Finite Group Databasebeta

← #25968923

Subgroups — #25968923

Order 11008.

1788 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic, complemented
2C2×#14583428C211yesmaximal, characteristic
3#19145832C212yesmaximal, complemented
4#19145830C212yesmaximal, complemented
5#19145821C212yesmaximal, complemented
6#19145812C212yesmaximal, complemented
7#19145769C214yesmaximal, complemented
8#19145758C214yesmaximal, complemented
9#19145148C211yesmaximal, characteristic, complemented
10#19145147C211yesmaximal, characteristic, complemented
11#19144981C211yesmaximal, characteristic, complemented
12#19144541C212yesmaximal, complemented
13#19144533C212yesmaximal
14#19144397C212yesmaximal, complemented
15#19144389C212yesmaximal, complemented
16#19143226C211yesmaximal, characteristic, complemented
17C43×#3140C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455C2212yescomplemented
20#14583454C2211yescharacteristic, complemented
21#14583454C2211yescharacteristic, complemented
22#14583453—21no—
23#14583453—21no—
24#14583452C2212yes—
25#14583451—21no—
26#14583451—21no—
27C4⋊Q8×D43C2211yescharacteristic, complemented
28C4⋊Q8×D43C2211yescharacteristic, complemented
29#14583428—21no—
30#14583428—21no—
31#14583428—21no—
32#14583428—21no—
33#14583428C2212yes—
34#14583428C2212yes—
35#14583428C2212yes—
36#14583428C2212yes—
37C2×#13063318—21no—
38C2×#13063317C2211yescharacteristic
39#125×D43C2212yescomplemented
40C2×#13063307—21no—
41C2×#13063301C2211yescharacteristic
42C22⋊Q8×D43—21no—
43C22⋊Q8×D43—21no—
44C2×#13063296C2211yescharacteristic
45C2×Q8×Dic43C2211yescharacteristic
46C4×Q8×D43—21no—
47C4×Q8×D43—21no—
48C2×D4×Dic43C2211yescharacteristic
49C2×(C22⋊D43)⋊C4—21no—
50C2×#13063281—21no—
51#117×D43C2212yes—
52C2×C42×D43C2211yescharacteristic
53#14583308C2212yescomplemented
54#14583308C2212yescomplemented
55#14583305C2212yescomplemented
56#14583305C2212yescomplemented
57#14583301C2214yescomplemented
58#14583298C2214yescomplemented
59#14583258C2212yescomplemented
60#14583258C2212yescomplemented
61#14583253C2214yescomplemented
62#14583239C2214yescomplemented
63#14583238C2214yescomplemented
64#14583233C2214yescomplemented
65#14583228C2214yescomplemented
66#14583222C2214yes—
67#14583221C2214yes—
68#14583216C2214yes—
69#14583211C2214yes—
70#14583208C2214yescomplemented
71#14583204C2214yescomplemented
72#14583201C2214yescomplemented
73#14583197C2214yescomplemented
74#14583192C2214yescomplemented
75#14583187C2214yescomplemented
76#14583182C2214yescomplemented
77#14583177C2214yescomplemented
78#14582954C2212yescomplemented
79#14582954C2212yescomplemented
80#14582950C2212yescomplemented
81#14582950C2212yescomplemented
82#14582942C2212yes—
83#14582942C2212yes—
84#14582941C2212yes—
85#14582941C2212yes—
86#14582922C2212yes—
87#14582908C2212yes—
88#14582904C2212yes—
89#14582862C2212yes—
90C4×#10621877C2211yescharacteristic
91C43×#533C2211yescharacteristic
92C2×#124×C43C2211yescharacteristic
93C43×#489C2212yescomplemented
94C43×#489C2212yescomplemented
95C43×#488C2214yescomplemented
96C43×#419C2212yes—
97C43×#418C2212yes—
98C4×M16×C43C2211yescharacteristic
99C2×Q8×D43—21no—
100C2×Q8×D43—21no—
101C22×C22⋊D43—21no—
102C23×Dic43—21no—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×#10621877C2312yes—
107#13063325C2311yescharacteristic
108#13063325C2311yescharacteristic
109#13063324—21no—
110#13063324—21no—
111#13063324C2312yes—
112#13063324C2312yes—
113#13063323—21no—
114#13063323—21no—
115#13063318—22no—
116#13063318—22no—
117#13063318—22no—
118#13063318—22no—
119#13063317—21no—
120#13063317—21no—
121#13063317C2312yes—
122#13063317C2312yes—
123#13063317C2312yes—
124#13063316C2312yes—
125#13063316C2312yes—
126#13063315—22no—
127#13063315—22no—
128#13063307—22no—
129#13063307—22no—
130#13063307—22no—
131#13063307—22no—
132#13063305—21no—
133#13063305—21no—
134#13063304—21no—
135#13063304—21no—
136#13063303—22no—
137#13063303—22no—
138#13063302—22no—
139#13063302—22no—
140#13063301—21no—
141#13063301—21no—
142#13063301—21no—
143#13063301—21no—
144#13063301C2312yes—
145#13063301C2312yes—
146#13063296—21no—
147#13063296—21no—
148#13063296C2312yes—
149#13063296C2312yes—
150Q8×Dic43—21no—
151Q8×Dic43—21no—
152Q8×Dic43—21no—
153Q8×Dic43—21no—
154Q8×Dic43C2312yes—
155Q8×Dic43C2312yes—
156C4×Dic86—21no—
157C4×Dic86—21no—
158C4×Dic86—22no—
159C4×Dic86—22no—
160#13063290—21no—
161#13063290—21no—
162#13063290—22no—
163#13063290—22no—
164D4×Dic43—21no—
165D4×Dic43—21no—
166D4×Dic43C2312yes—
167D4×Dic43C2312yes—
168(C22⋊D43)⋊C4—22no—
169(C22⋊D43)⋊C4—22no—
170(C22⋊D43)⋊C4—22no—
171(C22⋊D43)⋊C4—22no—
172#13063284C2312yes—
173#13063283C2312yes—
174#13063283C2312yes—
175#13063282—22no—
176#13063281—22no—
177#13063281—22no—
178#13063281—22no—
179#13063281—22no—
180#13063281—22no—
181C2×C4⋊Dic43—21no—
182C2×C4⋊Dic43C2311yescharacteristic
183C2×C4⋊Dic43C2311yescharacteristic
184C2×Dic43⋊C4—21no—
185C2×Dic43⋊C4—21no—
186C2×Dic43⋊C4—21no—
187C4⋊C4×D43—22no—
188C4⋊C4×D43—22no—
189C4⋊C4×D43—21no—
190C4⋊C4×D43—21no—
191C4⋊C4×D43C2312yes—
192C4⋊C4×D43C2312yes—
193C2×C22⋊Dic43—21no—
194C2×C22⋊Dic43—21no—
195C2×(C2×D43)⋊C4—21no—
196C22⋊C4×D43—22no—
197C2×C4×Dic43—21no—
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—
227C4×C43⋊C8C2312yes—
228C22×Q8×C43C2311yescharacteristic
229C22×D4×C43C2311yescharacteristic
230C2×M16×C43C2312yes—
231C4⋊Q8×C43C2311yescharacteristic
232C4⋊Q8×C43C2311yescharacteristic
233#125×C43C2312yes—
234#124×C43—21no—
235#124×C43—21no—
236#124×C43C2312yes—
237#124×C43C2312yes—
238C22⋊Q8×C43—21no—
239C22⋊Q8×C43—21no—
240C4×Q8×C43—21no—
241C4×Q8×C43—21no—
242#117×C43C2312yes—
243C2×C22⋊C4×C43—21no—
244C2×C22⋊C4×C43—21no—
245C2×C42×C43C2311yescharacteristic
246#103×C43C2314yes—
247#103×C43C2314yes—
248#102×C43C2314yes—
249#102×C43C2314yes—
250#97×C43C2312yes—
251C4×C8×C43C2312yes—
252C24×C43—21no—
253C23×D43C2×D411yescharacteristic
254C2×Q8×C43—21no—
255C2×Q8×C43—21no—
256C2×Q8×C43—21no—
257C2×Q8×C43—24no—
258C2×Q8×C43C2412yes—
259C2×D4×C43—21no—
260C2×D4×C43—24no—
261C2×D4×C43C2412yes—
262C22×C4×C43—21no—
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266C2×C22⋊D43—22no—
267C2×C22⋊D43—22no—
268C2×C22⋊D43—44no—
269C22×Dic43—22no—
270C22×Dic43—22no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—44no—
274C22×Dic43C2×D411yescharacteristic
275C22×Dic43C2×D411yescharacteristic
276C22×Dic43C2×D411yescharacteristic
277Q8×D43—44no—
278Q8×D43—44no—
279C2×C4×D43—24no—
280C2×C4×D43—22no—
281C2×C4×D43—22no—
282C2×C4×D43—42no—
283C2×C4×D43—42no—
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×D43C2×D411yescharacteristic
292C2×C4×D43C2×D411yescharacteristic
293C2×C4×D43C2×D411yescharacteristic
294C2×C4×D43C2411yescharacteristic
295C2×C4×D43C2411yescharacteristic
296C2×Dic86—21no—
297C2×Dic86—21no—
298C2×Dic86—22no—
299C2×Dic86—22no—
300M16×C43—24no—
301C2×C8×C43C2414yes—
302C4⋊C4×C43—22no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—21no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43C2412yes—
307C4⋊C4×C43C2412yes—
308C22⋊C4×C43—22no—
309C22⋊C4×C43—22no—
310C22⋊C4×C43—22no—
311C22⋊C4×C43—22no—
312C22⋊C4×C43—22no—
313C42×C43—22no—
314C42×C43C2×D411yescharacteristic
315C42×C43C2×D411yescharacteristic
316C42×C43C2411yescharacteristic
317C42×C43C2411yescharacteristic
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—
351Dic43⋊C4—22no—
352Dic43⋊C4—22no—
353C4×Dic43—22no—
354C4×Dic43—22no—
355C4×Dic43—22no—
356C4×Dic43—22no—
357C4×Dic43—22no—
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×Dic43C2×D411yescharacteristic
368C4×Dic43C2411yescharacteristic
369C4×Dic43C2411yescharacteristic
370#10621877—24no—
371C2×C43⋊C8C2414yes—
372C23×C43—22no—
373C23×C43—42no—
374C23×C43—42no—
375C23×C43—42no—
376C23×C43C22×D411yescharacteristic
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—41no—
380C22×D43C22×D411yescharacteristic
381C22×D43C22×D411yescharacteristic
382Q8×C43—24no—
383Q8×C43—42no—
384Q8×C43—42no—
385Q8×C43—42no—
386D4×C43—24no—
387D4×C43—42no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—42no—
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C22×D411yescharacteristic
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43C22×D411yescharacteristic
399C2×C4×C432−1+414yes—
400C2×C4×C43C2511yescharacteristic
401C22⋊D43—44no—
402C22⋊D43—44no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—41no—
410C2×Dic43—44no—
411C2×Dic43—42no—
412C2×Dic43—42no—
413C2×Dic43—44no—
414C2×Dic43C22×D411yescharacteristic
415C2×Dic43C22×D411yescharacteristic
416C2×Dic43C22×D411yescharacteristic
417C2×Dic43C22×D411yescharacteristic
418C2×Dic43C22×D411yescharacteristic
419C2×Dic43C22×D411yescharacteristic
420C4×D43—22no—
421C4×D43—22no—
422C4×D43—22no—
423C4×D43—22no—
424C4×D43—22no—
425C4×D43—22no—
426C4×D43—22no—
427C4×D43—22no—
428C4×D43—41no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—44no—
433C4×D43—44no—
434Dic86—44no—
435Dic86—42no—
436Dic86—42no—
437Dic86—44no—
438C8×C43—24no—
439C43⋊C8—24no—
440#60866—431nomaximal, Sylow
441C22×C43—21no—
442C22×C43—21no—
443C22×C43—42no—
444C22×C43—42no—
445C22×C43—42no—
446C22×C43—84no—
447C22×C43#53612yes—
448C22×C43C23×D411yescharacteristic
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—21no—
454C2×D43—44no—
455C2×D43#57512yes—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—42no—
461C4×C43—42no—
462C4×C43—42no—
463C4×C43#53612yes—
464C4×C43C2×2−1+412yes—
465Dic43—21no—
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—42no—
471Dic43—42no—
472Dic43—42no—
473Dic43—42no—
474Dic43#57512yes—
475C2×#533—431no—
476C2×#529—431no—
477#3240—432no—
478#3240—432no—
479#3239—432no—
480#3238—432no—
481#3233—434no—
482#3232—434no—
483#3166—431no—
484#3166—431no—
485#3140—431no—
486#3140D4311yescharacteristic, complemented
487#3095—432no—
488#3094—432no—
489#3078—432no—
490#3077—432no—
491#2920—431no—
492C2×C43—22no—
493C2×C43—82no—
494C2×C43C2×#53611yescharacteristic
495C2×C43C2×#57511yescharacteristic
496C2×C43C2×#57511yescharacteristic
497D43—22no—
498D43—41no—
499#533—431no—
500#533—431no—
501#533—432no—
502#533—432no—
503#533—431no—
504#533—861no—
505#533—861no—
506#533—861no—
507#533—861no—
508#533C2×D4311yescharacteristic
509C2×C4⋊Q8—431no—
510C2×C4⋊Q8—431no—
511#529—432no—
512#529—432no—
513#529—432no—
514#529—432no—
515#529—861no—
516#529—861no—
517#529—861no—
518#529—861no—
519C2×#126—861no—
520C2×#125—432no—
521C2×#125—431no—
522C2×#124C2×D4311yescharacteristic
523C2×#123—861no—
524C2×C22⋊Q8—431no—
525C2×C22⋊Q8—861no—
526C2×C22⋊Q8—861no—
527C2×#121—431no—
528C2×C4×Q8—431no—
529C2×C4×Q8—861no—
530C2×C4×Q8—861no—
531C2×C4×D4—431no—
532C2×C4×D4—861no—
533C2×#117—432no—
534C2×#117—861no—
535C22×C42—431no—
536#501—432no—
537#501—432no—
538#501—432no—
539#501—432no—
540#499—434no—
541#499—434no—
542#489—432no—
543#489—432no—
544#489C2×D4312yescomplemented
545#489C2×D4312yescomplemented
546#488—434no—
547#488C2×D4314yescomplemented
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#431—432no—
567#431—432no—
568#428—432no—
569#428—432no—
570#428—432no—
571#428—432no—
572#423—432no—
573#419—432no—
574#419C2×D4312yes—
575#418—432no—
576#418C2×D4312yes—
577#407—432no—
578C4×M16—431no—
579C4×M16C2×D4311yescharacteristic
580C43#6086611yescharacteristic, complemented, Sylow
581C22×Q8—861no—
582C22×Q8—861no—
583C22×Q8C22×D4311yescharacteristic
584C22×D4—861no—
585C22×D4C22×D4311yescharacteristic
586C23×C4—431no—
587C23×C4—431no—
588C23×C4—431no—
589C23×C4—861no—
590C2×M16—432no—
591C2×M16C22×D4312yes—
592C4⋊Q8—432no—
593C4⋊Q8—432no—
594C4⋊Q8—431no—
595C4⋊Q8—431no—
596C4⋊Q8—861no—
597C4⋊Q8—861no—
598C4⋊Q8—861no—
599C4⋊Q8—861no—
600C4⋊Q8C22×D4311yescharacteristic
601C4⋊Q8C22×D4311yescharacteristic
602#126—862no—
603#126—862no—
604#126—862no—
605#126—862no—
606#125—432no—
607#125—432no—
608#125—432no—
609#125—432no—
610#125—432no—
611#125—862no—
612#125—862no—
613#125—861no—
614#125—861no—
615#125C22×D4312yes—
616#124—21no—
617#124—21no—
618#124C22×D4312yes—
619#124C22×D4312yes—
620#123—862no—
621#123—862no—
622#123—862no—
623#123—862no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8—432no—
627C22⋊Q8—432no—
628C22⋊Q8—862no—
629C22⋊Q8—862no—
630C22⋊Q8—862no—
631C22⋊Q8—862no—
632C22⋊Q8—861no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635C22⋊Q8—861no—
636C22⋊Q8—861no—
637C22⋊Q8—861no—
638C22⋊Q8—861no—
639C22⋊Q8—861no—
640#121—432no—
641#121—432no—
642#121—861no—
643#121—861no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—432no—
647C4×Q8—432no—
648C4×Q8—862no—
649C4×Q8—862no—
650C4×Q8—862no—
651C4×Q8—861no—
652C4×Q8—862no—
653C4×Q8—861no—
654C4×Q8—861no—
655C4×Q8—861no—
656C4×Q8—861no—
657C4×Q8—861no—
658C4×Q8—861no—
659C4×Q8—861no—
660C4×D4—432no—
661C4×D4—432no—
662C4×D4—861no—
663C4×D4—861no—
664C4×D4—862no—
665C4×D4—862no—
666C4×D4—862no—
667C4×D4—862no—
668#117—432no—
669#117—432no—
670#117—432no—
671#117—862no—
672#117—862no—
673#117—862no—
674#117—862no—
675#117—862no—
676#117—862no—
677#117C22×D4312yes—
678C2×C4⋊C4—431no—
679C2×C4⋊C4—431no—
680C2×C4⋊C4—432no—
681C2×C4⋊C4—432no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—861no—
685C2×C4⋊C4—861no—
686C2×C4⋊C4—861no—
687C2×C4⋊C4—861no—
688C2×C4⋊C4—861no—
689C2×C4⋊C4—861no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C22⋊C4—861no—
696C2×C42—431no—
697C2×C42—431no—
698C2×C42—431no—
699C2×C42—431no—
700C2×C42—431no—
701C2×C42—431no—
702C2×C42—431no—
703C2×C42—431no—
704C2×C42—431no—
705C2×C42—431no—
706C2×C42—431no—
707C2×C42—862no—
708C2×C42—861no—
709C2×C42C22×D4311yescharacteristic
710#107—434no—
711#107—434no—
712#107—434no—
713#107—434no—
714#106—434no—
715#106—434no—
716#106—434no—
717#106—434no—
718C4⋊C8—434no—
719C4⋊C8—434no—
720#103—434no—
721#103—434no—
722#103C22×D4314yes—
723#103C22×D4314yes—
724#102—434no—
725#102—434no—
726#102C22×D4314yes—
727#102C22×D4314yes—
728C22⋊C8—434no—
729C22⋊C8—434no—
730#97—432no—
731#97C22×D4312yes—
732C4×C8—432no—
733C4×C8C22×D4312yes—
734C24—21no—
735C24—431no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—24no—
740C2×Q8—862no—
741C2×Q8—862no—
742C2×Q8—861no—
743C2×Q8—861no—
744C2×Q8—1724no—
745C2×Q8—1724no—
746C2×Q8C23×D4312yes—
747C2×D4—21no—
748C2×D4—24no—
749C2×D4—862no—
750C2×D4—862no—
751C2×D4—1724no—
752C2×D4C23×D4312yes—
753C22×C4—21no—
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—431no—
768C22×C4—431no—
769C22×C4—862no—
770C22×C4—862no—
771C22×C4—862no—
772C22×C4—862no—
773C22×C4—864no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—1722no—
777C22×C4—1722no—
778C22×C4—1724no—
779C22×C4D4×D4311yescharacteristic
780C22×C4D4×D4311yescharacteristic
781C22×C4C23×D4311yescharacteristic
782M16—24no—
783M16—864no—
784C2×C8—434no—
785C2×C8C23×D4314yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—432no—
791C4⋊C4—432no—
792C4⋊C4—432no—
793C4⋊C4—432no—
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—862no—
806C4⋊C4—861no—
807C4⋊C4—861no—
808C4⋊C4—862no—
809C4⋊C4—862no—
810C4⋊C4—862no—
811C4⋊C4—862no—
812C4⋊C4—862no—
813C4⋊C4—862no—
814C4⋊C4—861no—
815C4⋊C4—861no—
816C4⋊C4C23×D4312yes—
817C4⋊C4C23×D4312yes—
818C22⋊C4—22no—
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—862no—
824C22⋊C4—862no—
825C22⋊C4—862no—
826C22⋊C4—862no—
827C22⋊C4—862no—
828C22⋊C4—862no—
829C22⋊C4—862no—
830C22⋊C4—862no—
831C22⋊C4—862no—
832C42—22no—
833C42—431no—
834C42—431no—
835C42—431no—
836C42—431no—
837C42—431no—
838C42—431no—
839C42—431no—
840C42—431no—
841C42—431no—
842C42—431no—
843C42—431no—
844C42—431no—
845C42—862no—
846C42—862no—
847C42—862no—
848C42—862no—
849C42—862no—
850C42D4×D4311yescharacteristic
851C42D4×D4311yescharacteristic
852C42C23×D4311yescharacteristic
853C42C23×D4311yescharacteristic
854C23—22no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—431no—
859C23—431no—
860C23—862no—
861C23—862no—
862C23—1721no—
863C23C2×D4×D4311yescharacteristic
864Q8—24no—
865Q8—42no—
866Q8—42no—
867Q8—42no—
868Q8—1722no—
869Q8—1722no—
870Q8—1724no—
871Q8—1724no—
872D4—24no—
873D4—42no—
874D4—1724no—
875D4—1724no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—431no—
883C2×C4—431no—
884C2×C4—431no—
885C2×C4—431no—
886C2×C4—431no—
887C2×C4—431no—
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—862no—
898C2×C4—862no—
899C2×C4—862no—
900C2×C4—862no—
901C2×C4—862no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1724no—
907C2×C4—1724no—
908C2×C4—1724no—
909C2×C4—1721no—
910C2×C4—1724no—
911C2×C4—1722no—
912C2×C4—1722no—
913C2×C4C2×D4×D4311yescharacteristic
914C2×C4C2×D4×D4311yescharacteristic
915C2×C4C2×D4×D4311yescharacteristic
916C2×C4C2×D4×D4311yescharacteristic
917C2×C4C2×D4×D4311yescharacteristic
918C2×C4#1306337214yes—
919C2×C4C24×D4311yescharacteristic
920C8—24no—
921C8—864no—
922C22—21no—
923C22—21no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—84no—
928C22—432no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—861no—
934C22—1724no—
935C22#1458346912yes—
936C22C22×D4×D4311yescharacteristic
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—432no—
945C4—861no—
946C4—861no—
947C4—861no—
948C4—861no—
949C4—861no—
950C4—1722no—
951C4—1722no—
952C4—1722no—
953C4—1722no—
954C4#1458346912yes—
955C4C2×#1306337212yes—
956C2—22no—
957C2—82no—
958C2—862no—
959C2—1721no—
960C2C2×#1458346911yescharacteristic
961C2#575×D4311yescharacteristic
962C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3140C2
socleC22×C43C23×D4
prime radicalC2×#13063296C22
hypercenter#3140D43
hypocenterC43#60866
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3140

Complements

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

NH ≅ G/Ntype
1. #533×D43C2semidirect
3. #19145832C2semidirect
4. #19145830C2semidirect
5. #19145821C2semidirect
6. #19145812C2semidirect
7. #19145769C2semidirect
8. #19145758C2semidirect
9. #19145148C2semidirect
10. #19145147C2semidirect
11. #19144981C2semidirect
12. #19144541C2semidirect
14. #19144397C2semidirect
15. #19144389C2semidirect
16. #19143226C2semidirect
17. C43×#3140C2semidirect
19. #14583455C22semidirect
20. #14583454C22semidirect
21. #14583454C22semidirect
27. C4⋊Q8×D43C22semidirect
28. C4⋊Q8×D43C22semidirect
39. #125×D43C22semidirect
53. #14583308C22semidirect
54. #14583308C22semidirect
55. #14583305C22semidirect
56. #14583305C22semidirect
57. #14583301C22semidirect
58. #14583298C22semidirect
59. #14583258C22semidirect
60. #14583258C22semidirect
61. #14583253C22semidirect
62. #14583239C22semidirect
63. #14583238C22semidirect
64. #14583233C22semidirect
65. #14583228C22semidirect
70. #14583208C22semidirect
71. #14583204C22semidirect
72. #14583201C22semidirect
73. #14583197C22semidirect
74. #14583192C22semidirect
75. #14583187C22semidirect
76. #14583182C22semidirect
77. #14583177C22semidirect
78. #14582954C22semidirect
79. #14582954C22semidirect
80. #14582950C22semidirect
81. #14582950C22semidirect
93. C43×#489C22semidirect
94. C43×#489C22semidirect
95. C43×#488C22semidirect
486. #3140D43semidirect
544. #489C2×D43semidirect
545. #489C2×D43semidirect
547. #488C2×D43semidirect
580. C43#60866semidirect

Maximal subgroups

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

subgroupindex
#533×D432
C2×#145834282
#191458322
#191458302
#191458212
#191458122
#191457692
#191457582
#191451482
#191451472
#191449812
#191445412
#191445332
#191443972
#191443892
#191432262
C43×#31402
#6086643