Finite Group Databasebeta

← #25969643

Subgroups — #25969643

Order 11008.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147985C211yesmaximal, characteristic, complemented
2#19146060C214yesmaximal, complemented
3#19146051C214yesmaximal, complemented
4#19146021C214yesmaximal, complemented
5#19146006C214yesmaximal, complemented
6#19144404C212yesmaximal, complemented
7#19144400C211yesmaximal, characteristic, complemented
8#19144392C211yesmaximal, characteristic, complemented
9#19144221C212yesmaximal, complemented
10#19144210C212yesmaximal, complemented
11#19144085C212yesmaximal, complemented
12#19144067C211yesmaximal, characteristic, complemented
13#19144059C211yesmaximal, characteristic, complemented
14#19143159C211yesmaximal, characteristic, complemented
15C2×C43×#542C211yesmaximal, characteristic, complemented
16C2×#13063356C2212yes—
17C2×#13063351C2212yes—
18C22×#10621877C2212yes—
19#14583520C2212yescomplemented
20#14583520C2212yescomplemented
21#14583511C2212yescomplemented
22#14583504C2212yescomplemented
23#14583496—21no—
24#14583496—21no—
25#14583487—21no—
26#14583487—21no—
27#14583456C2211yescharacteristic
28#14583449C2211yescharacteristic
29#14583427—22no—
30#14583427—22no—
31#14583410C2212yes—
32C4×#10621898C2212yes—
33#14583206C2214yescomplemented
34#14583199C2214yescomplemented
35#14583194C2212yescomplemented
36#14583191C2214yescomplemented
37#14583189C2212yescomplemented
38#14583186C2214yescomplemented
39#14583184C2212yescomplemented
40#14583181C2214yescomplemented
41#14583179C2212yescomplemented
42#14583176C2214yescomplemented
43#14583155C2214yescomplemented
44#14583150C2214yes—
45#14583147C2214yescomplemented
46#14583143C2214yes—
47#14583138C2214yescomplemented
48#14583133C2214yes—
49#14583130C2214yescomplemented
50#14583126C2214yes—
51#14583121C2214yescomplemented
52#14583118C2214yescomplemented
53#14583118C2214yescomplemented
54#14583114C2214yescomplemented
55#14583111C2214yescomplemented
56#14583111C2214yescomplemented
57#14583109C2212yescomplemented
58#14583104C2212yescomplemented
59#14583099C2212yescomplemented
60#14583094C2212yescomplemented
61#14582939C2212yes—
62#14582939C2212yes—
63#14582926C2214yescomplemented
64#14582926C2214yescomplemented
65#14582923C2211yescharacteristic
66#14582923C2211yescharacteristic
67#14582923C2212yes—
68#14582908C2212yes—
69#14582904C2212yes—
70#14582898C2212yes—
71#14582898C2212yes—
72C43×#542—22no—
73C43×#542—22no—
74C43×#542C2214yes—
75C43×#542C2214yes—
76C2×C4⋊Q8×C43C2211yescharacteristic
77C2×#126×C43—21no—
78C2×#124×C43—21no—
79C2×#124×C43C2211yescharacteristic
80C2×#123×C43—21no—
81C2×C22⋊Q8×C43—21no—
82C2×C22⋊Q8×C43C2211yescharacteristic
83C2×#121×C43C2211yescharacteristic
84C2×C4×Q8×C43C2211yescharacteristic
85C2×C4×D4×C43C2211yescharacteristic
86C2×#117×C43C2211yescharacteristic
87C2×#10621898C2312yes—
88#13063356—44no—
89#13063351—44no—
90C2×#10621885C2314yes—
91C2×#10621883C2314yes—
92C2×#10621884C2314yes—
93C2×#10621882C2314yes—
94C2×#10621877—44no—
95C2×#10621877C2312yes—
96C2×#10621877C2312yes—
97C2×#10621877C2314yes—
98C22×C43⋊C8C2314yes—
99#13063325C2311yescharacteristic
100#13063325C2311yescharacteristic
101#13063325C2311yescharacteristic
102#13063322C2311yescharacteristic
103#13063320—22no—
104#13063320—22no—
105#13063318—22no—
106#13063318—22no—
107#13063317C2312yes—
108#13063315—22no—
109#13063315—22no—
110#13063313C2312yes—
111#13063311—22no—
112#13063311—22no—
113#13063310—22no—
114#13063310—22no—
115#13063308—22no—
116#13063307—22no—
117#13063307—22no—
118#13063304—21no—
119#13063304—21no—
120#13063304C2312yes—
121#13063304C2312yes—
122#13063303—22no—
123#13063303—22no—
124#13063299—21no—
125#13063299—21no—
126#13063299C2312yes—
127#13063299C2312yes—
128#13063298—22no—
129#13063298—22no—
130#13063294—22no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86C2312yes—
134C4×Dic86C2312yes—
135C4×D172—21no—
136C4×D172—21no—
137C4×D172C2312yes—
138C4×D172C2312yes—
139C4×C22⋊D43—22no—
140C4×C22⋊D43—22no—
141C4×C22⋊D43—22no—
142C4×C22⋊D43—22no—
143#13063284C2312yes—
144#13063282—22no—
145C42×D43—22no—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063256C2314yes—
149#13063256C2314yes—
150C4⋊(C43⋊C8)C2312yes—
151C4⋊(C43⋊C8)C2312yes—
152C4⋊(C43⋊C8)C2314yes—
153C4⋊(C43⋊C8)C2314yes—
154C4⋊(C43⋊C8)C2312yes—
155C4⋊(C43⋊C8)C2312yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063246C2314yes—
161#13063246C2314yes—
162#13063245C2314yes—
163#13063245C2314yes—
164C22×Q8×C43—21no—
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43—21no—
167C22×D4×C43C2311yescharacteristic
168C23×C4×C43—21no—
169C23×C4×C43C2311yescharacteristic
170C4⋊Q8×C43—22no—
171C4⋊Q8×C43C2314yes—
172#126×C43—24no—
173#126×C43—24no—
174#124×C43—24no—
175#124×C43—24no—
176#124×C43—22no—
177#124×C43C2314yes—
178#123×C43—24no—
179#123×C43—24no—
180C22⋊Q8×C43—22no—
181C22⋊Q8×C43—24no—
182C22⋊Q8×C43—24no—
183C22⋊Q8×C43C2314yes—
184#121×C43—22no—
185#121×C43C2314yes—
186C4×Q8×C43—21no—
187C4×Q8×C43—21no—
188C4×Q8×C43C2312yes—
189C4×Q8×C43C2312yes—
190C4×D4×C43—21no—
191C4×D4×C43—21no—
192C4×D4×C43C2312yes—
193C4×D4×C43C2312yes—
194#117×C43D412yes—
195#117×C43D412yes—
196#117×C43C2312yes—
197#117×C43C2312yes—
198C2×C4⋊C4×C43—21no—
199C2×C4⋊C4×C43—21no—
200C2×C4⋊C4×C43—21no—
201C2×C4⋊C4×C43D411yescharacteristic
202C2×C4⋊C4×C43D411yescharacteristic
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C22⋊C4×C43—21no—
206C2×C22⋊C4×C43—21no—
207C2×C22⋊C4×C43—21no—
208C2×C22⋊C4×C43—21no—
209C2×C22⋊C4×C43—21no—
210C2×C22⋊C4×C43D411yescharacteristic
211C2×C22⋊C4×C43D411yescharacteristic
212C2×C42×C43—21no—
213C2×C42×C43C2311yescharacteristic
214C2×C42×C43C2311yescharacteristic
215C24×C43—21no—
216C24×C43C2×D411yescharacteristic
217C2×Q8×C43—21no—
218C2×Q8×C43—24no—
219C2×Q8×C43—22no—
220C2×Q8×C43—22no—
221C2×Q8×C43—82no—
222C2×Q8×C43C2412yes—
223C2×D4×C43—21no—
224C2×D4×C43—24no—
225C2×D4×C43—22no—
226C2×D4×C43—22no—
227C2×D4×C43—82no—
228C2×D4×C43C2412yes—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—22no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—82no—
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2412yes—
244C22×C4×C43C2411yescharacteristic
245C2×C22⋊D43—22no—
246C2×C22⋊D43—22no—
247C2×C22⋊D43—22no—
248#10621898—24no—
249#10621898—24no—
250C2×D172—21no—
251C2×D172—21no—
252C2×D172C2412yes—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×Dic86—21no—
257C2×Dic86—21no—
258C2×Dic86C2412yes—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—22no—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—24no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43C2×D412yes—
266C4⋊C4×C43C2×D412yes—
267C4⋊C4×C43C2×D412yes—
268C4⋊C4×C43C2×D412yes—
269C4⋊C4×C43C2412yes—
270C4⋊C4×C43C2412yes—
271C22⋊C4×C43—22no—
272C22⋊C4×C43—22no—
273C22⋊C4×C43—24no—
274C22⋊C4×C43—24no—
275C22⋊C4×C43—24no—
276C22⋊C4×C43—24no—
277C22⋊C4×C43C2×D412yes—
278C22⋊C4×C43C2×D412yes—
279C22⋊C4×C43C2×D412yes—
280C22⋊C4×C43C2×D412yes—
281C42×C43—22no—
282C42×C43—22no—
283C42×C43C2×D411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D412yes—
286C42×C43C2411yescharacteristic
287C42×C43C2411yescharacteristic
288C42×C43C2412yes—
289C22⋊Dic43—22no—
290C22⋊Dic43—22no—
291C22⋊Dic43—22no—
292#10621885—44no—
293#10621884—44no—
294#10621883—44no—
295#10621882—44no—
296(C2×D43)⋊C4—22no—
297(C2×D43)⋊C4—22no—
298(C2×D43)⋊C4—22no—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—22no—
301(C2×D43)⋊C4—22no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43C2412yes—
307C4⋊Dic43C2412yes—
308Dic43⋊C4—22no—
309Dic43⋊C4—22no—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4—22no—
313Dic43⋊C4—22no—
314C4×Dic43—22no—
315C4×Dic43—22no—
316C4×Dic43—22no—
317#10621877—24no—
318#10621877—24no—
319#10621877—44no—
320C2×C43⋊C8—44no—
321C2×C43⋊C8C2414yes—
322C2×C43⋊C8C2414yes—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—42no—
328C23×C43—42no—
329C23×C43—42no—
330C23×C43C22×D412yes—
331C23×C43C22×D411yescharacteristic
332C22×D43—22no—
333Q8×C43—22no—
334Q8×C43—22no—
335Q8×C43—42no—
336Q8×C43—84no—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—42no—
340D4×C43—84no—
341C2×C4×C43—22no—
342C2×C4×C43—24no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—42no—
353C2×C4×C43—42no—
354C2×C4×C43—42no—
355C2×C4×C43—82no—
356C2×C4×C43—82no—
357C2×C4×C43C22×D412yes—
358C2×C4×C43C22×D412yes—
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D412yes—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43H(5,𝔽2)12yes—
366C2×C4×C432−1+412yes—
367C2×C4×C43C2511yescharacteristic
368C22⋊D43—44no—
369C22⋊D43—82no—
370C22⋊D43—82no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374D172—22no—
375D172—22no—
376D172—81no—
377D172—81no—
378C4×D43—44no—
379C4×D43—82no—
380C4×D43—82no—
381Dic86—22no—
382Dic86—22no—
383Dic86—81no—
384Dic86—81no—
385C43⋊C8—24no—
386C43⋊C8—24no—
387#60919—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—82no—
397C22×C43—84no—
398C22×C43#53712yes—
399C22×C43C23×D411yescharacteristic
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C4×C43—21no—
404C4×C43—22no—
405C4×C43—21no—
406C4×C43—21no—
407C4×C43—22no—
408C4×C43—21no—
409C4×C43—22no—
410C4×C43—42no—
411C4×C43—42no—
412C4×C43—42no—
413C4×C43#53712yes—
414C4×C43C2×H(5,𝔽2)11yescharacteristic
415C4×C43C2×2−1+411yescharacteristic
416Dic43—42no—
417Dic43—42no—
418Dic43—42no—
419#3455—431no—
420C2×#542D4311yescharacteristic, complemented
421#3263—434no—
422#3262—434no—
423#3258—434no—
424#3257—434no—
425#3079—432no—
426#3078—431no—
427#3077—431no—
428#3056—432no—
429#3055—432no—
430#3040—432no—
431#3037—431no—
432#3036—431no—
433#2905—431no—
434C2×C43—22no—
435C2×C43—42no—
436C2×C43—82no—
437C2×C43C2×#53711yescharacteristic
438C2×C43#358511yescharacteristic
439C2×C43#358611yescharacteristic
440D43—82no—
441C2×#137—432no—
442C2×AGL(1,ℤ/8)—432no—
443C22×M16—432no—
444#542—22no—
445#542—22no—
446#542—432no—
447#542—432no—
448#542C2×D4314yes—
449#542C2×D4314yes—
450#541—432no—
451#540—432no—
452#539—861no—
453#539—861no—
454#538—861no—
455#538—861no—
456#533—431no—
457#532—431no—
458C2×C4⋊Q8C2×D4311yescharacteristic
459#529—862no—
460#529—862no—
461C2×#126—21no—
462C2×#124—21no—
463C2×#124C2×D4311yescharacteristic
464#525—432no—
465C2×#123—21no—
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8C2×D4311yescharacteristic
468C2×#121C2×D4311yescharacteristic
469C4×#41—432no—
470C2×C4×Q8C2×D4311yescharacteristic
471C2×C4×D4C2×D4311yescharacteristic
472C2×#117C2×D4311yescharacteristic
473#479—434no—
474#478—434no—
475#477—434no—
476#477—432no—
477#476—434no—
478#476—432no—
479#475—434no—
480#475—432no—
481#474—434no—
482#474—432no—
483#470—434no—
484#469—434no—
485#468—434no—
486#468—434no—
487#467—434no—
488#466—434no—
489#465—434no—
490#465—434no—
491#464—434no—
492#464—434no—
493#464—434no—
494#463—434no—
495#463—434no—
496#463—434no—
497#462—432no—
498#461—432no—
499#460—432no—
500#459—432no—
501#428—432no—
502#428—432no—
503#424—434no—
504#424—434no—
505#423—431no—
506#423—431no—
507#423—432no—
508#419—432no—
509#418—432no—
510#417—432no—
511#417—432no—
512C43#6091911yescharacteristic, complemented, Sylow
513C2×#41—432no—
514C22×Q8—21no—
515C22×Q8C22×D4311yescharacteristic
516C22×D4—21no—
517C22×D4C22×D4311yescharacteristic
518C23×C4—21no—
519C23×C4C22×D4311yescharacteristic
520#137—1724no—
521AGL(1,ℤ/8)—1724no—
522C2×Q16—434no—
523C2×SD16—434no—
524C2×SD16—434no—
525C2×D8—434no—
526C2×M16—432no—
527C2×M16—432no—
528C2×M16—434no—
529C2×M16—1724no—
530C22×C8—434no—
531C4⋊Q8—22no—
532C4⋊Q8—431no—
533C4⋊Q8—431no—
534C4⋊Q8—431no—
535C4⋊Q8C22×D4314yes—
536#127—431no—
537#126—24no—
538#126—24no—
539#126—862no—
540#126—862no—
541#126—862no—
542#126—862no—
543#125—432no—
544#125—862no—
545#125—862no—
546#124—24no—
547#124—24no—
548#124—22no—
549#124—432no—
550#124—862no—
551#124—862no—
552#124C22×D4314yes—
553#123—24no—
554#123—24no—
555#123—862no—
556#123—862no—
557#123—862no—
558#123—862no—
559#123—862no—
560C22⋊Q8—22no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563C22⋊Q8—432no—
564C22⋊Q8—432no—
565C22⋊Q8—861no—
566C22⋊Q8—861no—
567C22⋊Q8—862no—
568C22⋊Q8—862no—
569C22⋊Q8C22×D4314yes—
570#121—22no—
571#121—432no—
572#121—432no—
573#121—861no—
574#121—861no—
575#121—862no—
576#121—862no—
577#121C22×D4314yes—
578#120—862no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—432no—
582C4×Q8—432no—
583C4×Q8—861no—
584C4×Q8—861no—
585C4×Q8C22×D4312yes—
586C4×Q8C22×D4312yes—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—432no—
590C4×D4—432no—
591C4×D4—862no—
592C4×D4—862no—
593C4×D4—862no—
594C4×D4—862no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4C22×D4312yes—
598C4×D4C22×D4312yes—
599#117—432no—
600#117—862no—
601#117C22⋊D4312yes—
602#117C22⋊D4312yes—
603#117C22×D4312yes—
604#117C22×D4312yes—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4C22⋊D4311yescharacteristic
609C2×C4⋊C4C22⋊D4311yescharacteristic
610C2×C4⋊C4C22×D4311yescharacteristic
611C2×C4⋊C4C22×D4311yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4C22⋊D4311yescharacteristic
618C2×C22⋊C4C22⋊D4311yescharacteristic
619C2×C42—21no—
620C2×C42—862no—
621C2×C42C22×D4311yescharacteristic
622C2×C42C22×D4311yescharacteristic
623#107—434no—
624#107—434no—
625#106—434no—
626#106—434no—
627C4⋊C8—432no—
628C4⋊C8—432no—
629C4⋊C8—432no—
630C4⋊C8—434no—
631C4⋊C8—434no—
632C4⋊C8—432no—
633#103—434no—
634#103—434no—
635#103—434no—
636#103—434no—
637#102—434no—
638#102—434no—
639#102—434no—
640#102—434no—
641C24—21no—
642C24C2×C22⋊D4311yescharacteristic
643#41—864no—
644#41—864no—
645C2×Q8—21no—
646C2×Q8—24no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—82no—
650C2×Q8—432no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8C23×D4312yes—
654C2×D4—24no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—82no—
659C2×D4—432no—
660C2×D4—862no—
661C2×D4—862no—
662C2×D4—862no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4C23×D4312yes—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—82no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—862no—
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C2×C22⋊D4312yes—
679C22×C4C2×C22⋊D4311yescharacteristic
680C22×C4C2×C22⋊D4311yescharacteristic
681C22×C4C2×C22⋊D4311yescharacteristic
682C22×C4C2×C22⋊D4311yescharacteristic
683C22×C4C23×D4312yes—
684C22×C4C23×D4311yescharacteristic
685Q16—1724no—
686SD16—1724no—
687SD16—1724no—
688D8—1724no—
689M16—864no—
690M16—864no—
691M16—1724no—
692C2×C8—434no—
693C2×C8—434no—
694C2×C8—1724no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—432no—
702C4⋊C4—432no—
703C4⋊C4—862no—
704C4⋊C4—862no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—862no—
708C4⋊C4—862no—
709C4⋊C4—862no—
710C4⋊C4—862no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4C2×C22⋊D4312yes—
714C4⋊C4C2×C22⋊D4312yes—
715C4⋊C4C2×C22⋊D4312yes—
716C4⋊C4C2×C22⋊D4312yes—
717C4⋊C4C23×D4312yes—
718C4⋊C4C23×D4312yes—
719C22⋊C4—24no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—862no—
726C22⋊C4—862no—
727C22⋊C4—862no—
728C22⋊C4—862no—
729C22⋊C4—862no—
730C22⋊C4—862no—
731C22⋊C4—862no—
732C22⋊C4—862no—
733C22⋊C4—862no—
734C22⋊C4C2×C22⋊D4312yes—
735C22⋊C4C2×C22⋊D4312yes—
736C22⋊C4C2×C22⋊D4312yes—
737C22⋊C4C2×C22⋊D4312yes—
738C42—22no—
739C42—22no—
740C42—862no—
741C42—862no—
742C42—862no—
743C42C2×C22⋊D4312yes—
744C42C2×C22⋊D4311yescharacteristic
745C42C2×C22⋊D4311yescharacteristic
746C42C23×D4312yes—
747C42C23×D4311yescharacteristic
748C42C23×D4311yescharacteristic
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—862no—
757C23C22×C22⋊D4312yes—
758C23C22×C22⋊D4311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—42no—
762Q8—84no—
763Q8—862no—
764Q8—862no—
765Q8—3441no—
766Q8—3441no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—84no—
771D4—862no—
772D4—862no—
773D4—3441no—
774D4—3441no—
775D4—3442no—
776D4—3442no—
777D4—1724no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—3442no—
798C2×C4—3442no—
799C2×C4—1724no—
800C2×C4C22×C22⋊D4311yescharacteristic
801C2×C4C22×C22⋊D4311yescharacteristic
802C2×C4C22×C22⋊D4312yes—
803C2×C4C22×C22⋊D4312yes—
804C2×C4C22×C22⋊D4311yescharacteristic
805C2×C4C22×C22⋊D4311yescharacteristic
806C2×C4C22×C22⋊D4312yes—
807C2×C4C22×C22⋊D4311yescharacteristic
808C2×C4#1306337112yes—
809C2×C4#1306337212yes—
810C2×C4C24×D4311yescharacteristic
811C8—864no—
812C8—864no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—84no—
823C22—1722no—
824C22—1722no—
825C22—1722no—
826C22#1458347712yes—
827C22C23×C22⋊D4311yescharacteristic
828C4—21no—
829C4—21no—
830C4—22no—
831C4—22no—
832C4—21no—
833C4—21no—
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—1722no—
839C4—1722no—
840C4—1722no—
841C4#1458347712yes—
842C4C2×#1306337111yescharacteristic
843C4C2×#1306337211yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—3442no—
848C2C2×#1458347711yescharacteristic
849C2#1914937511yescharacteristic
850C2#1914938211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#542C2
socleC22×C43C23×D4
hypercenterC2×#542D43
hypocenterC43#60919
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #19147985C2semidirect
2. #19146060C2semidirect
3. #19146051C2semidirect
4. #19146021C2semidirect
5. #19146006C2semidirect
6. #19144404C2semidirect
7. #19144400C2semidirect
8. #19144392C2semidirect
9. #19144221C2semidirect
10. #19144210C2semidirect
11. #19144085C2semidirect
12. #19144067C2semidirect
13. #19144059C2semidirect
14. #19143159C2semidirect
15. C2×C43×#542C2semidirect
19. #14583520C22semidirect
20. #14583520C22semidirect
21. #14583511C22semidirect
22. #14583504C22semidirect
33. #14583206C22semidirect
34. #14583199C22semidirect
35. #14583194C22semidirect
36. #14583191C22semidirect
37. #14583189C22semidirect
38. #14583186C22semidirect
39. #14583184C22semidirect
40. #14583181C22semidirect
41. #14583179C22semidirect
42. #14583176C22semidirect
43. #14583155C22semidirect
45. #14583147C22semidirect
47. #14583138C22semidirect
49. #14583130C22semidirect
51. #14583121C22semidirect
52. #14583118C22semidirect
53. #14583118C22semidirect
54. #14583114C22semidirect
55. #14583111C22semidirect
56. #14583111C22semidirect
57. #14583109C22semidirect
58. #14583104C22semidirect
59. #14583099C22semidirect
60. #14583094C22semidirect
63. #14582926C22semidirect
64. #14582926C22semidirect
420. C2×#542D43semidirect
512. C43#60919semidirect

Maximal subgroups

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

subgroupindex
#191479852
#191460602
#191460512
#191460212
#191460062
#191444042
#191444002
#191443922
#191442212
#191442102
#191440852
#191440672
#191440592
#191431592
C2×C43×#5422
#6091943