Finite Group Databasebeta

← #25968932

Subgroups — #25968932

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×#14583434C211yesmaximal, characteristic
3#19145838C212yesmaximal, complemented
4#19145836C212yesmaximal, complemented
5#19145826C212yesmaximal, complemented
6#19145817C212yesmaximal, complemented
7#19145775C214yesmaximal, complemented
8#19145764C214yesmaximal, complemented
9#19145144C211yesmaximal, characteristic, complemented
10#19144984C211yesmaximal, characteristic, complemented
11#19144982C211yesmaximal, characteristic, complemented
12#19144545C212yesmaximal, complemented
13#19144537C212yesmaximal
14#19144399C212yesmaximal, complemented
15#19144391C212yesmaximal, complemented
16#19143226C211yesmaximal, characteristic, complemented
17C43×#3166C211yesmaximal, 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#14583434—21no—
30#14583434—21no—
31#14583434—21no—
32#14583434—21no—
33#14583434C2212yes—
34#14583434C2212yes—
35#14583434C2212yes—
36#14583434C2212yes—
37C2×#13063320—21no—
38#125×D43C2212yescomplemented
39C2×#13063313C2211yescharacteristic
40C2×#13063310—21no—
41C2×#13063305C2211yescharacteristic
42C22⋊Q8×D43—21no—
43C22⋊Q8×D43—21no—
44C2×#13063300C2211yescharacteristic
45C2×#13063290C2211yescharacteristic
46C4×Q8×D43—21no—
47C4×Q8×D43—21no—
48C2×#13063287—21no—
49C2×#13063287C2211yescharacteristic
50C2×#13063283—21no—
51#117×D43C2212yes—
52C2×C42×D43C2211yescharacteristic
53#14583309C2212yescomplemented
54#14583309C2212yescomplemented
55#14583298C2214yescomplemented
56#14583261C2212yescomplemented
57#14583261C2212yescomplemented
58#14583259C2212yescomplemented
59#14583259C2212yescomplemented
60#14583256C2214yescomplemented
61#14583254C2214yescomplemented
62#14583243C2214yescomplemented
63#14583242C2214yescomplemented
64#14583236C2214yescomplemented
65#14583231C2214yescomplemented
66#14583226C2214yes—
67#14583225C2214yes—
68#14583219C2214yes—
69#14583214C2214yes—
70#14583209C2214yescomplemented
71#14583205C2214yescomplemented
72#14583202C2214yescomplemented
73#14583198C2214yescomplemented
74#14583193C2214yescomplemented
75#14583188C2214yescomplemented
76#14583183C2214yescomplemented
77#14583178C2214yescomplemented
78#14582954C2212yescomplemented
79#14582954C2212yescomplemented
80#14582950C2212yescomplemented
81#14582950C2212yescomplemented
82#14582939C2212yes—
83#14582939C2212yes—
84#14582922C2212yes—
85#14582909C2212yes—
86#14582907C2212yes—
87#14582905C2212yes—
88#14582903C2212yes—
89#14582862C2212yes—
90C4×#10621877C2211yescharacteristic
91C43×#533C2211yescharacteristic
92C2×#125×C43C2211yescharacteristic
93C43×#501C2212yescomplemented
94C43×#501C2212yescomplemented
95C43×#499C2214yescomplemented
96C43×#428C2212yes—
97C43×#428C2212yes—
98C4×M16×C43C2211yescharacteristic
99C22×Dic86C2311yescharacteristic
100C2×Q8×D43—21no—
101C2×Q8×D43—21no—
102C22×D172—21no—
103C22×D172C2311yescharacteristic
104C22×C4×D43—21no—
105C22×C4×D43D411yescharacteristic
106C22×C4×D43D411yescharacteristic
107C22×C4×D43C2311yescharacteristic
108C2×#10621877C2312yes—
109#13063325C2311yescharacteristic
110#13063325C2311yescharacteristic
111#13063324—21no—
112#13063324—21no—
113#13063324C2312yes—
114#13063324C2312yes—
115#13063323—21no—
116#13063323—21no—
117#13063320—22no—
118#13063320—22no—
119#13063320—22no—
120#13063320—22no—
121#13063317C2312yes—
122#13063316C2312yes—
123#13063316C2312yes—
124#13063315—22no—
125#13063315—22no—
126#13063313—21no—
127#13063313—21no—
128#13063313C2312yes—
129#13063313C2312yes—
130#13063310—22no—
131#13063310—22no—
132#13063310—22no—
133#13063310—22no—
134#13063305—21no—
135#13063305—21no—
136#13063305—21no—
137#13063305—21no—
138#13063305C2312yes—
139#13063305C2312yes—
140#13063304—21no—
141#13063304—21no—
142#13063303—22no—
143#13063303—22no—
144#13063302—22no—
145#13063302—22no—
146#13063301—21no—
147#13063301—21no—
148#13063300—21no—
149#13063300—21no—
150#13063300C2312yes—
151#13063300C2312yes—
152Q8×Dic43—21no—
153Q8×Dic43—21no—
154C4×Dic86—21no—
155C4×Dic86—21no—
156C4×Dic86—22no—
157C4×Dic86—22no—
158#13063290—21no—
159#13063290—21no—
160#13063290—22no—
161#13063290—22no—
162#13063290—21no—
163#13063290—21no—
164#13063290C2312yes—
165#13063290C2312yes—
166#13063287—22no—
167#13063287—22no—
168#13063287—22no—
169#13063287—22no—
170#13063287—21no—
171#13063287—21no—
172#13063287C2312yes—
173#13063287C2312yes—
174#13063284C2312yes—
175#13063283—22no—
176#13063283—22no—
177#13063283—22no—
178#13063283—22no—
179#13063283C2312yes—
180#13063283C2312yes—
181#13063282—22no—
182#13063281—22no—
183C2×C4⋊Dic43—21no—
184C2×Dic43⋊C4—21no—
185C4⋊C4×D43—22no—
186C4⋊C4×D43—22no—
187C4⋊C4×D43—21no—
188C4⋊C4×D43—21no—
189C4⋊C4×D43C2312yes—
190C4⋊C4×D43C2312yes—
191C2×(C2×D43)⋊C4—21no—
192C2×(C2×D43)⋊C4—21no—
193C2×(C2×D43)⋊C4—21no—
194C2×(C2×D43)⋊C4—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#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—
227C4×C43⋊C8C2312yes—
228C2×M16×C43C2312yes—
229C4⋊Q8×C43C2311yescharacteristic
230C4⋊Q8×C43C2311yescharacteristic
231#125×C43—21no—
232#125×C43—21no—
233#125×C43C2312yes—
234#125×C43C2312yes—
235#125×C43C2312yes—
236C22⋊Q8×C43—21no—
237C22⋊Q8×C43—21no—
238C4×Q8×C43—21no—
239C4×Q8×C43—21no—
240#117×C43C2312yes—
241C2×C4⋊C4×C43—21no—
242C2×C4⋊C4×C43—21no—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C42×C43C2311yescharacteristic
246#107×C43C2314yes—
247#107×C43C2314yes—
248#106×C43C2314yes—
249#106×C43C2314yes—
250#97×C43C2312yes—
251C4×C8×C43C2312yes—
252C23×D43—21no—
253C23×D43C2×D411yescharacteristic
254C2×Q8×C43—21no—
255C2×Q8×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2411yescharacteristic
261C22×Dic43—21no—
262C22×Dic43C2×D411yescharacteristic
263C22×Dic43C2×D411yescharacteristic
264C22×Dic43C2×D411yescharacteristic
265Q8×D43—44no—
266Q8×D43—44no—
267C2×D172—21no—
268C2×D172—22no—
269C2×D172—22no—
270C2×D172—24no—
271C2×D172—44no—
272C2×D172C2412yes—
273C2×C4×D43—24no—
274C2×C4×D43—22no—
275C2×C4×D43—22no—
276C2×C4×D43—22no—
277C2×C4×D43—22no—
278C2×C4×D43—42no—
279C2×C4×D43—42no—
280C2×C4×D43—44no—
281C2×C4×D43C2×D411yescharacteristic
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×D43C2411yescharacteristic
292C2×C4×D43C2411yescharacteristic
293C2×Dic86—24no—
294C2×Dic86—21no—
295C2×Dic86—21no—
296C2×Dic86—21no—
297C2×Dic86—22no—
298C2×Dic86—22no—
299C2×Dic86C2412yes—
300M16×C43—24no—
301C2×C8×C43C2414yes—
302C4⋊C4×C43—22no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—22no—
305C4⋊C4×C43—22no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43—21no—
308C4⋊C4×C43—22no—
309C4⋊C4×C43—22no—
310C4⋊C4×C43—21no—
311C4⋊C4×C43—21no—
312C4⋊C4×C43C2412yes—
313C4⋊C4×C43C2412yes—
314C4⋊C4×C43C2412yes—
315C4⋊C4×C43C2412yes—
316C22⋊C4×C43—22no—
317C42×C43—22no—
318C42×C43C2×D411yescharacteristic
319C42×C43C2×D411yescharacteristic
320C42×C43C2411yescharacteristic
321C42×C43C2411yescharacteristic
322C22⋊Dic43—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—
332(C2×D43)⋊C4—22no—
333(C2×D43)⋊C4—22no—
334(C2×D43)⋊C4—22no—
335C4⋊Dic43—21no—
336C4⋊Dic43—21no—
337C4⋊Dic43—22no—
338C4⋊Dic43—22no—
339C4⋊Dic43—22no—
340C4⋊Dic43—22no—
341C4⋊Dic43C2412yes—
342C4⋊Dic43C2412yes—
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×C43C22×D411yescharacteristic
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—41no—
377C22×D43—42no—
378C22×D43—42no—
379C22×D43—42no—
380C22×D43C22×D411yescharacteristic
381C22×D43C22×D411yescharacteristic
382Q8×C43—42no—
383Q8×C43—42no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—42no—
391C2×C4×C43—42no—
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C22×D411yescharacteristic
397C2×C4×C432−1+414yes—
398C2×C4×C43C2511yescharacteristic
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—41no—
405C2×Dic43—42no—
406C2×Dic43C22×D411yescharacteristic
407C2×Dic43C22×D411yescharacteristic
408C2×Dic43C22×D411yescharacteristic
409C2×Dic43C22×D411yescharacteristic
410C2×Dic43C22×D411yescharacteristic
411C2×Dic43C22×D411yescharacteristic
412D172—24no—
413D172—44no—
414D172—44no—
415D172—42no—
416C4×D43—22no—
417C4×D43—22no—
418C4×D43—22no—
419C4×D43—22no—
420C4×D43—22no—
421C4×D43—22no—
422C4×D43—22no—
423C4×D43—22no—
424C4×D43—41no—
425C4×D43—41no—
426C4×D43—41no—
427C4×D43—41no—
428C4×D43—44no—
429C4×D43—44no—
430C4×D43—44no—
431C4×D43—44no—
432Dic86—24no—
433Dic86—44no—
434Dic86—42no—
435Dic86—42no—
436Dic86—42no—
437Dic86—44no—
438C8×C43—24no—
439C43⋊C8—24no—
440#60866—431nomaximal, Sylow
441C22×C43—21no—
442C22×C43—21no—
443C22×C43#53612yes—
444C22×C43C23×D411yescharacteristic
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—44no—
451C2×D43—42no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—84no—
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—42no—
464C4×C43#53612yes—
465C4×C43C2×2−1+412yes—
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—21no—
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#3166D4311yescharacteristic, complemented
485#3140—431no—
486#3140—431no—
487#3095—432no—
488#3094—432no—
489#3078—432no—
490#3077—432no—
491#2920—431no—
492C2×C43—22no—
493C2×C43C2×#53611yescharacteristic
494C2×C43C2×#57511yescharacteristic
495C2×C43C2×#57511yescharacteristic
496D43—22no—
497D43—41no—
498D43—82no—
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×#125C2×D4311yescharacteristic
522C2×#124—431no—
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#501C2×D4312yescomplemented
539#501C2×D4312yescomplemented
540#499—434no—
541#499C2×D4314yescomplemented
542#489—432no—
543#489—432no—
544#489—432no—
545#489—432no—
546#488—434no—
547#488—434no—
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#428C2×D4312yes—
571#428C2×D4312yes—
572#423—432no—
573#419—432no—
574#419—432no—
575#418—432no—
576#418—432no—
577#407—432no—
578C4×M16—431no—
579C4×M16C2×D4311yescharacteristic
580C43#6086611yescharacteristic, complemented, Sylow
581C22×Q8—431no—
582C22×Q8—861no—
583C22×Q8—861no—
584C22×D4—431no—
585C22×D4—861no—
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—21no—
607#125—21no—
608#125—432no—
609#125—432no—
610#125—432no—
611#125—862no—
612#125—862no—
613#125C22×D4312yes—
614#125C22×D4312yes—
615#125C22×D4312yes—
616#124—432no—
617#124—432no—
618#124—861no—
619#124—861no—
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—861no—
631C22⋊Q8—861no—
632C22⋊Q8—862no—
633C22⋊Q8—862no—
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—861no—
651C4×Q8—861no—
652C4×Q8—862no—
653C4×Q8—861no—
654C4×Q8—862no—
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—21no—
679C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
689C2×C4⋊C4C22×D4311yescharacteristic
690C2×C22⋊C4—862no—
691C2×C22⋊C4—861no—
692C2×C22⋊C4—861no—
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#107C22×D4314yes—
713#107C22×D4314yes—
714#106—434no—
715#106—434no—
716#106C22×D4314yes—
717#106C22×D4314yes—
718C4⋊C8—434no—
719C4⋊C8—434no—
720#103—434no—
721#103—434no—
722#103—434no—
723#103—434no—
724#102—434no—
725#102—434no—
726#102—434no—
727#102—434no—
728C22⋊C8—434no—
729C22⋊C8—434no—
730#97—432no—
731#97C22×D4312yes—
732C4×C8—432no—
733C4×C8C22×D4312yes—
734C24—431no—
735C24—861no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—432no—
739C2×Q8—862no—
740C2×Q8—862no—
741C2×Q8—861no—
742C2×Q8—861no—
743C2×Q8—861no—
744C2×Q8—864no—
745C2×Q8—1724no—
746C2×Q8—1724no—
747C2×D4—432no—
748C2×D4—862no—
749C2×D4—862no—
750C2×D4—861no—
751C2×D4—864no—
752C2×D4—1724no—
753C22×C4—21no—
754C22×C4—21no—
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—431no—
770C22×C4—862no—
771C22×C4—862no—
772C22×C4—862no—
773C22×C4—862no—
774C22×C4—864no—
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—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—432no—
797C4⋊C4—432no—
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—862no—
807C4⋊C4—862no—
808C4⋊C4—862no—
809C4⋊C4—862no—
810C4⋊C4—862no—
811C4⋊C4—862no—
812C4⋊C4—861no—
813C4⋊C4—861no—
814C4⋊C4C23×D4312yes—
815C4⋊C4C23×D4312yes—
816C4⋊C4C23×D4312yes—
817C4⋊C4C23×D4312yes—
818C22⋊C4—22no—
819C22⋊C4—862no—
820C22⋊C4—862no—
821C22⋊C4—862no—
822C22⋊C4—862no—
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—431no—
855C23—431no—
856C23—862no—
857C23—862no—
858C23—862no—
859C23—1721no—
860C23—1722no—
861C23—1722no—
862C23—1722no—
863C23C2×D4×D4311yescharacteristic
864Q8—42no—
865Q8—42no—
866Q8—864no—
867Q8—1722no—
868Q8—1722no—
869Q8—1724no—
870Q8—1724no—
871Q8—1722no—
872D4—864no—
873D4—1724no—
874D4—1724no—
875D4—1722no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—431no—
885C2×C4—431no—
886C2×C4—431no—
887C2×C4—431no—
888C2×C4—431no—
889C2×C4—431no—
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—862no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1724no—
908C2×C4—1724no—
909C2×C4—1724no—
910C2×C4—1724no—
911C2×C4—1721no—
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#1306337314yes—
919C2×C4C24×D4311yescharacteristic
920C8—24no—
921C8—864no—
922C22—21no—
923C22—21no—
924C22—432no—
925C22—861no—
926C22—861no—
927C22—861no—
928C22—861no—
929C22—861no—
930C22—3444no—
931C22—1724no—
932C22—1722no—
933C22—1722no—
934C22—1722no—
935C22#1458347412yes—
936C22C22×D4×D4311yescharacteristic
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—432no—
946C4—861no—
947C4—861no—
948C4—861no—
949C4—861no—
950C4—861no—
951C4—1722no—
952C4—1722no—
953C4—1722no—
954C4#1458347412yes—
955C4C2×#1306337312yes—
956C2—22no—
957C2—862no—
958C2—3442no—
959C2—1721no—
960C2C2×#1458347411yescharacteristic
961C2#575×D4311yescharacteristic
962C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3166C2
socleC22×C43C23×D4
prime radicalC2×#13063300C22
hypercenter#3166D43
hypocenterC43#60866
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
1. #533×D43C2semidirect
3. #19145838C2semidirect
4. #19145836C2semidirect
5. #19145826C2semidirect
6. #19145817C2semidirect
7. #19145775C2semidirect
8. #19145764C2semidirect
9. #19145144C2semidirect
10. #19144984C2semidirect
11. #19144982C2semidirect
12. #19144545C2semidirect
14. #19144399C2semidirect
15. #19144391C2semidirect
16. #19143226C2semidirect
17. C43×#3166C2semidirect
19. #14583455C22semidirect
20. #14583454C22semidirect
21. #14583454C22semidirect
27. C4⋊Q8×D43C22semidirect
28. C4⋊Q8×D43C22semidirect
38. #125×D43C22semidirect
53. #14583309C22semidirect
54. #14583309C22semidirect
55. #14583298C22semidirect
56. #14583261C22semidirect
57. #14583261C22semidirect
58. #14583259C22semidirect
59. #14583259C22semidirect
60. #14583256C22semidirect
61. #14583254C22semidirect
62. #14583243C22semidirect
63. #14583242C22semidirect
64. #14583236C22semidirect
65. #14583231C22semidirect
70. #14583209C22semidirect
71. #14583205C22semidirect
72. #14583202C22semidirect
73. #14583198C22semidirect
74. #14583193C22semidirect
75. #14583188C22semidirect
76. #14583183C22semidirect
77. #14583178C22semidirect
78. #14582954C22semidirect
79. #14582954C22semidirect
80. #14582950C22semidirect
81. #14582950C22semidirect
93. C43×#501C22semidirect
94. C43×#501C22semidirect
95. C43×#499C22semidirect
484. #3166D43semidirect
538. #501C2×D43semidirect
539. #501C2×D43semidirect
541. #499C2×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×#145834342
#191458382
#191458362
#191458262
#191458172
#191457752
#191457642
#191451442
#191449842
#191449822
#191445452
#191445372
#191443992
#191443912
#191432262
C43×#31662
#6086643