Finite Group Databasebeta

← #25968765

Subgroups — #25968765

Order 11008.

1780 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#533×D43C211yesmaximal, characteristic, complemented
3#19145832C212yesmaximal, complemented
4#19145830C212yesmaximal, complemented
5#19145821C212yesmaximal, complemented
6#19145812C212yesmaximal, complemented
7#19145804C212yesmaximal, complemented
8#19145796C212yesmaximal, complemented
9#19145788C212yesmaximal, complemented
10#19145780C212yesmaximal, complemented
11#19145119C211yesmaximal, characteristic, complemented
12#19145117C211yesmaximal, characteristic, complemented
13#19144940C211yesmaximal, characteristic, complemented
14#19144506C214yesmaximal, complemented
15#19144379C214yesmaximal, complemented
16C2×#14582954C211yesmaximal, characteristic, complemented
17C43×#3135C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583456C2211yescharacteristic
20#14583455C2212yes—
21#14583454C2211yescharacteristic
22#14583454C2211yescharacteristic
23#14583454C2211yescharacteristic
24#14583454C2211yescharacteristic
25#14583453—21no—
26#14583453—21no—
27#14583452C2212yes—
28#14583451—21no—
29#14583451—21no—
30#14583447C2211yescharacteristic
31#14583447C2211yescharacteristic
32C4⋊Q8×D43C2211yescharacteristic
33C4⋊Q8×D43C2211yescharacteristic
34#14583431—21no—
35#14583431—21no—
36#14583430—21no—
37#14583430—21no—
38#14583428C2212yes—
39#14583428C2212yes—
40#125×D43C2212yes—
41#14583409—21no—
42#14583409—21no—
43#14583406C2212yes—
44C22⋊Q8×D43—21no—
45C22⋊Q8×D43—21no—
46#41×Dic43C2212yes—
47C4×#10621900—21no—
48C4×#10621900—21no—
49C4×Q8×D43—21no—
50C4×Q8×D43—21no—
51#117×D43C2212yes—
52C2×C42×D43C2211yescharacteristic
53#14583309C2212yescomplemented
54#14583309C2212yescomplemented
55#14583308C2212yescomplemented
56#14583308C2212yescomplemented
57#14583308C2212yescomplemented
58#14583308C2212yescomplemented
59#14583305C2212yescomplemented
60#14583305C2212yescomplemented
61#14583267C2212yescomplemented
62#14583263C2212yescomplemented
63#14583258C2212yescomplemented
64#14583258C2212yescomplemented
65#14583239C2214yes—
66#14583238C2214yes—
67#14583233C2214yes—
68#14583228C2214yes—
69#14583222C2214yes—
70#14583221C2214yes—
71#14583216C2214yes—
72#14583211C2214yes—
73#14583208C2214yescomplemented
74#14583204C2214yescomplemented
75#14583201C2214yescomplemented
76#14583197C2214yescomplemented
77#14583192C2214yescomplemented
78#14583187C2214yescomplemented
79#14583182C2214yescomplemented
80#14583177C2214yescomplemented
81#14582954C2212yes—
82#14582954C2212yes—
83#14582954C2212yes—
84#14582954C2212yes—
85#14582937C2214yes—
86#14582935C2214yes—
87C2×Dic43⋊C8C2212yes—
88#14582895C2214yes—
89C2×(C2×D43)⋊C8C2212yes—
90C2×#13063236C2211yescharacteristic
91C43×#533C2211yescharacteristic
92C43×#532C2211yescharacteristic
93C43×#491C2212yescomplemented
94C43×#490C2212yescomplemented
95C43×#489C2212yescomplemented
96C43×#489C2212yescomplemented
97C43×#416C2214yes—
98C2×#97×C43C2211yescharacteristic
99C2×#10621900—21no—
100C2×#10621900—21no—
101C2×Q8×D43—21no—
102C2×Q8×D43—21no—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C22×C43⋊C8C2312yes—
107#13063325C2311yescharacteristic
108#13063325C2311yescharacteristic
109#13063325C2311yescharacteristic
110#13063325C2311yescharacteristic
111#13063324—21no—
112#13063324—21no—
113#13063324C2312yes—
114#13063324C2312yes—
115#13063323—21no—
116#13063323—21no—
117#13063318—22no—
118#13063318—22no—
119#13063317C2312yes—
120#13063317C2312yes—
121#13063316—21no—
122#13063316—21no—
123#13063316C2312yes—
124#13063316C2312yes—
125#13063315—22no—
126#13063315—22no—
127#13063312—21no—
128#13063312—21no—
129#13063307—22no—
130#13063307—22no—
131#13063306—22no—
132#13063305—21no—
133#13063305—21no—
134#13063305—21no—
135#13063305—21no—
136#13063304—21no—
137#13063304—21no—
138#13063304—21no—
139#13063304—21no—
140#13063303—22no—
141#13063303—22no—
142#13063302—22no—
143#13063302—22no—
144#13063301—21no—
145#13063301—21no—
146#13063301C2312yes—
147#13063301C2312yes—
148#13063296—21no—
149#13063296—21no—
150#13063296C2312yes—
151#13063296C2312yes—
152#13063293—22no—
153Q8×Dic43—21no—
154Q8×Dic43—21no—
155Q8×Dic43C2312yes—
156Q8×Dic43C2312yes—
157C4×Dic86—21no—
158C4×Dic86—21no—
159C4×Dic86—21no—
160C4×Dic86—21no—
161C4×Dic86—22no—
162C4×Dic86—22no—
163#13063290—21no—
164#13063290—21no—
165#13063290—22no—
166#13063290—22no—
167#13063290—21no—
168#13063290—21no—
169D4×Dic43—22no—
170D4×Dic43—22no—
171D4×Dic43—21no—
172D4×Dic43—21no—
173D4×Dic43C2312yes—
174D4×Dic43C2312yes—
175C4×C22⋊D43—22no—
176C4×C22⋊D43—22no—
177(C22⋊D43)⋊C4—22no—
178(C22⋊D43)⋊C4—22no—
179#13063284—22no—
180#13063284C2312yes—
181#13063284C2312yes—
182#13063283—21no—
183#13063283—21no—
184#13063283C2312yes—
185#13063283C2312yes—
186#13063282—22no—
187#13063281—22no—
188#13063281—22no—
189#13063281—22no—
190C4⋊C4×D43—22no—
191C4⋊C4×D43—22no—
192C4⋊C4×D43—21no—
193C4⋊C4×D43—21no—
194C4⋊C4×D43C2312yes—
195C4⋊C4×D43C2312yes—
196C22⋊C4×D43—22no—
197C2×C4×Dic43—22no—
198C2×C4×Dic43D411yescharacteristic
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C42×D43—22no—
202C42×D43D411yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43C2311yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210#13063259C2314yes—
211#13063259C2314yes—
212#13063258C2314yes—
213#13063258C2314yes—
214#13063257C2314yes—
215#13063257C2314yes—
216#13063256C2314yes—
217#13063256C2314yes—
218Dic43⋊C8C2314yes—
219Dic43⋊C8C2314yes—
220#13063249C2314yes—
221#13063249C2314yes—
222#13063246C2314yes—
223#13063246C2314yes—
224(C2×D43)⋊C8C2314yes—
225(C2×D43)⋊C8C2314yes—
226#13063236C2312yes—
227#13063236C2312yes—
228C2×#41×C43C2312yes—
229C22×C8×C43C2312yes—
230C4⋊Q8×C43C2311yescharacteristic
231C4⋊Q8×C43C2311yescharacteristic
232C4⋊Q8×C43C2311yescharacteristic
233#127×C43C2311yescharacteristic
234#125×C43C2312yes—
235#124×C43C2312yes—
236C22⋊Q8×C43—21no—
237C22⋊Q8×C43—21no—
238#121×C43—21no—
239#121×C43—21no—
240C4×Q8×C43—21no—
241C4×Q8×C43—21no—
242C4×D4×C43—21no—
243C4×D4×C43—21no—
244#117×C43C2312yes—
245C2×C42×C43C2311yescharacteristic
246#103×C43C2314yes—
247#103×C43C2314yes—
248#102×C43C2314yes—
249#102×C43C2314yes—
250#97×C43C2312yes—
251#97×C43C2312yes—
252C23×D43C2×D411yescharacteristic
253#41×C43—28no—
254C2×Q8×C43—21no—
255C2×Q8×C43—21no—
256C2×Q8×C43C2412yes—
257C2×D4×C43—21no—
258C2×D4×C43—21no—
259C2×D4×C43—22no—
260C2×D4×C43C2412yes—
261C22×C4×C43—22no—
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×Dic43C2×D411yescharacteristic
270C22×Dic43C2×D411yescharacteristic
271C22×Dic43C2×D411yescharacteristic
272Q8×D43—44no—
273Q8×D43—44no—
274#10621900—44no—
275#10621900—44no—
276C2×C4×D43—24no—
277C2×C4×D43—22no—
278C2×C4×D43—22no—
279C2×C4×D43—42no—
280C2×C4×D43—42no—
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×D43C2×D411yescharacteristic
290C2×C4×D43C2×D411yescharacteristic
291C2×C4×D43C2411yescharacteristic
292C2×C4×D43C2411yescharacteristic
293C2×Dic86—21no—
294C2×Dic86—21no—
295C2×Dic86—21no—
296C2×Dic86—21no—
297C2×Dic86—22no—
298C2×Dic86—22no—
299C2×C8×C43—24no—
300C2×C8×C43C2414yes—
301C4⋊C4×C43—21no—
302C4⋊C4×C43—21no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—22no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43C2412yes—
308C4⋊C4×C43C2412yes—
309C22⋊C4×C43—22no—
310C22⋊C4×C43—22no—
311C22⋊C4×C43—22no—
312C42×C43—22no—
313C42×C43C2×D411yescharacteristic
314C42×C43C2×D411yescharacteristic
315C42×C43C2411yescharacteristic
316C42×C43C2411yescharacteristic
317C22⋊Dic43—22no—
318C22⋊Dic43—22no—
319C22⋊Dic43—22no—
320C22⋊Dic43—22no—
321C22⋊Dic43—22no—
322C22⋊Dic43—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—22no—
332C4⋊Dic43—22no—
333C4⋊Dic43—22no—
334C4⋊Dic43—22no—
335C4⋊Dic43C2412yes—
336C4⋊Dic43C2412yes—
337C4⋊Dic43C2412yes—
338C4⋊Dic43C2412yes—
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—
349Dic43⋊C4—22no—
350Dic43⋊C4—22no—
351C4×Dic43—22no—
352C4×Dic43—22no—
353C4×Dic43—22no—
354C4×Dic43—22no—
355C4×Dic43—22no—
356C4×Dic43—22no—
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×Dic43C2×D411yescharacteristic
367C4×Dic43C2411yescharacteristic
368C4×Dic43C2411yescharacteristic
369C2×C43⋊C8—24no—
370C2×C43⋊C8C2414yes—
371C23×C43—22no—
372C23×C43C22×D411yescharacteristic
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—41no—
376C22×D43C22×D411yescharacteristic
377C22×D43C22×D411yescharacteristic
378Q8×C43—24no—
379Q8×C43—42no—
380Q8×C43—42no—
381D4×C43—24no—
382D4×C43—42no—
383D4×C43—42no—
384D4×C43—44no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—44no—
391C2×C4×C43C22×D411yescharacteristic
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C432−1+414yes—
397C2×C4×C43C2511yescharacteristic
398C22⋊D43—44no—
399C22⋊D43—44no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—41no—
407C2×Dic43—44no—
408C2×Dic43—44no—
409C2×Dic43C22×D411yescharacteristic
410C2×Dic43C22×D411yescharacteristic
411C2×Dic43C22×D411yescharacteristic
412C2×Dic43C22×D411yescharacteristic
413C2×Dic43C22×D411yescharacteristic
414C2×Dic43C22×D411yescharacteristic
415C4×D43—22no—
416C4×D43—22no—
417C4×D43—22no—
418C4×D43—22no—
419C4×D43—22no—
420C4×D43—22no—
421C4×D43—22no—
422C4×D43—22no—
423C4×D43—41no—
424C4×D43—41no—
425C4×D43—41no—
426C4×D43—41no—
427C4×D43—44no—
428C4×D43—44no—
429Dic86—44no—
430Dic86—42no—
431Dic86—42no—
432Dic86—42no—
433Dic86—42no—
434Dic86—44no—
435C8×C43—24no—
436C43⋊C8—24no—
437#60854—431nomaximal, Sylow
438C22×C43—21no—
439C22×C43—21no—
440C22×C43—42no—
441C22×C43—42no—
442C22×C43—42no—
443C22×C43#53612yes—
444C22×C43C23×D411yescharacteristic
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—44no—
451C2×D43#57512yes—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43—42no—
459C4×C43#53612yes—
460C4×C43C2×2−1+412yes—
461Dic43—21no—
462Dic43—21no—
463Dic43—21no—
464Dic43—21no—
465Dic43—21no—
466Dic43—42no—
467Dic43—42no—
468Dic43—42no—
469Dic43—42no—
470Dic43#57512yes—
471#3444—431no—
472C2×#533—431no—
473#3240—432no—
474#3240—432no—
475#3239—432no—
476#3238—432no—
477#3237—432no—
478#3236—432no—
479#3235—432no—
480#3234—432no—
481#3162—431no—
482#3162—431no—
483#3135—431no—
484#3135D4311yescharacteristic, complemented
485#3091—434no—
486#3076—434no—
487C2×#432—431no—
488C2×C43—22no—
489C2×C43—82no—
490C2×C43C2×#53611yescharacteristic
491C2×C43C2×#57511yescharacteristic
492C2×C43C2×#57511yescharacteristic
493D43—22no—
494D43—41no—
495#533—431no—
496#533—431no—
497#533—432no—
498#533—432no—
499#533—431no—
500#533—431no—
501#533—431no—
502#533—431no—
503#533—861no—
504#533—861no—
505#533—861no—
506#533—861no—
507#533C2×D4311yescharacteristic
508#532—431no—
509#532—431no—
510#532C2×D4311yescharacteristic
511C2×C4⋊Q8—431no—
512C2×C4⋊Q8—431no—
513#529—432no—
514#529—432no—
515#529—861no—
516#529—861no—
517#529—861no—
518#529—861no—
519C2×#125—432no—
520#525—432no—
521#525—861no—
522#525—861no—
523C2×C22⋊Q8—861no—
524C2×C22⋊Q8—861no—
525C4×#41—432no—
526C4×#41—861no—
527C4×#41—861no—
528C2×C4×Q8—861no—
529C2×C4×Q8—861no—
530C2×#117—432no—
531C22×C42—431no—
532#501—432no—
533#501—432no—
534#501—432no—
535#501—432no—
536#501—432no—
537#501—432no—
538#501—432no—
539#501—432no—
540#491—432no—
541#491C2×D4312yescomplemented
542#490—432no—
543#490C2×D4312yescomplemented
544#489—432no—
545#489—432no—
546#489C2×D4312yescomplemented
547#489C2×D4312yescomplemented
548#485—434no—
549#485—434no—
550#484—434no—
551#483—434no—
552#482—434no—
553#482—434no—
554#481—434no—
555#480—434no—
556#479—434no—
557#479—434no—
558#478—434no—
559#478—434no—
560#477—434no—
561#476—434no—
562#475—434no—
563#474—434no—
564#432—432no—
565#432—432no—
566#432—432no—
567#432—432no—
568#427—434no—
569#427—434no—
570C2×C4⋊C8—432no—
571#416—434no—
572#416C2×D4314yes—
573C2×C22⋊C8—432no—
574C2×#97—431no—
575C2×#97C2×D4311yescharacteristic
576C43#6085411yescharacteristic, complemented, Sylow
577C2×#41—861no—
578C2×#41—861no—
579C2×#41C22×D4312yes—
580C22×Q8—861no—
581C22×Q8—861no—
582C23×C4—431no—
583C23×C4—431no—
584C23×C4—431no—
585C22×C8—432no—
586C22×C8C22×D4312yes—
587C4⋊Q8—432no—
588C4⋊Q8—432no—
589C4⋊Q8—431no—
590C4⋊Q8—431no—
591C4⋊Q8—431no—
592C4⋊Q8—431no—
593C4⋊Q8—861no—
594C4⋊Q8—861no—
595C4⋊Q8—861no—
596C4⋊Q8—861no—
597C4⋊Q8C22×D4311yescharacteristic
598C4⋊Q8C22×D4311yescharacteristic
599C4⋊Q8C22×D4311yescharacteristic
600#127C22×D4311yescharacteristic
601#126—862no—
602#126—862no—
603#125—432no—
604#125—432no—
605#125—432no—
606#125—432no—
607#125—862no—
608#125—862no—
609#125—861no—
610#125—861no—
611#125C22×D4312yes—
612#124—861no—
613#124—861no—
614#124C22×D4312yes—
615#123—862no—
616#123—862no—
617#123—862no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—432no—
621C22⋊Q8—432no—
622C22⋊Q8—862no—
623C22⋊Q8—862no—
624C22⋊Q8—862no—
625C22⋊Q8—862no—
626C22⋊Q8—861no—
627C22⋊Q8—861no—
628C22⋊Q8—861no—
629C22⋊Q8—861no—
630C22⋊Q8—861no—
631C22⋊Q8—861no—
632C22⋊Q8—861no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635C22⋊Q8—861no—
636#121—21no—
637#121—21no—
638#121—432no—
639#121—432no—
640#121—861no—
641#121—861no—
642#120—862no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—432no—
646C4×Q8—432no—
647C4×Q8—862no—
648C4×Q8—862no—
649C4×Q8—861no—
650C4×Q8—862no—
651C4×Q8—862no—
652C4×Q8—861no—
653C4×Q8—861no—
654C4×Q8—861no—
655C4×Q8—861no—
656C4×Q8—861no—
657C4×Q8—861no—
658C4×Q8—861no—
659C4×Q8—861no—
660C4×Q8—861no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—432no—
664C4×D4—432no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—862no—
668C4×D4—862no—
669C4×D4—862no—
670C4×D4—862no—
671C4×D4—862no—
672C4×D4—862no—
673#117—432no—
674#117—432no—
675#117—432no—
676#117—432no—
677#117—862no—
678#117—862no—
679#117—862no—
680#117—862no—
681#117—862no—
682#117—861no—
683#117—861no—
684#117C22×D4312yes—
685C2×C4⋊C4—432no—
686C2×C4⋊C4—432no—
687C2×C4⋊C4—862no—
688C2×C4⋊C4—862no—
689C2×C4⋊C4—861no—
690C2×C4⋊C4—861no—
691C2×C22⋊C4—862no—
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—431no—
701C2×C42—431no—
702C2×C42—431no—
703C2×C42—862no—
704C2×C42—862no—
705C2×C42C22×D4311yescharacteristic
706#107—434no—
707#107—434no—
708#107—434no—
709#107—434no—
710#106—434no—
711#106—434no—
712#106—434no—
713#106—434no—
714C4⋊C8—434no—
715C4⋊C8—434no—
716#103—434no—
717#103—434no—
718#103C22×D4314yes—
719#103C22×D4314yes—
720#102—434no—
721#102—434no—
722#102C22×D4314yes—
723#102C22×D4314yes—
724C22⋊C8—434no—
725C22⋊C8—434no—
726#97—432no—
727#97—432no—
728#97C22×D4312yes—
729#97C22×D4312yes—
730C24—431no—
731#41—28no—
732#41—1724no—
733#41—1724no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—862no—
737C2×Q8—862no—
738C2×Q8—861no—
739C2×Q8—861no—
740C2×Q8—861no—
741C2×Q8—861no—
742C2×Q8—1724no—
743C2×Q8—1724no—
744C2×Q8C23×D4312yes—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—862no—
749C2×D4—862no—
750C2×D4C23×D4312yes—
751C22×C4—22no—
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—431no—
767C22×C4—862no—
768C22×C4—862no—
769C22×C4—862no—
770C22×C4—862no—
771C22×C4—864no—
772C22×C4—1722no—
773C22×C4—1722no—
774C22×C4D4×D4311yescharacteristic
775C22×C4D4×D4311yescharacteristic
776C22×C4C23×D4311yescharacteristic
777C2×C8—24no—
778C2×C8—434no—
779C2×C8—864no—
780C2×C8C23×D4314yes—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—432no—
788C4⋊C4—432no—
789C4⋊C4—432no—
790C4⋊C4—432no—
791C4⋊C4—862no—
792C4⋊C4—862no—
793C4⋊C4—862no—
794C4⋊C4—862no—
795C4⋊C4—862no—
796C4⋊C4—862no—
797C4⋊C4—862no—
798C4⋊C4—862no—
799C4⋊C4—862no—
800C4⋊C4—862no—
801C4⋊C4—862no—
802C4⋊C4—862no—
803C4⋊C4—862no—
804C4⋊C4—862no—
805C4⋊C4—861no—
806C4⋊C4—861no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—862no—
810C4⋊C4—862no—
811C4⋊C4C23×D4312yes—
812C4⋊C4C23×D4312yes—
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—22no—
816C22⋊C4—862no—
817C22⋊C4—862no—
818C22⋊C4—862no—
819C22⋊C4—862no—
820C22⋊C4—862no—
821C22⋊C4—862no—
822C22⋊C4—862no—
823C22⋊C4—862no—
824C22⋊C4—862no—
825C22⋊C4—862no—
826C42—22no—
827C42—431no—
828C42—431no—
829C42—431no—
830C42—431no—
831C42—431no—
832C42—431no—
833C42—431no—
834C42—431no—
835C42—431no—
836C42—431no—
837C42—431no—
838C42—431no—
839C42—862no—
840C42—862no—
841C42—862no—
842C42—862no—
843C42—862no—
844C42—862no—
845C42D4×D4311yescharacteristic
846C42D4×D4311yescharacteristic
847C42C23×D4311yescharacteristic
848C42C23×D4311yescharacteristic
849C23—22no—
850C23—431no—
851C23—431no—
852C23—862no—
853C23—862no—
854C23—1721no—
855C23C2×D4×D4311yescharacteristic
856Q8—24no—
857Q8—42no—
858Q8—42no—
859Q8—1722no—
860Q8—1722no—
861Q8—1722no—
862Q8—1722no—
863Q8—1724no—
864Q8—1724no—
865D4—24no—
866D4—42no—
867D4—42no—
868D4—44no—
869D4—1724no—
870D4—1724no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—44no—
877C2×C4—431no—
878C2×C4—431no—
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—862no—
896C2×C4—862no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1724no—
902C2×C4—1724no—
903C2×C4—1724no—
904C2×C4—1721no—
905C2×C4—1724no—
906C2×C4C2×D4×D4311yescharacteristic
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4C2×D4×D4311yescharacteristic
911C2×C4#1306337214yes—
912C2×C4C24×D4311yescharacteristic
913C8—24no—
914C8—864no—
915C22—21no—
916C22—21no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—432no—
921C22—861no—
922C22—861no—
923C22—861no—
924C22—861no—
925C22—861no—
926C22—1724no—
927C22#1458346912yes—
928C22C22×D4×D4311yescharacteristic
929C4—21no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—432no—
937C4—861no—
938C4—861no—
939C4—861no—
940C4—861no—
941C4—861no—
942C4—1722no—
943C4—1722no—
944C4—1722no—
945C4—1722no—
946C4#1458346912yes—
947C4C2×#1306337212yes—
948C2—22no—
949C2—82no—
950C2—862no—
951C2—1721no—
952C2C2×#1458346911yescharacteristic
953C2#575×D4311yescharacteristic
954C2#575×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3135C2
socleC22×C43C23×D4
prime radical#19147890C2
hypercenter#3135D43
hypocenterC43#60854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3135

Complements

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

NH ≅ G/Ntype
2. #533×D43C2semidirect
3. #19145832C2semidirect
4. #19145830C2semidirect
5. #19145821C2semidirect
6. #19145812C2semidirect
7. #19145804C2semidirect
8. #19145796C2semidirect
9. #19145788C2semidirect
10. #19145780C2semidirect
11. #19145119C2semidirect
12. #19145117C2semidirect
13. #19144940C2semidirect
14. #19144506C2semidirect
15. #19144379C2semidirect
16. C2×#14582954C2semidirect
17. C43×#3135C2semidirect
53. #14583309C22semidirect
54. #14583309C22semidirect
55. #14583308C22semidirect
56. #14583308C22semidirect
57. #14583308C22semidirect
58. #14583308C22semidirect
59. #14583305C22semidirect
60. #14583305C22semidirect
61. #14583267C22semidirect
62. #14583263C22semidirect
63. #14583258C22semidirect
64. #14583258C22semidirect
73. #14583208C22semidirect
74. #14583204C22semidirect
75. #14583201C22semidirect
76. #14583197C22semidirect
77. #14583192C22semidirect
78. #14583187C22semidirect
79. #14583182C22semidirect
80. #14583177C22semidirect
93. C43×#491C22semidirect
94. C43×#490C22semidirect
95. C43×#489C22semidirect
96. C43×#489C22semidirect
484. #3135D43semidirect
541. #491C2×D43semidirect
543. #490C2×D43semidirect
546. #489C2×D43semidirect
547. #489C2×D43semidirect
576. C43#60854semidirect

Maximal subgroups

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

subgroupindex
#191478902
#533×D432
#191458322
#191458302
#191458212
#191458122
#191458042
#191457962
#191457882
#191457802
#191451192
#191451172
#191449402
#191445062
#191443792
C2×#145829542
C43×#31352
#6085443