Finite Group Databasebeta

← #25976437

Subgroups — #25976437

Order 11008.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148192C211yesmaximal, characteristic, complemented
2C2×#14583608C211yesmaximal, characteristic, complemented
3#19147426C212yesmaximal, complemented
4#19147415C212yesmaximal, complemented
5#19147371C212yesmaximal, complemented
6#19147352C212yesmaximal, complemented
7#19147341C212yesmaximal, complemented
8#19147297C212yesmaximal, complemented
9#19147250C212yesmaximal, complemented
10#19147239C212yesmaximal, complemented
11#19144995C211yesmaximal, characteristic, complemented
12#19144993C211yesmaximal, characteristic, complemented
13#19144986C211yesmaximal, characteristic, complemented
14#19144418C211yesmaximal, characteristic, complemented
15#19144415C211yesmaximal, characteristic, complemented
16#19144406C211yesmaximal, characteristic, complemented
17#19144056C211yesmaximal, characteristic, complemented
18#19144056C211yesmaximal, characteristic, complemented
19#19143546C211yesmaximal, characteristic, complemented
20AGL(1,ℤ/8)×Dic43C211yesmaximal, characteristic, complemented
21AGL(1,ℤ/8)×Dic43C211yesmaximal, characteristic, complemented
22C4×#13063351C211yesmaximal, characteristic, complemented
23C43×#3036C211yesmaximal, characteristic, complemented
24C2×#13063351C2211yescharacteristic
25#14583635C2211yescharacteristic, complemented
26#14583631C2211yescharacteristic, complemented
27#14583631C2211yescharacteristic, complemented
28#14583624C2211yescharacteristic, complemented
29#14583623C2211yescharacteristic, complemented
30#14583618C2211yescharacteristic, complemented
31#14583618C2211yescharacteristic, complemented
32#14583608—21no—
33#14583608—21no—
34#14583608—21no—
35#14583608—21no—
36#14583608C2212yes—
37#14583608C2212yes—
38#14583608C2212yes—
39#14583608C2212yes—
40#14583601—21no—
41#14583592—21no—
42#14583592—21no—
43#14583569C2211yescharacteristic, complemented
44#14583555—21no—
45#14583445C2211yescharacteristic
46#14583445C2211yescharacteristic
47C2×#13063324C2211yescharacteristic
48#14583431—21no—
49#14583429—21no—
50#14583429—21no—
51C2×#13063317C2211yescharacteristic
52C2×#13063316C2211yescharacteristic
53C2×#13063304—21no—
54C2×#13063302—21no—
55C2×#13063302—21no—
56#41×Dic43C2211yescharacteristic
57#41×Dic43C2211yescharacteristic
58C4×#10621898C2211yescharacteristic
59C4×#10621900—21no—
60C2×C4×Dic86C2211yescharacteristic
61C2×D4×Dic43C2211yescharacteristic
62C2×D4×Dic43C2211yescharacteristic
63C22×Dic43⋊C4—21no—
64#14583267C2212yescomplemented
65#14583266C2212yescomplemented
66#14583263C2212yescomplemented
67#14583262C2212yescomplemented
68#14583260C2212yescomplemented
69#14583257C2212yescomplemented
70#14583255C2212yescomplemented
71#14583253C2212yescomplemented
72#14583253C2212yescomplemented
73#14583252C2212yescomplemented
74#14583248C2212yescomplemented
75#14583244C2212yescomplemented
76#14583208C2212yescomplemented
77#14583207C2212yescomplemented
78#14583207C2212yescomplemented
79#14583204C2212yescomplemented
80#14583201C2212yescomplemented
81#14583200C2212yescomplemented
82#14583200C2212yescomplemented
83#14583197C2212yescomplemented
84#14583192C2212yescomplemented
85#14583187C2212yescomplemented
86#14583182C2212yescomplemented
87#14583177C2212yescomplemented
88#14583116C2212yes—
89#14583116C2212yes—
90#14583112C2212yes—
91#14583112C2212yes—
92#14583102C2212yes—
93#14583102C2212yes—
94#14583092C2212yes—
95#14583092C2212yes—
96#14583028C2212yescomplemented
97#14583028C2212yescomplemented
98#14583026C2212yescomplemented
99#14583023C2212yescomplemented
100#14583011C2212yes—
101#14583011C2212yes—
102#14583009C2212yes—
103#14583000C2212yes—
104#14583000C2212yes—
105#14582999C2212yes—
106SD16×Dic43C2212yes—
107SD16×Dic43C2212yes—
108C4×#10621883C2212yes—
109D8×Dic43C2212yes—
110D8×Dic43C2212yes—
111C4×#10621882C2212yes—
112#14582941C2211yescharacteristic
113#14582941C2211yescharacteristic
114#14582939C2211yescharacteristic
115#14582922C2211yescharacteristic
116#14582922C2211yescharacteristic
117#14582904C2211yescharacteristic
118#14582901C2211yescharacteristic
119#14582901C2211yescharacteristic
120#14582900C2211yescharacteristic
121#14582900C2211yescharacteristic
122#14582900C2211yescharacteristic
123#14582900C2211yescharacteristic
124#14582898C2211yescharacteristic
125C4×#10621877C2211yescharacteristic
126M16×Dic43C2211yescharacteristic
127M16×Dic43C2211yescharacteristic
128C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
129C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
130C43×#532C2211yescharacteristic
131C2×C4×D4×C43C2211yescharacteristic
132C43×#463C2212yes—
133C43×#463C2212yes—
134C43×#461C2212yes—
135C43×#459C2212yes—
136C43×#423C2211yescharacteristic
137C43×#417C2211yescharacteristic
138C43×#417C2211yescharacteristic
139C2×#10621898C2311yescharacteristic
140C2×#10621900—21no—
141C22×Dic86—21no—
142C22×Dic86D411yescharacteristic
143C23×Dic43—21no—
144C23×Dic43—21no—
145#13063351—24no—
146C2×#10621883C2312yes—
147C2×#10621882C2312yes—
148C2×#10621877C2311yescharacteristic
149C2×#10621877C2311yescharacteristic
150#13063324—21no—
151#13063324—21no—
152#13063324C2312yes—
153#13063324C2312yes—
154#13063323C2311yescharacteristic
155#13063323C2311yescharacteristic
156#13063321C2311yescharacteristic
157#13063321C2311yescharacteristic
158#13063320—21no—
159#13063320—21no—
160#13063318—21no—
161#13063318—21no—
162#13063318—21no—
163#13063318—21no—
164#13063317—21no—
165#13063317—21no—
166#13063317C2312yes—
167#13063317C2312yes—
168#13063316—21no—
169#13063316—21no—
170#13063316—21no—
171#13063316C2312yes—
172#13063316C2312yes—
173#13063315—21no—
174#13063315—21no—
175#13063314C2311yescharacteristic
176#13063314C2311yescharacteristic
177#13063312—21no—
178#13063312C2311yescharacteristic
179#13063312C2311yescharacteristic
180#13063311—21no—
181#13063311—21no—
182#13063309—21no—
183#13063309—21no—
184#13063307—21no—
185#13063307—21no—
186#13063306—21no—
187#13063306—21no—
188#13063305—21no—
189#13063304—22no—
190#13063304—22no—
191#13063304—22no—
192#13063304—22no—
193#13063302—21no—
194#13063302—21no—
195#13063302—22no—
196#13063302—22no—
197#13063302—22no—
198#13063302—22no—
199#13063302—22no—
200#13063302—22no—
201#13063302—22no—
202#13063302—22no—
203#13063297—21no—
204#13063297—21no—
205#13063297—21no—
206#13063297—21no—
207#13063297—21no—
208#13063297—21no—
209#13063296—21no—
210Q8×Dic43C2311yescharacteristic
211Q8×Dic43C2311yescharacteristic
212Q8×Dic43C2311yescharacteristic
213Q8×Dic43C2311yescharacteristic
214C4×Dic86D411yescharacteristic
215C4×Dic86D411yescharacteristic
216C4×Dic86D411yescharacteristic
217C4×Dic86D411yescharacteristic
218C4×Dic86C2311yescharacteristic
219C4×Dic86C2311yescharacteristic
220C4×Dic86C2311yescharacteristic
221C4×Dic86C2311yescharacteristic
222C4×Dic86C2311yescharacteristic
223C4×Dic86C2311yescharacteristic
224#13063290—21no—
225C4×D172C2311yescharacteristic
226C4×D172C2311yescharacteristic
227D4×Dic43—21no—
228D4×Dic43—21no—
229D4×Dic43—21no—
230D4×Dic43—21no—
231D4×Dic43—21no—
232D4×Dic43—21no—
233D4×Dic43—21no—
234D4×Dic43—21no—
235D4×Dic43—21no—
236D4×Dic43C2311yescharacteristic
237D4×Dic43C2311yescharacteristic
238D4×Dic43C2312yes—
239D4×Dic43C2312yes—
240D4×Dic43C2312yes—
241D4×Dic43C2312yes—
242D4×Dic43C2311yescharacteristic
243D4×Dic43C2311yescharacteristic
244C4×C22⋊D43—21no—
245C4×C22⋊D43—21no—
246C4×C22⋊D43—21no—
247C4×C22⋊D43—21no—
248C4×C22⋊D43—21no—
249C4×C22⋊D43—21no—
250(C22⋊D43)⋊C4—21no—
251(C22⋊D43)⋊C4—21no—
252#13063284—21no—
253#13063284—21no—
254#13063284C2311yescharacteristic
255#13063283—21no—
256#13063282—21no—
257#13063281—21no—
258#13063281—21no—
259C2×C4⋊Dic43—21no—
260C2×C4⋊Dic43D411yescharacteristic
261C2×C4⋊Dic43C2311yescharacteristic
262C2×C4⋊Dic43C2311yescharacteristic
263C2×Dic43⋊C4—21no—
264C2×Dic43⋊C4—21no—
265C2×Dic43⋊C4—21no—
266C2×Dic43⋊C4—21no—
267C2×Dic43⋊C4—22no—
268C2×Dic43⋊C4—22no—
269C2×Dic43⋊C4—22no—
270C2×Dic43⋊C4—22no—
271C2×Dic43⋊C4D411yescharacteristic
272C2×Dic43⋊C4D411yescharacteristic
273C2×C22⋊Dic43—21no—
274C2×C22⋊Dic43—21no—
275C2×C4×Dic43—21no—
276C2×C4×Dic43—21no—
277C2×C4×Dic43C2311yescharacteristic
278C2×C4×Dic43C2311yescharacteristic
279C42×D43—21no—
280#13063259C2312yes—
281#13063259C2312yes—
282#13063258C2312yes—
283#13063257C2312yes—
284#13063257C2312yes—
285#13063256C2312yes—
286Dic43⋊C8C2312yes—
287Dic43⋊C8C2312yes—
288Dic43⋊C8C2312yes—
289Dic43⋊C8C2312yes—
290#13063250C2312yes—
291#13063250C2312yes—
292#13063249C2312yes—
293#13063249C2312yes—
294#13063249C2312yes—
295#13063249C2312yes—
296#13063248C2312yes—
297#13063247C2312yes—
298#13063247C2312yes—
299#13063246C2312yes—
300#13063246C2312yes—
301#13063246C2312yes—
302#13063246C2312yes—
303#13063246C2312yes—
304#13063246C2312yes—
305#13063245C2312yes—
306#13063236C2312yes—
307#13063235C2312yes—
308#13063235C2312yes—
309C4×C43⋊C8C2312yes—
310C8×Dic43C2312yes—
311C8×Dic43C2312yes—
312C2×#41×C43C2311yescharacteristic
313C2×#41×C43C2311yescharacteristic
314C22×D4×C43C2311yescharacteristic
315C23×C4×C43—21no—
316AGL(1,ℤ/8)×C43—24no—
317AGL(1,ℤ/8)×C43—24no—
318C2×SD16×C43C2312yes—
319C2×SD16×C43C2312yes—
320C2×D8×C43C2312yes—
321C2×D8×C43C2312yes—
322C2×M16×C43C2311yescharacteristic
323C2×M16×C43C2311yescharacteristic
324C4⋊Q8×C43C2311yescharacteristic
325#127×C43C2311yescharacteristic
326#124×C43C2311yescharacteristic
327#124×C43C2311yescharacteristic
328#121×C43—21no—
329#121×C43—21no—
330C4×D4×C43—21no—
331C4×D4×C43—21no—
332C4×D4×C43—21no—
333C4×D4×C43—21no—
334C4×D4×C43C2312yes—
335C4×D4×C43C2312yes—
336C2×C4⋊C4×C43C2311yescharacteristic
337C2×C22⋊C4×C43—21no—
338C2×C42×C43C2311yescharacteristic
339C4⋊C8×C43C2312yes—
340C4⋊C8×C43C2312yes—
341#103×C43C2312yes—
342#103×C43C2312yes—
343#102×C43C2312yes—
344#102×C43C2312yes—
345C24×C43—21no—
346#41×C43—22no—
347#41×C43—22no—
348#41×C43—22no—
349#41×C43—22no—
350C2×Q8×C43C2411yescharacteristic
351C2×Q8×C43C2411yescharacteristic
352C2×D4×C43—21no—
353C2×D4×C43—21no—
354C2×D4×C43—21no—
355C2×D4×C43—22no—
356C2×D4×C43—21no—
357C2×D4×C43—21no—
358C2×D4×C43#4114yescomplemented
359C2×D4×C43C2411yescharacteristic
360C2×D4×C43C2411yescharacteristic
361C2×D4×C43C2412yes—
362C22×C4×C43—21no—
363C22×C4×C43—21no—
364C22×C4×C43—22no—
365C22×C4×C43—22no—
366C22×C4×C43—21no—
367C22×C4×C43—82no—
368C22×C4×C43C2×D411yescharacteristic
369C22×C4×C43C2×D411yescharacteristic
370C22×C4×C43C2411yescharacteristic
371C2×C22⋊D43—21no—
372C2×C22⋊D43—21no—
373C2×C22⋊D43—21no—
374C2×C22⋊D43—21no—
375C2×C22⋊D43—21no—
376C22×Dic43—21no—
377C22×Dic43—21no—
378C22×Dic43—22no—
379C22×Dic43—22no—
380C22×Dic43—21no—
381C22×Dic43—21no—
382C22×Dic43—22no—
383C22×Dic43—22no—
384C22×Dic43—21no—
385C22×Dic43—21no—
386C22×Dic43—44no—
387C22×Dic43—82no—
388C22×Dic43C2×D411yescharacteristic
389C22×Dic43C2×D411yescharacteristic
390C22×Dic43C2×D411yescharacteristic
391C22×Dic43C2×D411yescharacteristic
392#10621900—44no—
393#10621898—22no—
394#10621898—22no—
395C2×D172C2411yescharacteristic
396C2×C4×D43—21no—
397C2×C4×D43—21no—
398C2×C4×D43—21no—
399C2×Dic86—22no—
400C2×Dic86—22no—
401C2×Dic86—42no—
402C2×Dic86—82no—
403C2×Dic86C2×D411yescharacteristic
404C2×Dic86C2×D411yescharacteristic
405C2×Dic86C2×D411yescharacteristic
406C2×Dic86C2×D411yescharacteristic
407C2×Dic86C2411yescharacteristic
408SD16×C43—24no—
409SD16×C43—24no—
410D8×C43—24no—
411D8×C43—24no—
412M16×C43—22no—
413M16×C43—22no—
414C2×C8×C43C2412yes—
415C2×C8×C43C2412yes—
416C4⋊C4×C43—21no—
417C4⋊C4×C43—21no—
418C4⋊C4×C43—21no—
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×C43C2×D411yescharacteristic
427C42×C43C2×D411yescharacteristic
428C42×C43C2411yescharacteristic
429C42×C43C2411yescharacteristic
430C22⋊Dic43—22no—
431C22⋊Dic43—22no—
432C22⋊Dic43—22no—
433C22⋊Dic43—22no—
434C22⋊Dic43—21no—
435C22⋊Dic43—21no—
436C22⋊Dic43—21no—
437C22⋊Dic43—21no—
438C22⋊Dic43—21no—
439C22⋊Dic43—21no—
440C22⋊Dic43—21no—
441C22⋊Dic43—21no—
442C22⋊Dic43—21no—
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—
451C4⋊Dic43—21no—
452C4⋊Dic43—21no—
453C4⋊Dic43—22no—
454C4⋊Dic43—22no—
455C4⋊Dic43—21no—
456C4⋊Dic43—21no—
457C4⋊Dic43—21no—
458C4⋊Dic43—21no—
459C4⋊Dic43C2×D411yescharacteristic
460C4⋊Dic43C2×D411yescharacteristic
461C4⋊Dic43C2×D411yescharacteristic
462C4⋊Dic43C2×D411yescharacteristic
463C4⋊Dic43C2412yes—
464C4⋊Dic43C2412yes—
465C4⋊Dic43C2411yescharacteristic
466C4⋊Dic43C2411yescharacteristic
467Dic43⋊C4—22no—
468Dic43⋊C4—22no—
469Dic43⋊C4—22no—
470Dic43⋊C4—22no—
471Dic43⋊C4—21no—
472Dic43⋊C4—21no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—22no—
477Dic43⋊C4—21no—
478Dic43⋊C4—21no—
479Dic43⋊C4—21no—
480Dic43⋊C4—21no—
481Dic43⋊C4C2×D411yescharacteristic
482Dic43⋊C4C2×D411yescharacteristic
483Dic43⋊C4C2×D411yescharacteristic
484Dic43⋊C4C2×D411yescharacteristic
485Dic43⋊C4C2×D411yescharacteristic
486Dic43⋊C4C2×D411yescharacteristic
487Dic43⋊C4C2×D411yescharacteristic
488Dic43⋊C4C2×D411yescharacteristic
489C4×Dic43—21no—
490C4×Dic43—21no—
491C4×Dic43—21no—
492C4×Dic43—21no—
493C4×Dic43—21no—
494C4×Dic43—21no—
495C4×Dic43—21no—
496C4×Dic43C2×D411yescharacteristic
497C4×Dic43C2×D411yescharacteristic
498C4×Dic43C2×D411yescharacteristic
499C4×Dic43C2×D411yescharacteristic
500C4×Dic43C2411yescharacteristic
501C4×Dic43C2411yescharacteristic
502C4×Dic43C2411yescharacteristic
503C4×Dic43C2411yescharacteristic
504#10621877—22no—
505#10621877—22no—
506C2×C43⋊C8C2412yes—
507C2×C43⋊C8C2412yes—
508C23×C43—24no—
509C23×C43—22no—
510C23×C43—21no—
511C23×C43—21no—
512C23×C43—42no—
513C23×C43—42no—
514C23×C43C22×D411yescharacteristic
515C22×D43—21no—
516Q8×C43—21no—
517Q8×C43—21no—
518Q8×C43—21no—
519Q8×C43—21no—
520D4×C43—24no—
521D4×C43—21no—
522D4×C43—21no—
523D4×C43—22no—
524D4×C43—21no—
525D4×C43—21no—
526D4×C43—42no—
527D4×C43—42no—
528D4×C43—42no—
529D4×C43—81no—
530D4×C43C2×#4114yes—
531C2×C4×C43—21no—
532C2×C4×C43—21no—
533C2×C4×C43—22no—
534C2×C4×C43—41no—
535C2×C4×C43—41no—
536C2×C4×C43—42no—
537C2×C4×C43—42no—
538C2×C4×C43—42no—
539C2×C4×C43—82no—
540C2×C4×C43—82no—
541C2×C4×C43C22×D411yescharacteristic
542C2×C4×C43C22×D411yescharacteristic
543C2×C4×C43C22×D411yescharacteristic
544C2×C4×C43C22×D411yescharacteristic
545C2×C4×C43C22×D411yescharacteristic
546C2×C4×C43C2×#4112yes—
547C2×C4×C432−1+412yes—
548C2×C4×C43C2511yescharacteristic
549C22⋊D43—42no—
550C22⋊D43—42no—
551C22⋊D43—42no—
552C22⋊D43—81no—
553C22⋊D43—81no—
554C2×Dic43—22no—
555C2×Dic43—21no—
556C2×Dic43—21no—
557C2×Dic43—21no—
558C2×Dic43—22no—
559C2×Dic43—22no—
560C2×Dic43—41no—
561C2×Dic43—41no—
562C2×Dic43—41no—
563C2×Dic43—42no—
564C2×Dic43—44no—
565C2×Dic43—42no—
566C2×Dic43—42no—
567C2×Dic43—42no—
568C2×Dic43—44no—
569C2×Dic43—81no—
570C2×Dic43—81no—
571C2×Dic43—82no—
572C2×Dic43—82no—
573C2×Dic43C22×D411yescharacteristic
574C2×Dic43C22×D411yescharacteristic
575C2×Dic43C22×D411yescharacteristic
576C2×Dic43C22×D411yescharacteristic
577C2×Dic43C22×D411yescharacteristic
578C2×Dic43C22×D411yescharacteristic
579C2×Dic43C22×D411yescharacteristic
580C2×Dic43C22×D411yescharacteristic
581D172—21no—
582D172—21no—
583C4×D43—42no—
584C4×D43—42no—
585C4×D43—81no—
586Dic86—22no—
587Dic86—22no—
588Dic86—21no—
589Dic86—21no—
590Dic86—41no—
591Dic86—41no—
592Dic86—82no—
593Dic86—82no—
594C8×C43—22no—
595C8×C43—22no—
596C43⋊C8—22no—
597C43⋊C8—22no—
598#61318—431nomaximal, Sylow
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—24no—
602C22×C43—48no—
603C22×C43—42no—
604C22×C43—42no—
605C22×C43—41no—
606C22×C43—41no—
607C22×C43—41no—
608C22×C43—41no—
609C22×C43—41no—
610C22×C43—41no—
611C22×C43#54812yes—
612C22×C43C23×D411yescharacteristic
613C2×D43—41no—
614C2×D43—41no—
615C2×D43—41no—
616C4×C43—21no—
617C4×C43—21no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—42no—
621C4×C43—41no—
622C4×C43—41no—
623C4×C43#54812yes—
624C4×C43C22×#4111yescharacteristic
625C4×C43C2×2−1+411yescharacteristic
626Dic43—21no—
627Dic43—21no—
628Dic43—21no—
629Dic43—21no—
630Dic43—21no—
631Dic43—21no—
632Dic43—21no—
633Dic43—42no—
634Dic43—41no—
635Dic43—41no—
636Dic43—41no—
637Dic43—42no—
638Dic43#57512yes—
639#3480—431no—
640C2×#554—431no—
641#3376—432no—
642#3376—432no—
643#3372—432no—
644#3370—432no—
645#3370—432no—
646#3366—432no—
647#3361—432no—
648#3360—432no—
649#3142—431no—
650#3142—431no—
651#3141—431no—
652#3080—431no—
653#3080—431no—
654#3079—431no—
655#3036—431no—
656#3036—431no—
657#3036D4311yescharacteristic, complemented
658Q8×M16—431no—
659C4×AGL(1,ℤ/8)—431no—
660C4×AGL(1,ℤ/8)—431no—
661C4×AGL(1,ℤ/8)—431no—
662C2×C43—22no—
663C2×C43—44no—
664C2×C43—81no—
665C2×C43—81no—
666C2×C43C2×#54811yescharacteristic
667C2×C43C2×#57511yescharacteristic
668C2×C43#358511yescharacteristic
669D43—81no—
670C2×AGL(1,ℤ/8)—431no—
671C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
672C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
673#559—431no—
674#559—431no—
675#559—431no—
676#557—431no—
677#556—431no—
678#556—431no—
679#556—431no—
680#554—432no—
681#554—432no—
682#554—432no—
683#554—432no—
684#554—861no—
685#554—861no—
686#554—861no—
687#554—861no—
688#553—861no—
689#553—861no—
690#553—861no—
691#550—431no—
692#548—861no—
693#532—431no—
694#532—431no—
695#532C2×D4311yescharacteristic
696C2×C4⋊Q8—431no—
697#529—861no—
698#529—861no—
699#529—861no—
700C2×#125—431no—
701C2×#125—431no—
702C2×C22⋊Q8—861no—
703C2×C22⋊Q8—861no—
704C2×C22⋊Q8—861no—
705C4×#41—431no—
706C4×#41—431no—
707C4×#41—431no—
708C4×#41—861no—
709C2×C4×Q8—431no—
710C2×C4×D4—431no—
711C2×C4×D4—431no—
712C2×C4×D4C2×D4311yescharacteristic
713C22×C4⋊C4—861no—
714#491—432no—
715#491—432no—
716#490—432no—
717#490—432no—
718#489—432no—
719#489—432no—
720#488—432no—
721#488—432no—
722#488—432no—
723#488—432no—
724#487—432no—
725#486—432no—
726#479—432no—
727#479—432no—
728#479—432no—
729#479—432no—
730#478—432no—
731#478—432no—
732#478—432no—
733#478—432no—
734#477—432no—
735#476—432no—
736#475—432no—
737#474—432no—
738#463—432no—
739#463—432no—
740#463—432no—
741#463—432no—
742#463C2×D4312yes—
743#463C2×D4312yes—
744#461—432no—
745#461—432no—
746#461C2×D4312yes—
747#459—432no—
748#459—432no—
749#459C2×D4312yes—
750#446—432no—
751#446—432no—
752#446—432no—
753C8×Q8—432no—
754#442—432no—
755#442—432no—
756#442—432no—
757#440—432no—
758#440—432no—
759#440—432no—
760C4×SD16—432no—
761C4×SD16—432no—
762C4×SD16—432no—
763C4×D8—432no—
764C4×D8—432no—
765C4×D8—432no—
766#428—431no—
767#428—431no—
768#428—431no—
769#423—431no—
770#423—431no—
771#423C2×D4311yescharacteristic
772#418—431no—
773#417—431no—
774#417—431no—
775#417—431no—
776#417—431no—
777#417—431no—
778#417—431no—
779#417—431no—
780#417C2×D4311yescharacteristic
781#417C2×D4311yescharacteristic
782C4×M16—431no—
783C4×M16—431no—
784C4×M16—431no—
785C43#6131811yescharacteristic, complemented, Sylow
786C2×#41—431no—
787C2×#41—861no—
788C2×#41C22×D4311yescharacteristic
789C2×#41C22×D4311yescharacteristic
790C22×Q8—431no—
791C22×Q8—861no—
792C22×D4C22×D4311yescharacteristic
793C23×C4—21no—
794C23×C4—861no—
795C23×C4—861no—
796AGL(1,ℤ/8)—24no—
797AGL(1,ℤ/8)—24no—
798AGL(1,ℤ/8)—864no—
799C2×SD16—432no—
800C2×SD16C22×D4312yes—
801C2×SD16C22×D4312yes—
802C2×D8—432no—
803C2×D8C22×D4312yes—
804C2×D8C22×D4312yes—
805C2×M16—431no—
806C2×M16—431no—
807C2×M16C22×D4311yescharacteristic
808C2×M16C22×D4311yescharacteristic
809C4⋊Q8—432no—
810C4⋊Q8—432no—
811C4⋊Q8—431no—
812C4⋊Q8—431no—
813C4⋊Q8—861no—
814C4⋊Q8—861no—
815C4⋊Q8C22×D4311yescharacteristic
816#127—431no—
817#127—431no—
818#127C22×D4311yescharacteristic
819#126—861no—
820#126—861no—
821#126—861no—
822#126—861no—
823#126—861no—
824#126—861no—
825#125—432no—
826#125—432no—
827#125—432no—
828#125—432no—
829#125—861no—
830#125—861no—
831#125—861no—
832#125—861no—
833#125—861no—
834#125—861no—
835#125—861no—
836#124—431no—
837#124—431no—
838#124—431no—
839#124—431no—
840#124—861no—
841#124—861no—
842#124—861no—
843#124C22×D4311yescharacteristic
844#124C22×D4311yescharacteristic
845#123—861no—
846#123—861no—
847#123—861no—
848#123—861no—
849#123—861no—
850#123—861no—
851C22⋊Q8—862no—
852C22⋊Q8—862no—
853C22⋊Q8—862no—
854C22⋊Q8—862no—
855C22⋊Q8—862no—
856C22⋊Q8—862no—
857C22⋊Q8—862no—
858C22⋊Q8—862no—
859C22⋊Q8—861no—
860C22⋊Q8—861no—
861C22⋊Q8—861no—
862C22⋊Q8—862no—
863C22⋊Q8—862no—
864C22⋊Q8—862no—
865C22⋊Q8—862no—
866#121—21no—
867#121—21no—
868#121—861no—
869#121—861no—
870#121—861no—
871#121—861no—
872#121—861no—
873#121—861no—
874#121—861no—
875C4×Q8—431no—
876C4×Q8—431no—
877C4×Q8—431no—
878C4×Q8—431no—
879C4×Q8—431no—
880C4×Q8—431no—
881C4×Q8—431no—
882C4×Q8—431no—
883C4×Q8—431no—
884C4×Q8—431no—
885C4×Q8—431no—
886C4×Q8—431no—
887C4×Q8—431no—
888C4×Q8—431no—
889C4×Q8—861no—
890C4×D4—21no—
891C4×D4—21no—
892C4×D4—21no—
893C4×D4—21no—
894C4×D4—432no—
895C4×D4—432no—
896C4×D4—432no—
897C4×D4—432no—
898C4×D4—431no—
899C4×D4—431no—
900C4×D4—431no—
901C4×D4—431no—
902C4×D4—431no—
903C4×D4—431no—
904C4×D4—861no—
905C4×D4—861no—
906C4×D4—861no—
907C4×D4—861no—
908C4×D4—861no—
909C4×D4—861no—
910C4×D4—861no—
911C4×D4—861no—
912C4×D4—861no—
913C4×D4—861no—
914C4×D4—861no—
915C4×D4—861no—
916C4×D4—861no—
917C4×D4—861no—
918C4×D4—861no—
919C4×D4—861no—
920C4×D4—861no—
921C4×D4C22×D4312yes—
922C4×D4C22×D4312yes—
923#117—431no—
924#117—861no—
925#117—861no—
926#117—861no—
927#117—861no—
928#117—861no—
929#117—861no—
930C2×C4⋊C4—431no—
931C2×C4⋊C4—431no—
932C2×C4⋊C4—431no—
933C2×C4⋊C4—431no—
934C2×C4⋊C4—431no—
935C2×C4⋊C4—862no—
936C2×C4⋊C4—862no—
937C2×C4⋊C4—862no—
938C2×C4⋊C4—862no—
939C2×C4⋊C4—861no—
940C2×C4⋊C4—861no—
941C2×C4⋊C4—861no—
942C2×C4⋊C4—861no—
943C2×C4⋊C4—861no—
944C2×C4⋊C4C22×D4311yescharacteristic
945C2×C22⋊C4—21no—
946C2×C22⋊C4—861no—
947C2×C22⋊C4—861no—
948C2×C42—431no—
949C2×C42—431no—
950C2×C42—861no—
951C2×C42—861no—
952C2×C42—861no—
953C2×C42C22×D4311yescharacteristic
954#107—432no—
955#107—432no—
956#107—432no—
957#106—432no—
958#106—432no—
959#106—432no—
960C4⋊C8—432no—
961C4⋊C8—432no—
962C4⋊C8—432no—
963C4⋊C8—432no—
964C4⋊C8C22×D4312yes—
965C4⋊C8C22×D4312yes—
966#103—432no—
967#103—432no—
968#103—432no—
969#103—432no—
970#103—432no—
971#103—432no—
972#103—432no—
973#103C22×D4312yes—
974#103C22×D4312yes—
975#102—432no—
976#102—432no—
977#102—432no—
978#102—432no—
979#102—432no—
980#102—432no—
981#102—432no—
982#102—432no—
983#102—432no—
984#102C22×D4312yes—
985#102C22×D4312yes—
986#97—432no—
987#97—432no—
988#97—432no—
989C4×C8—432no—
990C4×C8—432no—
991C4×C8—432no—
992C24—21no—
993#41—22no—
994#41—22no—
995#41—22no—
996#41—22no—
997#41—862no—
998#41—862no—
999#41—1724no—
1000C2×Q8—431no—
1001C2×Q8—431no—
1002C2×Q8—431no—
1003C2×Q8—431no—
1004C2×Q8—431no—
1005C2×Q8—862no—
1006C2×Q8—862no—
1007C2×Q8—3442no—
1008C2×Q8—1722no—
1009C2×Q8C23×D4311yescharacteristic
1010C2×Q8C23×D4311yescharacteristic
1011C2×D4—21no—
1012C2×D4—21no—
1013C2×D4—21no—
1014C2×D4—21no—
1015C2×D4—21no—
1016C2×D4—22no—
1017C2×D4—431no—
1018C2×D4—861no—
1019C2×D4—861no—
1020C2×D4—861no—
1021C2×D4—861no—
1022C2×D4—861no—
1023C2×D4#1062190014yescomplemented
1024C2×D4C23×D4311yescharacteristic
1025C2×D4C23×D4311yescharacteristic
1026C2×D4C23×D4312yes—
1027C22×C4—21no—
1028C22×C4—21no—
1029C22×C4—21no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—82no—
1033C22×C4—431no—
1034C22×C4—431no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—861no—
1038C22×C4—861no—
1039C22×C4—862no—
1040C22×C4—862no—
1041C22×C4—861no—
1042C22×C4—861no—
1043C22×C4—862no—
1044C22×C4—862no—
1045C22×C4—861no—
1046C22×C4—861no—
1047C22×C4—861no—
1048C22×C4—861no—
1049C22×C4—861no—
1050C22×C4—3442no—
1051C22×C4—1724no—
1052C22×C4D4×D4311yescharacteristic
1053C22×C4D4×D4311yescharacteristic
1054C22×C4C23×D4311yescharacteristic
1055SD16—24no—
1056SD16—24no—
1057SD16—864no—
1058D8—24no—
1059D8—24no—
1060D8—864no—
1061M16—22no—
1062M16—22no—
1063M16—862no—
1064M16—862no—
1065C2×C8—432no—
1066C2×C8—432no—
1067C2×C8C23×D4312yes—
1068C2×C8C23×D4312yes—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—431no—
1073C4⋊C4—431no—
1074C4⋊C4—431no—
1075C4⋊C4—431no—
1076C4⋊C4—431no—
1077C4⋊C4—431no—
1078C4⋊C4—431no—
1079C4⋊C4—431no—
1080C4⋊C4—431no—
1081C4⋊C4—431no—
1082C4⋊C4—431no—
1083C4⋊C4—431no—
1084C4⋊C4—432no—
1085C4⋊C4—432no—
1086C4⋊C4—431no—
1087C4⋊C4—431no—
1088C4⋊C4—862no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—861no—
1095C4⋊C4—861no—
1096C4⋊C4—861no—
1097C4⋊C4—861no—
1098C4⋊C4—861no—
1099C4⋊C4—861no—
1100C4⋊C4—861no—
1101C4⋊C4—861no—
1102C4⋊C4—861no—
1103C4⋊C4—861no—
1104C4⋊C4—862no—
1105C4⋊C4—862no—
1106C4⋊C4—862no—
1107C4⋊C4—862no—
1108C4⋊C4—861no—
1109C4⋊C4—861no—
1110C4⋊C4C23×D4312yes—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—21no—
1114C22⋊C4—21no—
1115C22⋊C4—21no—
1116C22⋊C4—21no—
1117C22⋊C4—861no—
1118C22⋊C4—861no—
1119C22⋊C4—861no—
1120C22⋊C4—861no—
1121C22⋊C4—862no—
1122C22⋊C4—862no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C22⋊C4—861no—
1126C22⋊C4—861no—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—861no—
1130C22⋊C4—861no—
1131C22⋊C4—861no—
1132C22⋊C4—861no—
1133C22⋊C4—861no—
1134C22⋊C4—861no—
1135C22⋊C4—861no—
1136C42—431no—
1137C42—431no—
1138C42—431no—
1139C42—431no—
1140C42—431no—
1141C42—431no—
1142C42—431no—
1143C42—431no—
1144C42—861no—
1145C42—861no—
1146C42—861no—
1147C42—861no—
1148C42—861no—
1149C42—861no—
1150C42—861no—
1151C42D4×D4311yescharacteristic
1152C42D4×D4311yescharacteristic
1153C42C23×D4311yescharacteristic
1154C42C23×D4311yescharacteristic
1155C23—24no—
1156C23—22no—
1157C23—21no—
1158C23—21no—
1159C23—42no—
1160C23—42no—
1161C23—861no—
1162C23C2×D4×D4311yescharacteristic
1163Q8—21no—
1164Q8—21no—
1165Q8—21no—
1166Q8—21no—
1167Q8—862no—
1168Q8—862no—
1169Q8—861no—
1170Q8—861no—
1171Q8—3442no—
1172Q8—3442no—
1173Q8—1721no—
1174Q8—1721no—
1175D4—24no—
1176D4—21no—
1177D4—21no—
1178D4—22no—
1179D4—21no—
1180D4—21no—
1181D4—42no—
1182D4—42no—
1183D4—42no—
1184D4—81no—
1185D4—861no—
1186D4—861no—
1187D4—3441no—
1188D4—3441no—
1189D4—1722no—
1190D4—1722no—
1191D4—1722no—
1192D4C2×#1062190014yes—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—82no—
1202C2×C4—82no—
1203C2×C4—431no—
1204C2×C4—431no—
1205C2×C4—431no—
1206C2×C4—431no—
1207C2×C4—431no—
1208C2×C4—431no—
1209C2×C4—431no—
1210C2×C4—431no—
1211C2×C4—862no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—861no—
1215C2×C4—862no—
1216C2×C4—862no—
1217C2×C4—3441no—
1218C2×C4—3442no—
1219C2×C4—3442no—
1220C2×C4—3441no—
1221C2×C4—3441no—
1222C2×C4—1722no—
1223C2×C4—1724no—
1224C2×C4—1722no—
1225C2×C4—1721no—
1226C2×C4—1721no—
1227C2×C4—1721no—
1228C2×C4—1724no—
1229C2×C4—1722no—
1230C2×C4—1722no—
1231C2×C4—1722no—
1232C2×C4—1722no—
1233C2×C4C2×D4×D4311yescharacteristic
1234C2×C4C2×D4×D4311yescharacteristic
1235C2×C4C2×D4×D4311yescharacteristic
1236C2×C4C2×D4×D4311yescharacteristic
1237C2×C4C2×D4×D4311yescharacteristic
1238C2×C4C2×#1062190012yes—
1239C2×C4#1306337212yes—
1240C2×C4C24×D4311yescharacteristic
1241C8—22no—
1242C8—22no—
1243C8—862no—
1244C8—862no—
1245C22—21no—
1246C22—21no—
1247C22—24no—
1248C22—48no—
1249C22—42no—
1250C22—42no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—1721no—
1258C22—1721no—
1259C22—1721no—
1260C22#1458355512yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—21no—
1265C4—21no—
1266C4—41no—
1267C4—41no—
1268C4—42no—
1269C4—432no—
1270C4—861no—
1271C4—861no—
1272C4—861no—
1273C4—861no—
1274C4—861no—
1275C4—861no—
1276C4—861no—
1277C4—1721no—
1278C4—1722no—
1279C4—1721no—
1280C4—1721no—
1281C4—1722no—
1282C4#1458355512yes—
1283C4C22×#1062190011yescharacteristic
1284C4C2×#1306337211yescharacteristic
1285C2—22no—
1286C2—44no—
1287C2—81no—
1288C2—81no—
1289C2—3441no—
1290C2C2×#1458355511yescharacteristic
1291C2#575×D4311yescharacteristic
1292C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3036C2
socleC22×C43C23×D4
hypercenter#3036D43
hypocenterC43#61318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #19148192C2semidirect
2. C2×#14583608C2semidirect
3. #19147426C2semidirect
4. #19147415C2semidirect
5. #19147371C2semidirect
6. #19147352C2semidirect
7. #19147341C2semidirect
8. #19147297C2semidirect
9. #19147250C2semidirect
10. #19147239C2semidirect
11. #19144995C2semidirect
12. #19144993C2semidirect
13. #19144986C2semidirect
14. #19144418C2semidirect
15. #19144415C2semidirect
16. #19144406C2semidirect
17. #19144056C2semidirect
18. #19144056C2semidirect
19. #19143546C2semidirect
20. AGL(1,ℤ/8)×Dic43C2semidirect
21. AGL(1,ℤ/8)×Dic43C2semidirect
22. C4×#13063351C2semidirect
23. C43×#3036C2semidirect
25. #14583635C22semidirect
26. #14583631C22semidirect
27. #14583631C22semidirect
28. #14583624C22semidirect
29. #14583623C22semidirect
30. #14583618C22semidirect
31. #14583618C22semidirect
43. #14583569C22semidirect
64. #14583267C22semidirect
65. #14583266C22semidirect
66. #14583263C22semidirect
67. #14583262C22semidirect
68. #14583260C22semidirect
69. #14583257C22semidirect
70. #14583255C22semidirect
71. #14583253C22semidirect
72. #14583253C22semidirect
73. #14583252C22semidirect
74. #14583248C22semidirect
75. #14583244C22semidirect
76. #14583208C22semidirect
77. #14583207C22semidirect
78. #14583207C22semidirect
79. #14583204C22semidirect
80. #14583201C22semidirect
81. #14583200C22semidirect
82. #14583200C22semidirect
83. #14583197C22semidirect
84. #14583192C22semidirect
85. #14583187C22semidirect
86. #14583182C22semidirect
87. #14583177C22semidirect
96. #14583028C22semidirect
97. #14583028C22semidirect
98. #14583026C22semidirect
99. #14583023C22semidirect
358. C2×D4×C43#41semidirect
657. #3036D43semidirect
785. C43#61318semidirect
1023. C2×D4#10621900semidirect

Maximal subgroups

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

subgroupindex
#191481922
C2×#145836082
#191474262
#191474152
#191473712
#191473522
#191473412
#191472972
#191472502
#191472392
#191449952
#191449932
#191449862
#191444182
#191444152
#191444062
#191440562
#191435462
AGL(1,ℤ/8)×Dic432
C4×#130633512
C43×#30362
#6131843