Finite Group Databasebeta

← #25969588

Subgroups — #25969588

Order 11008.

2168 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic, complemented
2#532×D43C211yesmaximal, characteristic, complemented
3#19145984C212yesmaximal, complemented
4#19145974C212yesmaximal, complemented
5#19145959C212yesmaximal, complemented
6#19145953C212yesmaximal, complemented
7#19145914C214yesmaximal, complemented
8#19145912C211yesmaximal, characteristic, complemented
9#19145911C211yesmaximal, characteristic, complemented
10#19145902C211yesmaximal, characteristic, complemented
11#19144403C212yesmaximal, complemented
12#19144387C212yesmaximal, complemented
13#19144211C214yesmaximal, complemented
14#19144070C212yesmaximal, complemented
15#19144054C212yesmaximal, complemented
16C2×#14582921C211yesmaximal, characteristic, complemented
17C43×#3245C211yesmaximal, characteristic, complemented
18C2×#41×D43—21no—
19C2×#13063349C2214yes—
20C22×#10621872C2212yes—
21#14583456C2211yescharacteristic, complemented
22#14583454C2211yescharacteristic
23#14583454C2211yescharacteristic, complemented
24#14583450C2211yescharacteristic
25#14583449C2211yescharacteristic
26#14583448—21no—
27#14583447C2211yescharacteristic
28#14583447C2211yescharacteristic
29#14583447C2211yescharacteristic, complemented
30#14583446—21no—
31#14583446C2212yes—
32#14583445—21no—
33#14583444—21no—
34#14583444C2212yes—
35C4⋊Q8×D43C2211yescharacteristic
36#127×D43C2211yescharacteristic
37#14583431—21no—
38#14583431C2212yescomplemented
39#14583430—21no—
40#14583430C2212yescomplemented
41#14583428—21no—
42#14583428—21no—
43#124×D43—21no—
44#14583409—21no—
45#14583409C2212yes—
46#14583406—21no—
47#121×D43—21no—
48#121×D43C2212yes—
49#41×Dic43—21no—
50C4×#10621900—21no—
51C4×#10621900C2212yes—
52C4×D4×D43—21no—
53C4×D4×D43C2212yes—
54C2×C42×D43C2211yescharacteristic
55#14583202C2214yescomplemented
56#14583201C2214yescomplemented
57#14583193C2214yescomplemented
58#14583190C2212yescomplemented
59#14583189C2212yescomplemented
60#14583187C2214yescomplemented
61#14583185C2212yescomplemented
62#14583181C2212yescomplemented
63#14583179C2212yescomplemented
64#14583176C2212yescomplemented
65#14583151C2214yescomplemented
66#14583149C2214yescomplemented
67#14583146C2214yescomplemented
68#14583144C2214yescomplemented
69#14583133C2214yescomplemented
70#14583128C2214yescomplemented
71#14583126C2214yescomplemented
72#14583113C2214yescomplemented
73#14583112C2214yescomplemented
74#14583105C2212yescomplemented
75#14583104C2212yescomplemented
76#14583100C2212yescomplemented
77#14583098C2214yescomplemented
78#14583096C2212yescomplemented
79#14583094C2212yescomplemented
80#14583092C2214yescomplemented
81#14583091C2212yescomplemented
82#14582940C2214yes—
83#14582921C2212yes—
84#14582921C2212yes—
85#14582921C2212yescomplemented
86#14582921C2212yescomplemented
87C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
88C2×Dic43⋊C8C2212yescomplemented
89#14582902C2214yes—
90#14582897C2214yes—
91C43×#532C2211yescharacteristic
92C43×#532C2211yescharacteristic, complemented
93C43×#474C2212yescomplemented
94C43×#474C2212yescomplemented
95C43×#466C2214yescomplemented
96C43×#459C2212yescomplemented
97C43×#459C2212yescomplemented
98C2×C4⋊C8×C43C2211yescharacteristic, complemented
99C2×#10621902—21no—
100C2×#10621898—21no—
101C2×#10621898—22no—
102C2×#10621900—22no—
103C2×#10621900—21no—
104C2×#10621900—21no—
105C2×#10621900C2312yes—
106#41×D43—48no—
107C2×Q8×D43—21no—
108C2×D4×D43—22no—
109C2×D4×D43—21no—
110C2×D4×D43—21no—
111C2×D4×D43C2312yes—
112C22×C4×D43—22no—
113C22×C4×D43D411yescharacteristic
114C22×C4×D43D411yescharacteristic
115C22×C4×D43C2311yescharacteristic
116#13063349—48no—
117C2×#10621873C2314yes—
118C2×#10621883C2314yes—
119C2×#10621882C2314yes—
120C2×#10621872—44no—
121C2×#10621872C2314yes—
122C2×#10621872C2314yes—
123C22×C43⋊C8C2312yes—
124#13063325C2311yescharacteristic
125#13063325C2311yescharacteristic
126#13063325C2311yescharacteristic
127#13063324—21no—
128#13063324C2312yes—
129#13063323—21no—
130#13063322C2311yescharacteristic
131#13063321—21no—
132#13063321—21no—
133#13063321C2312yes—
134#13063318—22no—
135#13063318—22no—
136#13063317—21no—
137#13063316—21no—
138#13063316C2312yes—
139#13063314—21no—
140#13063313—21no—
141#13063312—21no—
142#13063312—21no—
143#13063312C2312yes—
144#13063311—22no—
145#13063311—22no—
146#13063307—22no—
147#13063307—22no—
148#13063306—22no—
149#13063305—21no—
150#13063305C2312yes—
151#13063304—21no—
152#13063304C2312yes—
153#13063301—21no—
154#13063301—21no—
155#13063300—21no—
156#13063300C2312yes—
157#13063299—21no—
158#13063299C2312yes—
159#13063298—22no—
160#13063298—22no—
161#13063297—22no—
162#13063297—22no—
163#13063296—21no—
164#13063296—21no—
165#13063296—21no—
166#13063296—21no—
167#13063296C2312yes—
168#13063296C2312yes—
169#13063293—22no—
170Q8×Dic43—21no—
171Q8×Dic43—21no—
172C4×Dic86—21no—
173C4×Dic86C2312yes—
174#13063290—21no—
175#13063290C2312yes—
176C4×D172—21no—
177C4×D172C2312yes—
178D4×Dic43—22no—
179D4×Dic43—22no—
180D4×Dic43—21no—
181D4×Dic43—21no—
182D4×Dic43—21no—
183D4×Dic43—21no—
184D4×Dic43C2312yes—
185D4×Dic43C2312yes—
186#13063287—21no—
187#13063287C2312yes—
188C4×C22⋊D43—22no—
189C4×C22⋊D43—22no—
190C4×C22⋊D43—22no—
191C4×C22⋊D43—22no—
192(C22⋊D43)⋊C4—22no—
193(C22⋊D43)⋊C4—22no—
194(C22⋊D43)⋊C4—22no—
195(C22⋊D43)⋊C4—22no—
196#13063284—21no—
197#13063284—22no—
198#13063283—21no—
199#13063283C2312yes—
200#13063281—22no—
201#13063281—22no—
202C4⋊C4×D43—21no—
203C4⋊C4×D43C2312yes—
204C22⋊C4×D43—22no—
205C22⋊C4×D43—22no—
206C2×C4×Dic43—22no—
207C2×C4×Dic43D411yescharacteristic
208C2×C4×Dic43D411yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C42×D43D411yescharacteristic
211C42×D43D411yescharacteristic
212C42×D43D411yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43C2311yescharacteristic
215C42×D43C2311yescharacteristic
216C42×D43C2311yescharacteristic
217C42×D43C2311yescharacteristic
218#13063258C2314yes—
219#13063257C2314yes—
220#13063256C2314yes—
221C4⋊(C43⋊C8)C2312yes—
222C4⋊(C43⋊C8)C2312yes—
223Dic43⋊C8C2314yes—
224Dic43⋊C8C2314yes—
225#13063250C2314yes—
226#13063248C2314yes—
227#13063247C2314yes—
228#13063246C2314yes—
229#13063246C2314yes—
230#13063245C2314yes—
231C2×#41×C43—21no—
232C2×#41×C43—21no—
233C2×D8×C43C2314yes—
234C22×C8×C43C2312yes—
235C4⋊Q8×C43C2311yescharacteristic
236C4⋊Q8×C43C2311yescharacteristic
237#127×C43C2311yescharacteristic
238#127×C43C2311yescharacteristic
239#124×C43—21no—
240#124×C43—21no—
241#121×C43—21no—
242#121×C43—21no—
243#121×C43C2312yes—
244#121×C43C2312yes—
245C4×D4×C43—21no—
246C4×D4×C43—21no—
247C4×D4×C43C2312yes—
248C4×D4×C43C2312yes—
249C2×C42×C43C2311yescharacteristic
250#107×C43C2314yes—
251C4⋊C8×C43C2312yes—
252C4⋊C8×C43C2312yes—
253#102×C43C2314yes—
254#102×C43C2314yes—
255C23×D43—22no—
256C23×D43C2×D411yescharacteristic
257#41×C43—44no—
258#41×C43—44no—
259C2×Q8×C43—21no—
260C2×Q8×C43—21no—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—22no—
266C2×D4×C43—22no—
267C2×D4×C43C2412yes—
268C2×D4×C43C2412yes—
269C22×C4×C43—22no—
270C22×C4×C43—22no—
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2411yescharacteristic
274C2×C22⋊D43—22no—
275C2×C22⋊D43—22no—
276C2×C22⋊D43—22no—
277C2×C22⋊D43—22no—
278C2×C22⋊D43—22no—
279C2×C22⋊D43—22no—
280C2×C22⋊D43—22no—
281C22×Dic43—22no—
282C22×Dic43—22no—
283C22×Dic43—22no—
284C22×Dic43C2×D411yescharacteristic
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287#10621902—44no—
288Q8×D43—44no—
289#10621900—24no—
290#10621900—24no—
291#10621900—44no—
292#10621900—44no—
293#10621900—48no—
294D4×D43—24no—
295D4×D43—24no—
296D4×D43—48no—
297D4×D43—44no—
298D4×D43—44no—
299#10621898—48no—
300#10621898—44no—
301C2×D172—21no—
302C2×D172—21no—
303C2×D172—22no—
304C2×D172C2412yes—
305C2×C4×D43—24no—
306C2×C4×D43—22no—
307C2×C4×D43—22no—
308C2×C4×D43—22no—
309C2×C4×D43—22no—
310C2×C4×D43—22no—
311C2×C4×D43—42no—
312C2×C4×D43—48no—
313C2×C4×D43C2×D411yescharacteristic
314C2×C4×D43C2×D411yescharacteristic
315C2×C4×D43C2×D411yescharacteristic
316C2×C4×D43C2×D411yescharacteristic
317C2×C4×D43C2×D411yescharacteristic
318C2×C4×D43C2×D411yescharacteristic
319C2×C4×D43C2×D411yescharacteristic
320C2×C4×D43C2×D411yescharacteristic
321C2×C4×D43C2×D411yescharacteristic
322C2×C4×D43C2×D411yescharacteristic
323C2×C4×D43C2411yescharacteristic
324C2×C4×D43C2411yescharacteristic
325C2×Dic86—21no—
326C2×Dic86—21no—
327C2×Dic86—22no—
328C2×Dic86C2412yes—
329D8×C43—44no—
330C2×C8×C43—42no—
331C2×C8×C43C2414yes—
332C4⋊C4×C43—21no—
333C4⋊C4×C43—21no—
334C4⋊C4×C43C2412yes—
335C4⋊C4×C43C2412yes—
336C22⋊C4×C43—22no—
337C22⋊C4×C43—22no—
338C22⋊C4×C43—22no—
339C22⋊C4×C43—22no—
340C42×C43C2×D411yescharacteristic
341C42×C43C2×D411yescharacteristic
342C42×C43C2411yescharacteristic
343C42×C43C2411yescharacteristic
344C22⋊Dic43—22no—
345C22⋊Dic43—22no—
346C22⋊Dic43—22no—
347C22⋊Dic43—22no—
348C22⋊Dic43—22no—
349C22⋊Dic43—22no—
350C22⋊Dic43—22no—
351#10621883—44no—
352#10621882—44no—
353(C2×D43)⋊C4—22no—
354(C2×D43)⋊C4—22no—
355(C2×D43)⋊C4—22no—
356(C2×D43)⋊C4—22no—
357(C2×D43)⋊C4—22no—
358(C2×D43)⋊C4—22no—
359C4⋊Dic43—21no—
360C4⋊Dic43—21no—
361C4⋊Dic43—21no—
362C4⋊Dic43—21no—
363C4⋊Dic43—22no—
364C4⋊Dic43—22no—
365C4⋊Dic43C2412yes—
366C4⋊Dic43C2412yes—
367Dic43⋊C4—22no—
368Dic43⋊C4—22no—
369Dic43⋊C4—22no—
370Dic43⋊C4—22no—
371Dic43⋊C4—22no—
372Dic43⋊C4—22no—
373C4×Dic43—22no—
374C4×Dic43—22no—
375C4×Dic43—22no—
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2×D411yescharacteristic
386C4×Dic43C2411yescharacteristic
387C4×Dic43C2411yescharacteristic
388C2×C43⋊C8—42no—
389C2×C43⋊C8C2414yes—
390#10621873—44no—
391#10621872—28no—
392#10621872—44no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43C22×D411yescharacteristic
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—41no—
400C22×D43—44no—
401C22×D43—44no—
402C22×D43—44no—
403C22×D43C22×D411yescharacteristic
404C22×D43C22×D411yescharacteristic
405Q8×C43—42no—
406Q8×C43—42no—
407D4×C43—22no—
408D4×C43—22no—
409D4×C43—22no—
410D4×C43—22no—
411D4×C43—42no—
412D4×C43—42no—
413D4×C43—44no—
414D4×C43—44no—
415D4×C43—42no—
416D4×C43—42no—
417C2×C4×C43—21no—
418C2×C4×C43—21no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—41no—
422C2×C4×C43—44no—
423C2×C4×C43—44no—
424C2×C4×C43AGL(1,ℤ/8)14yescomplemented
425C2×C4×C43C22×D411yescharacteristic
426C2×C4×C43C22×D411yescharacteristic
427C2×C4×C43C22×D411yescharacteristic
428C2×C4×C43C22×D411yescharacteristic
429C2×C4×C43C22×D411yescharacteristic
430C2×C4×C43C2511yescharacteristic
431C22⋊D43—44no—
432C22⋊D43—44no—
433C22⋊D43—44no—
434C22⋊D43—44no—
435C22⋊D43—44no—
436C22⋊D43—44no—
437C22⋊D43—44no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—44no—
445C2×Dic43—44no—
446C2×Dic43—44no—
447C2×Dic43C22×D411yescharacteristic
448C2×Dic43C22×D411yescharacteristic
449C2×Dic43C22×D411yescharacteristic
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452C2×Dic43C22×D411yescharacteristic
453D172—22no—
454D172—22no—
455D172—42no—
456D172—44no—
457D172—42no—
458C4×D43—22no—
459C4×D43—22no—
460C4×D43—22no—
461C4×D43—22no—
462C4×D43—22no—
463C4×D43—21no—
464C4×D43—21no—
465C4×D43—22no—
466C4×D43—22no—
467C4×D43—22no—
468C4×D43—41no—
469C4×D43—41no—
470C4×D43—44no—
471C4×D43—44no—
472C4×D43—44no—
473C4×D43H(5,𝔽2)12yes—
474C4×D432−1+412yes—
475Dic86—22no—
476Dic86—22no—
477Dic86—44no—
478Dic86—42no—
479Dic86—42no—
480C8×C43—24no—
481C43⋊C8—24no—
482#60916—431nomaximal, Sylow
483C22×C43—21no—
484C22×C43—21no—
485C22×C43—42no—
486C22×C43—42no—
487C22×C43—42no—
488C22×C43—42no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43C2×AGL(1,ℤ/8)12yes—
492C22×C43C23×D411yescharacteristic
493C2×D43—21no—
494C2×D43—21no—
495C2×D43—21no—
496C2×D43—21no—
497C2×D43—21no—
498C2×D43—44no—
499C2×D43—42no—
500C2×D43—42no—
501C2×D43—42no—
502C2×D43—88no—
503C2×D43#53712yes—
504C4×C43—21no—
505C4×C43—21no—
506C4×C43—21no—
507C4×C43—42no—
508C4×C43—42no—
509C4×C43C2×AGL(1,ℤ/8)12yes—
510C4×C43C2×AGL(1,ℤ/8)12yes—
511C4×C43C2×H(5,𝔽2)11yescharacteristic
512C4×C43C2×2−1+411yescharacteristic
513Dic43—21no—
514Dic43—21no—
515Dic43—21no—
516Dic43—21no—
517Dic43—42no—
518Dic43—42no—
519Dic43—42no—
520Dic43#53712yes—
521Dic43#57512yes—
522#3444—431no—
523C2×#532—431no—
524#3254—432no—
525#3253—432no—
526#3251—432no—
527#3251—432no—
528#3247—434no—
529#3246—431no—
530#3246—431no—
531#3245—431no—
532#3245D4311yescharacteristic, complemented
533#3079—432no—
534#3077—432no—
535#3055—434no—
536#3038—432no—
537#3036—432no—
538C2×#423—431no—
539C2×C43—22no—
540C2×C43—82no—
541C2×C43—82no—
542C2×C43C2×#53711yescharacteristic
543C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
544C2×C43C2×#57511yescharacteristic
545D43—22no—
546D43—41no—
547D43—82no—
548C22×#41—861no—
549C2×AGL(1,ℤ/8)—434no—
550C22×M16—432no—
551#533—431no—
552#533—431no—
553#533—431no—
554#532—431no—
555#532—431no—
556#532—431no—
557#532—432no—
558#532—432no—
559#532—431no—
560#532—431no—
561#532—861no—
562#532—861no—
563#532—861no—
564#532—861no—
565#532C2×D4311yescharacteristic
566#532C2×D4311yescharacteristic, complemented
567C2×C4⋊Q8—431no—
568C2×#127—431no—
569#529—432no—
570#529—432no—
571#529—861no—
572#529—861no—
573#529—861no—
574#529—861no—
575C2×#124—861no—
576#525—432no—
577#525—861no—
578#525—861no—
579C2×#121—432no—
580C2×#121—861no—
581C4×#41—432no—
582C4×#41—861no—
583C4×#41—861no—
584C2×C4×D4—432no—
585C2×C4×D4—861no—
586C22×C42—431no—
587#478—434no—
588#478—434no—
589#477—434no—
590#476—432no—
591#476—432no—
592#476—434no—
593#475—432no—
594#475—432no—
595#474—432no—
596#474—432no—
597#474C2×D4312yescomplemented
598#474C2×D4312yescomplemented
599#469—434no—
600#469—434no—
601#468—434no—
602#468—434no—
603#466—434no—
604#466C2×D4314yescomplemented
605#465—434no—
606#465—434no—
607#463—434no—
608#463—434no—
609#461—432no—
610#461—432no—
611#460—432no—
612#460—432no—
613#460—434no—
614#459—434no—
615#459—432no—
616#459—432no—
617#459C2×D4312yescomplemented
618#459C2×D4312yescomplemented
619#428—434no—
620#423—432no—
621#423—432no—
622#423—432no—
623#423—432no—
624C2×C4⋊C8—432no—
625C2×C4⋊C8—431no—
626C2×C4⋊C8C2×D4311yescharacteristic, complemented
627#418—434no—
628#417—434no—
629C43#6091611yescharacteristic, complemented, Sylow
630C2×#41—21no—
631C2×#41—21no—
632C2×#41—432no—
633C2×#41—862no—
634C2×#41—861no—
635C2×#41—862no—
636C2×#41—861no—
637C2×#41—861no—
638C2×#41—861no—
639C2×#41—1728no—
640C22×Q8—861no—
641C22×D4—432no—
642C22×D4—861no—
643C22×D4—861no—
644C22×D4—862no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—862no—
649AGL(1,ℤ/8)—1728no—
650C2×SD16—434no—
651C2×SD16—434no—
652C2×D8—434no—
653C2×D8C22×D4314yes—
654C2×M16—434no—
655C2×M16—434no—
656C2×M16—1724no—
657C22×C8—432no—
658C22×C8C22×D4312yes—
659C4⋊Q8—432no—
660C4⋊Q8—431no—
661C4⋊Q8—431no—
662C4⋊Q8—431no—
663C4⋊Q8—861no—
664C4⋊Q8—861no—
665C4⋊Q8C22×D4311yescharacteristic
666C4⋊Q8C22×D4311yescharacteristic
667#127—432no—
668#127—431no—
669#127—861no—
670#127—861no—
671#127C22×D4311yescharacteristic
672#127C22×D4311yescharacteristic
673#126—862no—
674#126—862no—
675#125—432no—
676#125—861no—
677#125—861no—
678#124—21no—
679#124—21no—
680#124—432no—
681#124—862no—
682#124—862no—
683#124—861no—
684#124—861no—
685#124—861no—
686#124—861no—
687#123—862no—
688#123—862no—
689#123—862no—
690C22⋊Q8—432no—
691C22⋊Q8—432no—
692C22⋊Q8—861no—
693C22⋊Q8—861no—
694C22⋊Q8—861no—
695C22⋊Q8—861no—
696#121—21no—
697#121—21no—
698#121—432no—
699#121—432no—
700#121—432no—
701#121—432no—
702#121—862no—
703#121—862no—
704#121—861no—
705#121—862no—
706#121—861no—
707#121—862no—
708#121—861no—
709#121—861no—
710#121—861no—
711#121—861no—
712#121C22×D4312yes—
713#121C22×D4312yes—
714#120—862no—
715C4×Q8—432no—
716C4×Q8—432no—
717C4×Q8—861no—
718C4×Q8—861no—
719C4×Q8—861no—
720C4×Q8—861no—
721C4×D4—21no—
722C4×D4—21no—
723C4×D4—432no—
724C4×D4—432no—
725C4×D4—432no—
726C4×D4—432no—
727C4×D4—862no—
728C4×D4—862no—
729C4×D4—861no—
730C4×D4—862no—
731C4×D4—862no—
732C4×D4—861no—
733C4×D4—861no—
734C4×D4—861no—
735C4×D4—861no—
736C4×D4—862no—
737C4×D4—862no—
738C4×D4—862no—
739C4×D4—862no—
740C4×D4—862no—
741C4×D4—862no—
742C4×D4—861no—
743C4×D4C22×D4312yes—
744C4×D4C22×D4312yes—
745#117—432no—
746#117—862no—
747#117—862no—
748#117—862no—
749#117—861no—
750#117—861no—
751C2×C4⋊C4—432no—
752C2×C4⋊C4—861no—
753C2×C22⋊C4—862no—
754C2×C22⋊C4—862no—
755C2×C42—431no—
756C2×C42—431no—
757C2×C42—431no—
758C2×C42—431no—
759C2×C42—431no—
760C2×C42—431no—
761C2×C42—431no—
762C2×C42—431no—
763C2×C42—431no—
764C2×C42—431no—
765C2×C42—431no—
766C2×C42—862no—
767C2×C42C22×D4311yescharacteristic
768#107—434no—
769#107C22×D4314yes—
770#106—434no—
771#106—434no—
772C4⋊C8—434no—
773C4⋊C8—434no—
774C4⋊C8—432no—
775C4⋊C8—432no—
776C4⋊C8C22×D4312yes—
777C4⋊C8C22×D4312yes—
778#103—434no—
779#103—434no—
780#102—434no—
781#102—434no—
782#102—434no—
783#102—434no—
784#102C22×D4314yes—
785#102C22×D4314yes—
786C24—431no—
787C24—862no—
788#41—44no—
789#41—44no—
790#41—864no—
791#41—864no—
792#41—1728no—
793#41—1728no—
794#41—1724no—
795#41—1724no—
796#41—1724no—
797#41—1724no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—432no—
801C2×Q8—862no—
802C2×Q8—861no—
803C2×Q8—861no—
804C2×Q8—1724no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—432no—
812C2×D4—862no—
813C2×D4—864no—
814C2×D4—864no—
815C2×D4—862no—
816C2×D4—862no—
817C2×D4—862no—
818C2×D4—862no—
819C2×D4—862no—
820C2×D4—862no—
821C2×D4—862no—
822C2×D4—861no—
823C2×D4—861no—
824C2×D4—1724no—
825C2×D4—1724no—
826C2×D4—1728no—
827C2×D4C23×D4312yes—
828C2×D4C23×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—431no—
838C22×C4—431no—
839C22×C4—431no—
840C22×C4—431no—
841C22×C4—431no—
842C22×C4—431no—
843C22×C4—431no—
844C22×C4—431no—
845C22×C4—431no—
846C22×C4—862no—
847C22×C4—862no—
848C22×C4—862no—
849C22×C4—862no—
850C22×C4—862no—
851C22×C4—862no—
852C22×C4—862no—
853C22×C4—864no—
854C22×C4—862no—
855C22×C4—1722no—
856C22×C4—1728no—
857C22×C4D4×D4311yescharacteristic
858C22×C4D4×D4311yescharacteristic
859C22×C4C23×D4311yescharacteristic
860SD16—1724no—
861SD16—1724no—
862D8—44no—
863D8—1724no—
864M16—868no—
865M16—1724no—
866C2×C8—42no—
867C2×C8—434no—
868C2×C8—1722no—
869C2×C8C23×D4314yes—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—432no—
873C4⋊C4—432no—
874C4⋊C4—862no—
875C4⋊C4—862no—
876C4⋊C4—862no—
877C4⋊C4—862no—
878C4⋊C4—862no—
879C4⋊C4—862no—
880C4⋊C4—861no—
881C4⋊C4—862no—
882C4⋊C4—861no—
883C4⋊C4—861no—
884C4⋊C4—861no—
885C4⋊C4—862no—
886C4⋊C4C23×D4312yes—
887C4⋊C4C23×D4312yes—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—862no—
893C22⋊C4—862no—
894C22⋊C4—862no—
895C22⋊C4—862no—
896C22⋊C4—862no—
897C22⋊C4—862no—
898C22⋊C4—862no—
899C22⋊C4—862no—
900C22⋊C4—862no—
901C22⋊C4—862no—
902C22⋊C4—862no—
903C22⋊C4—862no—
904C22⋊C4—862no—
905C42—431no—
906C42—431no—
907C42—431no—
908C42—431no—
909C42—431no—
910C42—431no—
911C42—431no—
912C42—431no—
913C42—431no—
914C42—431no—
915C42—431no—
916C42—431no—
917C42—862no—
918C42—862no—
919C42—862no—
920C42D4×D4311yescharacteristic
921C42D4×D4311yescharacteristic
922C42C23×D4311yescharacteristic
923C42C23×D4311yescharacteristic
924C23—22no—
925C23—22no—
926C23—431no—
927C23—431no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—1721no—
932C23—1724no—
933C23—1724no—
934C23—1724no—
935C23C2×D4×D4311yescharacteristic
936Q8—42no—
937Q8—42no—
938Q8—862no—
939Q8—862no—
940Q8—1722no—
941Q8—1724no—
942Q8—1722no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—42no—
948D4—42no—
949D4—44no—
950D4—44no—
951D4—42no—
952D4—42no—
953D4—862no—
954D4—862no—
955D4—1722no—
956D4—1724no—
957D4—1724no—
958D4—1724no—
959D4—1724no—
960D4—1724no—
961D4—1724no—
962D4—1724no—
963D4—1724no—
964D4—1722no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—41no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—431no—
973C2×C4—431no—
974C2×C4—432no—
975C2×C4—432no—
976C2×C4—431no—
977C2×C4—431no—
978C2×C4—431no—
979C2×C4—431no—
980C2×C4—862no—
981C2×C4—862no—
982C2×C4—862no—
983C2×C4—862no—
984C2×C4—862no—
985C2×C4—862no—
986C2×C4—862no—
987C2×C4—862no—
988C2×C4—862no—
989C2×C4—862no—
990C2×C4—862no—
991C2×C4—861no—
992C2×C4—861no—
993C2×C4—862no—
994C2×C4—862no—
995C2×C4—862no—
996C2×C4—1721no—
997C2×C4—1721no—
998C2×C4—1724no—
999C2×C4—1724no—
1000C2×C4—1724no—
1001C2×C4—1724no—
1002C2×C4—1724no—
1003C2×C4—1724no—
1004C2×C4#1306334914yescomplemented
1005C2×C4C2×D4×D4311yescharacteristic
1006C2×C4C2×D4×D4311yescharacteristic
1007C2×C4C2×D4×D4311yescharacteristic
1008C2×C4C2×D4×D4311yescharacteristic
1009C2×C4C2×D4×D4311yescharacteristic
1010C2×C4C24×D4311yescharacteristic
1011C8—24no—
1012C8—864no—
1013C22—21no—
1014C22—21no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—432no—
1022C22—861no—
1023C22—861no—
1024C22—861no—
1025C22—861no—
1026C22—861no—
1027C22—3448no—
1028C22—1724no—
1029C22—1722no—
1030C22—1722no—
1031C22—1722no—
1032C22C2×#1306334912yes—
1033C22C22×D4×D4311yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—42no—
1038C4—42no—
1039C4—432no—
1040C4—432no—
1041C4—861no—
1042C4—861no—
1043C4—861no—
1044C4—861no—
1045C4—1722no—
1046C4—1722no—
1047C4—1722no—
1048C4C2×#1306334912yes—
1049C4C2×#1306334912yes—
1050C4H(5,𝔽2)×D4311yescharacteristic
1051C42−1+4×D4311yescharacteristic
1052C2—22no—
1053C2—82no—
1054C2—82no—
1055C2—862no—
1056C2—3442no—
1057C2—1721no—
1058C2#537×D4311yescharacteristic
1059C2C22×#1306334911yescharacteristic
1060C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3245C2
socleC22×C43C23×D4
hypercenter#3245D43
hypocenterC43#60916
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #19147890C2semidirect
2. #532×D43C2semidirect
3. #19145984C2semidirect
4. #19145974C2semidirect
5. #19145959C2semidirect
6. #19145953C2semidirect
7. #19145914C2semidirect
8. #19145912C2semidirect
9. #19145911C2semidirect
10. #19145902C2semidirect
11. #19144403C2semidirect
12. #19144387C2semidirect
13. #19144211C2semidirect
14. #19144070C2semidirect
15. #19144054C2semidirect
16. C2×#14582921C2semidirect
17. C43×#3245C2semidirect
21. #14583456C22semidirect
23. #14583454C22semidirect
29. #14583447C22semidirect
38. #14583431C22semidirect
40. #14583430C22semidirect
55. #14583202C22semidirect
56. #14583201C22semidirect
57. #14583193C22semidirect
58. #14583190C22semidirect
59. #14583189C22semidirect
60. #14583187C22semidirect
61. #14583185C22semidirect
62. #14583181C22semidirect
63. #14583179C22semidirect
64. #14583176C22semidirect
65. #14583151C22semidirect
66. #14583149C22semidirect
67. #14583146C22semidirect
68. #14583144C22semidirect
69. #14583133C22semidirect
70. #14583128C22semidirect
71. #14583126C22semidirect
72. #14583113C22semidirect
73. #14583112C22semidirect
74. #14583105C22semidirect
75. #14583104C22semidirect
76. #14583100C22semidirect
77. #14583098C22semidirect
78. #14583096C22semidirect
79. #14583094C22semidirect
80. #14583092C22semidirect
81. #14583091C22semidirect
85. #14582921C22semidirect
86. #14582921C22semidirect
87. C2×C4⋊(C43⋊C8)C22semidirect
88. C2×Dic43⋊C8C22semidirect
92. C43×#532C22semidirect
93. C43×#474C22semidirect
94. C43×#474C22semidirect
95. C43×#466C22semidirect
96. C43×#459C22semidirect
97. C43×#459C22semidirect
98. C2×C4⋊C8×C43C22semidirect
424. C2×C4×C43AGL(1,ℤ/8)semidirect
532. #3245D43semidirect
566. #532C2×D43semidirect
597. #474C2×D43semidirect
598. #474C2×D43semidirect
604. #466C2×D43semidirect
617. #459C2×D43semidirect
618. #459C2×D43semidirect
626. C2×C4⋊C8C2×D43semidirect
629. C43#60916semidirect
1004. C2×C4#13063349semidirect

Maximal subgroups

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

subgroupindex
#191478902
#532×D432
#191459842
#191459742
#191459592
#191459532
#191459142
#191459122
#191459112
#191459022
#191444032
#191443872
#191442112
#191440702
#191440542
C2×#145829212
C43×#32452
#6091643