Finite Group Databasebeta

← #25098495

Subgroups — #25098495

Order 11008.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583699C211yesmaximal, characteristic
2#19147796C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4#19143115C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19135088C214yesmaximal, complemented
7#19135081C214yesmaximal, complemented
8C2×#14582656C211yesmaximal, characteristic, complemented
9C2×C43×#344C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C22×#10621898C2211yescharacteristic
12#14583699—22no—
13#14583699—22no—
14#14583699—22no—
15#14583699—22no—
16C2×#13063358C412yescomplemented
17C2×#13063358C2212yes—
18C2×#13063353C412yescomplemented
19C2×#13063353C2212yes—
20C2×#13063347C414yescomplemented
21#14583380—22no—
22#14583379—22no—
23#14583376C2212yescomplemented
24#14583373C2212yescomplemented
25#14583372—22no—
26C4×#10621898—22no—
27#14583367—22no—
28C2×#13063284C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30#117×D43—22no—
31#14582915—22no—
32#14582915C2214yes—
33C2×#13063251—22no—
34#14582909C2212yescomplemented
35#14582905C2212yescomplemented
36#14582901—22no—
37#14582896—22no—
38#14582872—22no—
39#14582872C2214yes—
40C2×#13063239—22no—
41#14582656C2214yescomplemented
42C22×M16×C43C2211yescharacteristic
43C22×M16×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C43×#344C2214yescomplemented
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898—21no—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898—21no—
56C2×#10621898—21no—
57C2×#10621898—21no—
58C2×#10621898—21no—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898—21no—
62C2×#10621898C2×C412yes—
63C2×#10621898C2×C412yes—
64C2×#10621898C2×C412yescomplemented
65C2×#10621898D412yes—
66C2×#10621898D412yes—
67C2×#10621898D412yes—
68C2×#10621898D412yes—
69C2×#10621898C2312yes—
70C22×Dic86C2×C411yescharacteristic, complemented
71C22×Dic86C2311yescharacteristic
72C22×D172C2×C411yescharacteristic, complemented
73C22×D172C2311yescharacteristic
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78#13063358—24no—
79#13063358—24no—
80#13063358—24no—
81#13063358—24no—
82#13063353—24no—
83#13063353—24no—
84#13063353—24no—
85#13063353—24no—
86#13063347—28no—
87#13063347—28no—
88C2×Dic172C2×C414yescomplemented
89C2×#10621873C2×C414yescomplemented
90C2×#10621873C2×C414yescomplemented
91C2×D344C2×C414yescomplemented
92C4×Dic86—24no—
93#13063290—24no—
94C4×D172—24no—
95#13063287—24no—
96C4×C22⋊D43—28no—
97(C22⋊D43)⋊C4—28no—
98#13063284—21no—
99#13063284—21no—
100#13063284—21no—
101#13063284—21no—
102#13063284—21no—
103#13063284D412yes—
104#13063284C2312yes—
105#13063284C2312yes—
106#13063283—24no—
107#13063282—24no—
108#13063281—24no—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43—21no—
111C4⋊C4×D43—24no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C22⋊C4×D43—24no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43D412yes—
117C42×D43—24no—
118#13063251—28no—
119#13063250—24no—
120#13063247—24no—
121#13063239—28no—
122C23×C4×C43C2311yescharacteristic
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×M16×C43—21no—
131C2×M16×C43—21no—
132C2×M16×C43C2×C412yescomplemented
133C2×M16×C43C2312yes—
134C2×M16×C43C2312yes—
135C22×C8×C43—21no—
136C22×C8×C43C2×C412yescomplemented
137#117×C43—21no—
138#117×C43—21no—
139#117×C43D412yes—
140#117×C43C2312yes—
141C2×C4⋊C4×C43—21no—
142C2×C22⋊C4×C43D412yes—
143C2×C42×C43—21no—
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C23×D43—21no—
147C22×C4×C43—22no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—41no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—41no—
174C22×Dic43—21no—
175C22×Dic43—22no—
176C22×Dic43—21no—
177C22×Dic43—41no—
178#10621898—22no—
179#10621898—22no—
180#10621898—22no—
181#10621898—22no—
182#10621898—22no—
183#10621898—22no—
184#10621898—22no—
185#10621898—22no—
186#10621898—22no—
187#10621898—22no—
188#10621898—22no—
189#10621898—22no—
190#10621898—22no—
191#10621898—22no—
192#10621898—22no—
193#10621898—22no—
194#10621898—22no—
195#10621898—22no—
196#10621898—22no—
197#10621898—22no—
198#10621898—41no—
199#10621898—41no—
200#10621898—41no—
201#10621898—41no—
202#10621898—41no—
203#10621898—41no—
204#10621898—41no—
205#10621898—41no—
206#10621898C22⋊C414yes—
207#10621898C22⋊C414yes—
208#10621898C22⋊C414yes—
209#10621898C22⋊C414yes—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172C22×C412yes—
219C2×D172C22×C412yes—
220C2×D172C2×D412yes—
221C2×D172C2×D412yes—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—28no—
231C2×C4×D43—41no—
232C2×C4×D43—41no—
233C2×C4×D43—41no—
234C2×C4×D43—41no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C22×C412yes—
244C2×Dic86C22×C412yes—
245C2×Dic86C2×D412yes—
246C2×Dic86C2×D412yes—
247M16×C43—22no—
248M16×C43—22no—
249M16×C43—22no—
250M16×C43—22no—
251M16×C43—22no—
252M16×C43—22no—
253M16×C43—41no—
254M16×C43—41no—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43—41no—
259C2×C8×C43—41no—
260C2×C8×C43C22×C414yes—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—22no—
263C22⋊C4×C43—22no—
264C22⋊C4×C43C2×D414yes—
265C42×C43—22no—
266C42×C43—22no—
267C22⋊Dic43—22no—
268C22⋊Dic43—22no—
269C22⋊Dic43—22no—
270C22⋊Dic43—41no—
271(C2×D43)⋊C4—28no—
272C4⋊Dic43—22no—
273C4⋊Dic43—22no—
274C4⋊Dic43—22no—
275C4⋊Dic43—41no—
276Dic43⋊C4—28no—
277C4×Dic43—28no—
278C4×Dic43—22no—
279C4×Dic43—22no—
280C4×Dic43—41no—
281C4×Dic43C2×D414yes—
282Dic172—28no—
283D344—28no—
284#10621873—28no—
285#10621873—28no—
286C23×C43—81no—
287C23×C43C4×D411yescharacteristic
288C23×C43C4×D411yescharacteristic
289C23×C43#12011yescharacteristic
290C23×C43#12011yescharacteristic
291C23×C43#12111yescharacteristic
292C23×C43#12111yescharacteristic
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—82no—
301C22×D43—82no—
302C2×C4×C43—24no—
303C2×C4×C43—82no—
304C2×C4×C43C2×C22⋊C411yescharacteristic
305C2×C4×C43C2×C22⋊C411yescharacteristic
306C2×C4×C43C2×C22⋊C411yescharacteristic
307C2×C4×C43C2×C22⋊C411yescharacteristic
308C2×C4×C43C4×D411yescharacteristic
309C2×C4×C43C4×D411yescharacteristic
310C2×C4×C43C4×D411yescharacteristic
311C2×C4×C43C4×D411yescharacteristic
312C2×C4×C43C4×D411yescharacteristic
313C2×C4×C43C4×D411yescharacteristic
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12011yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12311yescharacteristic
323C2×C4×C43#12311yescharacteristic
324C2×C4×C43#12311yescharacteristic
325C2×C4×C43#12311yescharacteristic
326C2×C4×C43C23×C411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C22⋊D43—24no—
333C22⋊D43—24no—
334C22⋊D43—24no—
335C22⋊D43—24no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—42no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—24no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—42no—
348C2×Dic43—82no—
349C2×Dic43—82no—
350D172—22no—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—41no—
356D172—41no—
357D172C2×C22⋊C414yes—
358C4×D43—24no—
359C4×D43—24no—
360C4×D43—24no—
361C4×D43—24no—
362C4×D43—42no—
363C4×D43—42no—
364C4×D43—42no—
365C4×D43—42no—
366C4×D43—88no—
367Dic86—22no—
368Dic86—22no—
369Dic86—22no—
370Dic86—22no—
371Dic86—22no—
372Dic86—41no—
373Dic86—41no—
374Dic86C2×C22⋊C414yes—
375C8×C43—24no—
376C8×C43—42no—
377#20998—431nomaximal, Sylow
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43#38611yescharacteristic
386C22×C43#38611yescharacteristic
387C22×C43#38611yescharacteristic
388C22×C43#38611yescharacteristic
389C22×C43C2×C4×D411yescharacteristic
390C22×C43C2×#12011yescharacteristic
391C22×C43C2×#12111yescharacteristic
392C2×D43—24no—
393C2×D43—44no—
394C2×D43—42no—
395C2×D43—82no—
396C2×D43—82no—
397C2×D43—82no—
398C2×D43—82no—
399C2×D43—82no—
400C4×C43—44no—
401C4×C43#38611yescharacteristic
402C4×C43#38611yescharacteristic
403C4×C43#38611yescharacteristic
404C4×C43#38611yescharacteristic
405C4×C43C22×C22⋊C411yescharacteristic
406C4×C43C2×C4×D411yescharacteristic
407C4×C43C2×#12111yescharacteristic
408C4×C43C2×#12311yescharacteristic
409Dic43—24no—
410Dic43—44no—
411Dic43—42no—
412Dic43—82no—
413C2×#575—431no—
414#3428—431no—
415C2×#421—431no—
416#2896—431no—
417C2×#410—431no—
418#1905—434no—
419#1904—434no—
420C2×#344D4311yescharacteristic, complemented
421C2×H(3,ℤ/4)—431no—
422C2×C43—21no—
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—21no—
426C2×C43—21no—
427C2×C43—21no—
428C2×C43—21no—
429C2×C43C2×#38611yescharacteristic
430D43—44no—
431D43—82no—
432C22×#41—431no—
433C22×#41—431no—
434#575—862no—
435#575—862no—
436#575—862no—
437#575—862no—
438C2×#137—432no—
439C2×#137—432no—
440C2×AGL(1,ℤ/8)—432no—
441C2×AGL(1,ℤ/8)—432no—
442C2×#135—434no—
443C22×M16C2×D4311yescharacteristic
444C22×M16C2×D4311yescharacteristic
445#520—862no—
446#520—862no—
447#519—432no—
448#518—432no—
449#518—862no—
450C4×#41—862no—
451C4×#41—862no—
452C2×#117—431no—
453C2×#117—431no—
454C2×#117—862no—
455C2×#117C2×D4311yescharacteristic
456#421—434no—
457#421—862no—
458C2×#104—862no—
459#419—432no—
460#418—432no—
461#417—862no—
462#416—862no—
463#410—434no—
464#410—862no—
465C2×#99—862no—
466#344C2×D4314yescomplemented
467H(3,ℤ/4)—434no—
468C43#2099811yescharacteristic, complemented, Sylow
469C2×#41—432no—
470C2×#41—432no—
471C2×#41—432no—
472C2×#41—432no—
473C2×#41—432no—
474C2×#41—432no—
475C2×#41—432no—
476C2×#41—432no—
477C2×#41—861no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—861no—
481C2×#41—861no—
482C2×#41—861no—
483C2×#41—861no—
484C2×#41—861no—
485C2×#41—861no—
486C2×#41—861no—
487C2×#41—861no—
488C2×#41—861no—
489C2×#41—861no—
490C2×#41—861no—
491C2×#41—861no—
492C2×#41—861no—
493C22×Q8—431no—
494C22×Q8—431no—
495C22×D4—431no—
496C22×D4—431no—
497C22×D4—861no—
498C22×D4—861no—
499C23×C4—861no—
500C23×C4—861no—
501C23×C4C22×D4311yescharacteristic
502#137—864no—
503#137—864no—
504#137—864no—
505#137—864no—
506AGL(1,ℤ/8)—864no—
507AGL(1,ℤ/8)—864no—
508AGL(1,ℤ/8)—864no—
509AGL(1,ℤ/8)—864no—
510#135—868no—
511#135—868no—
512C2×Q16—434no—
513C2×SD16—434no—
514C2×SD16—434no—
515C2×D8—434no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16C4×D4312yescomplemented
526C2×M16C22×D4312yes—
527C2×M16C22×D4312yes—
528C22×C8—21no—
529C22×C8C4×D4312yescomplemented
530C4×Q8—864no—
531C4×Q8—864no—
532C4×D4—864no—
533C4×D4—864no—
534C4×D4—868no—
535C4×D4—868no—
536#117—21no—
537#117—21no—
538#117—432no—
539#117—432no—
540#117—432no—
541#117—864no—
542#117—864no—
543#117—861no—
544#117—861no—
545#117—864no—
546#117—861no—
547#117—861no—
548#117—861no—
549#117D17212yes—
550#117C22×D4312yes—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—864no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—864no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4D17212yes—
559C2×C42—21no—
560C2×C42—432no—
561C2×C42—864no—
562C2×C42—861no—
563#104—868no—
564#103—864no—
565#102—864no—
566#99—868no—
567C24—861no—
568C24—861no—
569C24C2×D17211yescharacteristic
570#41—434no—
571#41—434no—
572#41—434no—
573#41—434no—
574#41—862no—
575#41—862no—
576#41—862no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584#41—862no—
585#41—862no—
586#41—862no—
587#41—862no—
588#41—862no—
589#41—862no—
590#41—862no—
591#41—862no—
592#41—862no—
593#41—862no—
594#41—1721no—
595#41—1721no—
596#41—1721no—
597#41—1721no—
598#41—1721no—
599#41—1721no—
600#41—1721no—
601#41—1721no—
602C2×Q8—432no—
603C2×Q8—432no—
604C2×Q8—432no—
605C2×Q8—432no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×D4—432no—
615C2×D4—432no—
616C2×D4—432no—
617C2×D4—432no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—1721no—
635C2×D4—1721no—
636C2×D4—1721no—
637C2×D4—1721no—
638C22×C4—22no—
639C22×C4—868no—
640C22×C4—861no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—861no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—1721no—
652C22×C4—1721no—
653C22×C4—1721no—
654C22×C4—1721no—
655C22×C4—1721no—
656C22×C4C2×C4×D4311yescharacteristic
657C22×C4C2×C4×D4311yescharacteristic
658C22×C4C2×D17211yescharacteristic
659C22×C4#1062189811yescharacteristic
660C22×C4#1062189811yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4D4×D4311yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4D4×D4311yescharacteristic
666C22×C4D4×D4311yescharacteristic
667C22×C4#1062190211yescharacteristic
668C22×C4#1062190211yescharacteristic
669C22×C4C23×D4311yescharacteristic
670Q16—868no—
671SD16—868no—
672SD16—868no—
673D8—868no—
674M16—22no—
675M16—22no—
676M16—22no—
677M16—22no—
678M16—22no—
679M16—22no—
680M16—41no—
681M16—41no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—41no—
686C2×C8—41no—
687C2×C8C2×C4×D4314yes—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—868no—
691C4⋊C4—862no—
692C4⋊C4—862no—
693C4⋊C4—862no—
694C4⋊C4—1721no—
695C22⋊C4—22no—
696C22⋊C4—868no—
697C22⋊C4—862no—
698C22⋊C4—862no—
699C22⋊C4—862no—
700C22⋊C4—1721no—
701C22⋊C4C2×D17214yes—
702C42—22no—
703C42—22no—
704C42—434no—
705C42—868no—
706C42—862no—
707C42—862no—
708C42—1721no—
709C23—81no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—3442no—
715C23—3442no—
716C23—1721no—
717C23—1721no—
718C23C4×D17211yescharacteristic
719C23C4×D17211yescharacteristic
720C23#1306329511yescharacteristic
721C23#1306329511yescharacteristic
722C23#1306330011yescharacteristic
723C23#1306330011yescharacteristic
724C23C22×D17211yescharacteristic
725Q8—434no—
726Q8—862no—
727Q8—862no—
728Q8—862no—
729Q8—862no—
730Q8—862no—
731Q8—1721no—
732Q8—1721no—
733D4—434no—
734D4—864no—
735D4—864no—
736D4—864no—
737D4—864no—
738D4—862no—
739D4—862no—
740D4—862no—
741D4—862no—
742D4—862no—
743D4—1722no—
744D4—1722no—
745D4—1722no—
746D4—1722no—
747D4—1721no—
748D4—1721no—
749C2×C4—24no—
750C2×C4—82no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—864no—
755C2×C4—864no—
756C2×C4—864no—
757C2×C4—864no—
758C2×C4—862no—
759C2×C4—864no—
760C2×C4—3448no—
761C2×C4—3442no—
762C2×C4—3442no—
763C2×C4—1722no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4C22⋊C4×D4311yescharacteristic
771C2×C4C22⋊C4×D4311yescharacteristic
772C2×C4C22⋊C4×D4311yescharacteristic
773C2×C4C22⋊C4×D4311yescharacteristic
774C2×C4#1306328711yescharacteristic
775C2×C4#1306328711yescharacteristic
776C2×C4#1306328711yescharacteristic
777C2×C4#1306328711yescharacteristic
778C2×C4C4×D17211yescharacteristic
779C2×C4C4×D17211yescharacteristic
780C2×C4#1306329511yescharacteristic
781C2×C4#1306329511yescharacteristic
782C2×C4#1306329811yescharacteristic
783C2×C4#1306329811yescharacteristic
784C2×C4#1306329811yescharacteristic
785C2×C4#1306329811yescharacteristic
786C2×C4#1306330011yescharacteristic
787C2×C4#1306330011yescharacteristic
788C2×C4#1306331011yescharacteristic
789C2×C4#1306331011yescharacteristic
790C2×C4#1306331011yescharacteristic
791C2×C4#1306331011yescharacteristic
792C2×C4C22×C4×D4311yescharacteristic
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4C2×#1062189811yescharacteristic
797C2×C4C2×#1062190211yescharacteristic
798C8—24no—
799C8—42no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—864no—
808C22—3442no—
809C22—3442no—
810C22—3442no—
811C22—3442no—
812C22—3442no—
813C22—1724no—
814C22—1722no—
815C22#1458277711yescharacteristic
816C22#1458277711yescharacteristic
817C22#1458277711yescharacteristic
818C22#1458277711yescharacteristic
819C22C2×C4×D17211yescharacteristic
820C22C2×#1306329511yescharacteristic
821C22C2×#1306330011yescharacteristic
822C4—44no—
823C4—864no—
824C4—3442no—
825C4—1724no—
826C4—1722no—
827C4#1458277711yescharacteristic
828C4#1458277711yescharacteristic
829C4#1458277711yescharacteristic
830C4#1458277711yescharacteristic
831C4C2×C22⋊C4×D4311yescharacteristic
832C4C2×#1306328711yescharacteristic
833C4C2×#1306329811yescharacteristic
834C4C2×#1306331011yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—3442no—
843C2—1724no—
844C2C2×#1458277711yescharacteristic
subgroupG/H
centerC4#14582777
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC2×C43C2×#386
prime radicalC2×#14583699C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43#20998
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
2. #19147796C2semidirect
3. C2×#14582915C2semidirect
4. #19143115C2semidirect
5. C2×#14582872C2semidirect
6. #19135088C2semidirect
7. #19135081C2semidirect
8. C2×#14582656C2semidirect
9. C2×C43×#344C2semidirect
16. C2×#13063358C4semidirect
18. C2×#13063353C4semidirect
20. C2×#13063347C4semidirect
23. #14583376C22semidirect
24. #14583373C22semidirect
34. #14582909C22semidirect
35. #14582905C22semidirect
41. #14582656C22semidirect
45. C43×#344C22semidirect
64. C2×#10621898C2×C4semidirect
70. C22×Dic86C2×C4semidirect
72. C22×D172C2×C4semidirect
88. C2×Dic172C2×C4semidirect
89. C2×#10621873C2×C4semidirect
90. C2×#10621873C2×C4semidirect
91. C2×D344C2×C4semidirect
132. C2×M16×C43C2×C4semidirect
136. C22×C8×C43C2×C4semidirect
420. C2×#344D43semidirect
466. #344C2×D43semidirect
468. C43#20998semidirect
525. C2×M16C4×D43semidirect
529. C22×C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836992
#191477962
C2×#145829152
#191431152
C2×#145828722
#191350882
#191350812
C2×#145826562
C2×C43×#3442
#2099843