Finite Group Databasebeta

← #25988937

Subgroups — #25988937

Order 11008.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148465C211yesmaximal, characteristic, complemented
2D4×#10621900C211yesmaximal, characteristic, complemented
3#19147642C211yesmaximal, characteristic, complemented
4#19147636C211yesmaximal, characteristic, complemented
5#19147391C211yesmaximal, characteristic, complemented
6#19147385C211yesmaximal, characteristic, complemented
7#19146923C211yesmaximal, characteristic, complemented
8#19146922C211yesmaximal, characteristic, complemented
9#19146551C212yesmaximal, complemented
10#19146549C212yesmaximal, complemented
11#19146211C211yesmaximal, characteristic, complemented
12#19146073C212yesmaximal, complemented
13#19146069C212yesmaximal, complemented
14#19145972C212yesmaximal, complemented
15#19145909C211yesmaximal, characteristic, complemented
16#19145587C212yesmaximal, complemented
17#19145509C211yesmaximal, characteristic, complemented
18#19144681C212yesmaximal, complemented
19#19144601C211yesmaximal, characteristic, complemented
20#19144056C212yesmaximal, complemented
21#459×D43C211yesmaximal, characteristic, complemented
22#19143710C211yesmaximal, characteristic, complemented
23C43×#3274C211yesmaximal, characteristic, complemented
24C22×#10621900—21no—
25C2×#13063351C2212yescomplemented
26C2×D8×D43C2212yes—
27#14583635C2211yescharacteristic, complemented
28#14583634C2211yescharacteristic, complemented
29#14583632—21no—
30#14583570C2211yescharacteristic, complemented
31#14583569—21no—
32#14583569C2211yescharacteristic, complemented
33D4×Dic86C2211yescharacteristic, complemented
34#14583555—21no—
35#14583553C2211yescharacteristic, complemented
36#14583549C2212yes—
37#14583546C2212yescomplemented
38#14583543—21no—
39#14583538—22no—
40#14583537C2212yescomplemented
41#14583536—22no—
42D4×C22⋊D43C2212yes—
43#14583499—22no—
44#14583462—21no—
45#14583453C2211yescharacteristic, complemented
46#14583447C2211yescharacteristic
47#14583445C2212yescomplemented
48#14583444C2212yescomplemented
49#14583444C2212yescomplemented
50#127×D43C2211yescharacteristic, complemented
51#14583409—21no—
52#14583405—22no—
53#14583371—21no—
54C4×#10621900C2211yescharacteristic
55C2×D4×Dic43C2212yescomplemented
56C4×D4×D43C2211yescharacteristic
57#14583287C2212yescomplemented
58#14583285C2212yescomplemented
59#14583275C2211yescharacteristic, complemented
60#14583260C2212yescomplemented
61#14583257C2212yescomplemented
62#14583246C2211yescharacteristic, complemented
63#14583245C2211yescharacteristic, complemented
64#14583231C2211yescharacteristic, complemented
65#14583228C2211yescharacteristic, complemented
66#14583218C2212yescomplemented
67#14583215C2212yescomplemented
68#14583188C2212yescomplemented
69#14583188C2211yescharacteristic, complemented
70#14583187C2212yescomplemented
71#14583187C2211yescharacteristic, complemented
72#14583187C2212yescomplemented
73#14583185C2211yescharacteristic, complemented
74#14583184C2211yescharacteristic, complemented
75#14583152C2212yescomplemented
76#14583150C2212yescomplemented
77#14583150C2212yescomplemented
78#14583127C2212yescomplemented
79#14583125C2212yescomplemented
80#14583116C2212yescomplemented
81#14583116C2212yescomplemented
82#14583112C2212yescomplemented
83#14583112C2212yescomplemented
84#14583103C2211yescharacteristic, complemented
85#14583102C2212yescomplemented
86#14583102C2211yescharacteristic, complemented
87#14583096C2211yescharacteristic, complemented
88#14583095C2211yescharacteristic, complemented
89#14583094C2211yescharacteristic
90#14583093C2212yescomplemented
91#14583093C2212yescomplemented
92#14583092C2212yes—
93#14583092C2212yescomplemented
94#14583092C2212yescomplemented
95#14583092C2212yescomplemented
96#14583091C2211yescharacteristic, complemented
97#14583051C2211yescharacteristic
98#14583048C2211yescharacteristic
99#14583046C2212yescomplemented
100#14583044C2212yescomplemented
101#14583042C2212yescomplemented
102#14583033C2212yescomplemented
103#14583031C2212yescomplemented
104#14583031C2212yescomplemented
105#14583029C2211yescharacteristic, complemented
106#14583026C2211yescharacteristic, complemented
107#14583011C2212yescomplemented
108#14583011C2212yescomplemented
109#14583008C2212yescomplemented
110#14583008C2212yescomplemented
111C4×#10621873C2211yescharacteristic, complemented
112C4×#10621884C2211yescharacteristic, complemented
113C4×#10621883C2211yescharacteristic, complemented
114#14582977C2211yescharacteristic, complemented
115#14582973C2212yescomplemented
116#14582968C2212yescomplemented
117#14582953C2212yescomplemented
118#14582950C2211yescharacteristic, complemented
119#14582922C2212yescomplemented
120C4⋊C8×D43C2211yescharacteristic, complemented
121#14582901C2212yescomplemented
122#14582900C2212yescomplemented
123#102×D43C2212yescomplemented
124C2×AGL(1,ℤ/8)×C43C2212yescomplemented
125C43×#550C2211yescharacteristic, complemented
126D42×C43C2211yescharacteristic, complemented
127C43×#493C2211yescharacteristic, complemented
128C43×#469C2212yescomplemented
129C43×#460C2211yescharacteristic, complemented
130C43×#459C2211yescharacteristic
131C43×#449C2212yescomplemented
132C43×#447C2212yescomplemented
133C4×SD16×C43C2211yescharacteristic, complemented
134C43×#436C2211yescharacteristic, complemented
135C2×#10621898C2312yes—
136C2×#10621900—21no—
137C2×#10621900—22no—
138C2×#10621900—22no—
139C2×#10621900—22no—
140C2×#10621900—21no—
141C2×#10621900—21no—
142C2×#10621900—48no—
143C2×#10621900D411yescharacteristic
144C22×Dic86—21no—
145C22×C22⋊D43—22no—
146C2×D4×D43—21no—
147C2×D4×D43—21no—
148C2×D4×D43C2311yescharacteristic
149C2×D4×D43C2312yes—
150C23×Dic43—22no—
151C22×C4×D43—21no—
152#13063351—44no—
153C2×#10621873C2311yescharacteristic
154C2×#10621883C2311yescharacteristic
155C2×#10621883C2312yes—
156C2×#10621884C2311yescharacteristic
157C2×D344C2312yes—
158C2×#10621882C2312yes—
159C2×#10621882C2312yes—
160C2×#10621882C2312yes—
161C2×#10621882C2312yes—
162D8×D43—44no—
163C2×#10621877C2312yes—
164C2×C8×D43C2312yes—
165#13063325C2311yescharacteristic
166#13063324C2312yes—
167#13063324C2311yescharacteristic
168#13063323C2311yescharacteristic
169#13063322C2311yescharacteristic
170#13063321—21no—
171#13063321—21no—
172#13063321—21no—
173#13063321C2312yes—
174#13063321C2312yes—
175#13063315—21no—
176#13063314C2312yes—
177#13063313—21no—
178#13063312—21no—
179#13063312—21no—
180#13063312C2312yes—
181#13063311—22no—
182#13063311—22no—
183#13063310—22no—
184#13063309—22no—
185#13063308—22no—
186#13063307—22no—
187#13063307—22no—
188#13063306—22no—
189#13063306—22no—
190#13063305—21no—
191#13063305C2311yescharacteristic
192#13063304—21no—
193#13063303—21no—
194#13063302—22no—
195#13063302—22no—
196#13063301C2311yescharacteristic
197#13063299C2312yes—
198#13063299C2312yes—
199#13063298—22no—
200#13063297—22no—
201#13063297—22no—
202#13063297—22no—
203#13063297—22no—
204#13063297—22no—
205#13063297—22no—
206#13063297—22no—
207#13063296—21no—
208#13063296—22no—
209#13063296—21no—
210#13063296C2312yes—
211#13063294—22no—
212#13063293—22no—
213#13063293—22no—
214#13063293—22no—
215C4×Dic86—21no—
216C4×Dic86C2311yescharacteristic
217C4×Dic86C2311yescharacteristic
218#13063290D411yescharacteristic
219C4×D172—21no—
220C4×D172C2311yescharacteristic
221D4×Dic43—21no—
222D4×Dic43—22no—
223D4×Dic43—22no—
224D4×Dic43—21no—
225D4×Dic43D411yescharacteristic
226D4×Dic43C2312yes—
227D4×Dic43C2312yes—
228D4×Dic43C2311yescharacteristic
229D4×Dic43C2312yes—
230D4×Dic43C2312yes—
231#13063287—21no—
232#13063287C2311yescharacteristic
233#13063287C2312yes—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—22no—
236C4×C22⋊D43—22no—
237C4×C22⋊D43C2312yes—
238(C22⋊D43)⋊C4—21no—
239(C22⋊D43)⋊C4—22no—
240(C22⋊D43)⋊C4—22no—
241(C22⋊D43)⋊C4D412yes—
242#13063283D411yescharacteristic
243#13063282—21no—
244#13063281D412yes—
245C2×C4⋊Dic43C2312yes—
246C4⋊C4×D43C2311yescharacteristic
247C2×C22⋊Dic43—22no—
248C2×(C2×D43)⋊C4—22no—
249C22⋊C4×D43—21no—
250C22⋊C4×D43—22no—
251C2×C4×Dic43C2312yes—
252C42×D43C2311yescharacteristic
253#13063257C2312yes—
254#13063257C2311yescharacteristic
255#13063256C2312yes—
256#13063256C2311yescharacteristic
257#13063256C2311yescharacteristic
258C4⋊(C43⋊C8)C2311yescharacteristic
259Dic43⋊C8C2312yes—
260Dic43⋊C8C2311yescharacteristic
261Dic43⋊C8C2311yescharacteristic
262Dic43⋊C8C2312yes—
263Dic43⋊C8C2312yes—
264#13063250C2312yes—
265#13063250C2311yescharacteristic
266#13063249C2312yes—
267#13063249C2311yescharacteristic
268#13063248C2311yescharacteristic
269#13063247C2312yes—
270#13063247C2311yescharacteristic
271#13063247C2312yes—
272#13063247C2312yes—
273#13063246C2312yes—
274#13063246C2311yescharacteristic
275#13063246C2312yes—
276#13063246C2312yes—
277#13063246C2312yes—
278#13063245C2312yes—
279#13063245C2311yescharacteristic
280C22⋊(C43⋊C8)C2312yes—
281(C2×D43)⋊C8C2311yescharacteristic
282(C2×D43)⋊C8C2311yescharacteristic
283#13063235C2312yes—
284#13063235C2312yes—
285C4×C43⋊C8C2311yescharacteristic
286C2×#41×C43C2312yes—
287C22×D4×C43—21no—
288C22×D4×C43C2312yes—
289AGL(1,ℤ/8)×C43—44no—
290C2×SD16×C43C2311yescharacteristic
291C2×SD16×C43C2312yes—
292C2×D8×C43C2312yes—
293C2×D8×C43C2312yes—
294C2×D8×C43C2312yes—
295C2×M16×C43C2312yes—
296#127×C43—21no—
297#127×C43C2311yescharacteristic
298#127×C43C2311yescharacteristic
299#121×C43—21no—
300#121×C43—22no—
301#121×C43C2312yes—
302#121×C43C2312yes—
303#120×C43—22no—
304C4×Q8×C43C2311yescharacteristic
305C4×D4×C43—21no—
306C4×D4×C43C2311yescharacteristic
307C4×D4×C43C2311yescharacteristic
308#106×C43C2311yescharacteristic
309C4⋊C8×C43C2311yescharacteristic
310#103×C43C2311yescharacteristic
311#102×C43C2311yescharacteristic
312#102×C43C2312yes—
313#102×C43C2312yes—
314C22⋊C8×C43C2312yes—
315C4×C8×C43C2311yescharacteristic
316C24×C43—22no—
317C23×D43—21no—
318C23×D43—22no—
319#41×C43—42no—
320#41×C43—42no—
321C2×Q8×C43C2411yescharacteristic
322C2×D4×C43—21no—
323C2×D4×C43—22no—
324C2×D4×C43—21no—
325C2×D4×C43—21no—
326C2×D4×C43—21no—
327C2×D4×C43—22no—
328C2×D4×C43—22no—
329C2×D4×C43—22no—
330C2×D4×C43—24no—
331C2×D4×C43—42no—
332C2×D4×C43—44no—
333C2×D4×C43C2×D411yescharacteristic
334C2×D4×C43C2412yes—
335C2×D4×C43C2412yes—
336C2×D4×C43C2411yescharacteristic
337C22×C4×C43—21no—
338C22×C4×C43—22no—
339C22×C4×C43C2412yes—
340C2×C22⋊D43—21no—
341C2×C22⋊D43—22no—
342C2×C22⋊D43—22no—
343C2×C22⋊D43—22no—
344C2×C22⋊D43—22no—
345C2×C22⋊D43—22no—
346C2×C22⋊D43—22no—
347C2×C22⋊D43—22no—
348C2×C22⋊D43—22no—
349C2×C22⋊D43—22no—
350C2×C22⋊D43—48no—
351C2×C22⋊D43C2×D412yes—
352C22×Dic43—21no—
353C22×Dic43—22no—
354C22×Dic43—22no—
355C22×Dic43—22no—
356C22×Dic43—22no—
357C22×Dic43—22no—
358C22×Dic43—48no—
359C22×Dic43C2×D412yes—
360C22×Dic43C2×D412yes—
361#10621900—24no—
362#10621900—44no—
363#10621900—48no—
364#10621900—48no—
365#10621900—44no—
366#10621900—44no—
367#10621900—84no—
368D4×D43—22no—
369D4×D43—41no—
370D4×D43—44no—
371D4×D43—42no—
372D4×D43—42no—
373D4×D43—82no—
374#10621898—42no—
375#10621898—42no—
376C2×D172—21no—
377C2×D172—21no—
378C2×D172C2412yes—
379C2×D172C2411yescharacteristic
380C2×C4×D43—21no—
381C2×C4×D43—21no—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×C4×D43—21no—
385C2×C4×D43—44no—
386C2×C4×D43C2×D411yescharacteristic
387C2×C4×D43C2×D411yescharacteristic
388C2×C4×D43C2411yescharacteristic
389C2×Dic86—21no—
390C2×Dic86—21no—
391C2×Dic86—22no—
392C2×Dic86—44no—
393C2×Dic86C2×D411yescharacteristic
394C2×Dic86C2411yescharacteristic
395SD16×C43—22no—
396SD16×C43—42no—
397D8×C43—24no—
398D8×C43—42no—
399D8×C43—42no—
400M16×C43—42no—
401C2×C8×C43C2411yescharacteristic
402C2×C8×C43C2411yescharacteristic
403C2×C8×C43C2412yes—
404C4⋊C4×C43—21no—
405C4⋊C4×C43C2×D411yescharacteristic
406C4⋊C4×C43C2411yescharacteristic
407C4⋊C4×C43C2411yescharacteristic
408C22⋊C4×C43—22no—
409C22⋊C4×C43—21no—
410C22⋊C4×C43—22no—
411C22⋊C4×C43C2×D412yes—
412C42×C43—21no—
413C42×C43C2411yescharacteristic
414C22⋊Dic43—21no—
415C22⋊Dic43—22no—
416C22⋊Dic43—22no—
417C22⋊Dic43—22no—
418C22⋊Dic43—22no—
419C22⋊Dic43—22no—
420C22⋊Dic43—22no—
421C22⋊Dic43—22no—
422C22⋊Dic43C2×D412yes—
423#10621884—41no—
424#10621883—22no—
425#10621883—42no—
426#10621882—24no—
427#10621882—42no—
428#10621882—42no—
429#10621882—42no—
430(C2×D43)⋊C4—21no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—22no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4C2×D412yes—
440C4⋊Dic43—22no—
441C4⋊Dic43—21no—
442C4⋊Dic43—21no—
443C4⋊Dic43C2×D411yescharacteristic
444C4⋊Dic43C2411yescharacteristic
445C4⋊Dic43C2411yescharacteristic
446C4⋊Dic43C2412yes—
447Dic43⋊C4—21no—
448Dic43⋊C4—21no—
449Dic43⋊C4—21no—
450Dic43⋊C4—21no—
451Dic43⋊C4—22no—
452Dic43⋊C4—21no—
453Dic43⋊C4—21no—
454Dic43⋊C4C2×D412yes—
455Dic43⋊C4C2×D412yes—
456C4×Dic43—21no—
457C4×Dic43C2×D411yescharacteristic
458C4×Dic43C2×D411yescharacteristic
459C4×Dic43C2×D412yes—
460C4×Dic43C2×D412yes—
461C4×Dic43C2412yes—
462C4×Dic43C2411yescharacteristic
463#10621877—42no—
464C2×C43⋊C8C2411yescharacteristic
465C2×C43⋊C8C2411yescharacteristic
466C2×C43⋊C8C2412yes—
467D344—42no—
468#10621873—41no—
469C8×D43—42no—
470C23×C43—21no—
471C23×C43—22no—
472C23×C43—22no—
473C23×C43—44no—
474C23×C43—44no—
475C23×C43—82no—
476C23×C43C22×D412yes—
477C22×D43—22no—
478C22×D43—21no—
479C22×D43—42no—
480C22×D43—42no—
481C22×D43—44no—
482C22×D43—81no—
483C22×D43—82no—
484C22×D43—82no—
485C22×D43C22×D411yescharacteristic
486Q8×C43—21no—
487Q8×C43—21no—
488D4×C43—22no—
489D4×C43—22no—
490D4×C43—22no—
491D4×C43—21no—
492D4×C43—22no—
493D4×C43—22no—
494D4×C43—44no—
495D4×C43—44no—
496D4×C43—42no—
497D4×C43—42no—
498D4×C43—81no—
499D4×C43—81no—
500D4×C43—82no—
501D4×C43—82no—
502D4×C43H(5,𝔽2)12yes—
503C2×C4×C43—22no—
504C2×C4×C43—22no—
505C2×C4×C43—21no—
506C2×C4×C43—21no—
507C2×C4×C43—21no—
508C2×C4×C43—42no—
509C2×C4×C43—82no—
510C2×C4×C43C22×D412yes—
511C2×C4×C43C22×D411yescharacteristic
512C2×C4×C43C22×D411yescharacteristic
513C2×C4×C43C2511yescharacteristic
514C22⋊D43—24no—
515C22⋊D43—42no—
516C22⋊D43—44no—
517C22⋊D43—44no—
518C22⋊D43—44no—
519C22⋊D43—44no—
520C22⋊D43—44no—
521C22⋊D43—82no—
522C22⋊D43—82no—
523C22⋊D43—82no—
524C22⋊D43—82no—
525C2×Dic43—24no—
526C2×Dic43—21no—
527C2×Dic43—21no—
528C2×Dic43—22no—
529C2×Dic43—21no—
530C2×Dic43—42no—
531C2×Dic43—44no—
532C2×Dic43—44no—
533C2×Dic43—44no—
534C2×Dic43—42no—
535C2×Dic43—44no—
536C2×Dic43—82no—
537C2×Dic43C22×D411yescharacteristic
538C2×Dic43C22×D411yescharacteristic
539C2×Dic43C22×D412yes—
540C2×Dic43C22×D412yes—
541C2×Dic43C22×D411yescharacteristic
542D172—21no—
543D172—22no—
544D172—21no—
545D172—22no—
546D172—42no—
547D172—81no—
548C4×D43—21no—
549C4×D43—21no—
550C4×D43—41no—
551C4×D43—42no—
552C4×D43—42no—
553C4×D43—42no—
554C4×D43—82no—
555C4×D43—82no—
556C4×D43AGL(1,ℤ/8)14yescomplemented
557Dic86—22no—
558Dic86—21no—
559Dic86—21no—
560Dic86—44no—
561Dic86—42no—
562Dic86—42no—
563C8×C43—22no—
564C8×C43—21no—
565C8×C43—21no—
566C43⋊C8—22no—
567C43⋊C8—21no—
568C43⋊C8—21no—
569#61961—431nomaximal, Sylow
570C22×C43—22no—
571C22×C43—22no—
572C22×C43—22no—
573C22×C43—22no—
574C22×C43—41no—
575C22×C43—41no—
576C22×C43—42no—
577C22×C43—42no—
578C22×C43—42no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—42no—
582C22×C43—88no—
583C22×C43C23×D411yescharacteristic
584C2×D43—21no—
585C2×D43—21no—
586C2×D43—42no—
587C2×D43—41no—
588C2×D43—41no—
589C2×D43—42no—
590C2×D43—41no—
591C2×D43—42no—
592C2×D43—84no—
593C2×D43—164no—
594C2×D43C2×AGL(1,ℤ/8)12yes—
595C4×C43—21no—
596C4×C43—22no—
597C4×C43—41no—
598C4×C43—41no—
599C4×C43—41no—
600C4×C43C2×AGL(1,ℤ/8)12yes—
601C4×C43C2×H(5,𝔽2)11yescharacteristic
602C4×C43#58511yescharacteristic
603Dic43—21no—
604Dic43—22no—
605Dic43—21no—
606Dic43—22no—
607Dic43—41no—
608Dic43—41no—
609Dic43—42no—
610Dic43—41no—
611Dic43C2×AGL(1,ℤ/8)12yes—
612#3508—431no—
613D4×#41—431no—
614#3399—431no—
615#3399—431no—
616#3373—431no—
617#3373—431no—
618#3332—431no—
619#3332—431no—
620#3306—432no—
621#3306—432no—
622#3274—431no—
623#3274D4311yescharacteristic, complemented
624#3264—432no—
625#3264—432no—
626#3253—432no—
627#3246—431no—
628#3214—432no—
629#3205—431no—
630#3109—432no—
631#3101—431no—
632#3036—432no—
633C2×#459—431no—
634#2989—431no—
635C2×C43—42no—
636C2×C43—42no—
637C2×C43—82no—
638C2×C43—82no—
639C2×C43#348811yescharacteristic
640C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
641C2×C43#358511yescharacteristic
642D43—22no—
643D43—81no—
644D43—82no—
645C22×#41—861no—
646C2×AGL(1,ℤ/8)—432no—
647C2×AGL(1,ℤ/8)C2×D4312yescomplemented
648C22×D8—432no—
649#559—431no—
650#559—431no—
651#559—861no—
652#550—431no—
653#550—431no—
654#550—861no—
655#550C2×D4311yescharacteristic, complemented
656D4×Q8—431no—
657#548—861no—
658#547—432no—
659#547—431no—
660#546—432no—
661#546—432no—
662#546—862no—
663#546—862no—
664#546—861no—
665D42—432no—
666D42C2×D4311yescharacteristic, complemented
667#540—862no—
668#535—861no—
669#533—431no—
670#532—431no—
671#532—432no—
672#532—432no—
673#532—432no—
674C2×#127—431no—
675#525—862no—
676#525—861no—
677#518—861no—
678C4×#41—431no—
679C2×C4×D4—432no—
680C2×C4×D4—431no—
681#496—432no—
682#496—432no—
683#493—431no—
684#493C2×D4311yescharacteristic, complemented
685#489—432no—
686#489—432no—
687#486—431no—
688#486—431no—
689#483—431no—
690#483—431no—
691#481—432no—
692#481—432no—
693#476—431no—
694#476—432no—
695#476—431no—
696#476—432no—
697#476—432no—
698#475—431no—
699#475—431no—
700#469—432no—
701#469—432no—
702#469—432no—
703#469C2×D4312yescomplemented
704#465—432no—
705#465—432no—
706#463—432no—
707#463—432no—
708#463—432no—
709#463—432no—
710#461—431no—
711#461—432no—
712#461—431no—
713#460—431no—
714#460C2×D4311yescharacteristic, complemented
715#459—432no—
716#459—432no—
717#459—432no—
718#459—432no—
719#459—431no—
720#459—431no—
721#459—431no—
722#459—432no—
723#459—432no—
724#459C2×D4311yescharacteristic
725#450—431no—
726#450—431no—
727#449—432no—
728#449—432no—
729#449—432no—
730#449C2×D4312yescomplemented
731#447—432no—
732#447—432no—
733#447—432no—
734#447C2×D4312yescomplemented
735#446—431no—
736#446—431no—
737#442—432no—
738#442—432no—
739#442—432no—
740#442—432no—
741C4×SD16—431no—
742C4×SD16—431no—
743C4×SD16—431no—
744C4×SD16C2×D4311yescharacteristic, complemented
745#436—431no—
746#436C2×D4311yescharacteristic, complemented
747#435—432no—
748#435—432no—
749#432—432no—
750#431—431no—
751#423—432no—
752C2×C4⋊C8—431no—
753#417—432no—
754#417—432no—
755C2×#102—432no—
756C43#6196111yescharacteristic, complemented, Sylow
757C2×#41—431no—
758C2×#41—432no—
759C2×#41—862no—
760C2×#41—861no—
761C2×#41—862no—
762C2×#41—862no—
763C2×#41—861no—
764C2×#41—861no—
765C2×#41—1728no—
766C2×#41C22×D4312yes—
767C22×Q8—861no—
768C22×D4—21no—
769C22×D4—431no—
770C22×D4—432no—
771C22×D4—861no—
772C22×D4—861no—
773C22×D4—862no—
774C22×D4C22×D4312yes—
775C23×C4—861no—
776C23×C4—862no—
777AGL(1,ℤ/8)—44no—
778AGL(1,ℤ/8)—1724no—
779C2×SD16—431no—
780C2×SD16—431no—
781C2×SD16—432no—
782C2×SD16—431no—
783C2×SD16C22×D4311yescharacteristic
784C2×SD16C22×D4312yes—
785C2×D8—432no—
786C2×D8—432no—
787C2×D8—432no—
788C2×D8—432no—
789C2×D8—432no—
790C2×D8—1724no—
791C2×D8C22×D4312yes—
792C2×D8C22×D4312yes—
793C2×D8C22×D4312yes—
794C2×M16—432no—
795C2×M16C22×D4312yes—
796C22×C8—432no—
797C4⋊Q8—431no—
798C4⋊Q8—432no—
799C4⋊Q8—431no—
800C4⋊Q8—431no—
801#127—21no—
802#127—432no—
803#127—432no—
804#127—431no—
805#127—861no—
806#127—861no—
807#127—861no—
808#127C22×D4311yescharacteristic
809#127C22×D4311yescharacteristic
810#125—861no—
811#124—432no—
812#124—432no—
813#124—861no—
814#124—862no—
815#124—862no—
816#124—861no—
817#124—861no—
818#123—862no—
819#123—862no—
820#123—862no—
821#123—862no—
822#123—862no—
823#123—862no—
824#123—862no—
825C22⋊Q8—431no—
826C22⋊Q8—431no—
827C22⋊Q8—862no—
828C22⋊Q8—862no—
829C22⋊Q8—861no—
830C22⋊Q8—861no—
831C22⋊Q8—861no—
832#121—21no—
833#121—22no—
834#121—432no—
835#121—432no—
836#121—432no—
837#121—862no—
838#121—862no—
839#121—862no—
840#121—861no—
841#121—862no—
842#121—862no—
843#121—862no—
844#121—861no—
845#121—862no—
846#121—862no—
847#121—862no—
848#121C22×D4312yes—
849#121C22×D4312yes—
850#120—22no—
851#120—862no—
852#120—862no—
853#120—862no—
854#120—862no—
855C4×Q8—431no—
856C4×Q8—431no—
857C4×Q8—431no—
858C4×Q8—861no—
859C4×Q8C22×D4311yescharacteristic
860C4×D4—21no—
861C4×D4—431no—
862C4×D4—432no—
863C4×D4—432no—
864C4×D4—431no—
865C4×D4—432no—
866C4×D4—432no—
867C4×D4—432no—
868C4×D4—432no—
869C4×D4—431no—
870C4×D4—432no—
871C4×D4—431no—
872C4×D4—861no—
873C4×D4—861no—
874C4×D4—862no—
875C4×D4—862no—
876C4×D4—861no—
877C4×D4—862no—
878C4×D4—862no—
879C4×D4—862no—
880C4×D4—862no—
881C4×D4—861no—
882C4×D4—861no—
883C4×D4—861no—
884C4×D4C22×D4311yescharacteristic
885C4×D4C22×D4311yescharacteristic
886#117—431no—
887#117—432no—
888#117—861no—
889C2×C4⋊C4—432no—
890C2×C4⋊C4—431no—
891C2×C22⋊C4—862no—
892C2×C22⋊C4—861no—
893C2×C22⋊C4—862no—
894C2×C22⋊C4—862no—
895C2×C42—432no—
896C2×C42—431no—
897#106—431no—
898#106—432no—
899#106—431no—
900#106—431no—
901#106—432no—
902#106C22×D4311yescharacteristic
903C4⋊C8—432no—
904C4⋊C8—431no—
905C4⋊C8—432no—
906C4⋊C8—432no—
907C4⋊C8—431no—
908C4⋊C8—431no—
909C4⋊C8C22×D4311yescharacteristic
910#103—431no—
911#103—432no—
912#103—431no—
913#103—432no—
914#103—431no—
915#103C22×D4311yescharacteristic
916#102—432no—
917#102—432no—
918#102—431no—
919#102—432no—
920#102—432no—
921#102—432no—
922#102—432no—
923#102—431no—
924#102—432no—
925#102—432no—
926#102—431no—
927#102C22×D4312yes—
928#102C22×D4311yescharacteristic
929#102C22×D4312yes—
930C22⋊C8—432no—
931C22⋊C8—431no—
932C22⋊C8—431no—
933C22⋊C8C22×D4312yes—
934#97—432no—
935#97—432no—
936C4×C8—431no—
937C4×C8C22×D4311yescharacteristic
938C24—22no—
939C24—862no—
940C24—861no—
941#41—42no—
942#41—42no—
943#41—864no—
944#41—3444no—
945#41—1722no—
946#41—1722no—
947#41—1724no—
948#41—1728no—
949#41—1724no—
950#41—1728no—
951#41—1724no—
952C2×Q8—431no—
953C2×Q8—431no—
954C2×Q8—861no—
955C2×Q8—862no—
956C2×Q8—861no—
957C2×Q8—1724no—
958C2×Q8C23×D4311yescharacteristic
959C2×D4—24no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—21no—
964C2×D4—22no—
965C2×D4—21no—
966C2×D4—21no—
967C2×D4—21no—
968C2×D4—42no—
969C2×D4—44no—
970C2×D4—432no—
971C2×D4—432no—
972C2×D4—431no—
973C2×D4—862no—
974C2×D4—862no—
975C2×D4—861no—
976C2×D4—862no—
977C2×D4—862no—
978C2×D4—862no—
979C2×D4—862no—
980C2×D4—862no—
981C2×D4—862no—
982C2×D4—862no—
983C2×D4—862no—
984C2×D4—861no—
985C2×D4—861no—
986C2×D4—3442no—
987C2×D4—1724no—
988C2×D4—1722no—
989C2×D4—1722no—
990C2×D4—1721no—
991C2×D4—1728no—
992C2×D4D4×D4311yescharacteristic
993C2×D4C23×D4312yes—
994C2×D4C23×D4312yes—
995C2×D4C23×D4311yescharacteristic
996C22×C4—21no—
997C22×C4—22no—
998C22×C4—431no—
999C22×C4—432no—
1000C22×C4—432no—
1001C22×C4—431no—
1002C22×C4—431no—
1003C22×C4—862no—
1004C22×C4—861no—
1005C22×C4—861no—
1006C22×C4—862no—
1007C22×C4—861no—
1008C22×C4—862no—
1009C22×C4—862no—
1010C22×C4—862no—
1011C22×C4—862no—
1012C22×C4—862no—
1013C22×C4—861no—
1014C22×C4—1724no—
1015C22×C4—1728no—
1016C22×C4C23×D4312yes—
1017SD16—22no—
1018SD16—42no—
1019SD16—862no—
1020SD16—1721no—
1021SD16—1722no—
1022SD16—1721no—
1023D8—24no—
1024D8—42no—
1025D8—42no—
1026D8—864no—
1027D8—1722no—
1028D8—1722no—
1029D8—1722no—
1030D8—1722no—
1031M16—42no—
1032M16—1722no—
1033C2×C8—431no—
1034C2×C8—431no—
1035C2×C8—432no—
1036C2×C8—1722no—
1037C2×C8C23×D4311yescharacteristic
1038C2×C8C23×D4311yescharacteristic
1039C2×C8C23×D4312yes—
1040C4⋊C4—21no—
1041C4⋊C4—431no—
1042C4⋊C4—432no—
1043C4⋊C4—432no—
1044C4⋊C4—431no—
1045C4⋊C4—432no—
1046C4⋊C4—431no—
1047C4⋊C4—861no—
1048C4⋊C4—861no—
1049C4⋊C4—861no—
1050C4⋊C4—861no—
1051C4⋊C4—862no—
1052C4⋊C4—861no—
1053C4⋊C4—861no—
1054C4⋊C4—862no—
1055C4⋊C4—861no—
1056C4⋊C4—861no—
1057C4⋊C4D4×D4311yescharacteristic
1058C4⋊C4C23×D4311yescharacteristic
1059C4⋊C4C23×D4311yescharacteristic
1060C22⋊C4—22no—
1061C22⋊C4—21no—
1062C22⋊C4—22no—
1063C22⋊C4—432no—
1064C22⋊C4—432no—
1065C22⋊C4—861no—
1066C22⋊C4—862no—
1067C22⋊C4—862no—
1068C22⋊C4—862no—
1069C22⋊C4—861no—
1070C22⋊C4—861no—
1071C22⋊C4—861no—
1072C22⋊C4—862no—
1073C22⋊C4—862no—
1074C22⋊C4—862no—
1075C22⋊C4—862no—
1076C22⋊C4—862no—
1077C22⋊C4—862no—
1078C22⋊C4—862no—
1079C22⋊C4—861no—
1080C22⋊C4—862no—
1081C22⋊C4—862no—
1082C22⋊C4D4×D4312yes—
1083C42—21no—
1084C42—432no—
1085C42—431no—
1086C42—432no—
1087C42—431no—
1088C42—432no—
1089C42—431no—
1090C42—861no—
1091C42C23×D4311yescharacteristic
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—44no—
1096C23—44no—
1097C23—82no—
1098C23—431no—
1099C23—861no—
1100C23—862no—
1101C23—3441no—
1102C23—3442no—
1103C23—3442no—
1104C23—1722no—
1105C23—1722no—
1106C23—1724no—
1107C23C2×D4×D4312yes—
1108Q8—21no—
1109Q8—21no—
1110Q8—862no—
1111Q8—861no—
1112Q8—861no—
1113Q8—1724no—
1114Q8—1722no—
1115Q8—1722no—
1116D4—22no—
1117D4—22no—
1118D4—22no—
1119D4—21no—
1120D4—22no—
1121D4—22no—
1122D4—44no—
1123D4—44no—
1124D4—42no—
1125D4—42no—
1126D4—81no—
1127D4—81no—
1128D4—82no—
1129D4—82no—
1130D4—864no—
1131D4—862no—
1132D4—861no—
1133D4—862no—
1134D4—861no—
1135D4—3441no—
1136D4—3442no—
1137D4—3442no—
1138D4—3442no—
1139D4—3442no—
1140D4—1724no—
1141D4—1722no—
1142D4—1724no—
1143D4—1724no—
1144D4—1724no—
1145D4—1724no—
1146D4—1722no—
1147D4#1306337012yes—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—42no—
1154C2×C4—82no—
1155C2×C4—431no—
1156C2×C4—434no—
1157C2×C4—431no—
1158C2×C4—432no—
1159C2×C4—431no—
1160C2×C4—432no—
1161C2×C4—864no—
1162C2×C4—861no—
1163C2×C4—861no—
1164C2×C4—861no—
1165C2×C4—861no—
1166C2×C4—861no—
1167C2×C4—862no—
1168C2×C4—3442no—
1169C2×C4—3442no—
1170C2×C4—3442no—
1171C2×C4—1721no—
1172C2×C4—1722no—
1173C2×C4—1722no—
1174C2×C4—1722no—
1175C2×C4—1724no—
1176C2×C4—1722no—
1177C2×C4—1724no—
1178C2×C4—1724no—
1179C2×C4—1724no—
1180C2×C4—1722no—
1181C2×C4C2×D4×D4312yes—
1182C2×C4C2×D4×D4311yescharacteristic
1183C2×C4C2×D4×D4311yescharacteristic
1184C2×C4C24×D4311yescharacteristic
1185C8—22no—
1186C8—21no—
1187C8—21no—
1188C8—862no—
1189C8—861no—
1190C8—861no—
1191C22—22no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—41no—
1196C22—41no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—88no—
1204C22—432no—
1205C22—861no—
1206C22—861no—
1207C22—3444no—
1208C22—1721no—
1209C22—1722no—
1210C22—1722no—
1211C22—1721no—
1212C22—1722no—
1213C22—1721no—
1214C22—6884no—
1215C22C22×D4×D4311yescharacteristic
1216C4—21no—
1217C4—22no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—432no—
1222C4—862no—
1223C4—862no—
1224C4—861no—
1225C4—861no—
1226C4—1721no—
1227C4—1722no—
1228C4—1721no—
1229C4—1721no—
1230C4AGL(1,ℤ/8)×D4312yes—
1231C4C2×#1306337011yescharacteristic
1232C4#1458373411yescharacteristic
1233C2—42no—
1234C2—42no—
1235C2—82no—
1236C2—82no—
1237C2—862no—
1238C2—3441no—
1239C2—3442no—
1240C2#1914825511yescharacteristic
1241C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1242C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3274C2
socleC22×C43C23×D4
hypercenter#3274D43
hypocenterC43#61961
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #19148465C2semidirect
2. D4×#10621900C2semidirect
3. #19147642C2semidirect
4. #19147636C2semidirect
5. #19147391C2semidirect
6. #19147385C2semidirect
7. #19146923C2semidirect
8. #19146922C2semidirect
9. #19146551C2semidirect
10. #19146549C2semidirect
11. #19146211C2semidirect
12. #19146073C2semidirect
13. #19146069C2semidirect
14. #19145972C2semidirect
15. #19145909C2semidirect
16. #19145587C2semidirect
17. #19145509C2semidirect
18. #19144681C2semidirect
19. #19144601C2semidirect
20. #19144056C2semidirect
21. #459×D43C2semidirect
22. #19143710C2semidirect
23. C43×#3274C2semidirect
25. C2×#13063351C22semidirect
27. #14583635C22semidirect
28. #14583634C22semidirect
30. #14583570C22semidirect
32. #14583569C22semidirect
33. D4×Dic86C22semidirect
35. #14583553C22semidirect
37. #14583546C22semidirect
40. #14583537C22semidirect
45. #14583453C22semidirect
47. #14583445C22semidirect
48. #14583444C22semidirect
49. #14583444C22semidirect
50. #127×D43C22semidirect
55. C2×D4×Dic43C22semidirect
57. #14583287C22semidirect
58. #14583285C22semidirect
59. #14583275C22semidirect
60. #14583260C22semidirect
61. #14583257C22semidirect
62. #14583246C22semidirect
63. #14583245C22semidirect
64. #14583231C22semidirect
65. #14583228C22semidirect
66. #14583218C22semidirect
67. #14583215C22semidirect
68. #14583188C22semidirect
69. #14583188C22semidirect
70. #14583187C22semidirect
71. #14583187C22semidirect
72. #14583187C22semidirect
73. #14583185C22semidirect
74. #14583184C22semidirect
75. #14583152C22semidirect
76. #14583150C22semidirect
77. #14583150C22semidirect
78. #14583127C22semidirect
79. #14583125C22semidirect
80. #14583116C22semidirect
81. #14583116C22semidirect
82. #14583112C22semidirect
83. #14583112C22semidirect
84. #14583103C22semidirect
85. #14583102C22semidirect
86. #14583102C22semidirect
87. #14583096C22semidirect
88. #14583095C22semidirect
90. #14583093C22semidirect
91. #14583093C22semidirect
93. #14583092C22semidirect
94. #14583092C22semidirect
95. #14583092C22semidirect
96. #14583091C22semidirect
99. #14583046C22semidirect
100. #14583044C22semidirect
101. #14583042C22semidirect
102. #14583033C22semidirect
103. #14583031C22semidirect
104. #14583031C22semidirect
105. #14583029C22semidirect
106. #14583026C22semidirect
107. #14583011C22semidirect
108. #14583011C22semidirect
109. #14583008C22semidirect
110. #14583008C22semidirect
111. C4×#10621873C22semidirect
112. C4×#10621884C22semidirect
113. C4×#10621883C22semidirect
114. #14582977C22semidirect
115. #14582973C22semidirect
116. #14582968C22semidirect
117. #14582953C22semidirect
118. #14582950C22semidirect
119. #14582922C22semidirect
120. C4⋊C8×D43C22semidirect
121. #14582901C22semidirect
122. #14582900C22semidirect
123. #102×D43C22semidirect
124. C2×AGL(1,ℤ/8)×C43C22semidirect
125. C43×#550C22semidirect
126. D42×C43C22semidirect
127. C43×#493C22semidirect
128. C43×#469C22semidirect
129. C43×#460C22semidirect
131. C43×#449C22semidirect
132. C43×#447C22semidirect
133. C4×SD16×C43C22semidirect
134. C43×#436C22semidirect
556. C4×D43AGL(1,ℤ/8)semidirect
623. #3274D43semidirect
647. C2×AGL(1,ℤ/8)C2×D43semidirect
655. #550C2×D43semidirect
666. D42C2×D43semidirect
684. #493C2×D43semidirect
703. #469C2×D43semidirect
714. #460C2×D43semidirect
730. #449C2×D43semidirect
734. #447C2×D43semidirect
744. C4×SD16C2×D43semidirect
746. #436C2×D43semidirect
756. C43#61961semidirect

Maximal subgroups

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

subgroupindex
#191484652
D4×#106219002
#191476422
#191476362
#191473912
#191473852
#191469232
#191469222
#191465512
#191465492
#191462112
#191460732
#191460692
#191459722
#191459092
#191455872
#191455092
#191446812
#191446012
#191440562
#459×D432
#191437102
C43×#32742
#6196143