Finite Group Databasebeta

← #25098472

Subgroups — #25098472

Order 11008.

1664 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×#14583699C211yesmaximal, characteristic
2C2×#14583665C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4#19143115C211yesmaximal, characteristic, complemented
5C2×#14582881C211yesmaximal, characteristic, complemented
6#19135076C214yesmaximal, complemented
7#19135069C214yesmaximal, complemented
8C2×#14582670C211yesmaximal, characteristic, complemented
9C2×C43×#338C211yesmaximal, 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#14583665—22no—
22#14583665—22no—
23#14583665—22no—
24#14583665C2214yes—
25C2×#13063333—22no—
26C2×#13063331—22no—
27C22×#10621877C2211yescharacteristic
28C2×M16×D43—22no—
29C2×#13063284C2211yescharacteristic
30#14582915—22no—
31#14582915C2214yes—
32C2×#13063251—22no—
33#14582909C2212yescomplemented
34#14582905C2212yescomplemented
35#14582901—22no—
36#14582896—22no—
37#14582881—22no—
38#14582881—22no—
39C2×#13063243C2212yescomplemented
40C2×#13063241C2212yescomplemented
41#14582670C2214yescomplemented
42C22×M16×C43C2211yescharacteristic
43C22×M16×C43C2211yescharacteristic
44C22×M16×C43C2211yescharacteristic
45C43×#338C2214yescomplemented
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×C412yes—
65C2×#10621898D412yes—
66C2×#10621898D412yes—
67C2×#10621898D412yes—
68C2×#10621898D412yes—
69C2×#10621898C2312yes—
70C22×Dic86C2×C411yescharacteristic
71C22×Dic86C2311yescharacteristic
72C22×D172C2×C411yescharacteristic
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
92#13063333—28no—
93#13063333—28no—
94#13063331—28no—
95#13063331—28no—
96C2×#10621877—21no—
97C2×#10621877—21no—
98C2×#10621877—21no—
99C2×#10621877D412yes—
100C2×#10621877D412yes—
101C2×#10621877C2312yes—
102C2×#10621872—24no—
103M16×D43—28no—
104M16×D43—28no—
105C22×C43⋊C8—21no—
106C2×C8×D43—24no—
107#13063284—21no—
108#13063284—21no—
109#13063284—21no—
110#13063284C2312yes—
111C2×C4⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C4×Dic43—21no—
114#13063251—28no—
115#13063250—24no—
116#13063247—24no—
117#13063243—24no—
118#13063241—24no—
119C23×C4×C43C2311yescharacteristic
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43—21no—
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×C43—21no—
133C2×M16×C43C2×C412yes—
134C2×M16×C43D412yes—
135C2×M16×C43C2312yes—
136C2×M16×C43C2312yes—
137C2×M16×C43C2312yes—
138C22×C8×C43—21no—
139C22×C8×C43C2×C412yes—
140C22×C8×C43D412yes—
141C24×C43#4111yescharacteristic
142C23×D43—21no—
143C23×D43—21no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168C2×C22⋊D43—41no—
169C2×C22⋊D43—41no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—41no—
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—41no—
194#10621898—41no—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
199#10621898—41no—
200#10621898—41no—
201#10621898C22⋊C414yes—
202#10621898C22⋊C414yes—
203#10621898C2×D414yes—
204#10621898C2×D414yes—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172C22⋊C412yes—
214C2×D172C22⋊C412yes—
215C2×D172C22×C412yes—
216C2×D172C22×C412yes—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—41no—
226C2×C4×D43—41no—
227C2×C4×D43—41no—
228C2×C4×D43—41no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86C22⋊C412yes—
238C2×Dic86C22⋊C412yes—
239C2×Dic86C22×C412yes—
240C2×Dic86C22×C412yes—
241M16×C43—22no—
242M16×C43—22no—
243M16×C43—22no—
244M16×C43—22no—
245M16×C43—22no—
246M16×C43—22no—
247M16×C43—22no—
248M16×C43—22no—
249M16×C43—22no—
250M16×C43—22no—
251M16×C43—41no—
252M16×C43—41no—
253C2×C8×C43—22no—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43—41no—
259C2×C8×C43—41no—
260C2×C8×C43C22×C414yes—
261C2×C8×C43C2×D414yes—
262C22⋊Dic43—22no—
263C22⋊Dic43—41no—
264C4⋊Dic43—22no—
265C4⋊Dic43—41no—
266C4×Dic43—22no—
267C4×Dic43—41no—
268#10621877—22no—
269#10621877—22no—
270#10621877—22no—
271#10621877C2×D414yes—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275Dic172—28no—
276D344—28no—
277#10621873—28no—
278#10621873—28no—
279#10621872—216no—
280C8×D43—216no—
281C23×C43—81no—
282C23×C43C4×D411yescharacteristic
283C23×C43C4×D411yescharacteristic
284C23×C43#12111yescharacteristic
285C23×C43#12111yescharacteristic
286C23×C43#12311yescharacteristic
287C23×C43#12311yescharacteristic
288C23×C43C2×#4111yescharacteristic
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—82no—
296C22×D43—82no—
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C2×C4×C43C2×C22⋊C411yescharacteristic
300C2×C4×C43C2×C22⋊C411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43C4×D411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43C4×D411yescharacteristic
305C2×C4×C43C4×D411yescharacteristic
306C2×C4×C43C4×D411yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12311yescharacteristic
318C2×C4×C43#12311yescharacteristic
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C22⋊D43—24no—
326C22⋊D43—24no—
327C22⋊D43—24no—
328C22⋊D43—24no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—42no—
340C2×Dic43—82no—
341D172—22no—
342D172—22no—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—41no—
347D172—41no—
348D172C2×C22⋊C414yes—
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—41no—
363Dic86—41no—
364Dic86C2×C22⋊C414yes—
365C8×C43—24no—
366C8×C43—24no—
367C8×C43—42no—
368C43⋊C8—24no—
369#20995—431nomaximal, Sylow
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43#38611yescharacteristic
378C22×C43#38611yescharacteristic
379C22×C43#38611yescharacteristic
380C22×C43#38611yescharacteristic
381C22×C43C2×C4×D411yescharacteristic
382C22×C43C2×#12111yescharacteristic
383C22×C43C2×#12311yescharacteristic
384C2×D43—24no—
385C2×D43—44no—
386C2×D43—42no—
387C2×D43—82no—
388C2×D43—82no—
389C2×D43—82no—
390C2×D43—82no—
391C2×D43—82no—
392C4×C43#38611yescharacteristic
393C4×C43#38611yescharacteristic
394C4×C43#38611yescharacteristic
395C4×C43#38611yescharacteristic
396C4×C43C22×C22⋊C411yescharacteristic
397C4×C43C2×C4×D411yescharacteristic
398C4×C43C2×#12011yescharacteristic
399C4×C43C2×#12111yescharacteristic
400Dic43—24no—
401Dic43—42no—
402Dic43—82no—
403C2×#575—431no—
404C2×#568—431no—
405C2×#421—431no—
406#2896—431no—
407C2×#413—431no—
408#1903—434no—
409#1902—434no—
410C2×#344—431no—
411C2×#338D4311yescharacteristic, complemented
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—21no—
419C2×C43C2×#38611yescharacteristic
420D43—44no—
421D43—82no—
422C22×#41—431no—
423C22×#41—431no—
424#575—862no—
425#575—862no—
426#575—862no—
427#575—862no—
428C2×#137—432no—
429C2×#137—432no—
430C2×AGL(1,ℤ/8)—432no—
431C2×AGL(1,ℤ/8)—432no—
432C2×#135—434no—
433#568—434no—
434#568—862no—
435#568—862no—
436#568—862no—
437C2×#131—862no—
438C2×#131—862no—
439C22×M16—431no—
440C22×M16—862no—
441C22×M16C2×D4311yescharacteristic
442C22×M16C2×D4311yescharacteristic
443C22×M16C2×D4311yescharacteristic
444C2×#117—431no—
445#421—434no—
446#421—862no—
447C2×#104—862no—
448#419—432no—
449#418—432no—
450#417—862no—
451#416—862no—
452#413—862no—
453#413—862no—
454C2×#101—432no—
455C2×#100—432no—
456#344—434no—
457#338C2×D4314yescomplemented
458C43#2099511yescharacteristic, complemented, Sylow
459C2×#41—432no—
460C2×#41—432no—
461C2×#41—432no—
462C2×#41—432no—
463C2×#41—432no—
464C2×#41—432no—
465C2×#41—432no—
466C2×#41—432no—
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—
480C2×#41—861no—
481C2×#41—861no—
482C2×#41—861no—
483C22×Q8—431no—
484C22×Q8—431no—
485C22×D4—431no—
486C22×D4—431no—
487C22×D4—861no—
488C22×D4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492#137—864no—
493#137—864no—
494#137—864no—
495#137—864no—
496AGL(1,ℤ/8)—864no—
497AGL(1,ℤ/8)—864no—
498AGL(1,ℤ/8)—864no—
499AGL(1,ℤ/8)—864no—
500#135—868no—
501#135—868no—
502C2×Q16—434no—
503C2×SD16—434no—
504C2×SD16—434no—
505C2×D8—434no—
506#131—868no—
507#131—868no—
508#131—868no—
509#131—868no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—432no—
524C2×M16—432no—
525C2×M16—432no—
526C2×M16—864no—
527C2×M16—868no—
528C2×M16—868no—
529C2×M16—861no—
530C2×M16—861no—
531C2×M16—861no—
532C2×M16C4×D4312yes—
533C2×M16D17212yes—
534C2×M16C22×D4312yes—
535C2×M16C22×D4312yes—
536C2×M16C22×D4312yes—
537C22×C8—21no—
538C22×C8—864no—
539C22×C8—861no—
540C22×C8C4×D4312yes—
541C22×C8D17212yes—
542#117—432no—
543#117—861no—
544#117—861no—
545#117—861no—
546C2×C4⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C42—861no—
549#104—868no—
550#103—864no—
551#102—864no—
552#101—864no—
553#100—864no—
554C24—861no—
555C24—861no—
556C24#1062190211yescharacteristic
557#41—434no—
558#41—434no—
559#41—434no—
560#41—434no—
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—862no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—1721no—
582#41—1721no—
583#41—1721no—
584#41—1721no—
585#41—1721no—
586#41—1721no—
587#41—1721no—
588#41—1721no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—432no—
592C2×Q8—432no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—861no—
601C2×D4—432no—
602C2×D4—432no—
603C2×D4—432no—
604C2×D4—432no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—1721no—
622C2×D4—1721no—
623C2×D4—1721no—
624C2×D4—1721no—
625C22×C4—861no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—861no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—1721no—
636C22×C4—1721no—
637C22×C4—1721no—
638C22×C4—1721no—
639C22×C4—1721no—
640C22×C4C2×C4×D4311yescharacteristic
641C22×C4C2×C4×D4311yescharacteristic
642C22×C4C2×D17211yescharacteristic
643C22×C4C2×D17211yescharacteristic
644C22×C4#1062189811yescharacteristic
645C22×C4#1062189811yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4D4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4#1062190211yescharacteristic
653C22×C4C23×D4311yescharacteristic
654Q16—868no—
655SD16—868no—
656SD16—868no—
657D8—868no—
658M16—22no—
659M16—22no—
660M16—22no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—22no—
667M16—22no—
668M16—41no—
669M16—41no—
670M16—434no—
671M16—8616no—
672M16—862no—
673M16—862no—
674M16—862no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—8616no—
683C2×C8—862no—
684C2×C8—862no—
685C2×C8—862no—
686C2×C8C2×C4×D4314yes—
687C2×C8C2×D17214yes—
688C4⋊C4—862no—
689C4⋊C4—1721no—
690C22⋊C4—862no—
691C22⋊C4—1721no—
692C42—862no—
693C42—1721no—
694C23—81no—
695C23—862no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23—3442no—
700C23—3442no—
701C23—1721no—
702C23—1721no—
703C23#1306328711yescharacteristic
704C23#1306328711yescharacteristic
705C23#1306330011yescharacteristic
706C23#1306330011yescharacteristic
707C23#1306331011yescharacteristic
708C23#1306331011yescharacteristic
709C23C2×#1062190211yescharacteristic
710Q8—434no—
711Q8—862no—
712Q8—862no—
713Q8—862no—
714Q8—862no—
715Q8—862no—
716Q8—1721no—
717Q8—1721no—
718D4—434no—
719D4—864no—
720D4—864no—
721D4—864no—
722D4—864no—
723D4—862no—
724D4—862no—
725D4—862no—
726D4—862no—
727D4—862no—
728D4—1722no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732D4—1721no—
733D4—1721no—
734C2×C4—862no—
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×C4C22⋊C4×D4311yescharacteristic
753C2×C4C22⋊C4×D4311yescharacteristic
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#1306329811yescharacteristic
767C2×C4#1306329811yescharacteristic
768C2×C4#1306330011yescharacteristic
769C2×C4#1306330011yescharacteristic
770C2×C4#1306331011yescharacteristic
771C2×C4#1306331011yescharacteristic
772C2×C4C22×C4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×D4×D4311yescharacteristic
776C2×C4C22×D17211yescharacteristic
777C2×C4C2×#1062189811yescharacteristic
778C8—24no—
779C8—24no—
780C8—42no—
781C8—864no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—864no—
790C22—3442no—
791C22—3442no—
792C22—3442no—
793C22—3442no—
794C22—3442no—
795C22—1724no—
796C22—1722no—
797C22#1458277711yescharacteristic
798C22#1458277711yescharacteristic
799C22#1458277711yescharacteristic
800C22#1458277711yescharacteristic
801C22C2×#1306328711yescharacteristic
802C22C2×#1306330011yescharacteristic
803C22C2×#1306331011yescharacteristic
804C4—864no—
805C4—3442no—
806C4—1722no—
807C4#1458277711yescharacteristic
808C4#1458277711yescharacteristic
809C4#1458277711yescharacteristic
810C4#1458277711yescharacteristic
811C4C2×C22⋊C4×D4311yescharacteristic
812C4C2×C4×D17211yescharacteristic
813C4C2×#1306329511yescharacteristic
814C4C2×#1306329811yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—3442no—
823C2—1724no—
824C2C2×#1458277711yescharacteristic
subgroupG/H
centerC4#14582777
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#338C2
socleC2×C43C2×#386
prime radicalC2×#14583699C2
cosocleC22×C4×C43C24
hypercenterC2×#338D43
hypocenterC43#20995
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#338

Complements

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

NH ≅ G/Ntype
2. C2×#14583665C2semidirect
3. C2×#14582915C2semidirect
4. #19143115C2semidirect
5. C2×#14582881C2semidirect
6. #19135076C2semidirect
7. #19135069C2semidirect
8. C2×#14582670C2semidirect
9. C2×C43×#338C2semidirect
16. C2×#13063358C4semidirect
18. C2×#13063353C4semidirect
20. C2×#13063347C4semidirect
33. #14582909C22semidirect
34. #14582905C22semidirect
39. C2×#13063243C22semidirect
40. C2×#13063241C22semidirect
41. #14582670C22semidirect
45. C43×#338C22semidirect
88. C2×Dic172C2×C4semidirect
89. C2×#10621873C2×C4semidirect
90. C2×#10621873C2×C4semidirect
91. C2×D344C2×C4semidirect
411. C2×#338D43semidirect
457. #338C2×D43semidirect
458. C43#20995semidirect

Maximal subgroups

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

subgroupindex
C2×#145836992
C2×#145836652
C2×#145829152
#191431152
C2×#145828812
#191350762
#191350692
C2×#145826702
C2×C43×#3382
#2099543