Finite Group Databasebeta

← #25968029

Subgroups — #25968029

Order 11008.

2262 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic, complemented
2C2×#124×D43C211yesmaximal, characteristic, complemented
3#19145600C211yesmaximal, characteristic, complemented
4#19145599C212yesmaximal, complemented
5#19145598C211yesmaximal, characteristic, complemented
6#19145578C211yesmaximal, characteristic, complemented
7#19145577C212yesmaximal, complemented
8#19145559C212yesmaximal, complemented
9#19145558C214yesmaximal, complemented
10#19145557C212yesmaximal, complemented
11#19145060C212yesmaximal, complemented
12#19144980C212yesmaximal, complemented
13#19144084C214yesmaximal, complemented
14#19143826C212yesmaximal, complemented
15#19143819C212yesmaximal, complemented
16#19143225C211yesmaximal, characteristic, complemented
17C43×#3213C211yesmaximal, characteristic, complemented
18C22×Q8×D43C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C2×#13063354C2214yescomplemented
21C2×#13063349C2214yes—
22#14583456C2211yescharacteristic, complemented
23#14583454C2211yescharacteristic, complemented
24#14583454C2211yescharacteristic, complemented
25#14583447C2211yescharacteristic, complemented
26#14583447C2211yescharacteristic, complemented
27#14583431—21no—
28#14583431C2212yescomplemented
29#14583430—21no—
30#14583430C2212yescomplemented
31#14583428—21no—
32#14583428—21no—
33C2×#13063314C2211yescharacteristic
34C2×#13063313C2211yescharacteristic
35C2×#13063312C2211yescharacteristic
36C2×#13063311—21no—
37C2×#13063311—21no—
38#124×D43—21no—
39#124×D43—21no—
40#124×D43—21no—
41#124×D43—21no—
42#124×D43C2212yes—
43#124×D43C2212yes—
44#124×D43C2212yes—
45#124×D43C2212yes—
46#14583409—21no—
47#14583409C2212yes—
48#14583406—21no—
49#41×Dic43—21no—
50C4×#10621900—21no—
51C4×#10621900C2212yescomplemented
52C2×C22⋊C4×D43—21no—
53C2×C22⋊C4×D43—21no—
54C2×C42×D43C2211yescharacteristic
55#14583294C2212yescomplemented
56#14583293C2212yescomplemented
57#14583286C2212yescomplemented
58#14583282C2214yescomplemented
59#14583280C2214yescomplemented
60#14583261C2212yescomplemented
61#14583259C2212yescomplemented
62#14583258C2212yescomplemented
63#14583255C2214yescomplemented
64#14583252C2214yescomplemented
65#14583124C2214yescomplemented
66#14583122C2214yescomplemented
67#14583120C2214yescomplemented
68#14583118C2214yescomplemented
69#14583116C2214yescomplemented
70#14583114C2214yescomplemented
71#14583112C2214yescomplemented
72#14583057C2212yescomplemented
73#14583056C2214yescomplemented
74#14583055C2212yescomplemented
75#14583052C2212yes—
76#14583051C2214yes—
77#14583050C2212yes—
78#14583037C2212yescomplemented
79#14583036C2214yescomplemented
80#14583032C2212yes—
81#14583031C2214yes—
82#14582956C2211yescharacteristic, complemented
83#14582954C2212yescomplemented
84#14582951C2212yescomplemented
85#14582949C2212yescomplemented
86#14582921C2212yescomplemented
87#14582906C2214yescomplemented
88#14582902C2214yes—
89#14582861C2212yes—
90#14582851C2212yescomplemented
91C43×#532C2211yescharacteristic, complemented
92C2×#124×C43C2211yescharacteristic
93C43×#496C2212yescomplemented
94C43×#489C2212yescomplemented
95C43×#463C2214yescomplemented
96C43×#448C2212yescomplemented
97C43×#447C2212yes—
98C43×#432C2211yescharacteristic, complemented
99C24×D43—21no—
100C2×#10621900—21no—
101C2×#10621900C2312yes—
102C22×Dic86—21no—
103C22×Dic86C2311yescharacteristic
104C2×Q8×D43—21no—
105C2×Q8×D43—21no—
106C2×Q8×D43—44no—
107C2×Q8×D43C2312yes—
108C2×Q8×D43C2312yes—
109C22×D172C2311yescharacteristic
110C22×C22⋊D43—21no—
111C2×D4×D43—21no—
112C2×D4×D43—21no—
113C2×D4×D43—44no—
114C2×D4×D43C2312yes—
115C2×D4×D43C2312yes—
116C22×C4×D43—21no—
117C22×C4×D43D411yescharacteristic
118C22×C4×D43D411yescharacteristic
119C22×C4×D43C2311yescharacteristic
120#13063354—48no—
121#13063349—48no—
122C2×Dic172C2314yescomplemented
123C2×#10621885C2314yescomplemented
124C2×#10621873C2314yes—
125C2×#10621883C2314yes—
126C2×#10621883C2314yescomplemented
127C2×#10621882C2314yes—
128C2×#10621872C2314yes—
129#13063325C2311yescharacteristic, complemented
130#13063325C2311yescharacteristic, complemented
131#13063318—22no—
132#13063318—22no—
133#13063317—21no—
134#13063316—21no—
135#13063316C2312yescomplemented
136#13063314—21no—
137#13063314—21no—
138#13063314C2312yes—
139#13063314C2312yes—
140#13063313—21no—
141#13063313—21no—
142#13063313C2312yes—
143#13063313C2312yes—
144#13063312—21no—
145#13063312—21no—
146#13063312—21no—
147#13063312C2312yes—
148#13063312C2312yes—
149#13063312C2312yescomplemented
150#13063311—22no—
151#13063311—22no—
152#13063311—22no—
153#13063311—22no—
154#13063311—22no—
155#13063311—22no—
156#13063311—22no—
157#13063311—22no—
158#13063307—22no—
159#13063307—22no—
160#13063306—22no—
161#13063305—21no—
162#13063305C2312yes—
163#13063304—21no—
164#13063304C2312yes—
165#13063301—21no—
166#13063301—21no—
167#13063296—21no—
168#13063296—21no—
169#13063296—21no—
170#13063296C2312yes—
171#13063293—22no—
172Q8×Dic43—21no—
173Q8×Dic43—21no—
174C4×Dic86—21no—
175C4×Dic86C2312yescomplemented
176#13063290—21no—
177#13063290C2312yescomplemented
178D4×Dic43—22no—
179D4×Dic43—22no—
180D4×Dic43—21no—
181D4×Dic43—21no—
182D4×Dic43—21no—
183D4×Dic43C2312yescomplemented
184C4×C22⋊D43—22no—
185C4×C22⋊D43—22no—
186(C22⋊D43)⋊C4—22no—
187(C22⋊D43)⋊C4—22no—
188#13063284—21no—
189#13063284—22no—
190#13063283—21no—
191#13063283C2312yes—
192#13063281—22no—
193#13063281—22no—
194C2×C22⋊Dic43—21no—
195C2×C22⋊Dic43—21no—
196C2×(C2×D43)⋊C4—21no—
197C2×(C2×D43)⋊C4—21no—
198C2×(C2×D43)⋊C4—21no—
199C2×(C2×D43)⋊C4—21no—
200C22⋊C4×D43—22no—
201C22⋊C4×D43—22no—
202C22⋊C4×D43—22no—
203C22⋊C4×D43—22no—
204C22⋊C4×D43—22no—
205C22⋊C4×D43—22no—
206C22⋊C4×D43—22no—
207C22⋊C4×D43—22no—
208C2×C4×Dic43—22no—
209C2×C4×Dic43D411yescharacteristic
210C2×C4×Dic43D411yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C42×D43D411yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43D411yescharacteristic
215C42×D43D411yescharacteristic
216C42×D43C2311yescharacteristic
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219C42×D43C2311yescharacteristic
220C4⋊(C43⋊C8)C2312yescomplemented
221Dic43⋊C8C2314yescomplemented
222#13063250C2314yescomplemented
223#13063249C2314yescomplemented
224#13063248C2314yescomplemented
225#13063247C2314yes—
226#13063246C2314yes—
227#13063245C2314yes—
228C22⋊(C43⋊C8)C2312yes—
229(C2×D43)⋊C8C2314yes—
230#13063236C2312yescomplemented
231C8×Dic43C2314yescomplemented
232C2×#41×C43—21no—
233C22×Q8×C43C2311yescharacteristic
234C22×D4×C43C2311yescharacteristic
235C2×SD16×C43C2314yescomplemented
236C2×D8×C43C2314yes—
237C4⋊Q8×C43C2311yescharacteristic, complemented
238#127×C43C2311yescharacteristic, complemented
239#124×C43—21no—
240#124×C43—21no—
241#124×C43—21no—
242#124×C43C2312yes—
243#124×C43C2312yes—
244#121×C43—21no—
245#121×C43C2312yes—
246C4×D4×C43—21no—
247C4×D4×C43C2312yescomplemented
248C2×C22⋊C4×C43—21no—
249C2×C22⋊C4×C43—21no—
250C2×C42×C43C2311yescharacteristic
251C4⋊C8×C43C2312yescomplemented
252#103×C43C2314yescomplemented
253#102×C43C2314yes—
254C22⋊C8×C43C2312yes—
255#97×C43C2312yescomplemented
256C24×C43—21no—
257C23×D43—21no—
258C23×D43—22no—
259C23×D43—22no—
260C23×D43—44no—
261C23×D43—44no—
262C23×D43—44no—
263C23×D43C2×D411yescharacteristic
264#41×C43—44no—
265C2×Q8×C43—21no—
266C2×Q8×C43—21no—
267C2×Q8×C43—42no—
268C2×Q8×C43C2412yes—
269C2×D4×C43—21no—
270C2×D4×C43—21no—
271C2×D4×C43—21no—
272C2×D4×C43—22no—
273C2×D4×C43—42no—
274C2×D4×C43C2412yes—
275C2×D4×C43C2412yes—
276C22×C4×C43—22no—
277C22×C4×C43—21no—
278C22×C4×C43C2×D411yescharacteristic
279C22×C4×C43C2×D411yescharacteristic
280C22×C4×C43C2411yescharacteristic
281C2×C22⋊D43—22no—
282C2×C22⋊D43—22no—
283C2×C22⋊D43—22no—
284C2×C22⋊D43—22no—
285C2×C22⋊D43—44no—
286C22×Dic43—22no—
287C22×Dic43—22no—
288C22×Dic43—21no—
289C22×Dic43C2×D411yescharacteristic
290C22×Dic43C2×D411yescharacteristic
291C22×Dic43C2×D411yescharacteristic
292Q8×D43—28no—
293Q8×D43—44no—
294Q8×D43—44no—
295Q8×D43—44no—
296#10621900—28no—
297#10621900—44no—
298D4×D43—28no—
299D4×D43—44no—
300D4×D43—44no—
301D4×D43—44no—
302C2×D172—21no—
303C2×D172—42no—
304C2×D172C2412yes—
305C2×C4×D43—24no—
306C2×C4×D43—22no—
307C2×C4×D43—22no—
308C2×C4×D43—42no—
309C2×C4×D43—42no—
310C2×C4×D43—44no—
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×D43C2×D411yescharacteristic
321C2×C4×D43C2411yescharacteristic
322C2×C4×D43C2411yescharacteristic
323C2×Dic86—21no—
324C2×Dic86—21no—
325C2×Dic86—22no—
326C2×Dic86—22no—
327C2×Dic86—42no—
328C2×Dic86—44no—
329C2×Dic86C2412yes—
330C2×Dic86C2412yes—
331SD16×C43—44no—
332D8×C43—44no—
333C2×C8×C43C2414yes—
334C4⋊C4×C43—21no—
335C4⋊C4×C43C2412yes—
336C22⋊C4×C43—22no—
337C22⋊C4×C43—22no—
338C22⋊C4×C43—22no—
339C22⋊C4×C43—22no—
340C22⋊C4×C43—22no—
341C22⋊C4×C43—22no—
342C42×C43C2×D411yescharacteristic
343C42×C43C2×D411yescharacteristic
344C42×C43C2411yescharacteristic
345C42×C43C2411yescharacteristic
346C22⋊Dic43—22no—
347C22⋊Dic43—22no—
348C22⋊Dic43—22no—
349C22⋊Dic43—22no—
350C22⋊Dic43—22no—
351C22⋊Dic43—22no—
352C22⋊Dic43—22no—
353C22⋊Dic43—22no—
354C22⋊Dic43—22no—
355#10621885—44no—
356#10621883—44no—
357#10621883—44no—
358#10621882—44no—
359(C2×D43)⋊C4—22no—
360(C2×D43)⋊C4—22no—
361(C2×D43)⋊C4—22no—
362(C2×D43)⋊C4—22no—
363(C2×D43)⋊C4—22no—
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—
369C4⋊Dic43—21no—
370C4⋊Dic43—21no—
371C4⋊Dic43—21no—
372C4⋊Dic43—22no—
373C4⋊Dic43—22no—
374C4⋊Dic43C2412yes—
375Dic43⋊C4—22no—
376Dic43⋊C4—22no—
377Dic43⋊C4—22no—
378Dic43⋊C4—22no—
379C4×Dic43—22no—
380C4×Dic43—22no—
381C4×Dic43—22no—
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2×D411yescharacteristic
386C4×Dic43C2×D411yescharacteristic
387C4×Dic43C2×D411yescharacteristic
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2×D411yescharacteristic
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2×D411yescharacteristic
392C4×Dic43C2411yescharacteristic
393C4×Dic43C2411yescharacteristic
394C2×C43⋊C8C2414yes—
395Dic172—44no—
396#10621873—44no—
397#10621872—28no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—42no—
401C23×C43—42no—
402C23×C43—42no—
403C23×C43C22×D411yescharacteristic
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—22no—
407C22×D43—22no—
408C22×D43—44no—
409C22×D43—44no—
410C22×D43—44no—
411C22×D43—44no—
412C22×D43—42no—
413C22×D43—42no—
414C22×D43—42no—
415C22×D43—44no—
416C22×D43—44no—
417C22×D43—816no—
418C22×D43C22×D411yescharacteristic
419C22×D43C22×D411yescharacteristic
420Q8×C43—24no—
421Q8×C43—42no—
422Q8×C43—42no—
423D4×C43—24no—
424D4×C43—24no—
425D4×C43—42no—
426D4×C43—42no—
427D4×C43—42no—
428D4×C43—44no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—41no—
434C2×C4×C43—44no—
435C2×C4×C43—42no—
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C22×D411yescharacteristic
440C2×C4×C43C22×D411yescharacteristic
441C2×C4×C43C2511yescharacteristic
442C22⋊D43—44no—
443C22⋊D43—44no—
444C22⋊D43—44no—
445C22⋊D43—44no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—41no—
452C2×Dic43—44no—
453C2×Dic43—42no—
454C2×Dic43—44no—
455C2×Dic43C22×D411yescharacteristic
456C2×Dic43C22×D411yescharacteristic
457C2×Dic43C22×D411yescharacteristic
458C2×Dic43C22×D411yescharacteristic
459C2×Dic43C22×D411yescharacteristic
460C2×Dic43C22×D411yescharacteristic
461D172—24no—
462D172—42no—
463C4×D43—22no—
464C4×D43—22no—
465C4×D43—22no—
466C4×D43—22no—
467C4×D43—22no—
468C4×D43—41no—
469C4×D43—41no—
470C4×D43—41no—
471C4×D43—41no—
472C4×D43—41no—
473C4×D43—41no—
474C4×D43—44no—
475C4×D43—44no—
476C4×D43H(5,𝔽2)14yes—
477Dic86—24no—
478Dic86—24no—
479Dic86—44no—
480Dic86—42no—
481Dic86—42no—
482Dic86—44no—
483C8×C43—24no—
484C43⋊C8—24no—
485#60799—431nomaximal, Sylow
486C22×C43—21no—
487C22×C43—21no—
488C22×C43—42no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43—42no—
492C22×C43—42no—
493C22×C43—42no—
494C22×C43—84no—
495C22×C43#57512yes—
496C22×C43C23×D411yescharacteristic
497C2×D43—28no—
498C2×D43—21no—
499C2×D43—21no—
500C2×D43—21no—
501C2×D43—21no—
502C2×D43—42no—
503C2×D43—42no—
504C2×D43—42no—
505C2×D43—88no—
506C2×D43—88no—
507C2×D43—84no—
508C2×D43#53512yes—
509C2×D43#57512yes—
510C4×C43—21no—
511C4×C43—21no—
512C4×C43—21no—
513C4×C43—21no—
514C4×C43—21no—
515C4×C43—42no—
516C4×C43—42no—
517C4×C43C2×H(5,𝔽2)12yes—
518Dic43—21no—
519Dic43—21no—
520Dic43—21no—
521Dic43—21no—
522Dic43—21no—
523Dic43—42no—
524Dic43—42no—
525Dic43—42no—
526Dic43#53512yes—
527#3444—431no—
528C22×#124—431no—
529#3215—432no—
530#3215—431no—
531#3215—431no—
532#3213—432no—
533#3213—431no—
534#3213D4311yescharacteristic, complemented
535#3211—434no—
536#3211—432no—
537#3211—432no—
538#3153—432no—
539#3140—432no—
540#3040—434no—
541#3004—432no—
542#3003—432no—
543#2920—431no—
544C2×C43—22no—
545C2×C43—82no—
546C2×C43—82no—
547C2×C43C2×#53511yescharacteristic
548C2×C43C2×#57511yescharacteristic
549C2×C43C2×#57511yescharacteristic
550D43—22no—
551D43—22no—
552D43—82no—
553C23×Q8—431no—
554C23×D4—431no—
555C2×#137—434no—
556C2×AGL(1,ℤ/8)—434no—
557#533—431no—
558#533—431no—
559#533—431no—
560#532—431no—
561#532—431no—
562#532C2×D4311yescharacteristic, complemented
563#529—432no—
564#529—432no—
565#529—861no—
566#529—861no—
567#529—861no—
568#529—861no—
569C2×#124—431no—
570C2×#124—431no—
571C2×#124—432no—
572C2×#124—432no—
573C2×#124—432no—
574C2×#124—432no—
575C2×#124—431no—
576C2×#124—861no—
577C2×#124—861no—
578C2×#124—861no—
579C2×#124—861no—
580C2×#124—861no—
581C2×#124—861no—
582C2×#124C2×D4311yescharacteristic
583#525—432no—
584#525—861no—
585#525—861no—
586C4×#41—432no—
587C4×#41—861no—
588C4×#41—861no—
589C22×C22⋊C4—861no—
590C22×C22⋊C4—861no—
591C22×C42—431no—
592#497—432no—
593#497—432no—
594#496—432no—
595#496C2×D4312yescomplemented
596#495—434no—
597#495—434no—
598#489—432no—
599#489—432no—
600#489—432no—
601#489C2×D4312yescomplemented
602#488—434no—
603#488—434no—
604#464—434no—
605#464—434no—
606#464—434no—
607#464—434no—
608#463—434no—
609#463—434no—
610#463—434no—
611#463C2×D4314yescomplemented
612#451—432no—
613#451—434no—
614#451—432no—
615#450—432no—
616#450—434no—
617#450—432no—
618#448—434no—
619#448—432no—
620#448C2×D4312yescomplemented
621#447—434no—
622#447—432no—
623#447C2×D4312yes—
624#432—431no—
625#432—432no—
626#432C2×D4311yescharacteristic, complemented
627#431—432no—
628#431—432no—
629#423—432no—
630#419—434no—
631#418—434no—
632#407—432no—
633C4×M16—432no—
634C43#6079911yescharacteristic, complemented, Sylow
635C25—861no—
636C2×#41—21no—
637C2×#41—432no—
638C2×#41—861no—
639C22×Q8—432no—
640C22×Q8—432no—
641C22×Q8—431no—
642C22×Q8—861no—
643C22×Q8—861no—
644C22×Q8—861no—
645C22×Q8—1724no—
646C22×Q8C22×D4311yescharacteristic
647C22×D4—432no—
648C22×D4—432no—
649C22×D4—431no—
650C22×D4—861no—
651C22×D4—861no—
652C22×D4—861no—
653C22×D4—1724no—
654C22×D4C22×D4311yescharacteristic
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—861no—
659#137—1728no—
660AGL(1,ℤ/8)—1728no—
661C2×Q16—434no—
662C2×Q16—434no—
663C2×SD16—434no—
664C2×SD16—434no—
665C2×SD16—434no—
666C2×SD16C22×D4314yescomplemented
667C2×D8—434no—
668C2×D8C22×D4314yes—
669C2×M16—434no—
670C4⋊Q8—431no—
671C4⋊Q8—431no—
672C4⋊Q8C22×D4311yescharacteristic, complemented
673#127C22×D4311yescharacteristic, complemented
674#126—862no—
675#126—862no—
676#125—432no—
677#125—861no—
678#125—861no—
679#124—21no—
680#124—21no—
681#124—21no—
682#124—432no—
683#124—432no—
684#124—432no—
685#124—432no—
686#124—432no—
687#124—432no—
688#124—432no—
689#124—862no—
690#124—862no—
691#124—862no—
692#124—862no—
693#124—862no—
694#124—862no—
695#124—862no—
696#124—862no—
697#124—861no—
698#124—861no—
699#124—861no—
700#124—861no—
701#124—861no—
702#124—861no—
703#124—861no—
704#124C22×D4312yes—
705#124C22×D4312yes—
706#123—862no—
707#123—862no—
708#123—862no—
709C22⋊Q8—432no—
710C22⋊Q8—432no—
711C22⋊Q8—861no—
712C22⋊Q8—861no—
713C22⋊Q8—861no—
714C22⋊Q8—861no—
715#121—21no—
716#121—432no—
717#121—861no—
718#121—861no—
719#121—861no—
720#121C22×D4312yes—
721#120—862no—
722C4×Q8—432no—
723C4×Q8—432no—
724C4×Q8—861no—
725C4×Q8—861no—
726C4×Q8—861no—
727C4×Q8—861no—
728C4×D4—21no—
729C4×D4—432no—
730C4×D4—861no—
731C4×D4—861no—
732C4×D4—861no—
733C4×D4—862no—
734C4×D4—862no—
735C4×D4—862no—
736C4×D4—862no—
737C4×D4—862no—
738C4×D4—862no—
739C4×D4C22×D4312yescomplemented
740#117—432no—
741#117—862no—
742#117—862no—
743#117—862no—
744#117—861no—
745#117—861no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—862no—
749C2×C22⋊C4—862no—
750C2×C22⋊C4—862no—
751C2×C22⋊C4—862no—
752C2×C22⋊C4—862no—
753C2×C22⋊C4—862no—
754C2×C22⋊C4—862no—
755C2×C22⋊C4—862no—
756C2×C22⋊C4—861no—
757C2×C22⋊C4—861no—
758C2×C22⋊C4—861no—
759C2×C22⋊C4—861no—
760C2×C22⋊C4—861no—
761C2×C22⋊C4—861no—
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—431no—
773C2×C42—862no—
774C2×C42C22×D4311yescharacteristic
775C4⋊C8—434no—
776C4⋊C8—432no—
777C4⋊C8C22×D4312yescomplemented
778#103—434no—
779#103—434no—
780#103—434no—
781#103C22×D4314yescomplemented
782#102—434no—
783#102—434no—
784#102—434no—
785#102C22×D4314yes—
786C22⋊C8—432no—
787C22⋊C8—434no—
788C22⋊C8C22×D4312yes—
789#97—432no—
790#97C22×D4312yescomplemented
791C4×C8—434no—
792C24—21no—
793C24—431no—
794C24—862no—
795C24—862no—
796C24—861no—
797C24—1724no—
798C24—1724no—
799C24—1724no—
800#41—44no—
801#41—868no—
802#41—1724no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—42no—
806C2×Q8—432no—
807C2×Q8—432no—
808C2×Q8—862no—
809C2×Q8—862no—
810C2×Q8—868no—
811C2×Q8—861no—
812C2×Q8—861no—
813C2×Q8—1722no—
814C2×Q8—1724no—
815C2×Q8—1724no—
816C2×Q8—1724no—
817C2×Q8—1724no—
818C2×Q8C23×D4312yes—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—42no—
824C2×D4—432no—
825C2×D4—868no—
826C2×D4—862no—
827C2×D4—862no—
828C2×D4—862no—
829C2×D4—862no—
830C2×D4—861no—
831C2×D4—1722no—
832C2×D4—1724no—
833C2×D4—1724no—
834C2×D4—1724no—
835C2×D4—1724no—
836C2×D4C23×D4312yes—
837C2×D4C23×D4312yes—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—431no—
841C22×C4—431no—
842C22×C4—431no—
843C22×C4—431no—
844C22×C4—431no—
845C22×C4—431no—
846C22×C4—431no—
847C22×C4—431no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—864no—
856C22×C4—862no—
857C22×C4—862no—
858C22×C4—862no—
859C22×C4—862no—
860C22×C4—861no—
861C22×C4—1722no—
862C22×C4—1722no—
863C22×C4—1724no—
864C22×C4D4×D4311yescharacteristic
865C22×C4D4×D4311yescharacteristic
866C22×C4C23×D4311yescharacteristic
867Q16—1724no—
868Q16—1724no—
869SD16—44no—
870SD16—1724no—
871SD16—1724no—
872SD16—1724no—
873D8—44no—
874D8—1724no—
875M16—868no—
876C2×C8—434no—
877C2×C8C23×D4314yes—
878C4⋊C4—21no—
879C4⋊C4—432no—
880C4⋊C4—862no—
881C4⋊C4—862no—
882C4⋊C4—862no—
883C4⋊C4—862no—
884C4⋊C4—862no—
885C4⋊C4—861no—
886C4⋊C4—861no—
887C4⋊C4—861no—
888C4⋊C4—862no—
889C4⋊C4C23×D4312yes—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
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—
905C22⋊C4—862no—
906C22⋊C4—862no—
907C22⋊C4—862no—
908C22⋊C4—862no—
909C22⋊C4—862no—
910C22⋊C4—862no—
911C22⋊C4—862no—
912C22⋊C4—862no—
913C22⋊C4—862no—
914C22⋊C4—862no—
915C42—431no—
916C42—431no—
917C42—431no—
918C42—431no—
919C42—431no—
920C42—431no—
921C42—431no—
922C42—431no—
923C42—431no—
924C42—431no—
925C42—431no—
926C42—431no—
927C42—862no—
928C42—862no—
929C42—862no—
930C42D4×D4311yescharacteristic
931C42D4×D4311yescharacteristic
932C42C23×D4311yescharacteristic
933C42C23×D4311yescharacteristic
934C23—22no—
935C23—22no—
936C23—42no—
937C23—42no—
938C23—42no—
939C23—431no—
940C23—431no—
941C23—862no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—34416no—
946C23—1722no—
947C23—1722no—
948C23—1724no—
949C23—1724no—
950C23—1724no—
951C23—1724no—
952C23—1724no—
953C23—1724no—
954C23—1722no—
955C23C2×D4×D4311yescharacteristic
956Q8—24no—
957Q8—42no—
958Q8—42no—
959Q8—864no—
960Q8—864no—
961Q8—1722no—
962Q8—1722no—
963Q8—1724no—
964Q8—1724no—
965D4—24no—
966D4—24no—
967D4—42no—
968D4—42no—
969D4—42no—
970D4—44no—
971D4—864no—
972D4—1722no—
973D4—1724no—
974D4—1724no—
975D4—1724no—
976D4—1724no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—41no—
982C2×C4—44no—
983C2×C4—42no—
984C2×C4—431no—
985C2×C4—434no—
986C2×C4—431no—
987C2×C4—431no—
988C2×C4—431no—
989C2×C4—431no—
990C2×C4—431no—
991C2×C4—862no—
992C2×C4—862no—
993C2×C4—862no—
994C2×C4—862no—
995C2×C4—862no—
996C2×C4—862no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—1721no—
1002C2×C4—1721no—
1003C2×C4—1721no—
1004C2×C4—1721no—
1005C2×C4—1721no—
1006C2×C4—1721no—
1007C2×C4—1724no—
1008C2×C4—1724no—
1009C2×C4—1724no—
1010C2×C4—1721no—
1011C2×C4—1724no—
1012C2×C4—1722no—
1013C2×C4C2×D4×D4311yescharacteristic
1014C2×C4C2×D4×D4311yescharacteristic
1015C2×C4C2×D4×D4311yescharacteristic
1016C2×C4C2×D4×D4311yescharacteristic
1017C2×C4C2×D4×D4311yescharacteristic
1018C2×C4C24×D4311yescharacteristic
1019C8—24no—
1020C8—864no—
1021C22—21no—
1022C22—21no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—84no—
1030C22—432no—
1031C22—432no—
1032C22—868no—
1033C22—861no—
1034C22—861no—
1035C22—861no—
1036C22—861no—
1037C22—3444no—
1038C22—3448no—
1039C22—3448no—
1040C22—1722no—
1041C22—1722no—
1042C22—1722no—
1043C22#1458369512yes—
1044C22C22×D4×D4311yescharacteristic
1045C4—21no—
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—42no—
1051C4—42no—
1052C4—432no—
1053C4—861no—
1054C4—861no—
1055C4—861no—
1056C4—861no—
1057C4—861no—
1058C4—1722no—
1059C4—1722no—
1060C4—1722no—
1061C4H(5,𝔽2)×D4312yes—
1062C2—22no—
1063C2—82no—
1064C2—82no—
1065C2—862no—
1066C2—862no—
1067C2—3442no—
1068C2#535×D4311yescharacteristic
1069C2#575×D4311yescharacteristic
1070C2C2×#1458369511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3213C2
socleC22×C43C23×D4
hypercenter#3213D43
hypocenterC43#60799
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. #19147890C2semidirect
2. C2×#124×D43C2semidirect
3. #19145600C2semidirect
4. #19145599C2semidirect
5. #19145598C2semidirect
6. #19145578C2semidirect
7. #19145577C2semidirect
8. #19145559C2semidirect
9. #19145558C2semidirect
10. #19145557C2semidirect
11. #19145060C2semidirect
12. #19144980C2semidirect
13. #19144084C2semidirect
14. #19143826C2semidirect
15. #19143819C2semidirect
16. #19143225C2semidirect
17. C43×#3213C2semidirect
20. C2×#13063354C22semidirect
22. #14583456C22semidirect
23. #14583454C22semidirect
24. #14583454C22semidirect
25. #14583447C22semidirect
26. #14583447C22semidirect
28. #14583431C22semidirect
30. #14583430C22semidirect
51. C4×#10621900C22semidirect
55. #14583294C22semidirect
56. #14583293C22semidirect
57. #14583286C22semidirect
58. #14583282C22semidirect
59. #14583280C22semidirect
60. #14583261C22semidirect
61. #14583259C22semidirect
62. #14583258C22semidirect
63. #14583255C22semidirect
64. #14583252C22semidirect
65. #14583124C22semidirect
66. #14583122C22semidirect
67. #14583120C22semidirect
68. #14583118C22semidirect
69. #14583116C22semidirect
70. #14583114C22semidirect
71. #14583112C22semidirect
72. #14583057C22semidirect
73. #14583056C22semidirect
74. #14583055C22semidirect
78. #14583037C22semidirect
79. #14583036C22semidirect
82. #14582956C22semidirect
83. #14582954C22semidirect
84. #14582951C22semidirect
85. #14582949C22semidirect
86. #14582921C22semidirect
87. #14582906C22semidirect
90. #14582851C22semidirect
91. C43×#532C22semidirect
93. C43×#496C22semidirect
94. C43×#489C22semidirect
95. C43×#463C22semidirect
96. C43×#448C22semidirect
98. C43×#432C22semidirect
122. C2×Dic172C23semidirect
123. C2×#10621885C23semidirect
126. C2×#10621883C23semidirect
129. #13063325C23semidirect
130. #13063325C23semidirect
135. #13063316C23semidirect
149. #13063312C23semidirect
175. C4×Dic86C23semidirect
177. #13063290C23semidirect
183. D4×Dic43C23semidirect
220. C4⋊(C43⋊C8)C23semidirect
221. Dic43⋊C8C23semidirect
222. #13063250C23semidirect
223. #13063249C23semidirect
224. #13063248C23semidirect
230. #13063236C23semidirect
231. C8×Dic43C23semidirect
235. C2×SD16×C43C23semidirect
237. C4⋊Q8×C43C23semidirect
238. #127×C43C23semidirect
247. C4×D4×C43C23semidirect
251. C4⋊C8×C43C23semidirect
252. #103×C43C23semidirect
255. #97×C43C23semidirect
534. #3213D43semidirect
562. #532C2×D43semidirect
595. #496C2×D43semidirect
601. #489C2×D43semidirect
611. #463C2×D43semidirect
620. #448C2×D43semidirect
626. #432C2×D43semidirect
634. C43#60799semidirect
666. C2×SD16C22×D43semidirect
672. C4⋊Q8C22×D43semidirect
673. #127C22×D43semidirect
739. C4×D4C22×D43semidirect
777. C4⋊C8C22×D43semidirect
781. #103C22×D43semidirect
790. #97C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191478902
C2×#124×D432
#191456002
#191455992
#191455982
#191455782
#191455772
#191455592
#191455582
#191455572
#191450602
#191449802
#191440842
#191438262
#191438192
#191432252
C43×#32132
#6079943