Finite Group Databasebeta

← #25988941

Subgroups — #25988941

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
2#19148082C211yesmaximal, characteristic, complemented
3#19147641C211yesmaximal, characteristic, complemented
4#19147635C211yesmaximal, characteristic, complemented
5#19147392C211yesmaximal, characteristic, complemented
6#19147386C211yesmaximal, characteristic, complemented
7#19146916C211yesmaximal, characteristic, complemented
8#19146559C212yesmaximal, complemented
9#19146557C212yesmaximal, complemented
10#19146217C211yesmaximal, characteristic, complemented
11#19146215C211yesmaximal, characteristic, complemented
12#19146082C212yesmaximal, complemented
13#19146078C212yesmaximal, complemented
14#19145972C212yesmaximal, complemented
15#19145910C211yesmaximal, characteristic, complemented
16#19145587C212yesmaximal, complemented
17#19145514C211yesmaximal, characteristic, complemented
18#19144683C212yesmaximal, complemented
19#19144601C211yesmaximal, characteristic, complemented
20#19144058C212yesmaximal, complemented
21#459×D43C211yesmaximal, characteristic, complemented
22#19143710C211yesmaximal, characteristic, complemented
23C43×#3332C211yesmaximal, characteristic, complemented
24C2×#41×D43—21no—
25C2×#13063353C2212yescomplemented
26C2×#13063350C2212yescomplemented
27C2×D8×D43C2212yes—
28#14583635C2211yescharacteristic, complemented
29#14583634C2211yescharacteristic, complemented
30#14583632—21no—
31#14583570C2211yescharacteristic, complemented
32#14583570C2211yescharacteristic, complemented
33#14583569—21no—
34#14583564C2211yescharacteristic, complemented
35#14583559—21no—
36#14583550C2212yes—
37#14583546C2212yescomplemented
38#14583541—22no—
39#14583538—22no—
40#14583537—21no—
41#14583537C2212yescomplemented
42D4×D172C2211yescharacteristic, complemented
43#14583533C2212yes—
44#14583499—22no—
45#14583462—21no—
46#14583453C2211yescharacteristic, complemented
47#14583450C2211yescharacteristic
48#14583445C2212yescomplemented
49#14583444C2212yescomplemented
50#14583444C2212yescomplemented
51#127×D43C2211yescharacteristic, complemented
52#14583412—21no—
53#14583407—22no—
54#14583371—21no—
55C4×#10621900C2211yescharacteristic
56C2×#13063287C2212yescomplemented
57C4×D4×D43C2211yescharacteristic
58#14583287C2212yescomplemented
59#14583285C2212yescomplemented
60#14583276C2211yescharacteristic, complemented
61#14583275C2211yescharacteristic, complemented
62#14583260C2212yescomplemented
63#14583257C2212yescomplemented
64#14583247C2211yescharacteristic, complemented
65#14583231C2211yescharacteristic, complemented
66#14583228C2211yescharacteristic, complemented
67#14583217C2212yescomplemented
68#14583188C2212yescomplemented
69#14583188C2211yescharacteristic, complemented
70#14583188C2212yescomplemented
71#14583187C2212yescomplemented
72#14583187C2211yescharacteristic, complemented
73#14583181C2211yescharacteristic, complemented
74#14583152C2212yescomplemented
75#14583150C2212yescomplemented
76#14583150C2212yescomplemented
77#14583131C2212yescomplemented
78#14583129C2212yescomplemented
79#14583117C2212yescomplemented
80#14583117C2212yescomplemented
81#14583113C2212yescomplemented
82#14583113C2212yescomplemented
83#14583103C2212yescomplemented
84#14583103C2211yescharacteristic, complemented
85#14583102C2211yescharacteristic, complemented
86#14583100C2211yescharacteristic, complemented
87#14583099C2211yescharacteristic, complemented
88#14583095C2211yescharacteristic
89#14583094C2211yescharacteristic, complemented
90#14583093C2212yes—
91#14583093C2212yescomplemented
92#14583093C2212yescomplemented
93#14583093C2212yescomplemented
94#14583092C2212yescomplemented
95#14583092C2212yescomplemented
96#14583091C2211yescharacteristic
97#14583051C2211yescharacteristic
98#14583048C2211yescharacteristic
99#14583046C2212yescomplemented
100#14583044C2212yescomplemented
101#14583042C2212yescomplemented
102#14583035C2212yescomplemented
103#14583034C2212yescomplemented
104#14583034C2212yescomplemented
105#14583032C2212yescomplemented
106#14583029C2211yescharacteristic, complemented
107#14583026C2211yescharacteristic, complemented
108#14583010C2212yescomplemented
109#14583010C2212yescomplemented
110#14583008C2212yescomplemented
111#14583008C2212yescomplemented
112C4×#10621873C2211yescharacteristic, complemented
113C4×#10621884C2211yescharacteristic, complemented
114C4×#10621883C2211yescharacteristic, complemented
115#14582977C2211yescharacteristic, complemented
116#14582973C2212yescomplemented
117#14582968C2212yescomplemented
118#14582953C2212yescomplemented
119#14582950C2211yescharacteristic, complemented
120#14582922C2212yescomplemented
121C4⋊C8×D43C2211yescharacteristic, complemented
122#14582898C2212yescomplemented
123#102×D43C2212yescomplemented
124C43×#550C2211yescharacteristic, complemented
125C43×#547C2211yescharacteristic, complemented
126C43×#486C2211yescharacteristic, complemented
127C43×#481C2212yescomplemented
128C43×#475C2211yescharacteristic, complemented
129C43×#469C2212yescomplemented
130C43×#459C2211yescharacteristic, complemented
131C43×#449C2212yescomplemented
132C4×SD16×C43C2211yescharacteristic, complemented
133C43×#436C2211yescharacteristic, complemented
134C43×#417C2212yescomplemented
135C2×#10621902—21no—
136C2×#10621898—22no—
137C2×#10621898—21no—
138C2×#10621898C2312yes—
139C2×#10621900—22no—
140C2×#10621900—22no—
141C2×#10621900D411yescharacteristic
142#41×D43—48no—
143C2×Q8×D43—21no—
144C22×D172C2312yes—
145C2×D4×D43—21no—
146C2×D4×D43—22no—
147C2×D4×D43—21no—
148C2×D4×D43—21no—
149C2×D4×D43C2311yescharacteristic
150C2×D4×D43C2312yes—
151C22×C4×D43—22no—
152C22×C4×D43—21no—
153#13063353—44no—
154#13063350—44no—
155C2×#10621873C2311yescharacteristic
156C2×#10621873C2312yes—
157C2×#10621883C2311yescharacteristic
158C2×#10621884C2311yescharacteristic
159C2×#10621884C2312yes—
160C2×D344C2312yes—
161C2×D344C2312yes—
162C2×D344C2312yes—
163C2×#10621882C2312yes—
164C2×#10621882C2312yes—
165C2×#10621882C2312yes—
166C2×#10621882C2312yes—
167D8×D43—44no—
168C2×#10621877C2312yes—
169C2×C8×D43C2312yes—
170#13063324C2312yes—
171#13063324C2311yescharacteristic
172#13063323C2311yescharacteristic
173#13063322C2311yescharacteristic
174#13063322C2311yescharacteristic
175#13063321—21no—
176#13063321—21no—
177#13063321—21no—
178#13063321C2312yes—
179#13063321C2312yes—
180#13063315—21no—
181#13063314—21no—
182#13063314C2312yes—
183#13063313—21no—
184#13063312—21no—
185#13063312C2312yes—
186#13063311—22no—
187#13063311—22no—
188#13063310—22no—
189#13063310—22no—
190#13063308—22no—
191#13063308—22no—
192#13063307—22no—
193#13063306—22no—
194#13063305C2311yescharacteristic
195#13063303—21no—
196#13063303—22no—
197#13063303—22no—
198#13063301—21no—
199#13063301C2311yescharacteristic
200#13063300—21no—
201#13063300—21no—
202#13063300C2312yes—
203#13063299—21no—
204#13063299C2312yes—
205#13063299C2312yes—
206#13063298—22no—
207#13063298—22no—
208#13063298—22no—
209#13063297—22no—
210#13063297—22no—
211#13063297—22no—
212#13063297—22no—
213#13063297—22no—
214#13063296—22no—
215#13063295—22no—
216#13063295—22no—
217#13063293—22no—
218#13063293—22no—
219#13063293—22no—
220C4×Dic86—21no—
221C4×Dic86C2311yescharacteristic
222C4×Dic86C2311yescharacteristic
223#13063290D411yescharacteristic
224C4×D172—21no—
225C4×D172C2311yescharacteristic
226D4×Dic43—21no—
227D4×Dic43D411yescharacteristic
228D4×Dic43C2311yescharacteristic
229D4×Dic43C2312yes—
230#13063287—21no—
231#13063287—22no—
232#13063287—22no—
233#13063287—21no—
234#13063287C2312yes—
235#13063287C2312yes—
236#13063287C2311yescharacteristic
237#13063287C2312yes—
238#13063287C2312yes—
239C4×C22⋊D43—21no—
240C4×C22⋊D43—22no—
241C4×C22⋊D43—22no—
242C4×C22⋊D43C2312yes—
243(C22⋊D43)⋊C4—21no—
244(C22⋊D43)⋊C4—22no—
245(C22⋊D43)⋊C4—22no—
246(C22⋊D43)⋊C4D412yes—
247#13063283D411yescharacteristic
248#13063282—21no—
249#13063281D412yes—
250C4⋊C4×D43C2311yescharacteristic
251C2×(C2×D43)⋊C4—22no—
252C2×(C2×D43)⋊C4—22no—
253C22⋊C4×D43—21no—
254C22⋊C4×D43—22no—
255C2×C4×Dic43C2312yes—
256C42×D43C2311yescharacteristic
257#13063257C2311yescharacteristic
258#13063256C2312yes—
259#13063256C2311yescharacteristic
260#13063256C2311yescharacteristic
261C4⋊(C43⋊C8)C2311yescharacteristic
262Dic43⋊C8C2312yes—
263Dic43⋊C8C2312yes—
264Dic43⋊C8C2311yescharacteristic
265Dic43⋊C8C2311yescharacteristic
266Dic43⋊C8C2312yes—
267#13063250C2311yescharacteristic
268#13063249C2311yescharacteristic
269#13063248C2312yes—
270#13063248C2311yescharacteristic
271#13063247C2312yes—
272#13063247C2311yescharacteristic
273#13063247C2312yes—
274#13063246C2312yes—
275#13063246C2311yescharacteristic
276#13063245C2312yes—
277#13063245C2311yescharacteristic
278#13063245C2312yes—
279#13063245C2312yes—
280#13063245C2312yes—
281C22⋊(C43⋊C8)C2312yes—
282(C2×D43)⋊C8C2311yescharacteristic
283(C2×D43)⋊C8C2311yescharacteristic
284#13063235C2312yes—
285#13063235C2312yes—
286C4×C43⋊C8C2311yescharacteristic
287C2×#41×C43—21no—
288C2×#41×C43C2312yes—
289C2×SD16×C43C2311yescharacteristic
290C2×D8×C43C2312yes—
291C2×M16×C43C2312yes—
292C4⋊Q8×C43C2311yescharacteristic
293#127×C43—21no—
294#127×C43C2311yescharacteristic
295#123×C43—22no—
296C22⋊Q8×C43—21no—
297#121×C43—22no—
298#121×C43C2312yes—
299#121×C43C2312yes—
300C4×Q8×C43C2311yescharacteristic
301C4×D4×C43—21no—
302C4×D4×C43C2311yescharacteristic
303C4×D4×C43C2311yescharacteristic
304C2×C4⋊C4×C43C2312yes—
305#106×C43C2312yes—
306#106×C43C2311yescharacteristic
307C4⋊C8×C43C2311yescharacteristic
308#103×C43C2311yescharacteristic
309#103×C43C2312yes—
310#102×C43C2311yescharacteristic
311#102×C43C2312yes—
312#102×C43C2312yes—
313#102×C43C2312yes—
314C22⋊C8×C43C2312yes—
315C4×C8×C43C2311yescharacteristic
316C23×D43—22no—
317C23×D43—21no—
318C23×D43—22no—
319#41×C43—42no—
320#41×C43—42no—
321#41×C43—44no—
322C2×Q8×C43—21no—
323C2×Q8×C43C2411yescharacteristic
324C2×D4×C43—21no—
325C2×D4×C43—21no—
326C2×D4×C43—22no—
327C2×D4×C43—22no—
328C2×D4×C43—22no—
329C2×D4×C43C2×D411yescharacteristic
330C2×D4×C43C2412yes—
331C2×D4×C43C2411yescharacteristic
332C22×C4×C43—21no—
333C22×C4×C43—22no—
334C22×C4×C43—22no—
335C22×C4×C43C2412yes—
336C2×C22⋊D43—21no—
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—
344C2×C22⋊D43—22no—
345C2×C22⋊D43C2×D412yes—
346C22×Dic43—21no—
347C22×Dic43—22no—
348C22×Dic43C2×D412yes—
349C22×Dic43C2×D412yes—
350#10621902—44no—
351Q8×D43—44no—
352#10621900—24no—
353#10621900—48no—
354#10621900—84no—
355D4×D43—22no—
356D4×D43—41no—
357D4×D43—48no—
358D4×D43—44no—
359D4×D43—44no—
360D4×D43—42no—
361D4×D43—42no—
362D4×D43—82no—
363#10621898—44no—
364#10621898—42no—
365#10621898—42no—
366#10621898—48no—
367C2×D172—22no—
368C2×D172—21no—
369C2×D172—21no—
370C2×D172—21no—
371C2×D172—21no—
372C2×D172—22no—
373C2×D172—24no—
374C2×D172—42no—
375C2×D172C2412yes—
376C2×D172C2412yes—
377C2×D172C2411yescharacteristic
378C2×C4×D43—21no—
379C2×C4×D43—21no—
380C2×C4×D43—22no—
381C2×C4×D43—22no—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×C4×D43—22no—
385C2×C4×D43—21no—
386C2×C4×D43—48no—
387C2×C4×D43—44no—
388C2×C4×D43C2×D411yescharacteristic
389C2×C4×D43C2×D411yescharacteristic
390C2×C4×D43C2411yescharacteristic
391C2×Dic86—21no—
392C2×Dic86—22no—
393C2×Dic86C2×D411yescharacteristic
394C2×Dic86C2411yescharacteristic
395SD16×C43—41no—
396D8×C43—42no—
397M16×C43—42no—
398C2×C8×C43C2411yescharacteristic
399C2×C8×C43C2411yescharacteristic
400C2×C8×C43C2412yes—
401C4⋊C4×C43—22no—
402C4⋊C4×C43—21no—
403C4⋊C4×C43—21no—
404C4⋊C4×C43C2×D411yescharacteristic
405C4⋊C4×C43C2411yescharacteristic
406C4⋊C4×C43C2412yes—
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—22no—
415C22⋊Dic43—21no—
416C22⋊Dic43—22no—
417C22⋊Dic43—22no—
418C22⋊Dic43C2×D412yes—
419#10621884—22no—
420#10621884—42no—
421#10621883—41no—
422#10621882—24no—
423#10621882—42no—
424#10621882—42no—
425#10621882—42no—
426(C2×D43)⋊C4—21no—
427(C2×D43)⋊C4—22no—
428(C2×D43)⋊C4—22no—
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—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—21no—
441C4⋊Dic43C2×D411yescharacteristic
442C4⋊Dic43C2411yescharacteristic
443C4⋊Dic43C2411yescharacteristic
444Dic43⋊C4—21no—
445Dic43⋊C4—21no—
446Dic43⋊C4—21no—
447Dic43⋊C4—21no—
448Dic43⋊C4—22no—
449Dic43⋊C4—21no—
450Dic43⋊C4—21no—
451Dic43⋊C4C2×D412yes—
452Dic43⋊C4C2×D412yes—
453C4×Dic43—21no—
454C4×Dic43C2×D411yescharacteristic
455C4×Dic43C2×D411yescharacteristic
456C4×Dic43C2×D412yes—
457C4×Dic43C2×D412yes—
458C4×Dic43C2412yes—
459C4×Dic43C2411yescharacteristic
460#10621877—42no—
461C2×C43⋊C8C2411yescharacteristic
462C2×C43⋊C8C2411yescharacteristic
463C2×C43⋊C8C2412yes—
464D344—24no—
465D344—42no—
466D344—42no—
467#10621873—22no—
468#10621873—42no—
469C8×D43—42no—
470C23×C43—22no—
471C23×C43—21no—
472C23×C43C22×D412yes—
473C22×D43—21no—
474C22×D43—22no—
475C22×D43—22no—
476C22×D43—42no—
477C22×D43—44no—
478C22×D43—44no—
479C22×D43—42no—
480C22×D43—44no—
481C22×D43—81no—
482C22×D43—82no—
483C22×D43—82no—
484C22×D43—82no—
485C22×D43C22×D411yescharacteristic
486Q8×C43—21no—
487Q8×C43—21no—
488Q8×C43—42no—
489D4×C43—22no—
490D4×C43—22no—
491D4×C43—21no—
492D4×C43—22no—
493D4×C43—21no—
494D4×C43—44no—
495D4×C43—42no—
496D4×C43—81no—
497D4×C43—82no—
498D4×C43—82no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—21no—
502C2×C4×C43—21no—
503C2×C4×C43—22no—
504C2×C4×C43—21no—
505C2×C4×C43—44no—
506C2×C4×C43—42no—
507C2×C4×C43—82no—
508C2×C4×C43C22×D412yes—
509C2×C4×C43C22×D411yescharacteristic
510C2×C4×C43C22×D411yescharacteristic
511C2×C4×C43C2511yescharacteristic
512C22⋊D43—24no—
513C22⋊D43—42no—
514C22⋊D43—44no—
515C22⋊D43—44no—
516C22⋊D43—44no—
517C22⋊D43—44no—
518C22⋊D43—82no—
519C22⋊D43—82no—
520C22⋊D43—82no—
521C22⋊D43—82no—
522C2×Dic43—24no—
523C2×Dic43—21no—
524C2×Dic43—21no—
525C2×Dic43—21no—
526C2×Dic43—42no—
527C2×Dic43—42no—
528C2×Dic43—82no—
529C2×Dic43C22×D411yescharacteristic
530C2×Dic43C22×D411yescharacteristic
531C2×Dic43C22×D412yes—
532C2×Dic43C22×D412yes—
533C2×Dic43C22×D411yescharacteristic
534D172—22no—
535D172—22no—
536D172—21no—
537D172—22no—
538D172—22no—
539D172—44no—
540D172—44no—
541D172—42no—
542D172—42no—
543D172—81no—
544D172—81no—
545D172H(5,𝔽2)12yes—
546C4×D43—21no—
547C4×D43—21no—
548C4×D43—41no—
549C4×D43—44no—
550C4×D43—44no—
551C4×D43—42no—
552C4×D43—42no—
553C4×D43—42no—
554C4×D43—44no—
555C4×D43—82no—
556C4×D43—82no—
557C4×D43AGL(1,ℤ/8)14yescomplemented
558Dic86—22no—
559Dic86—21no—
560Dic86—21no—
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—22no—
571C22×C43—22no—
572C22×C43—22no—
573C22×C43—42no—
574C22×C43—41no—
575C22×C43—41no—
576C22×C43—42no—
577C22×C43—41no—
578C22×C43—42no—
579C22×C43C23×D411yescharacteristic
580C2×D43—21no—
581C2×D43—21no—
582C2×D43—22no—
583C2×D43—41no—
584C2×D43—41no—
585C2×D43—42no—
586C2×D43—42no—
587C2×D43—42no—
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—21no—
596C4×C43—22no—
597C4×C43—41no—
598C4×C43—41no—
599C4×C43—42no—
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—22no—
608Dic43—41no—
609Dic43—41no—
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#3332D4311yescharacteristic, complemented
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—42no—
636C2×C43—81no—
637C2×C43—82no—
638C2×C43#348811yescharacteristic
639C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
640C2×C43#358511yescharacteristic
641D43—22no—
642D43—42no—
643D43—82no—
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—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#547C2×D4311yescharacteristic, complemented
660#546—432no—
661#546—432no—
662#546—862no—
663#546—862no—
664#546—861no—
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#496—432no—
683#493—431no—
684#493—431no—
685#489—432no—
686#489—432no—
687#486—431no—
688#486C2×D4311yescharacteristic, complemented
689#483—431no—
690#483—431no—
691#481—432no—
692#481C2×D4312yescomplemented
693#476—431no—
694#476—432no—
695#476—432no—
696#476—431no—
697#476—432no—
698#475—431no—
699#475C2×D4311yescharacteristic, complemented
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—431no—
712#461—432no—
713#460—431no—
714#460—431no—
715#459—432no—
716#459—432no—
717#459—431no—
718#459—431no—
719#459—431no—
720#459—432no—
721#459—432no—
722#459—432no—
723#459—432no—
724#459C2×D4311yescharacteristic, complemented
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#447—432no—
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#417C2×D4312yescomplemented
755C2×#102—432no—
756C43#6196111yescharacteristic, complemented, Sylow
757C2×#41—21no—
758C2×#41—431no—
759C2×#41—432no—
760C2×#41—862no—
761C2×#41—861no—
762C2×#41—862no—
763C2×#41—862no—
764C2×#41—861no—
765C2×#41—1728no—
766C2×#41C22×D4312yes—
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—862no—
776C23×C4—861no—
777AGL(1,ℤ/8)—1724no—
778AGL(1,ℤ/8)—1724no—
779C2×SD16—431no—
780C2×SD16—432no—
781C2×SD16—431no—
782C2×SD16—431no—
783C2×SD16—432no—
784C2×SD16C22×D4311yescharacteristic
785C2×D8—432no—
786C2×D8—432no—
787C2×D8—432no—
788C2×D8—432no—
789C2×D8—432no—
790C2×D8—432no—
791C2×D8—432no—
792C2×D8—1724no—
793C2×D8C22×D4312yes—
794C2×M16—432no—
795C2×M16C22×D4312yes—
796C22×C8—432no—
797C4⋊Q8—431no—
798C4⋊Q8—432no—
799C4⋊Q8—431no—
800C4⋊Q8C22×D4311yescharacteristic
801#127—21no—
802#127—432no—
803#127—432no—
804#127—431no—
805#127—431no—
806#127—861no—
807#127—861no—
808#127—861no—
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—22no—
819#123—862no—
820#123—862no—
821#123—862no—
822#123—862no—
823#123—862no—
824#123—862no—
825C22⋊Q8—21no—
826C22⋊Q8—431no—
827C22⋊Q8—431no—
828C22⋊Q8—862no—
829C22⋊Q8—862no—
830C22⋊Q8—861no—
831C22⋊Q8—861no—
832#121—22no—
833#121—432no—
834#121—432no—
835#121—432no—
836#121—862no—
837#121—862no—
838#121—862no—
839#121—862no—
840#121—861no—
841#121—861no—
842#121—862no—
843#121—862no—
844#121—862no—
845#121—862no—
846#121—861no—
847#121—862no—
848#121C22×D4312yes—
849#121C22×D4312yes—
850#120—862no—
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—431no—
867C4×D4—432no—
868C4×D4—432no—
869C4×D4—432no—
870C4×D4—432no—
871C4×D4—431no—
872C4×D4—861no—
873C4×D4—861no—
874C4×D4—862no—
875C4×D4—862no—
876C4×D4—862no—
877C4×D4—862no—
878C4×D4—861no—
879C4×D4—861no—
880C4×D4—862no—
881C4×D4—862no—
882C4×D4—861no—
883C4×D4—861no—
884C4×D4C22×D4311yescharacteristic
885C4×D4C22×D4311yescharacteristic
886#117—431no—
887#117—432no—
888#117—861no—
889C2×C4⋊C4—431no—
890C2×C4⋊C4C22×D4312yes—
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—431no—
899#106—431no—
900#106—432no—
901#106C22×D4311yescharacteristic
902#106C22×D4312yes—
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—431no—
912#103—431no—
913#103—432no—
914#103C22×D4311yescharacteristic
915#103C22×D4312yes—
916#102—432no—
917#102—431no—
918#102—432no—
919#102—431no—
920#102—432no—
921#102—432no—
922#102—432no—
923#102—431no—
924#102—432no—
925#102—432no—
926#102C22×D4312yes—
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—862no—
939C24—861no—
940C24—862no—
941#41—42no—
942#41—42no—
943#41—44no—
944#41—864no—
945#41—3444no—
946#41—1722no—
947#41—1722no—
948#41—1728no—
949#41—1724no—
950#41—1724no—
951#41—1728no—
952C2×Q8—21no—
953C2×Q8—431no—
954C2×Q8—431no—
955C2×Q8—861no—
956C2×Q8—862no—
957C2×Q8—1724no—
958C2×Q8C23×D4311yescharacteristic
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—21no—
963C2×D4—21no—
964C2×D4—432no—
965C2×D4—431no—
966C2×D4—432no—
967C2×D4—432no—
968C2×D4—864no—
969C2×D4—862no—
970C2×D4—862no—
971C2×D4—862no—
972C2×D4—861no—
973C2×D4—862no—
974C2×D4—862no—
975C2×D4—862no—
976C2×D4—862no—
977C2×D4—862no—
978C2×D4—862no—
979C2×D4—862no—
980C2×D4—861no—
981C2×D4—861no—
982C2×D4—862no—
983C2×D4—861no—
984C2×D4—861no—
985C2×D4—3442no—
986C2×D4—1722no—
987C2×D4—1724no—
988C2×D4—1722no—
989C2×D4—1722no—
990C2×D4—1721no—
991C2×D4—1724no—
992C2×D4—1728no—
993C2×D4D4×D4311yescharacteristic
994C2×D4C23×D4312yes—
995C2×D4C23×D4311yescharacteristic
996C22×C4—22no—
997C22×C4—21no—
998C22×C4—22no—
999C22×C4—431no—
1000C22×C4—432no—
1001C22×C4—432no—
1002C22×C4—431no—
1003C22×C4—431no—
1004C22×C4—862no—
1005C22×C4—861no—
1006C22×C4—862no—
1007C22×C4—862no—
1008C22×C4—862no—
1009C22×C4—861no—
1010C22×C4—862no—
1011C22×C4—861no—
1012C22×C4—862no—
1013C22×C4—861no—
1014C22×C4—1724no—
1015C22×C4—1728no—
1016C22×C4C23×D4312yes—
1017SD16—41no—
1018SD16—862no—
1019SD16—862no—
1020SD16—1722no—
1021SD16—1721no—
1022SD16—1722no—
1023D8—42no—
1024D8—864no—
1025D8—864no—
1026D8—1722no—
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—22no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—431no—
1044C4⋊C4—432no—
1045C4⋊C4—432no—
1046C4⋊C4—431no—
1047C4⋊C4—431no—
1048C4⋊C4—861no—
1049C4⋊C4—861no—
1050C4⋊C4—861no—
1051C4⋊C4—861no—
1052C4⋊C4—862no—
1053C4⋊C4—861no—
1054C4⋊C4—861no—
1055C4⋊C4—861no—
1056C4⋊C4D4×D4311yescharacteristic
1057C4⋊C4C23×D4311yescharacteristic
1058C4⋊C4C23×D4311yescharacteristic
1059C4⋊C4C23×D4312yes—
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—862no—
1070C22⋊C4—862no—
1071C22⋊C4—862no—
1072C22⋊C4—862no—
1073C22⋊C4—861no—
1074C22⋊C4—861no—
1075C22⋊C4—861no—
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—431no—
1095C23—861no—
1096C23—862no—
1097C23—862no—
1098C23—3442no—
1099C23—3441no—
1100C23—3442no—
1101C23—3442no—
1102C23—1724no—
1103C23—1724no—
1104C23—1722no—
1105C23—1724no—
1106C23—1722no—
1107C23C2×D4×D4312yes—
1108Q8—21no—
1109Q8—21no—
1110Q8—42no—
1111Q8—862no—
1112Q8—861no—
1113Q8—861no—
1114Q8—1724no—
1115Q8—1722no—
1116D4—22no—
1117D4—21no—
1118D4—22no—
1119D4—22no—
1120D4—21no—
1121D4—44no—
1122D4—42no—
1123D4—81no—
1124D4—82no—
1125D4—82no—
1126D4—432no—
1127D4—864no—
1128D4—862no—
1129D4—862no—
1130D4—861no—
1131D4—862no—
1132D4—862no—
1133D4—3441no—
1134D4—3441no—
1135D4—3442no—
1136D4—3442no—
1137D4—3442no—
1138D4—3442no—
1139D4—1724no—
1140D4—1724no—
1141D4—1724no—
1142D4—1722no—
1143D4—1724no—
1144D4—1724no—
1145D4—1724no—
1146D4—1722no—
1147D4—1722no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—44no—
1155C2×C4—42no—
1156C2×C4—82no—
1157C2×C4—431no—
1158C2×C4—434no—
1159C2×C4—431no—
1160C2×C4—432no—
1161C2×C4—431no—
1162C2×C4—432no—
1163C2×C4—864no—
1164C2×C4—861no—
1165C2×C4—861no—
1166C2×C4—861no—
1167C2×C4—861no—
1168C2×C4—861no—
1169C2×C4—3442no—
1170C2×C4—3442no—
1171C2×C4—3442no—
1172C2×C4—1721no—
1173C2×C4—1722no—
1174C2×C4—1724no—
1175C2×C4—1724no—
1176C2×C4—1724no—
1177C2×C4—1722no—
1178C2×C4—1722no—
1179C2×C4—1722no—
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—41no—
1195C22—42no—
1196C22—42no—
1197C22—41no—
1198C22—42no—
1199C22—41no—
1200C22—432no—
1201C22—861no—
1202C22—861no—
1203C22—862no—
1204C22—3448no—
1205C22—3444no—
1206C22—1722no—
1207C22—1722no—
1208C22—1722no—
1209C22—1722no—
1210C22—1722no—
1211C22—1722no—
1212C22—1721no—
1213C22—1721no—
1214C22—6884no—
1215C22C22×D4×D4311yescharacteristic
1216C4—21no—
1217C4—22no—
1218C4—41no—
1219C4—42no—
1220C4—41no—
1221C4—41no—
1222C4—432no—
1223C4—862no—
1224C4—862no—
1225C4—861no—
1226C4—861no—
1227C4—1721no—
1228C4—1721no—
1229C4—1721no—
1230C4AGL(1,ℤ/8)×D4312yes—
1231C4H(5,𝔽2)×D4311yescharacteristic
1232C4#1458373511yescharacteristic
1233C2—42no—
1234C2—81no—
1235C2—82no—
1236C2—862no—
1237C2—3442no—
1238C2—3442no—
1239C2—1722no—
1240C2#1914825811yescharacteristic
1241C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1242C2#1914937311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3332C2
socleC22×C43C23×D4
hypercenter#3332D43
hypocenterC43#61961
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3332

Complements

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

NH ≅ G/Ntype
1. #19148465C2semidirect
2. #19148082C2semidirect
3. #19147641C2semidirect
4. #19147635C2semidirect
5. #19147392C2semidirect
6. #19147386C2semidirect
7. #19146916C2semidirect
8. #19146559C2semidirect
9. #19146557C2semidirect
10. #19146217C2semidirect
11. #19146215C2semidirect
12. #19146082C2semidirect
13. #19146078C2semidirect
14. #19145972C2semidirect
15. #19145910C2semidirect
16. #19145587C2semidirect
17. #19145514C2semidirect
18. #19144683C2semidirect
19. #19144601C2semidirect
20. #19144058C2semidirect
21. #459×D43C2semidirect
22. #19143710C2semidirect
23. C43×#3332C2semidirect
25. C2×#13063353C22semidirect
26. C2×#13063350C22semidirect
28. #14583635C22semidirect
29. #14583634C22semidirect
31. #14583570C22semidirect
32. #14583570C22semidirect
34. #14583564C22semidirect
37. #14583546C22semidirect
41. #14583537C22semidirect
42. D4×D172C22semidirect
46. #14583453C22semidirect
48. #14583445C22semidirect
49. #14583444C22semidirect
50. #14583444C22semidirect
51. #127×D43C22semidirect
56. C2×#13063287C22semidirect
58. #14583287C22semidirect
59. #14583285C22semidirect
60. #14583276C22semidirect
61. #14583275C22semidirect
62. #14583260C22semidirect
63. #14583257C22semidirect
64. #14583247C22semidirect
65. #14583231C22semidirect
66. #14583228C22semidirect
67. #14583217C22semidirect
68. #14583188C22semidirect
69. #14583188C22semidirect
70. #14583188C22semidirect
71. #14583187C22semidirect
72. #14583187C22semidirect
73. #14583181C22semidirect
74. #14583152C22semidirect
75. #14583150C22semidirect
76. #14583150C22semidirect
77. #14583131C22semidirect
78. #14583129C22semidirect
79. #14583117C22semidirect
80. #14583117C22semidirect
81. #14583113C22semidirect
82. #14583113C22semidirect
83. #14583103C22semidirect
84. #14583103C22semidirect
85. #14583102C22semidirect
86. #14583100C22semidirect
87. #14583099C22semidirect
89. #14583094C22semidirect
91. #14583093C22semidirect
92. #14583093C22semidirect
93. #14583093C22semidirect
94. #14583092C22semidirect
95. #14583092C22semidirect
99. #14583046C22semidirect
100. #14583044C22semidirect
101. #14583042C22semidirect
102. #14583035C22semidirect
103. #14583034C22semidirect
104. #14583034C22semidirect
105. #14583032C22semidirect
106. #14583029C22semidirect
107. #14583026C22semidirect
108. #14583010C22semidirect
109. #14583010C22semidirect
110. #14583008C22semidirect
111. #14583008C22semidirect
112. C4×#10621873C22semidirect
113. C4×#10621884C22semidirect
114. C4×#10621883C22semidirect
115. #14582977C22semidirect
116. #14582973C22semidirect
117. #14582968C22semidirect
118. #14582953C22semidirect
119. #14582950C22semidirect
120. #14582922C22semidirect
121. C4⋊C8×D43C22semidirect
122. #14582898C22semidirect
123. #102×D43C22semidirect
124. C43×#550C22semidirect
125. C43×#547C22semidirect
126. C43×#486C22semidirect
127. C43×#481C22semidirect
128. C43×#475C22semidirect
129. C43×#469C22semidirect
130. C43×#459C22semidirect
131. C43×#449C22semidirect
132. C4×SD16×C43C22semidirect
133. C43×#436C22semidirect
134. C43×#417C22semidirect
557. C4×D43AGL(1,ℤ/8)semidirect
619. #3332D43semidirect
655. #550C2×D43semidirect
659. #547C2×D43semidirect
688. #486C2×D43semidirect
692. #481C2×D43semidirect
699. #475C2×D43semidirect
703. #469C2×D43semidirect
724. #459C2×D43semidirect
730. #449C2×D43semidirect
744. C4×SD16C2×D43semidirect
746. #436C2×D43semidirect
754. #417C2×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
#191480822
#191476412
#191476352
#191473922
#191473862
#191469162
#191465592
#191465572
#191462172
#191462152
#191460822
#191460782
#191459722
#191459102
#191455872
#191455142
#191446832
#191446012
#191440582
#459×D432
#191437102
C43×#33322
#6196143