteristic
738C2×C4#1306329811yescharacteristic
739C2×C4#1306329811yescharacteristic
740C2×C4#1306329811yescharacteristic
741C2×C4#1306330011yescharacteristic
742C2×C4#1306330011yescharacteristic
743C2×C4#1306331011yescharacteristic
744C2×C4#1306331011yescharacteristic
745C2×C4#1306331011yescharacteristic
746C2×C4#1306331011yescharacteristic
747C2×C4C22×C4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4C2×D4×D4311yescharacteristic
750C2×C4C2×D4×D4311yescharacteristic
751C2×C4C2×#1062189811yescharacteristic
752C2×C4C2×#1062190211yescharacteristic
753C8—24no—
754C8—42no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—868no—
763C22—3442no—
764C22—3442no—
765C22—3444no—
766C22—3444no—
767C22—3444no—
768C22—3444no—
769C22—3442no—
770C22—1728no—
771C22—1728no—
772C22—1722no—
773C22—1728no—
774C22#1458277711yescharacteristic
775C22#1458277711yescharacteristic
776C22#1458277711yescharacteristic
777C22#1458277711yescharacteristic
778C22C2×C4×D17211yescharacteristic
779C22C2×#1306329511yescharacteristic
780C22C2×#1306330011yescharacteristic
781C4—44no—
782C4—3442no—
783C4—1724no—
784C4—1722no—
785C4#1458277711yescharacteristic
786C4#1458277711yescharacteristic
787C4#1458277711yescharacteristic
788C4#1458277711yescharacteristic
789C4C2×C22⋊C4×D4311yescharacteristic
790C4C2×#1306328711yescharacteristic
791C4C2×#1306329811yescharacteristic
792C4C2×#1306331011yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—3442no—
800C2—1728no—
801C2#1913508112yesdirect product factor
802C2C2×#1458277711yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC22×#13063353C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43C2×#1904
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
2. C2×#14583373C2semidirect
3. C2×#14582915C2semidirect
4. C2×#14582905C2semidirect
5. C2×#14582872C2semidirect
6. #19135081C2direct (N × H)
7. C2×#14582656C2semidirect
8. C2×C43×#344C2semidirect
15. C2×#13063353C4semidirect
17. C22×#10621873C4semidirect
18. C22×D344C4semidirect
22. #14583373C22semidirect
29. #14582915C22semidirect
32. #14582905C22semidirect
35. #14582872C22semidirect
37. #14582656C22semidirect
41. C43×#344C22semidirect
53. C2×#10621898C2×C4semidirect
55. C22×Dic86C2×C4semidirect
65. C22×D172C2×C4semidirect
80. C2×#10621873C2×C4semidirect
83. C2×D344C2×C4semidirect
118. C2×M16×C43C2×C4semidirect
122. C22×C8×C43C2×C4semidirect
211. C2×D172C22×C4semidirect
227. C2×Dic86C22×C4semidirect
241. C2×C8×C43C22×C4semidirect
398. C2×#344D43semidirect
406. C2×C43#1904semidirect
441. #344C2×D43semidirect
443. C43C2×#1904semidirect
496. C2×M16C4×D43semidirect
500. C22×C8C4×D43semidirect
645. C2×C8C2×C4×D43semidirect
801. C2#19135081direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633532
C2×#145833732
C2×#145829152
C2×#145829052
C2×#145828722
#191350812
C2×#145826562
C2×C43×#3442
C2×#190443