Finite Group Databasebeta

← #25968544

Subgroups — #25968544

Order 11008.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148383C211yesmaximal, characteristic, complemented
2#19148012C211yesmaximal, characteristic, complemented
3#19145708C212yesmaximal, complemented
4#19145693C212yesmaximal, complemented
5#19145654C212yesmaximal, complemented
6#19145641C212yesmaximal, complemented
7#19145636C212yesmaximal, complemented
8#19145579C212yesmaximal, complemented
9#19145563C212yesmaximal, complemented
10#19145526C212yesmaximal, complemented
11#19145080C211yesmaximal, characteristic, complemented
12#19145072C211yesmaximal, characteristic, complemented
13#19144963C211yesmaximal, characteristic, complemented
14#19144947C211yesmaximal, characteristic, complemented
15#19144087C211yesmaximal, characteristic, complemented
16#19144058C211yesmaximal, characteristic, complemented
17#19144046C211yesmaximal, characteristic, complemented
18C2×#14583113C211yesmaximal, characteristic, complemented
19#19143907C211yesmaximal, characteristic, complemented
20#19143883C211yesmaximal, characteristic, complemented
21#19143863C211yesmaximal, characteristic, complemented
22#19143257C211yesmaximal, characteristic, complemented
23C43×#3012C211yesmaximal, characteristic, complemented
24C2×#13063372C2211yescharacteristic
25C2×#13063355C2211yescharacteristic, complemented
26C2×#13063353C2211yescharacteristic, complemented
27C2×#13063350C2211yescharacteristic
28C2×#13063345C2211yescharacteristic, complemented
29C22×#10621873C2211yescharacteristic, complemented
30C22×#10621882C2211yescharacteristic
31#14583556—21no—
32#14583556—21no—
33#14583543—22no—
34#14583543—22no—
35#14583543—21no—
36#14583543—21no—
37#14583530C2211yescharacteristic, complemented
38#14583522—21no—
39#14583522C2212yescomplemented
40#14583502—21no—
41#14583502C2212yescomplemented
42#14583486—22no—
43#14583470C2211yescharacteristic
44#14583470C2212yescomplemented
45#14583466C2211yescharacteristic
46#14583466C2212yescomplemented
47#14583463C2211yescharacteristic
48#14583463C2211yescharacteristic, complemented
49#14583445C2211yescharacteristic
50#14583445C2212yescomplemented
51#14583444—21no—
52#14583444C2212yescomplemented
53#14583435—21no—
54#14583435C2212yescomplemented
55C2×#13063312C2211yescharacteristic
56C2×#13063312C2212yescomplemented
57#14583409—22no—
58#41×Dic43C2211yescharacteristic
59#41×Dic43C2211yescharacteristic, complemented
60C2×#13063287C2211yescharacteristic, complemented
61#14583292C2212yescomplemented
62#14583287C2212yescomplemented
63#14583287C2212yescomplemented
64#14583285C2212yescomplemented
65#14583280C2212yescomplemented
66#14583280C2212yescomplemented
67#14583274C2212yescomplemented
68#14583270C2212yescomplemented
69#14583266C2212yescomplemented
70#14583262C2212yescomplemented
71#14583257C2212yescomplemented
72#14583257C2212yescomplemented
73#14583252C2212yescomplemented
74#14583252C2212yescomplemented
75#14583248C2212yescomplemented
76#14583244C2212yescomplemented
77#14583123C2211yescharacteristic, complemented
78#14583119C2211yescharacteristic, complemented
79#14583119C2212yescomplemented
80#14583119C2212yescomplemented
81#14583117C2212yescomplemented
82#14583116C2211yescharacteristic, complemented
83#14583113C2212yescomplemented
84#14583113C2212yescomplemented
85#14583113C2212yescomplemented
86#14583113C2212yescomplemented
87#14583113C2212yescomplemented
88#14583112C2212yescomplemented
89#14583112C2211yescharacteristic, complemented
90#14583112C2212yescomplemented
91#14583107C2211yescharacteristic, complemented
92#14583103C2212yescomplemented
93#14583102C2211yescharacteristic, complemented
94#14583097C2211yescharacteristic, complemented
95#14583093C2212yescomplemented
96#14583092C2211yescharacteristic, complemented
97#14583059C2212yescomplemented
98#14583054C2212yescomplemented
99#14583046C2212yescomplemented
100#14583046C2212yescomplemented
101#14583044C2212yes—
102#14583044C2212yes—
103#14583042C2212yescomplemented
104#14583040C2212yescomplemented
105#14583040C2212yescomplemented
106#14583037C2212yescomplemented
107#14583033C2212yes—
108#14583033C2212yes—
109#14582957C2212yescomplemented
110#14582957C2212yescomplemented
111#14582953C2212yescomplemented
112#14582949C2212yescomplemented
113#14582922C2211yescharacteristic, complemented
114C2×Dic43⋊C8C2211yescharacteristic, complemented
115#14582909C2211yescharacteristic, complemented
116#14582904C2211yescharacteristic
117#14582898C2211yescharacteristic, complemented
118#14582896C2211yescharacteristic, complemented
119#14582895C2211yescharacteristic
120C2×#13063248C2211yescharacteristic, complemented
121#14582866C2211yescharacteristic
122#14582857C2211yescharacteristic, complemented
123#14582854C2211yescharacteristic, complemented
124C2×H(5,𝔽2)×C43C2211yescharacteristic
125C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
126C2×#135×C43C2211yescharacteristic
127C43×#537C2211yescharacteristic
128C43×#452C2212yescomplemented
129C43×#450C2212yescomplemented
130C43×#449C2212yescomplemented
131C43×#447C2212yescomplemented
132C43×#417C2211yescharacteristic
133C2×#102×C43C2211yescharacteristic
134C43×#408C2211yescharacteristic
135#13063372—42no—
136#13063372—42no—
137C2×#10621898C2311yescharacteristic
138C2×#10621898C2312yes—
139C2×#10621900—22no—
140C2×#10621900—21no—
141C2×#10621900—22no—
142C22×Dic86C2311yescharacteristic
143C22×Dic86C2312yes—
144C2×Q8×D43—21no—
145C22×D172C2311yescharacteristic
146C22×C4×D43—21no—
147#13063355—42no—
148#13063353—42no—
149#13063350—42no—
150#13063345—42no—
151C2×#10621885C2311yescharacteristic
152C2×#10621885C2312yes—
153C2×#10621873—42no—
154C2×#10621873C2312yes—
155C2×#10621873C2312yes—
156C2×#10621873C2312yes—
157C2×#10621883C2312yes—
158C2×#10621883C2311yescharacteristic
159C2×#10621884C2312yes—
160C2×#10621884C2311yescharacteristic
161C2×D344C2312yes—
162C2×#10621882—42no—
163C2×#10621882C2311yescharacteristic
164C2×#10621882C2312yes—
165C2×#10621882C2312yes—
166C2×#10621882C2312yes—
167C2×#10621877C2311yescharacteristic
168C22×C43⋊C8C2311yescharacteristic
169#13063324—21no—
170#13063324C2312yes—
171#13063323C2311yescharacteristic
172#13063323C2312yes—
173#13063321—21no—
174#13063321C2311yescharacteristic
175#13063321C2312yes—
176#13063321C2312yes—
177#13063320—22no—
178#13063320—22no—
179#13063316—21no—
180#13063316C2312yes—
181#13063314—21no—
182#13063314C2311yescharacteristic
183#13063314C2312yes—
184#13063312—21no—
185#13063312—21no—
186#13063312—22no—
187#13063312—22no—
188#13063312C2312yes—
189#13063312C2312yes—
190#13063312C2311yescharacteristic
191#13063312C2312yes—
192#13063312C2312yes—
193#13063311—22no—
194#13063311—22no—
195#13063309—22no—
196#13063309—22no—
197#13063307—22no—
198#13063307—22no—
199#13063306—22no—
200#13063306—22no—
201#13063306—22no—
202#13063305—22no—
203#13063304—22no—
204#13063304—21no—
205#13063304—21no—
206#13063304—22no—
207#13063304—22no—
208#13063299—21no—
209#13063299—21no—
210#13063299C2312yes—
211#13063299C2312yes—
212#13063297—22no—
213#13063297—21no—
214#13063297—21no—
215#13063297—22no—
216#13063297—22no—
217#13063297—22no—
218#13063296—22no—
219#13063296—21no—
220#13063296—21no—
221#13063296—22no—
222#13063296—22no—
223#13063294—22no—
224#13063294—22no—
225#13063294—22no—
226#13063293—22no—
227#13063293—22no—
228Q8×Dic43D411yescharacteristic
229Q8×Dic43D411yescharacteristic
230Q8×Dic43C2311yescharacteristic
231Q8×Dic43C2311yescharacteristic
232D4×Dic43—21no—
233D4×Dic43—21no—
234D4×Dic43D412yes—
235D4×Dic43D411yescharacteristic
236D4×Dic43D412yes—
237D4×Dic43D411yescharacteristic
238D4×Dic43C2311yescharacteristic
239D4×Dic43C2311yescharacteristic
240#13063287—21no—
241#13063287—21no—
242#13063287C2312yes—
243#13063287C2312yes—
244C4×C22⋊D43—21no—
245C4×C22⋊D43—21no—
246C4×C22⋊D43—22no—
247C4×C22⋊D43—22no—
248(C22⋊D43)⋊C4—22no—
249(C22⋊D43)⋊C4—22no—
250#13063284—21no—
251#13063284C2311yescharacteristic
252#13063284C2311yescharacteristic
253#13063284C2312yes—
254#13063283—22no—
255C2×C22⋊Dic43—21no—
256C2×C22⋊Dic43—21no—
257C2×C22⋊Dic43—22no—
258C2×C22⋊Dic43—22no—
259C2×(C2×D43)⋊C4—21no—
260C2×C4×Dic43—21no—
261C2×C4×Dic43C2311yescharacteristic
262C2×C4×Dic43C2312yes—
263Dic43⋊C8C2311yescharacteristic
264Dic43⋊C8C2312yes—
265Dic43⋊C8C2311yescharacteristic
266Dic43⋊C8C2311yescharacteristic
267Dic43⋊C8C2312yes—
268Dic43⋊C8C2311yescharacteristic
269#13063250C2311yescharacteristic
270#13063250C2311yescharacteristic
271#13063250C2312yes—
272#13063250C2312yes—
273#13063249C2311yescharacteristic
274#13063249C2311yescharacteristic
275#13063248C2312yes—
276#13063248C2312yes—
277#13063248C2312yes—
278#13063247C2311yescharacteristic
279#13063247C2311yescharacteristic
280#13063246C2312yes—
281#13063246C2312yes—
282#13063246C2311yescharacteristic
283#13063246C2311yescharacteristic
284#13063245C2312yes—
285C22⋊(C43⋊C8)C2312yes—
286C22⋊(C43⋊C8)C2312yes—
287#13063235C2312yes—
288#13063235C2312yes—
289C8×Dic43C2312yes—
290C8×Dic43C2312yes—
291H(5,𝔽2)×C43—42no—
292H(5,𝔽2)×C43—42no—
293C2×#41×C43—21no—
294C2×#41×C43C2311yescharacteristic
295C2×#41×C43C2311yescharacteristic
296C2×#41×C43C2312yes—
297C2×#41×C43C2311yescharacteristic
298C22×D4×C43—22no—
299C22×D4×C43—21no—
300C22×D4×C43C2311yescharacteristic
301C22×D4×C43C2312yes—
302AGL(1,ℤ/8)×C43—42no—
303#135×C43—42no—
304C2×Q16×C43C2311yescharacteristic
305C2×SD16×C43C2311yescharacteristic
306C2×SD16×C43C2311yescharacteristic
307C2×SD16×C43C2312yes—
308C2×D8×C43C2311yescharacteristic
309C2×D8×C43C2312yes—
310C2×M16×C43C2311yescharacteristic
311C22×C8×C43C2311yescharacteristic
312C22⋊Q8×C43—21no—
313C22⋊Q8×C43C2312yes—
314#121×C43—22no—
315#121×C43—21no—
316#121×C43C2312yes—
317C2×C4⋊C4×C43C2311yescharacteristic
318#103×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2312yes—
321#102×C43C2312yes—
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C24×C43—22no—
325C24×C43—21no—
326C23×D43—21no—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—22no—
333#41×C43—42no—
334#41×C43—42no—
335#41×C43—44no—
336C2×Q8×C43C2×D411yescharacteristic
337C2×Q8×C43C2411yescharacteristic
338C2×Q8×C43C2411yescharacteristic
339C2×D4×C43—22no—
340C2×D4×C43—21no—
341C2×D4×C43—21no—
342C2×D4×C43—22no—
343C2×D4×C43—21no—
344C2×D4×C43—22no—
345C2×D4×C43—22no—
346C2×D4×C43—22no—
347C2×D4×C43—42no—
348C2×D4×C43—42no—
349C2×D4×C43—44no—
350C2×D4×C43—48no—
351C2×D4×C43C2×D412yes—
352C2×D4×C43C2×D411yescharacteristic
353C2×D4×C43C2412yes—
354C2×D4×C43C2411yescharacteristic
355C2×D4×C43C2411yescharacteristic
356C22×C4×C43—21no—
357C22×C4×C43—22no—
358C22×C4×C43—21no—
359C22×C4×C43—21no—
360C22×C4×C43C2412yes—
361C22×C4×C43C2411yescharacteristic
362C2×C22⋊D43—22no—
363C2×C22⋊D43—21no—
364C2×C22⋊D43—22no—
365C2×C22⋊D43—22no—
366C2×C22⋊D43—21no—
367C2×C22⋊D43—22no—
368C2×C22⋊D43—22no—
369C2×C22⋊D43—21no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43—22no—
372C22×Dic43—21no—
373C22×Dic43—21no—
374C22×Dic43—22no—
375C22×Dic43—21no—
376C22×Dic43C2×D411yescharacteristic
377C22×Dic43C2×D412yes—
378C22×Dic43C2×D411yescharacteristic
379C22×Dic43C2×D412yes—
380Q8×D43—44no—
381#10621900—48no—
382#10621900—44no—
383#10621900—84no—
384#10621898—22no—
385#10621898—22no—
386#10621898—42no—
387#10621898—42no—
388C2×D172—21no—
389C2×D172—22no—
390C2×D172—22no—
391C2×D172C2411yescharacteristic
392C2×D172C2412yes—
393C2×C4×D43—22no—
394C2×C4×D43—21no—
395C2×C4×D43—22no—
396C2×C4×D43—22no—
397C2×C4×D43—82no—
398C2×Dic86—22no—
399C2×Dic86—22no—
400C2×Dic86—22no—
401C2×Dic86—21no—
402C2×Dic86—22no—
403C2×Dic86—42no—
404C2×Dic86—42no—
405C2×Dic86C2412yes—
406C2×Dic86C2411yescharacteristic
407Q16×C43—41no—
408SD16×C43—41no—
409SD16×C43—41no—
410SD16×C43—42no—
411D8×C43—41no—
412D8×C43—42no—
413M16×C43—22no—
414C2×C8×C43—22no—
415C2×C8×C43C2411yescharacteristic
416C2×C8×C43C2411yescharacteristic
417C2×C8×C43C2412yes—
418C4⋊C4×C43—21no—
419C4⋊C4×C43—22no—
420C4⋊C4×C43C2412yes—
421C22⋊C4×C43—22no—
422C22⋊C4×C43—22no—
423C22⋊Dic43—22no—
424C22⋊Dic43—21no—
425C22⋊Dic43—22no—
426C22⋊Dic43—21no—
427C22⋊Dic43—22no—
428C22⋊Dic43—22no—
429C22⋊Dic43—22no—
430C22⋊Dic43—22no—
431C22⋊Dic43—22no—
432C22⋊Dic43—22no—
433C22⋊Dic43—21no—
434C22⋊Dic43—21no—
435C22⋊Dic43—21no—
436C22⋊Dic43C2×D412yes—
437C22⋊Dic43C2×D412yes—
438C22⋊Dic43C2×D412yes—
439#10621885—41no—
440#10621885—42no—
441#10621884—41no—
442#10621884—42no—
443#10621883—41no—
444#10621883—42no—
445#10621882—42no—
446#10621882—42no—
447#10621882—41no—
448#10621882—42no—
449(C2×D43)⋊C4—22no—
450(C2×D43)⋊C4—22no—
451(C2×D43)⋊C4—22no—
452(C2×D43)⋊C4—22no—
453(C2×D43)⋊C4—22no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—21no—
456(C2×D43)⋊C4—21no—
457C4⋊Dic43—22no—
458C4⋊Dic43—21no—
459C4⋊Dic43—21no—
460C4⋊Dic43C2×D411yescharacteristic
461C4⋊Dic43C2×D411yescharacteristic
462C4⋊Dic43C2×D412yes—
463C4⋊Dic43C2×D412yes—
464C4⋊Dic43C2411yescharacteristic
465C4⋊Dic43C2411yescharacteristic
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—21no—
469Dic43⋊C4—22no—
470Dic43⋊C4—22no—
471Dic43⋊C4—21no—
472C4×Dic43—21no—
473C4×Dic43—21no—
474C4×Dic43—21no—
475C4×Dic43C2×D411yescharacteristic
476C4×Dic43C2×D412yes—
477C4×Dic43C2×D411yescharacteristic
478C4×Dic43C2×D412yes—
479C4×Dic43C2412yes—
480C4×Dic43C2411yescharacteristic
481C4×Dic43C2411yescharacteristic
482#10621877—22no—
483C2×C43⋊C8—22no—
484C2×C43⋊C8C2411yescharacteristic
485C2×C43⋊C8C2412yes—
486C2×C43⋊C8C2411yescharacteristic
487D344—42no—
488#10621873—42no—
489#10621873—42no—
490#10621873—42no—
491C23×C43—21no—
492C23×C43—22no—
493C23×C43—21no—
494C23×C43—44no—
495C23×C43—42no—
496C23×C43—81no—
497C23×C43—81no—
498C23×C43—82no—
499C23×C43—82no—
500C23×C43C22×D412yes—
501C23×C43C22×D411yescharacteristic
502C22×D43—22no—
503C22×D43—21no—
504C22×D43—42no—
505C22×D43—81no—
506C22×D43—81no—
507Q8×C43—22no—
508Q8×C43—21no—
509Q8×C43—21no—
510Q8×C43—21no—
511Q8×C43—21no—
512D4×C43—24no—
513D4×C43—22no—
514D4×C43—22no—
515D4×C43—21no—
516D4×C43—21no—
517D4×C43—21no—
518D4×C43—22no—
519D4×C43—21no—
520D4×C43—44no—
521D4×C43—44no—
522D4×C43—42no—
523D4×C43—42no—
524D4×C43—42no—
525D4×C43—82no—
526C2×C4×C43—22no—
527C2×C4×C43—22no—
528C2×C4×C43—21no—
529C2×C4×C43—21no—
530C2×C4×C43—22no—
531C2×C4×C43—44no—
532C2×C4×C43—42no—
533C2×C4×C43—42no—
534C2×C4×C43—81no—
535C2×C4×C43C22×D412yes—
536C2×C4×C43C22×D411yescharacteristic
537C2×C4×C43H(5,𝔽2)12yes—
538C2×C4×C43H(5,𝔽2)12yes—
539C2×C4×C43C2511yescharacteristic
540C22⋊D43—44no—
541C22⋊D43—42no—
542C22⋊D43—82no—
543C22⋊D43—81no—
544C22⋊D43—82no—
545C22⋊D43—82no—
546C22⋊D43—82no—
547C22⋊D43—81no—
548C22⋊D43—82no—
549C22⋊D43—82no—
550C2×Dic43—21no—
551C2×Dic43—21no—
552C2×Dic43—22no—
553C2×Dic43—21no—
554C2×Dic43—41no—
555C2×Dic43—42no—
556C2×Dic43—41no—
557C2×Dic43—42no—
558C2×Dic43—42no—
559C2×Dic43—44no—
560C2×Dic43—42no—
561C2×Dic43—81no—
562C2×Dic43C22×D411yescharacteristic
563C2×Dic43C22×D411yescharacteristic
564C2×Dic43C22×D411yescharacteristic
565C2×Dic43C22×D412yes—
566C2×Dic43C22×D412yes—
567C2×Dic43C22×D411yescharacteristic
568D172—22no—
569D172—22no—
570D172—21no—
571D172—21no—
572D172—42no—
573C4×D43—44no—
574C4×D43—44no—
575C4×D43—42no—
576C4×D43—82no—
577Dic86—22no—
578Dic86—21no—
579Dic86—22no—
580Dic86—21no—
581Dic86—44no—
582Dic86—42no—
583Dic86—82no—
584C8×C43—21no—
585C8×C43—21no—
586C8×C43—22no—
587C43⋊C8—21no—
588C43⋊C8—21no—
589C43⋊C8—22no—
590#60834—431nomaximal, Sylow
591C22×C43—21no—
592C22×C43—21no—
593C22×C43—22no—
594C22×C43—22no—
595C22×C43—22no—
596C22×C43—42no—
597C22×C43—41no—
598C22×C43—41no—
599C22×C43—42no—
600C22×C43—41no—
601C22×C43—41no—
602C22×C43—41no—
603C22×C43—42no—
604C22×C43—41no—
605C22×C43—162no—
606C22×C43—164no—
607C22×C43#53512yes—
608C22×C43C23×D411yescharacteristic
609C2×D43—42no—
610C2×D43—41no—
611C2×D43—42no—
612C2×D43—41no—
613C2×D43—42no—
614C2×D43—41no—
615C2×D43—84no—
616C4×C43—22no—
617C4×C43—42no—
618C4×C43—41no—
619C4×C43—41no—
620C4×C43#53512yes—
621C4×C43C2×H(5,𝔽2)11yescharacteristic
622C4×C43C2×H(5,𝔽2)11yescharacteristic
623Dic43—21no—
624Dic43—21no—
625Dic43—22no—
626Dic43—22no—
627Dic43—21no—
628Dic43—21no—
629Dic43—41no—
630Dic43—41no—
631Dic43—42no—
632Dic43—41no—
633#3500—431no—
634#3460—431no—
635#3225—432no—
636#3224—432no—
637#3221—432no—
638#3220—432no—
639#3219—432no—
640#3213—432no—
641#3211—432no—
642#3207—432no—
643#3155—431no—
644#3154—431no—
645#3137—431no—
646#3136—431no—
647#3040—431no—
648#3036—431no—
649#3035—431no—
650C2×#463—431no—
651#3013—431no—
652#3012D4311yescharacteristic, complemented
653#3010—431no—
654#3008—431no—
655#2925—431no—
656C2×C43—22no—
657C2×C43—42no—
658C2×C43—81no—
659C2×C43—82no—
660C2×C43—81no—
661C2×C43C2×#53511yescharacteristic
662C2×C43#358411yescharacteristic
663C2×C43#358511yescharacteristic
664D43—81no—
665D43—82no—
666C2×2−1+4—431no—
667C2×H(5,𝔽2)C2×D4311yescharacteristic
668C2×#137—431no—
669C2×AGL(1,ℤ/8)—431no—
670C2×AGL(1,ℤ/8)—431no—
671C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
672C2×#135—431no—
673C2×#135C2×D4311yescharacteristic
674C22×SD16—431no—
675C22×D8—431no—
676#548—861no—
677#548—861no—
678#546—862no—
679#546—861no—
680#546—862no—
681#546—861no—
682#544—431no—
683#542—432no—
684#542—861no—
685#540—432no—
686#540—861no—
687#538—862no—
688#537C2×D4311yescharacteristic
689#536—431no—
690#536—432no—
691#535—431no—
692#535—431no—
693#535—431no—
694#535—432no—
695#532—432no—
696#532—432no—
697#532—431no—
698#532—861no—
699#529—432no—
700#529—861no—
701C2×#124—431no—
702C2×#124—432no—
703#525—862no—
704C4×#41—431no—
705C4×#41—431no—
706C2×C4×D4—431no—
707#497—432no—
708#496—432no—
709#496—432no—
710#496—432no—
711#495—432no—
712#495—432no—
713#493—432no—
714#492—432no—
715#491—432no—
716#490—432no—
717#489—432no—
718#489—432no—
719#488—432no—
720#488—432no—
721#487—432no—
722#486—432no—
723#464—431no—
724#464—431no—
725#464—432no—
726#464—432no—
727#463—431no—
728#463—432no—
729#463—431no—
730#463—432no—
731#463—432no—
732#463—432no—
733#463—432no—
734#463—432no—
735#463—432no—
736#463—432no—
737#462—431no—
738#461—431no—
739#461—432no—
740#460—431no—
741#459—431no—
742#459—432no—
743#452—432no—
744#452C2×D4312yescomplemented
745#451—432no—
746#450C2×D4312yescomplemented
747#449—432no—
748#449—432no—
749#449—432no—
750#449—432no—
751#449—432no—
752#449C2×D4312yescomplemented
753#448—432no—
754#448—432no—
755#448—432no—
756#447—432no—
757#447—432no—
758#447C2×D4312yescomplemented
759#433—432no—
760#433—432no—
761#432—432no—
762#431—432no—
763#423—431no—
764C2×C4⋊C8—431no—
765#419—431no—
766#418—431no—
767#417—431no—
768#417C2×D4311yescharacteristic
769#416—431no—
770#416—431no—
771C2×#103—431no—
772C2×#102C2×D4311yescharacteristic
773#408—431no—
774#408C2×D4311yescharacteristic
775#405—431no—
776#405—431no—
777C43#6083411yescharacteristic, complemented, Sylow
7782−1+4—1722no—
7792−1+4—1722no—
780H(5,𝔽2)—42no—
781H(5,𝔽2)—42no—
782C2×#41—21no—
783C2×#41—431no—
784C2×#41—432no—
785C2×#41—862no—
786C2×#41—862no—
787C2×#41—861no—
788C2×#41C22×D4311yescharacteristic
789C2×#41C22×D4311yescharacteristic
790C2×#41C22×D4312yes—
791C2×#41C22×D4311yescharacteristic
792C22×Q8—431no—
793C22×Q8—432no—
794C22×Q8—861no—
795C22×D4—22no—
796C22×D4—21no—
797C22×D4—431no—
798C22×D4C22×D4311yescharacteristic
799C22×D4C22×D4312yes—
800C23×C4—861no—
801#137—1722no—
802AGL(1,ℤ/8)—42no—
803AGL(1,ℤ/8)—1722no—
804AGL(1,ℤ/8)—1722no—
805#135—42no—
806#135—1722no—
807C2×Q16—431no—
808C2×Q16—432no—
809C2×Q16C22×D4311yescharacteristic
810C2×SD16—431no—
811C2×SD16—432no—
812C2×SD16—431no—
813C2×SD16—432no—
814C2×SD16—432no—
815C2×SD16—432no—
816C2×SD16—432no—
817C2×SD16—1722no—
818C2×SD16C22×D4311yescharacteristic
819C2×SD16C22×D4311yescharacteristic
820C2×SD16C22×D4312yes—
821C2×D8—432no—
822C2×D8—432no—
823C2×D8—431no—
824C2×D8—432no—
825C2×D8—432no—
826C2×D8—1722no—
827C2×D8C22×D4311yescharacteristic
828C2×D8C22×D4312yes—
829C2×M16—431no—
830C2×M16C22×D4311yescharacteristic
831C22×C8—431no—
832C22×C8C22×D4311yescharacteristic
833C4⋊Q8—432no—
834C4⋊Q8—431no—
835C4⋊Q8—432no—
836C4⋊Q8—861no—
837#127—431no—
838#127—432no—
839#127—432no—
840#127—861no—
841#126—862no—
842#126—862no—
843#125—432no—
844#125—861no—
845#124—432no—
846#124—431no—
847#124—432no—
848#124—431no—
849#124—432no—
850#124—432no—
851#124—432no—
852#124—862no—
853#124—861no—
854#124—861no—
855#124—862no—
856#124—862no—
857#124—862no—
858#124—861no—
859#123—862no—
860#123—862no—
861#123—862no—
862#123—862no—
863#123—862no—
864#123—862no—
865#123—862no—
866C22⋊Q8—21no—
867C22⋊Q8—862no—
868C22⋊Q8—862no—
869C22⋊Q8—861no—
870C22⋊Q8—861no—
871C22⋊Q8—862no—
872C22⋊Q8—862no—
873C22⋊Q8C22×D4312yes—
874#121—22no—
875#121—21no—
876#121—432no—
877#121—432no—
878#121—862no—
879#121—862no—
880#121—861no—
881#121—861no—
882#121—861no—
883#121—861no—
884#121—862no—
885#121—862no—
886#121—862no—
887#121—861no—
888#121—861no—
889#121—862no—
890#121—862no—
891#121C22×D4312yes—
892#120—862no—
893#120—862no—
894#120—862no—
895#120—862no—
896#120—862no—
897C4×Q8—431no—
898C4×Q8—431no—
899C4×Q8—431no—
900C4×Q8—431no—
901C4×D4—432no—
902C4×D4—431no—
903C4×D4—432no—
904C4×D4—431no—
905C4×D4—431no—
906C4×D4—431no—
907C4×D4—432no—
908C4×D4—432no—
909C4×D4—862no—
910C4×D4—861no—
911C4×D4—861no—
912C4×D4—861no—
913C4×D4—862no—
914C4×D4—861no—
915C4×D4—862no—
916C4×D4—862no—
917C4×D4—861no—
918C4×D4—861no—
919#117—431no—
920#117—432no—
921#117—431no—
922#117—862no—
923#117—861no—
924C2×C4⋊C4C22×D4311yescharacteristic
925C2×C22⋊C4—861no—
926C2×C22⋊C4—861no—
927C2×C22⋊C4—861no—
928C2×C22⋊C4—862no—
929C2×C22⋊C4—862no—
930C2×C42—431no—
931C2×C42—432no—
932C2×C42—861no—
933C4⋊C8—431no—
934C4⋊C8—431no—
935C4⋊C8—431no—
936C4⋊C8—431no—
937C4⋊C8—432no—
938C4⋊C8—432no—
939#103—431no—
940#103—431no—
941#103—431no—
942#103—431no—
943#103—432no—
944#103—432no—
945#103—432no—
946#103—432no—
947#103—432no—
948#103C22×D4312yes—
949#102—431no—
950#102—431no—
951#102—432no—
952#102—432no—
953#102—431no—
954#102—431no—
955#102—432no—
956#102C22×D4312yes—
957#102C22×D4312yes—
958#102C22×D4312yes—
959C22⋊C8—432no—
960C22⋊C8—432no—
961C22⋊C8C22×D4312yes—
962C22⋊C8C22×D4312yes—
963#97—432no—
964#97—432no—
965C4×C8—432no—
966C4×C8—432no—
967C24—22no—
968C24—21no—
969C24—861no—
970#41—22no—
971#41—22no—
972#41—22no—
973#41—22no—
974#41—22no—
975#41—22no—
976#41—42no—
977#41—42no—
978#41—44no—
979#41—862no—
980#41—862no—
981#41—3444no—
982#41—1722no—
983#41—1722no—
984#41—1728no—
985#41—1724no—
986C2×Q8—432no—
987C2×Q8—431no—
988C2×Q8—862no—
989C2×Q8—862no—
990C2×Q8—861no—
991C2×Q8—862no—
992C2×Q8—862no—
993C2×Q8—1722no—
994C2×Q8—1722no—
995C2×Q8—1724no—
996C2×Q8D4×D4311yescharacteristic
997C2×Q8C23×D4311yescharacteristic
998C2×Q8C23×D4311yescharacteristic
999C2×D4—21no—
1000C2×D4—22no—
1001C2×D4—21no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—21no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—48no—
1010C2×D4—44no—
1011C2×D4—431no—
1012C2×D4—432no—
1013C2×D4—861no—
1014C2×D4—862no—
1015C2×D4—861no—
1016C2×D4—862no—
1017C2×D4—862no—
1018C2×D4—862no—
1019C2×D4—862no—
1020C2×D4—862no—
1021C2×D4—862no—
1022C2×D4—861no—
1023C2×D4—861no—
1024C2×D4—862no—
1025C2×D4—862no—
1026C2×D4D4×D4312yes—
1027C2×D4D4×D4311yescharacteristic
1028C2×D4C23×D4312yes—
1029C2×D4C23×D4311yescharacteristic
1030C2×D4C23×D4311yescharacteristic
1031C22×C4—21no—
1032C22×C4—21no—
1033C22×C4—22no—
1034C22×C4—21no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—432no—
1038C22×C4—432no—
1039C22×C4—862no—
1040C22×C4—862no—
1041C22×C4—861no—
1042C22×C4—861no—
1043C22×C4—862no—
1044C22×C4—861no—
1045C22×C4—862no—
1046C22×C4—861no—
1047C22×C4—3442no—
1048C22×C4C23×D4312yes—
1049C22×C4C23×D4311yescharacteristic
1050Q16—41no—
1051Q16—1721no—
1052Q16—1722no—
1053SD16—41no—
1054SD16—41no—
1055SD16—42no—
1056SD16—1722no—
1057SD16—1722no—
1058SD16—1722no—
1059SD16—1721no—
1060SD16—1722no—
1061SD16—1721no—
1062SD16—1722no—
1063D8—41no—
1064D8—42no—
1065D8—1722no—
1066D8—1722no—
1067D8—1722no—
1068D8—1721no—
1069D8—1722no—
1070M16—22no—
1071M16—862no—
1072C2×C8—22no—
1073C2×C8—431no—
1074C2×C8—432no—
1075C2×C8—431no—
1076C2×C8—862no—
1077C2×C8C23×D4311yescharacteristic
1078C2×C8C23×D4312yes—
1079C2×C8C23×D4311yescharacteristic
1080C4⋊C4—21no—
1081C4⋊C4—22no—
1082C4⋊C4—431no—
1083C4⋊C4—431no—
1084C4⋊C4—432no—
1085C4⋊C4—432no—
1086C4⋊C4—431no—
1087C4⋊C4—431no—
1088C4⋊C4—861no—
1089C4⋊C4—861no—
1090C4⋊C4—862no—
1091C4⋊C4—861no—
1092C4⋊C4—862no—
1093C4⋊C4—861no—
1094C4⋊C4—862no—
1095C4⋊C4—862no—
1096C4⋊C4—862no—
1097C4⋊C4C23×D4312yes—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—432no—
1101C22⋊C4—432no—
1102C22⋊C4—432no—
1103C22⋊C4—862no—
1104C22⋊C4—862no—
1105C22⋊C4—862no—
1106C22⋊C4—861no—
1107C22⋊C4—861no—
1108C22⋊C4—862no—
1109C22⋊C4—862no—
1110C22⋊C4—861no—
1111C22⋊C4—862no—
1112C22⋊C4—861no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—862no—
1117C22⋊C4—862no—
1118C22⋊C4—862no—
1119C22⋊C4—861no—
1120C22⋊C4—861no—
1121C22⋊C4—861no—
1122C22⋊C4—862no—
1123C22⋊C4—862no—
1124C42—431no—
1125C42—432no—
1126C42—431no—
1127C42—432no—
1128C42—432no—
1129C42—431no—
1130C42—431no—
1131C42—861no—
1132C42—861no—
1133C42—861no—
1134C23—21no—
1135C23—22no—
1136C23—21no—
1137C23—44no—
1138C23—42no—
1139C23—81no—
1140C23—81no—
1141C23—82no—
1142C23—82no—
1143C23—862no—
1144C23—861no—
1145C23—3441no—
1146C23—3441no—
1147C23—1722no—
1148C23C2×D4×D4312yes—
1149C23C2×D4×D4311yescharacteristic
1150Q8—22no—
1151Q8—21no—
1152Q8—21no—
1153Q8—21no—
1154Q8—21no—
1155Q8—862no—
1156Q8—861no—
1157Q8—862no—
1158Q8—861no—
1159Q8—3442no—
1160Q8—1724no—
1161Q8—1722no—
1162D4—24no—
1163D4—22no—
1164D4—21no—
1165D4—21no—
1166D4—22no—
1167D4—21no—
1168D4—22no—
1169D4—21no—
1170D4—44no—
1171D4—44no—
1172D4—42no—
1173D4—42no—
1174D4—42no—
1175D4—82no—
1176D4—862no—
1177D4—862no—
1178D4—861no—
1179D4—861no—
1180D4—3442no—
1181D4—3441no—
1182D4—3442no—
1183D4—3442no—
1184D4—3441no—
1185D4—3442no—
1186D4—3442no—
1187D4—3442no—
1188D4—1724no—
1189D4—1722no—
1190D4—1722no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—44no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—81no—
1200C2×C4—431no—
1201C2×C4—431no—
1202C2×C4—431no—
1203C2×C4—432no—
1204C2×C4—431no—
1205C2×C4—432no—
1206C2×C4—861no—
1207C2×C4—861no—
1208C2×C4—862no—
1209C2×C4—861no—
1210C2×C4—3442no—
1211C2×C4—3441no—
1212C2×C4—1724no—
1213C2×C4—1724no—
1214C2×C4—1721no—
1215C2×C4—1722no—
1216C2×C4—1721no—
1217C2×C4—1722no—
1218C2×C4—1722no—
1219C2×C4—1724no—
1220C2×C4—1722no—
1221C2×C4—1722no—
1222C2×C4C2×D4×D4312yes—
1223C2×C4C2×D4×D4311yescharacteristic
1224C2×C4#1306337012yes—
1225C2×C4#1306337012yes—
1226C2×C4C24×D4311yescharacteristic
1227C8—21no—
1228C8—21no—
1229C8—22no—
1230C8—861no—
1231C8—861no—
1232C8—862no—
1233C22—21no—
1234C22—21no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—41no—
1239C22—42no—
1240C22—41no—
1241C22—41no—
1242C22—42no—
1243C22—41no—
1244C22—42no—
1245C22—41no—
1246C22—41no—
1247C22—162no—
1248C22—164no—
1249C22—3444no—
1250C22—1721no—
1251C22—1722no—
1252C22—1722no—
1253C22—1721no—
1254C22—1721no—
1255C22—1722no—
1256C22#1458346412yes—
1257C22C22×D4×D4311yescharacteristic
1258C4—22no—
1259C4—42no—
1260C4—41no—
1261C4—41no—
1262C4—861no—
1263C4—861no—
1264C4—862no—
1265C4—861no—
1266C4—861no—
1267C4—862no—
1268C4—1721no—
1269C4—1721no—
1270C4—1722no—
1271C4—1721no—
1272C4#1458346412yes—
1273C4C2×#1306337011yescharacteristic
1274C4C2×#1306337011yescharacteristic
1275C2—22no—
1276C2—42no—
1277C2—82no—
1278C2—81no—
1279C2—81no—
1280C2—3442no—
1281C2—3441no—
1282C2C2×#1458346411yescharacteristic
1283C2#1914936711yescharacteristic
1284C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3012C2
socleC22×C43C23×D4
hypercenter#3012D43
hypocenterC43#60834
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3012

Complements

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

NH ≅ G/Ntype
1. #19148383C2semidirect
2. #19148012C2semidirect
3. #19145708C2semidirect
4. #19145693C2semidirect
5. #19145654C2semidirect
6. #19145641C2semidirect
7. #19145636C2semidirect
8. #19145579C2semidirect
9. #19145563C2semidirect
10. #19145526C2semidirect
11. #19145080C2semidirect
12. #19145072C2semidirect
13. #19144963C2semidirect
14. #19144947C2semidirect
15. #19144087C2semidirect
16. #19144058C2semidirect
17. #19144046C2semidirect
18. C2×#14583113C2semidirect
19. #19143907C2semidirect
20. #19143883C2semidirect
21. #19143863C2semidirect
22. #19143257C2semidirect
23. C43×#3012C2semidirect
25. C2×#13063355C22semidirect
26. C2×#13063353C22semidirect
28. C2×#13063345C22semidirect
29. C22×#10621873C22semidirect
37. #14583530C22semidirect
39. #14583522C22semidirect
41. #14583502C22semidirect
44. #14583470C22semidirect
46. #14583466C22semidirect
48. #14583463C22semidirect
50. #14583445C22semidirect
52. #14583444C22semidirect
54. #14583435C22semidirect
56. C2×#13063312C22semidirect
59. #41×Dic43C22semidirect
60. C2×#13063287C22semidirect
61. #14583292C22semidirect
62. #14583287C22semidirect
63. #14583287C22semidirect
64. #14583285C22semidirect
65. #14583280C22semidirect
66. #14583280C22semidirect
67. #14583274C22semidirect
68. #14583270C22semidirect
69. #14583266C22semidirect
70. #14583262C22semidirect
71. #14583257C22semidirect
72. #14583257C22semidirect
73. #14583252C22semidirect
74. #14583252C22semidirect
75. #14583248C22semidirect
76. #14583244C22semidirect
77. #14583123C22semidirect
78. #14583119C22semidirect
79. #14583119C22semidirect
80. #14583119C22semidirect
81. #14583117C22semidirect
82. #14583116C22semidirect
83. #14583113C22semidirect
84. #14583113C22semidirect
85. #14583113C22semidirect
86. #14583113C22semidirect
87. #14583113C22semidirect
88. #14583112C22semidirect
89. #14583112C22semidirect
90. #14583112C22semidirect
91. #14583107C22semidirect
92. #14583103C22semidirect
93. #14583102C22semidirect
94. #14583097C22semidirect
95. #14583093C22semidirect
96. #14583092C22semidirect
97. #14583059C22semidirect
98. #14583054C22semidirect
99. #14583046C22semidirect
100. #14583046C22semidirect
103. #14583042C22semidirect
104. #14583040C22semidirect
105. #14583040C22semidirect
106. #14583037C22semidirect
109. #14582957C22semidirect
110. #14582957C22semidirect
111. #14582953C22semidirect
112. #14582949C22semidirect
113. #14582922C22semidirect
114. C2×Dic43⋊C8C22semidirect
115. #14582909C22semidirect
117. #14582898C22semidirect
118. #14582896C22semidirect
120. C2×#13063248C22semidirect
122. #14582857C22semidirect
123. #14582854C22semidirect
128. C43×#452C22semidirect
129. C43×#450C22semidirect
130. C43×#449C22semidirect
131. C43×#447C22semidirect
652. #3012D43semidirect
744. #452C2×D43semidirect
746. #450C2×D43semidirect
752. #449C2×D43semidirect
758. #447C2×D43semidirect
777. C43#60834semidirect

Maximal subgroups

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

subgroupindex
#191483832
#191480122
#191457082
#191456932
#191456542
#191456412
#191456362
#191455792
#191455632
#191455262
#191450802
#191450722
#191449632
#191449472
#191440872
#191440582
#191440462
C2×#145831132
#191439072
#191438832
#191438632
#191432572
C43×#30122
#6083443