Finite Group Databasebeta

← #25968934

Subgroups — #25968934

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
1C2×#14583452C211yesmaximal, characteristic, complemented
2C2×#14583435C211yesmaximal, characteristic
3#19145839C214yesmaximal, complemented
4#19145828C212yesmaximal, complemented
5#19145819C212yesmaximal, complemented
6#19145777C214yesmaximal, complemented
7#19145768C212yesmaximal, complemented
8#19145766C212yesmaximal, complemented
9#19145145C212yesmaximal, complemented
10#19144983C212yesmaximal, complemented
11#19144539C211yesmaximal, characteristic, complemented
12#19144536C211yesmaximal, characteristic
13#19144535C211yesmaximal, characteristic
14#19144397C212yesmaximal, complemented
15#19144391C212yesmaximal, complemented
16#19143224C211yesmaximal, characteristic, complemented
17C43×#3095C211yesmaximal, characteristic, complemented
18#14583452—21no—
19#14583452—21no—
20#14583452—21no—
21#14583452—21no—
22#14583452C2212yes—
23#14583452C2212yes—
24#14583452C2212yescomplemented
25#14583452C2212yescomplemented
26C2×#13063324C2211yescharacteristic, complemented
27C2×#13063324C2211yescharacteristic, complemented
28#14583435—21no—
29#14583435—21no—
30#14583435—21no—
31#14583435—21no—
32#14583435C2212yes—
33#14583435C2212yes—
34#14583435C2212yes—
35#14583435C2212yes—
36C2×#13063320—21no—
37C2×#13063316C2211yescharacteristic
38C2×#13063316C2211yescharacteristic, complemented
39C2×#13063316C2211yescharacteristic, complemented
40C2×#13063314C2211yescharacteristic
41C2×#13063309—21no—
42C2×#13063302—21no—
43C2×#13063302—21no—
44C2×#13063299C2211yescharacteristic
45C2×Q8×Dic43C2211yescharacteristic
46C2×C4×Dic86—21no—
47C2×C4×Dic86—21no—
48C2×#13063287C2211yescharacteristic
49C2×(C22⋊D43)⋊C4—21no—
50C2×#13063284C2211yescharacteristic
51C2×#13063283—21no—
52C22×C4×Dic43C2211yescharacteristic
53#14583307C2214yescomplemented
54#14583306C2214yescomplemented
55#14583300C2214yescomplemented
56#14583299C2214yescomplemented
57#14583260C2214yescomplemented
58#14583260C2214yescomplemented
59#14583255C2214yescomplemented
60#14583255C2214yescomplemented
61#14583237C2214yescomplemented
62#14583232C2212yescomplemented
63#14583227C2212yescomplemented
64#14583224C2214yes—
65#14583223C2214yes—
66#14583218C2212yes—
67#14583217C2212yes—
68#14583213C2212yes—
69#14583212C2212yes—
70#14583208C2214yescomplemented
71#14583204C2214yescomplemented
72#14583202C2214yescomplemented
73#14583198C2214yescomplemented
74#14583192C2214yescomplemented
75#14583188C2214yescomplemented
76#14583182C2214yescomplemented
77#14583178C2214yescomplemented
78#14582953C2212yescomplemented
79#14582953C2212yescomplemented
80#14582949C2212yescomplemented
81#14582949C2212yescomplemented
82#14582942C2212yes—
83#14582941C2212yes—
84#14582939C2212yes—
85#14582922C2212yes—
86#14582908C2212yes—
87#14582905C2212yes—
88#14582903C2212yes—
89#14582863C2211yescharacteristic
90M16×Dic43C2212yes—
91C2×C22⋊Q8×C43C2211yescharacteristic
92C2×#117×C43C2211yescharacteristic
93C43×#485C2214yescomplemented
94C43×#484C2212yescomplemented
95C43×#483C2212yescomplemented
96C43×#428C2212yes—
97C43×#419C2212yes—
98C43×#407C2211yescharacteristic
99C22×Dic86—21no—
100C22×Dic86—21no—
101C22×D172C2311yescharacteristic
102C22×C22⋊D43—21no—
103C23×Dic43D411yescharacteristic
104C23×Dic43D411yescharacteristic
105C22×C4×D43—21no—
106C2×#10621877C2312yes—
107#13063324—21no—
108#13063324—21no—
109#13063324—21no—
110#13063324—21no—
111#13063324C2312yes—
112#13063324C2312yes—
113#13063324C2312yes—
114#13063324C2312yes—
115#13063320—22no—
116#13063320—22no—
117#13063320—22no—
118#13063320—22no—
119#13063316—21no—
120#13063316—21no—
121#13063316—21no—
122#13063316—21no—
123#13063316—21no—
124#13063316—21no—
125#13063316C2312yes—
126#13063316C2312yes—
127#13063316C2312yes—
128#13063316C2312yes—
129#13063316C2312yes—
130#13063316C2312yes—
131#13063314—21no—
132#13063314—21no—
133#13063314C2312yes—
134#13063314C2312yes—
135#13063309—22no—
136#13063309—22no—
137#13063309—22no—
138#13063309—22no—
139#13063302—22no—
140#13063302—22no—
141#13063302—22no—
142#13063302—22no—
143#13063302—22no—
144#13063302—22no—
145#13063302—22no—
146#13063302—22no—
147#13063299—21no—
148#13063299—21no—
149#13063299C2312yes—
150#13063299C2312yes—
151Q8×Dic43—21no—
152Q8×Dic43—21no—
153Q8×Dic43C2312yes—
154Q8×Dic43C2312yes—
155C4×Dic86—22no—
156C4×Dic86—22no—
157C4×Dic86—22no—
158C4×Dic86—22no—
159C4×Dic86—22no—
160C4×Dic86—22no—
161C4×Dic86—22no—
162C4×Dic86—22no—
163#13063287—21no—
164#13063287—21no—
165#13063287C2312yes—
166#13063287C2312yes—
167(C22⋊D43)⋊C4—22no—
168(C22⋊D43)⋊C4—22no—
169(C22⋊D43)⋊C4—22no—
170(C22⋊D43)⋊C4—22no—
171#13063284—21no—
172#13063284—21no—
173#13063284C2312yes—
174#13063284C2312yes—
175#13063283—22no—
176#13063283—22no—
177#13063283—22no—
178#13063283—22no—
179C2×C4⋊Dic43—21no—
180C2×C4⋊Dic43—21no—
181C2×C4⋊Dic43—21no—
182C2×C4⋊Dic43—21no—
183C2×C4⋊Dic43C2311yescharacteristic
184C2×C4⋊Dic43C2311yescharacteristic
185C2×C4⋊Dic43C2311yescharacteristic
186C2×Dic43⋊C4—21no—
187C2×Dic43⋊C4—21no—
188C2×Dic43⋊C4—21no—
189C2×Dic43⋊C4—21no—
190C2×Dic43⋊C4—21no—
191C2×C22⋊Dic43—21no—
192C2×(C2×D43)⋊C4—21no—
193C2×(C2×D43)⋊C4—21no—
194C2×(C2×D43)⋊C4—21no—
195C2×(C2×D43)⋊C4—21no—
196C2×C4×Dic43—21no—
197C2×C4×Dic43—21no—
198C2×C4×Dic43D411yescharacteristic
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43D411yescharacteristic
201C2×C4×Dic43D411yescharacteristic
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43D411yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210#13063259C2314yes—
211#13063258C2314yes—
212#13063258C2314yes—
213#13063257C2314yes—
214#13063256C2314yes—
215#13063256C2314yes—
216Dic43⋊C8C2314yes—
217Dic43⋊C8C2314yes—
218#13063249C2314yes—
219#13063249C2314yes—
220#13063247C2314yes—
221#13063247C2314yes—
222#13063245C2314yes—
223#13063245C2314yes—
224C22⋊(C43⋊C8)C2312yes—
225C22⋊(C43⋊C8)C2312yes—
226#13063235C2314yes—
227C8×Dic43C2314yes—
228C22×Q8×C43C2311yescharacteristic
229C23×C4×C43C2311yescharacteristic
230C2×M16×C43C2312yes—
231C22⋊Q8×C43—21no—
232C22⋊Q8×C43—21no—
233C22⋊Q8×C43C2312yes—
234C22⋊Q8×C43C2312yes—
235#117×C43—21no—
236#117×C43—21no—
237#117×C43C2312yes—
238#117×C43C2312yes—
239C2×C4⋊C4×C43—21no—
240C2×C4⋊C4×C43C2311yescharacteristic
241C2×C4⋊C4×C43C2311yescharacteristic
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C22⋊C4×C43—21no—
244C2×C22⋊C4×C43—21no—
245C2×C42×C43—21no—
246#107×C43C2314yes—
247#106×C43C2314yes—
248#103×C43C2314yes—
249#103×C43C2314yes—
250C22⋊C8×C43C2312yes—
251C22⋊C8×C43C2312yes—
252C24×C43C2×D411yescharacteristic
253C23×D43—21no—
254C2×Q8×C43—21no—
255C2×Q8×C43—24no—
256C2×Q8×C43C2412yes—
257C22×C4×C43—24no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266C22×C4×C43C2411yescharacteristic
267C22×C4×C43C2411yescharacteristic
268C2×C22⋊D43—22no—
269C2×C22⋊D43—22no—
270C2×C22⋊D43—44no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—42no—
275C22×Dic43—42no—
276C22×Dic43C2×D411yescharacteristic
277C22×Dic43C2×D411yescharacteristic
278C22×Dic43C2×D411yescharacteristic
279C22×Dic43C2×D411yescharacteristic
280C22×Dic43C2×D411yescharacteristic
281C22×Dic43C2×D411yescharacteristic
282C22×Dic43C2×D411yescharacteristic
283C22×Dic43C2×D411yescharacteristic
284C22×Dic43C2×D411yescharacteristic
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287C22×Dic43C2×D411yescharacteristic
288C2×D172—21no—
289C2×D172—24no—
290C2×D172C2412yes—
291C2×C4×D43—22no—
292C2×C4×D43—22no—
293C2×C4×D43—44no—
294C2×Dic86—22no—
295C2×Dic86—22no—
296C2×Dic86—22no—
297C2×Dic86—22no—
298C2×Dic86—44no—
299C2×Dic86—44no—
300M16×C43—24no—
301C2×C8×C43C2414yes—
302C4⋊C4×C43—22no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—21no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43C2412yes—
308C4⋊C4×C43C2412yes—
309C4⋊C4×C43C2412yes—
310C22⋊C4×C43—22no—
311C22⋊C4×C43—22no—
312C22⋊C4×C43—22no—
313C22⋊C4×C43—22no—
314C42×C43—22no—
315C42×C43—22no—
316C22⋊Dic43—22no—
317C22⋊Dic43—22no—
318(C2×D43)⋊C4—22no—
319(C2×D43)⋊C4—22no—
320(C2×D43)⋊C4—22no—
321(C2×D43)⋊C4—22no—
322(C2×D43)⋊C4—22no—
323(C2×D43)⋊C4—22no—
324(C2×D43)⋊C4—22no—
325(C2×D43)⋊C4—22no—
326C4⋊Dic43—21no—
327C4⋊Dic43—21no—
328C4⋊Dic43—21no—
329C4⋊Dic43—22no—
330C4⋊Dic43—22no—
331C4⋊Dic43—22no—
332C4⋊Dic43—22no—
333C4⋊Dic43—22no—
334C4⋊Dic43—22no—
335C4⋊Dic43—22no—
336C4⋊Dic43—22no—
337C4⋊Dic43C2412yes—
338C4⋊Dic43C2412yes—
339C4⋊Dic43C2412yes—
340Dic43⋊C4—22no—
341Dic43⋊C4—22no—
342Dic43⋊C4—22no—
343Dic43⋊C4—22no—
344Dic43⋊C4—22no—
345Dic43⋊C4—22no—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349Dic43⋊C4—22no—
350C4×Dic43—22no—
351C4×Dic43—22no—
352C4×Dic43—22no—
353C4×Dic43—22no—
354C4×Dic43C2×D411yescharacteristic
355C4×Dic43C2×D411yescharacteristic
356C4×Dic43C2×D411yescharacteristic
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×Dic43C2411yescharacteristic
367C4×Dic43C2411yescharacteristic
368C4×Dic43C2411yescharacteristic
369C4×Dic43C2411yescharacteristic
370#10621877—24no—
371C2×C43⋊C8C2414yes—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—41no—
375C23×C43C22×D411yescharacteristic
376C23×C43C22×D411yescharacteristic
377C23×C43C22×D411yescharacteristic
378C22×D43—22no—
379C22×D43—42no—
380C22×D43—42no—
381C22×D43—42no—
382Q8×C43—24no—
383Q8×C43—42no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—42no—
394C2×C4×C43—42no—
395C2×C4×C43—42no—
396C2×C4×C43—42no—
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43C22×D411yescharacteristic
399C2×C4×C43C22×D411yescharacteristic
400C2×C4×C432−1+414yes—
401C2×C4×C43C2511yescharacteristic
402C22⋊D43—44no—
403C22⋊D43—44no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—42no—
420C2×Dic43—42no—
421C2×Dic43—42no—
422C2×Dic43C22×D411yescharacteristic
423C2×Dic43C22×D411yescharacteristic
424C2×Dic43C22×D411yescharacteristic
425C2×Dic43C22×D411yescharacteristic
426C2×Dic43C22×D411yescharacteristic
427C2×Dic43C22×D411yescharacteristic
428C2×Dic43C22×D411yescharacteristic
429C2×Dic43C22×D411yescharacteristic
430D172—24no—
431D172—42no—
432C4×D43—44no—
433C4×D43—44no—
434Dic86—44no—
435Dic86—44no—
436Dic86—44no—
437Dic86—44no—
438C8×C43—24no—
439C43⋊C8—24no—
440#60866—431nomaximal, Sylow
441C22×C43—21no—
442C22×C43—21no—
443C22×C43—21no—
444C22×C43—21no—
445C22×C43—21no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—44no—
449C22×C43#53612yes—
450C22×C43#57512yes—
451C22×C43C23×D411yescharacteristic
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—42no—
455C2×D43—84no—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—42no—
459C4×C43—42no—
460C4×C43—42no—
461C4×C43—42no—
462C4×C43#53612yes—
463C4×C43C2×2−1+412yes—
464Dic43—21no—
465Dic43—21no—
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—434no—
478#3239—432no—
479#3238—432no—
480#3233—434no—
481#3232—432no—
482#3232—432no—
483#3166—432no—
484#3140—432no—
485#3095—431no—
486#3095D4311yescharacteristic, complemented
487#3094—431no—
488#3094—431no—
489#3078—432no—
490#3077—432no—
491#2920—431no—
492C2×C43—22no—
493C2×C43—22no—
494C2×C43—41no—
495C2×C43C2×#53611yescharacteristic
496C2×C43C2×#57511yescharacteristic
497C2×C43C2×#57511yescharacteristic
498D43—82no—
499#533—432no—
500#533—432no—
501#533—432no—
502#533—432no—
503#533—861no—
504#533—861no—
505#533—861no—
506#533—861no—
507C2×C4⋊Q8—431no—
508C2×C4⋊Q8—431no—
509#529—432no—
510#529—432no—
511#529—432no—
512#529—432no—
513#529—861no—
514#529—861no—
515#529—861no—
516#529—861no—
517C2×#126—861no—
518C2×#125—431no—
519C2×#125—431no—
520C2×#125—431no—
521C2×#124—431no—
522C2×#123—861no—
523C2×C22⋊Q8—861no—
524C2×C22⋊Q8—861no—
525C2×C22⋊Q8C2×D4311yescharacteristic
526C2×#121—431no—
527C2×C4×Q8—431no—
528C2×C4×Q8—861no—
529C2×C4×Q8—861no—
530C2×C4×D4—431no—
531C2×C4×D4—861no—
532C2×#117—431no—
533C2×#117—861no—
534C2×#117C2×D4311yescharacteristic
535C22×C42—431no—
536#501—434no—
537#501—434no—
538#499—434no—
539#499—434no—
540#489—434no—
541#489—434no—
542#488—434no—
543#488—434no—
544#485—434no—
545#485C2×D4314yescomplemented
546#484—432no—
547#484C2×D4312yescomplemented
548#483—432no—
549#483C2×D4312yescomplemented
550#482—434no—
551#482—434no—
552#481—432no—
553#481—432no—
554#480—432no—
555#480—432no—
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#428—432no—
571#428C2×D4312yes—
572#423—432no—
573#419—432no—
574#419C2×D4312yes—
575#418—432no—
576#418—432no—
577#407—431no—
578#407C2×D4311yescharacteristic
579C4×M16—432no—
580C43#6086611yescharacteristic, complemented, Sylow
581C22×Q8—861no—
582C22×Q8—861no—
583C22×Q8C22×D4311yescharacteristic
584C22×D4—431no—
585C22×D4—861no—
586C23×C4—431no—
587C23×C4—431no—
588C23×C4—861no—
589C23×C4C22×D4311yescharacteristic
590C2×M16—432no—
591C2×M16C22×D4312yes—
592C4⋊Q8—432no—
593C4⋊Q8—432no—
594C4⋊Q8—432no—
595C4⋊Q8—432no—
596C4⋊Q8—861no—
597C4⋊Q8—861no—
598C4⋊Q8—861no—
599C4⋊Q8—861no—
600#126—862no—
601#126—862no—
602#126—862no—
603#126—862no—
604#125—432no—
605#125—432no—
606#125—432no—
607#125—432no—
608#125—432no—
609#125—432no—
610#125—861no—
611#125—861no—
612#125—861no—
613#125—861no—
614#125—861no—
615#125—861no—
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—862no—
627C22⋊Q8—862no—
628C22⋊Q8—862no—
629C22⋊Q8—862no—
630C22⋊Q8—862no—
631C22⋊Q8—862no—
632C22⋊Q8—862no—
633C22⋊Q8—862no—
634C22⋊Q8C22×D4312yes—
635C22⋊Q8C22×D4312yes—
636#121—432no—
637#121—432no—
638#121—861no—
639#121—861no—
640C4×Q8—432no—
641C4×Q8—432no—
642C4×Q8—862no—
643C4×Q8—862no—
644C4×Q8—862no—
645C4×Q8—862no—
646C4×Q8—862no—
647C4×Q8—862no—
648C4×Q8—862no—
649C4×Q8—862no—
650C4×Q8—861no—
651C4×Q8—861no—
652C4×D4—432no—
653C4×D4—432no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—862no—
657C4×D4—862no—
658C4×D4—862no—
659C4×D4—862no—
660#117—21no—
661#117—21no—
662#117—432no—
663#117—432no—
664#117—862no—
665#117—862no—
666#117—862no—
667#117—862no—
668#117—861no—
669#117—861no—
670#117C22×D4312yes—
671#117C22×D4312yes—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—431no—
674C2×C4⋊C4—431no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—861no—
677C2×C4⋊C4—861no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4—861no—
680C2×C4⋊C4—861no—
681C2×C4⋊C4—861no—
682C2×C4⋊C4—861no—
683C2×C4⋊C4—861no—
684C2×C4⋊C4—861no—
685C2×C4⋊C4C22×D4311yescharacteristic
686C2×C4⋊C4C22×D4311yescharacteristic
687C2×C4⋊C4C22×D4311yescharacteristic
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—861no—
691C2×C22⋊C4—861no—
692C2×C22⋊C4—861no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C42—21no—
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—431no—
708C2×C42—861no—
709C2×C42—861no—
710#107—434no—
711#107—434no—
712#107—434no—
713#107C22×D4314yes—
714#106—434no—
715#106—434no—
716#106—434no—
717#106C22×D4314yes—
718C4⋊C8—434no—
719C4⋊C8—434no—
720#103—434no—
721#103—434no—
722#103C22×D4314yes—
723#103C22×D4314yes—
724#102—434no—
725#102—434no—
726#102—434no—
727#102—434no—
728C22⋊C8—432no—
729C22⋊C8—432no—
730C22⋊C8C22×D4312yes—
731C22⋊C8C22×D4312yes—
732#97—434no—
733C4×C8—434no—
734C24—861no—
735C24D4×D4311yescharacteristic
736C2×Q8—21no—
737C2×Q8—24no—
738C2×Q8—862no—
739C2×Q8—862no—
740C2×Q8—862no—
741C2×Q8—862no—
742C2×Q8—1724no—
743C2×Q8—1724no—
744C2×Q8C23×D4312yes—
745C2×D4—432no—
746C2×D4—862no—
747C2×D4—862no—
748C2×D4—861no—
749C2×D4—864no—
750C2×D4—1724no—
751C22×C4—24no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
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—862no—
769C22×C4—862no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—1724no—
774C22×C4—1722no—
775C22×C4—1722no—
776C22×C4D4×D4311yescharacteristic
777C22×C4D4×D4311yescharacteristic
778C22×C4D4×D4311yescharacteristic
779C22×C4C23×D4311yescharacteristic
780C22×C4C23×D4311yescharacteristic
781C22×C4C23×D4311yescharacteristic
782M16—24no—
783M16—864no—
784C2×C8—434no—
785C2×C8C23×D4314yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—432no—
792C4⋊C4—432no—
793C4⋊C4—432no—
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—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⋊C4—861no—
815C4⋊C4C23×D4312yes—
816C4⋊C4C23×D4312yes—
817C4⋊C4C23×D4312yes—
818C22⋊C4—22no—
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
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—22no—
834C42—431no—
835C42—431no—
836C42—431no—
837C42—431no—
838C42—431no—
839C42—431no—
840C42—431no—
841C42—431no—
842C42—431no—
843C42—431no—
844C42—431no—
845C42—431no—
846C42—431no—
847C42—431no—
848C42—431no—
849C42—431no—
850C42—862no—
851C42—862no—
852C42—862no—
853C42—862no—
854C23—22no—
855C23—22no—
856C23—41no—
857C23—862no—
858C23—1722no—
859C23—1722no—
860C23—1722no—
861C23C2×D4×D4311yescharacteristic
862C23C2×D4×D4311yescharacteristic
863C23C2×D4×D4311yescharacteristic
864Q8—24no—
865Q8—42no—
866Q8—1724no—
867Q8—1724no—
868Q8—1724no—
869Q8—1724no—
870D4—864no—
871D4—1724no—
872D4—1724no—
873D4—1722no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—431no—
888C2×C4—431no—
889C2×C4—431no—
890C2×C4—431no—
891C2×C4—431no—
892C2×C4—431no—
893C2×C4—431no—
894C2×C4—431no—
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—1724no—
904C2×C4—1724no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1722no—
913C2×C4—1722no—
914C2×C4—1722no—
915C2×C4C2×D4×D4311yescharacteristic
916C2×C4C2×D4×D4311yescharacteristic
917C2×C4C2×D4×D4311yescharacteristic
918C2×C4#1306337214yes—
919C2×C4C24×D4311yescharacteristic
920C8—24no—
921C8—864no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—44no—
930C22—3444no—
931C22—1722no—
932C22—1722no—
933C22—1722no—
934C22#1458347112yes—
935C22#1458369812yes—
936C22C22×D4×D4311yescharacteristic
937C4—21no—
938C4—21no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—432no—
944C4—861no—
945C4—861no—
946C4—861no—
947C4—861no—
948C4—861no—
949C4—861no—
950C4—861no—
951C4—1722no—
952C4—1722no—
953C4—1722no—
954C4#1458347112yes—
955C4C2×#1306337212yes—
956C2—22no—
957C2—22no—
958C2—41no—
959C2—3442no—
960C2C2×#1458347111yescharacteristic
961C2#575×D4311yescharacteristic
962C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3095C2
socleC22×C43C23×D4
prime radicalC2×#13063299C22
hypercenter#3095D43
hypocenterC43#60866
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. C2×#14583452C2semidirect
3. #19145839C2semidirect
4. #19145828C2semidirect
5. #19145819C2semidirect
6. #19145777C2semidirect
7. #19145768C2semidirect
8. #19145766C2semidirect
9. #19145145C2semidirect
10. #19144983C2semidirect
11. #19144539C2semidirect
14. #19144397C2semidirect
15. #19144391C2semidirect
16. #19143224C2semidirect
17. C43×#3095C2semidirect
24. #14583452C22semidirect
25. #14583452C22semidirect
26. C2×#13063324C22semidirect
27. C2×#13063324C22semidirect
38. C2×#13063316C22semidirect
39. C2×#13063316C22semidirect
53. #14583307C22semidirect
54. #14583306C22semidirect
55. #14583300C22semidirect
56. #14583299C22semidirect
57. #14583260C22semidirect
58. #14583260C22semidirect
59. #14583255C22semidirect
60. #14583255C22semidirect
61. #14583237C22semidirect
62. #14583232C22semidirect
63. #14583227C22semidirect
70. #14583208C22semidirect
71. #14583204C22semidirect
72. #14583202C22semidirect
73. #14583198C22semidirect
74. #14583192C22semidirect
75. #14583188C22semidirect
76. #14583182C22semidirect
77. #14583178C22semidirect
78. #14582953C22semidirect
79. #14582953C22semidirect
80. #14582949C22semidirect
81. #14582949C22semidirect
93. C43×#485C22semidirect
94. C43×#484C22semidirect
95. C43×#483C22semidirect
486. #3095D43semidirect
545. #485C2×D43semidirect
547. #484C2×D43semidirect
549. #483C2×D43semidirect
580. C43#60866semidirect

Maximal subgroups

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

subgroupindex
C2×#145834522
C2×#145834352
#191458392
#191458282
#191458192
#191457772
#191457682
#191457662
#191451452
#191449832
#191445392
#191445362
#191445352
#191443972
#191443912
#191432242
C43×#30952
#6086643