Finite Group Databasebeta

← #25968775

Subgroups — #25968775

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#19147892C211yesmaximal, characteristic
2#533×D43C211yesmaximal, characteristic, complemented
3#19145838C212yesmaximal, complemented
4#19145836C212yesmaximal, complemented
5#19145826C212yesmaximal, complemented
6#19145817C212yesmaximal, complemented
7#19145810C212yesmaximal, complemented
8#19145802C212yesmaximal, complemented
9#19145794C212yesmaximal, complemented
10#19145786C212yesmaximal, complemented
11#19145117C211yesmaximal, characteristic, complemented
12#19144943C211yesmaximal, characteristic, complemented
13#19144941C211yesmaximal, characteristic, complemented
14#19144512C214yesmaximal, complemented
15#19144381C214yesmaximal, complemented
16C2×#14582954C211yesmaximal, characteristic, complemented
17C43×#3162C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455C2212yes—
20#14583454C2211yescharacteristic
21#14583454C2211yescharacteristic
22#14583454C2211yescharacteristic
23#14583454C2211yescharacteristic
24#14583453—21no—
25#14583453—21no—
26#14583452C2212yes—
27#14583451—21no—
28#14583451—21no—
29#14583450C2211yescharacteristic
30#14583450C2211yescharacteristic
31#14583449C2211yescharacteristic
32C4⋊Q8×D43C2211yescharacteristic
33C4⋊Q8×D43C2211yescharacteristic
34#14583436—21no—
35#14583436—21no—
36#14583435—21no—
37#14583435—21no—
38#14583434C2212yes—
39#14583434C2212yes—
40#125×D43C2212yes—
41#14583412—21no—
42#14583412—21no—
43#14583411C2212yes—
44C22⋊Q8×D43—21no—
45C22⋊Q8×D43—21no—
46C4×#10621902—21no—
47C4×#10621902—21no—
48#14583367C2212yes—
49C4×Q8×D43—21no—
50C4×Q8×D43—21no—
51#117×D43C2212yes—
52C2×C42×D43C2211yescharacteristic
53#14583309C2212yescomplemented
54#14583309C2212yescomplemented
55#14583305C2212yescomplemented
56#14583305C2212yescomplemented
57#14583269C2212yescomplemented
58#14583268C2212yescomplemented
59#14583265C2212yescomplemented
60#14583264C2212yescomplemented
61#14583261C2212yescomplemented
62#14583261C2212yescomplemented
63#14583259C2212yescomplemented
64#14583259C2212yescomplemented
65#14583243C2214yes—
66#14583242C2214yes—
67#14583236C2214yes—
68#14583231C2214yes—
69#14583226C2214yes—
70#14583225C2214yes—
71#14583219C2214yes—
72#14583214C2214yes—
73#14583209C2214yescomplemented
74#14583205C2214yescomplemented
75#14583202C2214yescomplemented
76#14583198C2214yescomplemented
77#14583193C2214yescomplemented
78#14583188C2214yescomplemented
79#14583183C2214yescomplemented
80#14583178C2214yescomplemented
81#14582954C2212yes—
82#14582954C2212yes—
83#14582954C2212yes—
84#14582954C2212yes—
85#14582935C2214yes—
86C2×Dic43⋊C8C2212yes—
87#14582896C2214yes—
88#14582893C2214yes—
89C2×(C2×D43)⋊C8C2212yes—
90C2×#13063236C2211yescharacteristic
91C43×#533C2211yescharacteristic
92C43×#533C2211yescharacteristic
93C43×#501C2212yescomplemented
94C43×#501C2212yescomplemented
95C43×#501C2212yescomplemented
96C43×#501C2212yescomplemented
97C43×#427C2214yes—
98C2×#97×C43C2211yescharacteristic
99C2×#10621902—21no—
100C2×#10621902—21no—
101C2×#10621898C2312yes—
102C2×Q8×D43—21no—
103C2×Q8×D43—21no—
104C22×C4×D43D411yescharacteristic
105C22×C4×D43D411yescharacteristic
106C22×C4×D43C2311yescharacteristic
107C22×C43⋊C8C2312yes—
108#13063325C2311yescharacteristic
109#13063325C2311yescharacteristic
110#13063325C2311yescharacteristic
111#13063324—21no—
112#13063324—21no—
113#13063324C2312yes—
114#13063324C2312yes—
115#13063323—21no—
116#13063323—21no—
117#13063322C2311yescharacteristic
118#13063320—22no—
119#13063320—22no—
120#13063317C2312yes—
121#13063316—21no—
122#13063316—21no—
123#13063316C2312yes—
124#13063316C2312yes—
125#13063315—22no—
126#13063315—22no—
127#13063314—21no—
128#13063314—21no—
129#13063313C2312yes—
130#13063310—22no—
131#13063310—22no—
132#13063309—22no—
133#13063305—21no—
134#13063305—21no—
135#13063305C2312yes—
136#13063305C2312yes—
137#13063304—21no—
138#13063304—21no—
139#13063303—22no—
140#13063303—22no—
141#13063302—22no—
142#13063302—22no—
143#13063301—21no—
144#13063301—21no—
145#13063301—21no—
146#13063301—21no—
147#13063300—21no—
148#13063300—21no—
149#13063300C2312yes—
150#13063300C2312yes—
151#13063299—21no—
152#13063299—21no—
153#13063295—22no—
154Q8×Dic43—21no—
155Q8×Dic43—21no—
156Q8×Dic43—21no—
157Q8×Dic43—21no—
158C4×Dic86—21no—
159C4×Dic86—21no—
160C4×Dic86—22no—
161C4×Dic86—22no—
162#13063290—21no—
163#13063290—21no—
164#13063290—22no—
165#13063290—22no—
166#13063290C2312yes—
167#13063290C2312yes—
168C4×D172—22no—
169C4×D172—22no—
170C4×D172—21no—
171C4×D172—21no—
172#13063287—22no—
173#13063287—22no—
174#13063287—21no—
175#13063287—21no—
176#13063287C2312yes—
177#13063287C2312yes—
178(C22⋊D43)⋊C4—22no—
179(C22⋊D43)⋊C4—22no—
180#13063284C2312yes—
181#13063283—21no—
182#13063283—21no—
183#13063283—22no—
184#13063283—22no—
185#13063283C2312yes—
186#13063283C2312yes—
187#13063282—22no—
188#13063282—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×Dic43D411yescharacteristic
198C2×C4×Dic43D411yescharacteristic
199C2×C4×Dic43C2311yescharacteristic
200C42×D43—22no—
201C42×D43—22no—
202C42×D43D411yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43C2311yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210#13063258C2314yes—
211#13063258C2314yes—
212#13063256C2314yes—
213#13063256C2314yes—
214Dic43⋊C8C2314yes—
215Dic43⋊C8C2314yes—
216#13063250C2314yes—
217#13063250C2314yes—
218#13063248C2314yes—
219#13063248C2314yes—
220#13063247C2314yes—
221#13063247C2314yes—
222#13063245C2314yes—
223#13063245C2314yes—
224(C2×D43)⋊C8C2314yes—
225(C2×D43)⋊C8C2314yes—
226#13063236C2312yes—
227#13063236C2312yes—
228C22×C8×C43C2312yes—
229C4⋊Q8×C43C2311yescharacteristic
230C4⋊Q8×C43C2311yescharacteristic
231C4⋊Q8×C43C2311yescharacteristic
232C4⋊Q8×C43C2311yescharacteristic
233#125×C43C2312yes—
234#125×C43C2312yes—
235C22⋊Q8×C43—21no—
236C22⋊Q8×C43—21no—
237C22⋊Q8×C43—21no—
238C22⋊Q8×C43—21no—
239C4×Q8×C43—21no—
240C4×Q8×C43—21no—
241C4×Q8×C43—21no—
242C4×Q8×C43—21no—
243#117×C43C2312yes—
244#117×C43C2312yes—
245C2×C42×C43C2311yescharacteristic
246#107×C43C2314yes—
247#107×C43C2314yes—
248#106×C43C2314yes—
249#106×C43C2314yes—
250#97×C43C2312yes—
251#97×C43C2312yes—
252C23×D43C2×D411yescharacteristic
253C2×Q8×C43—21no—
254C2×Q8×C43—21no—
255C2×Q8×C43—21no—
256C2×Q8×C43—21no—
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C2×C22⋊D43—22no—
261C22×Dic43C2×D411yescharacteristic
262C22×Dic43C2×D411yescharacteristic
263C22×Dic43C2×D411yescharacteristic
264#10621902—44no—
265#10621902—44no—
266Q8×D43—44no—
267Q8×D43—44no—
268#10621898—28no—
269C2×D172—21no—
270C2×D172—21no—
271C2×D172—22no—
272C2×D172—22no—
273C2×D172C2412yes—
274C2×C4×D43—24no—
275C2×C4×D43—22no—
276C2×C4×D43—22no—
277C2×C4×D43—22no—
278C2×C4×D43—22no—
279C2×C4×D43—22no—
280C2×C4×D43—42no—
281C2×C4×D43—42no—
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×D43C2×D411yescharacteristic
292C2×C4×D43C2411yescharacteristic
293C2×C4×D43C2411yescharacteristic
294C2×Dic86—21no—
295C2×Dic86—21no—
296C2×Dic86—22no—
297C2×Dic86—22no—
298C2×Dic86C2412yes—
299C2×C8×C43—24no—
300C2×C8×C43C2414yes—
301C4⋊C4×C43—22no—
302C4⋊C4×C43—22no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—22no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43—21no—
308C4⋊C4×C43—21no—
309C4⋊C4×C43C2412yes—
310C4⋊C4×C43C2412yes—
311C4⋊C4×C43C2412yes—
312C4⋊C4×C43C2412yes—
313C22⋊C4×C43—22no—
314C22⋊C4×C43—22no—
315C42×C43—22no—
316C42×C43—22no—
317C42×C43C2×D411yescharacteristic
318C42×C43C2×D411yescharacteristic
319C42×C43C2411yescharacteristic
320C42×C43C2411yescharacteristic
321C22⋊Dic43—22no—
322(C2×D43)⋊C4—22no—
323(C2×D43)⋊C4—22no—
324(C2×D43)⋊C4—22no—
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)⋊C4—22no—
331(C2×D43)⋊C4—22no—
332C4⋊Dic43—21no—
333C4⋊Dic43—21no—
334C4⋊Dic43—21no—
335C4⋊Dic43—21no—
336C4⋊Dic43—22no—
337C4⋊Dic43—22no—
338C4⋊Dic43—22no—
339C4⋊Dic43—22no—
340C4⋊Dic43C2412yes—
341C4⋊Dic43C2412yes—
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—
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×C43C22×D411yescharacteristic
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—41no—
376C22×D43C22×D411yescharacteristic
377C22×D43C22×D411yescharacteristic
378Q8×C43—42no—
379Q8×C43—42no—
380Q8×C43—42no—
381Q8×C43—42no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C22×D411yescharacteristic
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C432−1+414yes—
394C2×C4×C43C2511yescharacteristic
395C22⋊D43—44no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—41no—
402C2×Dic43C22×D411yescharacteristic
403C2×Dic43C22×D411yescharacteristic
404C2×Dic43C22×D411yescharacteristic
405C2×Dic43C22×D411yescharacteristic
406C2×Dic43C22×D411yescharacteristic
407C2×Dic43C22×D411yescharacteristic
408D172—24no—
409D172—42no—
410D172—42no—
411D172—44no—
412D172—44no—
413C4×D43—22no—
414C4×D43—22no—
415C4×D43—22no—
416C4×D43—22no—
417C4×D43—22no—
418C4×D43—22no—
419C4×D43—22no—
420C4×D43—22no—
421C4×D43—41no—
422C4×D43—41no—
423C4×D43—41no—
424C4×D43—41no—
425C4×D43—44no—
426C4×D43—44no—
427C4×D43—44no—
428C4×D43—44no—
429C4×D43—44no—
430Dic86—24no—
431Dic86—44no—
432Dic86—42no—
433Dic86—42no—
434Dic86—44no—
435C8×C43—24no—
436C43⋊C8—24no—
437#60854—431nomaximal, Sylow
438C22×C43—21no—
439C22×C43—21no—
440C22×C43#53612yes—
441C22×C43C23×D411yescharacteristic
442C2×D43—21no—
443C2×D43—21no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—44no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43—42no—
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—42no—
460C4×C43#53612yes—
461C4×C43C2×2−1+412yes—
462Dic43—21no—
463Dic43—21no—
464Dic43—21no—
465Dic43—21no—
466Dic43—21no—
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#3162D4311yescharacteristic, complemented
483#3135—431no—
484#3135—431no—
485#3091—434no—
486#3076—434no—
487C2×#432—431no—
488C2×C43—22no—
489C2×C43C2×#53611yescharacteristic
490C2×C43C2×#57511yescharacteristic
491C2×C43C2×#57511yescharacteristic
492D43—22no—
493D43—41no—
494D43—82no—
495#533—431no—
496#533—431no—
497#533—432no—
498#533—432no—
499#533—431no—
500#533—431no—
501#533—431no—
502#533—861no—
503#533—861no—
504#533—861no—
505#533—861no—
506#533C2×D4311yescharacteristic
507#533C2×D4311yescharacteristic
508#532—431no—
509#532—431no—
510#532—431no—
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#501C2×D4312yescomplemented
537#501C2×D4312yescomplemented
538#501C2×D4312yescomplemented
539#501C2×D4312yescomplemented
540#491—432no—
541#491—432no—
542#490—432no—
543#490—432no—
544#489—432no—
545#489—432no—
546#489—432no—
547#489—432no—
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#427C2×D4314yes—
570C2×C4⋊C8—432no—
571#416—434no—
572#416—434no—
573C2×C22⋊C8—432no—
574C2×#97—431no—
575C2×#97C2×D4311yescharacteristic
576C43#6085411yescharacteristic, complemented, Sylow
577C2×#41—432no—
578C2×#41—861no—
579C2×#41—861no—
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—861no—
593C4⋊Q8—861no—
594C4⋊Q8—861no—
595C4⋊Q8—861no—
596C4⋊Q8C22×D4311yescharacteristic
597C4⋊Q8C22×D4311yescharacteristic
598C4⋊Q8C22×D4311yescharacteristic
599C4⋊Q8C22×D4311yescharacteristic
600#127—431no—
601#126—862no—
602#126—862no—
603#125—432no—
604#125—432no—
605#125—432no—
606#125—862no—
607#125—862no—
608#125—861no—
609#125—861no—
610#125C22×D4312yes—
611#125C22×D4312yes—
612#124—432no—
613#124—861no—
614#124—861no—
615#123—862no—
616#123—862no—
617#123—862no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C22⋊Q8—432no—
623C22⋊Q8—432no—
624C22⋊Q8—862no—
625C22⋊Q8—862no—
626C22⋊Q8—862no—
627C22⋊Q8—862no—
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—432no—
637#121—432no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#120—862no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—432no—
648C4×Q8—432no—
649C4×Q8—862no—
650C4×Q8—862no—
651C4×Q8—861no—
652C4×Q8—862no—
653C4×Q8—862no—
654C4×Q8—861no—
655C4×Q8—861no—
656C4×Q8—861no—
657C4×Q8—861no—
658C4×Q8—861no—
659C4×Q8—861no—
660C4×Q8—861no—
661C4×D4—432no—
662C4×D4—432no—
663C4×D4—862no—
664C4×D4—862no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—862no—
668C4×D4—862no—
669C4×D4—862no—
670C4×D4—862no—
671C4×D4—861no—
672C4×D4—861no—
673#117—432no—
674#117—432no—
675#117—432no—
676#117—862no—
677#117—862no—
678#117—862no—
679#117—862no—
680#117—862no—
681#117—861no—
682#117—861no—
683#117C22×D4312yes—
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#107C22×D4314yes—
709#107C22×D4314yes—
710#106—434no—
711#106—434no—
712#106C22×D4314yes—
713#106C22×D4314yes—
714C4⋊C8—434no—
715C4⋊C8—434no—
716#103—434no—
717#103—434no—
718#103—434no—
719#103—434no—
720#102—434no—
721#102—434no—
722#102—434no—
723#102—434no—
724C22⋊C8—434no—
725C22⋊C8—434no—
726#97—432no—
727#97—432no—
728#97C22×D4312yes—
729#97C22×D4312yes—
730C24—431no—
731#41—868no—
732#41—1724no—
733#41—1724no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—432no—
739C2×Q8—862no—
740C2×Q8—862no—
741C2×Q8—861no—
742C2×Q8—861no—
743C2×Q8—1724no—
744C2×Q8—1724no—
745C2×D4—432no—
746C2×D4—862no—
747C2×D4—862no—
748C2×D4—862no—
749C2×D4—861no—
750C2×D4—861no—
751C22×C4—431no—
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—862no—
767C22×C4—862no—
768C22×C4—862no—
769C22×C4—862no—
770C22×C4—864no—
771C22×C4—862no—
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—22no—
788C4⋊C4—22no—
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⋊C4C23×D4312yes—
810C4⋊C4C23×D4312yes—
811C4⋊C4C23×D4312yes—
812C4⋊C4C23×D4312yes—
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—862no—
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—22no—
828C42—431no—
829C42—431no—
830C42—431no—
831C42—431no—
832C42—431no—
833C42—431no—
834C42—431no—
835C42—431no—
836C42—431no—
837C42—431no—
838C42—431no—
839C42—431no—
840C42—862no—
841C42—862no—
842C42—862no—
843C42—862no—
844C42—862no—
845C42D4×D4311yescharacteristic
846C42D4×D4311yescharacteristic
847C42C23×D4311yescharacteristic
848C42C23×D4311yescharacteristic
849C23—431no—
850C23—431no—
851C23—862no—
852C23—862no—
853C23—862no—
854C23—1721no—
855C23C2×D4×D4311yescharacteristic
856Q8—42no—
857Q8—42no—
858Q8—42no—
859Q8—42no—
860Q8—864no—
861Q8—1722no—
862Q8—1722no—
863Q8—1724no—
864Q8—1724no—
865D4—864no—
866D4—1722no—
867D4—1722no—
868D4—1724no—
869D4—1724no—
870D4—1724no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—41no—
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—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1724no—
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#1306337314yes—
912C2×C4C24×D4311yescharacteristic
913C8—24no—
914C8—864no—
915C22—21no—
916C22—21no—
917C22—432no—
918C22—861no—
919C22—861no—
920C22—861no—
921C22—861no—
922C22—861no—
923C22—1724no—
924C22—1722no—
925C22—1722no—
926C22—1722no—
927C22#1458347412yes—
928C22C22×D4×D4311yescharacteristic
929C4—21no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—432no—
938C4—861no—
939C4—861no—
940C4—861no—
941C4—861no—
942C4—861no—
943C4—1722no—
944C4—1722no—
945C4—1722no—
946C4#1458347412yes—
947C4C2×#1306337312yes—
948C2—22no—
949C2—862no—
950C2—3442no—
951C2—1721no—
952C2C2×#1458347411yescharacteristic
953C2#575×D4311yescharacteristic
954C2#575×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3162C2
socleC22×C43C23×D4
prime radical#19147892C2
hypercenter#3162D43
hypocenterC43#60854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
2. #533×D43C2semidirect
3. #19145838C2semidirect
4. #19145836C2semidirect
5. #19145826C2semidirect
6. #19145817C2semidirect
7. #19145810C2semidirect
8. #19145802C2semidirect
9. #19145794C2semidirect
10. #19145786C2semidirect
11. #19145117C2semidirect
12. #19144943C2semidirect
13. #19144941C2semidirect
14. #19144512C2semidirect
15. #19144381C2semidirect
16. C2×#14582954C2semidirect
17. C43×#3162C2semidirect
53. #14583309C22semidirect
54. #14583309C22semidirect
55. #14583305C22semidirect
56. #14583305C22semidirect
57. #14583269C22semidirect
58. #14583268C22semidirect
59. #14583265C22semidirect
60. #14583264C22semidirect
61. #14583261C22semidirect
62. #14583261C22semidirect
63. #14583259C22semidirect
64. #14583259C22semidirect
73. #14583209C22semidirect
74. #14583205C22semidirect
75. #14583202C22semidirect
76. #14583198C22semidirect
77. #14583193C22semidirect
78. #14583188C22semidirect
79. #14583183C22semidirect
80. #14583178C22semidirect
93. C43×#501C22semidirect
94. C43×#501C22semidirect
95. C43×#501C22semidirect
96. C43×#501C22semidirect
482. #3162D43semidirect
536. #501C2×D43semidirect
537. #501C2×D43semidirect
538. #501C2×D43semidirect
539. #501C2×D43semidirect
576. C43#60854semidirect

Maximal subgroups

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

subgroupindex
#191478922
#533×D432
#191458382
#191458362
#191458262
#191458172
#191458102
#191458022
#191457942
#191457862
#191451172
#191449432
#191449412
#191445122
#191443812
C2×#145829542
C43×#31622
#6085443