Finite Group Databasebeta

← #25974486

Subgroups — #25974486

Order 11008.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148308C211yesmaximal, characteristic, complemented
2#19148262C211yesmaximal, characteristic, complemented
3#19146855C212yesmaximal, complemented
4#19146829C212yesmaximal, complemented
5#19146758C212yesmaximal, complemented
6#19146743C212yesmaximal, complemented
7#19146728C212yesmaximal, complemented
8#19146668C212yesmaximal, complemented
9#19146548C212yesmaximal, complemented
10#19146437C212yesmaximal, complemented
11#19144949C211yesmaximal, characteristic, complemented
12#19144583C211yesmaximal, characteristic, complemented
13C2×#14583221C211yesmaximal, characteristic, complemented
14#19144448C211yesmaximal, characteristic, complemented
15#19144261C211yesmaximal, characteristic, complemented
16#19144208C211yesmaximal, characteristic, complemented
17#19143898C211yesmaximal, characteristic, complemented
18#19143809C211yesmaximal, characteristic, complemented
19#19143476C211yesmaximal, characteristic, complemented
20#19143319C211yesmaximal, characteristic, complemented
21#19143116C211yesmaximal, characteristic, complemented
22#19143111C211yesmaximal, characteristic, complemented
23C43×#3045C211yesmaximal, characteristic, complemented
24C2×#13063370C2211yescharacteristic
25C2×#41×D43C2211yescharacteristic
26C2×#13063345C2211yescharacteristic
27C2×#13063331C2211yescharacteristic, complemented
28C2×M16×D43C2211yescharacteristic, complemented
29#14583622C2212yescomplemented
30#14583617—21no—
31#14583614C2212yescomplemented
32#14583612—21no—
33#14583599C2212yescomplemented
34#14583597—21no—
35#14583590C2212yescomplemented
36#14583584—21no—
37#14583569C2212yes—
38#14583557C2212yes—
39#14583542C2212yes—
40#14583536—22no—
41#14583534C2212yes—
42#14583531—22no—
43#14583527C2211yescharacteristic, complemented
44#14583482—22no—
45#14583478—21no—
46#14583477C2211yescharacteristic
47#14583477C2211yescharacteristic, complemented
48#14583465—21no—
49#14583429—22no—
50#14583411C2211yescharacteristic
51#14583409—21no—
52#14583406C2211yescharacteristic, complemented
53C2×#13063296C2211yescharacteristic
54#121×D43—21no—
55#14583380C2211yescharacteristic, complemented
56#14583379C2211yescharacteristic
57C2×#13063283C2211yescharacteristic, complemented
58#14583263C2212yescomplemented
59#14583258C2212yescomplemented
60#14583253C2212yescomplemented
61#14583245C2212yescomplemented
62#14583239C2212yescomplemented
63#14583228C2212yescomplemented
64#14583221C2212yescomplemented
65#14583221C2212yescomplemented
66#14583221C2212yescomplemented
67#14583221C2212yescomplemented
68#14583221C2212yescomplemented
69#14583216C2212yescomplemented
70#14583207C2212yescomplemented
71#14583200C2212yescomplemented
72#14583195C2212yescomplemented
73#14583180C2212yescomplemented
74#14583149C2212yescomplemented
75#14583142C2212yescomplemented
76#14583142C2212yescomplemented
77#14583142C2212yescomplemented
78#14583137C2212yescomplemented
79#14583132C2212yescomplemented
80#14583132C2212yescomplemented
81#14583125C2212yescomplemented
82#14583060C2211yescharacteristic, complemented
83#14583058C2211yescharacteristic, complemented
84#14583058C2212yescomplemented
85#14583053C2211yescharacteristic, complemented
86#14583048C2211yescharacteristic, complemented
87#14583048C2212yescomplemented
88#14583043C2211yescharacteristic, complemented
89#14583041C2211yescharacteristic, complemented
90#14583041C2212yescomplemented
91#14583036C2211yescharacteristic, complemented
92#14583031C2212yescomplemented
93#14583031C2211yescharacteristic, complemented
94#14583009C2212yescomplemented
95#14583004C2212yescomplemented
96C4×#10621884C2212yescomplemented
97C4×#10621883C2212yescomplemented
98#14582976C2212yescomplemented
99#14582969C2212yescomplemented
100#14582969C2212yescomplemented
101#14582964C2212yescomplemented
102#14582941C2211yescharacteristic, complemented
103C2×#13063259C2211yescharacteristic, complemented
104C2×#13063256C2211yescharacteristic, complemented
105#14582906C2212yescomplemented
106#14582904C2211yescharacteristic, complemented
107#14582902C2212yescomplemented
108#14582902C2212yescomplemented
109#14582901C2211yescharacteristic
110#14582900C2211yescharacteristic, complemented
111#14582900C2211yescharacteristic, complemented
112#14582898C2211yescharacteristic
113#14582897C2212yescomplemented
114#14582896C2211yescharacteristic
115#14582895C2211yescharacteristic, complemented
116#14582894C2212yescomplemented
117#14582892C2212yescomplemented
118#14582892C2212yescomplemented
119C2×#13063246C2211yescharacteristic, complemented
120#102×D43C2212yescomplemented
121#14582867C2211yescharacteristic, complemented
122C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
123#14582855C2211yescharacteristic, complemented
124C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
125C2×#135×C43C2211yescharacteristic, complemented
126C43×#535C2211yescharacteristic
127C43×#520C2211yescharacteristic, complemented
128C43×#464C2212yescomplemented
129C43×#463C2212yescomplemented
130C43×#460C2212yescomplemented
131C43×#459C2212yescomplemented
132C43×#424C2211yescharacteristic, complemented
133C43×#417C2211yescharacteristic, complemented
134C2×#102×C43C2211yescharacteristic, complemented
135#13063370—24no—
136#13063370—42no—
137C2×#10621902C2311yescharacteristic
138C2×#10621898—21no—
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2311yescharacteristic
141C2×#10621900—21no—
142C2×#10621900—21no—
143C2×#10621900C2312yes—
144C2×#10621900C2311yescharacteristic
145#41×D43—24no—
146#41×D43—42no—
147C2×Q8×D43C2311yescharacteristic
148C22×C22⋊D43—21no—
149C22×C22⋊D43—22no—
150C2×D4×D43—21no—
151C2×D4×D43—21no—
152C2×D4×D43—22no—
153C2×D4×D43C2312yes—
154C2×D4×D43C2311yescharacteristic
155C22×C4×D43—21no—
156C22×C4×D43C2311yescharacteristic
157#13063345—24no—
158C2×#10621885C2311yescharacteristic
159C2×#10621883C2311yescharacteristic
160C2×#10621884C2311yescharacteristic
161C2×#10621882C2311yescharacteristic
162#13063331—42no—
163C2×#10621877C2311yescharacteristic
164C2×#10621872C2312yes—
165C2×#10621872C2312yes—
166M16×D43—42no—
167C22×C43⋊C8C2311yescharacteristic
168C2×C8×D43C2312yes—
169C2×C8×D43C2312yes—
170#13063325C2312yes—
171#13063324—21no—
172#13063321—22no—
173#13063320—22no—
174#13063320—22no—
175#13063319—22no—
176#13063318—22no—
177#13063317C2312yes—
178#13063316—21no—
179#13063315—22no—
180#13063313—22no—
181#13063311—22no—
182#13063311—22no—
183#13063311—22no—
184#13063310—22no—
185#13063309D412yes—
186#13063308—22no—
187#13063307—22no—
188#13063306—21no—
189#13063305D411yescharacteristic
190#13063305D411yescharacteristic
191#13063304—21no—
192#13063304—21no—
193#13063302—22no—
194#13063302—22no—
195#13063301C2312yes—
196#13063301C2311yescharacteristic
197#13063301C2312yes—
198#13063301C2311yescharacteristic
199#13063300D411yescharacteristic
200#13063300D411yescharacteristic
201#13063299—21no—
202#13063299—22no—
203#13063299—21no—
204#13063298—22no—
205#13063298—22no—
206#13063298—22no—
207#13063297—22no—
208#13063297—22no—
209#13063297—22no—
210#13063297—22no—
211#13063296—21no—
212#13063296—21no—
213#13063296—22no—
214#13063296C2311yescharacteristic
215#13063296C2312yes—
216#13063296C2312yes—
217#13063296C2312yes—
218#13063296C2312yes—
219#13063296C2311yescharacteristic
220#13063295—22no—
221#13063295D412yes—
222#13063293—21no—
223#13063293—22no—
224#13063293—22no—
225C4×Dic86—22no—
226C4×Dic86C2312yes—
227#13063290—21no—
228C4×D172C2312yes—
229C4×D172C2312yes—
230C4×D172C2312yes—
231D4×Dic43—22no—
232#13063287—21no—
233C4×C22⋊D43—22no—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—21no—
236C4×C22⋊D43—22no—
237(C22⋊D43)⋊C4—22no—
238(C22⋊D43)⋊C4—22no—
239#13063284—22no—
240#13063284C2311yescharacteristic
241#13063283—21no—
242#13063283—21no—
243#13063283—21no—
244#13063283C2312yes—
245#13063283C2312yes—
246#13063283C2312yes—
247#13063282—22no—
248C2×C4⋊Dic43C2311yescharacteristic
249C2×C4⋊Dic43C2311yescharacteristic
250C4⋊C4×D43—21no—
251C4⋊C4×D43C2312yes—
252C2×C22⋊Dic43—21no—
253C2×(C2×D43)⋊C4—21no—
254C22⋊C4×D43—22no—
255C2×C4×Dic43—21no—
256#13063259C2312yes—
257#13063259C2312yes—
258#13063259C2312yes—
259#13063257C2312yes—
260#13063256C2312yes—
261#13063256C2312yes—
262#13063250C2311yescharacteristic
263#13063250C2312yes—
264#13063250C2311yescharacteristic
265#13063249C2311yescharacteristic
266#13063249C2311yescharacteristic
267#13063249C2312yes—
268#13063249C2312yes—
269#13063248C2312yes—
270#13063247C2311yescharacteristic
271#13063247C2312yes—
272#13063247C2311yescharacteristic
273#13063246C2312yes—
274#13063246C2311yescharacteristic
275#13063246C2312yes—
276#13063246C2311yescharacteristic
277#13063246C2312yes—
278#13063246C2312yes—
279#13063246C2312yes—
280#13063246C2312yes—
281#13063245C2312yes—
282(C2×D43)⋊C8C2312yes—
283(C2×D43)⋊C8C2311yescharacteristic
284(C2×D43)⋊C8C2311yescharacteristic
285(C2×D43)⋊C8C2311yescharacteristic
286(C2×D43)⋊C8C2311yescharacteristic
287(C2×D43)⋊C8C2312yes—
288#13063236C2312yes—
289C4×C43⋊C8C2312yes—
290C2×#41×C43C2311yescharacteristic
291C2×#41×C43C2311yescharacteristic
292C22×D4×C43C2311yescharacteristic
293AGL(1,ℤ/8)×C43—42no—
294#135×C43—42no—
295C2×Q16×C43C2311yescharacteristic
296C2×SD16×C43C2311yescharacteristic
297C2×SD16×C43C2311yescharacteristic
298C2×SD16×C43C2312yes—
299C2×D8×C43C2311yescharacteristic
300C2×D8×C43C2312yes—
301C2×M16×C43C2311yescharacteristic
302C22×C8×C43C2311yescharacteristic
303#127×C43C2312yes—
304#124×C43C2312yes—
305#121×C43—21no—
306#121×C43—21no—
307#120×C43—22no—
308C4×Q8×C43C2312yes—
309C4×D4×C43—22no—
310C4×D4×C43C2312yes—
311#117×C43—21no—
312#117×C43C2311yescharacteristic
313C2×C4⋊C4×C43—21no—
314C2×C4⋊C4×C43C2311yescharacteristic
315C4⋊C8×C43C2312yes—
316C4⋊C8×C43C2312yes—
317#103×C43C2312yes—
318#102×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2312yes—
321C24×C43—21no—
322C23×D43—21no—
323C23×D43—22no—
324C23×D43C2×D411yescharacteristic
325#41×C43—22no—
326#41×C43—22no—
327#41×C43—22no—
328#41×C43—22no—
329C2×Q8×C43C2411yescharacteristic
330C2×Q8×C43C2411yescharacteristic
331C2×D4×C43—21no—
332C2×D4×C43—22no—
333C2×D4×C43—22no—
334C2×D4×C43—21no—
335C2×D4×C43—21no—
336C2×D4×C43—22no—
337C2×D4×C43—22no—
338C2×D4×C43C2412yes—
339C2×D4×C43C2411yescharacteristic
340C2×D4×C43C2411yescharacteristic
341C22×C4×C43—21no—
342C22×C4×C43—21no—
343C22×C4×C43—22no—
344C22×C4×C43—21no—
345C22×C4×C43C2411yescharacteristic
346C2×C22⋊D43—21no—
347C2×C22⋊D43—22no—
348C2×C22⋊D43—21no—
349C2×C22⋊D43—22no—
350C2×C22⋊D43—21no—
351C2×C22⋊D43—22no—
352C2×C22⋊D43—21no—
353C2×C22⋊D43—21no—
354C2×C22⋊D43—22no—
355C2×C22⋊D43—22no—
356C2×C22⋊D43—22no—
357C2×C22⋊D43—48no—
358C2×C22⋊D43—82no—
359C2×C22⋊D43C2×D412yes—
360C22×Dic43—22no—
361C22×Dic43—21no—
362C22×Dic43—21no—
363C22×Dic43—21no—
364C22×Dic43C2×D411yescharacteristic
365#10621902—22no—
366#10621902—41no—
367Q8×D43—22no—
368Q8×D43—41no—
369#10621900—22no—
370#10621900—24no—
371#10621900—41no—
372#10621900—42no—
373#10621900—44no—
374#10621900—44no—
375D4×D43—22no—
376D4×D43—24no—
377D4×D43—44no—
378D4×D43—41no—
379D4×D43—42no—
380D4×D43—44no—
381D4×D43—84no—
382#10621898—22no—
383#10621898—22no—
384#10621898—22no—
385#10621898—44no—
386#10621898#4114yes—
387C2×D172—21no—
388C2×D172C2×D411yescharacteristic
389C2×D172C2×D412yes—
390C2×D172C2×D412yes—
391C2×D172C2411yescharacteristic
392C2×C4×D43—21no—
393C2×C4×D43—22no—
394C2×C4×D43—22no—
395C2×C4×D43—21no—
396C2×C4×D43—22no—
397C2×C4×D43—21no—
398C2×C4×D43—22no—
399C2×C4×D43—44no—
400C2×C4×D43C2×D411yescharacteristic
401C2×C4×D43C2×D411yescharacteristic
402C2×C4×D43C2412yes—
403C2×C4×D43C2411yescharacteristic
404C2×C4×D43C2411yescharacteristic
405C2×Dic86—21no—
406C2×Dic86—22no—
407C2×Dic86C2×D411yescharacteristic
408C2×Dic86C2411yescharacteristic
409Q16×C43—41no—
410SD16×C43—41no—
411SD16×C43—41no—
412SD16×C43—42no—
413D8×C43—41no—
414D8×C43—42no—
415M16×C43—22no—
416C2×C8×C43—22no—
417C2×C8×C43C2411yescharacteristic
418C2×C8×C43C2411yescharacteristic
419C2×C8×C43C2412yes—
420C4⋊C4×C43—21no—
421C4⋊C4×C43—22no—
422C4⋊C4×C43C2×D411yescharacteristic
423C4⋊C4×C43C2×D411yescharacteristic
424C4⋊C4×C43C2412yes—
425C22⋊C4×C43—22no—
426C22⋊C4×C43—22no—
427C22⋊C4×C43—22no—
428C22⋊C4×C43C2×D412yes—
429C42×C43—22no—
430C42×C43C2412yes—
431C22⋊Dic43—22no—
432C22⋊Dic43—22no—
433C22⋊Dic43—21no—
434C22⋊Dic43—22no—
435C22⋊Dic43—21no—
436C22⋊Dic43—22no—
437C22⋊Dic43—21no—
438#10621885—22no—
439#10621884—22no—
440#10621883—22no—
441#10621882—22no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—22no—
444(C2×D43)⋊C4—22no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—21no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4C2×D412yes—
451(C2×D43)⋊C4C2×D412yes—
452(C2×D43)⋊C4C2×D412yes—
453(C2×D43)⋊C4C2×D412yes—
454C4⋊Dic43—21no—
455C4⋊Dic43—21no—
456C4⋊Dic43—22no—
457C4⋊Dic43C2×D412yes—
458C4⋊Dic43C2×D412yes—
459C4⋊Dic43C2411yescharacteristic
460C4⋊Dic43C2412yes—
461C4⋊Dic43C2411yescharacteristic
462C4⋊Dic43C2412yes—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—21no—
468Dic43⋊C4—22no—
469Dic43⋊C4—21no—
470Dic43⋊C4—22no—
471C4×Dic43—22no—
472C4×Dic43—21no—
473C4×Dic43—22no—
474C4×Dic43—22no—
475C4×Dic43—22no—
476#10621877—22no—
477C2×C43⋊C8—22no—
478C2×C43⋊C8C2411yescharacteristic
479C2×C43⋊C8C2412yes—
480C2×C43⋊C8C2411yescharacteristic
481#10621872—42no—
482#10621872—42no—
483C8×D43—42no—
484C8×D43—42no—
485C23×C43—21no—
486C23×C43—22no—
487C23×C43—21no—
488C23×C43—42no—
489C23×C43—81no—
490C23×C43—81no—
491C23×C43C22×D411yescharacteristic
492C22×D43—21no—
493C22×D43—22no—
494C22×D43—41no—
495C22×D43—41no—
496C22×D43—42no—
497C22×D43—44no—
498C22×D43—42no—
499C22×D43—81no—
500C22×D43—82no—
501C22×D43—82no—
502C22×D43C22×D411yescharacteristic
503C22×D43C22×D412yes—
504C22×D43C22×D411yescharacteristic
505Q8×C43—21no—
506Q8×C43—21no—
507Q8×C43—21no—
508Q8×C43—21no—
509D4×C43—21no—
510D4×C43—22no—
511D4×C43—21no—
512D4×C43—21no—
513D4×C43—22no—
514D4×C43—21no—
515D4×C43—42no—
516D4×C43—42no—
517D4×C43—42no—
518D4×C43—82no—
519D4×C43—82no—
520C2×C4×C43—22no—
521C2×C4×C43—21no—
522C2×C4×C43—21no—
523C2×C4×C43—42no—
524C2×C4×C43—42no—
525C2×C4×C43—82no—
526C2×C4×C43—81no—
527C2×C4×C43C22×D412yes—
528C2×C4×C43C22×D412yes—
529C2×C4×C43C22×D411yescharacteristic
530C2×C4×C43C2×#4112yes—
531C2×C4×C43H(5,𝔽2)12yes—
532C2×C4×C43C2511yescharacteristic
533C22⋊D43—24no—
534C22⋊D43—24no—
535C22⋊D43—42no—
536C22⋊D43—42no—
537C22⋊D43—44no—
538C22⋊D43—44no—
539C22⋊D43—44no—
540C22⋊D43—82no—
541C22⋊D43—81no—
542C22⋊D43—81no—
543C22⋊D43—82no—
544C22⋊D43—82no—
545C2×Dic43—22no—
546C2×Dic43—21no—
547C2×Dic43—21no—
548C2×Dic43—22no—
549C2×Dic43—21no—
550C2×Dic43—22no—
551C2×Dic43—42no—
552C2×Dic43—44no—
553C2×Dic43—81no—
554C2×Dic43—81no—
555C2×Dic43C22×D411yescharacteristic
556C2×Dic43C22×D411yescharacteristic
557C2×Dic43C22×D412yes—
558D172—22no—
559D172—21no—
560D172—42no—
561D172—42no—
562D172—42no—
563D172C2×#4112yes—
564C4×D43—22no—
565C4×D43—22no—
566C4×D43—24no—
567C4×D43—21no—
568C4×D43—21no—
569C4×D43—22no—
570C4×D43—21no—
571C4×D43—22no—
572C4×D43—21no—
573C4×D43—42no—
574C4×D43—42no—
575C4×D43—82no—
576C4×D43—82no—
577Dic86—22no—
578Dic86—21no—
579Dic86—42no—
580Dic86—82no—
581Dic86C2×#4112yes—
582C8×C43—21no—
583C8×C43—22no—
584C8×C43—21no—
585C43⋊C8—21no—
586C43⋊C8—21no—
587C43⋊C8—22no—
588#61196—431nomaximal, Sylow
589C22×C43—21no—
590C22×C43—21no—
591C22×C43—42no—
592C22×C43—41no—
593C22×C43—41no—
594C22×C43—41no—
595C22×C43—42no—
596C22×C43—41no—
597C22×C43—42no—
598C22×C43—41no—
599C22×C43—41no—
600C22×C43—162no—
601C22×C43#54612yes—
602C22×C43C23×D411yescharacteristic
603C2×D43—21no—
604C2×D43—21no—
605C2×D43—22no—
606C2×D43—21no—
607C2×D43—21no—
608C2×D43—22no—
609C2×D43—21no—
610C2×D43—21no—
611C2×D43—22no—
612C2×D43—22no—
613C2×D43—41no—
614C2×D43—41no—
615C2×D43—82no—
616C2×D43—84no—
617C2×D43—164no—
618C4×C43—22no—
619C4×C43—22no—
620C4×C43—42no—
621C4×C43—41no—
622C4×C43—41no—
623C4×C43#54612yes—
624C4×C43C22×#4111yescharacteristic
625C4×C43C2×H(5,𝔽2)11yescharacteristic
626Dic43—22no—
627Dic43—22no—
628Dic43—21no—
629Dic43—21no—
630Dic43—41no—
631Dic43—41no—
632Dic43—42no—
633Dic43—42no—
634#3493—431no—
635#3488—431no—
636#3326—432no—
637#3324—432no—
638#3319—432no—
639#3318—432no—
640#3317—432no—
641#3313—432no—
642#3305—432no—
643#3296—432no—
644#3136—431no—
645#3099—431no—
646C2×#482—431no—
647#3083—431no—
648#3061—431no—
649#3055—431no—
650#3045D4311yescharacteristic, complemented
651#3012—431no—
652#3002—431no—
653#2952—431no—
654#2933—431no—
655#2897—431no—
656#2896—431no—
657C2×C43—22no—
658C2×C43—81no—
659C2×C43—82no—
660C2×C43—81no—
661C2×C43C2×#54611yescharacteristic
662C2×C43#358411yescharacteristic
663C2×C43#358511yescharacteristic
664D43—41no—
665D43—41no—
666D43—42no—
667D43—42no—
668C2×H(5,𝔽2)—431no—
669C22×#41—431no—
670C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
671C2×#135—431no—
672C2×#135C2×D4311yescharacteristic, complemented
673C2×#131—431no—
674C22×M16—431no—
675#556—432no—
676#556—861no—
677#555—432no—
678#555—861no—
679#553—432no—
680#553—861no—
681#552—432no—
682#552—861no—
683#550—432no—
684#548—432no—
685#546—432no—
686#546—862no—
687D42—432no—
688D42—862no—
689#544—431no—
690#538—862no—
691#537—431no—
692#537—431no—
693#537—861no—
694#535—861no—
695#535C2×D4311yescharacteristic
696#529—862no—
697#525—431no—
698#525—431no—
699#525—861no—
700C2×#121—431no—
701C2×#121—861no—
702#520—431no—
703#520—431no—
704#520C2×D4311yescharacteristic, complemented
705C2×#117—431no—
706#490—432no—
707#489—432no—
708#488—432no—
709#486—432no—
710#485—432no—
711#483—432no—
712#482—432no—
713#482—432no—
714#482—432no—
715#482—432no—
716#482—432no—
717#481—432no—
718#479—432no—
719#478—432no—
720#477—432no—
721#474—432no—
722#469—432no—
723#468—432no—
724#468—432no—
725#468—432no—
726#467—432no—
727#466—432no—
728#466—432no—
729#465—432no—
730#464C2×D4312yescomplemented
731#463C2×D4312yescomplemented
732#460C2×D4312yescomplemented
733#459C2×D4312yescomplemented
734#452—431no—
735#452—431no—
736#452—432no—
737#451—431no—
738#450—431no—
739#450—432no—
740#449—431no—
741#449—431no—
742#449—432no—
743#448—431no—
744#447—431no—
745#447—432no—
746#442—432no—
747#441—432no—
748C4×SD16—432no—
749C4×SD16—432no—
750#436—432no—
751#435—432no—
752#435—432no—
753C8×D4—432no—
754#428—431no—
755C2×#107—431no—
756C2×#106—431no—
757#424C2×D4311yescharacteristic, complemented
758#419—432no—
759#418—431no—
760#418—432no—
761#418—432no—
762#417—431no—
763#417—431no—
764#417—431no—
765#417—431no—
766#417—432no—
767#417C2×D4311yescharacteristic, complemented
768#416—431no—
769#416—431no—
770#416—432no—
771#416—432no—
772#416—432no—
773C2×#102—431no—
774C2×#102—432no—
775C2×#102C2×D4311yescharacteristic, complemented
776#408—431no—
777C2×C22⋊C8—431no—
778#405—431no—
779C43#6119611yescharacteristic, complemented, Sylow
780H(5,𝔽2)—864no—
781H(5,𝔽2)—1722no—
782C2×#41—431no—
783C2×#41—431no—
784C2×#41—432no—
785C2×#41—431no—
786C2×#41—431no—
787C2×#41—861no—
788C2×#41—861no—
789C2×#41—861no—
790C2×#41—864no—
791C2×#41—1722no—
792C2×#41C22×D4311yescharacteristic
793C2×#41C22×D4311yescharacteristic
794C22×Q8—431no—
795C22×D4—431no—
796C22×D4—432no—
797C22×D4—862no—
798C22×D4—861no—
799C22×D4—861no—
800C22×D4—862no—
801C22×D4—861no—
802C22×D4C22×D4311yescharacteristic
803C23×C4—431no—
804C23×C4—861no—
805AGL(1,ℤ/8)—42no—
806#135—42no—
807#135—864no—
808C2×Q16—431no—
809C2×Q16C22×D4311yescharacteristic
810C2×SD16—431no—
811C2×SD16—431no—
812C2×SD16C22×D4311yescharacteristic
813C2×SD16C22×D4311yescharacteristic
814C2×SD16C22×D4312yes—
815C2×D8—431no—
816C2×D8C22×D4311yescharacteristic
817C2×D8C22×D4312yes—
818#131—1722no—
819C2×M16—431no—
820C2×M16—432no—
821C2×M16—432no—
822C2×M16—1722no—
823C2×M16C22×D4311yescharacteristic
824C22×C8—431no—
825C22×C8—432no—
826C22×C8—432no—
827C22×C8C22×D4311yescharacteristic
828C4⋊Q8—432no—
829C4⋊Q8—861no—
830#127—862no—
831#127C22×D4312yes—
832#126—862no—
833#126—862no—
834#126—862no—
835#126—862no—
836#125—432no—
837#125—862no—
838#125—861no—
839#124—862no—
840#124—862no—
841#124—862no—
842#124—862no—
843#124C22×D4312yes—
844#123—432no—
845#123—862no—
846#123—862no—
847#123—862no—
848#123—861no—
849C22⋊Q8—431no—
850C22⋊Q8—431no—
851C22⋊Q8—431no—
852C22⋊Q8—431no—
853C22⋊Q8—432no—
854C22⋊Q8—432no—
855C22⋊Q8—862no—
856C22⋊Q8—861no—
857C22⋊Q8—861no—
858C22⋊Q8—862no—
859#121—21no—
860#121—21no—
861#121—431no—
862#121—431no—
863#121—432no—
864#121—432no—
865#121—431no—
866#121—431no—
867#121—432no—
868#121—432no—
869#121—862no—
870#121—862no—
871#121—862no—
872#121—862no—
873#121—862no—
874#121—862no—
875#121—861no—
876#121—861no—
877#121—862no—
878#121—861no—
879#121—861no—
880#121—862no—
881#121—862no—
882#120—22no—
883#120—432no—
884#120—862no—
885#120—862no—
886#120—862no—
887#120—861no—
888C4×Q8—432no—
889C4×Q8—862no—
890C4×Q8—861no—
891C4×Q8C22×D4312yes—
892C4×D4—22no—
893C4×D4—432no—
894C4×D4—432no—
895C4×D4—432no—
896C4×D4—862no—
897C4×D4—862no—
898C4×D4—861no—
899C4×D4—862no—
900C4×D4—861no—
901C4×D4—861no—
902C4×D4—862no—
903C4×D4—862no—
904C4×D4C22×D4312yes—
905#117—21no—
906#117—431no—
907#117—432no—
908#117—432no—
909#117—432no—
910#117—862no—
911#117—861no—
912#117—861no—
913#117—862no—
914#117—861no—
915#117C22×D4311yescharacteristic
916C2×C4⋊C4—21no—
917C2×C4⋊C4—431no—
918C2×C4⋊C4—431no—
919C2×C4⋊C4—432no—
920C2×C4⋊C4—861no—
921C2×C4⋊C4C22×D4311yescharacteristic
922C2×C22⋊C4—862no—
923C2×C22⋊C4—861no—
924C2×C22⋊C4—861no—
925C2×C42—861no—
926#107—432no—
927#107—432no—
928#107—432no—
929#106—432no—
930#106—432no—
931#106—432no—
932C4⋊C8C22×D4312yes—
933C4⋊C8C22×D4312yes—
934#103—432no—
935#103—431no—
936#103—431no—
937#103—432no—
938#103—431no—
939#103—431no—
940#103—432no—
941#103—432no—
942#103C22×D4312yes—
943#102—432no—
944#102—432no—
945#102—432no—
946#102—432no—
947#102—432no—
948#102—431no—
949#102—431no—
950#102—432no—
951#102—431no—
952#102—432no—
953#102—431no—
954#102—432no—
955#102C22×D4312yes—
956#102C22×D4312yes—
957#102C22×D4312yes—
958C22⋊C8—431no—
959C22⋊C8—431no—
960C22⋊C8—431no—
961C22⋊C8—431no—
962C22⋊C8—432no—
963C22⋊C8—432no—
964#97—432no—
965C4×C8—432no—
966C24—21no—
967C24—431no—
968C24—862no—
969C24—861no—
970#41—22no—
971#41—22no—
972#41—22no—
973#41—22no—
974#41—434no—
975#41—862no—
976#41—862no—
977#41—862no—
978#41—862no—
979#41—864no—
980#41—862no—
981#41—1724no—
982#41—1721no—
983#41—1722no—
984#41—1724no—
985#41—1724no—
986#41—1721no—
987C2×Q8—431no—
988C2×Q8—431no—
989C2×Q8—861no—
990C2×Q8—862no—
991C2×Q8—862no—
992C2×Q8—1721no—
993C2×Q8C23×D4311yescharacteristic
994C2×Q8C23×D4311yescharacteristic
995C2×D4—21no—
996C2×D4—21no—
997C2×D4—21no—
998C2×D4—22no—
999C2×D4—22no—
1000C2×D4—22no—
1001C2×D4—22no—
1002C2×D4—432no—
1003C2×D4—431no—
1004C2×D4—432no—
1005C2×D4—432no—
1006C2×D4—431no—
1007C2×D4—861no—
1008C2×D4—861no—
1009C2×D4—862no—
1010C2×D4—862no—
1011C2×D4—864no—
1012C2×D4—861no—
1013C2×D4—861no—
1014C2×D4—861no—
1015C2×D4—862no—
1016C2×D4—862no—
1017C2×D4—862no—
1018C2×D4—862no—
1019C2×D4—862no—
1020C2×D4—861no—
1021C2×D4—3444no—
1022C2×D4—3442no—
1023C2×D4—1721no—
1024C2×D4—1722no—
1025C2×D4—1724no—
1026C2×D4—1724no—
1027C2×D4—1728no—
1028C2×D4C23×D4312yes—
1029C2×D4C23×D4311yescharacteristic
1030C2×D4C23×D4311yescharacteristic
1031C22×C4—21no—
1032C22×C4—21no—
1033C22×C4—21no—
1034C22×C4—22no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—431no—
1038C22×C4—432no—
1039C22×C4—431no—
1040C22×C4—431no—
1041C22×C4—861no—
1042C22×C4—862no—
1043C22×C4—861no—
1044C22×C4—861no—
1045C22×C4—862no—
1046C22×C4—861no—
1047C22×C4—862no—
1048C22×C4—862no—
1049C22×C4—861no—
1050C22×C4—861no—
1051C22×C4—862no—
1052C22×C4—1724no—
1053C22×C4C23×D4311yescharacteristic
1054Q16—41no—
1055Q16—862no—
1056SD16—41no—
1057SD16—41no—
1058SD16—42no—
1059SD16—862no—
1060SD16—862no—
1061D8—41no—
1062D8—42no—
1063D8—862no—
1064M16—22no—
1065M16—862no—
1066M16—1722no—
1067M16—1722no—
1068C2×C8—22no—
1069C2×C8—431no—
1070C2×C8—432no—
1071C2×C8—431no—
1072C2×C8—862no—
1073C2×C8—1722no—
1074C2×C8—1722no—
1075C2×C8C23×D4311yescharacteristic
1076C2×C8C23×D4311yescharacteristic
1077C2×C8C23×D4312yes—
1078C4⋊C4—21no—
1079C4⋊C4—22no—
1080C4⋊C4—432no—
1081C4⋊C4—432no—
1082C4⋊C4—431no—
1083C4⋊C4—432no—
1084C4⋊C4—431no—
1085C4⋊C4—432no—
1086C4⋊C4—862no—
1087C4⋊C4—861no—
1088C4⋊C4—861no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—861no—
1092C4⋊C4—861no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4—862no—
1096C4⋊C4—862no—
1097C4⋊C4D4×D4311yescharacteristic
1098C4⋊C4D4×D4311yescharacteristic
1099C4⋊C4C23×D4312yes—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—432no—
1104C22⋊C4—432no—
1105C22⋊C4—432no—
1106C22⋊C4—432no—
1107C22⋊C4—862no—
1108C22⋊C4—862no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—861no—
1113C22⋊C4—861no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—861no—
1117C22⋊C4—862no—
1118C22⋊C4—861no—
1119C22⋊C4—862no—
1120C22⋊C4—861no—
1121C22⋊C4—862no—
1122C22⋊C4D4×D4312yes—
1123C42—22no—
1124C42—862no—
1125C42—862no—
1126C42—862no—
1127C42—861no—
1128C42—862no—
1129C42C23×D4312yes—
1130C23—21no—
1131C23—22no—
1132C23—21no—
1133C23—42no—
1134C23—81no—
1135C23—81no—
1136C23—431no—
1137C23—431no—
1138C23—432no—
1139C23—862no—
1140C23—861no—
1141C23—3441no—
1142C23—3442no—
1143C23—3442no—
1144C23—1721no—
1145C23—1721no—
1146C23—1722no—
1147C23—1724no—
1148C23—1722no—
1149C23C2×D4×D4311yescharacteristic
1150Q8—21no—
1151Q8—21no—
1152Q8—21no—
1153Q8—21no—
1154Q8—432no—
1155Q8—861no—
1156Q8—862no—
1157Q8—3442no—
1158Q8—1722no—
1159D4—21no—
1160D4—22no—
1161D4—21no—
1162D4—21no—
1163D4—22no—
1164D4—21no—
1165D4—42no—
1166D4—42no—
1167D4—42no—
1168D4—82no—
1169D4—82no—
1170D4—432no—
1171D4—864no—
1172D4—864no—
1173D4—861no—
1174D4—862no—
1175D4—3442no—
1176D4—3442no—
1177D4—3441no—
1178D4—3442no—
1179D4—3441no—
1180D4—1722no—
1181D4—1722no—
1182D4—1722no—
1183D4—1724no—
1184D4—1722no—
1185D4—1724no—
1186D4—1722no—
1187D4—1724no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—82no—
1194C2×C4—81no—
1195C2×C4—431no—
1196C2×C4—431no—
1197C2×C4—432no—
1198C2×C4—861no—
1199C2×C4—862no—
1200C2×C4—861no—
1201C2×C4—861no—
1202C2×C4—862no—
1203C2×C4—861no—
1204C2×C4—862no—
1205C2×C4—861no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—864no—
1209C2×C4—861no—
1210C2×C4—862no—
1211C2×C4—862no—
1212C2×C4—861no—
1213C2×C4—3442no—
1214C2×C4—3442no—
1215C2×C4—3441no—
1216C2×C4—3441no—
1217C2×C4—1722no—
1218C2×C4—1722no—
1219C2×C4—1722no—
1220C2×C4—1724no—
1221C2×C4C2×D4×D4312yes—
1222C2×C4C2×D4×D4312yes—
1223C2×C4C2×D4×D4311yescharacteristic
1224C2×C4#41×D4312yes—
1225C2×C4#1306337012yes—
1226C2×C4C24×D4311yescharacteristic
1227C8—21no—
1228C8—21no—
1229C8—22no—
1230C8—861no—
1231C8—861no—
1232C8—862no—
1233C22—21no—
1234C22—21no—
1235C22—41no—
1236C22—41no—
1237C22—42no—
1238C22—41no—
1239C22—41no—
1240C22—42no—
1241C22—41no—
1242C22—42no—
1243C22—41no—
1244C22—162no—
1245C22—861no—
1246C22—861no—
1247C22—862no—
1248C22—862no—
1249C22—862no—
1250C22—861no—
1251C22—861no—
1252C22—861no—
1253C22—862no—
1254C22—861no—
1255C22—3442no—
1256C22—3444no—
1257C22—1721no—
1258C22—1721no—
1259C22—6884no—
1260C22#1458354612yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—41no—
1265C4—41no—
1266C4—42no—
1267C4—861no—
1268C4—861no—
1269C4—862no—
1270C4—862no—
1271C4—1721no—
1272C4—1722no—
1273C4—1722no—
1274C4—1721no—
1275C4#1458354612yes—
1276C4C2×#41×D4311yescharacteristic
1277C4C2×#1306337011yescharacteristic
1278C2—22no—
1279C2—82no—
1280C2—81no—
1281C2—81no—
1282C2—1721no—
1283C2—1721no—
1284C2—1722no—
1285C2—1722no—
1286C2C2×#1458354611yescharacteristic
1287C2#1914936311yescharacteristic
1288C2#1914937311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3045C2
socleC22×C43C23×D4
hypercenter#3045D43
hypocenterC43#61196
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #3045

Complements

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

NH ≅ G/Ntype
1. #19148308C2semidirect
2. #19148262C2semidirect
3. #19146855C2semidirect
4. #19146829C2semidirect
5. #19146758C2semidirect
6. #19146743C2semidirect
7. #19146728C2semidirect
8. #19146668C2semidirect
9. #19146548C2semidirect
10. #19146437C2semidirect
11. #19144949C2semidirect
12. #19144583C2semidirect
13. C2×#14583221C2semidirect
14. #19144448C2semidirect
15. #19144261C2semidirect
16. #19144208C2semidirect
17. #19143898C2semidirect
18. #19143809C2semidirect
19. #19143476C2semidirect
20. #19143319C2semidirect
21. #19143116C2semidirect
22. #19143111C2semidirect
23. C43×#3045C2semidirect
27. C2×#13063331C22semidirect
28. C2×M16×D43C22semidirect
29. #14583622C22semidirect
31. #14583614C22semidirect
33. #14583599C22semidirect
35. #14583590C22semidirect
43. #14583527C22semidirect
47. #14583477C22semidirect
52. #14583406C22semidirect
55. #14583380C22semidirect
57. C2×#13063283C22semidirect
58. #14583263C22semidirect
59. #14583258C22semidirect
60. #14583253C22semidirect
61. #14583245C22semidirect
62. #14583239C22semidirect
63. #14583228C22semidirect
64. #14583221C22semidirect
65. #14583221C22semidirect
66. #14583221C22semidirect
67. #14583221C22semidirect
68. #14583221C22semidirect
69. #14583216C22semidirect
70. #14583207C22semidirect
71. #14583200C22semidirect
72. #14583195C22semidirect
73. #14583180C22semidirect
74. #14583149C22semidirect
75. #14583142C22semidirect
76. #14583142C22semidirect
77. #14583142C22semidirect
78. #14583137C22semidirect
79. #14583132C22semidirect
80. #14583132C22semidirect
81. #14583125C22semidirect
82. #14583060C22semidirect
83. #14583058C22semidirect
84. #14583058C22semidirect
85. #14583053C22semidirect
86. #14583048C22semidirect
87. #14583048C22semidirect
88. #14583043C22semidirect
89. #14583041C22semidirect
90. #14583041C22semidirect
91. #14583036C22semidirect
92. #14583031C22semidirect
93. #14583031C22semidirect
94. #14583009C22semidirect
95. #14583004C22semidirect
96. C4×#10621884C22semidirect
97. C4×#10621883C22semidirect
98. #14582976C22semidirect
99. #14582969C22semidirect
100. #14582969C22semidirect
101. #14582964C22semidirect
102. #14582941C22semidirect
103. C2×#13063259C22semidirect
104. C2×#13063256C22semidirect
105. #14582906C22semidirect
106. #14582904C22semidirect
107. #14582902C22semidirect
108. #14582902C22semidirect
110. #14582900C22semidirect
111. #14582900C22semidirect
113. #14582897C22semidirect
115. #14582895C22semidirect
116. #14582894C22semidirect
117. #14582892C22semidirect
118. #14582892C22semidirect
119. C2×#13063246C22semidirect
120. #102×D43C22semidirect
121. #14582867C22semidirect
122. C2×(C2×D43)⋊C8C22semidirect
123. #14582855C22semidirect
124. C2×AGL(1,ℤ/8)×C43C22semidirect
125. C2×#135×C43C22semidirect
127. C43×#520C22semidirect
128. C43×#464C22semidirect
129. C43×#463C22semidirect
130. C43×#460C22semidirect
131. C43×#459C22semidirect
132. C43×#424C22semidirect
133. C43×#417C22semidirect
134. C2×#102×C43C22semidirect
650. #3045D43semidirect
670. C2×AGL(1,ℤ/8)C2×D43semidirect
672. C2×#135C2×D43semidirect
704. #520C2×D43semidirect
730. #464C2×D43semidirect
731. #463C2×D43semidirect
732. #460C2×D43semidirect
733. #459C2×D43semidirect
757. #424C2×D43semidirect
767. #417C2×D43semidirect
775. C2×#102C2×D43semidirect
779. C43#61196semidirect

Maximal subgroups

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

subgroupindex
#191483082
#191482622
#191468552
#191468292
#191467582
#191467432
#191467282
#191466682
#191465482
#191464372
#191449492
#191445832
C2×#145832212
#191444482
#191442612
#191442082
#191438982
#191438092
#191434762
#191433192
#191431162
#191431112
C43×#30452
#6119643