Finite Group Databasebeta

← #25968764

Subgroups — #25968764

Order 11008.

1780 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2C2×#14583455C211yesmaximal, characteristic, complemented
3#19145834C214yesmaximal, complemented
4#19145823C212yesmaximal, complemented
5#19145814C212yesmaximal, complemented
6#19145810C212yesmaximal, complemented
7#19145803C211yesmaximal, characteristic, complemented
8#19145801C211yesmaximal, characteristic, complemented
9#19145788C212yesmaximal, complemented
10#19145781C211yesmaximal, characteristic, complemented
11#19145116C212yesmaximal, complemented
12#19144939C212yesmaximal, complemented
13#19144505C212yesmaximal, complemented
14#19144503C212yesmaximal, complemented
15#19144380C214yesmaximal, complemented
16#432×D43C211yesmaximal, characteristic, complemented
17C43×#3234C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455—21no—
20#14583455—21no—
21#14583455—21no—
22#14583455—21no—
23#14583455C2212yes—
24#14583455C2212yes—
25#14583455C2212yes—
26#14583455C2212yes—
27#14583454C2211yescharacteristic
28#14583454C2211yescharacteristic
29#14583447C2211yescharacteristic
30#14583447C2211yescharacteristic
31C2×#13063324C2211yescharacteristic
32C2×#13063324C2211yescharacteristic
33#14583431—21no—
34#14583431C2212yes—
35#14583430—21no—
36#14583430C2212yes—
37#14583428—21no—
38#14583428—21no—
39C2×#13063317C2211yescharacteristic
40#14583409—21no—
41#14583409C2212yes—
42#14583406—21no—
43C2×#13063303—21no—
44C2×#13063303—21no—
45#41×Dic43—21no—
46C4×#10621900—21no—
47C4×#10621900C2212yes—
48C2×#13063290—21no—
49C2×#13063290—21no—
50C2×#13063283C2211yescharacteristic
51C2×#13063283C2211yescharacteristic
52C2×C42×D43C2211yescharacteristic
53#14583309C2212yescomplemented
54#14583308C2212yescomplemented
55#14583307C2214yescomplemented
56#14583306C2214yescomplemented
57#14583305C2212yescomplemented
58#14583269C2212yescomplemented
59#14583268C2212yescomplemented
60#14583263C2212yescomplemented
61#14583257C2214yescomplemented
62#14583257C2214yescomplemented
63#14583243C2214yes—
64#14583242C2214yes—
65#14583235C2212yes—
66#14583234C2212yes—
67#14583230C2212yes—
68#14583229C2212yes—
69#14583222C2214yes—
70#14583221C2214yes—
71#14583215C2212yes—
72#14583210C2212yes—
73#14583207C2214yescomplemented
74#14583203C2214yescomplemented
75#14583199C2214yescomplemented
76#14583193C2214yescomplemented
77#14583187C2214yescomplemented
78#14583183C2214yescomplemented
79#14583177C2214yescomplemented
80#14582956C2211yescharacteristic
81#14582955C2212yes—
82#14582954C2212yes—
83#14582953C2212yes—
84#14582936C2214yes—
85#14582934C2214yes—
86C4⋊C8×D43C2212yes—
87#14582892C2214yes—
88#14582892C2214yes—
89C22⋊C8×D43C2212yes—
90#97×D43C2212yes—
91C43×#532C2211yescharacteristic
92C2×#125×C43C2211yescharacteristic
93C43×#501C2212yescomplemented
94C43×#490C2212yescomplemented
95C43×#481C2212yes—
96C43×#480C2212yes—
97C43×#478C2214yescomplemented
98C43×#432C2211yescharacteristic
99C2×#10621900—21no—
100C2×#10621900C2312yes—
101C22×Dic86—21no—
102C22×Dic86—21no—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×C8×D43C2314yes—
107#13063325C2311yescharacteristic
108#13063325C2311yescharacteristic
109#13063324—21no—
110#13063324—21no—
111#13063324—21no—
112#13063324—21no—
113#13063324C2312yes—
114#13063324C2312yes—
115#13063324C2312yes—
116#13063324C2312yes—
117#13063318—22no—
118#13063318—22no—
119#13063317—21no—
120#13063317—21no—
121#13063317—21no—
122#13063317C2312yes—
123#13063317C2312yes—
124#13063316—21no—
125#13063316C2312yes—
126#13063312—21no—
127#13063312C2312yes—
128#13063307—22no—
129#13063307—22no—
130#13063306—22no—
131#13063305—21no—
132#13063305C2312yes—
133#13063304—21no—
134#13063304C2312yes—
135#13063303—22no—
136#13063303—22no—
137#13063303—22no—
138#13063303—22no—
139#13063303—22no—
140#13063303—22no—
141#13063303—22no—
142#13063303—22no—
143#13063301—21no—
144#13063301—21no—
145#13063296—21no—
146#13063296—21no—
147#13063296—21no—
148#13063296C2312yes—
149#13063293—22no—
150Q8×Dic43—21no—
151Q8×Dic43—21no—
152C4×Dic86—21no—
153C4×Dic86C2312yes—
154#13063290—22no—
155#13063290—22no—
156#13063290—22no—
157#13063290—22no—
158#13063290—22no—
159#13063290—22no—
160#13063290—22no—
161#13063290—22no—
162#13063290—21no—
163#13063290C2312yes—
164D4×Dic43—22no—
165D4×Dic43—22no—
166D4×Dic43—21no—
167D4×Dic43—21no—
168D4×Dic43—21no—
169D4×Dic43C2312yes—
170C4×C22⋊D43—22no—
171C4×C22⋊D43—22no—
172(C22⋊D43)⋊C4—22no—
173(C22⋊D43)⋊C4—22no—
174#13063284—21no—
175#13063284—22no—
176#13063283—21no—
177#13063283—21no—
178#13063283—21no—
179#13063283—21no—
180#13063283—21no—
181#13063283C2312yes—
182#13063283C2312yes—
183#13063283C2312yes—
184#13063283C2312yes—
185#13063283C2312yes—
186#13063281—22no—
187#13063281—22no—
188C2×C4⋊Dic43C2311yescharacteristic
189C2×C4⋊Dic43C2311yescharacteristic
190C2×Dic43⋊C4—21no—
191C2×Dic43⋊C4—21no—
192C2×Dic43⋊C4—21no—
193C2×Dic43⋊C4—21no—
194C2×(C2×D43)⋊C4—21no—
195C2×(C2×D43)⋊C4—21no—
196C2×C4×Dic43—21no—
197C2×C4×Dic43—21no—
198C2×C4×Dic43—22no—
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43D411yescharacteristic
201C2×C4×Dic43C2311yescharacteristic
202C42×D43D411yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43C2311yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210#13063259C2314yes—
211#13063258C2314yes—
212#13063258C2314yes—
213#13063257C2314yes—
214#13063256C2314yes—
215#13063256C2314yes—
216C4⋊(C43⋊C8)C2312yes—
217Dic43⋊C8C2314yes—
218#13063250C2314yes—
219#13063250C2314yes—
220#13063248C2314yes—
221#13063248C2314yes—
222#13063246C2314yes—
223#13063246C2314yes—
224C22⋊(C43⋊C8)C2312yes—
225(C2×D43)⋊C8C2314yes—
226#13063236C2312yes—
227#13063235C2314yes—
228C2×#41×C43—21no—
229C4⋊Q8×C43C2311yescharacteristic
230#127×C43C2311yescharacteristic
231#125×C43—21no—
232#125×C43—21no—
233#125×C43C2312yes—
234#125×C43C2312yes—
235#124×C43—21no—
236#121×C43—21no—
237#121×C43C2312yes—
238C4×D4×C43—21no—
239C4×D4×C43C2312yes—
240C2×C4⋊C4×C43—21no—
241C2×C4⋊C4×C43—21no—
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C42×C43C2311yescharacteristic
245#107×C43C2314yes—
246#106×C43C2314yes—
247C4⋊C8×C43C2312yes—
248#102×C43C2314yes—
249#102×C43C2314yes—
250C22⋊C8×C43C2312yes—
251#97×C43C2312yes—
252C23×D43C2×D411yescharacteristic
253#41×C43—44no—
254C2×Q8×C43—21no—
255C2×D4×C43—21no—
256C2×D4×C43—21no—
257C2×D4×C43—22no—
258C2×D4×C43C2412yes—
259C22×C4×C43—22no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2411yescharacteristic
265C2×C22⋊D43—22no—
266C2×C22⋊D43—22no—
267C22×Dic43—22no—
268C22×Dic43—22no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43C2×D411yescharacteristic
272C22×Dic43C2×D411yescharacteristic
273C22×Dic43C2×D411yescharacteristic
274#10621900—28no—
275#10621900—44no—
276C2×C4×D43—24no—
277C2×C4×D43—42no—
278C2×C4×D43—42no—
279C2×C4×D43C2×D411yescharacteristic
280C2×C4×D43C2×D411yescharacteristic
281C2×C4×D43C2×D411yescharacteristic
282C2×C4×D43C2×D411yescharacteristic
283C2×C4×D43C2×D411yescharacteristic
284C2×C4×D43C2×D411yescharacteristic
285C2×C4×D43C2×D411yescharacteristic
286C2×C4×D43C2×D411yescharacteristic
287C2×C4×D43C2×D411yescharacteristic
288C2×C4×D43C2×D411yescharacteristic
289C2×C4×D43C2411yescharacteristic
290C2×C4×D43C2411yescharacteristic
291C2×Dic86—21no—
292C2×Dic86—22no—
293C2×Dic86—22no—
294C2×Dic86—22no—
295C2×Dic86—22no—
296C2×Dic86—44no—
297C2×Dic86—44no—
298C2×Dic86C2412yes—
299C2×C8×C43C2414yes—
300C4⋊C4×C43—22no—
301C4⋊C4×C43—22no—
302C4⋊C4×C43—22no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—21no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43C2412yes—
308C4⋊C4×C43C2412yes—
309C4⋊C4×C43C2412yes—
310C22⋊C4×C43—22no—
311C22⋊C4×C43—22no—
312C42×C43C2×D411yescharacteristic
313C42×C43C2×D411yescharacteristic
314C42×C43C2411yescharacteristic
315C42×C43C2411yescharacteristic
316C22⋊Dic43—22no—
317C22⋊Dic43—22no—
318C22⋊Dic43—22no—
319C22⋊Dic43—22no—
320C22⋊Dic43—22no—
321(C2×D43)⋊C4—22no—
322(C2×D43)⋊C4—22no—
323(C2×D43)⋊C4—22no—
324(C2×D43)⋊C4—22no—
325(C2×D43)⋊C4—22no—
326(C2×D43)⋊C4—22no—
327C4⋊Dic43—21no—
328C4⋊Dic43—21no—
329C4⋊Dic43—21no—
330C4⋊Dic43—21no—
331C4⋊Dic43—21no—
332C4⋊Dic43—22no—
333C4⋊Dic43—22no—
334C4⋊Dic43C2412yes—
335C4⋊Dic43C2412yes—
336C4⋊Dic43C2412yes—
337Dic43⋊C4—22no—
338Dic43⋊C4—22no—
339Dic43⋊C4—22no—
340Dic43⋊C4—22no—
341Dic43⋊C4—22no—
342Dic43⋊C4—22no—
343Dic43⋊C4—22no—
344Dic43⋊C4—22no—
345Dic43⋊C4—22no—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349C4×Dic43—22no—
350C4×Dic43—22no—
351C4×Dic43—22no—
352C4×Dic43—22no—
353C4×Dic43—22no—
354C4×Dic43—22no—
355C4×Dic43—22no—
356C4×Dic43C2×D411yescharacteristic
357C4×Dic43C2×D411yescharacteristic
358C4×Dic43C2×D411yescharacteristic
359C4×Dic43C2×D411yescharacteristic
360C4×Dic43C2×D411yescharacteristic
361C4×Dic43C2×D411yescharacteristic
362C4×Dic43C2×D411yescharacteristic
363C4×Dic43C2×D411yescharacteristic
364C4×Dic43C2×D411yescharacteristic
365C4×Dic43C2×D411yescharacteristic
366C4×Dic43C2411yescharacteristic
367C4×Dic43C2411yescharacteristic
368C2×C43⋊C8C2414yes—
369C8×D43—28no—
370C23×C43—22no—
371C23×C43C22×D411yescharacteristic
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—41no—
375C22×D43C22×D411yescharacteristic
376C22×D43C22×D411yescharacteristic
377Q8×C43—42no—
378D4×C43—24no—
379D4×C43—42no—
380D4×C43—42no—
381D4×C43—44no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—41no—
388C2×C4×C43—44no—
389C2×C4×C43—42no—
390C2×C4×C43—42no—
391C2×C4×C43C22×D411yescharacteristic
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C2511yescharacteristic
397C22⋊D43—44no—
398C22⋊D43—44no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—42no—
407C2×Dic43—42no—
408C2×Dic43—44no—
409C2×Dic43—44no—
410C2×Dic43C22×D411yescharacteristic
411C2×Dic43C22×D411yescharacteristic
412C2×Dic43C22×D411yescharacteristic
413C2×Dic43C22×D411yescharacteristic
414C2×Dic43C22×D411yescharacteristic
415C2×Dic43C22×D411yescharacteristic
416C4×D43—22no—
417C4×D43—22no—
418C4×D43—22no—
419C4×D43—22no—
420C4×D43—22no—
421C4×D43—41no—
422C4×D43—41no—
423C4×D43—41no—
424C4×D43—41no—
425C4×D43—41no—
426C4×D43—41no—
427C4×D432−1+414yes—
428Dic86—24no—
429Dic86—44no—
430Dic86—44no—
431Dic86—44no—
432Dic86—42no—
433Dic86—44no—
434C8×C43—24no—
435C43⋊C8—24no—
436#60854—431nomaximal, Sylow
437C22×C43—21no—
438C22×C43—21no—
439C22×C43—42no—
440C22×C43—42no—
441C22×C43—42no—
442C22×C43#57512yes—
443C22×C43C23×D411yescharacteristic
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—44no—
450C2×D43#53612yes—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43—42no—
459C4×C43C2×2−1+412yes—
460Dic43—21no—
461Dic43—21no—
462Dic43—21no—
463Dic43—21no—
464Dic43—42no—
465Dic43—42no—
466Dic43—42no—
467Dic43—42no—
468Dic43#53612yes—
469Dic43#57512yes—
470#3444—431no—
471C2×#533—431no—
472#3240—434no—
473#3239—432no—
474#3238—432no—
475#3237—432no—
476#3236—431no—
477#3236—431no—
478#3235—432no—
479#3234—431no—
480#3234D4311yescharacteristic, complemented
481#3162—432no—
482#3135—432no—
483#3091—432no—
484#3091—432no—
485#3076—434no—
486C2×#432—431no—
487C2×C43—22no—
488C2×C43—82no—
489C2×C43C2×#53611yescharacteristic
490C2×C43C2×#57511yescharacteristic
491C2×C43C2×#57511yescharacteristic
492D43—22no—
493D43—41no—
494#533—431no—
495#533—432no—
496#533—432no—
497#533—432no—
498#533—432no—
499#533—431no—
500#533—431no—
501#533—861no—
502#533—861no—
503#533—861no—
504#533—861no—
505#532—431no—
506#532—431no—
507#532C2×D4311yescharacteristic
508C2×C4⋊Q8—431no—
509C2×C4⋊Q8—431no—
510#529—432no—
511#529—432no—
512#529—861no—
513#529—861no—
514#529—861no—
515#529—861no—
516C2×#125—431no—
517C2×#125C2×D4311yescharacteristic
518#525—432no—
519#525—861no—
520#525—861no—
521C2×C22⋊Q8—861no—
522C2×C22⋊Q8—861no—
523C4×#41—432no—
524C4×#41—861no—
525C4×#41—861no—
526C2×C4×Q8—861no—
527C2×C4×Q8—861no—
528C2×#117—431no—
529C2×#117—431no—
530C22×C42—431no—
531#501—432no—
532#501—432no—
533#501—434no—
534#501—434no—
535#501—432no—
536#501C2×D4312yescomplemented
537#491—432no—
538#491—432no—
539#490—432no—
540#490C2×D4312yescomplemented
541#489—434no—
542#489—434no—
543#485—434no—
544#485—434no—
545#484—432no—
546#484—432no—
547#483—432no—
548#483—432no—
549#482—434no—
550#482—434no—
551#481—432no—
552#481C2×D4312yes—
553#480—432no—
554#480C2×D4312yes—
555#479—434no—
556#479—434no—
557#478—434no—
558#478C2×D4314yescomplemented
559#477—434no—
560#476—434no—
561#475—434no—
562#474—434no—
563#432—431no—
564#432—432no—
565#432—432no—
566#432—432no—
567#432C2×D4311yescharacteristic
568#427—434no—
569#427—434no—
570C2×C4⋊C8—432no—
571#416—434no—
572#416—434no—
573C2×C22⋊C8—432no—
574C2×#97—432no—
575C43#6085411yescharacteristic, complemented, Sylow
576C2×#41—21no—
577C2×#41—432no—
578C2×#41—861no—
579C22×Q8—861no—
580C22×Q8—861no—
581C23×C4—431no—
582C23×C4—431no—
583C23×C4—431no—
584C22×C8—434no—
585C4⋊Q8—432no—
586C4⋊Q8—432no—
587C4⋊Q8—432no—
588C4⋊Q8—432no—
589C4⋊Q8—431no—
590C4⋊Q8—431no—
591C4⋊Q8—861no—
592C4⋊Q8—861no—
593C4⋊Q8—861no—
594C4⋊Q8—861no—
595C4⋊Q8C22×D4311yescharacteristic
596#127C22×D4311yescharacteristic
597#126—862no—
598#126—862no—
599#125—21no—
600#125—21no—
601#125—432no—
602#125—432no—
603#125—432no—
604#125—861no—
605#125—861no—
606#125—861no—
607#125—861no—
608#125C22×D4312yes—
609#125C22×D4312yes—
610#124—21no—
611#124—432no—
612#124—861no—
613#123—862no—
614#123—862no—
615#123—862no—
616C22⋊Q8—432no—
617C22⋊Q8—432no—
618C22⋊Q8—862no—
619C22⋊Q8—862no—
620C22⋊Q8—862no—
621C22⋊Q8—862no—
622C22⋊Q8—862no—
623C22⋊Q8—862no—
624C22⋊Q8—862no—
625C22⋊Q8—862no—
626C22⋊Q8—861no—
627C22⋊Q8—861no—
628C22⋊Q8—861no—
629C22⋊Q8—861no—
630#121—21no—
631#121—432no—
632#121—861no—
633#121—861no—
634#121—861no—
635#121C22×D4312yes—
636#120—862no—
637C4×Q8—432no—
638C4×Q8—432no—
639C4×Q8—862no—
640C4×Q8—862no—
641C4×Q8—862no—
642C4×Q8—862no—
643C4×Q8—862no—
644C4×Q8—862no—
645C4×Q8—862no—
646C4×Q8—862no—
647C4×Q8—861no—
648C4×Q8—861no—
649C4×Q8—861no—
650C4×Q8—861no—
651C4×D4—21no—
652C4×D4—432no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—862no—
657C4×D4—862no—
658C4×D4—862no—
659C4×D4—862no—
660C4×D4—862no—
661C4×D4—862no—
662C4×D4C22×D4312yes—
663#117—432no—
664#117—432no—
665#117—432no—
666#117—432no—
667#117—432no—
668#117—862no—
669#117—862no—
670#117—862no—
671#117—861no—
672#117—861no—
673#117—861no—
674#117—861no—
675#117—861no—
676#117—861no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—431no—
680C2×C4⋊C4—431no—
681C2×C4⋊C4—861no—
682C2×C4⋊C4—861no—
683C2×C4⋊C4—861no—
684C2×C4⋊C4—861no—
685C2×C4⋊C4C22×D4311yescharacteristic
686C2×C4⋊C4C22×D4311yescharacteristic
687C2×C22⋊C4—861no—
688C2×C22⋊C4—861no—
689C2×C42—431no—
690C2×C42—431no—
691C2×C42—431no—
692C2×C42—431no—
693C2×C42—431no—
694C2×C42—431no—
695C2×C42—431no—
696C2×C42—431no—
697C2×C42—431no—
698C2×C42—431no—
699C2×C42—431no—
700C2×C42—862no—
701C2×C42—861no—
702C2×C42—861no—
703C2×C42C22×D4311yescharacteristic
704#107—434no—
705#107—434no—
706#107—434no—
707#107C22×D4314yes—
708#106—434no—
709#106—434no—
710#106—434no—
711#106C22×D4314yes—
712C4⋊C8—434no—
713C4⋊C8—432no—
714C4⋊C8C22×D4312yes—
715#103—434no—
716#103—434no—
717#103—434no—
718#103—434no—
719#102—434no—
720#102—434no—
721#102C22×D4314yes—
722#102C22×D4314yes—
723C22⋊C8—432no—
724C22⋊C8—434no—
725C22⋊C8C22×D4312yes—
726#97—434no—
727#97—432no—
728#97C22×D4312yes—
729C24—431no—
730#41—44no—
731#41—868no—
732#41—1724no—
733C2×Q8—21no—
734C2×Q8—432no—
735C2×Q8—862no—
736C2×Q8—862no—
737C2×Q8—862no—
738C2×Q8—862no—
739C2×Q8—861no—
740C2×Q8—1724no—
741C2×Q8—1724no—
742C2×D4—22no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—862no—
746C2×D4—862no—
747C2×D4C23×D4312yes—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—431no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—431no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—864no—
767C22×C4—862no—
768C22×C4—862no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—1722no—
772C22×C4—1722no—
773C22×C4D4×D4311yescharacteristic
774C22×C4D4×D4311yescharacteristic
775C22×C4C23×D4311yescharacteristic
776C2×C8—434no—
777C2×C8—868no—
778C2×C8C23×D4314yes—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—432no—
787C4⋊C4—432no—
788C4⋊C4—432no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C4⋊C4—862no—
793C4⋊C4—862no—
794C4⋊C4—862no—
795C4⋊C4—862no—
796C4⋊C4—862no—
797C4⋊C4—861no—
798C4⋊C4—861no—
799C4⋊C4—862no—
800C4⋊C4—862no—
801C4⋊C4—862no—
802C4⋊C4—862no—
803C4⋊C4—862no—
804C4⋊C4—861no—
805C4⋊C4—861no—
806C4⋊C4—861no—
807C4⋊C4—862no—
808C4⋊C4C23×D4312yes—
809C4⋊C4C23×D4312yes—
810C4⋊C4C23×D4312yes—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—862no—
814C22⋊C4—862no—
815C22⋊C4—862no—
816C22⋊C4—862no—
817C22⋊C4—862no—
818C22⋊C4—862no—
819C22⋊C4—862no—
820C22⋊C4—862no—
821C22⋊C4—862no—
822C22⋊C4—862no—
823C22⋊C4—862no—
824C42—431no—
825C42—431no—
826C42—431no—
827C42—431no—
828C42—431no—
829C42—431no—
830C42—431no—
831C42—431no—
832C42—431no—
833C42—431no—
834C42—431no—
835C42—431no—
836C42—862no—
837C42—862no—
838C42—862no—
839C42—862no—
840C42—862no—
841C42—862no—
842C42—862no—
843C42D4×D4311yescharacteristic
844C42D4×D4311yescharacteristic
845C42C23×D4311yescharacteristic
846C42C23×D4311yescharacteristic
847C23—22no—
848C23—431no—
849C23—431no—
850C23—862no—
851C23—862no—
852C23—1721no—
853C23C2×D4×D4311yescharacteristic
854Q8—42no—
855Q8—864no—
856Q8—1722no—
857Q8—1724no—
858Q8—1724no—
859Q8—1724no—
860Q8—1724no—
861D4—24no—
862D4—42no—
863D4—42no—
864D4—44no—
865D4—1724no—
866D4—1724no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—41no—
873C2×C4—44no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—431no—
877C2×C4—431no—
878C2×C4—434no—
879C2×C4—431no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—431no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1724no—
902C2×C4—1724no—
903C2×C4—1722no—
904C2×C4—1722no—
905C2×C4C2×D4×D4311yescharacteristic
906C2×C4C2×D4×D4311yescharacteristic
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4C24×D4311yescharacteristic
911C8—24no—
912C8—864no—
913C22—21no—
914C22—21no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—432no—
919C22—861no—
920C22—861no—
921C22—861no—
922C22—861no—
923C22—861no—
924C22—1724no—
925C22#1458369512yes—
926C22C22×D4×D4311yescharacteristic
927C4—21no—
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—42no—
934C4—42no—
935C4—432no—
936C4—432no—
937C4—861no—
938C4—861no—
939C4—861no—
940C4—861no—
941C4—1722no—
942C4—1722no—
943C4—1722no—
944C4—1722no—
945C42−1+4×D4312yes—
946C2—22no—
947C2—82no—
948C2—862no—
949C2—1721no—
950C2#536×D4311yescharacteristic
951C2#575×D4311yescharacteristic
952C2C2×#1458369511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3234C2
socleC22×C43C23×D4
prime radical#19147890C2
hypercenter#3234D43
hypocenterC43#60854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3234

Complements

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

NH ≅ G/Ntype
2. C2×#14583455C2semidirect
3. #19145834C2semidirect
4. #19145823C2semidirect
5. #19145814C2semidirect
6. #19145810C2semidirect
7. #19145803C2semidirect
8. #19145801C2semidirect
9. #19145788C2semidirect
10. #19145781C2semidirect
11. #19145116C2semidirect
12. #19144939C2semidirect
13. #19144505C2semidirect
14. #19144503C2semidirect
15. #19144380C2semidirect
16. #432×D43C2semidirect
17. C43×#3234C2semidirect
53. #14583309C22semidirect
54. #14583308C22semidirect
55. #14583307C22semidirect
56. #14583306C22semidirect
57. #14583305C22semidirect
58. #14583269C22semidirect
59. #14583268C22semidirect
60. #14583263C22semidirect
61. #14583257C22semidirect
62. #14583257C22semidirect
73. #14583207C22semidirect
74. #14583203C22semidirect
75. #14583199C22semidirect
76. #14583193C22semidirect
77. #14583187C22semidirect
78. #14583183C22semidirect
79. #14583177C22semidirect
93. C43×#501C22semidirect
94. C43×#490C22semidirect
97. C43×#478C22semidirect
480. #3234D43semidirect
536. #501C2×D43semidirect
540. #490C2×D43semidirect
558. #478C2×D43semidirect
575. C43#60854semidirect

Maximal subgroups

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

subgroupindex
#191478902
C2×#145834552
#191458342
#191458232
#191458142
#191458102
#191458032
#191458012
#191457882
#191457812
#191451162
#191449392
#191445052
#191445032
#191443802
#432×D432
C43×#32342
#6085443