Finite Group Databasebeta

← #25968321

Subgroups — #25968321

Order 11008.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148464C211yesmaximal, characteristic, complemented
2#19148378C211yesmaximal, characteristic, complemented
3#19145655C214yesmaximal, complemented
4#19145652C214yesmaximal, complemented
5#19145531C211yesmaximal, characteristic, complemented
6#19145530C211yesmaximal, characteristic, complemented
7#19145525C211yesmaximal, characteristic, complemented
8#19145524C211yesmaximal, characteristic, complemented
9#19145521C211yesmaximal, characteristic, complemented
10#19145520C211yesmaximal, characteristic, complemented
11#19145516C211yesmaximal, characteristic, complemented
12#19145042C211yesmaximal, characteristic, complemented
13#492×D43C211yesmaximal, characteristic, complemented
14#19144972C211yesmaximal, characteristic, complemented
15#19144919C211yesmaximal, characteristic, complemented
16#19144102C214yesmaximal, complemented
17#19143876C214yesmaximal, complemented
18#19143234C211yesmaximal, characteristic, complemented
19C43×#3206C211yesmaximal, characteristic, complemented
20C2×#13063373C2212yes—
21C2×#13063352C2214yes—
22C2×SD16×D43C2214yes—
23#14583632—21no—
24#14583631—21no—
25#14583568—21no—
26#14583567—21no—
27#14583564—21no—
28#14583564—21no—
29#14583552—21no—
30#14583552—21no—
31#14583550—21no—
32#14583550—21no—
33#14583550—21no—
34#14583550—21no—
35#14583546—21no—
36#14583544—21no—
37#14583542—21no—
38#14583537—21no—
39#14583502C2212yes—
40#14583500C2212yes—
41#14583474C2212yes—
42#14583474C2212yescomplemented
43#14583473C2212yescomplemented
44#14583465C2212yes—
45#14583454C2211yescharacteristic
46#14583450C2211yescharacteristic
47#14583450C2211yescharacteristic
48#14583450C2211yescharacteristic, complemented
49#14583449C2211yescharacteristic
50#14583449C2211yescharacteristic, complemented
51#14583447C2211yescharacteristic
52C4⋊Q8×D43C2211yescharacteristic
53C4⋊Q8×D43C2211yescharacteristic, complemented
54#127×D43C2211yescharacteristic
55#14583371C2212yes—
56C4×#10621898C2211yescharacteristic
57#14583285C2214yes—
58#14583276C2211yescharacteristic
59#14583275C2211yescharacteristic
60#14583273C2211yescharacteristic
61#14583273C2211yescharacteristic
62#14583272C2211yescharacteristic
63#14583271C2211yescharacteristic
64#14583270C2214yes—
65#14583266C2214yescomplemented
66#14583255C2214yescomplemented
67#14583251C2211yescharacteristic, complemented
68#14583250C2211yescharacteristic, complemented
69#14583249C2211yescharacteristic, complemented
70#14583249C2211yescharacteristic, complemented
71#14583247C2211yescharacteristic, complemented
72#14583246C2211yescharacteristic, complemented
73#14583117C2214yescomplemented
74#14583116C2214yescomplemented
75#14583115C2214yescomplemented
76#14583114C2214yescomplemented
77#14583103C2214yescomplemented
78#14583102C2214yescomplemented
79#14583101C2214yescomplemented
80#14583047C2214yescomplemented
81#14583046C2214yescomplemented
82#14583043C2214yescomplemented
83#14583042C2214yescomplemented
84#14583039C2214yescomplemented
85#14583038C2214yescomplemented
86#14583036C2214yescomplemented
87#14582959C2212yescomplemented
88#14582957C2212yescomplemented
89#14582952C2211yescharacteristic, complemented
90#14582950C2211yescharacteristic, complemented
91#14582950C2211yescharacteristic, complemented
92#14582924C2212yes—
93#14582906C2214yes—
94#14582894C2214yes—
95#14582864C2212yes—
96C4×#10621872C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#532C2211yescharacteristic
99C2×C4⋊Q8×C43C2211yescharacteristic, complemented
100C43×#492C2211yescharacteristic
101C43×#492C2211yescharacteristic
102C43×#487C2211yescharacteristic, complemented
103C43×#487C2211yescharacteristic, complemented
104C43×#461C2214yescomplemented
105C43×#448C2214yescomplemented
106C43×#431C2211yescharacteristic, complemented
107#13063373—48no—
108C2×#10621902—22no—
109C2×#10621902—21no—
110C2×#10621902C2312yes—
111C2×#10621902C2312yes—
112C2×#10621898—22no—
113C2×#10621898—22no—
114C2×#10621898—21no—
115C2×#10621898C2311yescharacteristic
116C2×#10621898C2312yes—
117C2×#10621900—21no—
118C2×Q8×D43—22no—
119C2×Q8×D43C2312yes—
120C2×Q8×D43C2312yes—
121C2×D4×D43—21no—
122C2×D4×D43—21no—
123C2×D4×D43C2312yes—
124#13063352—48no—
125C2×#10621873C2314yes—
126C2×#10621883C2314yes—
127C2×#10621884C2314yes—
128C2×#10621884C2314yes—
129SD16×D43—48no—
130C2×D344C2314yes—
131C2×#10621882C2314yes—
132C2×#10621872C2312yes—
133C2×C8×D43C2312yes—
134#13063325C2311yescharacteristic
135#13063325C2311yescharacteristic
136#13063324—21no—
137#13063324—21no—
138#13063324—21no—
139#13063324—21no—
140#13063323C2312yes—
141#13063323C2312yes—
142#13063322C2311yescharacteristic
143#13063322C2311yescharacteristic
144#13063321—22no—
145#13063321—21no—
146#13063321—21no—
147#13063321C2312yes—
148#13063316C2312yes—
149#13063314—21no—
150#13063314C2312yes—
151#13063314C2312yes—
152#13063313—21no—
153#13063313C2312yes—
154#13063312—21no—
155#13063311—22no—
156#13063310—22no—
157#13063310—22no—
158#13063310—22no—
159#13063310—22no—
160#13063309—22no—
161#13063308—22no—
162#13063308—22no—
163#13063308—22no—
164#13063307—22no—
165#13063307—22no—
166#13063305—21no—
167#13063303—22no—
168#13063303—22no—
169#13063303—22no—
170#13063303—22no—
171#13063301—21no—
172#13063301—22no—
173#13063301—22no—
174#13063300—21no—
175#13063300—21no—
176#13063300—21no—
177#13063300—21no—
178#13063300—21no—
179#13063300C2312yes—
180#13063299—21no—
181#13063299—21no—
182#13063299—21no—
183#13063299—22no—
184#13063299C2312yes—
185#13063298—22no—
186#13063297—22no—
187#13063296—21no—
188#13063296—22no—
189#13063296C2312yes—
190#13063295—22no—
191#13063293—22no—
192Q8×Dic43—21no—
193C4×Dic86D411yescharacteristic
194C4×Dic86D411yescharacteristic
195#13063290—21no—
196C4×D172—21no—
197C4×D172—21no—
198C4×D172—21no—
199C4×D172D411yescharacteristic
200C4×D172D411yescharacteristic
201C4×D172C2312yes—
202D4×Dic43—21no—
203D4×Dic43C2312yes—
204#13063287—21no—
205#13063287—21no—
206#13063287—21no—
207#13063287—21no—
208#13063287—21no—
209#13063287C2312yes—
210C4×C22⋊D43—22no—
211C4×C22⋊D43D411yescharacteristic
212C4×C22⋊D43D411yescharacteristic
213C4×C22⋊D43D411yescharacteristic
214C4×C22⋊D43D411yescharacteristic
215(C22⋊D43)⋊C4—22no—
216#13063284C2311yescharacteristic
217#13063283C2312yes—
218#13063282C2311yescharacteristic
219#13063282C2311yescharacteristic
220C4⋊C4×D43—21no—
221C4⋊C4×D43—21no—
222C4⋊C4×D43—21no—
223C4⋊C4×D43—21no—
224C2×(C2×D43)⋊C4—22no—
225C22⋊C4×D43—22no—
226C42×D43C2311yescharacteristic
227C42×D43C2311yescharacteristic
228C4⋊(C43⋊C8)C2312yes—
229Dic43⋊C8C2312yes—
230Dic43⋊C8C2312yes—
231#13063250C2314yes—
232#13063249C2314yes—
233#13063249C2314yes—
234#13063248C2314yes—
235#13063247C2314yes—
236#13063245C2314yes—
237C22⋊(C43⋊C8)C2312yes—
238(C2×D43)⋊C8C2312yes—
239(C2×D43)⋊C8C2312yes—
240#13063235C2312yes—
241C4×C43⋊C8C2311yescharacteristic
242C4×C43⋊C8C2311yescharacteristic
243C8×Dic43C2312yes—
244C2×#41×C43—21no—
245C22×Q8×C43C2312yes—
246C2×SD16×C43C2314yes—
247C2×SD16×C43C2314yes—
248C4⋊Q8×C43—21no—
249C4⋊Q8×C43—21no—
250C4⋊Q8×C43C2312yes—
251C4⋊Q8×C43C2311yescharacteristic
252C4⋊Q8×C43C2311yescharacteristic
253C4⋊Q8×C43C2311yescharacteristic
254#127×C43C2311yescharacteristic
255#124×C43—21no—
256#121×C43—21no—
257#121×C43C2312yes—
258C4×D4×C43—21no—
259C4×D4×C43C2312yes—
260C2×C4⋊C4×C43—21no—
261C2×C4⋊C4×C43—21no—
262C2×C42×C43C2311yescharacteristic
263C4⋊C8×C43C2312yes—
264#103×C43C2314yes—
265#103×C43C2314yes—
266C22⋊C8×C43C2312yes—
267C4×C8×C43C2311yescharacteristic
268C4×C8×C43C2311yescharacteristic
269C23×D43—22no—
270#41×C43—82no—
271C2×Q8×C43—21no—
272C2×Q8×C43—22no—
273C2×Q8×C43—44no—
274C2×Q8×C43C2412yes—
275C2×Q8×C43C2412yes—
276C2×D4×C43—21no—
277C2×D4×C43—21no—
278C2×D4×C43—22no—
279C2×D4×C43C2412yes—
280C22×C4×C43—22no—
281C22×C4×C43—22no—
282C22×C4×C43C2×D411yescharacteristic
283C22×C4×C43C2×D411yescharacteristic
284C22×C4×C43C2411yescharacteristic
285C2×C22⋊D43—22no—
286C2×C22⋊D43—22no—
287C2×C22⋊D43—22no—
288C2×C22⋊D43—22no—
289C2×C22⋊D43—22no—
290C2×C22⋊D43—22no—
291C2×C22⋊D43C2×D411yescharacteristic
292C2×C22⋊D43C2×D411yescharacteristic
293C22×Dic43—22no—
294#10621902—28no—
295#10621902—44no—
296#10621902—48no—
297#10621902—82no—
298Q8×D43—28no—
299Q8×D43—44no—
300Q8×D43—48no—
301#10621900—82no—
302D4×D43—28no—
303D4×D43—82no—
304D4×D43—82no—
305#10621898—24no—
306#10621898—44no—
307#10621898—48no—
308#10621898—48no—
309#10621898—82no—
310C2×D172—21no—
311C2×D172—21no—
312C2×D172—21no—
313C2×D172—21no—
314C2×D172—22no—
315C2×D172—22no—
316C2×D172—22no—
317C2×D172C2×D411yescharacteristic
318C2×D172C2412yes—
319C2×D172C2412yes—
320C2×C4×D43—22no—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—22no—
324C2×C4×D43—22no—
325C2×C4×D43—22no—
326C2×C4×D43—22no—
327C2×C4×D43C2×D411yescharacteristic
328C2×C4×D43C2×D411yescharacteristic
329C2×C4×D43C2×D411yescharacteristic
330C2×C4×D43C2×D411yescharacteristic
331C2×C4×D43C2411yescharacteristic
332C2×C4×D43C2411yescharacteristic
333C2×Dic86—21no—
334C2×Dic86—22no—
335C2×Dic86—22no—
336C2×Dic86C2×D411yescharacteristic
337C2×Dic86C2412yes—
338SD16×C43—44no—
339SD16×C43—44no—
340C2×C8×C43C2412yes—
341C2×C8×C43C2412yes—
342C4⋊C4×C43—21no—
343C4⋊C4×C43—21no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43—21no—
346C4⋊C4×C43—22no—
347C4⋊C4×C43—22no—
348C4⋊C4×C43—21no—
349C4⋊C4×C43C2412yes—
350C22⋊C4×C43—22no—
351C22⋊C4×C43—22no—
352C42×C43C2×D411yescharacteristic
353C42×C43C2×D411yescharacteristic
354C42×C43C2411yescharacteristic
355C42×C43C2411yescharacteristic
356C22⋊Dic43—22no—
357C22⋊Dic43—22no—
358C22⋊Dic43C2×D411yescharacteristic
359C22⋊Dic43C2×D411yescharacteristic
360#10621884—44no—
361#10621884—44no—
362#10621883—44no—
363#10621882—44no—
364(C2×D43)⋊C4—22no—
365(C2×D43)⋊C4—22no—
366(C2×D43)⋊C4—22no—
367(C2×D43)⋊C4—22no—
368(C2×D43)⋊C4—22no—
369(C2×D43)⋊C4—22no—
370(C2×D43)⋊C4—22no—
371(C2×D43)⋊C4—22no—
372(C2×D43)⋊C4—22no—
373(C2×D43)⋊C4—22no—
374(C2×D43)⋊C4—22no—
375(C2×D43)⋊C4C2×D411yescharacteristic
376(C2×D43)⋊C4C2×D411yescharacteristic
377(C2×D43)⋊C4C2×D411yescharacteristic
378(C2×D43)⋊C4C2×D411yescharacteristic
379C4⋊Dic43—21no—
380C4⋊Dic43—21no—
381C4⋊Dic43—21no—
382C4⋊Dic43—22no—
383C4⋊Dic43C2×D411yescharacteristic
384C4⋊Dic43C2×D411yescharacteristic
385C4⋊Dic43C2412yes—
386Dic43⋊C4—22no—
387Dic43⋊C4—22no—
388Dic43⋊C4—22no—
389Dic43⋊C4—22no—
390Dic43⋊C4—22no—
391Dic43⋊C4C2×D411yescharacteristic
392Dic43⋊C4C2×D411yescharacteristic
393Dic43⋊C4C2×D411yescharacteristic
394Dic43⋊C4C2×D411yescharacteristic
395C4×Dic43—22no—
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2×D411yescharacteristic
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2411yescharacteristic
401C4×Dic43C2411yescharacteristic
402C2×C43⋊C8C2412yes—
403C2×C43⋊C8C2412yes—
404D344—44no—
405#10621873—44no—
406#10621872—24no—
407C8×D43—24no—
408C23×C43—22no—
409C23×C43C22×D411yescharacteristic
410C22×D43—22no—
411C22×D43—22no—
412C22×D43—44no—
413C22×D43—82no—
414C22×D43—82no—
415C22×D43C22×D411yescharacteristic
416C22×D43C22×D411yescharacteristic
417Q8×C43—24no—
418Q8×C43—24no—
419Q8×C43—44no—
420Q8×C43—42no—
421D4×C43—24no—
422D4×C43—42no—
423D4×C43—42no—
424D4×C43—82no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—44no—
432C2×C4×C43—82no—
433C2×C4×C43C22×D411yescharacteristic
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C2511yescharacteristic
439C22⋊D43—22no—
440C22⋊D43—22no—
441C22⋊D43—44no—
442C22⋊D43—44no—
443C22⋊D43—82no—
444C22⋊D43—82no—
445C22⋊D43—82no—
446C22⋊D43—82no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—82no—
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452C2×Dic43C22×D411yescharacteristic
453C2×Dic43C22×D411yescharacteristic
454C2×Dic43C22×D411yescharacteristic
455C2×Dic43C22×D411yescharacteristic
456D172—22no—
457D172—24no—
458D172—24no—
459D172—44no—
460D172—44no—
461D172—42no—
462D172—42no—
463D172—42no—
464D172—42no—
465D172—82no—
466C4×D43—22no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—22no—
470C4×D43—22no—
471C4×D43—44no—
472C4×D43—44no—
473C4×D43—44no—
474C4×D43—44no—
475C4×D43—44no—
476C4×D43—82no—
477C4×D43—82no—
478C4×D43H(5,𝔽2)14yes—
479Dic86—22no—
480Dic86—24no—
481Dic86—44no—
482Dic86—42no—
483Dic86—44no—
484C8×C43—22no—
485C8×C43—22no—
486C43⋊C8—22no—
487C43⋊C8—22no—
488#60820—431nomaximal, Sylow
489C22×C43—21no—
490C22×C43—21no—
491C22×C43—21no—
492C22×C43—42no—
493C22×C43—42no—
494C22×C43—42no—
495C22×C43C23×D411yescharacteristic
496C2×D43—21no—
497C2×D43—21no—
498C2×D43—21no—
499C2×D43—21no—
500C2×D43—21no—
501C2×D43—42no—
502C2×D43—42no—
503C2×D43—42no—
504C2×D43—42no—
505C2×D43—42no—
506C2×D43—42no—
507C2×D43—164no—
508C2×D43#53512yes—
509C4×C43—21no—
510C4×C43—21no—
511C4×C43—21no—
512C4×C43—42no—
513C4×C43—42no—
514C4×C43—42no—
515C4×C43#57712yes—
516C4×C43#57712yes—
517C4×C43C2×H(5,𝔽2)12yes—
518Dic43—21no—
519Dic43—21no—
520Dic43—21no—
521Dic43—21no—
522Dic43—21no—
523Dic43—42no—
524Dic43—42no—
525Dic43#53512yes—
526#3508—431no—
527#3499—431no—
528#3221—434no—
529#3221—434no—
530#3207—431no—
531#3207—431no—
532#3207—431no—
533#3207—431no—
534#3206—431no—
535#3206—431no—
536#3206—431no—
537#3206D4311yescharacteristic, complemented
538#3151—431no—
539C2×#492—431no—
540#3139—431no—
541#3131—431no—
542#3042—434no—
543#3010—434no—
544#2922—431no—
545C2×C43—41no—
546C2×C43—82no—
547C2×C43C2×#53511yescharacteristic
548C2×C43C2×#57711yescharacteristic
549C2×C43C2×#57711yescharacteristic
550D43—22no—
551D43—41no—
552D43—82no—
553D43—82no—
554C2×2−1+4—432no—
555C2×AGL(1,ℤ/8)—434no—
556C22×SD16—434no—
557#559—861no—
558#559—861no—
559#550—861no—
560#550—861no—
561D4×Q8—861no—
562D4×Q8—861no—
563#547—861no—
564#547—861no—
565#547—861no—
566#547—861no—
567#547—861no—
568#547—861no—
569#546—861no—
570#546—861no—
571#546—861no—
572#546—861no—
573#540—432no—
574#540—432no—
575#536—432no—
576#536—432no—
577#536—432no—
578#535—432no—
579#533—431no—
580#532—431no—
581#532—431no—
582#532—431no—
583#532—431no—
584#532—431no—
585#532—431no—
586#532C2×D4311yescharacteristic
587C2×C4⋊Q8—431no—
588C2×C4⋊Q8—431no—
589C2×C4⋊Q8C2×D4311yescharacteristic, complemented
590C2×#127—431no—
591#518—432no—
592C4×#41—431no—
593#496—434no—
594#493—431no—
595#493—431no—
596#492—434no—
597#492—431no—
598#492—431no—
599#492—431no—
600#492—431no—
601#492C2×D4311yescharacteristic
602#492C2×D4311yescharacteristic
603#491—434no—
604#488—434no—
605#487—431no—
606#487—431no—
607#487—431no—
608#487—431no—
609#487C2×D4311yescharacteristic, complemented
610#487C2×D4311yescharacteristic, complemented
611#486—431no—
612#486—431no—
613#463—434no—
614#463—434no—
615#463—434no—
616#463—434no—
617#461—434no—
618#461—434no—
619#461—434no—
620#461C2×D4314yescomplemented
621#449—434no—
622#449—434no—
623#449—434no—
624#449—434no—
625#448—434no—
626#448—434no—
627#448—434no—
628#448C2×D4314yescomplemented
629#433—432no—
630#433—432no—
631#431—431no—
632#431—431no—
633#431—431no—
634#431C2×D4311yescharacteristic, complemented
635#424—432no—
636#419—434no—
637#416—434no—
638#408—432no—
639C4×M16—431no—
640C2×C4×C8—431no—
641C43#6082011yescharacteristic, complemented, Sylow
6422−1+4—1728no—
643C2×#41—21no—
644C2×#41—431no—
645C2×#41—432no—
646C2×#41—432no—
647C2×#41—432no—
648C2×#41—862no—
649C2×#41—862no—
650C2×#41—861no—
651C2×#41—861no—
652C2×#41—862no—
653C2×#41—861no—
654C22×Q8—432no—
655C22×Q8—432no—
656C22×Q8—862no—
657C22×Q8C22×D4312yes—
658C22×D4—432no—
659C22×D4—861no—
660C22×D4—861no—
661AGL(1,ℤ/8)—1728no—
662C2×SD16—434no—
663C2×SD16—434no—
664C2×SD16—434no—
665C2×SD16—434no—
666C2×SD16—1728no—
667C2×SD16C22×D4314yes—
668C2×SD16C22×D4314yes—
669C2×D8—434no—
670C2×D8—434no—
671C2×M16—432no—
672C22×C8—432no—
673C4⋊Q8—21no—
674C4⋊Q8—21no—
675C4⋊Q8—432no—
676C4⋊Q8—432no—
677C4⋊Q8—431no—
678C4⋊Q8—431no—
679C4⋊Q8—861no—
680C4⋊Q8—861no—
681C4⋊Q8—861no—
682C4⋊Q8—861no—
683C4⋊Q8C22×D4311yescharacteristic
684C4⋊Q8C22×D4311yescharacteristic
685C4⋊Q8C22×D4312yes—
686C4⋊Q8C22×D4311yescharacteristic
687#127—432no—
688#127—431no—
689#127—431no—
690#127—861no—
691#127—861no—
692#127—862no—
693#127C22×D4311yescharacteristic
694#125—432no—
695#124—21no—
696#124—432no—
697#124—432no—
698#124—432no—
699#124—861no—
700#124—861no—
701#124—862no—
702#124—861no—
703#123—862no—
704#123—862no—
705#123—862no—
706#123—862no—
707#123—862no—
708#123—862no—
709#123—862no—
710#123—862no—
711#123—862no—
712#123—862no—
713C22⋊Q8—862no—
714C22⋊Q8—862no—
715C22⋊Q8—862no—
716C22⋊Q8—862no—
717C22⋊Q8—861no—
718C22⋊Q8—862no—
719C22⋊Q8—862no—
720C22⋊Q8—861no—
721#121—21no—
722#121—432no—
723#121—432no—
724#121—432no—
725#121—862no—
726#121—862no—
727#121—862no—
728#121—862no—
729#121—861no—
730#121—861no—
731#121—861no—
732#121—861no—
733#121—861no—
734#121—861no—
735#121—861no—
736#121—861no—
737#121—861no—
738#121C22×D4312yes—
739#120—862no—
740#120—862no—
741C4×Q8—431no—
742C4×Q8—431no—
743C4×Q8—861no—
744C4×Q8—861no—
745C4×D4—21no—
746C4×D4—431no—
747C4×D4—431no—
748C4×D4—431no—
749C4×D4—431no—
750C4×D4—432no—
751C4×D4—432no—
752C4×D4—431no—
753C4×D4—431no—
754C4×D4—432no—
755C4×D4—861no—
756C4×D4—861no—
757C4×D4—861no—
758C4×D4—861no—
759C4×D4—861no—
760C4×D4—861no—
761C4×D4—862no—
762C4×D4—862no—
763C4×D4—861no—
764C4×D4—861no—
765C4×D4—861no—
766C4×D4C22×D4312yes—
767#117—431no—
768#117—431no—
769#117—431no—
770#117—432no—
771C2×C4⋊C4—21no—
772C2×C4⋊C4—21no—
773C2×C4⋊C4—861no—
774C2×C4⋊C4—861no—
775C2×C4⋊C4—861no—
776C2×C4⋊C4—861no—
777C2×C22⋊C4—862no—
778C2×C22⋊C4—862no—
779C2×C42—431no—
780C2×C42—431no—
781C2×C42C22×D4311yescharacteristic
782C4⋊C8—432no—
783C4⋊C8—432no—
784C4⋊C8—432no—
785C4⋊C8C22×D4312yes—
786#103—434no—
787#103—434no—
788#103—434no—
789#103—434no—
790#103C22×D4314yes—
791#103C22×D4314yes—
792#102—434no—
793#102—434no—
794C22⋊C8—432no—
795C22⋊C8—432no—
796C22⋊C8—432no—
797C22⋊C8C22×D4312yes—
798#97—432no—
799C4×C8—432no—
800C4×C8—431no—
801C4×C8—431no—
802C4×C8C22×D4311yescharacteristic
803C4×C8C22×D4311yescharacteristic
804C24—862no—
805#41—82no—
806#41—864no—
807#41—868no—
808#41—3442no—
809#41—3442no—
810#41—3442no—
811#41—1724no—
812#41—1728no—
813#41—1728no—
814#41—1724no—
815#41—1728no—
816C2×Q8—21no—
817C2×Q8—22no—
818C2×Q8—44no—
819C2×Q8—431no—
820C2×Q8—432no—
821C2×Q8—862no—
822C2×Q8—862no—
823C2×Q8—868no—
824C2×Q8—861no—
825C2×Q8—1724no—
826C2×Q8—1728no—
827C2×Q8C23×D4312yes—
828C2×Q8C23×D4312yes—
829C2×D4—22no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—431no—
833C2×D4—431no—
834C2×D4—431no—
835C2×D4—432no—
836C2×D4—432no—
837C2×D4—862no—
838C2×D4—862no—
839C2×D4—862no—
840C2×D4—868no—
841C2×D4—862no—
842C2×D4—862no—
843C2×D4—862no—
844C2×D4—862no—
845C2×D4—862no—
846C2×D4—862no—
847C2×D4—861no—
848C2×D4—861no—
849C2×D4—861no—
850C2×D4—861no—
851C2×D4—3442no—
852C2×D4—3442no—
853C2×D4C23×D4312yes—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—431no—
862C22×C4—862no—
863C22×C4—862no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—862no—
868C22×C4—862no—
869C22×C4—862no—
870C22×C4D4×D4311yescharacteristic
871C22×C4D4×D4311yescharacteristic
872C22×C4C23×D4311yescharacteristic
873SD16—44no—
874SD16—44no—
875SD16—1724no—
876SD16—1724no—
877SD16—1724no—
878SD16—1724no—
879D8—1724no—
880D8—1724no—
881M16—864no—
882C2×C8—432no—
883C2×C8—432no—
884C2×C8—864no—
885C2×C8C23×D4312yes—
886C2×C8C23×D4312yes—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—21no—
894C4⋊C4—431no—
895C4⋊C4—431no—
896C4⋊C4—431no—
897C4⋊C4—431no—
898C4⋊C4—431no—
899C4⋊C4—431no—
900C4⋊C4—432no—
901C4⋊C4—862no—
902C4⋊C4—862no—
903C4⋊C4—862no—
904C4⋊C4—862no—
905C4⋊C4—862no—
906C4⋊C4—862no—
907C4⋊C4—861no—
908C4⋊C4—861no—
909C4⋊C4—861no—
910C4⋊C4C23×D4312yes—
911C22⋊C4—22no—
912C22⋊C4—22no—
913C22⋊C4—431no—
914C22⋊C4—431no—
915C22⋊C4—431no—
916C22⋊C4—431no—
917C22⋊C4—431no—
918C22⋊C4—431no—
919C22⋊C4—862no—
920C22⋊C4—862no—
921C22⋊C4—862no—
922C22⋊C4—862no—
923C22⋊C4—862no—
924C22⋊C4—862no—
925C22⋊C4—862no—
926C22⋊C4—862no—
927C22⋊C4—862no—
928C22⋊C4—862no—
929C22⋊C4—862no—
930C22⋊C4—862no—
931C22⋊C4—862no—
932C42—431no—
933C42—431no—
934C42—431no—
935C42—431no—
936C42—431no—
937C42—431no—
938C42—862no—
939C42D4×D4311yescharacteristic
940C42D4×D4311yescharacteristic
941C42C23×D4311yescharacteristic
942C42C23×D4311yescharacteristic
943C23—22no—
944C23—431no—
945C23—431no—
946C23—862no—
947C23—862no—
948C23—3442no—
949C23—3442no—
950C23—1724no—
951C23C2×D4×D4311yescharacteristic
952Q8—24no—
953Q8—24no—
954Q8—44no—
955Q8—42no—
956Q8—862no—
957Q8—864no—
958Q8—1724no—
959Q8—1724no—
960Q8—1722no—
961D4—24no—
962D4—42no—
963D4—42no—
964D4—82no—
965D4—862no—
966D4—862no—
967D4—862no—
968D4—864no—
969D4—864no—
970D4—3442no—
971D4—3442no—
972D4—3442no—
973D4—3442no—
974D4—3442no—
975D4—1724no—
976D4—1724no—
977D4—1724no—
978D4—1724no—
979D4—1722no—
980D4—1722no—
981D4—1722no—
982D4—1722no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—44no—
990C2×C4—82no—
991C2×C4—431no—
992C2×C4—434no—
993C2×C4—431no—
994C2×C4—431no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—431no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—3442no—
1006C2×C4—3442no—
1007C2×C4—3442no—
1008C2×C4—1724no—
1009C2×C4—1724no—
1010C2×C4—1724no—
1011C2×C4—1724no—
1012C2×C4—1724no—
1013C2×C4C2×D4×D4311yescharacteristic
1014C2×C4C2×D4×D4311yescharacteristic
1015C2×C4C2×D4×D4311yescharacteristic
1016C2×C4C2×D4×D4311yescharacteristic
1017C2×C4C2×D4×D4311yescharacteristic
1018C2×C4C24×D4311yescharacteristic
1019C8—22no—
1020C8—22no—
1021C8—862no—
1022C8—862no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—432no—
1030C22—861no—
1031C22—861no—
1032C22—861no—
1033C22—861no—
1034C22—861no—
1035C22—1722no—
1036C22—1722no—
1037C22—1722no—
1038C22—1722no—
1039C22—1722no—
1040C22—1722no—
1041C22—6884no—
1042C22C22×D4×D4311yescharacteristic
1043C4—21no—
1044C4—21no—
1045C4—21no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—432no—
1050C4—861no—
1051C4—861no—
1052C4—861no—
1053C4—861no—
1054C4—861no—
1055C4—1722no—
1056C4—1722no—
1057C4#1458370512yes—
1058C4#1458370812yes—
1059C4H(5,𝔽2)×D4312yes—
1060C2—41no—
1061C2—82no—
1062C2—862no—
1063C2—3442no—
1064C2—3442no—
1065C2—1721no—
1066C2#535×D4311yescharacteristic
1067C2C2×#1458370511yescharacteristic
1068C2C2×#1458370811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3206C2
socleC22×C43C23×D4
hypercenter#3206D43
hypocenterC43#60820
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
1. #19148464C2semidirect
2. #19148378C2semidirect
3. #19145655C2semidirect
4. #19145652C2semidirect
5. #19145531C2semidirect
6. #19145530C2semidirect
7. #19145525C2semidirect
8. #19145524C2semidirect
9. #19145521C2semidirect
10. #19145520C2semidirect
11. #19145516C2semidirect
12. #19145042C2semidirect
13. #492×D43C2semidirect
14. #19144972C2semidirect
15. #19144919C2semidirect
16. #19144102C2semidirect
17. #19143876C2semidirect
18. #19143234C2semidirect
19. C43×#3206C2semidirect
42. #14583474C22semidirect
43. #14583473C22semidirect
48. #14583450C22semidirect
50. #14583449C22semidirect
53. C4⋊Q8×D43C22semidirect
65. #14583266C22semidirect
66. #14583255C22semidirect
67. #14583251C22semidirect
68. #14583250C22semidirect
69. #14583249C22semidirect
70. #14583249C22semidirect
71. #14583247C22semidirect
72. #14583246C22semidirect
73. #14583117C22semidirect
74. #14583116C22semidirect
75. #14583115C22semidirect
76. #14583114C22semidirect
77. #14583103C22semidirect
78. #14583102C22semidirect
79. #14583101C22semidirect
80. #14583047C22semidirect
81. #14583046C22semidirect
82. #14583043C22semidirect
83. #14583042C22semidirect
84. #14583039C22semidirect
85. #14583038C22semidirect
86. #14583036C22semidirect
87. #14582959C22semidirect
88. #14582957C22semidirect
89. #14582952C22semidirect
90. #14582950C22semidirect
91. #14582950C22semidirect
99. C2×C4⋊Q8×C43C22semidirect
102. C43×#487C22semidirect
103. C43×#487C22semidirect
104. C43×#461C22semidirect
105. C43×#448C22semidirect
106. C43×#431C22semidirect
537. #3206D43semidirect
589. C2×C4⋊Q8C2×D43semidirect
609. #487C2×D43semidirect
610. #487C2×D43semidirect
620. #461C2×D43semidirect
628. #448C2×D43semidirect
634. #431C2×D43semidirect
641. C43#60820semidirect

Maximal subgroups

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

subgroupindex
#191484642
#191483782
#191456552
#191456522
#191455312
#191455302
#191455252
#191455242
#191455212
#191455202
#191455162
#191450422
#492×D432
#191449722
#191449192
#191441022
#191438762
#191432342
C43×#32062
#6082043