Finite Group Databasebeta

← #25098142

Subgroups — #25098142

Order 11008.

1708 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19147928C211yesmaximal, characteristic
3C2×#14582917C211yesmaximal, characteristic, complemented
4C2×#14582915C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19134977C218yesmaximal, complemented
7#19134305C211yesmaximal, characteristic, complemented
8C43×#1733C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621898C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yescomplemented
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C2×M16×D43—22no—
19#14583480—22no—
20#14583475C412yescomplemented
21#14583475C412yescomplemented
22#14583468C412yescomplemented
23#14583468C412yescomplemented
24#14583461—22no—
25#14583449C2214yes—
26#14583411—22no—
27#14583411—22no—
28C2×#13063284C2211yescharacteristic
29#14582917—22no—
30#14582917C2214yescomplemented
31#14582915—22no—
32#14582915C2214yescomplemented
33C2×#13063253—22no—
34C2×#13063251—22no—
35#14582872—22no—
36#14582872C2214yescomplemented
37C2×#13063239—22no—
38#14582659C2214yescomplemented
39C22×M16×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C43×#339C2214yescomplemented
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×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898—21no—
56C2×#10621898—21no—
57C2×#10621898—21no—
58C2×#10621898—21no—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2×C412yes—
62C2×#10621898C2×C412yes—
63C2×#10621898D412yes—
64C2×#10621898D412yes—
65C2×#10621898C2312yes—
66C2×#10621898C2312yes—
67C22×Dic86C2×C411yescharacteristic
68C22×Dic86C2×C411yescharacteristic
69C22×D172C2×C411yescharacteristic
70C22×D172C2×C411yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43D412yes—
73C22×C4×D43—21no—
74C22×C4×D43D412yes—
75#13063333—28no—
76#13063333—28no—
77#13063331—28no—
78#13063331—28no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877D412yescomplemented
83C2×#10621877D412yescomplemented
84C2×#10621877C2312yes—
85C2×#10621872—24no—
86M16×D43—28no—
87M16×D43—28no—
88C22×C43⋊C8—21no—
89C2×C8×D43—24no—
90#13063325C2×C414yescomplemented
91#13063322C2×C414yescomplemented
92#13063313C2×C414yescomplemented
93#13063313C2×C414yescomplemented
94#13063309—24no—
95#13063309—24no—
96#13063305—24no—
97#13063305—24no—
98#13063300—24no—
99#13063300—24no—
100#13063299—28no—
101#13063295—24no—
102#13063295—24no—
103C4×D172—28no—
104#13063284—21no—
105#13063284—21no—
106#13063284—21no—
107#13063284C2312yes—
108C2×C4⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C4×Dic43—21no—
111#13063253—28no—
112#13063251—28no—
113#13063239—28no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43D412yescomplemented
119C2×M16×C43D412yescomplemented
120C2×M16×C43C2312yes—
121C22×C8×C43—21no—
122#117×C43—21no—
123#117×C43—21no—
124#117×C43—21no—
125#117×C43—21no—
126#117×C43—21no—
127#117×C43C2×C412yes—
128#117×C43C2×C412yes—
129#117×C43C2312yes—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2312yes—
136C24×C43C2×D411yescharacteristic
137C23×D43—21no—
138C23×D43C22⋊C412yes—
139C22×C4×C43—22no—
140C22×C4×C43—41no—
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—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—41no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43C22⋊C414yes—
166C2×C22⋊D43C2×D414yes—
167C22×Dic43—21no—
168C22×Dic43—41no—
169C22×Dic43C22⋊C412yes—
170#10621898—22no—
171#10621898—22no—
172#10621898—22no—
173#10621898—22no—
174#10621898—22no—
175#10621898—22no—
176#10621898—22no—
177#10621898—22no—
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—41no—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
199#10621898—41no—
200#10621898—41no—
201#10621898—41no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—28no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172C22⋊C412yes—
213C2×D172C22×C412yes—
214C2×D172C22×C412yes—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—41no—
222C2×C4×D43—41no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43C22⋊C414yes—
226C2×C4×D43C2×D414yes—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C22⋊C412yes—
237C2×Dic86C22×C412yes—
238C2×Dic86C22×C412yes—
239M16×C43—22no—
240M16×C43—22no—
241M16×C43—22no—
242M16×C43C2×D414yes—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43—22no—
246C4⋊C4×C43—22no—
247C4⋊C4×C43—22no—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—41no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—41no—
254C42×C43—22no—
255C42×C43—22no—
256C42×C43—41no—
257C42×C43C22×C414yes—
258C22⋊Dic43—22no—
259C22⋊Dic43—41no—
260(C2×D43)⋊C4—28no—
261(C2×D43)⋊C4—28no—
262C4⋊Dic43—28no—
263C4⋊Dic43—22no—
264C4⋊Dic43—41no—
265C4×Dic43—22no—
266C4×Dic43—41no—
267#10621877—22no—
268#10621877—22no—
269#10621877—22no—
270#10621877C2×D414yes—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274#10621872—216no—
275C8×D43—216no—
276C23×C43—81no—
277C23×C43C2×C22⋊C411yescharacteristic
278C23×C43C2×C22⋊C411yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12111yescharacteristic
281C23×C43#12111yescharacteristic
282C23×C43#12111yescharacteristic
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—82no—
290C22×D43—82no—
291C22×D43C2×C22⋊C414yes—
292C2×C4×C43—24no—
293C2×C4×C43—42no—
294C2×C4×C43—82no—
295C2×C4×C43—82no—
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C4×D411yescharacteristic
299C2×C4×C43C4×D411yescharacteristic
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43C4×D411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43C4×D411yescharacteristic
305C2×C4×C43C4×D411yescharacteristic
306C2×C4×C43#12011yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12311yescharacteristic
315C2×C4×C43#12311yescharacteristic
316C2×C4×C43#12311yescharacteristic
317C2×C4×C43#12311yescharacteristic
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C22⋊D43—24no—
325C22⋊D43—24no—
326C22⋊D43—24no—
327C22⋊D43—24no—
328C22⋊D43—42no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—42no—
338C2×Dic43—82no—
339C2×Dic43C2×C22⋊C414yes—
340D172—22no—
341D172—22no—
342D172—22no—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—41no—
347D172—41no—
348D172—88no—
349C4×D43—24no—
350C4×D43—24no—
351C4×D43—24no—
352C4×D43—24no—
353C4×D43—42no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43—42no—
357Dic86—22no—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—41no—
364Dic86—41no—
365C8×C43—24no—
366C43⋊C8—24no—
367#20947—431nomaximal, Sylow
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43#38611yescharacteristic
376C22×C43#38611yescharacteristic
377C22×C43#38611yescharacteristic
378C22×C43#38611yescharacteristic
379C22×C43C22×C22⋊C411yescharacteristic
380C22×C43C2×#12111yescharacteristic
381C22×C43C2×#12111yescharacteristic
382C2×D43—24no—
383C2×D43—44no—
384C2×D43—44no—
385C2×D43—44no—
386C2×D43—42no—
387C2×D43—82no—
388C2×D43—82no—
389C2×D43—82no—
390C4×C43—44no—
391C4×C43—82no—
392C4×C43#38611yescharacteristic
393C4×C43#38611yescharacteristic
394C4×C43#38611yescharacteristic
395C4×C43#38611yescharacteristic
396C4×C43C2×C4×D411yescharacteristic
397C4×C43C2×C4×D411yescharacteristic
398C4×C43C2×#12011yescharacteristic
399C4×C43C2×#12311yescharacteristic
400Dic43—24no—
401Dic43—42no—
402Dic43—82no—
403C2×#568—431no—
404#3449—431no—
405C2×#421—431no—
406C2×#421—431no—
407C2×#410—431no—
408#1884—438no—
409#1733—431no—
410#1733D4311yescharacteristic, complemented
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43C2×#38611yescharacteristic
419D43—44no—
420D43—82no—
421C22×#41—431no—
422C22×#41—431no—
423#568—434no—
424#568—862no—
425#568—862no—
426#568—862no—
427C2×#131—862no—
428C2×#131—862no—
429C22×M16—431no—
430C22×M16—862no—
431C22×M16C2×D4311yescharacteristic
432#537—862no—
433#536—432no—
434#536—432no—
435#535—432no—
436#535—432no—
437#534—862no—
438#532—434no—
439#525—862no—
440#525—862no—
441C2×#117—431no—
442C2×#117C2×D4311yescharacteristic
443C2×#117C2×D4311yescharacteristic
444#421—434no—
445#421—434no—
446#421—862no—
447#421—862no—
448C2×#104—862no—
449C2×#104—862no—
450#410—434no—
451#410—862no—
452C2×#99—862no—
453#339—434no—
454#339C2×D4314yescomplemented
455C43#2094711yescharacteristic, complemented, Sylow
456C2×#41—432no—
457C2×#41—432no—
458C2×#41—432no—
459C2×#41—432no—
460C2×#41—432no—
461C2×#41—432no—
462C2×#41—861no—
463C2×#41—861no—
464C2×#41—861no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41—861no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41—861no—
478C2×#41—861no—
479C2×#41—861no—
480C22×Q8—431no—
481C22×Q8—431no—
482C22×D4—432no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—861no—
486C23×C4—432no—
487C23×C4—861no—
488C23×C4C22×D4311yescharacteristic
489#131—868no—
490#131—868no—
491#131—868no—
492#131—868no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—432no—
497C2×M16—432no—
498C2×M16—432no—
499C2×M16—864no—
500C2×M16—868no—
501C2×M16—868no—
502C2×M16—861no—
503C2×M16—861no—
504C2×M16—861no—
505C2×M16D17212yescomplemented
506C2×M16D17212yescomplemented
507C2×M16C22×D4312yes—
508C22×C8—21no—
509C22×C8—864no—
510C22×C8—861no—
511C4⋊Q8—434no—
512#127—434no—
513#124—434no—
514#124—434no—
515#123—864no—
516#123—864no—
517C22⋊Q8—864no—
518C22⋊Q8—864no—
519#121—864no—
520#121—864no—
521#121—868no—
522#120—864no—
523#120—864no—
524C4×D4—868no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529#117—21no—
530#117—432no—
531#117—861no—
532#117—861no—
533#117—861no—
534#117C4×D4312yes—
535#117C4×D4312yes—
536#117C22×D4312yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—861no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—861no—
543C2×C42—21no—
544C2×C42—861no—
545C2×C42C22×D4312yes—
546#104—868no—
547#104—868no—
548#99—868no—
549C24—432no—
550C24—861no—
551C24D4×D4311yescharacteristic
552#41—862no—
553#41—862no—
554#41—862no—
555#41—862no—
556#41—862no—
557#41—862no—
558#41—862no—
559#41—862no—
560#41—862no—
561#41—862no—
562#41—862no—
563#41—862no—
564#41—862no—
565#41—862no—
566#41—862no—
567#41—862no—
568#41—862no—
569#41—862no—
570#41—862no—
571#41—862no—
572#41—862no—
573#41—862no—
574#41—862no—
575#41—862no—
576#41—1721no—
577#41—1721no—
578#41—1721no—
579#41—1721no—
580#41—1721no—
581#41—1721no—
582#41—1721no—
583#41—1721no—
584C2×Q8—432no—
585C2×Q8—432no—
586C2×Q8—432no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8—861no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×D4—434no—
597C2×D4—434no—
598C2×D4—432no—
599C2×D4—432no—
600C2×D4—432no—
601C2×D4—868no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—1721no—
618C2×D4—1721no—
619C2×D4—1721no—
620C2×D4—1721no—
621C22×C4—22no—
622C22×C4—41no—
623C22×C4—432no—
624C22×C4—434no—
625C22×C4—434no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—861no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—1721no—
634C22×C4—1721no—
635C22×C4—1721no—
636C22×C4—1721no—
637C22×C4—1721no—
638C22×C4C2×C4×D4311yescharacteristic
639C22×C4C2×C4×D4311yescharacteristic
640C22×C4C2×D17211yescharacteristic
641C22×C4C2×D17211yescharacteristic
642C22×C4#1062189811yescharacteristic
643C22×C4#1062189811yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4D4×D4311yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4#1062190211yescharacteristic
650C22×C4#1062190211yescharacteristic
651C22×C4C23×D4311yescharacteristic
652M16—22no—
653M16—22no—
654M16—22no—
655M16—434no—
656M16—8616no—
657M16—862no—
658M16—862no—
659M16—862no—
660M16C2×D17214yes—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—8616no—
665C2×C8—862no—
666C2×C8—862no—
667C2×C8—862no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—41no—
672C4⋊C4—868no—
673C4⋊C4—862no—
674C4⋊C4—1721no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—868no—
680C22⋊C4—868no—
681C22⋊C4—862no—
682C22⋊C4—1721no—
683C42—22no—
684C42—22no—
685C42—41no—
686C42—862no—
687C42—1721no—
688C42C2×C4×D4314yes—
689C23—81no—
690C23—434no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—3442no—
695C23—3442no—
696C23—1721no—
697C23—1721no—
698C23C22⋊C4×D4311yescharacteristic
699C23C22⋊C4×D4311yescharacteristic
700C23#1306329811yescharacteristic
701C23#1306329811yescharacteristic
702C23#1306330011yescharacteristic
703C23#1306330011yescharacteristic
704C23C2×D4×D4311yescharacteristic
705Q8—862no—
706Q8—862no—
707Q8—862no—
708Q8—862no—
709Q8—862no—
710Q8—862no—
711Q8—1721no—
712Q8—1721no—
713D4—864no—
714D4—864no—
715D4—864no—
716D4—864no—
717D4—862no—
718D4—862no—
719D4—862no—
720D4—862no—
721D4—862no—
722D4—862no—
723D4—3448no—
724D4—1722no—
725D4—1722no—
726D4—1722no—
727D4—1722no—
728D4—1721no—
729D4—1721no—
730C2×C4—24no—
731C2×C4—42no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—434no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—864no—
738C2×C4—864no—
739C2×C4—864no—
740C2×C4—864no—
741C2×C4—862no—
742C2×C4—3442no—
743C2×C4—1722no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4C22⋊C4×D4311yescharacteristic
751C2×C4C22⋊C4×D4311yescharacteristic
752C2×C4#1306328711yescharacteristic
753C2×C4#1306328711yescharacteristic
754C2×C4#1306328711yescharacteristic
755C2×C4#1306328711yescharacteristic
756C2×C4C4×D17211yescharacteristic
757C2×C4C4×D17211yescharacteristic
758C2×C4C4×D17211yescharacteristic
759C2×C4C4×D17211yescharacteristic
760C2×C4#1306329511yescharacteristic
761C2×C4#1306329511yescharacteristic
762C2×C4#1306329511yescharacteristic
763C2×C4#1306329511yescharacteristic
764C2×C4#1306329811yescharacteristic
765C2×C4#1306329811yescharacteristic
766C2×C4#1306330011yescharacteristic
767C2×C4#1306330011yescharacteristic
768C2×C4#1306331011yescharacteristic
769C2×C4#1306331011yescharacteristic
770C2×C4#1306331011yescharacteristic
771C2×C4#1306331011yescharacteristic
772C2×C4C22×C4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C22×D17211yescharacteristic
776C2×C4C2×#1062189811yescharacteristic
777C2×C4C2×#1062190211yescharacteristic
778C8—24no—
779C8—864no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—864no—
788C22—3442no—
789C22—3442no—
790C22—3442no—
791C22—1724no—
792C22—1724no—
793C22—1724no—
794C22—1722no—
795C22#1458277711yescharacteristic
796C22#1458277711yescharacteristic
797C22#1458277711yescharacteristic
798C22#1458277711yescharacteristic
799C22C2×C22⋊C4×D4311yescharacteristic
800C22C2×#1306329811yescharacteristic
801C22C2×#1306330011yescharacteristic
802C4—44no—
803C4—82no—
804C4—864no—
805C4—3442no—
806C4—1722no—
807C4#1458277711yescharacteristic
808C4#1458277711yescharacteristic
809C4#1458277711yescharacteristic
810C4#1458277711yescharacteristic
811C4C2×#1306328711yescharacteristic
812C4C2×C4×D17211yescharacteristic
813C4C2×#1306329511yescharacteristic
814C4C2×#1306331011yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—3442no—
823C2—1724no—
824C2C2×#1458277711yescharacteristic
subgroupG/H
centerC4C2×#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1733C2
socleC2×C43C2×#386
prime radical#19147928C2
cosocleC22×C4×C43C24
hypercenter#1733D43
hypocenterC43#20947
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582917C2semidirect
4. C2×#14582915C2semidirect
5. C2×#14582872C2semidirect
6. #19134977C2semidirect
7. #19134305C2semidirect
8. C43×#1733C2semidirect
14. #14583665C22semidirect
20. #14583475C4semidirect
21. #14583475C4semidirect
22. #14583468C4semidirect
23. #14583468C4semidirect
30. #14582917C22semidirect
32. #14582915C22semidirect
36. #14582872C22semidirect
38. #14582659C22semidirect
42. C43×#339C22semidirect
82. C2×#10621877D4semidirect
83. C2×#10621877D4semidirect
90. #13063325C2×C4semidirect
91. #13063322C2×C4semidirect
92. #13063313C2×C4semidirect
93. #13063313C2×C4semidirect
118. C2×M16×C43D4semidirect
119. C2×M16×C43D4semidirect
410. #1733D43semidirect
454. #339C2×D43semidirect
455. C43#20947semidirect
505. C2×M16D172semidirect
506. C2×M16D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479282
C2×#145829172
C2×#145829152
C2×#145828722
#191349772
#191343052
C43×#17332
#2094743