Finite Group Databasebeta

← #25969094

Subgroups — #25969094

Order 11008.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148464C211yesmaximal, characteristic
2#19148407C211yesmaximal, characteristic, complemented
3#19145854C214yesmaximal, complemented
4#19145845C214yesmaximal, complemented
5#19145734C211yesmaximal, characteristic, complemented
6#19145731C211yesmaximal, characteristic, complemented
7#19145726C211yesmaximal, characteristic, complemented
8#19145724C211yesmaximal, characteristic, complemented
9#19145720C211yesmaximal, characteristic, complemented
10#19145718C211yesmaximal, characteristic, complemented
11#19145712C211yesmaximal, characteristic, complemented
12#19145136C211yesmaximal, characteristic, complemented
13#19145106C211yesmaximal, characteristic, complemented
14#19144966C211yesmaximal, characteristic, complemented
15#486×D43C211yesmaximal, characteristic, complemented
16#19144550C214yesmaximal, complemented
17#19144423C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3228C211yesmaximal, characteristic, complemented
20#14583632—21no—
21#14583631—21no—
22Q8×Dic86—21no—
23#14583627—21no—
24#14583609—21no—
25#14583607—21no—
26#14583607—21no—
27#14583568—21no—
28#14583567—21no—
29Q8×D172—21no—
30#14583562—21no—
31#14583562—21no—
32#14583546—21no—
33#14583544—21no—
34#14583542—21no—
35#14583537—21no—
36#14583529C2212yes—
37#14583529C2212yescomplemented
38#14583527C2212yescomplemented
39#14583502C2212yes—
40#14583500C2212yes—
41#14583465C2212yes—
42#14583454C2211yescharacteristic
43#14583454C2211yescharacteristic
44#14583454C2211yescharacteristic, complemented
45#14583450C2211yescharacteristic
46#14583449C2211yescharacteristic
47#14583447C2211yescharacteristic
48C2×#13063325C2211yescharacteristic, complemented
49C4⋊Q8×D43C2211yescharacteristic
50C4⋊Q8×D43C2211yescharacteristic, complemented
51#127×D43C2211yescharacteristic
52#14583379C2212yes—
53#14583371C2212yes—
54C4×#10621898C2211yescharacteristic
55#14583306C2214yescomplemented
56#14583304C2211yescharacteristic, complemented
57#14583304C2211yescharacteristic, complemented
58#14583302C2211yescharacteristic, complemented
59#14583300C2214yescomplemented
60#14583295C2211yescharacteristic, complemented
61#14583295C2211yescharacteristic, complemented
62#14583295C2211yescharacteristic, complemented
63#14583262C2214yes—
64#14583247C2211yescharacteristic
65#14583247C2211yescharacteristic
66#14583246C2211yescharacteristic
67#14583246C2211yescharacteristic
68#14583245C2211yescharacteristic
69#14583245C2211yescharacteristic
70#14583244C2214yes—
71#14583226C2214yescomplemented
72#14583223C2214yescomplemented
73#14583221C2214yescomplemented
74#14583219C2214yescomplemented
75#14583215C2214yescomplemented
76#14583213C2214yescomplemented
77#14583211C2214yescomplemented
78#14583202C2214yescomplemented
79#14583197C2214yescomplemented
80#14583196C2214yescomplemented
81#14583189C2214yescomplemented
82#14583188C2214yescomplemented
83#14583180C2214yescomplemented
84#14583177C2214yescomplemented
85#14582959C2212yescomplemented
86#14582957C2212yescomplemented
87#14582952C2211yescharacteristic, complemented
88#14582950C2211yescharacteristic, complemented
89#14582950C2211yescharacteristic, complemented
90#14582938C2214yes—
91#14582936C2214yes—
92#14582924C2212yes—
93#14582902C2214yes—
94#102×D43C2214yes—
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#533C2211yescharacteristic, complemented
99C43×#532C2211yescharacteristic
100C43×#500C2211yescharacteristic, complemented
101C43×#498C2211yescharacteristic, complemented
102C43×#486C2211yescharacteristic
103C43×#486C2211yescharacteristic
104C43×#482C2214yescomplemented
105C43×#478C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107C2×#10621902—21no—
108C2×#10621898—21no—
109C2×#10621898C2311yescharacteristic
110C2×#10621900—21no—
111C22×Dic86—21no—
112C2×Q8×D43—21no—
113C2×Q8×D43—21no—
114C2×D4×D43—21no—
115C2×D4×D43—21no—
116C2×D4×D43C2312yes—
117C2×#10621872C2312yes—
118C2×C8×D43C2312yes—
119#13063325—21no—
120#13063325—21no—
121#13063325—22no—
122#13063325C2311yescharacteristic
123#13063325C2311yescharacteristic
124#13063325C2311yescharacteristic
125#13063325C2312yes—
126#13063324—22no—
127#13063324—22no—
128#13063324—21no—
129#13063324—21no—
130#13063324C2312yes—
131#13063324C2312yes—
132#13063323—21no—
133#13063323—21no—
134#13063322C2311yescharacteristic
135#13063321—22no—
136#13063321—21no—
137#13063321—21no—
138#13063321C2312yes—
139#13063317—22no—
140#13063316C2312yes—
141#13063316C2312yes—
142#13063316C2312yes—
143#13063315—22no—
144#13063315—22no—
145#13063314—21no—
146#13063313—21no—
147#13063312—21no—
148#13063311—22no—
149#13063309—22no—
150#13063308—22no—
151#13063307—22no—
152#13063307—22no—
153#13063305—21no—
154#13063305—21no—
155#13063305—21no—
156#13063305—22no—
157#13063305—22no—
158#13063303—22no—
159#13063303—22no—
160#13063302—22no—
161#13063302—22no—
162#13063301—21no—
163#13063301—21no—
164#13063301—21no—
165#13063300—21no—
166#13063300C2312yes—
167#13063299—21no—
168#13063299—22no—
169#13063299C2312yes—
170#13063298—22no—
171#13063297—22no—
172#13063296—21no—
173#13063296—22no—
174#13063296C2312yes—
175#13063295—22no—
176#13063293—22no—
177Q8×Dic43—21no—
178Q8×Dic43—21no—
179Q8×Dic43—21no—
180C4×Dic86—22no—
181C4×Dic86D411yescharacteristic
182C4×Dic86D411yescharacteristic
183#13063290—21no—
184#13063290—21no—
185#13063290—21no—
186C4×D172—22no—
187C4×D172—21no—
188C4×D172D411yescharacteristic
189C4×D172D411yescharacteristic
190C4×D172C2312yes—
191D4×Dic43—21no—
192D4×Dic43C2312yes—
193#13063287—21no—
194#13063287C2312yes—
195C4×C22⋊D43—22no—
196C4×C22⋊D43D411yescharacteristic
197C4×C22⋊D43D411yescharacteristic
198C4×C22⋊D43D411yescharacteristic
199C4×C22⋊D43D411yescharacteristic
200(C22⋊D43)⋊C4—22no—
201(C22⋊D43)⋊C4—22no—
202(C22⋊D43)⋊C4—22no—
203#13063284C2311yescharacteristic
204#13063283C2312yes—
205#13063283C2312yes—
206#13063283C2312yes—
207#13063282C2311yescharacteristic
208#13063282C2311yescharacteristic
209C2×C4⋊Dic43—21no—
210C2×C4⋊Dic43C2312yes—
211C4⋊C4×D43—21no—
212C4⋊C4×D43—21no—
213C4⋊C4×D43C2312yes—
214C4⋊C4×D43C2312yes—
215C2×(C2×D43)⋊C4—22no—
216C22⋊C4×D43—22no—
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219#13063259C2314yes—
220#13063259C2314yes—
221#13063258C2314yes—
222#13063256C2314yes—
223#13063256C2314yes—
224#13063256C2314yes—
225C4⋊(C43⋊C8)C2312yes—
226Dic43⋊C8C2312yes—
227Dic43⋊C8C2312yes—
228#13063247C2314yes—
229#13063247C2314yes—
230#13063246C2314yes—
231#13063246C2314yes—
232#13063245C2314yes—
233#13063245C2314yes—
234C22⋊(C43⋊C8)C2312yes—
235(C2×D43)⋊C8C2312yes—
236(C2×D43)⋊C8C2312yes—
237#13063235C2312yes—
238C4×C43⋊C8C2311yescharacteristic
239C4×C43⋊C8C2311yescharacteristic
240C8×Dic43C2312yes—
241C2×#41×C43—21no—
242C4⋊Q8×C43C2311yescharacteristic
243C4⋊Q8×C43C2311yescharacteristic
244C4⋊Q8×C43C2311yescharacteristic
245#127×C43C2311yescharacteristic
246#125×C43C2312yes—
247#124×C43—21no—
248C22⋊Q8×C43—21no—
249C22⋊Q8×C43—21no—
250#121×C43—21no—
251#121×C43C2312yes—
252C4×Q8×C43—21no—
253C4×Q8×C43—21no—
254C4×D4×C43—21no—
255C4×D4×C43C2312yes—
256#117×C43C2312yes—
257C2×C42×C43C2311yescharacteristic
258#107×C43C2314yes—
259#106×C43C2314yes—
260C4⋊C8×C43C2312yes—
261#102×C43C2314yes—
262#102×C43C2314yes—
263C22⋊C8×C43C2312yes—
264C4×C8×C43C2311yescharacteristic
265C4×C8×C43C2311yescharacteristic
266C23×D43—22no—
267#41×C43—82no—
268C2×Q8×C43—21no—
269C2×Q8×C43—21no—
270C2×Q8×C43—21no—
271C2×D4×C43—21no—
272C2×D4×C43—21no—
273C2×D4×C43—22no—
274C2×D4×C43C2412yes—
275C22×C4×C43—22no—
276C22×C4×C43C2×D411yescharacteristic
277C22×C4×C43C2×D411yescharacteristic
278C22×C4×C43C2411yescharacteristic
279C2×C22⋊D43—22no—
280C2×C22⋊D43—22no—
281C2×C22⋊D43—22no—
282C2×C22⋊D43—22no—
283C2×C22⋊D43—22no—
284C2×C22⋊D43C2×D411yescharacteristic
285C2×C22⋊D43C2×D411yescharacteristic
286C22×Dic43—22no—
287C22×Dic43—22no—
288#10621902—82no—
289Q8×D43—82no—
290Q8×D43—82no—
291#10621900—82no—
292D4×D43—28no—
293D4×D43—82no—
294D4×D43—82no—
295#10621898—24no—
296#10621898—82no—
297C2×D172—21no—
298C2×D172—21no—
299C2×D172—22no—
300C2×D172C2×D411yescharacteristic
301C2×D172C2412yes—
302C2×C4×D43—22no—
303C2×C4×D43—22no—
304C2×C4×D43—22no—
305C2×C4×D43—22no—
306C2×C4×D43C2×D411yescharacteristic
307C2×C4×D43C2×D411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2411yescharacteristic
311C2×C4×D43C2411yescharacteristic
312C2×Dic86—21no—
313C2×Dic86—21no—
314C2×Dic86—21no—
315C2×Dic86—22no—
316C2×Dic86—22no—
317C2×Dic86—22no—
318C2×Dic86—82no—
319C2×Dic86C2×D411yescharacteristic
320C2×C8×C43C2412yes—
321C2×C8×C43C2412yes—
322C4⋊C4×C43—21no—
323C4⋊C4×C43—22no—
324C4⋊C4×C43—22no—
325C4⋊C4×C43—21no—
326C4⋊C4×C43—21no—
327C4⋊C4×C43C2412yes—
328C4⋊C4×C43C2412yes—
329C4⋊C4×C43C2412yes—
330C22⋊C4×C43—22no—
331C22⋊C4×C43—22no—
332C22⋊C4×C43—22no—
333C42×C43—22no—
334C42×C43C2×D411yescharacteristic
335C42×C43C2×D411yescharacteristic
336C42×C43C2411yescharacteristic
337C42×C43C2411yescharacteristic
338C22⋊Dic43—22no—
339C22⋊Dic43—22no—
340C22⋊Dic43C2×D411yescharacteristic
341C22⋊Dic43C2×D411yescharacteristic
342(C2×D43)⋊C4—22no—
343(C2×D43)⋊C4—22no—
344(C2×D43)⋊C4—22no—
345(C2×D43)⋊C4—22no—
346(C2×D43)⋊C4—22no—
347(C2×D43)⋊C4—22no—
348(C2×D43)⋊C4—22no—
349(C2×D43)⋊C4C2×D411yescharacteristic
350(C2×D43)⋊C4C2×D411yescharacteristic
351(C2×D43)⋊C4C2×D411yescharacteristic
352(C2×D43)⋊C4C2×D411yescharacteristic
353C4⋊Dic43—21no—
354C4⋊Dic43—21no—
355C4⋊Dic43—22no—
356C4⋊Dic43—22no—
357C4⋊Dic43—21no—
358C4⋊Dic43—22no—
359C4⋊Dic43—22no—
360C4⋊Dic43—22no—
361C4⋊Dic43C2×D411yescharacteristic
362C4⋊Dic43C2×D411yescharacteristic
363C4⋊Dic43C2412yes—
364C4⋊Dic43C2412yes—
365C4⋊Dic43C2412yes—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368Dic43⋊C4—22no—
369Dic43⋊C4—22no—
370Dic43⋊C4—22no—
371Dic43⋊C4—22no—
372Dic43⋊C4—22no—
373Dic43⋊C4C2×D411yescharacteristic
374Dic43⋊C4C2×D411yescharacteristic
375Dic43⋊C4C2×D411yescharacteristic
376Dic43⋊C4C2×D411yescharacteristic
377C4×Dic43—22no—
378C4×Dic43—22no—
379C4×Dic43—22no—
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2411yescharacteristic
385C4×Dic43C2411yescharacteristic
386C2×C43⋊C8C2412yes—
387C2×C43⋊C8C2412yes—
388#10621872—24no—
389C8×D43—24no—
390C23×C43—22no—
391C23×C43C22×D411yescharacteristic
392C22×D43—22no—
393C22×D43—44no—
394C22×D43—82no—
395C22×D43—82no—
396C22×D43C22×D411yescharacteristic
397C22×D43C22×D411yescharacteristic
398Q8×C43—42no—
399Q8×C43—42no—
400Q8×C43—42no—
401D4×C43—24no—
402D4×C43—42no—
403D4×C43—42no—
404D4×C43—82no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—82no—
412C2×C4×C43C22×D411yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C22×D411yescharacteristic
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C2511yescharacteristic
418C22⋊D43—22no—
419C22⋊D43—22no—
420C22⋊D43—44no—
421C22⋊D43—82no—
422C22⋊D43—82no—
423C22⋊D43—82no—
424C22⋊D43—82no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—82no—
429C2×Dic43—82no—
430C2×Dic43C22×D411yescharacteristic
431C2×Dic43C22×D411yescharacteristic
432C2×Dic43C22×D411yescharacteristic
433C2×Dic43C22×D411yescharacteristic
434C2×Dic43C22×D411yescharacteristic
435C2×Dic43C22×D411yescharacteristic
436D172—22no—
437D172—24no—
438D172—42no—
439D172—42no—
440D172—82no—
441C4×D43—22no—
442C4×D43—22no—
443C4×D43—22no—
444C4×D43—22no—
445C4×D43—22no—
446C4×D43—82no—
447C4×D43—82no—
448C4×D43—82no—
449C4×D43—82no—
450C4×D432−1+414yes—
451Dic86—22no—
452Dic86—42no—
453Dic86—42no—
454Dic86—42no—
455Dic86—82no—
456Dic86—82no—
457Dic86—82no—
458C8×C43—22no—
459C8×C43—22no—
460C43⋊C8—22no—
461C43⋊C8—22no—
462#60877—431nomaximal, Sylow
463C22×C43—21no—
464C22×C43—21no—
465C22×C43—21no—
466C22×C43—42no—
467C22×C43—42no—
468C22×C43—42no—
469C22×C43C23×D411yescharacteristic
470C2×D43—21no—
471C2×D43—21no—
472C2×D43—21no—
473C2×D43—21no—
474C2×D43—21no—
475C2×D43—42no—
476C2×D43—42no—
477C2×D43—42no—
478C2×D43—164no—
479C2×D43#53612yes—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43—42no—
486C4×C43#57612yes—
487C4×C43#57712yes—
488C4×C43C2×2−1+412yes—
489Dic43—21no—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—42no—
495Dic43—42no—
496Dic43—42no—
497Dic43#53612yes—
498#3508—431no—
499#3503—431no—
500#3241—434no—
501#3241—434no—
502#3228—431no—
503#3228—431no—
504#3228—431no—
505#3228D4311yescharacteristic, complemented
506#3227—431no—
507#3227—431no—
508#3226—431no—
509#3226—431no—
510#3165—431no—
511#3160—431no—
512#3138—431no—
513C2×#486—431no—
514#3096—434no—
515#3081—434no—
516#2922—431no—
517C2×C43—41no—
518C2×C43—82no—
519C2×C43C2×#53611yescharacteristic
520C2×C43C2×#57611yescharacteristic
521C2×C43C2×#57711yescharacteristic
522D43—22no—
523D43—41no—
524D43—82no—
525#559—861no—
526#559—861no—
527Q82—861no—
528#557—861no—
529#554—861no—
530#554—861no—
531#554—861no—
532#550—861no—
533#550—861no—
534D4×Q8—861no—
535D4×Q8—861no—
536D4×Q8—861no—
537#546—861no—
538#546—861no—
539#546—861no—
540#546—861no—
541#544—432no—
542#544—432no—
543#544—432no—
544#540—432no—
545#540—432no—
546#535—432no—
547#533—431no—
548#533—431no—
549#533—431no—
550#533C2×D4311yescharacteristic, complemented
551#532—431no—
552#532—431no—
553#532—431no—
554#532C2×D4311yescharacteristic
555C2×C4⋊Q8—431no—
556C2×C4⋊Q8—431no—
557C2×C4⋊Q8—431no—
558C2×#127—431no—
559#520—432no—
560#518—432no—
561C4×#41—431no—
562#501—434no—
563#500—431no—
564#500—431no—
565#500—431no—
566#500C2×D4311yescharacteristic, complemented
567#499—434no—
568#498—431no—
569#498—431no—
570#498—431no—
571#498C2×D4311yescharacteristic, complemented
572#490—434no—
573#486—431no—
574#486—431no—
575#486—431no—
576#486—431no—
577#486—434no—
578#486—431no—
579#486—431no—
580#486C2×D4311yescharacteristic
581#486C2×D4311yescharacteristic
582#482—434no—
583#482—434no—
584#482—434no—
585#482C2×D4314yescomplemented
586#481—434no—
587#481—434no—
588#480—434no—
589#480—434no—
590#478—434no—
591#478—434no—
592#478—434no—
593#478C2×D4314yescomplemented
594#476—434no—
595#476—434no—
596#474—434no—
597#474—434no—
598#433—432no—
599#433—432no—
600#431—431no—
601#431—431no—
602#431—431no—
603#431C2×D4311yescharacteristic, complemented
604#428—434no—
605#427—434no—
606#424—432no—
607#418—434no—
608C2×#102—434no—
609#408—432no—
610C4×M16—431no—
611C2×C4×C8—431no—
612C43#6087711yescharacteristic, complemented, Sylow
613C2×#41—21no—
614C2×#41—431no—
615C2×#41—861no—
616C2×#41—861no—
617C2×#41—861no—
618C22×Q8—861no—
619C22×Q8—861no—
620C22×Q8—861no—
621C22×D4—432no—
622C22×D4—861no—
623C22×D4—861no—
624C2×M16—432no—
625C22×C8—432no—
626C4⋊Q8—432no—
627C4⋊Q8—432no—
628C4⋊Q8—431no—
629C4⋊Q8—431no—
630C4⋊Q8—432no—
631C4⋊Q8—431no—
632C4⋊Q8—862no—
633C4⋊Q8—861no—
634C4⋊Q8—861no—
635C4⋊Q8—861no—
636C4⋊Q8—861no—
637C4⋊Q8—862no—
638C4⋊Q8—862no—
639C4⋊Q8—861no—
640C4⋊Q8—861no—
641C4⋊Q8C22×D4311yescharacteristic
642C4⋊Q8C22×D4311yescharacteristic
643C4⋊Q8C22×D4311yescharacteristic
644#127—432no—
645#127—431no—
646#127—861no—
647#127—861no—
648#127—862no—
649#127C22×D4311yescharacteristic
650#125—432no—
651#125—432no—
652#125—432no—
653#125—862no—
654#125—862no—
655#125—862no—
656#125C22×D4312yes—
657#124—21no—
658#124—861no—
659#124—861no—
660#124—862no—
661#124—861no—
662#123—862no—
663#123—862no—
664#123—862no—
665#123—862no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—862no—
669C22⋊Q8—862no—
670C22⋊Q8—862no—
671C22⋊Q8—862no—
672C22⋊Q8—862no—
673C22⋊Q8—862no—
674C22⋊Q8—861no—
675C22⋊Q8—861no—
676C22⋊Q8—861no—
677C22⋊Q8—861no—
678C22⋊Q8—861no—
679C22⋊Q8—861no—
680#121—21no—
681#121—432no—
682#121—432no—
683#121—432no—
684#121—862no—
685#121—862no—
686#121—862no—
687#121—862no—
688#121—861no—
689#121—861no—
690#121—861no—
691#121C22×D4312yes—
692#120—862no—
693#120—862no—
694C4×Q8—21no—
695C4×Q8—21no—
696C4×Q8—431no—
697C4×Q8—431no—
698C4×Q8—862no—
699C4×Q8—861no—
700C4×Q8—861no—
701C4×Q8—861no—
702C4×Q8—861no—
703C4×Q8—861no—
704C4×Q8—861no—
705C4×D4—21no—
706C4×D4—431no—
707C4×D4—431no—
708C4×D4—431no—
709C4×D4—431no—
710C4×D4—432no—
711C4×D4—432no—
712C4×D4—431no—
713C4×D4—431no—
714C4×D4—432no—
715C4×D4—862no—
716C4×D4—861no—
717C4×D4—861no—
718C4×D4—862no—
719C4×D4—862no—
720C4×D4—862no—
721C4×D4—862no—
722C4×D4—861no—
723C4×D4C22×D4312yes—
724#117—431no—
725#117—431no—
726#117—431no—
727#117—432no—
728#117—432no—
729#117—432no—
730#117C22×D4312yes—
731C2×C4⋊C4—432no—
732C2×C4⋊C4—432no—
733C2×C4⋊C4—432no—
734C2×C4⋊C4—861no—
735C2×C4⋊C4—861no—
736C2×C4⋊C4—861no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C42—431no—
740C2×C42—431no—
741C2×C42C22×D4311yescharacteristic
742#107—434no—
743#107—434no—
744#107—434no—
745#107C22×D4314yes—
746#106—434no—
747#106—434no—
748#106—434no—
749#106C22×D4314yes—
750C4⋊C8—432no—
751C4⋊C8—432no—
752C4⋊C8—432no—
753C4⋊C8C22×D4312yes—
754#102—434no—
755#102—434no—
756#102—434no—
757#102—434no—
758#102—434no—
759#102—434no—
760#102C22×D4314yes—
761#102C22×D4314yes—
762C22⋊C8—432no—
763C22⋊C8—432no—
764C22⋊C8—432no—
765C22⋊C8C22×D4312yes—
766#97—432no—
767C4×C8—432no—
768C4×C8—431no—
769C4×C8—431no—
770C4×C8C22×D4311yescharacteristic
771C4×C8C22×D4311yescharacteristic
772C24—862no—
773#41—82no—
774#41—864no—
775#41—3442no—
776#41—3442no—
777#41—3442no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—431no—
782C2×Q8—862no—
783C2×Q8—862no—
784C2×Q8—862no—
785C2×Q8—861no—
786C2×Q8—861no—
787C2×Q8—861no—
788C2×Q8—3442no—
789C2×Q8—3442no—
790C2×Q8—3442no—
791C2×D4—22no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—431no—
795C2×D4—431no—
796C2×D4—431no—
797C2×D4—432no—
798C2×D4—862no—
799C2×D4—868no—
800C2×D4—862no—
801C2×D4—862no—
802C2×D4—862no—
803C2×D4—862no—
804C2×D4—862no—
805C2×D4—861no—
806C2×D4—861no—
807C2×D4—3442no—
808C2×D4—3442no—
809C2×D4C23×D4312yes—
810C22×C4—22no—
811C22×C4—431no—
812C22×C4—431no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—431no—
817C22×C4—862no—
818C22×C4—862no—
819C22×C4—862no—
820C22×C4—862no—
821C22×C4—862no—
822C22×C4—862no—
823C22×C4D4×D4311yescharacteristic
824C22×C4D4×D4311yescharacteristic
825C22×C4C23×D4311yescharacteristic
826M16—864no—
827C2×C8—432no—
828C2×C8—432no—
829C2×C8—864no—
830C2×C8C23×D4312yes—
831C2×C8C23×D4312yes—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—431no—
838C4⋊C4—431no—
839C4⋊C4—431no—
840C4⋊C4—431no—
841C4⋊C4—431no—
842C4⋊C4—431no—
843C4⋊C4—432no—
844C4⋊C4—432no—
845C4⋊C4—432no—
846C4⋊C4—862no—
847C4⋊C4—862no—
848C4⋊C4—862no—
849C4⋊C4—862no—
850C4⋊C4—862no—
851C4⋊C4—862no—
852C4⋊C4—862no—
853C4⋊C4—862no—
854C4⋊C4—862no—
855C4⋊C4—862no—
856C4⋊C4—862no—
857C4⋊C4—861no—
858C4⋊C4—861no—
859C4⋊C4—862no—
860C4⋊C4—861no—
861C4⋊C4C23×D4312yes—
862C4⋊C4C23×D4312yes—
863C4⋊C4C23×D4312yes—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—431no—
868C22⋊C4—431no—
869C22⋊C4—431no—
870C22⋊C4—431no—
871C22⋊C4—431no—
872C22⋊C4—431no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—862no—
876C22⋊C4—862no—
877C22⋊C4—862no—
878C22⋊C4—862no—
879C22⋊C4—862no—
880C22⋊C4—862no—
881C22⋊C4—862no—
882C42—22no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—862no—
890C42—862no—
891C42—862no—
892C42D4×D4311yescharacteristic
893C42D4×D4311yescharacteristic
894C42C23×D4311yescharacteristic
895C42C23×D4311yescharacteristic
896C23—22no—
897C23—431no—
898C23—431no—
899C23—862no—
900C23—3442no—
901C23—3442no—
902C23—1724no—
903C23C2×D4×D4311yescharacteristic
904Q8—42no—
905Q8—42no—
906Q8—42no—
907Q8—862no—
908Q8—3442no—
909Q8—3442no—
910Q8—3442no—
911Q8—1722no—
912Q8—1722no—
913Q8—1722no—
914D4—24no—
915D4—42no—
916D4—42no—
917D4—82no—
918D4—862no—
919D4—862no—
920D4—862no—
921D4—864no—
922D4—3442no—
923D4—3442no—
924D4—3442no—
925D4—3442no—
926D4—3442no—
927D4—1724no—
928D4—1722no—
929D4—1722no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—82no—
937C2×C4—431no—
938C2×C4—434no—
939C2×C4—431no—
940C2×C4—431no—
941C2×C4—431no—
942C2×C4—431no—
943C2×C4—431no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—862no—
949C2×C4—862no—
950C2×C4—862no—
951C2×C4—862no—
952C2×C4—3442no—
953C2×C4—3442no—
954C2×C4—3442no—
955C2×C4—3442no—
956C2×C4—3442no—
957C2×C4—3442no—
958C2×C4C2×D4×D4311yescharacteristic
959C2×C4C2×D4×D4311yescharacteristic
960C2×C4C2×D4×D4311yescharacteristic
961C2×C4C2×D4×D4311yescharacteristic
962C2×C4C2×D4×D4311yescharacteristic
963C2×C4C24×D4311yescharacteristic
964C8—22no—
965C8—22no—
966C8—862no—
967C8—862no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—432no—
975C22—861no—
976C22—861no—
977C22—861no—
978C22—861no—
979C22—861no—
980C22—1722no—
981C22—1722no—
982C22—1722no—
983C22—6884no—
984C22C22×D4×D4311yescharacteristic
985C4—21no—
986C4—21no—
987C4—21no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—432no—
992C4—861no—
993C4—861no—
994C4—861no—
995C4—861no—
996C4—861no—
997C4—1722no—
998C4—1722no—
999C4—1722no—
1000C4#1458370112yes—
1001C4#1458370912yes—
1002C42−1+4×D4312yes—
1003C2—41no—
1004C2—82no—
1005C2—862no—
1006C2—3442no—
1007C2—1721no—
1008C2#536×D4311yescharacteristic
1009C2C2×#1458370111yescharacteristic
1010C2C2×#1458370911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3228C2
socleC22×C43C23×D4
prime radical#19148464C2
hypercenter#3228D43
hypocenterC43#60877
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
2. #19148407C2semidirect
3. #19145854C2semidirect
4. #19145845C2semidirect
5. #19145734C2semidirect
6. #19145731C2semidirect
7. #19145726C2semidirect
8. #19145724C2semidirect
9. #19145720C2semidirect
10. #19145718C2semidirect
11. #19145712C2semidirect
12. #19145136C2semidirect
13. #19145106C2semidirect
14. #19144966C2semidirect
15. #486×D43C2semidirect
16. #19144550C2semidirect
17. #19144423C2semidirect
18. #19143234C2semidirect
19. C43×#3228C2semidirect
37. #14583529C22semidirect
38. #14583527C22semidirect
44. #14583454C22semidirect
48. C2×#13063325C22semidirect
50. C4⋊Q8×D43C22semidirect
55. #14583306C22semidirect
56. #14583304C22semidirect
57. #14583304C22semidirect
58. #14583302C22semidirect
59. #14583300C22semidirect
60. #14583295C22semidirect
61. #14583295C22semidirect
62. #14583295C22semidirect
71. #14583226C22semidirect
72. #14583223C22semidirect
73. #14583221C22semidirect
74. #14583219C22semidirect
75. #14583215C22semidirect
76. #14583213C22semidirect
77. #14583211C22semidirect
78. #14583202C22semidirect
79. #14583197C22semidirect
80. #14583196C22semidirect
81. #14583189C22semidirect
82. #14583188C22semidirect
83. #14583180C22semidirect
84. #14583177C22semidirect
85. #14582959C22semidirect
86. #14582957C22semidirect
87. #14582952C22semidirect
88. #14582950C22semidirect
89. #14582950C22semidirect
98. C43×#533C22semidirect
100. C43×#500C22semidirect
101. C43×#498C22semidirect
104. C43×#482C22semidirect
105. C43×#478C22semidirect
106. C43×#431C22semidirect
505. #3228D43semidirect
550. #533C2×D43semidirect
566. #500C2×D43semidirect
571. #498C2×D43semidirect
585. #482C2×D43semidirect
593. #478C2×D43semidirect
603. #431C2×D43semidirect
612. C43#60877semidirect

Maximal subgroups

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

subgroupindex
#191484642
#191484072
#191458542
#191458452
#191457342
#191457312
#191457262
#191457242
#191457202
#191457182
#191457122
#191451362
#191451062
#191449662
#486×D432
#191445502
#191444232
#191432342
C43×#32282
#6087743