Finite Group Databasebeta

← #25974038

Subgroups — #25974038

Order 11008.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148304C211yesmaximal, characteristic, complemented
2#19148237C211yesmaximal, characteristic, complemented
3#19146909C212yesmaximal, complemented
4#19146898C212yesmaximal, complemented
5#19146814C212yesmaximal, complemented
6#19146799C212yesmaximal, complemented
7#19146694C212yesmaximal, complemented
8#19146679C212yesmaximal, complemented
9#19146574C212yesmaximal, complemented
10#19146559C212yesmaximal, complemented
11#19144963C211yesmaximal, characteristic, complemented
12#19144566C211yesmaximal, characteristic, complemented
13#19144424C211yesmaximal, characteristic, complemented
14#19144287C211yesmaximal, characteristic, complemented
15#19144201C211yesmaximal, characteristic, complemented
16#19144144C211yesmaximal, characteristic, complemented
17#19143901C211yesmaximal, characteristic, complemented
18#19143840C211yesmaximal, characteristic, complemented
19#19143425C211yesmaximal, characteristic, complemented
20#19143294C211yesmaximal, characteristic, complemented
21#19143119C211yesmaximal, characteristic, complemented
22C2×#14582898C211yesmaximal, characteristic, complemented
23C43×#3092C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C2×#13063358C2211yescharacteristic, complemented
27C2×#13063353C2211yescharacteristic
28C2×#13063345C2211yescharacteristic
29C2×#13063333C2211yescharacteristic
30C22×#10621877C2211yescharacteristic, complemented
31#14583604—21no—
32#14583604C2212yescomplemented
33#14583597—21no—
34#14583597C2212yescomplemented
35#14583584—21no—
36#14583584C2212yescomplemented
37#14583554—21no—
38#14583554—21no—
39#14583551C2212yes—
40#14583551C2212yes—
41#14583550—21no—
42#14583550C2212yescomplemented
43#14583546C2212yes—
44#14583546C2212yes—
45#14583545—21no—
46#14583545—21no—
47#14583530C2211yescharacteristic, complemented
48#14583496—22no—
49#14583480C2211yescharacteristic
50#14583475C2211yescharacteristic
51#14583470C2211yescharacteristic
52#14583459—22no—
53#14583410—22no—
54#14583410C2211yescharacteristic
55#14583410C2211yescharacteristic, complemented
56#123×D43—22no—
57#14583380C2211yescharacteristic
58#14583380C2211yescharacteristic, complemented
59#14583373C2211yescharacteristic
60#14583266C2212yescomplemented
61#14583257C2212yescomplemented
62#14583252C2212yescomplemented
63#14583248C2212yescomplemented
64#14583243C2212yescomplemented
65#14583242C2212yescomplemented
66#14583236C2212yescomplemented
67#14583231C2212yescomplemented
68#14583202C2212yescomplemented
69#14583198C2212yescomplemented
70#14583188C2212yescomplemented
71#14583178C2212yescomplemented
72#14583158C2212yescomplemented
73#14583155C2211yescharacteristic, complemented
74#14583155C2211yescharacteristic, complemented
75#14583150C2211yescharacteristic, complemented
76#14583150C2211yescharacteristic, complemented
77#14583147C2211yescharacteristic, complemented
78#14583147C2211yescharacteristic, complemented
79#14583146C2212yescomplemented
80#14583143C2211yescharacteristic, complemented
81#14583143C2211yescharacteristic, complemented
82#14583141C2212yescomplemented
83#14583129C2212yescomplemented
84#14583120C2212yescomplemented
85#14583113C2212yescomplemented
86#14583108C2212yescomplemented
87#14583103C2212yescomplemented
88#14583064C2212yescomplemented
89#14583063C2212yescomplemented
90#14583063C2212yescomplemented
91#14583051C2212yescomplemented
92#14583047C2212yescomplemented
93#14583046C2212yescomplemented
94#14583046C2212yescomplemented
95#14583034C2212yescomplemented
96#14583010C2212yescomplemented
97#14582998C2212yescomplemented
98#14582986C2212yescomplemented
99#14582981C2212yescomplemented
100#14582974C2212yescomplemented
101#14582974C2212yescomplemented
102#14582973C2212yescomplemented
103#14582973C2212yescomplemented
104#14582935C2211yescharacteristic, complemented
105#14582927C2211yescharacteristic, complemented
106#14582909C2211yescharacteristic, complemented
107#14582905C2211yescharacteristic
108#14582902C2212yescomplemented
109#14582899C2212yescomplemented
110#14582898C2212yescomplemented
111#14582898C2212yescomplemented
112#14582898C2212yescomplemented
113#14582898C2212yescomplemented
114#14582895C2211yescharacteristic
115#14582894C2212yescomplemented
116#14582893C2211yescharacteristic, complemented
117C2×#13063248C2211yescharacteristic, complemented
118C2×#13063248C2211yescharacteristic, complemented
119C2×#13063245C2211yescharacteristic
120C2×#13063245C2211yescharacteristic
121#102×D43C2212yescomplemented
122#14582867C2211yescharacteristic
123#14582857C2211yescharacteristic, complemented
124C43×#525C2211yescharacteristic
125C22×C4⋊C4×C43C2211yescharacteristic, complemented
126C43×#484C2212yescomplemented
127C43×#483C2212yescomplemented
128C43×#481C2212yescomplemented
129C43×#480C2212yescomplemented
130C43×#428C2211yescharacteristic, complemented
131C43×#428C2211yescharacteristic, complemented
132C43×#417C2211yescharacteristic
133C43×#417C2211yescharacteristic
134C43×#407C2211yescharacteristic, complemented
135#13063371—24no—
136#13063371—42no—
137C2×#10621902C2312yes—
138C2×#10621898—21no—
139C2×#10621898—21no—
140C2×#10621898—22no—
141C2×#10621898—24no—
142C2×#10621898—21no—
143C2×#10621898—42no—
144C2×#10621898C2311yescharacteristic
145C2×#10621898C2311yescharacteristic
146C2×#10621898C2312yes—
147C2×#10621898C2312yes—
148C22×Dic86C2311yescharacteristic
149C22×D172—21no—
150C22×D172C2311yescharacteristic
151C22×C22⋊D43—21no—
152C2×D4×D43—22no—
153C2×D4×D43C2312yes—
154C22×C4×D43—21no—
155#13063358—42no—
156#13063353—24no—
157#13063345—42no—
158C2×Dic172C2312yes—
159C2×#10621885C2311yescharacteristic
160C2×#10621873C2312yes—
161C2×#10621873C2312yes—
162C2×#10621883C2311yescharacteristic
163C2×#10621884C2311yescharacteristic
164C2×D344C2312yes—
165C2×#10621882C2311yescharacteristic
166#13063333—42no—
167C2×#10621877—42no—
168C2×#10621877C2311yescharacteristic
169C2×#10621877C2311yescharacteristic
170C2×#10621877C2311yescharacteristic
171C2×#10621877C2311yescharacteristic
172C2×#10621872C2312yes—
173C22×C43⋊C8C2311yescharacteristic
174C22×C43⋊C8C2311yescharacteristic
175C2×C8×D43C2312yes—
176#13063325—21no—
177#13063324—21no—
178#13063324C2312yes—
179#13063323C2312yes—
180#13063320—22no—
181#13063320—22no—
182#13063316—21no—
183#13063316C2312yes—
184#13063315—22no—
185#13063315—22no—
186#13063313—21no—
187#13063312C2312yes—
188#13063310—22no—
189#13063310—22no—
190#13063310—22no—
191#13063310—22no—
192#13063309—22no—
193#13063308—21no—
194#13063308—22no—
195#13063308—22no—
196#13063308D412yes—
197#13063307—22no—
198#13063307—22no—
199#13063307—22no—
200#13063307—22no—
201#13063306—22no—
202#13063305—21no—
203#13063305C2312yes—
204#13063305C2312yes—
205#13063305C2312yes—
206#13063304—22no—
207#13063304—22no—
208#13063304—21no—
209#13063304—21no—
210#13063304D411yescharacteristic
211#13063304D411yescharacteristic
212#13063304C2311yescharacteristic
213#13063304C2311yescharacteristic
214#13063303—22no—
215#13063303—22no—
216#13063300—21no—
217#13063300C2312yes—
218#13063299—22no—
219#13063299—22no—
220#13063299D411yescharacteristic
221#13063299D411yescharacteristic
222#13063299C2311yescharacteristic
223#13063299C2311yescharacteristic
224#13063298—22no—
225#13063298—22no—
226#13063296—22no—
227#13063296—22no—
228#13063294—21no—
229#13063294D412yes—
230#13063293—22no—
231#13063293—22no—
232#13063290—21no—
233#13063290C2312yes—
234C4×D172—21no—
235C4×D172—21no—
236#13063287—21no—
237#13063287C2312yes—
238#13063287C2312yes—
239#13063287C2312yes—
240C4×C22⋊D43—21no—
241C4×C22⋊D43—21no—
242C4×C22⋊D43—22no—
243C4×C22⋊D43—22no—
244C4×C22⋊D43—22no—
245C4×C22⋊D43—22no—
246C4×C22⋊D43C2312yes—
247C4×C22⋊D43C2312yes—
248#13063284—22no—
249#13063284C2311yescharacteristic
250#13063284C2311yescharacteristic
251#13063283—21no—
252#13063283C2312yes—
253C4⋊C4×D43—21no—
254C4⋊C4×D43—22no—
255C4⋊C4×D43—22no—
256C4⋊C4×D43C2312yes—
257C22⋊C4×D43—22no—
258C22⋊C4×D43—22no—
259C22⋊C4×D43—22no—
260#13063258C2311yescharacteristic
261#13063258C2311yescharacteristic
262#13063256C2311yescharacteristic
263#13063256C2311yescharacteristic
264Dic43⋊C8C2312yes—
265Dic43⋊C8C2312yes—
266#13063250C2312yes—
267#13063250C2312yes—
268#13063249C2311yescharacteristic
269#13063249C2311yescharacteristic
270#13063248C2312yes—
271#13063248C2312yes—
272#13063248C2312yes—
273#13063248C2311yescharacteristic
274#13063248C2311yescharacteristic
275#13063248C2312yes—
276#13063247C2312yes—
277#13063247C2312yes—
278#13063246C2311yescharacteristic
279#13063246C2311yescharacteristic
280#13063245C2312yes—
281#13063245C2312yes—
282#13063245C2311yescharacteristic
283#13063245C2312yes—
284#13063245C2312yes—
285#13063245C2311yescharacteristic
286(C2×D43)⋊C8C2312yes—
287(C2×D43)⋊C8C2312yes—
288#13063235C2312yes—
289C8×Dic43C2312yes—
290C2×#41×C43C2311yescharacteristic
291C23×C4×C43—21no—
292C23×C4×C43C2311yescharacteristic
293C2×M16×C43C2311yescharacteristic
294C2×M16×C43C2311yescharacteristic
295#123×C43—21no—
296C22⋊Q8×C43C2311yescharacteristic
297C22⋊Q8×C43C2311yescharacteristic
298#121×C43C2311yescharacteristic
299#121×C43C2311yescharacteristic
300#120×C43—21no—
301C4×D4×C43—21no—
302C4×D4×C43—21no—
303#117×C43C2311yescharacteristic
304C2×C4⋊C4×C43—21no—
305C2×C4⋊C4×C43—21no—
306C2×C4⋊C4×C43—21no—
307C2×C4⋊C4×C43C2312yes—
308C2×C4⋊C4×C43C2312yes—
309C2×C4⋊C4×C43C2311yescharacteristic
310C2×C4⋊C4×C43C2311yescharacteristic
311#107×C43C2312yes—
312#107×C43C2312yes—
313#106×C43C2312yes—
314#106×C43C2312yes—
315#103×C43C2312yes—
316#103×C43C2312yes—
317#102×C43C2312yes—
318#102×C43C2312yes—
319C22⋊C8×C43C2312yes—
320C22⋊C8×C43C2312yes—
321C24×C43C2×D411yescharacteristic
322C23×D43—21no—
323C23×D43—22no—
324#41×C43—22no—
325#41×C43—22no—
326C2×Q8×C43C2411yescharacteristic
327C2×D4×C43—21no—
328C2×D4×C43—21no—
329C2×D4×C43—21no—
330C2×D4×C43C2411yescharacteristic
331C22×C4×C43—22no—
332C22×C4×C43—22no—
333C22×C4×C43—21no—
334C22×C4×C43—22no—
335C22×C4×C43—21no—
336C22×C4×C43—22no—
337C22×C4×C43—21no—
338C22×C4×C43—82no—
339C22×C4×C43C2×D411yescharacteristic
340C22×C4×C43C2×D411yescharacteristic
341C22×C4×C43C2×D411yescharacteristic
342C22×C4×C43C2411yescharacteristic
343C22×C4×C43C2411yescharacteristic
344C22×C4×C43C2411yescharacteristic
345C2×C22⋊D43—22no—
346C2×C22⋊D43—21no—
347C2×C22⋊D43—21no—
348C2×C22⋊D43—21no—
349C2×C22⋊D43—22no—
350C2×C22⋊D43—22no—
351C2×C22⋊D43—44no—
352C2×C22⋊D43C2×D412yes—
353C2×C22⋊D43C2×D412yes—
354C2×C22⋊D43C2×D412yes—
355C22×Dic43—21no—
356#10621902—24no—
357#10621902—42no—
358D4×D43—24no—
359D4×D43—48no—
360D4×D43—42no—
361#10621898—22no—
362#10621898—22no—
363#10621898—22no—
364#10621898—22no—
365#10621898—24no—
366#10621898—24no—
367#10621898—42no—
368#10621898—42no—
369#10621898—44no—
370#10621898—44no—
371#10621898—44no—
372#10621898—84no—
373C2×D172—21no—
374C2×D172—22no—
375C2×D172—22no—
376C2×D172—22no—
377C2×D172—44no—
378C2×D172C2×D411yescharacteristic
379C2×D172#4114yescomplemented
380C2×D172C2411yescharacteristic
381C2×D172C2412yes—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×C4×D43—21no—
385C2×C4×D43—22no—
386C2×C4×D43—22no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—22no—
390C2×C4×D43—44no—
391C2×C4×D43C2412yes—
392C2×Dic86—22no—
393C2×Dic86—22no—
394C2×Dic86—21no—
395C2×Dic86—22no—
396C2×Dic86C2×D411yescharacteristic
397C2×Dic86C2412yes—
398C2×Dic86C2411yescharacteristic
399M16×C43—22no—
400M16×C43—22no—
401C2×C8×C43C2412yes—
402C2×C8×C43C2412yes—
403C4⋊C4×C43—21no—
404C4⋊C4×C43—21no—
405C4⋊C4×C43—22no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43—21no—
408C4⋊C4×C43—21no—
409C4⋊C4×C43C2412yes—
410C4⋊C4×C43C2412yes—
411C4⋊C4×C43C2411yescharacteristic
412C4⋊C4×C43C2411yescharacteristic
413C22⋊C4×C43—21no—
414C22⋊C4×C43—21no—
415C22⋊C4×C43—21no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43—21no—
418C42×C43—21no—
419C22⋊Dic43—22no—
420C22⋊Dic43—22no—
421C22⋊Dic43—21no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424C22⋊Dic43C2×D412yes—
425C22⋊Dic43C2×D412yes—
426C22⋊Dic43C2×D412yes—
427#10621885—41no—
428#10621884—41no—
429#10621883—41no—
430#10621882—41no—
431(C2×D43)⋊C4—21no—
432(C2×D43)⋊C4—21no—
433(C2×D43)⋊C4—22no—
434(C2×D43)⋊C4—22no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4C2×D412yes—
442(C2×D43)⋊C4C2×D412yes—
443C4⋊Dic43—22no—
444C4⋊Dic43—22no—
445C4⋊Dic43—22no—
446C4⋊Dic43—22no—
447C4⋊Dic43C2×D411yescharacteristic
448C4⋊Dic43C2×D411yescharacteristic
449C4⋊Dic43C2411yescharacteristic
450C4⋊Dic43C2411yescharacteristic
451Dic43⋊C4—21no—
452Dic43⋊C4—21no—
453Dic43⋊C4—22no—
454Dic43⋊C4—22no—
455Dic43⋊C4—22no—
456Dic43⋊C4—22no—
457Dic43⋊C4—22no—
458Dic43⋊C4—22no—
459Dic43⋊C4C2×D412yes—
460Dic43⋊C4C2×D412yes—
461C4×Dic43—21no—
462C4×Dic43—22no—
463C4×Dic43—22no—
464C4×Dic43C2412yes—
465#10621877—41no—
466#10621877—41no—
467#10621877—41no—
468#10621877—41no—
469C2×C43⋊C8—22no—
470C2×C43⋊C8—22no—
471C2×C43⋊C8C2411yescharacteristic
472C2×C43⋊C8C2411yescharacteristic
473C2×C43⋊C8C2411yescharacteristic
474C2×C43⋊C8C2411yescharacteristic
475Dic172—42no—
476D344—24no—
477#10621873—24no—
478#10621873—42no—
479#10621872—42no—
480C8×D43—42no—
481C23×C43—22no—
482C23×C43—21no—
483C23×C43—41no—
484C23×C43—41no—
485C23×C43C22×D411yescharacteristic
486C23×C43C22×D411yescharacteristic
487C23×C43C22×D411yescharacteristic
488C22×D43—22no—
489C22×D43—24no—
490C22×D43—21no—
491C22×D43—44no—
492C22×D43—82no—
493C22×D43—82no—
494C22×D43—81no—
495C22×D43—81no—
496C22×D43C22×D412yes—
497Q8×C43—21no—
498Q8×C43—21no—
499D4×C43—21no—
500D4×C43—21no—
501D4×C43—42no—
502D4×C43—81no—
503D4×C43—81no—
504C2×C4×C43—22no—
505C2×C4×C43—22no—
506C2×C4×C43—22no—
507C2×C4×C43—21no—
508C2×C4×C43—21no—
509C2×C4×C43—21no—
510C2×C4×C43—21no—
511C2×C4×C43—22no—
512C2×C4×C43—21no—
513C2×C4×C43—22no—
514C2×C4×C43—21no—
515C2×C4×C43—21no—
516C2×C4×C43—44no—
517C2×C4×C43—42no—
518C2×C4×C43—81no—
519C2×C4×C43—82no—
520C2×C4×C43—81no—
521C2×C4×C43C22×D411yescharacteristic
522C2×C4×C43C22×D411yescharacteristic
523C2×C4×C43C22×D411yescharacteristic
524C2×C4×C43C2×#4112yes—
525C2×C4×C43H(5,𝔽2)12yes—
526C2×C4×C43C2511yescharacteristic
527C22⋊D43—24no—
528C22⋊D43—42no—
529C22⋊D43—42no—
530C22⋊D43—44no—
531C22⋊D43—44no—
532C22⋊D43—44no—
533C22⋊D43—42no—
534C22⋊D43—42no—
535C22⋊D43—42no—
536C2×Dic43—21no—
537C2×Dic43—21no—
538C2×Dic43—21no—
539C2×Dic43—22no—
540C2×Dic43—42no—
541C2×Dic43C22×D412yes—
542C2×Dic43C22×D412yes—
543C2×Dic43C22×D412yes—
544D172—24no—
545D172—22no—
546D172—21no—
547D172—22no—
548D172—21no—
549D172—44no—
550D172—82no—
551D172C2×#4114yes—
552C4×D43—22no—
553C4×D43—22no—
554C4×D43—44no—
555C4×D43—44no—
556C4×D43—44no—
557C4×D43—42no—
558C4×D43—82no—
559C4×D43—82no—
560C4×D43—82no—
561C4×D43—82no—
562Dic86—22no—
563Dic86—21no—
564Dic86—22no—
565Dic86—22no—
566Dic86—21no—
567Dic86—42no—
568Dic86—82no—
569C8×C43—22no—
570C8×C43—22no—
571C43⋊C8—21no—
572C43⋊C8—21no—
573C43⋊C8—21no—
574C43⋊C8—21no—
575#61177—431nomaximal, Sylow
576C22×C43—21no—
577C22×C43—21no—
578C22×C43—21no—
579C22×C43—21no—
580C22×C43—21no—
581C22×C43—21no—
582C22×C43—21no—
583C22×C43—21no—
584C22×C43—44no—
585C22×C43—41no—
586C22×C43—41no—
587C22×C43—41no—
588C22×C43#54612yes—
589C22×C43C23×D411yescharacteristic
590C2×D43—22no—
591C2×D43—22no—
592C2×D43—24no—
593C2×D43—22no—
594C2×D43—42no—
595C2×D43—42no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—41no—
599C2×D43—84no—
600C2×D43—164no—
601C4×C43—21no—
602C4×C43—21no—
603C4×C43—42no—
604C4×C43—42no—
605C4×C43—41no—
606C4×C43—41no—
607C4×C43—41no—
608C4×C43#54612yes—
609C4×C43C22×#4111yescharacteristic
610C4×C43C2×H(5,𝔽2)11yescharacteristic
611Dic43—22no—
612Dic43—22no—
613Dic43—22no—
614Dic43—41no—
615Dic43—41no—
616Dic43—42no—
617Dic43—41no—
618#3492—431no—
619#3485—431no—
620#3331—432no—
621#3330—432no—
622#3323—432no—
623#3322—432no—
624#3315—432no—
625#3314—432no—
626#3307—432no—
627#3306—432no—
628#3137—431no—
629#3097—431no—
630#3092D4311yescharacteristic, complemented
631#3081—431no—
632#3063—431no—
633#3054—431no—
634#3046—431no—
635#3012—431no—
636#3005—431no—
637#2946—431no—
638#2930—431no—
639#2897—431no—
640C2×#417—431no—
641C2×C43—22no—
642C2×C43—41no—
643C2×C43—41no—
644C2×C43—81no—
645C2×C43C2×#54611yescharacteristic
646C2×C43#358511yescharacteristic
647C2×C43#358611yescharacteristic
648D43—42no—
649D43—44no—
650D43—81no—
651C2×H(5,𝔽2)—431no—
652C22×#41—431no—
653C2×#137—431no—
654C2×AGL(1,ℤ/8)—431no—
655C2×#135—431no—
656C2×#131—431no—
657C22×M16—431no—
658#554—432no—
659#554—861no—
660#553—432no—
661#553—861no—
662#552—432no—
663#552—861no—
664#547—432no—
665#547—432no—
666#547—432no—
667#547—861no—
668#547—861no—
669#547—861no—
670#546—432no—
671#546—432no—
672#546—861no—
673#546—861no—
674#544—431no—
675#539—862no—
676#537—431no—
677#536—431no—
678#536—431no—
679#534—862no—
680#525—431no—
681#525—431no—
682#525—862no—
683#525C2×D4311yescharacteristic
684C2×#123—862no—
685#520—431no—
686#520—431no—
687#518—431no—
688C22×C4⋊C4C2×D4311yescharacteristic, complemented
689#491—432no—
690#489—432no—
691#488—432no—
692#487—432no—
693#485—432no—
694#485—432no—
695#484—432no—
696#484C2×D4312yescomplemented
697#483—432no—
698#483C2×D4312yescomplemented
699#481C2×D4312yescomplemented
700#480C2×D4312yescomplemented
701#478—432no—
702#478—432no—
703#476—432no—
704#474—432no—
705#470—431no—
706#470—431no—
707#470—432no—
708#469—431no—
709#469—431no—
710#468—431no—
711#468—431no—
712#468—431no—
713#468—431no—
714#468—432no—
715#467—432no—
716#465—432no—
717#464—432no—
718#463—432no—
719#462—432no—
720#461—432no—
721#452—432no—
722#452—432no—
723#452—432no—
724#450—432no—
725#449—432no—
726#449—432no—
727#449—432no—
728#447—432no—
729#442—432no—
730#440—432no—
731C4×SD16—432no—
732C4×D8—432no—
733#436—432no—
734#436—432no—
735#435—432no—
736#435—432no—
737#428C2×D4311yescharacteristic, complemented
738#428C2×D4311yescharacteristic, complemented
739#427—431no—
740#424—431no—
741#419—431no—
742#418—431no—
743#418—432no—
744#417—432no—
745#417—432no—
746#417—432no—
747#417—432no—
748#417—432no—
749#417C2×D4311yescharacteristic
750#417C2×D4311yescharacteristic
751#416—431no—
752#416—431no—
753#416—432no—
754C2×#103—431no—
755C2×#103—431no—
756C2×#102—431no—
757C2×#102—431no—
758C2×#102—432no—
759#408—431no—
760#407C2×D4311yescharacteristic, complemented
761#405—431no—
762C43#6117711yescharacteristic, complemented, Sylow
763H(5,𝔽2)—864no—
764H(5,𝔽2)—1722no—
765C2×#41—431no—
766C2×#41—432no—
767C2×#41—431no—
768C2×#41—432no—
769C2×#41—432no—
770C2×#41—862no—
771C2×#41—861no—
772C2×#41—864no—
773C2×#41—861no—
774C2×#41—861no—
775C2×#41—1722no—
776C2×#41C22×D4311yescharacteristic
777C22×Q8—431no—
778C22×D4—432no—
779C22×D4—431no—
780C22×D4—861no—
781C22×D4—862no—
782C22×D4—861no—
783C23×C4—21no—
784C23×C4—861no—
785C23×C4C22×D4311yescharacteristic
786#137—1722no—
787AGL(1,ℤ/8)—864no—
788#135—1722no—
789C2×Q16—431no—
790C2×Q16—432no—
791C2×SD16—431no—
792C2×SD16—431no—
793C2×SD16—432no—
794C2×SD16—432no—
795C2×D8—431no—
796C2×D8—432no—
797#131—1722no—
798C2×M16—431no—
799C2×M16—431no—
800C2×M16—431no—
801C2×M16—431no—
802C2×M16—432no—
803C2×M16—1722no—
804C2×M16C22×D4311yescharacteristic
805C2×M16C22×D4311yescharacteristic
806C22×C8—431no—
807C22×C8—431no—
808C22×C8—432no—
809C4⋊Q8—432no—
810C4⋊Q8—432no—
811C4⋊Q8—861no—
812C4⋊Q8—861no—
813#126—862no—
814#126—862no—
815#125—432no—
816#125—862no—
817#125—862no—
818#125—861no—
819#124—432no—
820#124—861no—
821#123—21no—
822#123—432no—
823#123—862no—
824#123—862no—
825#123—862no—
826#123—862no—
827#123—862no—
828#123—862no—
829#123—862no—
830#123—862no—
831#123—862no—
832#123—862no—
833#123—862no—
834#123—862no—
835#123—861no—
836C22⋊Q8—431no—
837C22⋊Q8—431no—
838C22⋊Q8—431no—
839C22⋊Q8—431no—
840C22⋊Q8—432no—
841C22⋊Q8—432no—
842C22⋊Q8—432no—
843C22⋊Q8—862no—
844C22⋊Q8—862no—
845C22⋊Q8—862no—
846C22⋊Q8—862no—
847C22⋊Q8—861no—
848C22⋊Q8—861no—
849C22⋊Q8—861no—
850C22⋊Q8C22×D4311yescharacteristic
851C22⋊Q8C22×D4311yescharacteristic
852#121—431no—
853#121—431no—
854#121—431no—
855#121—431no—
856#121—432no—
857#121—862no—
858#121—862no—
859#121—862no—
860#121—862no—
861#121—861no—
862#121—862no—
863#121—862no—
864#121C22×D4311yescharacteristic
865#121C22×D4311yescharacteristic
866#120—21no—
867#120—432no—
868#120—862no—
869#120—862no—
870#120—861no—
871C4×Q8—432no—
872C4×Q8—861no—
873C4×D4—21no—
874C4×D4—21no—
875C4×D4—432no—
876C4×D4—432no—
877C4×D4—432no—
878C4×D4—432no—
879C4×D4—432no—
880C4×D4—861no—
881C4×D4—861no—
882C4×D4—862no—
883C4×D4—862no—
884C4×D4—861no—
885C4×D4—862no—
886C4×D4—862no—
887C4×D4—861no—
888C4×D4—861no—
889#117—431no—
890#117—431no—
891#117—432no—
892#117—862no—
893#117—861no—
894#117C22×D4311yescharacteristic
895C2×C4⋊C4—21no—
896C2×C4⋊C4—21no—
897C2×C4⋊C4—21no—
898C2×C4⋊C4—432no—
899C2×C4⋊C4—861no—
900C2×C4⋊C4—862no—
901C2×C4⋊C4—862no—
902C2×C4⋊C4C22×D4311yescharacteristic
903C2×C4⋊C4C22×D4311yescharacteristic
904C2×C4⋊C4C22×D4312yes—
905C2×C4⋊C4C22×D4312yes—
906C2×C22⋊C4—862no—
907C2×C22⋊C4—862no—
908C2×C22⋊C4—862no—
909#107—431no—
910#107—431no—
911#107C22×D4312yes—
912#107C22×D4312yes—
913#106—431no—
914#106—431no—
915#106C22×D4312yes—
916#106C22×D4312yes—
917C4⋊C8—432no—
918C4⋊C8—432no—
919#103—431no—
920#103—431no—
921#103—432no—
922#103—432no—
923#103—432no—
924#103—432no—
925#103—432no—
926#103—432no—
927#103—431no—
928#103—431no—
929#103C22×D4312yes—
930#103C22×D4312yes—
931#102—431no—
932#102—431no—
933#102—432no—
934#102—432no—
935#102—432no—
936#102—432no—
937#102—432no—
938#102—432no—
939#102—431no—
940#102—431no—
941#102C22×D4312yes—
942#102C22×D4312yes—
943C22⋊C8—432no—
944C22⋊C8—432no—
945C22⋊C8C22×D4312yes—
946C22⋊C8C22×D4312yes—
947#97—432no—
948C4×C8—432no—
949C24—862no—
950C24—861no—
951C24D4×D4311yescharacteristic
952#41—22no—
953#41—22no—
954#41—864no—
955#41—864no—
956#41—862no—
957#41—862no—
958#41—864no—
959#41—862no—
960#41—862no—
961#41—3444no—
962#41—1722no—
963#41—1722no—
964#41—1724no—
965#41—1724no—
966#41—1724no—
967#41—1722no—
968C2×Q8—431no—
969C2×Q8—432no—
970C2×Q8—431no—
971C2×Q8—862no—
972C2×Q8—861no—
973C2×Q8—862no—
974C2×Q8—862no—
975C2×Q8C23×D4311yescharacteristic
976C2×D4—21no—
977C2×D4—21no—
978C2×D4—21no—
979C2×D4—432no—
980C2×D4—432no—
981C2×D4—432no—
982C2×D4—431no—
983C2×D4—434no—
984C2×D4—432no—
985C2×D4—431no—
986C2×D4—862no—
987C2×D4—862no—
988C2×D4—862no—
989C2×D4—864no—
990C2×D4—861no—
991C2×D4—861no—
992C2×D4—861no—
993C2×D4—862no—
994C2×D4—862no—
995C2×D4—861no—
996C2×D4—862no—
997C2×D4—1724no—
998C2×D4—1722no—
999C2×D4—1728no—
1000C2×D4—1724no—
1001C2×D4C23×D4311yescharacteristic
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—21no—
1006C22×C4—22no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—82no—
1010C22×C4—432no—
1011C22×C4—862no—
1012C22×C4—862no—
1013C22×C4—862no—
1014C22×C4—862no—
1015C22×C4—862no—
1016C22×C4—861no—
1017C22×C4—862no—
1018C22×C4—862no—
1019C22×C4—861no—
1020C22×C4—1724no—
1021C22×C4D4×D4311yescharacteristic
1022C22×C4D4×D4311yescharacteristic
1023C22×C4D4×D4311yescharacteristic
1024C22×C4C23×D4311yescharacteristic
1025C22×C4C23×D4311yescharacteristic
1026C22×C4C23×D4311yescharacteristic
1027Q16—1722no—
1028Q16—1721no—
1029SD16—864no—
1030SD16—1722no—
1031SD16—1721no—
1032SD16—1721no—
1033D8—864no—
1034D8—1721no—
1035M16—22no—
1036M16—22no—
1037M16—1722no—
1038M16—1721no—
1039M16—1721no—
1040M16—1721no—
1041M16—1721no—
1042C2×C8—431no—
1043C2×C8—431no—
1044C2×C8—431no—
1045C2×C8—431no—
1046C2×C8—862no—
1047C2×C8—862no—
1048C2×C8—1722no—
1049C2×C8C23×D4312yes—
1050C2×C8C23×D4312yes—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—431no—
1058C4⋊C4—432no—
1059C4⋊C4—432no—
1060C4⋊C4—431no—
1061C4⋊C4—431no—
1062C4⋊C4—431no—
1063C4⋊C4—862no—
1064C4⋊C4—862no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—862no—
1068C4⋊C4—862no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—862no—
1072C4⋊C4—862no—
1073C4⋊C4—861no—
1074C4⋊C4—861no—
1075C4⋊C4C23×D4312yes—
1076C4⋊C4C23×D4312yes—
1077C4⋊C4C23×D4311yescharacteristic
1078C4⋊C4C23×D4311yescharacteristic
1079C22⋊C4—21no—
1080C22⋊C4—21no—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—21no—
1084C22⋊C4—432no—
1085C22⋊C4—432no—
1086C22⋊C4—432no—
1087C22⋊C4—432no—
1088C22⋊C4—432no—
1089C22⋊C4—862no—
1090C22⋊C4—862no—
1091C22⋊C4—862no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—862no—
1095C22⋊C4—862no—
1096C22⋊C4—862no—
1097C22⋊C4—862no—
1098C22⋊C4—862no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—861no—
1102C22⋊C4—861no—
1103C22⋊C4—861no—
1104C42—21no—
1105C42—432no—
1106C42—862no—
1107C42—862no—
1108C42—861no—
1109C23—22no—
1110C23—21no—
1111C23—41no—
1112C23—41no—
1113C23—432no—
1114C23—864no—
1115C23—862no—
1116C23—861no—
1117C23—3441no—
1118C23—3441no—
1119C23—3442no—
1120C23—3442no—
1121C23—1724no—
1122C23C2×D4×D4311yescharacteristic
1123C23C2×D4×D4311yescharacteristic
1124C23C2×D4×D4311yescharacteristic
1125Q8—21no—
1126Q8—21no—
1127Q8—862no—
1128Q8—861no—
1129Q8—862no—
1130Q8—861no—
1131Q8—862no—
1132Q8—3442no—
1133Q8—1722no—
1134D4—21no—
1135D4—21no—
1136D4—42no—
1137D4—81no—
1138D4—81no—
1139D4—434no—
1140D4—864no—
1141D4—861no—
1142D4—862no—
1143D4—861no—
1144D4—864no—
1145D4—862no—
1146D4—3442no—
1147D4—1724no—
1148D4—1722no—
1149D4—1722no—
1150D4—1724no—
1151D4—1724no—
1152D4—1724no—
1153D4—1722no—
1154D4—1722no—
1155D4—1722no—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—44no—
1169C2×C4—42no—
1170C2×C4—81no—
1171C2×C4—82no—
1172C2×C4—81no—
1173C2×C4—432no—
1174C2×C4—432no—
1175C2×C4—432no—
1176C2×C4—862no—
1177C2×C4—862no—
1178C2×C4—861no—
1179C2×C4—861no—
1180C2×C4—861no—
1181C2×C4—862no—
1182C2×C4—3442no—
1183C2×C4—3442no—
1184C2×C4—3442no—
1185C2×C4—3442no—
1186C2×C4—1724no—
1187C2×C4—1724no—
1188C2×C4—1724no—
1189C2×C4—1722no—
1190C2×C4—1722no—
1191C2×C4C2×D4×D4311yescharacteristic
1192C2×C4C2×D4×D4311yescharacteristic
1193C2×C4C2×D4×D4311yescharacteristic
1194C2×C4#41×D4312yes—
1195C2×C4#1306337112yes—
1196C2×C4C24×D4311yescharacteristic
1197C8—22no—
1198C8—22no—
1199C8—861no—
1200C8—861no—
1201C8—861no—
1202C8—861no—
1203C22—21no—
1204C22—21no—
1205C22—21no—
1206C22—21no—
1207C22—21no—
1208C22—21no—
1209C22—21no—
1210C22—21no—
1211C22—44no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—862no—
1216C22—864no—
1217C22—862no—
1218C22—862no—
1219C22—3444no—
1220C22—1721no—
1221C22—1721no—
1222C22—1721no—
1223C22—1722no—
1224C22—1722no—
1225C22—6884no—
1226C22#1458354112yes—
1227C22C22×D4×D4311yescharacteristic
1228C4—21no—
1229C4—21no—
1230C4—41no—
1231C4—42no—
1232C4—42no—
1233C4—41no—
1234C4—41no—
1235C4—862no—
1236C4—862no—
1237C4—862no—
1238C4—1722no—
1239C4—1721no—
1240C4—1721no—
1241C4—1721no—
1242C4#1458354112yes—
1243C4C2×#41×D4311yescharacteristic
1244C4C2×#1306337111yescharacteristic
1245C2—22no—
1246C2—41no—
1247C2—41no—
1248C2—81no—
1249C2—3441no—
1250C2—1722no—
1251C2—1724no—
1252C2C2×#1458354111yescharacteristic
1253C2#1914937111yescharacteristic
1254C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3092C2
socleC22×C43C23×D4
hypercenter#3092D43
hypocenterC43#61177
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
1. #19148304C2semidirect
2. #19148237C2semidirect
3. #19146909C2semidirect
4. #19146898C2semidirect
5. #19146814C2semidirect
6. #19146799C2semidirect
7. #19146694C2semidirect
8. #19146679C2semidirect
9. #19146574C2semidirect
10. #19146559C2semidirect
11. #19144963C2semidirect
12. #19144566C2semidirect
13. #19144424C2semidirect
14. #19144287C2semidirect
15. #19144201C2semidirect
16. #19144144C2semidirect
17. #19143901C2semidirect
18. #19143840C2semidirect
19. #19143425C2semidirect
20. #19143294C2semidirect
21. #19143119C2semidirect
22. C2×#14582898C2semidirect
23. C43×#3092C2semidirect
26. C2×#13063358C22semidirect
30. C22×#10621877C22semidirect
32. #14583604C22semidirect
34. #14583597C22semidirect
36. #14583584C22semidirect
42. #14583550C22semidirect
47. #14583530C22semidirect
55. #14583410C22semidirect
58. #14583380C22semidirect
60. #14583266C22semidirect
61. #14583257C22semidirect
62. #14583252C22semidirect
63. #14583248C22semidirect
64. #14583243C22semidirect
65. #14583242C22semidirect
66. #14583236C22semidirect
67. #14583231C22semidirect
68. #14583202C22semidirect
69. #14583198C22semidirect
70. #14583188C22semidirect
71. #14583178C22semidirect
72. #14583158C22semidirect
73. #14583155C22semidirect
74. #14583155C22semidirect
75. #14583150C22semidirect
76. #14583150C22semidirect
77. #14583147C22semidirect
78. #14583147C22semidirect
79. #14583146C22semidirect
80. #14583143C22semidirect
81. #14583143C22semidirect
82. #14583141C22semidirect
83. #14583129C22semidirect
84. #14583120C22semidirect
85. #14583113C22semidirect
86. #14583108C22semidirect
87. #14583103C22semidirect
88. #14583064C22semidirect
89. #14583063C22semidirect
90. #14583063C22semidirect
91. #14583051C22semidirect
92. #14583047C22semidirect
93. #14583046C22semidirect
94. #14583046C22semidirect
95. #14583034C22semidirect
96. #14583010C22semidirect
97. #14582998C22semidirect
98. #14582986C22semidirect
99. #14582981C22semidirect
100. #14582974C22semidirect
101. #14582974C22semidirect
102. #14582973C22semidirect
103. #14582973C22semidirect
104. #14582935C22semidirect
105. #14582927C22semidirect
106. #14582909C22semidirect
108. #14582902C22semidirect
109. #14582899C22semidirect
110. #14582898C22semidirect
111. #14582898C22semidirect
112. #14582898C22semidirect
113. #14582898C22semidirect
115. #14582894C22semidirect
116. #14582893C22semidirect
117. C2×#13063248C22semidirect
118. C2×#13063248C22semidirect
121. #102×D43C22semidirect
123. #14582857C22semidirect
125. C22×C4⋊C4×C43C22semidirect
126. C43×#484C22semidirect
127. C43×#483C22semidirect
128. C43×#481C22semidirect
129. C43×#480C22semidirect
130. C43×#428C22semidirect
131. C43×#428C22semidirect
134. C43×#407C22semidirect
379. C2×D172#41semidirect
630. #3092D43semidirect
688. C22×C4⋊C4C2×D43semidirect
696. #484C2×D43semidirect
698. #483C2×D43semidirect
699. #481C2×D43semidirect
700. #480C2×D43semidirect
737. #428C2×D43semidirect
738. #428C2×D43semidirect
760. #407C2×D43semidirect
762. C43#61177semidirect

Maximal subgroups

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

subgroupindex
#191483042
#191482372
#191469092
#191468982
#191468142
#191467992
#191466942
#191466792
#191465742
#191465592
#191449632
#191445662
#191444242
#191442872
#191442012
#191441442
#191439012
#191438402
#191434252
#191432942
#191431192
C2×#145828982
C43×#30922
#6117743