Finite Group Databasebeta

← #25975439

Subgroups — #25975439

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148149C211yesmaximal, characteristic, complemented
2C2×#14583596C211yesmaximal, characteristic, complemented
3#19147201C212yesmaximal, complemented
4#19147159C212yesmaximal, complemented
5#19147144C212yesmaximal, complemented
6#19147099C212yesmaximal, complemented
7#19147083C212yesmaximal, complemented
8#19147058C212yesmaximal, complemented
9#19146990C212yesmaximal, complemented
10#19146967C212yesmaximal, complemented
11#19145145C211yesmaximal, characteristic, complemented
12#19144533C211yesmaximal, characteristic, complemented
13#19144528C211yesmaximal, characteristic, complemented
14#19144521C211yesmaximal, characteristic, complemented
15#19144416C211yesmaximal, characteristic, complemented
16#19144389C211yesmaximal, characteristic, complemented
17#19144212C211yesmaximal, characteristic, complemented
18#19144210C211yesmaximal, characteristic, complemented
19#19143399C211yesmaximal, characteristic, complemented
20#19143327C211yesmaximal, characteristic, complemented
21#19143184C211yesmaximal, characteristic, complemented
22#428×D43C211yesmaximal, characteristic, complemented
23C43×#3094C211yesmaximal, characteristic, complemented
24C2×#13063351C2211yescharacteristic
25C22×#10621877C2211yescharacteristic
26C2×M16×D43C2211yescharacteristic
27#14583617C2211yescharacteristic, complemented
28#14583612C2211yescharacteristic, complemented
29#14583604C2211yescharacteristic, complemented
30#14583597C2211yescharacteristic, complemented
31#14583596—21no—
32#14583596—21no—
33#14583596—21no—
34#14583596—21no—
35#14583596C2212yes—
36#14583596C2212yes—
37#14583596C2212yes—
38#14583596C2212yes—
39#14583593C2211yescharacteristic, complemented
40#14583588C2211yescharacteristic, complemented
41#14583584C2211yescharacteristic, complemented
42#14583582—21no—
43#14583575—21no—
44#14583573—21no—
45#14583550C2211yescharacteristic, complemented
46#14583539—21no—
47#14583452C2211yescharacteristic
48#14583433—21no—
49#14583427—21no—
50#14583427—21no—
51C2×#13063318—21no—
52C2×#13063316C2211yescharacteristic
53#14583411C2211yescharacteristic
54#14583410C2211yescharacteristic
55C2×#13063306—21no—
56C2×#13063296—21no—
57C2×#13063296C2211yescharacteristic
58C4×#10621898—21no—
59#14583367C2211yescharacteristic
60C2×D4×Dic43C2211yescharacteristic
61C2×C4×C22⋊D43C2211yescharacteristic
62C2×(C22⋊D43)⋊C4—21no—
63C2×#13063284C2211yescharacteristic
64#117×D43C2211yescharacteristic
65C2×C4⋊C4×D43C2211yescharacteristic
66#14583307C2212yescomplemented
67#14583306C2212yescomplemented
68#14583300C2212yescomplemented
69#14583299C2212yescomplemented
70#14583241C2212yescomplemented
71#14583241C2212yescomplemented
72#14583236C2212yescomplemented
73#14583231C2212yescomplemented
74#14583224C2212yescomplemented
75#14583224C2212yescomplemented
76#14583222C2212yescomplemented
77#14583221C2212yescomplemented
78#14583219C2212yescomplemented
79#14583216C2212yescomplemented
80#14583214C2212yescomplemented
81#14583211C2212yescomplemented
82#14583209C2212yescomplemented
83#14583205C2212yescomplemented
84#14583202C2212yescomplemented
85#14583201C2212yescomplemented
86#14583198C2212yescomplemented
87#14583197C2212yescomplemented
88#14583187C2212yescomplemented
89#14583177C2212yescomplemented
90#14583151C2212yescomplemented
91#14583150C2212yescomplemented
92#14583144C2212yescomplemented
93#14583143C2212yescomplemented
94#14583134C2212yescomplemented
95#14583133C2212yescomplemented
96#14583127C2212yescomplemented
97#14583126C2212yescomplemented
98#14583008C2212yescomplemented
99#14582996C2212yescomplemented
100#14582990C2212yescomplemented
101#14582979C2212yescomplemented
102#14582974C2212yescomplemented
103#14582973C2212yescomplemented
104#14582967C2212yescomplemented
105(C22⋊D43)⋊C8C2212yescomplemented
106#14582942C2211yescharacteristic
107#14582942C2211yescharacteristic
108#14582942C2211yescharacteristic
109#14582942C2211yescharacteristic
110#14582941C2211yescharacteristic
111#14582941C2211yescharacteristic
112#14582940C2212yescomplemented
113#14582939C2211yescharacteristic
114#14582939C2212yescomplemented
115#14582939C2212yescomplemented
116#14582938C2212yescomplemented
117#14582935C2212yescomplemented
118#14582935C2212yescomplemented
119#107×D43C2212yescomplemented
120#106×D43C2212yescomplemented
121#14582922C2211yescharacteristic
122#14582904C2211yescharacteristic
123#14582901C2211yescharacteristic
124#14582901C2211yescharacteristic
125#14582898C2211yescharacteristic
126#14582862C2211yescharacteristic
127M16×Dic43C2211yescharacteristic
128C2×#121×C43C2211yescharacteristic
129C2×#117×C43C2211yescharacteristic
130C43×#482C2212yescomplemented
131C43×#482C2212yescomplemented
132C43×#481C2212yescomplemented
133C43×#480C2212yescomplemented
134C43×#428C2211yescharacteristic
135C43×#428C2211yescharacteristic
136C43×#418C2211yescharacteristic
137C43×#418C2211yescharacteristic
138C43×#407C2211yescharacteristic
139C2×#10621898—21no—
140C2×#10621898C2311yescharacteristic
141C22×C22⋊D43—21no—
142C22×C22⋊D43D411yescharacteristic
143C23×Dic43—21no—
144C22×C4×D43—21no—
145C22×C4×D43C2311yescharacteristic
146#13063351—24no—
147C2×#10621883C2312yes—
148C2×#10621882C2312yes—
149C2×#10621877—24no—
150C2×#10621877C2311yescharacteristic
151C2×#10621877C2312yes—
152C2×#10621877C2311yescharacteristic
153C2×#10621872C2312yes—
154M16×D43—24no—
155C22×C43⋊C8C2312yes—
156C2×C8×D43C2312yes—
157#13063324C2311yescharacteristic
158#13063324C2311yescharacteristic
159#13063320—21no—
160#13063320—21no—
161#13063319—21no—
162#13063319—21no—
163#13063318—21no—
164#13063318—21no—
165#13063318—22no—
166#13063318—22no—
167#13063318—22no—
168#13063318—22no—
169#13063317—21no—
170#13063316—21no—
171#13063316—21no—
172#13063316C2311yescharacteristic
173#13063316C2312yes—
174#13063316C2311yescharacteristic
175#13063316C2312yes—
176#13063315—21no—
177#13063315—21no—
178#13063313—21no—
179#13063311—21no—
180#13063311—21no—
181#13063310—21no—
182#13063310—21no—
183#13063309—21no—
184#13063308—21no—
185#13063308—21no—
186#13063308—21no—
187#13063307—21no—
188#13063307—21no—
189#13063306—22no—
190#13063306—22no—
191#13063306—22no—
192#13063306—22no—
193#13063305C2311yescharacteristic
194#13063305C2311yescharacteristic
195#13063304—21no—
196#13063304C2311yescharacteristic
197#13063304C2311yescharacteristic
198#13063303—21no—
199#13063303—21no—
200#13063302—21no—
201#13063302—21no—
202#13063300C2311yescharacteristic
203#13063300C2311yescharacteristic
204#13063299—21no—
205#13063299C2311yescharacteristic
206#13063299C2311yescharacteristic
207#13063298—21no—
208#13063298—21no—
209#13063296—22no—
210#13063296—22no—
211#13063296—22no—
212#13063296—22no—
213#13063296—21no—
214#13063296—21no—
215#13063296C2312yes—
216#13063296C2312yes—
217#13063295—21no—
218#13063294—21no—
219C4×Dic86—21no—
220C4×Dic86—21no—
221C4×Dic86—21no—
222#13063290C2311yescharacteristic
223#13063290C2311yescharacteristic
224C4×D172—21no—
225C4×D172—21no—
226C4×D172—21no—
227D4×Dic43—21no—
228D4×Dic43—21no—
229D4×Dic43C2312yes—
230D4×Dic43C2312yes—
231#13063287C2311yescharacteristic
232#13063287C2311yescharacteristic
233C4×C22⋊D43—21no—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—21no—
236C4×C22⋊D43—21no—
237C4×C22⋊D43D411yescharacteristic
238C4×C22⋊D43D411yescharacteristic
239C4×C22⋊D43D411yescharacteristic
240C4×C22⋊D43D411yescharacteristic
241C4×C22⋊D43C2311yescharacteristic
242C4×C22⋊D43C2311yescharacteristic
243C4×C22⋊D43C2311yescharacteristic
244C4×C22⋊D43C2311yescharacteristic
245(C22⋊D43)⋊C4—21no—
246(C22⋊D43)⋊C4—21no—
247(C22⋊D43)⋊C4—22no—
248(C22⋊D43)⋊C4—22no—
249(C22⋊D43)⋊C4—22no—
250(C22⋊D43)⋊C4—22no—
251#13063284—21no—
252#13063284—21no—
253#13063284—21no—
254#13063284C2312yes—
255#13063284C2312yes—
256#13063284C2311yescharacteristic
257#13063283C2311yescharacteristic
258#13063283C2311yescharacteristic
259#13063282—21no—
260#13063282—21no—
261#13063282—21no—
262#13063282—21no—
263#13063281—21no—
264C2×C4⋊Dic43—21no—
265C2×C4⋊Dic43C2311yescharacteristic
266C2×C4⋊Dic43C2311yescharacteristic
267C2×Dic43⋊C4—21no—
268C2×Dic43⋊C4—21no—
269C2×Dic43⋊C4D411yescharacteristic
270C4⋊C4×D43—21no—
271C4⋊C4×D43—21no—
272C4⋊C4×D43C2311yescharacteristic
273C4⋊C4×D43C2311yescharacteristic
274C4⋊C4×D43C2312yes—
275C4⋊C4×D43C2312yes—
276C2×C22⋊Dic43—21no—
277C2×C22⋊Dic43—21no—
278C2×C22⋊Dic43—21no—
279C2×C22⋊Dic43D411yescharacteristic
280C2×(C2×D43)⋊C4D411yescharacteristic
281C22⋊C4×D43—21no—
282C2×C4×Dic43—21no—
283C2×C4×Dic43C2311yescharacteristic
284C42×D43—21no—
285C42×D43—21no—
286#13063259C2312yes—
287#13063259C2312yes—
288#13063258C2312yes—
289#13063258C2312yes—
290#13063258C2312yes—
291#13063258C2312yes—
292#13063258C2312yes—
293#13063257C2312yes—
294#13063257C2312yes—
295#13063256C2312yes—
296#13063256C2312yes—
297#13063256C2312yes—
298#13063256C2312yes—
299#13063256C2312yes—
300Dic43⋊C8C2312yes—
301Dic43⋊C8C2312yes—
302#13063250C2312yes—
303#13063250C2312yes—
304#13063248C2312yes—
305#13063247C2312yes—
306#13063247C2312yes—
307#13063246C2312yes—
308#13063246C2312yes—
309#13063245C2312yes—
310(C2×D43)⋊C8C2312yes—
311(C2×D43)⋊C8C2312yes—
312#13063235C2312yes—
313C8×Dic43C2312yes—
314C22×D4×C43—21no—
315C22×D4×C43C2311yescharacteristic
316C23×C4×C43C2311yescharacteristic
317C2×M16×C43C2311yescharacteristic
318C2×M16×C43C2311yescharacteristic
319#121×C43—21no—
320#121×C43—21no—
321#121×C43C2312yes—
322#121×C43C2312yes—
323#117×C43—21no—
324#117×C43—21no—
325#117×C43C2311yescharacteristic
326#117×C43C2311yescharacteristic
327#117×C43C2311yescharacteristic
328#117×C43C2311yescharacteristic
329C2×C4⋊C4×C43C2311yescharacteristic
330C2×C4⋊C4×C43C2311yescharacteristic
331C2×C4⋊C4×C43C2311yescharacteristic
332C2×C22⋊C4×C43—21no—
333C2×C22⋊C4×C43—21no—
334C2×C42×C43—21no—
335#107×C43C2312yes—
336#107×C43C2312yes—
337#106×C43C2312yes—
338#106×C43C2312yes—
339#102×C43C2312yes—
340#102×C43C2312yes—
341#102×C43C2312yes—
342#102×C43C2312yes—
343C22⋊C8×C43C2312yes—
344C22⋊C8×C43C2312yes—
345C24×C43—21no—
346C24×C43C2×D411yescharacteristic
347C23×D43C2×D411yescharacteristic
348C2×D4×C43—21no—
349C2×D4×C43—22no—
350C2×D4×C43—22no—
351C2×D4×C43—22no—
352C2×D4×C43—22no—
353C2×D4×C43—82no—
354C2×D4×C43C2412yes—
355C22×C4×C43—22no—
356C22×C4×C43—22no—
357C22×C4×C43—21no—
358C22×C4×C43—21no—
359C22×C4×C43—21no—
360C22×C4×C43C2×D411yescharacteristic
361C22×C4×C43C2×D411yescharacteristic
362C22×C4×C43C2×D411yescharacteristic
363C22×C4×C43C2411yescharacteristic
364C22×C4×C43C2411yescharacteristic
365C22×C4×C43C2411yescharacteristic
366C2×C22⋊D43—21no—
367C2×C22⋊D43—21no—
368C2×C22⋊D43—21no—
369C2×C22⋊D43—22no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43—42no—
372C2×C22⋊D43—44no—
373C2×C22⋊D43C2×D411yescharacteristic
374C2×C22⋊D43C2×D411yescharacteristic
375C2×C22⋊D43C2×D411yescharacteristic
376C2×C22⋊D43C2×D411yescharacteristic
377C22×Dic43—22no—
378C22×Dic43—22no—
379C22×Dic43—21no—
380C22×Dic43—21no—
381C22×Dic43—82no—
382C22×Dic43C2×D411yescharacteristic
383C22×Dic43C2×D411yescharacteristic
384C22×Dic43C2×D411yescharacteristic
385#10621898—22no—
386#10621898—22no—
387#10621898—44no—
388C2×D172—21no—
389C2×D172—21no—
390C2×D172C2411yescharacteristic
391C2×C4×D43—22no—
392C2×C4×D43—22no—
393C2×C4×D43—21no—
394C2×C4×D43—21no—
395C2×C4×D43—21no—
396C2×C4×D43—21no—
397C2×C4×D43—21no—
398C2×C4×D43—22no—
399C2×C4×D43—22no—
400C2×C4×D43—82no—
401C2×C4×D43C2×D411yescharacteristic
402C2×C4×D43C2×D411yescharacteristic
403C2×C4×D43C2411yescharacteristic
404C2×C4×D43C2411yescharacteristic
405C2×Dic86—21no—
406C2×Dic86—21no—
407C2×Dic86C2411yescharacteristic
408M16×C43—22no—
409M16×C43—22no—
410C2×C8×C43C2412yes—
411C2×C8×C43C2412yes—
412C4⋊C4×C43—21no—
413C4⋊C4×C43—21no—
414C4⋊C4×C43—21no—
415C4⋊C4×C43C2411yescharacteristic
416C4⋊C4×C43C2411yescharacteristic
417C4⋊C4×C43C2411yescharacteristic
418C4⋊C4×C43C2411yescharacteristic
419C4⋊C4×C43C2412yes—
420C22⋊C4×C43—22no—
421C22⋊C4×C43—22no—
422C22⋊C4×C43—21no—
423C22⋊C4×C43—21no—
424C22⋊C4×C43—21no—
425C22⋊C4×C43—21no—
426C42×C43—21no—
427C42×C43—21no—
428C42×C43—21no—
429C42×C43—21no—
430C22⋊Dic43—22no—
431C22⋊Dic43—22no—
432C22⋊Dic43—22no—
433C22⋊Dic43—22no—
434C22⋊Dic43—21no—
435C22⋊Dic43—22no—
436C22⋊Dic43—22no—
437C22⋊Dic43—21no—
438C22⋊Dic43—21no—
439C22⋊Dic43C2×D411yescharacteristic
440C22⋊Dic43C2×D411yescharacteristic
441C22⋊Dic43C2×D411yescharacteristic
442C22⋊Dic43C2×D411yescharacteristic
443#10621883—24no—
444#10621882—24no—
445(C2×D43)⋊C4—21no—
446(C2×D43)⋊C4—21no—
447(C2×D43)⋊C4—21no—
448(C2×D43)⋊C4—21no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—21no—
452(C2×D43)⋊C4—21no—
453(C2×D43)⋊C4—21no—
454(C2×D43)⋊C4—21no—
455(C2×D43)⋊C4C2×D411yescharacteristic
456(C2×D43)⋊C4C2×D411yescharacteristic
457(C2×D43)⋊C4C2×D411yescharacteristic
458(C2×D43)⋊C4C2×D411yescharacteristic
459C4⋊Dic43—21no—
460C4⋊Dic43—21no—
461C4⋊Dic43—22no—
462C4⋊Dic43—22no—
463C4⋊Dic43—21no—
464C4⋊Dic43—21no—
465C4⋊Dic43—21no—
466C4⋊Dic43—21no—
467C4⋊Dic43C2411yescharacteristic
468C4⋊Dic43C2411yescharacteristic
469C4⋊Dic43C2412yes—
470C4⋊Dic43C2412yes—
471Dic43⋊C4—21no—
472Dic43⋊C4—21no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—21no—
476Dic43⋊C4—21no—
477Dic43⋊C4—22no—
478Dic43⋊C4—22no—
479Dic43⋊C4—21no—
480Dic43⋊C4—21no—
481Dic43⋊C4—21no—
482Dic43⋊C4—21no—
483Dic43⋊C4—21no—
484Dic43⋊C4—21no—
485Dic43⋊C4C2×D411yescharacteristic
486Dic43⋊C4C2×D411yescharacteristic
487Dic43⋊C4C2×D411yescharacteristic
488Dic43⋊C4C2×D411yescharacteristic
489C4×Dic43—21no—
490C4×Dic43—22no—
491C4×Dic43—22no—
492C4×Dic43—21no—
493C4×Dic43—21no—
494C4×Dic43—21no—
495C4×Dic43—21no—
496C4×Dic43C2×D411yescharacteristic
497C4×Dic43C2×D411yescharacteristic
498C4×Dic43C2411yescharacteristic
499C4×Dic43C2411yescharacteristic
500#10621877—22no—
501#10621877—24no—
502#10621877#4114yescomplemented
503C2×C43⋊C8—24no—
504C2×C43⋊C8C2412yes—
505C2×C43⋊C8C2412yes—
506#10621872—24no—
507C8×D43—24no—
508C23×C43—22no—
509C23×C43—22no—
510C23×C43—41no—
511C23×C43—41no—
512C23×C43—42no—
513C23×C43—42no—
514C23×C43—42no—
515C23×C43C22×D411yescharacteristic
516C23×C43C22×D411yescharacteristic
517C23×C43C22×D411yescharacteristic
518C22×D43—22no—
519C22×D43—22no—
520C22×D43—21no—
521C22×D43—41no—
522C22×D43C22×D411yescharacteristic
523C22×D43C22×D411yescharacteristic
524D4×C43—22no—
525D4×C43—22no—
526D4×C43—42no—
527D4×C43—82no—
528D4×C43—82no—
529C2×C4×C43—22no—
530C2×C4×C43—22no—
531C2×C4×C43—22no—
532C2×C4×C43—21no—
533C2×C4×C43—21no—
534C2×C4×C43—21no—
535C2×C4×C43—21no—
536C2×C4×C43—21no—
537C2×C4×C43—21no—
538C2×C4×C43—22no—
539C2×C4×C43—21no—
540C2×C4×C43—21no—
541C2×C4×C43—42no—
542C2×C4×C43—42no—
543C2×C4×C43—81no—
544C2×C4×C43C22×D411yescharacteristic
545C2×C4×C43C22×D411yescharacteristic
546C2×C4×C43C22×D411yescharacteristic
547C2×C4×C43C2×#4112yes—
548C2×C4×C432−1+412yes—
549C2×C4×C43C2511yescharacteristic
550C22⋊D43—22no—
551C22⋊D43—22no—
552C22⋊D43—41no—
553C22⋊D43—41no—
554C22⋊D43—44no—
555C22⋊D43—42no—
556C22⋊D43—42no—
557C22⋊D43—44no—
558C22⋊D43—81no—
559C2×Dic43—22no—
560C2×Dic43—21no—
561C2×Dic43—21no—
562C2×Dic43—21no—
563C2×Dic43—22no—
564C2×Dic43—22no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—42no—
568C2×Dic43—42no—
569C2×Dic43—82no—
570C2×Dic43—82no—
571C2×Dic43C22×D411yescharacteristic
572C2×Dic43C22×D411yescharacteristic
573C2×Dic43C22×D411yescharacteristic
574C2×Dic43C22×D411yescharacteristic
575C2×Dic43C22×D411yescharacteristic
576C2×Dic43C22×D411yescharacteristic
577D172—21no—
578D172—21no—
579D172—42no—
580D172—81no—
581C4×D43—22no—
582C4×D43—22no—
583C4×D43—21no—
584C4×D43—21no—
585C4×D43—21no—
586C4×D43—21no—
587C4×D43—42no—
588C4×D43—42no—
589C4×D43—42no—
590C4×D43—81no—
591C4×D43—81no—
592C4×D43—82no—
593C4×D43—82no—
594Dic86—21no—
595Dic86—21no—
596Dic86—42no—
597Dic86—81no—
598C8×C43—22no—
599C8×C43—22no—
600C43⋊C8—22no—
601C43⋊C8C2×#4114yes—
602#61255—431nomaximal, Sylow
603C22×C43—21no—
604C22×C43—21no—
605C22×C43—21no—
606C22×C43—21no—
607C22×C43—21no—
608C22×C43—21no—
609C22×C43—21no—
610C22×C43—21no—
611C22×C43—42no—
612C22×C43—42no—
613C22×C43—42no—
614C22×C43—82no—
615C22×C43—84no—
616C22×C43#54712yes—
617C22×C43C23×D411yescharacteristic
618C2×D43—21no—
619C2×D43—21no—
620C2×D43—21no—
621C2×D43—21no—
622C2×D43—21no—
623C2×D43—44no—
624C2×D43—41no—
625C2×D43—41no—
626C2×D43—41no—
627C2×D43#57512yes—
628C4×C43—21no—
629C4×C43—21no—
630C4×C43—41no—
631C4×C43—42no—
632C4×C43—41no—
633C4×C43—41no—
634C4×C43—41no—
635C4×C43#54712yes—
636C4×C43C22×#4111yescharacteristic
637C4×C43C2×2−1+411yescharacteristic
638Dic43—21no—
639Dic43—21no—
640Dic43—21no—
641Dic43—21no—
642Dic43—21no—
643Dic43—21no—
644Dic43—41no—
645Dic43—42no—
646Dic43—41no—
647Dic43—41no—
648Dic43—42no—
649#3475—431no—
650C2×#553—431no—
651#3355—432no—
652#3351—432no—
653#3350—432no—
654#3347—432no—
655#3346—432no—
656#3345—432no—
657#3339—432no—
658#3337—432no—
659#3166—431no—
660#3094—431no—
661#3094D4311yescharacteristic, complemented
662#3093—431no—
663#3092—431no—
664#3080—431no—
665#3077—431no—
666#3055—431no—
667#3055—431no—
668C4×AGL(1,ℤ/8)—431no—
669D4×M16—431no—
670#2911—431no—
671C2×#428—431no—
672C2×C43—22no—
673C2×C43—41no—
674C2×C43—41no—
675C2×C43—82no—
676C2×C43C2×#54711yescharacteristic
677C2×C43C2×#57511yescharacteristic
678C2×C43#358511yescharacteristic
679D43—22no—
680D43—41no—
681D43—81no—
682C2×AGL(1,ℤ/8)—431no—
683C22×M16—431no—
684C22×M16—431no—
685#556—431no—
686#555—431no—
687#554—431no—
688#553—432no—
689#553—432no—
690#553—432no—
691#553—432no—
692#553—431no—
693#553—431no—
694#553—861no—
695#553—861no—
696#553—861no—
697#553—861no—
698#552—431no—
699#552—431no—
700#552—861no—
701#551—861no—
702#551—861no—
703#547—431no—
704#546—861no—
705#533—431no—
706#529—861no—
707#529—861no—
708#529—861no—
709C2×#126—861no—
710C2×#125—431no—
711#525—431no—
712#525—431no—
713C2×#123—861no—
714C2×#121—431no—
715C2×#121—861no—
716C2×#121C2×D4311yescharacteristic
717C4×#41—431no—
718C4×#41—861no—
719C2×C4×D4—431no—
720C2×C4×D4—431no—
721C2×C4×D4—861no—
722C2×#117—431no—
723C2×#117—431no—
724C2×#117C2×D4311yescharacteristic
725C22×C4⋊C4—431no—
726#501—432no—
727#501—432no—
728#499—432no—
729#499—432no—
730#485—432no—
731#485—432no—
732#484—432no—
733#483—432no—
734#482—432no—
735#482—432no—
736#482—432no—
737#482—432no—
738#482C2×D4312yescomplemented
739#482C2×D4312yescomplemented
740#481—432no—
741#481—432no—
742#481C2×D4312yescomplemented
743#480—432no—
744#480—432no—
745#480C2×D4312yescomplemented
746#479—432no—
747#479—432no—
748#478—432no—
749#478—432no—
750#478—432no—
751#478—432no—
752#476—432no—
753#474—432no—
754#469—432no—
755#469—432no—
756#468—432no—
757#468—432no—
758#466—432no—
759#466—432no—
760#465—432no—
761#465—432no—
762#442—432no—
763#440—432no—
764C4×SD16—432no—
765C4×D8—432no—
766#436—432no—
767#435—432no—
768#435—432no—
769C8×D4—432no—
770#428—431no—
771#428—431no—
772#428—431no—
773#428—431no—
774#428—431no—
775#428—431no—
776#428—432no—
777#428—432no—
778#428—431no—
779#428—432no—
780#428—432no—
781#428C2×D4311yescharacteristic
782#428C2×D4311yescharacteristic
783#427—432no—
784#427—432no—
785C2×#107—432no—
786C2×#106—432no—
787#423—431no—
788#418—431no—
789#418C2×D4311yescharacteristic
790#418C2×D4311yescharacteristic
791#417—431no—
792#417—431no—
793#417—431no—
794#407—431no—
795#407C2×D4311yescharacteristic
796C4×M16—431no—
797C43#6125511yescharacteristic, complemented, Sylow
798C2×#41—431no—
799C2×#41—861no—
800C22×D4—21no—
801C22×D4—431no—
802C22×D4—861no—
803C22×D4C22×D4311yescharacteristic
804C23×C4—431no—
805C23×C4—861no—
806C23×C4—861no—
807C23×C4C22×D4311yescharacteristic
808AGL(1,ℤ/8)—864no—
809C2×SD16—432no—
810C2×D8—432no—
811C2×M16—431no—
812C2×M16—431no—
813C2×M16—432no—
814C2×M16—432no—
815C2×M16—864no—
816C2×M16—864no—
817C2×M16C22×D4311yescharacteristic
818C2×M16C22×D4311yescharacteristic
819C22×C8—432no—
820C22×C8—432no—
821C4⋊Q8—431no—
822C4⋊Q8—431no—
823#126—861no—
824#126—861no—
825#126—861no—
826#126—861no—
827#126—862no—
828#126—862no—
829#126—862no—
830#126—862no—
831#126—861no—
832#126—861no—
833#125—432no—
834#125—432no—
835#125—431no—
836#125—431no—
837#125—861no—
838#125—861no—
839#125—861no—
840#125—861no—
841#125—861no—
842#124—861no—
843#124—861no—
844#124—861no—
845#123—861no—
846#123—861no—
847#123—861no—
848#123—861no—
849#123—861no—
850#123—861no—
851#123—862no—
852#123—862no—
853#123—862no—
854#123—862no—
855#123—861no—
856#123—861no—
857C22⋊Q8—431no—
858C22⋊Q8—431no—
859C22⋊Q8—431no—
860C22⋊Q8—431no—
861C22⋊Q8—861no—
862C22⋊Q8—861no—
863C22⋊Q8—861no—
864C22⋊Q8—861no—
865C22⋊Q8—861no—
866#121—21no—
867#121—21no—
868#121—432no—
869#121—432no—
870#121—431no—
871#121—431no—
872#121—431no—
873#121—431no—
874#121—861no—
875#121—861no—
876#121—861no—
877#121—861no—
878#121—861no—
879#121—862no—
880#121—862no—
881#121—862no—
882#121—862no—
883#121C22×D4312yes—
884#121C22×D4312yes—
885#120—861no—
886#120—861no—
887C4×Q8—431no—
888C4×Q8—431no—
889C4×Q8—861no—
890C4×Q8—861no—
891C4×Q8—861no—
892C4×D4—431no—
893C4×D4—431no—
894C4×D4—431no—
895C4×D4—431no—
896C4×D4—431no—
897C4×D4—431no—
898C4×D4—431no—
899C4×D4—431no—
900C4×D4—432no—
901C4×D4—432no—
902C4×D4—431no—
903C4×D4—431no—
904C4×D4—861no—
905C4×D4—861no—
906C4×D4—861no—
907C4×D4—861no—
908C4×D4—861no—
909C4×D4—862no—
910C4×D4—862no—
911C4×D4—862no—
912C4×D4—862no—
913C4×D4—861no—
914C4×D4—861no—
915C4×D4—861no—
916C4×D4—861no—
917C4×D4—861no—
918C4×D4—861no—
919#117—21no—
920#117—21no—
921#117—431no—
922#117—432no—
923#117—432no—
924#117—431no—
925#117—431no—
926#117—861no—
927#117—861no—
928#117—861no—
929#117—861no—
930#117—861no—
931#117—861no—
932#117—861no—
933#117—861no—
934#117C22×D4311yescharacteristic
935#117C22×D4311yescharacteristic
936#117C22×D4311yescharacteristic
937#117C22×D4311yescharacteristic
938C2×C4⋊C4—431no—
939C2×C4⋊C4—431no—
940C2×C4⋊C4—431no—
941C2×C4⋊C4—432no—
942C2×C4⋊C4—432no—
943C2×C4⋊C4—431no—
944C2×C4⋊C4—431no—
945C2×C4⋊C4—861no—
946C2×C4⋊C4—861no—
947C2×C4⋊C4—861no—
948C2×C4⋊C4—861no—
949C2×C4⋊C4—861no—
950C2×C4⋊C4C22×D4311yescharacteristic
951C2×C4⋊C4C22×D4311yescharacteristic
952C2×C4⋊C4C22×D4311yescharacteristic
953C2×C22⋊C4—21no—
954C2×C22⋊C4—21no—
955C2×C22⋊C4—431no—
956C2×C22⋊C4—431no—
957C2×C22⋊C4—861no—
958C2×C22⋊C4—861no—
959C2×C22⋊C4—861no—
960C2×C22⋊C4—861no—
961C2×C42—21no—
962C2×C42—431no—
963C2×C42—861no—
964C2×C42—861no—
965C2×C42—861no—
966#107—432no—
967#107—432no—
968#107—432no—
969#107—432no—
970#107—432no—
971#107—432no—
972#107—432no—
973#107C22×D4312yes—
974#107C22×D4312yes—
975#106—432no—
976#106—432no—
977#106—432no—
978#106—432no—
979#106—432no—
980#106—432no—
981#106—432no—
982#106C22×D4312yes—
983#106C22×D4312yes—
984C4⋊C8—432no—
985C4⋊C8—432no—
986#103—432no—
987#103—432no—
988#103—432no—
989#102—432no—
990#102—432no—
991#102—432no—
992#102—432no—
993#102—432no—
994#102C22×D4312yes—
995#102C22×D4312yes—
996#102C22×D4312yes—
997#102C22×D4312yes—
998C22⋊C8—432no—
999C22⋊C8—432no—
1000C22⋊C8C22×D4312yes—
1001C22⋊C8C22×D4312yes—
1002#97—432no—
1003C4×C8—432no—
1004C24—21no—
1005C24—431no—
1006C24D4×D4311yescharacteristic
1007#41—862no—
1008#41—862no—
1009#41—1724no—
1010C2×Q8—431no—
1011C2×Q8—861no—
1012C2×Q8—861no—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—21no—
1016C2×D4—22no—
1017C2×D4—22no—
1018C2×D4—82no—
1019C2×D4—431no—
1020C2×D4—431no—
1021C2×D4—431no—
1022C2×D4—431no—
1023C2×D4—431no—
1024C2×D4—861no—
1025C2×D4—861no—
1026C2×D4—861no—
1027C2×D4—862no—
1028C2×D4—862no—
1029C2×D4—861no—
1030C2×D4—861no—
1031C2×D4—1722no—
1032C2×D4—1724no—
1033C2×D4C23×D4312yes—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—21no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—431no—
1040C22×C4—431no—
1041C22×C4—431no—
1042C22×C4—431no—
1043C22×C4—431no—
1044C22×C4—431no—
1045C22×C4—431no—
1046C22×C4—861no—
1047C22×C4—861no—
1048C22×C4—861no—
1049C22×C4—862no—
1050C22×C4—862no—
1051C22×C4—861no—
1052C22×C4—862no—
1053C22×C4—862no—
1054C22×C4—862no—
1055C22×C4—862no—
1056C22×C4—861no—
1057C22×C4—861no—
1058C22×C4—861no—
1059C22×C4—3442no—
1060C22×C4—3442no—
1061C22×C4D4×D4311yescharacteristic
1062C22×C4D4×D4311yescharacteristic
1063C22×C4D4×D4311yescharacteristic
1064C22×C4C23×D4311yescharacteristic
1065C22×C4C23×D4311yescharacteristic
1066C22×C4C23×D4311yescharacteristic
1067SD16—864no—
1068D8—864no—
1069M16—22no—
1070M16—22no—
1071M16—434no—
1072M16—864no—
1073M16—864no—
1074M16—862no—
1075C2×C8—432no—
1076C2×C8—432no—
1077C2×C8—864no—
1078C2×C8—864no—
1079C2×C8C23×D4312yes—
1080C2×C8C23×D4312yes—
1081C4⋊C4—21no—
1082C4⋊C4—21no—
1083C4⋊C4—21no—
1084C4⋊C4—431no—
1085C4⋊C4—431no—
1086C4⋊C4—431no—
1087C4⋊C4—431no—
1088C4⋊C4—431no—
1089C4⋊C4—431no—
1090C4⋊C4—432no—
1091C4⋊C4—432no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—861no—
1095C4⋊C4—861no—
1096C4⋊C4—862no—
1097C4⋊C4—862no—
1098C4⋊C4—862no—
1099C4⋊C4—862no—
1100C4⋊C4—861no—
1101C4⋊C4—861no—
1102C4⋊C4—861no—
1103C4⋊C4—861no—
1104C4⋊C4—861no—
1105C4⋊C4—861no—
1106C4⋊C4—861no—
1107C4⋊C4—861no—
1108C4⋊C4—861no—
1109C4⋊C4—861no—
1110C4⋊C4—861no—
1111C4⋊C4—861no—
1112C4⋊C4—861no—
1113C4⋊C4—861no—
1114C4⋊C4C23×D4312yes—
1115C4⋊C4C23×D4311yescharacteristic
1116C4⋊C4C23×D4311yescharacteristic
1117C4⋊C4C23×D4311yescharacteristic
1118C4⋊C4C23×D4311yescharacteristic
1119C22⋊C4—21no—
1120C22⋊C4—21no—
1121C22⋊C4—21no—
1122C22⋊C4—21no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—431no—
1126C22⋊C4—431no—
1127C22⋊C4—431no—
1128C22⋊C4—431no—
1129C22⋊C4—431no—
1130C22⋊C4—431no—
1131C22⋊C4—431no—
1132C22⋊C4—431no—
1133C22⋊C4—861no—
1134C22⋊C4—861no—
1135C22⋊C4—861no—
1136C22⋊C4—861no—
1137C22⋊C4—861no—
1138C22⋊C4—861no—
1139C22⋊C4—861no—
1140C22⋊C4—861no—
1141C22⋊C4—862no—
1142C22⋊C4—862no—
1143C22⋊C4—862no—
1144C22⋊C4—862no—
1145C22⋊C4—861no—
1146C22⋊C4—862no—
1147C22⋊C4—862no—
1148C22⋊C4—861no—
1149C22⋊C4—861no—
1150C22⋊C4—861no—
1151C22⋊C4—861no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—431no—
1157C42—431no—
1158C42—431no—
1159C42—431no—
1160C42—861no—
1161C42—861no—
1162C42—861no—
1163C42—861no—
1164C42—861no—
1165C42—862no—
1166C42—862no—
1167C23—22no—
1168C23—22no—
1169C23—41no—
1170C23—41no—
1171C23—42no—
1172C23—42no—
1173C23—42no—
1174C23—431no—
1175C23—431no—
1176C23—862no—
1177C23—862no—
1178C23—861no—
1179C23—1721no—
1180C23C2×D4×D4311yescharacteristic
1181C23C2×D4×D4311yescharacteristic
1182C23C2×D4×D4311yescharacteristic
1183Q8—861no—
1184Q8—861no—
1185Q8—3441no—
1186Q8—1722no—
1187D4—22no—
1188D4—22no—
1189D4—42no—
1190D4—82no—
1191D4—82no—
1192D4—862no—
1193D4—862no—
1194D4—861no—
1195D4—861no—
1196D4—3441no—
1197D4—3441no—
1198D4—1722no—
1199D4—1721no—
1200D4—1721no—
1201D4—1722no—
1202D4—1724no—
1203D4—1724no—
1204D4—1722no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—81no—
1220C2×C4—431no—
1221C2×C4—431no—
1222C2×C4—431no—
1223C2×C4—431no—
1224C2×C4—431no—
1225C2×C4—431no—
1226C2×C4—862no—
1227C2×C4—861no—
1228C2×C4—861no—
1229C2×C4—861no—
1230C2×C4—861no—
1231C2×C4—862no—
1232C2×C4—862no—
1233C2×C4—862no—
1234C2×C4—861no—
1235C2×C4—861no—
1236C2×C4—862no—
1237C2×C4—861no—
1238C2×C4—3441no—
1239C2×C4—3442no—
1240C2×C4—3442no—
1241C2×C4—3441no—
1242C2×C4—3442no—
1243C2×C4—3442no—
1244C2×C4—1722no—
1245C2×C4—1722no—
1246C2×C4—1721no—
1247C2×C4—1721no—
1248C2×C4—1722no—
1249C2×C4—1722no—
1250C2×C4—1722no—
1251C2×C4C2×D4×D4311yescharacteristic
1252C2×C4C2×D4×D4311yescharacteristic
1253C2×C4C2×D4×D4311yescharacteristic
1254C2×C4#41×D4312yes—
1255C2×C4#1306337212yes—
1256C2×C4C24×D4311yescharacteristic
1257C8—22no—
1258C8—22no—
1259C8—434no—
1260C8—862no—
1261C22—21no—
1262C22—21no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—82no—
1273C22—84no—
1274C22—432no—
1275C22—861no—
1276C22—861no—
1277C22—861no—
1278C22—861no—
1279C22—861no—
1280C22—1724no—
1281C22—1721no—
1282C22—1721no—
1283C22—1721no—
1284C22#1458354712yes—
1285C22C22×D4×D4311yescharacteristic
1286C4—21no—
1287C4—21no—
1288C4—41no—
1289C4—41no—
1290C4—42no—
1291C4—41no—
1292C4—41no—
1293C4—861no—
1294C4—861no—
1295C4—861no—
1296C4—861no—
1297C4—861no—
1298C4—861no—
1299C4—1721no—
1300C4—1722no—
1301C4—1721no—
1302C4—1722no—
1303C4—1721no—
1304C4#1458354712yes—
1305C4C2×#41×D4311yescharacteristic
1306C4C2×#1306337211yescharacteristic
1307C2—22no—
1308C2—41no—
1309C2—41no—
1310C2—82no—
1311C2—862no—
1312C2—3441no—
1313C2—1721no—
1314C2C2×#1458354711yescharacteristic
1315C2#575×D4311yescharacteristic
1316C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
hypercenter#3094D43
hypocenterC43#61255
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #19148149C2semidirect
2. C2×#14583596C2semidirect
3. #19147201C2semidirect
4. #19147159C2semidirect
5. #19147144C2semidirect
6. #19147099C2semidirect
7. #19147083C2semidirect
8. #19147058C2semidirect
9. #19146990C2semidirect
10. #19146967C2semidirect
11. #19145145C2semidirect
12. #19144533C2semidirect
13. #19144528C2semidirect
14. #19144521C2semidirect
15. #19144416C2semidirect
16. #19144389C2semidirect
17. #19144212C2semidirect
18. #19144210C2semidirect
19. #19143399C2semidirect
20. #19143327C2semidirect
21. #19143184C2semidirect
22. #428×D43C2semidirect
23. C43×#3094C2semidirect
27. #14583617C22semidirect
28. #14583612C22semidirect
29. #14583604C22semidirect
30. #14583597C22semidirect
39. #14583593C22semidirect
40. #14583588C22semidirect
41. #14583584C22semidirect
45. #14583550C22semidirect
66. #14583307C22semidirect
67. #14583306C22semidirect
68. #14583300C22semidirect
69. #14583299C22semidirect
70. #14583241C22semidirect
71. #14583241C22semidirect
72. #14583236C22semidirect
73. #14583231C22semidirect
74. #14583224C22semidirect
75. #14583224C22semidirect
76. #14583222C22semidirect
77. #14583221C22semidirect
78. #14583219C22semidirect
79. #14583216C22semidirect
80. #14583214C22semidirect
81. #14583211C22semidirect
82. #14583209C22semidirect
83. #14583205C22semidirect
84. #14583202C22semidirect
85. #14583201C22semidirect
86. #14583198C22semidirect
87. #14583197C22semidirect
88. #14583187C22semidirect
89. #14583177C22semidirect
90. #14583151C22semidirect
91. #14583150C22semidirect
92. #14583144C22semidirect
93. #14583143C22semidirect
94. #14583134C22semidirect
95. #14583133C22semidirect
96. #14583127C22semidirect
97. #14583126C22semidirect
98. #14583008C22semidirect
99. #14582996C22semidirect
100. #14582990C22semidirect
101. #14582979C22semidirect
102. #14582974C22semidirect
103. #14582973C22semidirect
104. #14582967C22semidirect
105. (C22⋊D43)⋊C8C22semidirect
112. #14582940C22semidirect
114. #14582939C22semidirect
115. #14582939C22semidirect
116. #14582938C22semidirect
117. #14582935C22semidirect
118. #14582935C22semidirect
119. #107×D43C22semidirect
120. #106×D43C22semidirect
130. C43×#482C22semidirect
131. C43×#482C22semidirect
132. C43×#481C22semidirect
133. C43×#480C22semidirect
502. #10621877#41semidirect
661. #3094D43semidirect
738. #482C2×D43semidirect
739. #482C2×D43semidirect
742. #481C2×D43semidirect
745. #480C2×D43semidirect
797. C43#61255semidirect

Maximal subgroups

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

subgroupindex
#191481492
C2×#145835962
#191472012
#191471592
#191471442
#191470992
#191470832
#191470582
#191469902
#191469672
#191451452
#191445332
#191445282
#191445212
#191444162
#191443892
#191442122
#191442102
#191433992
#191433272
#191431842
#428×D432
C43×#30942
#6125543