Finite Group Databasebeta

← #25988947

Subgroups — #25988947

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#19148468C211yesmaximal, characteristic, complemented
2#19148085C211yesmaximal, characteristic, complemented
3#19147637C211yesmaximal, characteristic, complemented
4#19147389C211yesmaximal, characteristic, complemented
5#19147383C211yesmaximal, characteristic, complemented
6#19146925C211yesmaximal, characteristic, complemented
7#19146924C211yesmaximal, characteristic, complemented
8#19146563C212yesmaximal, complemented
9#19146561C212yesmaximal, complemented
10#19146214C211yesmaximal, characteristic, complemented
11#19146210C211yesmaximal, characteristic, complemented
12#19146074C212yesmaximal, complemented
13#19146070C212yesmaximal, complemented
14#19145974C212yesmaximal, complemented
15#19145909C211yesmaximal, characteristic, complemented
16#19145585C212yesmaximal, complemented
17#19145509C211yesmaximal, characteristic, complemented
18#19144684C212yesmaximal, complemented
19#19144601C211yesmaximal, characteristic, complemented
20#19144057C212yesmaximal, complemented
21#459×D43C211yesmaximal, characteristic, complemented
22#19143711C211yesmaximal, characteristic, complemented
23C43×#3399C211yesmaximal, characteristic, complemented
24C2×#41×D43—21no—
25C2×#13063352C2212yescomplemented
26C2×#13063349C2212yescomplemented
27C2×D8×D43C2212yes—
28#14583634C2211yescharacteristic, complemented
29#14583631—21no—
30#14583571C2211yescharacteristic, complemented
31#14583570—21no—
32#14583569C2211yescharacteristic, complemented
33Q8×D172C2211yescharacteristic, complemented
34#14583556—21no—
35#14583554C2212yes—
36#14583554C2211yescharacteristic, complemented
37#14583546—22no—
38#14583546—21no—
39#14583544C2212yescomplemented
40#14583542C2212yescomplemented
41#14583541—22no—
42#14583534C2212yes—
43#14583534C2211yescharacteristic, complemented
44#14583501—22no—
45#14583467—21no—
46#14583453C2211yescharacteristic, complemented
47#14583448C2212yescomplemented
48#14583447C2211yescharacteristic
49#14583447C2212yescomplemented
50#14583446C2212yescomplemented
51#127×D43C2211yescharacteristic, complemented
52#14583409—21no—
53#14583409—22no—
54#14583371—21no—
55C4×#10621902C2211yescharacteristic
56C4×D4×D43C2211yescharacteristic
57C4×D4×D43C2212yescomplemented
58#14583286C2212yescomplemented
59#14583275C2211yescharacteristic, complemented
60#14583259C2212yescomplemented
61#14583258C2212yescomplemented
62#14583246C2211yescharacteristic, complemented
63#14583245C2211yescharacteristic, complemented
64#14583231C2211yescharacteristic, complemented
65#14583228C2211yescharacteristic, complemented
66#14583219C2212yescomplemented
67#14583216C2212yescomplemented
68#14583190C2212yescomplemented
69#14583189C2212yescomplemented
70#14583188C2211yescharacteristic, complemented
71#14583187C2211yescharacteristic, complemented
72#14583187C2212yescomplemented
73#14583185C2211yescharacteristic, complemented
74#14583184C2211yescharacteristic, complemented
75#14583151C2212yescomplemented
76#14583151C2212yescomplemented
77#14583149C2212yescomplemented
78#14583149C2212yescomplemented
79#14583127C2212yescomplemented
80#14583125C2212yescomplemented
81#14583115C2212yescomplemented
82#14583114C2212yescomplemented
83#14583111C2212yescomplemented
84#14583103C2211yescharacteristic, complemented
85#14583102C2211yescharacteristic, complemented
86#14583102C2212yescomplemented
87#14583096C2211yescharacteristic, complemented
88#14583095C2211yescharacteristic
89#14583094C2211yescharacteristic, complemented
90#14583093C2212yes—
91#14583092C2212yescomplemented
92#14583092C2212yescomplemented
93#14583092C2212yescomplemented
94#14583091C2211yescharacteristic
95#14583091C2212yescomplemented
96#14583051C2211yescharacteristic
97#14583048C2211yescharacteristic
98#14583043C2212yescomplemented
99#14583043C2212yescomplemented
100#14583041C2212yescomplemented
101#14583041C2212yescomplemented
102#14583034C2212yescomplemented
103#14583031C2212yescomplemented
104#14583031C2212yescomplemented
105#14583031C2212yescomplemented
106#14583030C2211yescharacteristic, complemented
107#14583012C2212yescomplemented
108#14583009C2212yescomplemented
109#14583009C2212yescomplemented
110C4×#10621873C2211yescharacteristic, complemented
111C4×#10621884C2211yescharacteristic, complemented
112C4×#10621883C2211yescharacteristic, complemented
113#14582978C2211yescharacteristic, complemented
114#14582976C2211yescharacteristic, complemented
115#14582972C2212yescomplemented
116#14582969C2212yescomplemented
117#14582954C2212yescomplemented
118#14582950C2211yescharacteristic, complemented
119#14582921C2212yescomplemented
120C4⋊C8×D43C2211yescharacteristic, complemented
121#14582899C2212yescomplemented
122#14582897C2212yescomplemented
123#102×D43C2212yescomplemented
124C43×#559C2211yescharacteristic, complemented
125C43×#550C2211yescharacteristic, complemented
126C43×#496C2212yescomplemented
127C43×#493C2211yescharacteristic, complemented
128C43×#463C2212yescomplemented
129C43×#460C2211yescharacteristic, complemented
130C43×#459C2211yescharacteristic, complemented
131C43×#459C2212yescomplemented
132C43×#446C2211yescharacteristic, complemented
133C43×#442C2212yescomplemented
134C4×SD16×C43C2211yescharacteristic, complemented
135C2×#10621902D411yescharacteristic
136C2×#10621902C2312yes—
137C2×#10621898—22no—
138C2×#10621898—21no—
139C2×#10621898—22no—
140C2×#10621900—21no—
141C2×#10621900—22no—
142C2×#10621900C2312yes—
143#41×D43—48no—
144C2×Q8×D43—21no—
145C2×D4×D43—22no—
146C2×D4×D43—21no—
147C2×D4×D43—21no—
148C2×D4×D43—21no—
149C2×D4×D43C2311yescharacteristic
150C2×D4×D43C2312yes—
151C2×D4×D43C2312yes—
152C22×C4×D43—21no—
153C22×C4×D43—22no—
154#13063352—44no—
155#13063349—44no—
156C2×#10621873C2311yescharacteristic
157C2×#10621883C2311yescharacteristic
158C2×#10621883C2312yes—
159C2×#10621884C2311yescharacteristic
160C2×D344C2312yes—
161C2×#10621882C2312yes—
162C2×#10621882C2312yes—
163C2×#10621882C2312yes—
164C2×#10621882C2312yes—
165D8×D43—44no—
166C2×#10621872C2312yes—
167C2×#10621872C2312yes—
168C2×C8×D43C2312yes—
169#13063325C2312yes—
170#13063325C2311yescharacteristic
171#13063324C2311yescharacteristic
172#13063323C2311yescharacteristic
173#13063322—21no—
174#13063322C2311yescharacteristic
175#13063321—21no—
176#13063321—21no—
177#13063321—21no—
178#13063321C2312yes—
179#13063315—21no—
180#13063314—21no—
181#13063313C2312yes—
182#13063312—21no—
183#13063312—22no—
184#13063311—22no—
185#13063310—22no—
186#13063309—22no—
187#13063307—22no—
188#13063307—22no—
189#13063307—22no—
190#13063307—22no—
191#13063305—21no—
192#13063305—22no—
193#13063305C2311yescharacteristic
194#13063304—22no—
195#13063304—21no—
196#13063303—21no—
197#13063301C2311yescharacteristic
198#13063300—22no—
199#13063300C2312yes—
200#13063299—22no—
201#13063298—22no—
202#13063298—22no—
203#13063298—22no—
204#13063298—22no—
205#13063297—22no—
206#13063296—21no—
207#13063296—22no—
208#13063296—22no—
209#13063296—21no—
210#13063296C2312yes—
211#13063296C2312yes—
212#13063296C2312yes—
213#13063296C2312yes—
214#13063295—22no—
215#13063295—22no—
216#13063293—22no—
217#13063293—22no—
218#13063293—22no—
219Q8×Dic43D411yescharacteristic
220C4×Dic86—21no—
221C4×Dic86C2311yescharacteristic
222C4×D172—21no—
223C4×D172C2312yes—
224C4×D172C2311yescharacteristic
225C4×D172C2311yescharacteristic
226C4×D172C2312yes—
227C4×D172C2312yes—
228D4×Dic43—21no—
229D4×Dic43—21no—
230D4×Dic43—22no—
231D4×Dic43C2311yescharacteristic
232D4×Dic43C2312yes—
233#13063287—21no—
234#13063287D411yescharacteristic
235#13063287D412yes—
236#13063287C2311yescharacteristic
237C4×C22⋊D43—21no—
238C4×C22⋊D43—22no—
239C4×C22⋊D43—22no—
240(C22⋊D43)⋊C4—21no—
241(C22⋊D43)⋊C4—22no—
242(C22⋊D43)⋊C4—22no—
243(C22⋊D43)⋊C4—22no—
244#13063283D411yescharacteristic
245#13063283D412yes—
246#13063282—21no—
247C4⋊C4×D43C2311yescharacteristic
248C4⋊C4×D43C2312yes—
249C2×(C2×D43)⋊C4—22no—
250C22⋊C4×D43—21no—
251C22⋊C4×D43—22no—
252C22⋊C4×D43—22no—
253C42×D43C2311yescharacteristic
254C42×D43C2312yes—
255#13063257C2312yes—
256#13063257C2311yescharacteristic
257#13063256C2312yes—
258#13063256C2311yescharacteristic
259#13063256C2311yescharacteristic
260C4⋊(C43⋊C8)C2311yescharacteristic
261C4⋊(C43⋊C8)C2312yes—
262Dic43⋊C8C2311yescharacteristic
263Dic43⋊C8C2311yescharacteristic
264Dic43⋊C8C2312yes—
265#13063250C2311yescharacteristic
266#13063250C2312yes—
267#13063249C2311yescharacteristic
268#13063249C2312yes—
269#13063248C2311yescharacteristic
270#13063247C2312yes—
271#13063247C2312yes—
272#13063247C2311yescharacteristic
273#13063247C2312yes—
274#13063246C2312yes—
275#13063246C2312yes—
276#13063246C2311yescharacteristic
277#13063246C2312yes—
278#13063246C2312yes—
279#13063245C2311yescharacteristic
280#13063245C2312yes—
281(C2×D43)⋊C8C2312yes—
282(C2×D43)⋊C8C2312yes—
283(C2×D43)⋊C8C2311yescharacteristic
284(C2×D43)⋊C8C2311yescharacteristic
285#13063236C2312yes—
286C4×C43⋊C8C2311yescharacteristic
287C2×#41×C43—21no—
288C2×SD16×C43C2311yescharacteristic
289C2×SD16×C43C2312yes—
290C2×D8×C43C2312yes—
291C2×D8×C43C2312yes—
292C2×D8×C43C2312yes—
293#127×C43C2311yescharacteristic
294#127×C43C2312yes—
295#127×C43C2311yescharacteristic
296#124×C43—21no—
297#124×C43C2312yes—
298#123×C43—22no—
299#121×C43—21no—
300#121×C43—22no—
301C4×Q8×C43C2311yescharacteristic
302C4×Q8×C43C2311yescharacteristic
303C4×D4×C43—21no—
304C4×D4×C43C2312yes—
305C4×D4×C43C2311yescharacteristic
306C4×D4×C43C2312yes—
307#106×C43C2311yescharacteristic
308C4⋊C8×C43C2311yescharacteristic
309C4⋊C8×C43C2312yes—
310#103×C43C2311yescharacteristic
311#102×C43C2311yescharacteristic
312#102×C43C2312yes—
313#102×C43C2312yes—
314#97×C43C2312yes—
315C4×C8×C43C2311yescharacteristic
316C23×D43—22no—
317C23×D43—21no—
318C23×D43—22no—
319#41×C43—44no—
320C2×Q8×C43C2×D411yescharacteristic
321C2×Q8×C43C2411yescharacteristic
322C2×D4×C43—21no—
323C2×D4×C43—22no—
324C2×D4×C43—21no—
325C2×D4×C43—21no—
326C2×D4×C43—22no—
327C2×D4×C43—21no—
328C2×D4×C43C2412yes—
329C2×D4×C43C2411yescharacteristic
330C2×D4×C43C2412yes—
331C22×C4×C43—22no—
332C22×C4×C43—21no—
333C22×C4×C43—22no—
334C2×C22⋊D43—21no—
335C2×C22⋊D43—22no—
336C2×C22⋊D43—22no—
337C2×C22⋊D43—22no—
338C2×C22⋊D43—22no—
339C2×C22⋊D43—22no—
340C2×C22⋊D43—22no—
341C2×C22⋊D43—22no—
342C2×C22⋊D43—22no—
343C2×C22⋊D43—22no—
344C22×Dic43—21no—
345C22×Dic43—22no—
346C22×Dic43—22no—
347#10621902—24no—
348#10621902—42no—
349#10621902—42no—
350Q8×D43—44no—
351#10621900—42no—
352#10621900—42no—
353#10621900—48no—
354#10621900—44no—
355D4×D43—22no—
356D4×D43—24no—
357D4×D43—41no—
358D4×D43—42no—
359D4×D43—44no—
360D4×D43—48no—
361D4×D43—44no—
362D4×D43—42no—
363D4×D43—42no—
364D4×D43—82no—
365#10621898—48no—
366#10621898—44no—
367#10621898—84no—
368C2×D172—21no—
369C2×D172—21no—
370C2×D172—22no—
371C2×D172—22no—
372C2×D172C2×D412yes—
373C2×D172C2×D411yescharacteristic
374C2×D172C2412yes—
375C2×D172C2411yescharacteristic
376C2×C4×D43—22no—
377C2×C4×D43—21no—
378C2×C4×D43—21no—
379C2×C4×D43—22no—
380C2×C4×D43—22no—
381C2×C4×D43—22no—
382C2×C4×D43—21no—
383C2×C4×D43—48no—
384C2×C4×D43—44no—
385C2×C4×D43C2×D412yes—
386C2×C4×D43C2×D412yes—
387C2×C4×D43C2×D411yescharacteristic
388C2×C4×D43C2×D411yescharacteristic
389C2×C4×D43C2412yes—
390C2×C4×D43C2411yescharacteristic
391C2×Dic86—22no—
392C2×Dic86—21no—
393C2×Dic86—21no—
394C2×Dic86C2411yescharacteristic
395SD16×C43—41no—
396SD16×C43—42no—
397D8×C43—42no—
398D8×C43—42no—
399D8×C43—42no—
400C2×C8×C43C2411yescharacteristic
401C2×C8×C43C2411yescharacteristic
402C2×C8×C43C2412yes—
403C4⋊C4×C43—21no—
404C4⋊C4×C43C2×D411yescharacteristic
405C4⋊C4×C43C2×D412yes—
406C4⋊C4×C43C2411yescharacteristic
407C4⋊C4×C43C2411yescharacteristic
408C22⋊C4×C43—22no—
409C22⋊C4×C43—21no—
410C22⋊C4×C43—22no—
411C22⋊C4×C43—22no—
412C22⋊C4×C43—22no—
413C42×C43—21no—
414C42×C43C2411yescharacteristic
415C42×C43C2412yes—
416C22⋊Dic43—22no—
417C22⋊Dic43—21no—
418C22⋊Dic43—22no—
419C22⋊Dic43—22no—
420C22⋊Dic43—22no—
421C22⋊Dic43—22no—
422#10621884—22no—
423#10621883—41no—
424#10621883—42no—
425#10621882—24no—
426#10621882—42no—
427#10621882—42no—
428#10621882—42no—
429(C2×D43)⋊C4—21no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—22no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4—21no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4C2×D412yes—
439(C2×D43)⋊C4C2×D412yes—
440(C2×D43)⋊C4C2×D412yes—
441C4⋊Dic43—21no—
442C4⋊Dic43—22no—
443C4⋊Dic43—21no—
444C4⋊Dic43C2×D411yescharacteristic
445C4⋊Dic43C2×D412yes—
446C4⋊Dic43C2411yescharacteristic
447C4⋊Dic43C2411yescharacteristic
448C4⋊Dic43C2412yes—
449Dic43⋊C4—21no—
450Dic43⋊C4—21no—
451Dic43⋊C4—22no—
452Dic43⋊C4—21no—
453Dic43⋊C4—21no—
454Dic43⋊C4—21no—
455Dic43⋊C4—21no—
456C4×Dic43—21no—
457C4×Dic43C2×D412yes—
458C4×Dic43C2×D411yescharacteristic
459C4×Dic43C2×D412yes—
460C4×Dic43C2×D411yescharacteristic
461C4×Dic43C2411yescharacteristic
462C2×C43⋊C8C2411yescharacteristic
463C2×C43⋊C8C2411yescharacteristic
464C2×C43⋊C8C2412yes—
465D344—24no—
466#10621873—22no—
467#10621872—42no—
468#10621872—42no—
469C8×D43—42no—
470C23×C43—21no—
471C23×C43—22no—
472C23×C43—22no—
473C22×D43—21no—
474C22×D43—22no—
475C22×D43—42no—
476C22×D43—44no—
477C22×D43—44no—
478C22×D43—42no—
479C22×D43—44no—
480C22×D43—81no—
481C22×D43—82no—
482C22×D43—82no—
483C22×D43—82no—
484C22×D43C22×D412yes—
485C22×D43C22×D411yescharacteristic
486Q8×C43—22no—
487Q8×C43—21no—
488Q8×C43—21no—
489D4×C43—22no—
490D4×C43—21no—
491D4×C43—22no—
492D4×C43—22no—
493D4×C43—21no—
494D4×C43—22no—
495D4×C43—44no—
496D4×C43—42no—
497D4×C43—42no—
498D4×C43—81no—
499D4×C43—82no—
500D4×C43—81no—
501C2×C4×C43—21no—
502C2×C4×C43—21no—
503C2×C4×C43—21no—
504C2×C4×C43—44no—
505C2×C4×C43—42no—
506C2×C4×C43—82no—
507C2×C4×C43C22×D411yescharacteristic
508C2×C4×C43C22×D412yes—
509C2×C4×C43C22×D412yes—
510C2×C4×C43C22×D411yescharacteristic
511C2×C4×C43C2511yescharacteristic
512C22⋊D43—44no—
513C22⋊D43—42no—
514C22⋊D43—44no—
515C22⋊D43—44no—
516C22⋊D43—44no—
517C22⋊D43—44no—
518C22⋊D43—44no—
519C22⋊D43—82no—
520C22⋊D43—82no—
521C22⋊D43—82no—
522C2×Dic43—21no—
523C2×Dic43—21no—
524C2×Dic43—21no—
525C2×Dic43—22no—
526C2×Dic43—44no—
527C2×Dic43—42no—
528C2×Dic43—82no—
529C2×Dic43C22×D411yescharacteristic
530C2×Dic43C22×D411yescharacteristic
531C2×Dic43C22×D412yes—
532C2×Dic43C22×D411yescharacteristic
533D172—24no—
534D172—22no—
535D172—22no—
536D172—21no—
537D172—22no—
538D172—42no—
539D172—81no—
540D172—82no—
541D172—82no—
542D172H(5,𝔽2)12yes—
543C4×D43—21no—
544C4×D43—22no—
545C4×D43—21no—
546C4×D43—22no—
547C4×D43—24no—
548C4×D43—42no—
549C4×D43—41no—
550C4×D43—44no—
551C4×D43—44no—
552C4×D43—42no—
553C4×D43—42no—
554C4×D43—42no—
555C4×D43—82no—
556C4×D43—82no—
557C4×D43AGL(1,ℤ/8)14yescomplemented
558Dic86—21no—
559Dic86—21no—
560Dic86—42no—
561Dic86—44no—
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—42no—
571C22×C43—41no—
572C22×C43—42no—
573C22×C43—41no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—42no—
577C22×C43—41no—
578C22×C43—42no—
579C22×C43C23×D411yescharacteristic
580C2×D43—21no—
581C2×D43—21no—
582C2×D43—22no—
583C2×D43—22no—
584C2×D43—22no—
585C2×D43—22no—
586C2×D43—41no—
587C2×D43—41no—
588C2×D43—42no—
589C2×D43—42no—
590C2×D43—42no—
591C2×D43—84no—
592C2×D43—88no—
593C2×D43—164no—
594C2×D43C2×AGL(1,ℤ/8)12yes—
595C4×C43—22no—
596C4×C43—21no—
597C4×C43—22no—
598C4×C43—41no—
599C4×C43—41no—
600C4×C43—41no—
601C4×C43C2×AGL(1,ℤ/8)12yes—
602C4×C43C2×H(5,𝔽2)11yescharacteristic
603C4×C43#58511yescharacteristic
604Dic43—21no—
605Dic43—22no—
606Dic43—21no—
607Dic43—41no—
608Dic43—41no—
609Dic43—41no—
610Dic43—42no—
611Dic43C2×AGL(1,ℤ/8)12yes—
612#3508—431no—
613D4×#41—431no—
614#3399—431no—
615#3399D4311yescharacteristic, complemented
616#3373—431no—
617#3373—431no—
618#3332—431no—
619#3332—431no—
620#3306—432no—
621#3306—432no—
622#3274—431no—
623#3274—431no—
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—81no—
636C2×C43—82no—
637C2×C43—82no—
638C2×C43#348811yescharacteristic
639C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
640C2×C43#358511yescharacteristic
641D43—22no—
642D43—42no—
643D43—42no—
644D43—82no—
645C22×#41—861no—
646C2×AGL(1,ℤ/8)—432no—
647C2×AGL(1,ℤ/8)—432no—
648C22×D8—432no—
649#559—431no—
650#559—861no—
651#559C2×D4311yescharacteristic, complemented
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—861no—
664#546—862no—
665D42—432no—
666D42—431no—
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—861no—
676#525—862no—
677#518—861no—
678C4×#41—431no—
679C2×C4×D4—431no—
680C2×C4×D4—432no—
681#496—432no—
682#496C2×D4312yescomplemented
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—432no—
694#476—431no—
695#476—432no—
696#476—431no—
697#476—432no—
698#475—431no—
699#475—431no—
700#469—432no—
701#469—432no—
702#469—432no—
703#469—432no—
704#465—432no—
705#465—432no—
706#463—432no—
707#463—432no—
708#463—432no—
709#463C2×D4312yescomplemented
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—431no—
719#459—432no—
720#459—431no—
721#459—431no—
722#459—432no—
723#459C2×D4311yescharacteristic, complemented
724#459C2×D4312yescomplemented
725#450—431no—
726#450—431no—
727#449—432no—
728#449—432no—
729#449—432no—
730#449—432no—
731#447—432no—
732#447—432no—
733#447—432no—
734#447—432no—
735#446—431no—
736#446C2×D4311yescharacteristic, complemented
737#442—432no—
738#442—432no—
739#442—432no—
740#442C2×D4312yescomplemented
741C4×SD16—431no—
742C4×SD16—431no—
743C4×SD16—431no—
744C4×SD16C2×D4311yescharacteristic, complemented
745#436—431no—
746#436—431no—
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—21no—
758C2×#41—431no—
759C2×#41—432no—
760C2×#41—432no—
761C2×#41—862no—
762C2×#41—862no—
763C2×#41—861no—
764C2×#41—861no—
765C2×#41—862no—
766C2×#41—1728no—
767C22×Q8—861no—
768C22×D4—431no—
769C22×D4—432no—
770C22×D4—432no—
771C22×D4—861no—
772C22×D4—861no—
773C22×D4—862no—
774C22×D4—861no—
775C23×C4—861no—
776C23×C4—862no—
777AGL(1,ℤ/8)—1724no—
778AGL(1,ℤ/8)—1724no—
779C2×SD16—431no—
780C2×SD16—432no—
781C2×SD16—431no—
782C2×SD16—431no—
783C2×SD16C22×D4312yes—
784C2×SD16C22×D4311yescharacteristic
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×M16—432no—
796C22×C8—432no—
797C4⋊Q8—431no—
798C4⋊Q8—431no—
799C4⋊Q8—431no—
800C4⋊Q8—432no—
801#127—432no—
802#127—431no—
803#127—861no—
804#127—861no—
805#127—861no—
806#127—861no—
807#127C22×D4311yescharacteristic
808#127C22×D4312yes—
809#127C22×D4311yescharacteristic
810#125—861no—
811#124—21no—
812#124—432no—
813#124—862no—
814#124—862no—
815#124—861no—
816#124—861no—
817#124C22×D4312yes—
818#123—22no—
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—861no—
828C22⋊Q8—861no—
829C22⋊Q8—862no—
830C22⋊Q8—861no—
831C22⋊Q8—862no—
832#121—21no—
833#121—22no—
834#121—432no—
835#121—432no—
836#121—432no—
837#121—432no—
838#121—432no—
839#121—862no—
840#121—862no—
841#121—862no—
842#121—862no—
843#121—862no—
844#121—862no—
845#121—862no—
846#121—861no—
847#121—862no—
848#121—862no—
849#121—861no—
850#120—862no—
851#120—862no—
852#120—862no—
853#120—862no—
854#120—862no—
855C4×Q8—431no—
856C4×Q8—431no—
857C4×Q8—861no—
858C4×Q8C22×D4311yescharacteristic
859C4×Q8C22×D4311yescharacteristic
860C4×D4—21no—
861C4×D4—432no—
862C4×D4—431no—
863C4×D4—431no—
864C4×D4—432no—
865C4×D4—431no—
866C4×D4—432no—
867C4×D4—431no—
868C4×D4—431no—
869C4×D4—432no—
870C4×D4—432no—
871C4×D4—861no—
872C4×D4—862no—
873C4×D4—861no—
874C4×D4—862no—
875C4×D4—862no—
876C4×D4—862no—
877C4×D4—861no—
878C4×D4—862no—
879C4×D4—862no—
880C4×D4—861no—
881C4×D4—861no—
882C4×D4—861no—
883C4×D4C22×D4311yescharacteristic
884C4×D4C22×D4312yes—
885C4×D4C22×D4312yes—
886#117—431no—
887#117—432no—
888#117—861no—
889C2×C4⋊C4—431no—
890C2×C4⋊C4—432no—
891C2×C22⋊C4—862no—
892C2×C22⋊C4—862no—
893C2×C22⋊C4—861no—
894C2×C22⋊C4—862no—
895C2×C42—431no—
896C2×C42—432no—
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—431no—
906C4⋊C8—431no—
907C4⋊C8—432no—
908C4⋊C8C22×D4311yescharacteristic
909C4⋊C8C22×D4312yes—
910#103—432no—
911#103—431no—
912#103—432no—
913#103—431no—
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—431no—
931C22⋊C8—431no—
932C22⋊C8—432no—
933C22⋊C8—432no—
934#97—432no—
935#97C22×D4312yes—
936C4×C8—431no—
937C4×C8C22×D4311yescharacteristic
938C24—862no—
939C24—861no—
940C24—862no—
941#41—44no—
942#41—864no—
943#41—3444no—
944#41—1728no—
945#41—1724no—
946#41—1724no—
947#41—1722no—
948#41—1722no—
949#41—1722no—
950#41—1722no—
951#41—1728no—
952C2×Q8—431no—
953C2×Q8—861no—
954C2×Q8—862no—
955C2×Q8—861no—
956C2×Q8—1724no—
957C2×Q8D4×D4311yescharacteristic
958C2×Q8C23×D4311yescharacteristic
959C2×D4—21no—
960C2×D4—22no—
961C2×D4—21no—
962C2×D4—22no—
963C2×D4—21no—
964C2×D4—21no—
965C2×D4—432no—
966C2×D4—431no—
967C2×D4—431no—
968C2×D4—432no—
969C2×D4—862no—
970C2×D4—862no—
971C2×D4—862no—
972C2×D4—862no—
973C2×D4—861no—
974C2×D4—862no—
975C2×D4—862no—
976C2×D4—862no—
977C2×D4—864no—
978C2×D4—862no—
979C2×D4—862no—
980C2×D4—862no—
981C2×D4—862no—
982C2×D4—862no—
983C2×D4—861no—
984C2×D4—861no—
985C2×D4—3442no—
986C2×D4—1724no—
987C2×D4—1722no—
988C2×D4—1722no—
989C2×D4—1721no—
990C2×D4—1722no—
991C2×D4—1728no—
992C2×D4—1724no—
993C2×D4C23×D4312yes—
994C2×D4C23×D4311yescharacteristic
995C2×D4C23×D4312yes—
996C22×C4—22no—
997C22×C4—21no—
998C22×C4—22no—
999C22×C4—431no—
1000C22×C4—432no—
1001C22×C4—432no—
1002C22×C4—431no—
1003C22×C4—432no—
1004C22×C4—431no—
1005C22×C4—862no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—862no—
1009C22×C4—862no—
1010C22×C4—861no—
1011C22×C4—862no—
1012C22×C4—862no—
1013C22×C4—862no—
1014C22×C4—861no—
1015C22×C4—1724no—
1016C22×C4—1728no—
1017SD16—42no—
1018SD16—41no—
1019SD16—862no—
1020SD16—862no—
1021SD16—1722no—
1022SD16—1721no—
1023D8—42no—
1024D8—42no—
1025D8—42no—
1026D8—864no—
1027D8—864no—
1028D8—1722no—
1029D8—1722no—
1030D8—1722no—
1031M16—1722no—
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—431no—
1044C4⋊C4—432no—
1045C4⋊C4—431no—
1046C4⋊C4—862no—
1047C4⋊C4—861no—
1048C4⋊C4—861no—
1049C4⋊C4—861no—
1050C4⋊C4—861no—
1051C4⋊C4—861no—
1052C4⋊C4—861no—
1053C4⋊C4—862no—
1054C4⋊C4—861no—
1055C4⋊C4—861no—
1056C4⋊C4D4×D4311yescharacteristic
1057C4⋊C4D4×D4312yes—
1058C4⋊C4C23×D4311yescharacteristic
1059C4⋊C4C23×D4311yescharacteristic
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—21no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—432no—
1066C22⋊C4—432no—
1067C22⋊C4—432no—
1068C22⋊C4—861no—
1069C22⋊C4—862no—
1070C22⋊C4—861no—
1071C22⋊C4—861no—
1072C22⋊C4—862no—
1073C22⋊C4—861no—
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⋊C4—862no—
1083C42—21no—
1084C42—432no—
1085C42—431no—
1086C42—432no—
1087C42—431no—
1088C42—431no—
1089C42—861no—
1090C42C23×D4311yescharacteristic
1091C42C23×D4312yes—
1092C23—22no—
1093C23—22no—
1094C23—21no—
1095C23—431no—
1096C23—432no—
1097C23—861no—
1098C23—862no—
1099C23—3441no—
1100C23—3442no—
1101C23—3442no—
1102C23—3442no—
1103C23—1722no—
1104C23—1724no—
1105C23—1722no—
1106C23—1724no—
1107C23—1724no—
1108Q8—22no—
1109Q8—21no—
1110Q8—21no—
1111Q8—861no—
1112Q8—861no—
1113Q8—1724no—
1114Q8—1722no—
1115Q8—1722no—
1116D4—22no—
1117D4—21no—
1118D4—22no—
1119D4—22no—
1120D4—22no—
1121D4—21no—
1122D4—44no—
1123D4—42no—
1124D4—42no—
1125D4—81no—
1126D4—82no—
1127D4—81no—
1128D4—432no—
1129D4—864no—
1130D4—862no—
1131D4—862no—
1132D4—861no—
1133D4—862no—
1134D4—3441no—
1135D4—3442no—
1136D4—3442no—
1137D4—3442no—
1138D4—3442no—
1139D4—3442no—
1140D4—1724no—
1141D4—1724no—
1142D4—1722no—
1143D4—1724no—
1144D4—1724no—
1145D4—1724no—
1146D4—1724no—
1147D4—1722no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—44no—
1152C2×C4—42no—
1153C2×C4—82no—
1154C2×C4—431no—
1155C2×C4—434no—
1156C2×C4—431no—
1157C2×C4—432no—
1158C2×C4—431no—
1159C2×C4—864no—
1160C2×C4—861no—
1161C2×C4—862no—
1162C2×C4—861no—
1163C2×C4—862no—
1164C2×C4—861no—
1165C2×C4—861no—
1166C2×C4—862no—
1167C2×C4—861no—
1168C2×C4—3442no—
1169C2×C4—3442no—
1170C2×C4—3442no—
1171C2×C4—1721no—
1172C2×C4—1722no—
1173C2×C4—1724no—
1174C2×C4—1722no—
1175C2×C4—1722no—
1176C2×C4—1724no—
1177C2×C4—1722no—
1178C2×C4—1724no—
1179C2×C4—1722no—
1180C2×C4C2×D4×D4312yes—
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—42no—
1192C22—41no—
1193C22—42no—
1194C22—42no—
1195C22—41no—
1196C22—42no—
1197C22—42no—
1198C22—41no—
1199C22—42no—
1200C22—432no—
1201C22—861no—
1202C22—861no—
1203C22—862no—
1204C22—862no—
1205C22—862no—
1206C22—862no—
1207C22—3444no—
1208C22—3448no—
1209C22—1722no—
1210C22—1722no—
1211C22—1722no—
1212C22—1721no—
1213C22—1721no—
1214C22—6884no—
1215C22C22×D4×D4311yescharacteristic
1216C4—22no—
1217C4—22no—
1218C4—21no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—432no—
1223C4—861no—
1224C4—862no—
1225C4—861no—
1226C4—1722no—
1227C4—1721no—
1228C4—1721no—
1229C4—1721no—
1230C4AGL(1,ℤ/8)×D4312yes—
1231C4H(5,𝔽2)×D4311yescharacteristic
1232C4#1458373511yescharacteristic
1233C2—81no—
1234C2—82no—
1235C2—82no—
1236C2—862no—
1237C2—3442no—
1238C2—1722no—
1239C2—1722no—
1240C2#1914826311yescharacteristic
1241C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1242C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3399C2
socleC22×C43C23×D4
hypercenter#3399D43
hypocenterC43#61961
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3399

Complements

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

NH ≅ G/Ntype
1. #19148468C2semidirect
2. #19148085C2semidirect
3. #19147637C2semidirect
4. #19147389C2semidirect
5. #19147383C2semidirect
6. #19146925C2semidirect
7. #19146924C2semidirect
8. #19146563C2semidirect
9. #19146561C2semidirect
10. #19146214C2semidirect
11. #19146210C2semidirect
12. #19146074C2semidirect
13. #19146070C2semidirect
14. #19145974C2semidirect
15. #19145909C2semidirect
16. #19145585C2semidirect
17. #19145509C2semidirect
18. #19144684C2semidirect
19. #19144601C2semidirect
20. #19144057C2semidirect
21. #459×D43C2semidirect
22. #19143711C2semidirect
23. C43×#3399C2semidirect
25. C2×#13063352C22semidirect
26. C2×#13063349C22semidirect
28. #14583634C22semidirect
30. #14583571C22semidirect
32. #14583569C22semidirect
33. Q8×D172C22semidirect
36. #14583554C22semidirect
39. #14583544C22semidirect
40. #14583542C22semidirect
43. #14583534C22semidirect
46. #14583453C22semidirect
47. #14583448C22semidirect
49. #14583447C22semidirect
50. #14583446C22semidirect
51. #127×D43C22semidirect
57. C4×D4×D43C22semidirect
58. #14583286C22semidirect
59. #14583275C22semidirect
60. #14583259C22semidirect
61. #14583258C22semidirect
62. #14583246C22semidirect
63. #14583245C22semidirect
64. #14583231C22semidirect
65. #14583228C22semidirect
66. #14583219C22semidirect
67. #14583216C22semidirect
68. #14583190C22semidirect
69. #14583189C22semidirect
70. #14583188C22semidirect
71. #14583187C22semidirect
72. #14583187C22semidirect
73. #14583185C22semidirect
74. #14583184C22semidirect
75. #14583151C22semidirect
76. #14583151C22semidirect
77. #14583149C22semidirect
78. #14583149C22semidirect
79. #14583127C22semidirect
80. #14583125C22semidirect
81. #14583115C22semidirect
82. #14583114C22semidirect
83. #14583111C22semidirect
84. #14583103C22semidirect
85. #14583102C22semidirect
86. #14583102C22semidirect
87. #14583096C22semidirect
89. #14583094C22semidirect
91. #14583092C22semidirect
92. #14583092C22semidirect
93. #14583092C22semidirect
95. #14583091C22semidirect
98. #14583043C22semidirect
99. #14583043C22semidirect
100. #14583041C22semidirect
101. #14583041C22semidirect
102. #14583034C22semidirect
103. #14583031C22semidirect
104. #14583031C22semidirect
105. #14583031C22semidirect
106. #14583030C22semidirect
107. #14583012C22semidirect
108. #14583009C22semidirect
109. #14583009C22semidirect
110. C4×#10621873C22semidirect
111. C4×#10621884C22semidirect
112. C4×#10621883C22semidirect
113. #14582978C22semidirect
114. #14582976C22semidirect
115. #14582972C22semidirect
116. #14582969C22semidirect
117. #14582954C22semidirect
118. #14582950C22semidirect
119. #14582921C22semidirect
120. C4⋊C8×D43C22semidirect
121. #14582899C22semidirect
122. #14582897C22semidirect
123. #102×D43C22semidirect
124. C43×#559C22semidirect
125. C43×#550C22semidirect
126. C43×#496C22semidirect
127. C43×#493C22semidirect
128. C43×#463C22semidirect
129. C43×#460C22semidirect
130. C43×#459C22semidirect
131. C43×#459C22semidirect
132. C43×#446C22semidirect
133. C43×#442C22semidirect
134. C4×SD16×C43C22semidirect
557. C4×D43AGL(1,ℤ/8)semidirect
615. #3399D43semidirect
651. #559C2×D43semidirect
655. #550C2×D43semidirect
682. #496C2×D43semidirect
684. #493C2×D43semidirect
709. #463C2×D43semidirect
714. #460C2×D43semidirect
723. #459C2×D43semidirect
724. #459C2×D43semidirect
736. #446C2×D43semidirect
740. #442C2×D43semidirect
744. C4×SD16C2×D43semidirect
756. C43#61961semidirect

Maximal subgroups

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

subgroupindex
#191484682
#191480852
#191476372
#191473892
#191473832
#191469252
#191469242
#191465632
#191465612
#191462142
#191462102
#191460742
#191460702
#191459742
#191459092
#191455852
#191455092
#191446842
#191446012
#191440572
#459×D432
#191437112
C43×#33992
#6196143