Finite Group Databasebeta

← #25969110

Subgroups — #25969110

Order 11008.

1666 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#19148474C211yesmaximal, characteristic
2#19148407C211yesmaximal, characteristic
3#19145868C214yesmaximal, complemented
4#19145861C214yesmaximal, complemented
5#19145755C211yesmaximal, characteristic, complemented
6#19145754C211yesmaximal, characteristic, complemented
7#19145751C211yesmaximal, characteristic, complemented
8#19145748C211yesmaximal, characteristic, complemented
9#19145742C211yesmaximal, characteristic, complemented
10#19145740C211yesmaximal, characteristic, complemented
11#19145736C211yesmaximal, characteristic, complemented
12#19145136C211yesmaximal, characteristic, complemented
13#19145106C211yesmaximal, characteristic, complemented
14#19144972C211yesmaximal, characteristic, complemented
15#487×D43C211yesmaximal, characteristic, complemented
16#19144559C214yesmaximal
17#19144436C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic
19C43×#3231C211yesmaximal, characteristic, complemented
20Q8×Dic86—21no—
21#14583627—21no—
22#14583626—21no—
23#14583625—21no—
24#14583620—21no—
25#14583617—21no—
26#14583609—21no—
27#14583607—21no—
28#14583607—21no—
29#14583590—21no—
30#14583588—21no—
31#14583587—21no—
32#14583583—21no—
33Q8×D172—21no—
34#14583562—21no—
35#14583562—21no—
36#14583529C2212yes—
37#14583529C2212yes—
38#14583527C2212yes—
39#14583509C2212yes—
40#14583507C2212yes—
41#14583472C2212yes—
42#14583456C2211yescharacteristic
43#14583454C2211yescharacteristic
44#14583454C2211yescharacteristic
45#14583454C2211yescharacteristic
46#14583454C2211yescharacteristic
47#14583454C2211yescharacteristic
48C2×#13063325C2211yescharacteristic
49C4⋊Q8×D43C2211yescharacteristic
50C4⋊Q8×D43C2211yescharacteristic
51C4⋊Q8×D43C2211yescharacteristic
52#14583379C2212yes—
53#14583375C2212yes—
54C4×#10621898C2211yescharacteristic
55#14583306C2214yes—
56#14583304C2211yescharacteristic
57#14583304C2211yescharacteristic
58#14583302C2211yescharacteristic
59#14583300C2214yes—
60#14583295C2211yescharacteristic
61#14583295C2211yescharacteristic
62#14583295C2211yescharacteristic
63#14583266C2214yes—
64#14583251C2211yescharacteristic
65#14583251C2211yescharacteristic
66#14583250C2211yescharacteristic
67#14583250C2211yescharacteristic
68#14583249C2211yescharacteristic
69#14583249C2211yescharacteristic
70#14583248C2214yes—
71#14583242C2214yes—
72#14583240C2214yes—
73#14583239C2214yes—
74#14583235C2214yes—
75#14583233C2214yes—
76#14583231C2214yes—
77#14583227C2214yes—
78#14583208C2214yes—
79#14583205C2214yes—
80#14583203C2214yes—
81#14583195C2214yes—
82#14583192C2214yes—
83#14583184C2214yes—
84#14583183C2214yes—
85#14582959C2212yes—
86#14582957C2212yes—
87#14582952C2211yescharacteristic
88#14582950C2211yescharacteristic
89#14582950C2211yescharacteristic
90#14582938C2214yes—
91#14582936C2214yes—
92#14582924C2212yes—
93#14582906C2214yes—
94#103×D43C2214yes—
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#533C2211yescharacteristic
99C43×#533C2211yescharacteristic
100C43×#500C2211yescharacteristic
101C43×#498C2211yescharacteristic
102C43×#487C2211yescharacteristic
103C43×#487C2211yescharacteristic
104C43×#485C2214yes—
105C43×#479C2214yes—
106C43×#431C2211yescharacteristic
107C2×#10621898C2311yescharacteristic
108C22×Dic86—21no—
109C2×Q8×D43—21no—
110C2×Q8×D43—21no—
111C2×Q8×D43C2312yes—
112C2×#10621872C2312yes—
113C2×C8×D43C2312yes—
114#13063325—21no—
115#13063325—21no—
116#13063325—22no—
117#13063325C2311yescharacteristic
118#13063325C2311yescharacteristic
119#13063325C2311yescharacteristic
120#13063325C2311yescharacteristic
121#13063325C2312yes—
122#13063324—22no—
123#13063324—22no—
124#13063324—22no—
125#13063324—21no—
126#13063324—21no—
127#13063324—21no—
128#13063324—21no—
129#13063324C2312yes—
130#13063324C2312yes—
131#13063323—21no—
132#13063323—21no—
133#13063323C2312yes—
134#13063320—22no—
135#13063319—22no—
136#13063318—22no—
137#13063318—22no—
138#13063317—21no—
139#13063317—22no—
140#13063317—22no—
141#13063316—22no—
142#13063316—21no—
143#13063316—21no—
144#13063316C2312yes—
145#13063316C2312yes—
146#13063316C2312yes—
147#13063315—22no—
148#13063315—22no—
149#13063315—22no—
150#13063315—22no—
151#13063311—22no—
152#13063310—22no—
153#13063307—22no—
154#13063305—21no—
155#13063305—21no—
156#13063305—21no—
157#13063305—21no—
158#13063305—22no—
159#13063305—22no—
160#13063305C2312yes—
161#13063304—21no—
162#13063304C2312yes—
163#13063303—22no—
164#13063303—22no—
165#13063302—22no—
166#13063302—22no—
167#13063301—21no—
168#13063301—21no—
169#13063301—21no—
170#13063301—21no—
171#13063301C2312yes—
172Q8×Dic43—21no—
173Q8×Dic43—21no—
174Q8×Dic43—21no—
175Q8×Dic43—21no—
176Q8×Dic43C2312yes—
177C4×Dic86—22no—
178C4×Dic86—21no—
179C4×Dic86—22no—
180C4×Dic86D411yescharacteristic
181C4×Dic86D411yescharacteristic
182C4×Dic86C2312yes—
183#13063290—22no—
184#13063290—21no—
185#13063290—21no—
186#13063290—21no—
187#13063290—21no—
188#13063290C2312yes—
189C4×D172—22no—
190C4×D172D411yescharacteristic
191C4×D172D411yescharacteristic
192C4×C22⋊D43D411yescharacteristic
193C4×C22⋊D43D411yescharacteristic
194C4×C22⋊D43D411yescharacteristic
195C4×C22⋊D43D411yescharacteristic
196(C22⋊D43)⋊C4—22no—
197(C22⋊D43)⋊C4—22no—
198#13063284—21no—
199#13063284C2311yescharacteristic
200#13063283—21no—
201#13063283—21no—
202#13063283—22no—
203#13063283C2312yes—
204#13063283C2312yes—
205#13063283C2312yes—
206#13063282—22no—
207#13063282C2311yescharacteristic
208#13063282C2311yescharacteristic
209C2×C4⋊Dic43—21no—
210C2×C4⋊Dic43C2312yes—
211C4⋊C4×D43—21no—
212C4⋊C4×D43—21no—
213C4⋊C4×D43—21no—
214C4⋊C4×D43—21no—
215C4⋊C4×D43C2312yes—
216C4⋊C4×D43C2312yes—
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#13063250C2314yes—
229#13063250C2314yes—
230#13063249C2314yes—
231#13063249C2314yes—
232#13063248C2314yes—
233#13063248C2314yes—
234C22⋊(C43⋊C8)C2312yes—
235(C2×D43)⋊C8C2312yes—
236(C2×D43)⋊C8C2312yes—
237#13063235C2312yes—
238C4×C43⋊C8C2311yescharacteristic
239C4×C43⋊C8C2311yescharacteristic
240C8×Dic43C2312yes—
241C4⋊Q8×C43C2311yescharacteristic
242C4⋊Q8×C43C2311yescharacteristic
243C4⋊Q8×C43C2311yescharacteristic
244C4⋊Q8×C43C2311yescharacteristic
245#125×C43—21no—
246#125×C43C2312yes—
247C22⋊Q8×C43—21no—
248C22⋊Q8×C43—21no—
249C22⋊Q8×C43—21no—
250C22⋊Q8×C43C2312yes—
251C4×Q8×C43—21no—
252C4×Q8×C43—21no—
253C4×Q8×C43—21no—
254C4×Q8×C43C2312yes—
255#117×C43—21no—
256#117×C43C2312yes—
257C2×C42×C43C2311yescharacteristic
258#107×C43C2314yes—
259#106×C43C2314yes—
260C4⋊C8×C43C2312yes—
261#103×C43C2314yes—
262#103×C43C2314yes—
263C22⋊C8×C43C2312yes—
264C4×C8×C43C2311yescharacteristic
265C4×C8×C43C2311yescharacteristic
266C2×Q8×C43—21no—
267C2×Q8×C43—21no—
268C2×Q8×C43—21no—
269C2×Q8×C43C2412yes—
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2411yescharacteristic
273C2×C22⋊D43C2×D411yescharacteristic
274C2×C22⋊D43C2×D411yescharacteristic
275C22×Dic43—22no—
276Q8×D43—28no—
277Q8×D43—82no—
278Q8×D43—82no—
279#10621898—24no—
280C2×D172C2×D411yescharacteristic
281C2×C4×D43—22no—
282C2×C4×D43—22no—
283C2×C4×D43—22no—
284C2×C4×D43C2×D411yescharacteristic
285C2×C4×D43C2×D411yescharacteristic
286C2×C4×D43C2×D411yescharacteristic
287C2×C4×D43C2×D411yescharacteristic
288C2×C4×D43C2411yescharacteristic
289C2×C4×D43C2411yescharacteristic
290C2×Dic86—21no—
291C2×Dic86—21no—
292C2×Dic86—21no—
293C2×Dic86—22no—
294C2×Dic86—22no—
295C2×Dic86—22no—
296C2×Dic86—22no—
297C2×Dic86—82no—
298C2×Dic86C2×D411yescharacteristic
299C2×Dic86C2412yes—
300C2×C8×C43C2412yes—
301C2×C8×C43C2412yes—
302C4⋊C4×C43—21no—
303C4⋊C4×C43—21no—
304C4⋊C4×C43—22no—
305C4⋊C4×C43—22no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43—21no—
308C4⋊C4×C43—21no—
309C4⋊C4×C43—22no—
310C4⋊C4×C43—22no—
311C4⋊C4×C43C2412yes—
312C4⋊C4×C43C2412yes—
313C4⋊C4×C43C2412yes—
314C22⋊C4×C43—22no—
315C22⋊C4×C43—22no—
316C42×C43—22no—
317C42×C43—22no—
318C42×C43C2×D411yescharacteristic
319C42×C43C2×D411yescharacteristic
320C42×C43C2411yescharacteristic
321C42×C43C2411yescharacteristic
322C22⋊Dic43—22no—
323C22⋊Dic43C2×D411yescharacteristic
324C22⋊Dic43C2×D411yescharacteristic
325(C2×D43)⋊C4—22no—
326(C2×D43)⋊C4—22no—
327(C2×D43)⋊C4—22no—
328(C2×D43)⋊C4—22no—
329(C2×D43)⋊C4—22no—
330(C2×D43)⋊C4C2×D411yescharacteristic
331(C2×D43)⋊C4C2×D411yescharacteristic
332(C2×D43)⋊C4C2×D411yescharacteristic
333(C2×D43)⋊C4C2×D411yescharacteristic
334C4⋊Dic43—21no—
335C4⋊Dic43—21no—
336C4⋊Dic43—21no—
337C4⋊Dic43—21no—
338C4⋊Dic43—22no—
339C4⋊Dic43—22no—
340C4⋊Dic43—21no—
341C4⋊Dic43—22no—
342C4⋊Dic43—22no—
343C4⋊Dic43—22no—
344C4⋊Dic43—22no—
345C4⋊Dic43—22no—
346C4⋊Dic43C2×D411yescharacteristic
347C4⋊Dic43C2×D411yescharacteristic
348C4⋊Dic43C2412yes—
349C4⋊Dic43C2412yes—
350C4⋊Dic43C2412yes—
351Dic43⋊C4—22no—
352Dic43⋊C4—22no—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
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⋊C4C2×D411yescharacteristic
365Dic43⋊C4C2×D411yescharacteristic
366Dic43⋊C4C2×D411yescharacteristic
367Dic43⋊C4C2×D411yescharacteristic
368C4×Dic43—22no—
369C4×Dic43—22no—
370C4×Dic43—22no—
371C4×Dic43—22no—
372C4×Dic43—22no—
373C4×Dic43—22no—
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2411yescharacteristic
379C4×Dic43C2411yescharacteristic
380C2×C43⋊C8C2412yes—
381C2×C43⋊C8C2412yes—
382#10621872—24no—
383C8×D43—24no—
384C23×C43C22×D411yescharacteristic
385C22×D43C22×D411yescharacteristic
386C22×D43C22×D411yescharacteristic
387Q8×C43—24no—
388Q8×C43—42no—
389Q8×C43—42no—
390Q8×C43—42no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43C22×D411yescharacteristic
399C2×C4×C43C22×D411yescharacteristic
400C2×C4×C43C22×D411yescharacteristic
401C2×C4×C43C22×D411yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C2×C4×C43C2511yescharacteristic
404C22⋊D43—22no—
405C22⋊D43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—82no—
411C2×Dic43C22×D411yescharacteristic
412C2×Dic43C22×D411yescharacteristic
413C2×Dic43C22×D411yescharacteristic
414C2×Dic43C22×D411yescharacteristic
415C2×Dic43C22×D411yescharacteristic
416C2×Dic43C22×D411yescharacteristic
417D172—22no—
418C4×D43—22no—
419C4×D43—22no—
420C4×D43—22no—
421C4×D43—22no—
422C4×D43—22no—
423C4×D43—44no—
424C4×D43—82no—
425C4×D43—82no—
426C4×D432−1+414yes—
427Dic86—22no—
428Dic86—24no—
429Dic86—42no—
430Dic86—42no—
431Dic86—42no—
432Dic86—44no—
433Dic86—82no—
434Dic86—82no—
435Dic86—82no—
436C8×C43—22no—
437C8×C43—22no—
438C43⋊C8—22no—
439C43⋊C8—22no—
440#60878—431nomaximal, Sylow
441C22×C43—21no—
442C22×C43—21no—
443C22×C43—21no—
444C22×C43C23×D411yescharacteristic
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43#53612yes—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—42no—
455C4×C43—42no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43#57712yes—
459C4×C43#57812yes—
460C4×C43C2×2−1+412yes—
461Dic43—21no—
462Dic43—21no—
463Dic43—21no—
464Dic43—21no—
465Dic43—21no—
466Dic43—42no—
467Dic43—42no—
468Dic43—42no—
469Dic43—42no—
470Dic43#53612yes—
471#3509—431no—
472#3503—431no—
473#3242—434no—
474#3242—434no—
475#3231—431no—
476#3231—431no—
477#3231—431no—
478#3231D4311yescharacteristic, complemented
479#3230—431no—
480#3230—431no—
481#3229—431no—
482#3229—431no—
483#3165—431no—
484#3160—431no—
485#3139—431no—
486C2×#487—431no—
487#3097—434no—
488#3082—434no—
489#2922—431no—
490C2×C43—41no—
491C2×C43C2×#53611yescharacteristic
492C2×C43C2×#57711yescharacteristic
493C2×C43C2×#57811yescharacteristic
494D43—22no—
495D43—41no—
496Q82—861no—
497#557—861no—
498#557—861no—
499#557—861no—
500#556—861no—
501#556—861no—
502#554—861no—
503#554—861no—
504#554—861no—
505#552—861no—
506#552—861no—
507#552—861no—
508#552—861no—
509D4×Q8—861no—
510D4×Q8—861no—
511D4×Q8—861no—
512#544—432no—
513#544—432no—
514#544—432no—
515#541—432no—
516#541—432no—
517#536—432no—
518#533—431no—
519#533—431no—
520#533—431no—
521#533—431no—
522#533—431no—
523#533—431no—
524#533C2×D4311yescharacteristic
525#533C2×D4311yescharacteristic
526C2×C4⋊Q8—431no—
527C2×C4⋊Q8—431no—
528C2×C4⋊Q8—431no—
529C2×C4⋊Q8—431no—
530#520—432no—
531#519—432no—
532C4×#41—431no—
533#501—434no—
534#500—431no—
535#500—431no—
536#500—431no—
537#500C2×D4311yescharacteristic
538#499—434no—
539#498—431no—
540#498—431no—
541#498—431no—
542#498C2×D4311yescharacteristic
543#491—434no—
544#487—431no—
545#487—431no—
546#487—431no—
547#487—431no—
548#487—434no—
549#487—431no—
550#487—431no—
551#487C2×D4311yescharacteristic
552#487C2×D4311yescharacteristic
553#485—434no—
554#485—434no—
555#485—434no—
556#485C2×D4314yes—
557#484—434no—
558#484—434no—
559#483—434no—
560#483—434no—
561#479—434no—
562#479—434no—
563#479—434no—
564#479C2×D4314yes—
565#477—434no—
566#477—434no—
567#475—434no—
568#475—434no—
569#433—432no—
570#433—432no—
571#431—431no—
572#431—431no—
573#431—431no—
574#431C2×D4311yescharacteristic
575#428—434no—
576#427—434no—
577#424—432no—
578#419—434no—
579C2×#103—434no—
580#408—432no—
581C4×M16—431no—
582C2×C4×C8—431no—
583C43#6087811yescharacteristic, complemented, Sylow
584C2×#41—431no—
585C22×Q8—432no—
586C22×Q8—861no—
587C22×Q8—861no—
588C22×Q8—861no—
589C2×M16—432no—
590C22×C8—432no—
591C4⋊Q8—432no—
592C4⋊Q8—432no—
593C4⋊Q8—432no—
594C4⋊Q8—431no—
595C4⋊Q8—431no—
596C4⋊Q8—432no—
597C4⋊Q8—431no—
598C4⋊Q8—431no—
599C4⋊Q8—862no—
600C4⋊Q8—861no—
601C4⋊Q8—861no—
602C4⋊Q8—861no—
603C4⋊Q8—861no—
604C4⋊Q8—861no—
605C4⋊Q8—861no—
606C4⋊Q8—862no—
607C4⋊Q8—862no—
608C4⋊Q8—862no—
609C4⋊Q8—861no—
610C4⋊Q8—861no—
611C4⋊Q8C22×D4311yescharacteristic
612C4⋊Q8C22×D4311yescharacteristic
613C4⋊Q8C22×D4311yescharacteristic
614C4⋊Q8C22×D4311yescharacteristic
615#126—862no—
616#126—862no—
617#126—862no—
618#126—862no—
619#125—21no—
620#125—432no—
621#125—432no—
622#125—432no—
623#125—862no—
624#125—862no—
625#125—861no—
626#125—861no—
627#125—862no—
628#125—862no—
629#125—862no—
630#125—862no—
631#125—862no—
632#125—861no—
633#125C22×D4312yes—
634#124—862no—
635#123—862no—
636#123—862no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8—432no—
641C22⋊Q8—432no—
642C22⋊Q8—432no—
643C22⋊Q8—862no—
644C22⋊Q8—862no—
645C22⋊Q8—862no—
646C22⋊Q8—862no—
647C22⋊Q8—862no—
648C22⋊Q8—862no—
649C22⋊Q8—861no—
650C22⋊Q8—861no—
651C22⋊Q8—861no—
652C22⋊Q8—861no—
653C22⋊Q8—861no—
654C22⋊Q8—861no—
655C22⋊Q8—861no—
656C22⋊Q8—861no—
657C22⋊Q8—861no—
658C22⋊Q8C22×D4312yes—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—431no—
663C4×Q8—431no—
664C4×Q8—432no—
665C4×Q8—432no—
666C4×Q8—432no—
667C4×Q8—862no—
668C4×Q8—862no—
669C4×Q8—861no—
670C4×Q8—861no—
671C4×Q8—861no—
672C4×Q8—861no—
673C4×Q8—861no—
674C4×Q8—861no—
675C4×Q8—861no—
676C4×Q8—861no—
677C4×Q8—862no—
678C4×Q8—861no—
679C4×Q8C22×D4312yes—
680C4×D4—431no—
681C4×D4—431no—
682C4×D4—431no—
683C4×D4—431no—
684C4×D4—431no—
685C4×D4—431no—
686C4×D4—862no—
687C4×D4—862no—
688C4×D4—862no—
689#117—21no—
690#117—431no—
691#117—431no—
692#117—431no—
693#117—432no—
694#117—432no—
695#117—432no—
696#117—862no—
697#117—862no—
698#117—861no—
699#117—861no—
700#117—861no—
701#117C22×D4312yes—
702C2×C4⋊C4—432no—
703C2×C4⋊C4—432no—
704C2×C4⋊C4—432no—
705C2×C4⋊C4—861no—
706C2×C4⋊C4—861no—
707C2×C4⋊C4—861no—
708C2×C4⋊C4—861no—
709C2×C4⋊C4—861no—
710C2×C42—431no—
711C2×C42—431no—
712C2×C42C22×D4311yescharacteristic
713#107—434no—
714#107—434no—
715#107—434no—
716#107C22×D4314yes—
717#106—434no—
718#106—434no—
719#106—434no—
720#106C22×D4314yes—
721C4⋊C8—432no—
722C4⋊C8—432no—
723C4⋊C8—432no—
724C4⋊C8C22×D4312yes—
725#103—434no—
726#103—434no—
727#103—434no—
728#103—434no—
729#103—434no—
730#103—434no—
731#103C22×D4314yes—
732#103C22×D4314yes—
733C22⋊C8—432no—
734C22⋊C8—432no—
735C22⋊C8—432no—
736C22⋊C8C22×D4312yes—
737#97—432no—
738C4×C8—432no—
739C4×C8—431no—
740C4×C8—431no—
741C4×C8C22×D4311yescharacteristic
742C4×C8C22×D4311yescharacteristic
743#41—864no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—431no—
748C2×Q8—432no—
749C2×Q8—862no—
750C2×Q8—862no—
751C2×Q8—862no—
752C2×Q8—868no—
753C2×Q8—862no—
754C2×Q8—861no—
755C2×Q8—861no—
756C2×Q8—861no—
757C2×Q8—3442no—
758C2×Q8—3442no—
759C2×Q8—3442no—
760C2×Q8C23×D4312yes—
761C2×D4—431no—
762C2×D4—431no—
763C2×D4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—862no—
771C22×C4—862no—
772C22×C4—862no—
773C22×C4—862no—
774C22×C4D4×D4311yescharacteristic
775C22×C4D4×D4311yescharacteristic
776C22×C4C23×D4311yescharacteristic
777M16—864no—
778C2×C8—432no—
779C2×C8—432no—
780C2×C8—864no—
781C2×C8C23×D4312yes—
782C2×C8C23×D4312yes—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—22no—
788C4⋊C4—21no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—431no—
793C4⋊C4—431no—
794C4⋊C4—431no—
795C4⋊C4—431no—
796C4⋊C4—431no—
797C4⋊C4—431no—
798C4⋊C4—432no—
799C4⋊C4—432no—
800C4⋊C4—432no—
801C4⋊C4—862no—
802C4⋊C4—862no—
803C4⋊C4—862no—
804C4⋊C4—862no—
805C4⋊C4—862no—
806C4⋊C4—862no—
807C4⋊C4—862no—
808C4⋊C4—862no—
809C4⋊C4—862no—
810C4⋊C4—862no—
811C4⋊C4—862no—
812C4⋊C4—862no—
813C4⋊C4—862no—
814C4⋊C4—862no—
815C4⋊C4—862no—
816C4⋊C4—862no—
817C4⋊C4—862no—
818C4⋊C4—861no—
819C4⋊C4—861no—
820C4⋊C4—861no—
821C4⋊C4—861no—
822C4⋊C4—862no—
823C4⋊C4—861no—
824C4⋊C4—862no—
825C4⋊C4—862no—
826C4⋊C4C23×D4312yes—
827C4⋊C4C23×D4312yes—
828C4⋊C4C23×D4312yes—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—431no—
832C22⋊C4—431no—
833C22⋊C4—431no—
834C22⋊C4—431no—
835C22⋊C4—431no—
836C22⋊C4—431no—
837C22⋊C4—862no—
838C22⋊C4—862no—
839C22⋊C4—862no—
840C22⋊C4—862no—
841C22⋊C4—862no—
842C22⋊C4—862no—
843C42—22no—
844C42—22no—
845C42—431no—
846C42—431no—
847C42—431no—
848C42—431no—
849C42—431no—
850C42—431no—
851C42—862no—
852C42—862no—
853C42—862no—
854C42—862no—
855C42—862no—
856C42—862no—
857C42D4×D4311yescharacteristic
858C42D4×D4311yescharacteristic
859C42C23×D4311yescharacteristic
860C42C23×D4311yescharacteristic
861C23—431no—
862C23—431no—
863C23C2×D4×D4311yescharacteristic
864Q8—24no—
865Q8—42no—
866Q8—42no—
867Q8—42no—
868Q8—862no—
869Q8—864no—
870Q8—3442no—
871Q8—3442no—
872Q8—3442no—
873Q8—1724no—
874Q8—1722no—
875Q8—1722no—
876Q8—1722no—
877D4—862no—
878D4—862no—
879D4—862no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—431no—
888C2×C4—434no—
889C2×C4—431no—
890C2×C4—431no—
891C2×C4—431no—
892C2×C4—431no—
893C2×C4—431no—
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—862no—
903C2×C4—3442no—
904C2×C4—3442no—
905C2×C4—3442no—
906C2×C4—1724no—
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4C2×D4×D4311yescharacteristic
911C2×C4C2×D4×D4311yescharacteristic
912C2×C4C24×D4311yescharacteristic
913C8—22no—
914C8—22no—
915C8—862no—
916C8—862no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—432no—
921C22—861no—
922C22—861no—
923C22—861no—
924C22—861no—
925C22—861no—
926C22C22×D4×D4311yescharacteristic
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—432no—
935C4—861no—
936C4—861no—
937C4—861no—
938C4—861no—
939C4—861no—
940C4—1722no—
941C4—1722no—
942C4—1722no—
943C4—1722no—
944C4#1458370812yes—
945C4#1458371312yes—
946C42−1+4×D4312yes—
947C2—41no—
948C2—862no—
949C2—1721no—
950C2#536×D4311yescharacteristic
951C2C2×#1458370811yescharacteristic
952C2C2×#1458371311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3231C2
socleC22×C43C23×D4
prime radicalC2×#10621898C23
hypercenter#3231D43
hypocenterC43#60878
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
3. #19145868C2semidirect
4. #19145861C2semidirect
5. #19145755C2semidirect
6. #19145754C2semidirect
7. #19145751C2semidirect
8. #19145748C2semidirect
9. #19145742C2semidirect
10. #19145740C2semidirect
11. #19145736C2semidirect
12. #19145136C2semidirect
13. #19145106C2semidirect
14. #19144972C2semidirect
15. #487×D43C2semidirect
17. #19144436C2semidirect
19. C43×#3231C2semidirect
478. #3231D43semidirect
583. C43#60878semidirect

Maximal subgroups

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

subgroupindex
#191484742
#191484072
#191458682
#191458612
#191457552
#191457542
#191457512
#191457482
#191457422
#191457402
#191457362
#191451362
#191451062
#191449722
#487×D432
#191445592
#191444362
#191432342
C43×#32312
#6087843