Finite Group Databasebeta

← #25968769

Subgroups — #25968769

Order 11008.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2C2×#14583454C211yesmaximal, characteristic, complemented
3#19145836C212yesmaximal, complemented
4#19145830C212yesmaximal, complemented
5#19145827C211yesmaximal, characteristic, complemented
6#19145822C211yesmaximal, characteristic, complemented
7#19145816C211yesmaximal, characteristic, complemented
8#19145807C212yesmaximal, complemented
9#19145798C212yesmaximal, complemented
10#19145791C212yesmaximal, complemented
11#19145782C212yesmaximal, complemented
12#19145116C212yesmaximal, complemented
13#19144937C212yesmaximal, complemented
14#19144509C212yesmaximal, complemented
15#19144503C212yesmaximal, complemented
16#19144386C212yesmaximal, complemented
17#19144384C212yesmaximal, complemented
18#432×D43C211yesmaximal, characteristic, complemented
19C43×#3238C211yesmaximal, characteristic, complemented
20#14583455C2211yescharacteristic
21#14583454—21no—
22#14583454—21no—
23#14583454—21no—
24#14583454—21no—
25#14583454C2212yes—
26#14583454C2212yes—
27#14583454C2212yes—
28#14583454C2212yes—
29#14583453C2211yescharacteristic
30#14583451C2211yescharacteristic
31#14583448C2211yescharacteristic
32#14583446C2211yescharacteristic
33#14583444C2211yescharacteristic
34C2×#13063325C2211yescharacteristic
35#14583434C2211yescharacteristic
36#14583433C2211yescharacteristic
37#14583432—21no—
38#14583432—21no—
39#14583428C2211yescharacteristic
40#14583427—21no—
41#14583426—21no—
42C2×#13063316C2212yes—
43#14583412C2211yescharacteristic
44#14583409C2211yescharacteristic
45#14583408—21no—
46#14583407—21no—
47C2×#13063305—21no—
48C2×#13063301—21no—
49C4×#10621902C2211yescharacteristic
50#14583367—21no—
51C4×#10621900—21no—
52C4×#10621900C2211yescharacteristic
53C2×Q8×Dic43—21no—
54C2×#13063290—21no—
55C2×#13063283C2212yes—
56C2×C42×D43C2211yescharacteristic
57#14583309C2212yescomplemented
58#14583308C2212yescomplemented
59#14583307C2214yescomplemented
60#14583306C2214yescomplemented
61#14583305C2212yescomplemented
62#14583266C2214yescomplemented
63#14583262C2214yescomplemented
64#14583261C2212yescomplemented
65#14583259C2212yescomplemented
66#14583258C2212yescomplemented
67#14583242C2214yes—
68#14583238C2214yes—
69#14583235C2212yes—
70#14583232C2212yes—
71#14583229C2212yes—
72#14583225C2214yes—
73#14583221C2214yes—
74#14583218C2212yes—
75#14583215C2212yes—
76#14583212C2212yes—
77#14583209C2214yescomplemented
78#14583208C2214yescomplemented
79#14583202C2214yescomplemented
80#14583201C2214yescomplemented
81#14583191C2212yescomplemented
82#14583186C2212yescomplemented
83#14583185C2212yescomplemented
84#14583184C2212yescomplemented
85#14583180C2212yescomplemented
86#14583179C2212yescomplemented
87#14582956C2211yescharacteristic
88#14582955C2212yes—
89#14582954C2212yes—
90#14582953C2212yes—
91#14582936C2214yes—
92#14582934C2214yes—
93C4⋊C8×D43C2212yes—
94#14582894C2214yes—
95#14582892C2214yes—
96C22⋊C8×D43C2212yes—
97#97×D43C2212yes—
98C2×C4⋊Q8×C43C2211yescharacteristic
99C43×#529C2211yescharacteristic
100C43×#501C2212yescomplemented
101C43×#489C2212yescomplemented
102C43×#483C2212yes—
103C43×#480C2212yes—
104C43×#477C2212yescomplemented
105C43×#476C2212yescomplemented
106C43×#432C2211yescharacteristic
107C2×#10621902C2311yescharacteristic
108C2×#10621898—21no—
109C2×#10621900—21no—
110C2×#10621900C2311yescharacteristic
111C22×Dic86—21no—
112C22×C4×D43D411yescharacteristic
113C22×C4×D43D411yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C2×C8×D43C2314yes—
116#13063325—21no—
117#13063325—21no—
118#13063325C2312yes—
119#13063325C2312yes—
120#13063324C2311yescharacteristic
121#13063324C2311yescharacteristic
122#13063323C2311yescharacteristic
123#13063321C2311yescharacteristic
124#13063320—21no—
125#13063319—21no—
126#13063318—21no—
127#13063317C2311yescharacteristic
128#13063316—22no—
129#13063316—22no—
130#13063316C2314yes—
131#13063316C2314yes—
132#13063315—21no—
133#13063315—21no—
134#13063313C2311yescharacteristic
135#13063311—21no—
136#13063311—21no—
137#13063310—21no—
138#13063310—21no—
139#13063308—21no—
140#13063307—21no—
141#13063307—21no—
142#13063305—22no—
143#13063305—22no—
144#13063305—22no—
145#13063305—22no—
146#13063305C2311yescharacteristic
147#13063304C2311yescharacteristic
148#13063303—21no—
149#13063303—21no—
150#13063303—21no—
151#13063302—21no—
152#13063301—22no—
153#13063301—22no—
154#13063301—22no—
155#13063301—22no—
156#13063301C2311yescharacteristic
157#13063300C2311yescharacteristic
158#13063299C2311yescharacteristic
159#13063298—21no—
160#13063298—21no—
161#13063298—21no—
162#13063297—21no—
163#13063296C2311yescharacteristic
164#13063295—21no—
165#13063293—21no—
166Q8×Dic43—22no—
167Q8×Dic43—22no—
168Q8×Dic43—22no—
169Q8×Dic43—22no—
170Q8×Dic43C2311yescharacteristic
171C4×Dic86—21no—
172C4×Dic86C2311yescharacteristic
173#13063290—22no—
174#13063290—22no—
175#13063290—22no—
176#13063290—22no—
177#13063290—21no—
178#13063290—21no—
179#13063290—21no—
180#13063290C2311yescharacteristic
181C4×D172—21no—
182C4×D172C2311yescharacteristic
183D4×Dic43—21no—
184D4×Dic43C2311yescharacteristic
185#13063287—21no—
186#13063287—21no—
187#13063287—21no—
188#13063287C2311yescharacteristic
189C4×C22⋊D43—21no—
190C4×C22⋊D43—21no—
191C4×C22⋊D43—21no—
192(C22⋊D43)⋊C4—21no—
193(C22⋊D43)⋊C4—21no—
194(C22⋊D43)⋊C4—21no—
195(C22⋊D43)⋊C4—21no—
196(C22⋊D43)⋊C4—21no—
197(C22⋊D43)⋊C4—21no—
198(C22⋊D43)⋊C4—21no—
199#13063283—22no—
200#13063283—22no—
201#13063283—21no—
202#13063283—21no—
203#13063283C2314yes—
204#13063283C2314yes—
205#13063283C2311yescharacteristic
206#13063283C2311yescharacteristic
207#13063282—21no—
208#13063282—21no—
209#13063281—21no—
210#13063281—21no—
211#13063281—21no—
212C2×C4⋊Dic43—21no—
213C2×C4⋊Dic43—22no—
214C2×C4⋊Dic43C2312yes—
215C2×Dic43⋊C4—22no—
216C2×(C2×D43)⋊C4—22no—
217C2×C4×Dic43—22no—
218C2×C4×Dic43—21no—
219C2×C4×Dic43D411yescharacteristic
220C2×C4×Dic43D411yescharacteristic
221C2×C4×Dic43C2311yescharacteristic
222C42×D43—21no—
223C42×D43D411yescharacteristic
224C42×D43D411yescharacteristic
225C42×D43D411yescharacteristic
226C42×D43D411yescharacteristic
227C42×D43C2311yescharacteristic
228C42×D43C2311yescharacteristic
229C42×D43C2311yescharacteristic
230C42×D43C2311yescharacteristic
231#13063259C2314yes—
232#13063258C2314yes—
233#13063258C2314yes—
234#13063257C2314yes—
235#13063256C2314yes—
236#13063256C2314yes—
237C4⋊(C43⋊C8)C2312yes—
238Dic43⋊C8C2314yes—
239#13063250C2314yes—
240#13063249C2314yes—
241#13063248C2314yes—
242#13063247C2314yes—
243#13063246C2314yes—
244#13063245C2314yes—
245C22⋊(C43⋊C8)C2312yes—
246(C2×D43)⋊C8C2314yes—
247#13063236C2312yes—
248#13063235C2314yes—
249C22×Q8×C43—21no—
250C4⋊Q8×C43—21no—
251C4⋊Q8×C43—21no—
252C4⋊Q8×C43C2312yes—
253C4⋊Q8×C43C2312yes—
254#126×C43—21no—
255#125×C43C2311yescharacteristic
256#124×C43C2311yescharacteristic
257#123×C43—21no—
258C22⋊Q8×C43C2311yescharacteristic
259#121×C43C2311yescharacteristic
260C4×Q8×C43C2311yescharacteristic
261C4×D4×C43—21no—
262C4×D4×C43C2311yescharacteristic
263#117×C43—21no—
264C2×C4⋊C4×C43—21no—
265C2×C4⋊C4×C43C2312yes—
266C2×C42×C43C2311yescharacteristic
267#107×C43C2314yes—
268#106×C43C2314yes—
269C4⋊C8×C43C2312yes—
270#103×C43C2314yes—
271#102×C43C2314yes—
272C22⋊C8×C43C2312yes—
273#97×C43C2312yes—
274C23×D43C2×D411yescharacteristic
275C2×Q8×C43—22no—
276C2×Q8×C43—22no—
277C2×Q8×C43—44no—
278C2×Q8×C43C2411yescharacteristic
279C2×D4×C43—21no—
280C2×D4×C43C2411yescharacteristic
281C22×C4×C43—21no—
282C22×C4×C43—22no—
283C22×C4×C43C2×D411yescharacteristic
284C22×C4×C43C2×D411yescharacteristic
285C22×C4×C43C2411yescharacteristic
286C2×C22⋊D43—21no—
287C2×C22⋊D43—21no—
288C2×C22⋊D43—21no—
289C2×C22⋊D43—21no—
290C2×C22⋊D43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—22no—
294C22×Dic43C2×D411yescharacteristic
295C22×Dic43C2×D411yescharacteristic
296C22×Dic43C2×D411yescharacteristic
297#10621902—24no—
298#10621900—24no—
299#10621900—44no—
300#10621898—44no—
301C2×D172—21no—
302C2×D172—21no—
303C2×D172C2411yescharacteristic
304C2×C4×D43—24no—
305C2×C4×D43—21no—
306C2×C4×D43—21no—
307C2×C4×D43—21no—
308C2×C4×D43—42no—
309C2×C4×D43—42no—
310C2×C4×D43C2×D411yescharacteristic
311C2×C4×D43C2×D411yescharacteristic
312C2×C4×D43C2×D411yescharacteristic
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×D43C2411yescharacteristic
321C2×C4×D43C2411yescharacteristic
322C2×Dic86—22no—
323C2×Dic86—22no—
324C2×Dic86—21no—
325C2×Dic86—21no—
326C2×Dic86—44no—
327C2×Dic86C2411yescharacteristic
328C2×C8×C43C2414yes—
329C4⋊C4×C43—22no—
330C4⋊C4×C43—22no—
331C4⋊C4×C43—22no—
332C4⋊C4×C43—21no—
333C4⋊C4×C43—21no—
334C4⋊C4×C43—21no—
335C4⋊C4×C43—21no—
336C4⋊C4×C43C2414yes—
337C4⋊C4×C43C2411yescharacteristic
338C4⋊C4×C43C2411yescharacteristic
339C22⋊C4×C43—21no—
340C22⋊C4×C43—21no—
341C22⋊C4×C43—21no—
342C22⋊C4×C43—21no—
343C22⋊C4×C43—21no—
344C42×C43—21no—
345C42×C43C2×D411yescharacteristic
346C42×C43C2×D411yescharacteristic
347C42×C43C2411yescharacteristic
348C42×C43C2411yescharacteristic
349C22⋊Dic43—21no—
350C22⋊Dic43—21no—
351C22⋊Dic43—21no—
352(C2×D43)⋊C4—21no—
353(C2×D43)⋊C4—21no—
354(C2×D43)⋊C4—21no—
355(C2×D43)⋊C4—21no—
356(C2×D43)⋊C4—21no—
357(C2×D43)⋊C4—21no—
358(C2×D43)⋊C4—24no—
359(C2×D43)⋊C4—24no—
360(C2×D43)⋊C4—21no—
361(C2×D43)⋊C4—21no—
362(C2×D43)⋊C4—21no—
363(C2×D43)⋊C4—21no—
364C4⋊Dic43—22no—
365C4⋊Dic43—22no—
366C4⋊Dic43—22no—
367C4⋊Dic43—24no—
368C4⋊Dic43—24no—
369C4⋊Dic43—21no—
370C4⋊Dic43—21no—
371C4⋊Dic43C2414yes—
372C4⋊Dic43C2411yescharacteristic
373C4⋊Dic43C2411yescharacteristic
374Dic43⋊C4—21no—
375Dic43⋊C4—21no—
376Dic43⋊C4—21no—
377Dic43⋊C4—21no—
378Dic43⋊C4—24no—
379Dic43⋊C4—24no—
380Dic43⋊C4—21no—
381Dic43⋊C4—21no—
382Dic43⋊C4—21no—
383Dic43⋊C4—21no—
384Dic43⋊C4—21no—
385Dic43⋊C4—21no—
386C4×Dic43—21no—
387C4×Dic43—21no—
388C4×Dic43—21no—
389C4×Dic43—21no—
390C4×Dic43—21no—
391C4×Dic43—24no—
392C4×Dic43—24no—
393C4×Dic43C2×D411yescharacteristic
394C4×Dic43C2×D411yescharacteristic
395C4×Dic43C2×D411yescharacteristic
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2×D411yescharacteristic
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2×D411yescharacteristic
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2411yescharacteristic
404C4×Dic43C2411yescharacteristic
405C2×C43⋊C8C2414yes—
406C8×D43—28no—
407C23×C43—21no—
408C23×C43C22×D411yescharacteristic
409C22×D43—22no—
410C22×D43—22no—
411C22×D43—21no—
412C22×D43—41no—
413C22×D43C22×D411yescharacteristic
414C22×D43C22×D411yescharacteristic
415Q8×C43—22no—
416Q8×C43—44no—
417Q8×C43—44no—
418D4×C43—22no—
419D4×C43—42no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—24no—
424C2×C4×C43—21no—
425C2×C4×C43—21no—
426C2×C4×C43—21no—
427C2×C4×C43—44no—
428C2×C4×C43—42no—
429C2×C4×C43C22×D411yescharacteristic
430C2×C4×C43C22×D411yescharacteristic
431C2×C4×C43C22×D411yescharacteristic
432C2×C4×C43C22×D411yescharacteristic
433C2×C4×C43C22×D411yescharacteristic
434C2×C4×C43C2511yescharacteristic
435C22⋊D43—42no—
436C22⋊D43—42no—
437C22⋊D43—42no—
438C22⋊D43—42no—
439C22⋊D43—42no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—21no—
443C2×Dic43—21no—
444C2×Dic43—21no—
445C2×Dic43—24no—
446C2×Dic43—41no—
447C2×Dic43—42no—
448C2×Dic43—44no—
449C2×Dic43—42no—
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452C2×Dic43C22×D411yescharacteristic
453C2×Dic43C22×D411yescharacteristic
454C2×Dic43C22×D411yescharacteristic
455C2×Dic43C22×D411yescharacteristic
456D172—22no—
457D172—42no—
458D172—42no—
459C4×D43—22no—
460C4×D43—22no—
461C4×D43—22no—
462C4×D43—22no—
463C4×D43—22no—
464C4×D43—41no—
465C4×D43—41no—
466C4×D43—41no—
467C4×D43—41no—
468C4×D43—41no—
469C4×D43—41no—
470C4×D43—42no—
471C4×D43—42no—
472C4×D43—42no—
473C4×D432−1+414yes—
474Dic86—22no—
475Dic86—42no—
476Dic86—42no—
477Dic86—44no—
478Dic86—44no—
479C8×C43—24no—
480C43⋊C8—24no—
481#60854—431nomaximal, Sylow
482C22×C43—21no—
483C22×C43—21no—
484C22×C43—41no—
485C22×C43—41no—
486C22×C43—41no—
487C22×C43#57512yes—
488C22×C43C23×D411yescharacteristic
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—21no—
492C2×D43—21no—
493C2×D43—21no—
494C2×D43—44no—
495C2×D43—41no—
496C2×D43—41no—
497C2×D43—41no—
498C2×D43#53612yes—
499C4×C43—21no—
500C4×C43—21no—
501C4×C43—21no—
502C4×C43—21no—
503C4×C43—41no—
504C4×C43—41no—
505C4×C43—41no—
506C4×C43—44no—
507C4×C43#57512yes—
508C4×C43C2×2−1+412yes—
509Dic43—21no—
510Dic43—21no—
511Dic43—21no—
512Dic43—21no—
513Dic43—21no—
514Dic43—41no—
515Dic43—44no—
516Dic43—41no—
517Dic43—41no—
518Dic43#53612yes—
519#3444—431no—
520C2×#533—431no—
521#3240—432no—
522#3240—432no—
523#3239—431no—
524#3239—431no—
525#3238—431no—
526#3238D4311yescharacteristic, complemented
527#3237—432no—
528#3236—432no—
529#3235—432no—
530#3234—432no—
531#3162—432no—
532#3135—432no—
533#3091—432no—
534#3091—432no—
535#3076—432no—
536#3076—432no—
537C2×#432—431no—
538C2×C43—22no—
539C2×C43—81no—
540C2×C43C2×#53611yescharacteristic
541C2×C43C2×#57511yescharacteristic
542C2×C43C2×#57511yescharacteristic
543D43—22no—
544D43—41no—
545D43—81no—
546#533—432no—
547#533—432no—
548#533—432no—
549#533—432no—
550#533—431no—
551#533—431no—
552#533—431no—
553#533—861no—
554#533—861no—
555#533—861no—
556#533—861no—
557#532—431no—
558#532—431no—
559#532—431no—
560C2×C4⋊Q8—431no—
561C2×C4⋊Q8C2×D4311yescharacteristic
562#529—431no—
563#529—431no—
564#529—431no—
565#529—861no—
566#529—861no—
567#529—861no—
568#529—861no—
569#529C2×D4311yescharacteristic
570C2×#125—432no—
571#525—431no—
572#525—431no—
573#525—861no—
574#525—861no—
575C2×C22⋊Q8—861no—
576C2×C22⋊Q8—861no—
577C4×#41—431no—
578C4×#41—431no—
579C4×#41—861no—
580C4×#41—861no—
581C2×C4×Q8—861no—
582C2×C4×Q8—861no—
583C2×#117—432no—
584C22×C42—431no—
585#501—432no—
586#501—432no—
587#501—434no—
588#501—434no—
589#501—432no—
590#501C2×D4312yescomplemented
591#491—434no—
592#490—434no—
593#489—432no—
594#489—432no—
595#489—432no—
596#489C2×D4312yescomplemented
597#485—434no—
598#485—434no—
599#484—432no—
600#484—432no—
601#483—432no—
602#483C2×D4312yes—
603#482—434no—
604#482—434no—
605#481—432no—
606#481—432no—
607#480—432no—
608#480C2×D4312yes—
609#479—434no—
610#479—434no—
611#478—434no—
612#478—434no—
613#477—432no—
614#477C2×D4312yescomplemented
615#476—432no—
616#476C2×D4312yescomplemented
617#475—432no—
618#475—432no—
619#474—432no—
620#474—432no—
621#432—431no—
622#432—432no—
623#432—432no—
624#432—432no—
625#432C2×D4311yescharacteristic
626#427—434no—
627#427—434no—
628C2×C4⋊C8—432no—
629#416—434no—
630#416—434no—
631C2×C22⋊C8—432no—
632C2×#97—432no—
633C43#6085411yescharacteristic, complemented, Sylow
634C2×#41—431no—
635C2×#41—431no—
636C2×#41—861no—
637C2×#41—861no—
638C22×Q8—21no—
639C22×Q8—861no—
640C23×C4—431no—
641C23×C4—431no—
642C23×C4—431no—
643C22×C8—434no—
644C4⋊Q8—21no—
645C4⋊Q8—21no—
646C4⋊Q8—431no—
647C4⋊Q8—431no—
648C4⋊Q8—431no—
649C4⋊Q8—432no—
650C4⋊Q8—432no—
651C4⋊Q8—861no—
652C4⋊Q8—861no—
653C4⋊Q8C22×D4312yes—
654C4⋊Q8C22×D4312yes—
655#127—431no—
656#126—21no—
657#126—861no—
658#126—861no—
659#126—861no—
660#125—434no—
661#125—434no—
662#125—431no—
663#125—862no—
664#125—862no—
665#125—861no—
666#125—861no—
667#125C22×D4311yescharacteristic
668#124—431no—
669#124—861no—
670#124—861no—
671#124C22×D4311yescharacteristic
672#123—21no—
673#123—861no—
674#123—861no—
675#123—861no—
676#123—861no—
677#123—861no—
678C22⋊Q8—431no—
679C22⋊Q8—431no—
680C22⋊Q8—431no—
681C22⋊Q8—861no—
682C22⋊Q8—862no—
683C22⋊Q8—862no—
684C22⋊Q8—862no—
685C22⋊Q8—862no—
686C22⋊Q8—861no—
687C22⋊Q8—861no—
688C22⋊Q8—861no—
689C22⋊Q8—862no—
690C22⋊Q8—862no—
691C22⋊Q8—862no—
692C22⋊Q8—862no—
693C22⋊Q8C22×D4311yescharacteristic
694#121—431no—
695#121—431no—
696#121—431no—
697#121—861no—
698#121—861no—
699#121—861no—
700#121—861no—
701#121C22×D4311yescharacteristic
702#120—861no—
703#120—861no—
704C4×Q8—431no—
705C4×Q8—431no—
706C4×Q8—431no—
707C4×Q8—861no—
708C4×Q8—862no—
709C4×Q8—862no—
710C4×Q8—862no—
711C4×Q8—862no—
712C4×Q8—861no—
713C4×Q8—861no—
714C4×Q8—861no—
715C4×Q8—862no—
716C4×Q8—862no—
717C4×Q8—862no—
718C4×Q8—862no—
719C4×Q8C22×D4311yescharacteristic
720C4×D4—21no—
721C4×D4—431no—
722C4×D4—431no—
723C4×D4—431no—
724C4×D4—861no—
725C4×D4—861no—
726C4×D4—861no—
727C4×D4—861no—
728C4×D4—861no—
729C4×D4—861no—
730C4×D4—861no—
731C4×D4—861no—
732C4×D4—861no—
733C4×D4—861no—
734C4×D4—861no—
735C4×D4—861no—
736C4×D4—861no—
737C4×D4—861no—
738C4×D4—861no—
739C4×D4C22×D4311yescharacteristic
740#117—21no—
741#117—434no—
742#117—434no—
743#117—431no—
744#117—431no—
745#117—861no—
746#117—861no—
747#117—861no—
748#117—861no—
749#117—861no—
750#117—861no—
751#117—862no—
752#117—862no—
753#117—861no—
754C2×C4⋊C4—21no—
755C2×C4⋊C4—432no—
756C2×C4⋊C4—862no—
757C2×C4⋊C4—862no—
758C2×C4⋊C4—861no—
759C2×C4⋊C4C22×D4312yes—
760C2×C22⋊C4—862no—
761C2×C42—431no—
762C2×C42—431no—
763C2×C42—431no—
764C2×C42—431no—
765C2×C42—431no—
766C2×C42—431no—
767C2×C42—431no—
768C2×C42—431no—
769C2×C42—431no—
770C2×C42—431no—
771C2×C42—431no—
772C2×C42—861no—
773C2×C42—861no—
774C2×C42—862no—
775C2×C42C22×D4311yescharacteristic
776#107—434no—
777#107—434no—
778#107—434no—
779#107C22×D4314yes—
780#106—434no—
781#106—434no—
782#106—434no—
783#106C22×D4314yes—
784C4⋊C8—434no—
785C4⋊C8—432no—
786C4⋊C8C22×D4312yes—
787#103—434no—
788#103—434no—
789#103—434no—
790#103C22×D4314yes—
791#102—434no—
792#102—434no—
793#102—434no—
794#102C22×D4314yes—
795C22⋊C8—432no—
796C22⋊C8—434no—
797C22⋊C8C22×D4312yes—
798#97—434no—
799#97—432no—
800#97C22×D4312yes—
801C24—431no—
802#41—864no—
803#41—864no—
804#41—1724no—
805#41—1724no—
806C2×Q8—22no—
807C2×Q8—22no—
808C2×Q8—44no—
809C2×Q8—431no—
810C2×Q8—861no—
811C2×Q8—861no—
812C2×Q8—862no—
813C2×Q8—862no—
814C2×Q8—1724no—
815C2×Q8C23×D4311yescharacteristic
816C2×D4—21no—
817C2×D4—431no—
818C2×D4—861no—
819C2×D4—861no—
820C2×D4—861no—
821C2×D4—861no—
822C2×D4—861no—
823C2×D4—861no—
824C2×D4—861no—
825C2×D4C23×D4311yescharacteristic
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—431no—
829C22×C4—431no—
830C22×C4—431no—
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—864no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—862no—
849C22×C4—861no—
850C22×C4—1722no—
851C22×C4—1722no—
852C22×C4D4×D4311yescharacteristic
853C22×C4D4×D4311yescharacteristic
854C22×C4C23×D4311yescharacteristic
855C2×C8—434no—
856C2×C8—868no—
857C2×C8C23×D4314yes—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—434no—
866C4⋊C4—431no—
867C4⋊C4—431no—
868C4⋊C4—864no—
869C4⋊C4—864no—
870C4⋊C4—864no—
871C4⋊C4—864no—
872C4⋊C4—861no—
873C4⋊C4—861no—
874C4⋊C4—861no—
875C4⋊C4—861no—
876C4⋊C4—861no—
877C4⋊C4—861no—
878C4⋊C4—861no—
879C4⋊C4—861no—
880C4⋊C4—862no—
881C4⋊C4—862no—
882C4⋊C4—862no—
883C4⋊C4—861no—
884C4⋊C4—861no—
885C4⋊C4—861no—
886C4⋊C4—861no—
887C4⋊C4C23×D4314yes—
888C4⋊C4C23×D4311yescharacteristic
889C4⋊C4C23×D4311yescharacteristic
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—861no—
896C22⋊C4—861no—
897C22⋊C4—864no—
898C22⋊C4—864no—
899C22⋊C4—861no—
900C22⋊C4—861no—
901C22⋊C4—861no—
902C22⋊C4—861no—
903C22⋊C4—861no—
904C22⋊C4—861no—
905C22⋊C4—861no—
906C22⋊C4—861no—
907C22⋊C4—861no—
908C22⋊C4—861no—
909C22⋊C4—861no—
910C42—21no—
911C42—431no—
912C42—431no—
913C42—431no—
914C42—431no—
915C42—431no—
916C42—431no—
917C42—431no—
918C42—431no—
919C42—431no—
920C42—431no—
921C42—431no—
922C42—431no—
923C42—861no—
924C42—861no—
925C42—864no—
926C42—864no—
927C42—861no—
928C42—861no—
929C42—861no—
930C42D4×D4311yescharacteristic
931C42D4×D4311yescharacteristic
932C42C23×D4311yescharacteristic
933C42C23×D4311yescharacteristic
934C23—21no—
935C23—431no—
936C23—431no—
937C23—862no—
938C23—862no—
939C23—861no—
940C23—1721no—
941C23C2×D4×D4311yescharacteristic
942Q8—22no—
943Q8—44no—
944Q8—44no—
945Q8—862no—
946Q8—1724no—
947Q8—1722no—
948Q8—1722no—
949Q8—1724no—
950D4—22no—
951D4—42no—
952D4—862no—
953D4—1722no—
954D4—1722no—
955D4—1722no—
956D4—1722no—
957D4—1722no—
958D4—1722no—
959D4—1722no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—24no—
967C2×C4—44no—
968C2×C4—42no—
969C2×C4—431no—
970C2×C4—434no—
971C2×C4—431no—
972C2×C4—431no—
973C2×C4—431no—
974C2×C4—431no—
975C2×C4—431no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—862no—
979C2×C4—862no—
980C2×C4—862no—
981C2×C4—862no—
982C2×C4—862no—
983C2×C4—861no—
984C2×C4—861no—
985C2×C4—861no—
986C2×C4—864no—
987C2×C4—1721no—
988C2×C4—1721no—
989C2×C4—1721no—
990C2×C4—1721no—
991C2×C4—1721no—
992C2×C4—1721no—
993C2×C4—1722no—
994C2×C4—1722no—
995C2×C4—1722no—
996C2×C4—1721no—
997C2×C4—1722no—
998C2×C4—1724no—
999C2×C4—1722no—
1000C2×C4C2×D4×D4311yescharacteristic
1001C2×C4C2×D4×D4311yescharacteristic
1002C2×C4C2×D4×D4311yescharacteristic
1003C2×C4C2×D4×D4311yescharacteristic
1004C2×C4C2×D4×D4311yescharacteristic
1005C2×C4C24×D4311yescharacteristic
1006C8—24no—
1007C8—864no—
1008C22—21no—
1009C22—21no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—432no—
1014C22—861no—
1015C22—861no—
1016C22—861no—
1017C22—861no—
1018C22—861no—
1019C22—1724no—
1020C22—1721no—
1021C22—1721no—
1022C22—1721no—
1023C22#1458369512yes—
1024C22C22×D4×D4311yescharacteristic
1025C4—21no—
1026C4—21no—
1027C4—21no—
1028C4—21no—
1029C4—44no—
1030C4—41no—
1031C4—41no—
1032C4—41no—
1033C4—432no—
1034C4—861no—
1035C4—861no—
1036C4—861no—
1037C4—861no—
1038C4—861no—
1039C4—1721no—
1040C4—1721no—
1041C4—1724no—
1042C4—1721no—
1043C4#1458369812yes—
1044C42−1+4×D4312yes—
1045C2—22no—
1046C2—81no—
1047C2—862no—
1048C2—3441no—
1049C2—1721no—
1050C2#536×D4311yescharacteristic
1051C2C2×#1458369511yescharacteristic
1052C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3238C2
socleC22×C43C23×D4
prime radical#19147889C2
hypercenter#3238D43
hypocenterC43#60854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. C2×#14583454C2semidirect
3. #19145836C2semidirect
4. #19145830C2semidirect
5. #19145827C2semidirect
6. #19145822C2semidirect
7. #19145816C2semidirect
8. #19145807C2semidirect
9. #19145798C2semidirect
10. #19145791C2semidirect
11. #19145782C2semidirect
12. #19145116C2semidirect
13. #19144937C2semidirect
14. #19144509C2semidirect
15. #19144503C2semidirect
16. #19144386C2semidirect
17. #19144384C2semidirect
18. #432×D43C2semidirect
19. C43×#3238C2semidirect
57. #14583309C22semidirect
58. #14583308C22semidirect
59. #14583307C22semidirect
60. #14583306C22semidirect
61. #14583305C22semidirect
62. #14583266C22semidirect
63. #14583262C22semidirect
64. #14583261C22semidirect
65. #14583259C22semidirect
66. #14583258C22semidirect
77. #14583209C22semidirect
78. #14583208C22semidirect
79. #14583202C22semidirect
80. #14583201C22semidirect
81. #14583191C22semidirect
82. #14583186C22semidirect
83. #14583185C22semidirect
84. #14583184C22semidirect
85. #14583180C22semidirect
86. #14583179C22semidirect
100. C43×#501C22semidirect
101. C43×#489C22semidirect
104. C43×#477C22semidirect
105. C43×#476C22semidirect
526. #3238D43semidirect
590. #501C2×D43semidirect
596. #489C2×D43semidirect
614. #477C2×D43semidirect
616. #476C2×D43semidirect
633. C43#60854semidirect

Maximal subgroups

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

subgroupindex
#191478892
C2×#145834542
#191458362
#191458302
#191458272
#191458222
#191458162
#191458072
#191457982
#191457912
#191457822
#191451162
#191449372
#191445092
#191445032
#191443862
#191443842
#432×D432
C43×#32382
#6085443