Finite Group Databasebeta

← #25966696

Subgroups — #25966696

Order 11008.

2256 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic, complemented
2#532×D43C211yesmaximal, characteristic, complemented
3#19145334C211yesmaximal, characteristic, complemented
4#19145332C211yesmaximal, characteristic, complemented
5#19145316C211yesmaximal, characteristic, complemented
6#19145311C211yesmaximal, characteristic, complemented
7#19145286C214yesmaximal, complemented
8#19145186C214yesmaximal, complemented
9#19145174C211yesmaximal, characteristic, complemented
10#19145170C211yesmaximal, characteristic, complemented
11#19145155C211yesmaximal, characteristic, complemented
12#19145136C211yesmaximal, characteristic, complemented
13#19145042C211yesmaximal, characteristic, complemented
14#19144990C211yesmaximal, characteristic, complemented
15#19144966C211yesmaximal, characteristic, complemented
16#19144207C214yesmaximal, complemented
17C4×#13063352C214yesmaximal, complemented
18C2×C4×#10621872C211yesmaximal, characteristic, complemented
19C43×#3167C211yesmaximal, characteristic, complemented
20C2×#41×D43—21no—
21C2×#13063352C2214yes—
22C22×#10621872C2212yes—
23#14583454C2211yescharacteristic
24#14583454C2211yescharacteristic, complemented
25#14583450C2211yescharacteristic
26#14583450C2211yescharacteristic
27#14583450C2211yescharacteristic, complemented
28#14583449C2211yescharacteristic
29#14583449C2211yescharacteristic, complemented
30#14583448—21no—
31#14583447C2211yescharacteristic
32#14583446—21no—
33#14583446C2212yes—
34#14583445—21no—
35#14583444—21no—
36#14583444C2212yes—
37C4⋊Q8×D43C2211yescharacteristic
38#127×D43C2211yescharacteristic
39#14583436—21no—
40#14583436C2212yescomplemented
41#14583435—21no—
42#14583435C2212yescomplemented
43#14583434—21no—
44#14583434—21no—
45#124×D43—21no—
46#14583412—21no—
47#14583412C2212yes—
48#14583411—21no—
49#121×D43—21no—
50#121×D43C2212yes—
51C4×#10621902—21no—
52C4×#10621902C2212yes—
53#14583367—21no—
54C4×D4×D43—21no—
55C4×D4×D43C2212yes—
56C2×C42×D43C2211yescharacteristic
57#14583306C2214yescomplemented
58#14583304C2211yescharacteristic, complemented
59#14583302C2211yescharacteristic, complemented
60#14583295C2211yescharacteristic, complemented
61#14583285C2214yescomplemented
62#14583276C2211yescharacteristic, complemented
63#14583275C2211yescharacteristic, complemented
64#14583273C2211yescharacteristic, complemented
65#14583262C2214yescomplemented
66#14583260C2214yescomplemented
67#14583249C2211yescharacteristic, complemented
68#14583247C2211yescharacteristic, complemented
69#14583247C2211yescharacteristic, complemented
70#14583246C2211yescharacteristic, complemented
71#14583246C2211yescharacteristic, complemented
72#14583245C2211yescharacteristic, complemented
73#14583153C2214yescomplemented
74#14583151C2214yescomplemented
75#14583148C2214yescomplemented
76#14583142C2214yescomplemented
77#14583135C2214yescomplemented
78#14583133C2214yescomplemented
79#14583130C2214yescomplemented
80#14583010C2214yescomplemented
81#14583008C2214yescomplemented
82#14583002C2214yescomplemented
83#14583000C2214yescomplemented
84C4×#10621884C2214yescomplemented
85C4×D344C2214yescomplemented
86C4×#10621882C2214yescomplemented
87#14582938C2214yes—
88#14582902C2214yes—
89#14582899C2214yes—
90C4×#10621872C2211yescharacteristic
91C4×#10621872C2211yescharacteristic
92C4×#10621872C2212yes—
93C4×#10621872C2211yescharacteristic, complemented
94C4×#10621872C2211yescharacteristic, complemented
95C4×#10621872C2212yescomplemented
96C2×#13063235C2212yescomplemented
97C2×C4×C43⋊C8C2211yescharacteristic, complemented
98C43×#533C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic
100C43×#498C2211yescharacteristic, complemented
101C43×#492C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#486C2211yescharacteristic, complemented
104C43×#465C2214yescomplemented
105C4×SD16×C43C2214yescomplemented
106C2×C4×C8×C43C2211yescharacteristic, complemented
107C2×#10621902—21no—
108C2×#10621902—21no—
109C2×#10621902C2312yes—
110C2×#10621898—21no—
111C2×#10621898—21no—
112C2×#10621898—22no—
113C2×#10621900—22no—
114C2×#10621900—21no—
115#41×D43—48no—
116C2×Q8×D43—21no—
117C2×D4×D43—22no—
118C2×D4×D43—21no—
119C2×D4×D43—21no—
120C2×D4×D43C2312yes—
121C22×C4×D43—22no—
122C22×C4×D43D411yescharacteristic
123C22×C4×D43D411yescharacteristic
124C22×C4×D43C2311yescharacteristic
125#13063352—216no—
126C2×#10621884C2314yes—
127C2×D344C2314yes—
128C2×#10621882C2314yes—
129C2×#10621872—28no—
130C2×#10621872C2312yes—
131C2×#10621872C2312yes—
132C2×#10621872C2312yes—
133C2×#10621872C2312yes—
134C22×C43⋊C8C2312yes—
135#13063325C2311yescharacteristic
136#13063325C2311yescharacteristic
137#13063324—21no—
138#13063324C2312yes—
139#13063323—21no—
140#13063322C2311yescharacteristic
141#13063322C2311yescharacteristic
142#13063321—21no—
143#13063321—21no—
144#13063321C2312yes—
145#13063320—22no—
146#13063320—22no—
147#13063316—21no—
148#13063316C2312yes—
149#13063314—21no—
150#13063314—21no—
151#13063314C2312yes—
152#13063313—21no—
153#13063313—21no—
154#13063312—21no—
155#13063311—22no—
156#13063311—22no—
157#13063310—22no—
158#13063310—22no—
159#13063309—22no—
160#13063305—21no—
161#13063305—21no—
162#13063301—21no—
163#13063301C2312yes—
164#13063300—21no—
165#13063300—21no—
166#13063300—21no—
167#13063300—21no—
168#13063300C2312yes—
169#13063300C2312yes—
170#13063299—21no—
171#13063299—21no—
172#13063299C2312yes—
173#13063299C2312yes—
174#13063298—22no—
175#13063298—22no—
176#13063297—22no—
177#13063297—22no—
178#13063296—21no—
179#13063296C2312yes—
180#13063295—22no—
181Q8×Dic43—21no—
182Q8×Dic43C2312yes—
183#13063290—21no—
184#13063290—21no—
185C4×D172—22no—
186C4×D172—22no—
187C4×D172—21no—
188C4×D172—21no—
189C4×D172C2312yes—
190C4×D172C2312yes—
191D4×Dic43—21no—
192D4×Dic43C2312yes—
193#13063287—22no—
194#13063287—22no—
195#13063287—21no—
196#13063287—21no—
197#13063287—21no—
198#13063287—21no—
199#13063287C2312yes—
200#13063287C2312yes—
201C4×C22⋊D43—22no—
202C4×C22⋊D43—22no—
203(C22⋊D43)⋊C4—22no—
204(C22⋊D43)⋊C4—22no—
205(C22⋊D43)⋊C4—22no—
206(C22⋊D43)⋊C4—22no—
207#13063283—21no—
208#13063283—22no—
209#13063283—22no—
210#13063283C2312yes—
211#13063282—22no—
212C4⋊C4×D43—21no—
213C4⋊C4×D43C2312yes—
214C22⋊C4×D43—22no—
215C22⋊C4×D43—22no—
216C2×C4×Dic43D411yescharacteristic
217C2×C4×Dic43D411yescharacteristic
218C2×C4×Dic43C2311yescharacteristic
219C42×D43—22no—
220C42×D43D411yescharacteristic
221C42×D43D411yescharacteristic
222C42×D43D411yescharacteristic
223C42×D43D411yescharacteristic
224C42×D43C2311yescharacteristic
225C42×D43C2311yescharacteristic
226C42×D43C2311yescharacteristic
227C42×D43C2311yescharacteristic
228#13063259C2314yes—
229#13063258C2314yes—
230#13063256C2314yes—
231#13063249C2314yes—
232#13063247C2314yes—
233#13063247C2314yes—
234#13063246C2314yes—
235#13063245C2314yes—
236#13063245C2314yes—
237#13063235C2312yes—
238#13063235C2312yes—
239#13063235C2312yes—
240#13063235C2312yes—
241C4×C43⋊C8C2311yescharacteristic
242C4×C43⋊C8C2312yes—
243C4×C43⋊C8C2311yescharacteristic
244C2×#41×C43—21no—
245C2×SD16×C43C2314yes—
246C22×C8×C43C2312yes—
247C4⋊Q8×C43C2311yescharacteristic
248C4⋊Q8×C43C2311yescharacteristic
249C4⋊Q8×C43C2311yescharacteristic
250#127×C43C2311yescharacteristic
251#125×C43—21no—
252#124×C43—21no—
253C22⋊Q8×C43—21no—
254C22⋊Q8×C43C2312yes—
255#121×C43—21no—
256#121×C43C2312yes—
257C4×Q8×C43—21no—
258C4×Q8×C43C2312yes—
259C4×D4×C43—21no—
260C4×D4×C43C2312yes—
261#117×C43—21no—
262C2×C42×C43C2311yescharacteristic
263#106×C43C2314yes—
264#103×C43C2314yes—
265#102×C43C2314yes—
266C4×C8×C43C2311yescharacteristic
267C4×C8×C43C2312yes—
268C4×C8×C43C2311yescharacteristic
269C23×D43—22no—
270C23×D43C2×D411yescharacteristic
271#41×C43—44no—
272C2×Q8×C43—21no—
273C2×Q8×C43—21no—
274C2×Q8×C43C2412yes—
275C2×D4×C43—21no—
276C2×D4×C43—21no—
277C2×D4×C43—22no—
278C2×D4×C43C2412yes—
279C22×C4×C43—22no—
280C22×C4×C43C2×D411yescharacteristic
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2411yescharacteristic
283C2×C22⋊D43—22no—
284C2×C22⋊D43—22no—
285C2×C22⋊D43—22no—
286C2×C22⋊D43—22no—
287C2×C22⋊D43—22no—
288C2×C22⋊D43—22no—
289C22×Dic43—22no—
290C22×Dic43C2×D411yescharacteristic
291C22×Dic43C2×D411yescharacteristic
292C22×Dic43C2×D411yescharacteristic
293#10621902—28no—
294#10621902—44no—
295#10621902—44no—
296Q8×D43—44no—
297#10621900—44no—
298#10621900—48no—
299D4×D43—28no—
300D4×D43—48no—
301D4×D43—44no—
302D4×D43—44no—
303#10621898—48no—
304#10621898—44no—
305#10621898—44no—
306C2×D172—21no—
307C2×D172—21no—
308C2×D172—21no—
309C2×D172—21no—
310C2×D172—22no—
311C2×D172—22no—
312C2×D172—22no—
313C2×D172C2412yes—
314C2×D172C2412yes—
315C2×C4×D43—24no—
316C2×C4×D43—24no—
317C2×C4×D43—22no—
318C2×C4×D43—22no—
319C2×C4×D43—22no—
320C2×C4×D43—22no—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—42no—
324C2×C4×D43—48no—
325C2×C4×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2×D411yescharacteristic
328C2×C4×D43C2×D411yescharacteristic
329C2×C4×D43C2×D411yescharacteristic
330C2×C4×D43C2×D411yescharacteristic
331C2×C4×D43C2×D411yescharacteristic
332C2×C4×D43C2×D411yescharacteristic
333C2×C4×D43C2×D411yescharacteristic
334C2×C4×D43C2×D411yescharacteristic
335C2×C4×D43C2411yescharacteristic
336C2×C4×D43C2411yescharacteristic
337C2×Dic86—21no—
338C2×Dic86—21no—
339C2×Dic86—22no—
340SD16×C43—28no—
341C2×C8×C43—24no—
342C2×C8×C43C2412yes—
343C2×C8×C43C2412yes—
344C4⋊C4×C43—21no—
345C4⋊C4×C43—21no—
346C4⋊C4×C43—21no—
347C4⋊C4×C43—21no—
348C4⋊C4×C43—22no—
349C4⋊C4×C43—22no—
350C4⋊C4×C43C2412yes—
351C4⋊C4×C43C2412yes—
352C22⋊C4×C43—22no—
353C22⋊C4×C43—22no—
354C22⋊C4×C43—22no—
355C42×C43—22no—
356C42×C43C2×D411yescharacteristic
357C42×C43C2×D411yescharacteristic
358C42×C43C2411yescharacteristic
359C42×C43C2411yescharacteristic
360C22⋊Dic43—22no—
361C22⋊Dic43—22no—
362#10621884—28no—
363#10621882—28no—
364(C2×D43)⋊C4—22no—
365(C2×D43)⋊C4—22no—
366(C2×D43)⋊C4—22no—
367(C2×D43)⋊C4—22no—
368(C2×D43)⋊C4—22no—
369(C2×D43)⋊C4—22no—
370(C2×D43)⋊C4—22no—
371(C2×D43)⋊C4—22no—
372(C2×D43)⋊C4—22no—
373(C2×D43)⋊C4—22no—
374(C2×D43)⋊C4—22no—
375(C2×D43)⋊C4—22no—
376C4⋊Dic43—21no—
377C4⋊Dic43—21no—
378C4⋊Dic43—22no—
379C4⋊Dic43—22no—
380C4⋊Dic43C2412yes—
381C4⋊Dic43C2412yes—
382Dic43⋊C4—22no—
383Dic43⋊C4—22no—
384Dic43⋊C4—22no—
385Dic43⋊C4—22no—
386C4×Dic43—22no—
387C4×Dic43—22no—
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2×D411yescharacteristic
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2×D411yescharacteristic
392C4×Dic43C2×D411yescharacteristic
393C4×Dic43C2×D411yescharacteristic
394C4×Dic43C2×D411yescharacteristic
395C4×Dic43C2×D411yescharacteristic
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2411yescharacteristic
399C4×Dic43C2411yescharacteristic
400C2×C43⋊C8—24no—
401C2×C43⋊C8C2412yes—
402C2×C43⋊C8C2412yes—
403D344—28no—
404#10621872—24no—
405#10621872—24no—
406#10621872—24no—
407#10621872#4118yescomplemented
408C23×C43—22no—
409C23×C43C22×D411yescharacteristic
410C22×D43—22no—
411C22×D43—22no—
412C22×D43—22no—
413C22×D43—22no—
414C22×D43—41no—
415C22×D43—44no—
416C22×D43—44no—
417C22×D43—44no—
418C22×D43C22×D411yescharacteristic
419C22×D43C22×D411yescharacteristic
420Q8×C43—24no—
421Q8×C43—42no—
422Q8×C43—42no—
423D4×C43—24no—
424D4×C43—44no—
425D4×C43—42no—
426D4×C43—42no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—44no—
433C2×C4×C43AGL(1,ℤ/8)14yescomplemented
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C2511yescharacteristic
440C22⋊D43—44no—
441C22⋊D43—44no—
442C22⋊D43—44no—
443C22⋊D43—44no—
444C22⋊D43—44no—
445C22⋊D43—44no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—41no—
451C2×Dic43—44no—
452C2×Dic43C22×D411yescharacteristic
453C2×Dic43C22×D411yescharacteristic
454C2×Dic43C22×D411yescharacteristic
455C2×Dic43C22×D411yescharacteristic
456C2×Dic43C22×D411yescharacteristic
457C2×Dic43C22×D411yescharacteristic
458D172—24no—
459D172—24no—
460D172—44no—
461D172—44no—
462D172—44no—
463D172—42no—
464D172—42no—
465D172—42no—
466D172—42no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—22no—
470C4×D43—22no—
471C4×D43—22no—
472C4×D43—22no—
473C4×D43—22no—
474C4×D43—22no—
475C4×D43—22no—
476C4×D43—41no—
477C4×D43—41no—
478C4×D43—44no—
479C4×D43—44no—
480C4×D43—44no—
481C4×D43—44no—
482C4×D43—44no—
483C4×D43—44no—
484C4×D43C2×#4114yes—
485Dic86—44no—
486Dic86—42no—
487Dic86—42no—
488C8×C43—22no—
489C8×C43C2×#4114yescomplemented
490C43⋊C8—22no—
491C43⋊C8C2×#4114yescomplemented
492#60700—431nomaximal, Sylow
493C22×C43—21no—
494C22×C43—21no—
495C22×C43—42no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43C2×AGL(1,ℤ/8)12yes—
499C22×C43C23×D411yescharacteristic
500C2×D43—21no—
501C2×D43—21no—
502C2×D43—21no—
503C2×D43—21no—
504C2×D43—21no—
505C2×D43—44no—
506C2×D43—42no—
507C2×D43—42no—
508C2×D43—42no—
509C2×D43—42no—
510C2×D43—42no—
511C2×D43—42no—
512C2×D43—88no—
513C2×D43#53212yes—
514C4×C43—21no—
515C4×C43—21no—
516C4×C43—42no—
517C4×C43—42no—
518C4×C43—42no—
519C4×C43C2×AGL(1,ℤ/8)12yes—
520C4×C43C2×AGL(1,ℤ/8)12yes—
521C4×C43#57512yes—
522C4×C43C22×#4112yes—
523Dic43—21no—
524Dic43—21no—
525Dic43—21no—
526Dic43—21no—
527Dic43—21no—
528Dic43—42no—
529Dic43—42no—
530Dic43#53212yes—
531#3444—431no—
532C2×#532—431no—
533#3184—431no—
534#3184—431no—
535#3182—431no—
536#3182—431no—
537#3180—434no—
538#3171—434no—
539#3169—431no—
540#3169—431no—
541#3167—431no—
542#3167D4311yescharacteristic, complemented
543#3165—431no—
544#3151—431no—
545#3141—431no—
546#3138—431no—
547#3055—434no—
548C4×AGL(1,ℤ/8)—434no—
549C2×C4×M16—431no—
550C2×C43—22no—
551C2×C43—82no—
552C2×C43C2×#53211yescharacteristic
553C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
554C2×C43C2×#57511yescharacteristic
555D43—22no—
556D43—41no—
557D43—82no—
558D43—82no—
559C22×#41—861no—
560C2×AGL(1,ℤ/8)—434no—
561C22×M16—432no—
562#533—431no—
563#533—431no—
564#533C2×D4311yescharacteristic, complemented
565#532—431no—
566#532—431no—
567#532—431no—
568#532—432no—
569#532—432no—
570#532—431no—
571#532—431no—
572#532—431no—
573#532—861no—
574#532—861no—
575#532—861no—
576#532—861no—
577#532C2×D4311yescharacteristic
578C2×C4⋊Q8—431no—
579C2×#127—431no—
580#529—432no—
581#529—432no—
582#529—861no—
583#529—861no—
584#529—861no—
585#529—861no—
586C2×#124—861no—
587#525—432no—
588#525—861no—
589#525—861no—
590C2×#121—432no—
591C2×#121—861no—
592C4×#41—432no—
593C4×#41—861no—
594C4×#41—861no—
595C2×C4×D4—432no—
596C2×C4×D4—861no—
597C22×C42—431no—
598#501—434no—
599#500—431no—
600#500—431no—
601#498—431no—
602#498C2×D4311yescharacteristic, complemented
603#496—434no—
604#493—431no—
605#493—431no—
606#492—431no—
607#492C2×D4311yescharacteristic, complemented
608#490—434no—
609#489—434no—
610#487—431no—
611#487C2×D4311yescharacteristic, complemented
612#486—431no—
613#486—431no—
614#486—431no—
615#486—431no—
616#486—431no—
617#486C2×D4311yescharacteristic, complemented
618#469—434no—
619#469—434no—
620#468—434no—
621#468—434no—
622#466—434no—
623#466—434no—
624#465—434no—
625#465C2×D4314yescomplemented
626#442—434no—
627#442—434no—
628#440—434no—
629#440—434no—
630C4×SD16—434no—
631C4×SD16C2×D4314yescomplemented
632C4×D8—434no—
633C4×D8—434no—
634#428—434no—
635#418—434no—
636#417—434no—
637C4×M16—431no—
638C4×M16—431no—
639C4×M16—432no—
640C4×M16—432no—
641C4×M16—431no—
642C4×M16—431no—
643C2×#97—432no—
644C2×C4×C8—431no—
645C2×C4×C8C2×D4311yescharacteristic, complemented
646C43#6070011yescharacteristic, complemented, Sylow
647C2×#41—21no—
648C2×#41—432no—
649C2×#41—862no—
650C2×#41—862no—
651C2×#41—861no—
652C2×#41—861no—
653C2×#41—861no—
654C2×#41—861no—
655C2×#41—861no—
656C2×#41—1728no—
657C22×Q8—861no—
658C22×D4—432no—
659C22×D4—861no—
660C22×D4—861no—
661C22×D4—862no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—862no—
666AGL(1,ℤ/8)—8616no—
667C2×SD16—434no—
668C2×SD16C22×D4314yes—
669C2×D8—434no—
670C2×D8—434no—
671C2×M16—432no—
672C2×M16—432no—
673C2×M16—432no—
674C2×M16—432no—
675C2×M16—868no—
676C22×C8—432no—
677C22×C8C22×D4312yes—
678C4⋊Q8—432no—
679C4⋊Q8—431no—
680C4⋊Q8—431no—
681C4⋊Q8—861no—
682C4⋊Q8—861no—
683C4⋊Q8C22×D4311yescharacteristic
684C4⋊Q8C22×D4311yescharacteristic
685C4⋊Q8C22×D4311yescharacteristic
686#127—432no—
687#127—431no—
688#127—431no—
689#127—861no—
690#127—861no—
691#127C22×D4311yescharacteristic
692#126—862no—
693#126—862no—
694#125—21no—
695#125—432no—
696#125—861no—
697#124—21no—
698#124—432no—
699#124—862no—
700#124—862no—
701#124—861no—
702#124—861no—
703#124—861no—
704#124—861no—
705#124—861no—
706#123—862no—
707#123—862no—
708#123—862no—
709C22⋊Q8—21no—
710C22⋊Q8—432no—
711C22⋊Q8—861no—
712C22⋊Q8—861no—
713C22⋊Q8—861no—
714C22⋊Q8C22×D4312yes—
715#121—21no—
716#121—432no—
717#121—432no—
718#121—432no—
719#121—432no—
720#121—432no—
721#121—862no—
722#121—862no—
723#121—861no—
724#121—861no—
725#121—861no—
726#121—861no—
727#121—862no—
728#121—861no—
729#121—862no—
730#121—861no—
731#121—861no—
732#121C22×D4312yes—
733#120—862no—
734C4×Q8—21no—
735C4×Q8—432no—
736C4×Q8—861no—
737C4×Q8—861no—
738C4×Q8—861no—
739C4×Q8C22×D4312yes—
740C4×D4—21no—
741C4×D4—432no—
742C4×D4—432no—
743C4×D4—432no—
744C4×D4—432no—
745C4×D4—432no—
746C4×D4—862no—
747C4×D4—862no—
748C4×D4—862no—
749C4×D4—862no—
750C4×D4—861no—
751C4×D4—861no—
752C4×D4—861no—
753C4×D4—861no—
754C4×D4—862no—
755C4×D4—862no—
756C4×D4—861no—
757C4×D4—862no—
758C4×D4—862no—
759C4×D4—862no—
760C4×D4—862no—
761C4×D4—861no—
762C4×D4—861no—
763C4×D4C22×D4312yes—
764#117—21no—
765#117—432no—
766#117—862no—
767#117—862no—
768#117—862no—
769#117—861no—
770C2×C4⋊C4—432no—
771C2×C4⋊C4—861no—
772C2×C22⋊C4—862no—
773C2×C22⋊C4—862no—
774C2×C42—431no—
775C2×C42—431no—
776C2×C42—431no—
777C2×C42—431no—
778C2×C42—431no—
779C2×C42—431no—
780C2×C42—431no—
781C2×C42—431no—
782C2×C42—431no—
783C2×C42—431no—
784C2×C42—431no—
785C2×C42—862no—
786C2×C42C22×D4311yescharacteristic
787#107—434no—
788#107—434no—
789#106—434no—
790#106C22×D4314yes—
791#103—434no—
792#103C22×D4314yes—
793#102—434no—
794#102—434no—
795#102—434no—
796#102—434no—
797#102—434no—
798#102C22×D4314yes—
799#97—432no—
800#97—432no—
801#97—432no—
802#97—432no—
803C4×C8—432no—
804C4×C8—431no—
805C4×C8—431no—
806C4×C8C22×D4312yes—
807C4×C8C22×D4311yescharacteristic
808C4×C8C22×D4311yescharacteristic
809C24—431no—
810C24—862no—
811#41—44no—
812#41—868no—
813#41—1728no—
814#41—1728no—
815#41—1724no—
816#41—1724no—
817#41—1724no—
818#41—1724no—
819#41—1724no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—862no—
823C2×Q8—861no—
824C2×Q8—861no—
825C2×Q8—1724no—
826C2×Q8C23×D4312yes—
827C2×D4—22no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—432no—
831C2×D4—432no—
832C2×D4—862no—
833C2×D4—862no—
834C2×D4—862no—
835C2×D4—868no—
836C2×D4—862no—
837C2×D4—862no—
838C2×D4—862no—
839C2×D4—862no—
840C2×D4—862no—
841C2×D4—862no—
842C2×D4—861no—
843C2×D4—861no—
844C2×D4—861no—
845C2×D4—861no—
846C2×D4—1724no—
847C2×D4—1724no—
848C2×D4—1728no—
849C2×D4C23×D4312yes—
850C22×C4—22no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—431no—
862C22×C4—431no—
863C22×C4—431no—
864C22×C4—431no—
865C22×C4—431no—
866C22×C4—864no—
867C22×C4—862no—
868C22×C4—862no—
869C22×C4—862no—
870C22×C4—862no—
871C22×C4—862no—
872C22×C4—864no—
873C22×C4—862no—
874C22×C4—862no—
875C22×C4—1722no—
876C22×C4—1728no—
877C22×C4D4×D4311yescharacteristic
878C22×C4D4×D4311yescharacteristic
879C22×C4C23×D4311yescharacteristic
880SD16—28no—
881SD16—868no—
882D8—868no—
883D8—868no—
884M16—438no—
885M16—864no—
886M16—864no—
887M16—864no—
888C2×C8—24no—
889C2×C8—432no—
890C2×C8—432no—
891C2×C8—864no—
892C2×C8C23×D4312yes—
893C2×C8C23×D4312yes—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—432no—
901C4⋊C4—432no—
902C4⋊C4—862no—
903C4⋊C4—862no—
904C4⋊C4—862no—
905C4⋊C4—862no—
906C4⋊C4—862no—
907C4⋊C4—862no—
908C4⋊C4—861no—
909C4⋊C4—861no—
910C4⋊C4C23×D4312yes—
911C4⋊C4C23×D4312yes—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—862no—
916C22⋊C4—862no—
917C22⋊C4—862no—
918C22⋊C4—862no—
919C22⋊C4—862no—
920C22⋊C4—862no—
921C22⋊C4—862no—
922C22⋊C4—862no—
923C22⋊C4—862no—
924C22⋊C4—862no—
925C22⋊C4—862no—
926C22⋊C4—862no—
927C22⋊C4—862no—
928C22⋊C4—862no—
929C42—22no—
930C42—431no—
931C42—431no—
932C42—431no—
933C42—431no—
934C42—431no—
935C42—431no—
936C42—431no—
937C42—431no—
938C42—431no—
939C42—431no—
940C42—431no—
941C42—431no—
942C42—862no—
943C42—862no—
944C42D4×D4311yescharacteristic
945C42D4×D4311yescharacteristic
946C42C23×D4311yescharacteristic
947C42C23×D4311yescharacteristic
948C23—22no—
949C23—431no—
950C23—431no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—1721no—
956C23—1724no—
957C23—1724no—
958C23—1724no—
959C23C2×D4×D4311yescharacteristic
960Q8—24no—
961Q8—42no—
962Q8—42no—
963Q8—1724no—
964Q8—1722no—
965Q8—1722no—
966D4—24no—
967D4—44no—
968D4—42no—
969D4—42no—
970D4—864no—
971D4—864no—
972D4—1724no—
973D4—1724no—
974D4—1724no—
975D4—1724no—
976D4—1724no—
977D4—1724no—
978D4—1724no—
979D4—1724no—
980D4—1724no—
981D4—1722no—
982D4—1722no—
983D4—1722no—
984D4—1722no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—44no—
991C2×C4—431no—
992C2×C4—434no—
993C2×C4—431no—
994C2×C4—431no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—431no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—1721no—
1012C2×C4—1721no—
1013C2×C4—1724no—
1014C2×C4—1724no—
1015C2×C4—1724no—
1016C2×C4—1724no—
1017C2×C4—1721no—
1018C2×C4—1724no—
1019C2×C4—1724no—
1020C2×C4—1724no—
1021C2×C4#1306335214yescomplemented
1022C2×C4C2×D4×D4311yescharacteristic
1023C2×C4C2×D4×D4311yescharacteristic
1024C2×C4C2×D4×D4311yescharacteristic
1025C2×C4C2×D4×D4311yescharacteristic
1026C2×C4C2×D4×D4311yescharacteristic
1027C2×C4C24×D4311yescharacteristic
1028C8—22no—
1029C8—434no—
1030C8—862no—
1031C8#41×D4314yescomplemented
1032C22—21no—
1033C22—21no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—432no—
1038C22—861no—
1039C22—861no—
1040C22—861no—
1041C22—861no—
1042C22—861no—
1043C22—3448no—
1044C22—1724no—
1045C22—1722no—
1046C22—1722no—
1047C22—1722no—
1048C22—1722no—
1049C22—1722no—
1050C22—1722no—
1051C22C2×#1306335212yes—
1052C22C22×D4×D4311yescharacteristic
1053C4—21no—
1054C4—21no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—432no—
1059C4—861no—
1060C4—861no—
1061C4—861no—
1062C4—861no—
1063C4—861no—
1064C4—1722no—
1065C4—1722no—
1066C4C2×#1306335212yes—
1067C4C2×#1306335212yes—
1068C4#1458369612yes—
1069C4C2×#41×D4312yes—
1070C2—22no—
1071C2—82no—
1072C2—862no—
1073C2—3442no—
1074C2—3442no—
1075C2—1721no—
1076C2#532×D4311yescharacteristic
1077C2C22×#1306335211yescharacteristic
1078C2C2×#1458369611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3167C2
socleC22×C43C23×D4
hypercenter#3167D43
hypocenterC43#60700
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #19147892C2semidirect
2. #532×D43C2semidirect
3. #19145334C2semidirect
4. #19145332C2semidirect
5. #19145316C2semidirect
6. #19145311C2semidirect
7. #19145286C2semidirect
8. #19145186C2semidirect
9. #19145174C2semidirect
10. #19145170C2semidirect
11. #19145155C2semidirect
12. #19145136C2semidirect
13. #19145042C2semidirect
14. #19144990C2semidirect
15. #19144966C2semidirect
16. #19144207C2semidirect
17. C4×#13063352C2semidirect
18. C2×C4×#10621872C2semidirect
19. C43×#3167C2semidirect
24. #14583454C22semidirect
27. #14583450C22semidirect
29. #14583449C22semidirect
40. #14583436C22semidirect
42. #14583435C22semidirect
57. #14583306C22semidirect
58. #14583304C22semidirect
59. #14583302C22semidirect
60. #14583295C22semidirect
61. #14583285C22semidirect
62. #14583276C22semidirect
63. #14583275C22semidirect
64. #14583273C22semidirect
65. #14583262C22semidirect
66. #14583260C22semidirect
67. #14583249C22semidirect
68. #14583247C22semidirect
69. #14583247C22semidirect
70. #14583246C22semidirect
71. #14583246C22semidirect
72. #14583245C22semidirect
73. #14583153C22semidirect
74. #14583151C22semidirect
75. #14583148C22semidirect
76. #14583142C22semidirect
77. #14583135C22semidirect
78. #14583133C22semidirect
79. #14583130C22semidirect
80. #14583010C22semidirect
81. #14583008C22semidirect
82. #14583002C22semidirect
83. #14583000C22semidirect
84. C4×#10621884C22semidirect
85. C4×D344C22semidirect
86. C4×#10621882C22semidirect
93. C4×#10621872C22semidirect
94. C4×#10621872C22semidirect
95. C4×#10621872C22semidirect
96. C2×#13063235C22semidirect
97. C2×C4×C43⋊C8C22semidirect
98. C43×#533C22semidirect
100. C43×#498C22semidirect
101. C43×#492C22semidirect
102. C43×#487C22semidirect
103. C43×#486C22semidirect
104. C43×#465C22semidirect
105. C4×SD16×C43C22semidirect
106. C2×C4×C8×C43C22semidirect
407. #10621872#41semidirect
433. C2×C4×C43AGL(1,ℤ/8)semidirect
489. C8×C43C2×#41semidirect
491. C43⋊C8C2×#41semidirect
542. #3167D43semidirect
564. #533C2×D43semidirect
602. #498C2×D43semidirect
607. #492C2×D43semidirect
611. #487C2×D43semidirect
617. #486C2×D43semidirect
625. #465C2×D43semidirect
631. C4×SD16C2×D43semidirect
645. C2×C4×C8C2×D43semidirect
646. C43#60700semidirect
1021. C2×C4#13063352semidirect
1031. C8#41×D43semidirect

Maximal subgroups

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

subgroupindex
#191478922
#532×D432
#191453342
#191453322
#191453162
#191453112
#191452862
#191451862
#191451742
#191451702
#191451552
#191451362
#191450422
#191449902
#191449662
#191442072
C4×#130633522
C2×C4×#106218722
C43×#31672
#6070043