Finite Group Databasebeta

← #25969158

Subgroups — #25969158

Order 11008.

1722 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148496C211yesmaximal, characteristic
2#19148411C211yesmaximal, characteristic, complemented
3#19145890C214yesmaximal, complemented
4#19145889C214yesmaximal, complemented
5#19145757C211yesmaximal, characteristic, complemented
6#19145756C211yesmaximal, characteristic, complemented
7#19145740C211yesmaximal, characteristic, complemented
8#19145739C211yesmaximal, characteristic, complemented
9#19145727C211yesmaximal, characteristic, complemented
10#19145726C211yesmaximal, characteristic, complemented
11#19145719C211yesmaximal, characteristic, complemented
12#19145136C211yesmaximal, characteristic, complemented
13#498×D43C211yesmaximal, characteristic, complemented
14#19144985C211yesmaximal, characteristic, complemented
15#19144914C211yesmaximal, characteristic, complemented
16#19144585C214yesmaximal, complemented
17#19144452C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3227C211yesmaximal, characteristic, complemented
20#14583629—21no—
21#14583624—21no—
22#14583618—21no—
23#14583613—21no—
24#14583610—21no—
25#14583608—21no—
26#14583604—21no—
27#14583604—21no—
28#14583599—21no—
29#14583596—21no—
30#14583564—21no—
31Q8×C22⋊D43—21no—
32Q8×C22⋊D43—21no—
33#14583557—21no—
34#14583556—21no—
35#14583548—21no—
36#14583530C2212yes—
37#14583526C2212yes—
38#14583526C2212yes—
39#14583516C2212yes—
40#14583514C2212yes—
41#14583478C2212yes—
42#14583456C2211yescharacteristic
43#14583456C2211yescharacteristic
44#14583454C2211yescharacteristic
45#14583454C2211yescharacteristic
46#14583454C2211yescharacteristic
47#14583447C2211yescharacteristic
48#14583447C2211yescharacteristic
49C4⋊Q8×D43C2211yescharacteristic
50C4⋊Q8×D43C2211yescharacteristic
51C4⋊Q8×D43C2211yescharacteristic
52#14583380C2212yes—
53#14583378C2212yes—
54C4×#10621898C2211yescharacteristic
55#14583306C2214yes—
56#14583304C2211yescharacteristic
57#14583302C2211yescharacteristic
58#14583297C2211yescharacteristic
59#14583296C2214yes—
60#14583295C2211yescharacteristic
61#14583295C2211yescharacteristic
62#14583295C2211yescharacteristic
63#14583257C2214yes—
64#14583252C2214yes—
65#14583251C2211yescharacteristic
66#14583251C2211yescharacteristic
67#14583250C2211yescharacteristic
68#14583250C2211yescharacteristic
69#14583245C2211yescharacteristic
70#14583245C2211yescharacteristic
71#14583243C2214yes—
72#14583241C2214yes—
73#14583231C2214yes—
74#14583229C2214yes—
75#14583221C2214yes—
76#14583220C2214yes—
77#14583216C2214yes—
78#14583209C2214yes—
79#14583207C2214yes—
80#14583199C2214yes—
81#14583197C2214yes—
82#14583187C2214yes—
83#14583183C2214yes—
84#14583181C2214yes—
85#14582959C2212yes—
86#14582957C2212yes—
87#14582952C2211yescharacteristic
88#14582950C2211yescharacteristic
89#14582950C2211yescharacteristic
90#14582938C2214yes—
91#106×D43C2214yes—
92#14582924C2212yes—
93#14582897C2214yes—
94#14582892C2214yes—
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#532C2211yescharacteristic
99C2×C4⋊Q8×C43C2211yescharacteristic
100C43×#498C2211yescharacteristic
101C43×#498C2211yescharacteristic
102C43×#486C2211yescharacteristic
103C43×#486C2211yescharacteristic
104C43×#481C2214yes—
105C43×#476C2214yes—
106C43×#431C2211yescharacteristic
107C2×#10621898C2311yescharacteristic
108C2×#10621900—21no—
109C2×#10621900C2312yes—
110C2×Q8×D43—21no—
111C2×Q8×D43—21no—
112C2×Q8×D43—21no—
113C2×#10621872C2312yes—
114C2×C8×D43C2312yes—
115#13063325C2311yescharacteristic
116#13063325C2311yescharacteristic
117#13063325C2311yescharacteristic
118#13063325C2311yescharacteristic
119#13063324—22no—
120#13063324—21no—
121#13063324—21no—
122#13063324—21no—
123#13063324C2312yes—
124#13063324C2312yes—
125#13063324C2312yes—
126#13063323—22no—
127#13063323—22no—
128#13063323—21no—
129#13063323—21no—
130#13063323—21no—
131#13063318—22no—
132#13063318—22no—
133#13063317—21no—
134#13063317C2312yes—
135#13063316—22no—
136#13063316—21no—
137#13063316C2312yes—
138#13063316C2312yes—
139#13063315—22no—
140#13063315—22no—
141#13063312—22no—
142#13063312—21no—
143#13063312C2312yes—
144#13063311—22no—
145#13063308—22no—
146#13063306—22no—
147#13063305—21no—
148#13063305—21no—
149#13063305C2312yes—
150#13063304—21no—
151#13063304—21no—
152#13063304—21no—
153#13063304—22no—
154#13063304—22no—
155#13063304—22no—
156#13063304C2312yes—
157#13063303—22no—
158#13063303—22no—
159#13063302—22no—
160#13063302—22no—
161#13063301—21no—
162#13063301—21no—
163#13063301—21no—
164#13063301—22no—
165#13063301—22no—
166#13063298—22no—
167#13063297—22no—
168#13063296—22no—
169#13063296—21no—
170#13063296—21no—
171#13063296—21no—
172#13063296C2312yes—
173Q8×Dic43—21no—
174Q8×Dic43—21no—
175Q8×Dic43—21no—
176C4×Dic86—21no—
177C4×Dic86—21no—
178C4×Dic86—21no—
179C4×Dic86D411yescharacteristic
180C4×Dic86D411yescharacteristic
181C4×Dic86C2312yes—
182#13063290—22no—
183#13063290—21no—
184#13063290—21no—
185#13063290C2312yes—
186C4×D172D411yescharacteristic
187C4×D172D411yescharacteristic
188D4×Dic43—21no—
189D4×Dic43—21no—
190D4×Dic43—21no—
191D4×Dic43C2312yes—
192#13063287—22no—
193C4×C22⋊D43—22no—
194C4×C22⋊D43—22no—
195C4×C22⋊D43—22no—
196C4×C22⋊D43D411yescharacteristic
197C4×C22⋊D43D411yescharacteristic
198C4×C22⋊D43D411yescharacteristic
199C4×C22⋊D43D411yescharacteristic
200(C22⋊D43)⋊C4—22no—
201#13063284—21no—
202#13063284C2312yes—
203#13063284C2311yescharacteristic
204#13063283—21no—
205#13063283C2312yes—
206#13063283C2312yes—
207#13063282C2311yescharacteristic
208#13063282C2311yescharacteristic
209#13063281—22no—
210C2×Dic43⋊C4—22no—
211C4⋊C4×D43—21no—
212C4⋊C4×D43—21no—
213C4⋊C4×D43—21no—
214C4⋊C4×D43C2312yes—
215C4⋊C4×D43C2312yes—
216C4⋊C4×D43C2312yes—
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219#13063259C2314yes—
220#13063258C2314yes—
221#13063257C2314yes—
222#13063256C2314yes—
223#13063256C2314yes—
224#13063256C2314yes—
225C4⋊(C43⋊C8)C2312yes—
226Dic43⋊C8C2312yes—
227Dic43⋊C8C2312yes—
228#13063250C2314yes—
229#13063250C2314yes—
230#13063248C2314yes—
231#13063248C2314yes—
232#13063246C2314yes—
233#13063246C2314yes—
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—
242C22×Q8×C43—21no—
243C4⋊Q8×C43—21no—
244C4⋊Q8×C43—21no—
245C4⋊Q8×C43C2311yescharacteristic
246C4⋊Q8×C43C2311yescharacteristic
247C4⋊Q8×C43C2311yescharacteristic
248C4⋊Q8×C43C2312yes—
249#127×C43C2311yescharacteristic
250#124×C43—21no—
251#121×C43—21no—
252#121×C43C2312yes—
253C4×D4×C43—21no—
254C4×D4×C43C2312yes—
255C2×C4⋊C4×C43—21no—
256C2×C4⋊C4×C43C2312yes—
257C2×C42×C43C2311yescharacteristic
258#106×C43C2314yes—
259#106×C43C2314yes—
260C4⋊C8×C43C2312yes—
261#102×C43C2314yes—
262#102×C43C2314yes—
263C22⋊C8×C43C2312yes—
264C4×C8×C43C2311yescharacteristic
265C4×C8×C43C2311yescharacteristic
266#41×C43—82no—
267C2×Q8×C43—21no—
268C2×Q8×C43—21no—
269C2×Q8×C43—21no—
270C2×Q8×C43—22no—
271C2×Q8×C43—82no—
272C2×D4×C43—21no—
273C2×D4×C43—21no—
274C2×D4×C43—22no—
275C2×D4×C43C2412yes—
276C22×C4×C43—22no—
277C22×C4×C43—22no—
278C22×C4×C43C2×D411yescharacteristic
279C22×C4×C43C2×D411yescharacteristic
280C22×C4×C43C2411yescharacteristic
281C2×C22⋊D43—22no—
282C2×C22⋊D43—22no—
283C2×C22⋊D43C2×D411yescharacteristic
284C2×C22⋊D43C2×D411yescharacteristic
285C22×Dic43—22no—
286C22×Dic43—22no—
287Q8×D43—82no—
288Q8×D43—82no—
289Q8×D43—82no—
290#10621900—28no—
291#10621900—82no—
292#10621898—24no—
293C2×D172C2×D411yescharacteristic
294C2×C4×D43—22no—
295C2×C4×D43—22no—
296C2×C4×D43—22no—
297C2×C4×D43C2×D411yescharacteristic
298C2×C4×D43C2×D411yescharacteristic
299C2×C4×D43C2×D411yescharacteristic
300C2×C4×D43C2×D411yescharacteristic
301C2×C4×D43C2411yescharacteristic
302C2×C4×D43C2411yescharacteristic
303C2×Dic86—21no—
304C2×Dic86—21no—
305C2×Dic86—21no—
306C2×Dic86—22no—
307C2×Dic86—22no—
308C2×Dic86—22no—
309C2×Dic86C2×D411yescharacteristic
310C2×Dic86C2412yes—
311C2×C8×C43C2412yes—
312C2×C8×C43C2412yes—
313C4⋊C4×C43—21no—
314C4⋊C4×C43—21no—
315C4⋊C4×C43—22no—
316C4⋊C4×C43—22no—
317C4⋊C4×C43—21no—
318C4⋊C4×C43C2412yes—
319C4⋊C4×C43C2412yes—
320C4⋊C4×C43C2412yes—
321C22⋊C4×C43—22no—
322C22⋊C4×C43—22no—
323C42×C43C2×D411yescharacteristic
324C42×C43C2×D411yescharacteristic
325C42×C43C2411yescharacteristic
326C42×C43C2411yescharacteristic
327C22⋊Dic43—22no—
328C22⋊Dic43—22no—
329C22⋊Dic43—22no—
330C22⋊Dic43—22no—
331C22⋊Dic43—22no—
332C22⋊Dic43—22no—
333C22⋊Dic43C2×D411yescharacteristic
334C22⋊Dic43C2×D411yescharacteristic
335(C2×D43)⋊C4—22no—
336(C2×D43)⋊C4—22no—
337(C2×D43)⋊C4—22no—
338(C2×D43)⋊C4C2×D411yescharacteristic
339(C2×D43)⋊C4C2×D411yescharacteristic
340(C2×D43)⋊C4C2×D411yescharacteristic
341(C2×D43)⋊C4C2×D411yescharacteristic
342C4⋊Dic43—21no—
343C4⋊Dic43—21no—
344C4⋊Dic43—21no—
345C4⋊Dic43—21no—
346C4⋊Dic43—21no—
347C4⋊Dic43—22no—
348C4⋊Dic43—22no—
349C4⋊Dic43—22no—
350C4⋊Dic43C2×D411yescharacteristic
351C4⋊Dic43C2×D411yescharacteristic
352C4⋊Dic43C2412yes—
353C4⋊Dic43C2412yes—
354C4⋊Dic43C2412yes—
355Dic43⋊C4—22no—
356Dic43⋊C4—22no—
357Dic43⋊C4—22no—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368Dic43⋊C4C2×D411yescharacteristic
369Dic43⋊C4C2×D411yescharacteristic
370Dic43⋊C4C2×D411yescharacteristic
371Dic43⋊C4C2×D411yescharacteristic
372C4×Dic43—22no—
373C4×Dic43—22no—
374C4×Dic43—22no—
375C4×Dic43—22no—
376C4×Dic43—22no—
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2411yescharacteristic
382C4×Dic43C2411yescharacteristic
383C2×C43⋊C8C2412yes—
384C2×C43⋊C8C2412yes—
385#10621872—24no—
386C8×D43—24no—
387C23×C43—22no—
388C23×C43C22×D411yescharacteristic
389C22×D43C22×D411yescharacteristic
390C22×D43C22×D411yescharacteristic
391Q8×C43—42no—
392Q8×C43—42no—
393Q8×C43—42no—
394Q8×C43—82no—
395D4×C43—24no—
396D4×C43—42no—
397D4×C43—42no—
398D4×C43—82no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—82no—
406C2×C4×C43—82no—
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C22×D411yescharacteristic
410C2×C4×C43C22×D411yescharacteristic
411C2×C4×C43C22×D411yescharacteristic
412C2×C4×C43C2511yescharacteristic
413C22⋊D43—22no—
414C22⋊D43—22no—
415C22⋊D43—44no—
416C22⋊D43—82no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—22no—
421C2×Dic43—44no—
422C2×Dic43—82no—
423C2×Dic43C22×D411yescharacteristic
424C2×Dic43C22×D411yescharacteristic
425C2×Dic43C22×D411yescharacteristic
426C2×Dic43C22×D411yescharacteristic
427C2×Dic43C22×D411yescharacteristic
428C2×Dic43C22×D411yescharacteristic
429D172—22no—
430C4×D43—22no—
431C4×D43—22no—
432C4×D43—22no—
433C4×D43—22no—
434C4×D43—22no—
435C4×D43—82no—
436C4×D43—82no—
437C4×D43—82no—
438C4×D432−1+414yes—
439Dic86—22no—
440Dic86—24no—
441Dic86—42no—
442Dic86—42no—
443Dic86—42no—
444Dic86—82no—
445Dic86—82no—
446Dic86—82no—
447C8×C43—22no—
448C8×C43—22no—
449C43⋊C8—22no—
450C43⋊C8—22no—
451#60881—431nomaximal, Sylow
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—42no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43C23×D411yescharacteristic
459C2×D43—21no—
460C2×D43—21no—
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—21no—
464C2×D43#53612yes—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—21no—
468C4×C43—42no—
469C4×C43—42no—
470C4×C43—42no—
471C4×C43#57712yes—
472C4×C43#57712yes—
473C4×C43C2×2−1+412yes—
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—21no—
479Dic43—42no—
480Dic43—42no—
481Dic43—42no—
482Dic43—42no—
483Dic43#53612yes—
484#3511—431no—
485#3503—431no—
486#3244—434no—
487#3244—434no—
488#3231—431no—
489#3231—431no—
490#3229—431no—
491#3229—431no—
492#3228—431no—
493#3228—431no—
494#3227—431no—
495#3227D4311yescharacteristic, complemented
496#3165—431no—
497C2×#498—431no—
498#3141—431no—
499#3131—431no—
500#3099—434no—
501#3084—434no—
502#2922—431no—
503C2×C43—41no—
504C2×C43—82no—
505C2×C43C2×#53611yescharacteristic
506C2×C43C2×#57711yescharacteristic
507C2×C43C2×#57711yescharacteristic
508D43—22no—
509D43—41no—
510Q82—861no—
511#557—861no—
512#556—861no—
513#555—861no—
514#554—861no—
515#554—861no—
516#554—861no—
517#554—861no—
518#553—861no—
519#553—861no—
520D4×Q8—861no—
521D4×Q8—861no—
522D4×Q8—861no—
523#548—861no—
524#548—861no—
525#547—861no—
526#544—432no—
527#544—432no—
528#544—432no—
529#542—432no—
530#542—432no—
531#537—432no—
532#533—431no—
533#533—431no—
534#533—431no—
535#533—431no—
536#533—431no—
537#532—431no—
538#532—431no—
539#532C2×D4311yescharacteristic
540C2×C4⋊Q8—431no—
541C2×C4⋊Q8—431no—
542C2×C4⋊Q8—431no—
543C2×C4⋊Q8C2×D4311yescharacteristic
544#520—432no—
545#520—432no—
546C4×#41—431no—
547#501—434no—
548#500—431no—
549#500—431no—
550#498—431no—
551#498—431no—
552#498—431no—
553#498—434no—
554#498—431no—
555#498C2×D4311yescharacteristic
556#498C2×D4311yescharacteristic
557#489—434no—
558#488—434no—
559#487—431no—
560#487—431no—
561#487—431no—
562#487—431no—
563#486—431no—
564#486—431no—
565#486C2×D4311yescharacteristic
566#486C2×D4311yescharacteristic
567#485—434no—
568#485—434no—
569#483—434no—
570#483—434no—
571#482—434no—
572#482—434no—
573#481—434no—
574#481C2×D4314yes—
575#479—434no—
576#479—434no—
577#478—434no—
578#478—434no—
579#476—434no—
580#476C2×D4314yes—
581#475—434no—
582#475—434no—
583#433—432no—
584#433—432no—
585#431—431no—
586#431—431no—
587#431—431no—
588#431C2×D4311yescharacteristic
589#428—434no—
590C2×#106—434no—
591#424—432no—
592#417—434no—
593#416—434no—
594#408—432no—
595C4×M16—431no—
596C2×C4×C8—431no—
597C43#6088111yescharacteristic, complemented, Sylow
598C2×#41—21no—
599C2×#41—431no—
600C2×#41—432no—
601C2×#41—861no—
602C22×Q8—21no—
603C22×Q8—861no—
604C22×Q8—861no—
605C22×Q8—861no—
606C2×M16—432no—
607C22×C8—432no—
608C4⋊Q8—21no—
609C4⋊Q8—21no—
610C4⋊Q8—432no—
611C4⋊Q8—432no—
612C4⋊Q8—432no—
613C4⋊Q8—431no—
614C4⋊Q8—431no—
615C4⋊Q8—431no—
616C4⋊Q8—431no—
617C4⋊Q8—861no—
618C4⋊Q8—861no—
619C4⋊Q8—861no—
620C4⋊Q8—861no—
621C4⋊Q8—861no—
622C4⋊Q8—861no—
623C4⋊Q8—862no—
624C4⋊Q8—862no—
625C4⋊Q8—862no—
626C4⋊Q8C22×D4311yescharacteristic
627C4⋊Q8C22×D4311yescharacteristic
628C4⋊Q8C22×D4311yescharacteristic
629C4⋊Q8C22×D4312yes—
630#127C22×D4311yescharacteristic
631#126—862no—
632#126—862no—
633#125—432no—
634#125—432no—
635#125—432no—
636#125—861no—
637#125—862no—
638#125—862no—
639#125—862no—
640#125—861no—
641#124—21no—
642#124—432no—
643#124—861no—
644#124—862no—
645#124—862no—
646#123—862no—
647#123—862no—
648C22⋊Q8—432no—
649C22⋊Q8—432no—
650C22⋊Q8—862no—
651C22⋊Q8—862no—
652C22⋊Q8—862no—
653C22⋊Q8—862no—
654C22⋊Q8—862no—
655C22⋊Q8—862no—
656C22⋊Q8—862no—
657C22⋊Q8—862no—
658C22⋊Q8—861no—
659C22⋊Q8—861no—
660C22⋊Q8—862no—
661C22⋊Q8—861no—
662C22⋊Q8—861no—
663C22⋊Q8—861no—
664C22⋊Q8—861no—
665C22⋊Q8—861no—
666C22⋊Q8—861no—
667#121—21no—
668#121—432no—
669#121—862no—
670#121—861no—
671#121—861no—
672#121—861no—
673#121—862no—
674#121—862no—
675#121C22×D4312yes—
676C4×Q8—431no—
677C4×Q8—431no—
678C4×Q8—432no—
679C4×Q8—432no—
680C4×Q8—861no—
681C4×Q8—861no—
682C4×Q8—861no—
683C4×Q8—861no—
684C4×Q8—861no—
685C4×Q8—862no—
686C4×Q8—861no—
687C4×Q8—861no—
688C4×Q8—861no—
689C4×D4—21no—
690C4×D4—431no—
691C4×D4—431no—
692C4×D4—431no—
693C4×D4—431no—
694C4×D4—432no—
695C4×D4—431no—
696C4×D4—431no—
697C4×D4—861no—
698C4×D4—861no—
699C4×D4—861no—
700C4×D4—862no—
701C4×D4—862no—
702C4×D4—862no—
703C4×D4—862no—
704C4×D4—862no—
705C4×D4C22×D4312yes—
706#117—431no—
707#117—431no—
708#117—431no—
709#117—432no—
710#117—432no—
711#117—432no—
712#117—862no—
713#117—861no—
714#117—861no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—432no—
717C2×C4⋊C4—432no—
718C2×C4⋊C4—432no—
719C2×C4⋊C4—861no—
720C2×C4⋊C4—861no—
721C2×C4⋊C4—861no—
722C2×C4⋊C4—862no—
723C2×C4⋊C4C22×D4312yes—
724C2×C42—431no—
725C2×C42—431no—
726C2×C42C22×D4311yescharacteristic
727#107—434no—
728#107—434no—
729#106—434no—
730#106—434no—
731#106—434no—
732#106—434no—
733#106C22×D4314yes—
734#106C22×D4314yes—
735C4⋊C8—432no—
736C4⋊C8—432no—
737C4⋊C8—432no—
738C4⋊C8C22×D4312yes—
739#103—434no—
740#103—434no—
741#103—434no—
742#103—434no—
743#102—434no—
744#102—434no—
745#102C22×D4314yes—
746#102C22×D4314yes—
747C22⋊C8—432no—
748C22⋊C8—432no—
749C22⋊C8—432no—
750C22⋊C8C22×D4312yes—
751#97—432no—
752C4×C8—432no—
753C4×C8—431no—
754C4×C8—431no—
755C4×C8C22×D4311yescharacteristic
756C4×C8C22×D4311yescharacteristic
757#41—82no—
758#41—864no—
759#41—868no—
760#41—3442no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—22no—
765C2×Q8—82no—
766C2×Q8—431no—
767C2×Q8—432no—
768C2×Q8—862no—
769C2×Q8—862no—
770C2×Q8—862no—
771C2×Q8—861no—
772C2×Q8—861no—
773C2×Q8—861no—
774C2×Q8—3442no—
775C2×Q8—3442no—
776C2×Q8—3442no—
777C2×D4—22no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—431no—
781C2×D4—431no—
782C2×D4—431no—
783C2×D4—862no—
784C2×D4—862no—
785C2×D4C23×D4312yes—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—431no—
789C22×C4—431no—
790C22×C4—431no—
791C22×C4—431no—
792C22×C4—431no—
793C22×C4—431no—
794C22×C4—862no—
795C22×C4—862no—
796C22×C4—862no—
797C22×C4—862no—
798C22×C4—862no—
799C22×C4D4×D4311yescharacteristic
800C22×C4D4×D4311yescharacteristic
801C22×C4C23×D4311yescharacteristic
802M16—864no—
803C2×C8—432no—
804C2×C8—432no—
805C2×C8—864no—
806C2×C8C23×D4312yes—
807C2×C8C23×D4312yes—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—22no—
813C4⋊C4—431no—
814C4⋊C4—431no—
815C4⋊C4—431no—
816C4⋊C4—431no—
817C4⋊C4—431no—
818C4⋊C4—431no—
819C4⋊C4—432no—
820C4⋊C4—432no—
821C4⋊C4—432no—
822C4⋊C4—862no—
823C4⋊C4—862no—
824C4⋊C4—862no—
825C4⋊C4—862no—
826C4⋊C4—862no—
827C4⋊C4—862no—
828C4⋊C4—862no—
829C4⋊C4—862no—
830C4⋊C4—862no—
831C4⋊C4—862no—
832C4⋊C4—862no—
833C4⋊C4—862no—
834C4⋊C4—861no—
835C4⋊C4—861no—
836C4⋊C4—862no—
837C4⋊C4—861no—
838C4⋊C4—861no—
839C4⋊C4—861no—
840C4⋊C4—862no—
841C4⋊C4—862no—
842C4⋊C4—862no—
843C4⋊C4C23×D4312yes—
844C4⋊C4C23×D4312yes—
845C4⋊C4C23×D4312yes—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—431no—
849C22⋊C4—431no—
850C22⋊C4—431no—
851C22⋊C4—431no—
852C22⋊C4—431no—
853C22⋊C4—431no—
854C22⋊C4—862no—
855C22⋊C4—862no—
856C22⋊C4—862no—
857C22⋊C4—862no—
858C22⋊C4—862no—
859C22⋊C4—862no—
860C22⋊C4—862no—
861C22⋊C4—862no—
862C22⋊C4—862no—
863C42—431no—
864C42—431no—
865C42—431no—
866C42—431no—
867C42—431no—
868C42—431no—
869C42—862no—
870C42—862no—
871C42—862no—
872C42—862no—
873C42—862no—
874C42D4×D4311yescharacteristic
875C42D4×D4311yescharacteristic
876C42C23×D4311yescharacteristic
877C42C23×D4311yescharacteristic
878C23—22no—
879C23—431no—
880C23—431no—
881C23C2×D4×D4311yescharacteristic
882Q8—42no—
883Q8—42no—
884Q8—42no—
885Q8—82no—
886Q8—862no—
887Q8—864no—
888Q8—3442no—
889Q8—3442no—
890Q8—3442no—
891Q8—1722no—
892Q8—1722no—
893Q8—1722no—
894D4—24no—
895D4—42no—
896D4—42no—
897D4—82no—
898D4—862no—
899D4—862no—
900D4—862no—
901D4—3442no—
902D4—1724no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—82no—
910C2×C4—82no—
911C2×C4—431no—
912C2×C4—434no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—431no—
917C2×C4—431no—
918C2×C4—862no—
919C2×C4—862no—
920C2×C4—862no—
921C2×C4—862no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—862no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—3442no—
928C2×C4—3442no—
929C2×C4—3442no—
930C2×C4—3442no—
931C2×C4—1724no—
932C2×C4C2×D4×D4311yescharacteristic
933C2×C4C2×D4×D4311yescharacteristic
934C2×C4C2×D4×D4311yescharacteristic
935C2×C4C2×D4×D4311yescharacteristic
936C2×C4C2×D4×D4311yescharacteristic
937C2×C4C24×D4311yescharacteristic
938C8—22no—
939C8—22no—
940C8—862no—
941C8—862no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—432no—
949C22—861no—
950C22—861no—
951C22—861no—
952C22—861no—
953C22—861no—
954C22C22×D4×D4311yescharacteristic
955C4—21no—
956C4—21no—
957C4—21no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—432no—
962C4—861no—
963C4—861no—
964C4—861no—
965C4—861no—
966C4—861no—
967C4—1722no—
968C4—1722no—
969C4—1722no—
970C4—1722no—
971C4#1458370512yes—
972C4#1458370912yes—
973C42−1+4×D4312yes—
974C2—41no—
975C2—82no—
976C2—862no—
977C2—1721no—
978C2#536×D4311yescharacteristic
979C2C2×#1458370511yescharacteristic
980C2C2×#1458370911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3227C2
socleC22×C43C23×D4
prime radical#19148496C2
hypercenter#3227D43
hypocenterC43#60881
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #19148411C2semidirect
3. #19145890C2semidirect
4. #19145889C2semidirect
5. #19145757C2semidirect
6. #19145756C2semidirect
7. #19145740C2semidirect
8. #19145739C2semidirect
9. #19145727C2semidirect
10. #19145726C2semidirect
11. #19145719C2semidirect
12. #19145136C2semidirect
13. #498×D43C2semidirect
14. #19144985C2semidirect
15. #19144914C2semidirect
16. #19144585C2semidirect
17. #19144452C2semidirect
18. #19143234C2semidirect
19. C43×#3227C2semidirect
495. #3227D43semidirect
597. C43#60881semidirect

Maximal subgroups

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

subgroupindex
#191484962
#191484112
#191458902
#191458892
#191457572
#191457562
#191457402
#191457392
#191457272
#191457262
#191457192
#191451362
#498×D432
#191449852
#191449142
#191445852
#191444522
#191432342
C43×#32272
#6088143