Finite Group Databasebeta

← #25976504

Subgroups — #25976504

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic86C211yesmaximal, characteristic, complemented
2C2×#14583618C211yesmaximal, characteristic, complemented
3#19147441C212yesmaximal, complemented
4#19147434C212yesmaximal, complemented
5#19147426C212yesmaximal, complemented
6#19147419C212yesmaximal, complemented
7#19147330C212yesmaximal, complemented
8#19147308C212yesmaximal, complemented
9#19147275C212yesmaximal, complemented
10#19147239C212yesmaximal, complemented
11#19144981C211yesmaximal, characteristic, complemented
12#19144979C211yesmaximal, characteristic, complemented
13#19144973C211yesmaximal, characteristic, complemented
14#19144402C211yesmaximal, characteristic, complemented
15#19144397C211yesmaximal, characteristic, complemented
16#19144389C211yesmaximal, characteristic, complemented
17#19144087C211yesmaximal, characteristic
18#19144080C211yesmaximal, characteristic, complemented
19#19143546C211yesmaximal, characteristic, complemented
20#137×Dic43C211yesmaximal, characteristic, complemented
21C4×#13063355C211yesmaximal, characteristic, complemented
22AGL(1,ℤ/8)×Dic43C211yesmaximal, characteristic
23C43×#3040C211yesmaximal, characteristic
24C2×#13063355C2211yescharacteristic
25Q8×Dic86C2211yescharacteristic, complemented
26#14583628C2211yescharacteristic, complemented
27#14583625C2211yescharacteristic, complemented
28#14583625C2211yescharacteristic, complemented
29#14583618—21no—
30#14583618—21no—
31#14583618—21no—
32#14583618—21no—
33#14583618C2212yes—
34#14583618C2212yes—
35#14583618C2212yes—
36#14583618C2212yes—
37#14583608—21no—
38#14583608—21no—
39#14583608C2211yescharacteristic, complemented
40#14583608C2211yescharacteristic, complemented
41#14583606—21no—
42#14583606C2211yescharacteristic, complemented
43D4×Dic86—21no—
44D4×Dic86C2211yescharacteristic, complemented
45#14583456—21no—
46#14583456C2211yescharacteristic
47#14583452—21no—
48#14583452—21no—
49#14583452C2211yescharacteristic
50#14583452C2211yescharacteristic
51C2×#13063323C2211yescharacteristic
52C2×#13063318—21no—
53C2×#13063318—21no—
54C2×#13063312C2211yescharacteristic
55C2×#13063302—21no—
56#41×Dic43C2211yescharacteristic
57#41×Dic43C2211yescharacteristic
58C2×Q8×Dic43C2211yescharacteristic
59C2×C4×Dic86—21no—
60C2×C4×Dic86C2211yescharacteristic
61C2×C4×Dic86C2211yescharacteristic
62C2×D4×Dic43C2211yescharacteristic
63C2×#13063281—21no—
64#14583266C2212yescomplemented
65#14583266C2212yescomplemented
66#14583258C2212yes—
67#14583258C2212yes—
68#14583257C2212yes—
69#14583257C2212yes—
70#14583253C2212yes—
71#14583253C2212yes—
72#14583252C2212yes—
73#14583252C2212yes—
74#14583248C2212yescomplemented
75#14583248C2212yescomplemented
76#14583208C2212yescomplemented
77#14583207C2212yescomplemented
78#14583207C2212yescomplemented
79#14583204C2212yescomplemented
80#14583201C2212yes—
81#14583197C2212yes—
82#14583195C2212yescomplemented
83#14583192C2212yescomplemented
84#14583187C2212yes—
85#14583185C2212yescomplemented
86#14583182C2212yescomplemented
87#14583177C2212yes—
88#14583119C2212yes—
89#14583119C2212yes—
90#14583112C2212yes—
91#14583112C2212yes—
92#14583107C2212yescomplemented
93#14583107C2212yescomplemented
94#14583102C2212yescomplemented
95#14583102C2212yescomplemented
96#14583028C2212yescomplemented
97#14583028C2212yescomplemented
98#14583026C2212yescomplemented
99#14583023C2212yescomplemented
100#14583011C2212yes—
101#14583006C2212yescomplemented
102#14583004C2212yescomplemented
103#14583000C2212yes—
104#14583000C2212yescomplemented
105#14582999C2212yescomplemented
106Q16×Dic43C2212yescomplemented
107C4×#10621885C2212yescomplemented
108SD16×Dic43C2212yes—
109SD16×Dic43C2212yescomplemented
110C4×#10621883C2212yescomplemented
111D8×Dic43C2212yes—
112#14582942C2211yescharacteristic
113#14582941C2211yescharacteristic
114#14582941C2211yescharacteristic
115#14582922C2211yescharacteristic
116#14582922C2211yescharacteristic
117#14582909C2211yescharacteristic
118#14582909C2211yescharacteristic
119#14582908C2211yescharacteristic
120#14582908C2211yescharacteristic
121#14582907C2211yescharacteristic
122#14582904C2211yescharacteristic
123#14582904C2211yescharacteristic
124#14582900C2211yescharacteristic
125C4×#10621877C2211yescharacteristic
126M16×Dic43C2211yescharacteristic
127M16×Dic43C2211yescharacteristic
128C2×#137×C43C2211yescharacteristic
129C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
130C2×#124×C43C2211yescharacteristic
131C4×#41×C43C2211yescharacteristic
132C43×#464C2212yes—
133C43×#464C2212yes—
134C43×#463C2212yes—
135C43×#463C2212yes—
136C43×#423C2211yescharacteristic
137C43×#419C2211yescharacteristic
138C43×#418C2211yescharacteristic
139C22×Dic86—21no—
140C22×Dic86D411yescharacteristic
141C22×Dic86C2311yescharacteristic
142C23×Dic43—21no—
143#13063355—24no—
144C2×#10621885C2312yes—
145C2×#10621883C2312yes—
146C2×#10621877C2311yescharacteristic
147C2×#10621877C2311yescharacteristic
148#13063325—21no—
149#13063325—21no—
150#13063325C2311yescharacteristic
151#13063325C2311yescharacteristic
152#13063324—21no—
153#13063324—21no—
154#13063324—21no—
155#13063324—21no—
156#13063324C2311yescharacteristic
157#13063324C2311yescharacteristic
158#13063324C2311yescharacteristic
159#13063324C2311yescharacteristic
160#13063323—21no—
161#13063323—21no—
162#13063323C2312yes—
163#13063323C2312yes—
164#13063318—22no—
165#13063318—22no—
166#13063318—22no—
167#13063318—22no—
168#13063318—22no—
169#13063318—22no—
170#13063318—22no—
171#13063318—22no—
172#13063317—21no—
173#13063317—21no—
174#13063317C2311yescharacteristic
175#13063317C2311yescharacteristic
176#13063316—21no—
177#13063316—21no—
178#13063316—21no—
179#13063316—21no—
180#13063316C2311yescharacteristic
181#13063316C2311yescharacteristic
182#13063316C2311yescharacteristic
183#13063316C2311yescharacteristic
184#13063312—21no—
185#13063312—21no—
186#13063312C2312yes—
187#13063312C2312yes—
188#13063304—21no—
189#13063304—21no—
190#13063304—21no—
191#13063304—21no—
192#13063304—21no—
193#13063304—21no—
194#13063302—21no—
195#13063302—21no—
196#13063302—21no—
197#13063302—21no—
198#13063302—21no—
199#13063302—21no—
200#13063302—22no—
201#13063302—22no—
202#13063302—22no—
203#13063302—22no—
204#13063302—21no—
205#13063302—21no—
206#13063302—21no—
207#13063302—21no—
208#13063302—21no—
209#13063302—21no—
210Q8×Dic43—21no—
211Q8×Dic43—21no—
212Q8×Dic43C2312yes—
213Q8×Dic43C2312yes—
214Q8×Dic43C2311yescharacteristic
215Q8×Dic43C2311yescharacteristic
216Q8×Dic43C2311yescharacteristic
217Q8×Dic43C2311yescharacteristic
218C4×Dic86—21no—
219C4×Dic86—21no—
220C4×Dic86—21no—
221C4×Dic86—21no—
222C4×Dic86—21no—
223C4×Dic86—21no—
224C4×Dic86—21no—
225C4×Dic86—21no—
226C4×Dic86—21no—
227C4×Dic86—21no—
228C4×Dic86—21no—
229C4×Dic86—21no—
230C4×Dic86D411yescharacteristic
231C4×Dic86D411yescharacteristic
232C4×Dic86D411yescharacteristic
233C4×Dic86D411yescharacteristic
234C4×Dic86C2312yes—
235C4×Dic86C2312yes—
236C4×Dic86C2311yescharacteristic
237C4×Dic86C2311yescharacteristic
238C4×Dic86C2311yescharacteristic
239C4×Dic86C2311yescharacteristic
240D4×Dic43—21no—
241D4×Dic43—21no—
242D4×Dic43—21no—
243D4×Dic43—21no—
244D4×Dic43—21no—
245D4×Dic43—21no—
246D4×Dic43C2311yescharacteristic
247D4×Dic43C2311yescharacteristic
248D4×Dic43C2311yescharacteristic
249D4×Dic43C2311yescharacteristic
250D4×Dic43C2312yes—
251D4×Dic43C2312yes—
252#13063284—21no—
253#13063284—21no—
254#13063284C2311yescharacteristic
255#13063284C2311yescharacteristic
256#13063281—22no—
257#13063281—22no—
258#13063281—22no—
259#13063281—22no—
260C2×C4⋊Dic43—21no—
261C2×C4⋊Dic43—21no—
262C2×C4⋊Dic43D411yescharacteristic
263C2×C4⋊Dic43C2311yescharacteristic
264C2×Dic43⋊C4—21no—
265C2×Dic43⋊C4—21no—
266C2×Dic43⋊C4—21no—
267C2×Dic43⋊C4—21no—
268C2×Dic43⋊C4—21no—
269C2×Dic43⋊C4D411yescharacteristic
270C2×Dic43⋊C4D411yescharacteristic
271C2×C22⋊Dic43—21no—
272C2×C22⋊Dic43—21no—
273C2×C22⋊Dic43—21no—
274C2×C4×Dic43—21no—
275C2×C4×Dic43—21no—
276C2×C4×Dic43—21no—
277C2×C4×Dic43—21no—
278C2×C4×Dic43C2311yescharacteristic
279C2×C4×Dic43C2311yescharacteristic
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#13063250C2312yes—
293#13063250C2312yes—
294#13063249C2312yes—
295#13063249C2312yes—
296#13063249C2312yes—
297#13063249C2312yes—
298#13063249C2312yes—
299#13063248C2312yes—
300#13063248C2312yes—
301#13063246C2312yes—
302#13063246C2312yes—
303#13063246C2312yes—
304#13063246C2312yes—
305#13063246C2312yes—
306#13063236C2312yes—
307#13063235C2312yes—
308#13063235C2312yes—
309C4×C43⋊C8C2312yes—
310C8×Dic43C2312yes—
311C8×Dic43C2312yes—
312C2×#41×C43C2311yescharacteristic
313C22×Q8×C43C2311yescharacteristic
314C22×D4×C43C2311yescharacteristic
315#137×C43—24no—
316AGL(1,ℤ/8)×C43—24no—
317C2×Q16×C43C2312yes—
318C2×SD16×C43C2312yes—
319C2×SD16×C43C2312yes—
320C2×D8×C43C2312yes—
321C2×M16×C43C2311yescharacteristic
322C2×M16×C43C2311yescharacteristic
323#124×C43—21no—
324#124×C43—21no—
325#124×C43C2312yes—
326#124×C43C2312yes—
327C4×Q8×C43C2311yescharacteristic
328C4×Q8×C43C2311yescharacteristic
329C4×D4×C43—21no—
330C4×D4×C43—21no—
331C4×D4×C43C2311yescharacteristic
332C4×D4×C43C2311yescharacteristic
333#117×C43—21no—
334#117×C43C2311yescharacteristic
335C2×C22⋊C4×C43—21no—
336C2×C22⋊C4×C43—21no—
337C2×C42×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#4114yes—
348C2×Q8×C43—21no—
349C2×Q8×C43—22no—
350C2×Q8×C43—22no—
351C2×Q8×C43C2412yes—
352C2×Q8×C43C2411yescharacteristic
353C2×D4×C43—21no—
354C2×D4×C43—21no—
355C2×D4×C43—22no—
356C2×D4×C43—22no—
357C2×D4×C43C2412yes—
358C2×D4×C43C2411yescharacteristic
359C22×C4×C43—21no—
360C22×C4×C43—21no—
361C22×C4×C43—21no—
362C22×C4×C43—21no—
363C22×C4×C43C2×D411yescharacteristic
364C22×C4×C43C2×D411yescharacteristic
365C22×C4×C43C2411yescharacteristic
366C22×Dic43—21no—
367C22×Dic43—21no—
368C22×Dic43—22no—
369C22×Dic43—22no—
370C22×Dic43—21no—
371C22×Dic43—21no—
372C22×Dic43—21no—
373C22×Dic43—21no—
374C22×Dic43—44no—
375C22×Dic43C2×D411yescharacteristic
376C22×Dic43C2×D411yescharacteristic
377C22×Dic43C2×D411yescharacteristic
378C22×Dic43C2×D411yescharacteristic
379C2×Dic86—22no—
380C2×Dic86—22no—
381C2×Dic86—21no—
382C2×Dic86—21no—
383C2×Dic86—21no—
384C2×Dic86—21no—
385C2×Dic86—21no—
386C2×Dic86—21no—
387C2×Dic86—21no—
388C2×Dic86—42no—
389C2×Dic86—44no—
390C2×Dic86C2×D411yescharacteristic
391C2×Dic86C2×D411yescharacteristic
392C2×Dic86C2×D411yescharacteristic
393C2×Dic86C2×D411yescharacteristic
394C2×Dic86C2412yes—
395Q16×C43—24no—
396SD16×C43—24no—
397SD16×C43—24no—
398D8×C43—24no—
399M16×C43—22no—
400M16×C43—22no—
401C2×C8×C43C2412yes—
402C2×C8×C43C2412yes—
403C4⋊C4×C43—21no—
404C4⋊C4×C43—21no—
405C4⋊C4×C43C2411yescharacteristic
406C4⋊C4×C43C2411yescharacteristic
407C22⋊C4×C43—22no—
408C22⋊C4×C43—22no—
409C22⋊C4×C43—22no—
410C22⋊C4×C43—22no—
411C22⋊C4×C43—21no—
412C22⋊C4×C43—21no—
413C22⋊C4×C43—21no—
414C42×C43—21no—
415C42×C43—21no—
416C42×C43—21no—
417C42×C43C2×D411yescharacteristic
418C42×C43C2×D411yescharacteristic
419C42×C43C2411yescharacteristic
420C42×C43C2411yescharacteristic
421C22⋊Dic43—22no—
422C22⋊Dic43—22no—
423C22⋊Dic43—22no—
424C22⋊Dic43—22no—
425C22⋊Dic43—22no—
426C22⋊Dic43—22no—
427C22⋊Dic43—21no—
428C22⋊Dic43—21no—
429C22⋊Dic43—21no—
430C22⋊Dic43—21no—
431C22⋊Dic43—21no—
432C22⋊Dic43—21no—
433#10621885—24no—
434#10621883—24no—
435C4⋊Dic43—21no—
436C4⋊Dic43—21no—
437C4⋊Dic43—21no—
438C4⋊Dic43—21no—
439C4⋊Dic43—21no—
440C4⋊Dic43—22no—
441C4⋊Dic43—22no—
442C4⋊Dic43—21no—
443C4⋊Dic43—21no—
444C4⋊Dic43—21no—
445C4⋊Dic43—21no—
446C4⋊Dic43—21no—
447C4⋊Dic43—21no—
448C4⋊Dic43C2×D411yescharacteristic
449C4⋊Dic43C2×D411yescharacteristic
450C4⋊Dic43C2×D411yescharacteristic
451C4⋊Dic43C2×D411yescharacteristic
452C4⋊Dic43C2411yescharacteristic
453C4⋊Dic43C2411yescharacteristic
454C4⋊Dic43C2411yescharacteristic
455C4⋊Dic43C2411yescharacteristic
456C4⋊Dic43C2412yes—
457Dic43⋊C4—21no—
458Dic43⋊C4—21no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—21no—
462Dic43⋊C4—21no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—21no—
466Dic43⋊C4—21no—
467Dic43⋊C4—21no—
468Dic43⋊C4—21no—
469Dic43⋊C4—22no—
470Dic43⋊C4—22no—
471Dic43⋊C4—21no—
472Dic43⋊C4—21no—
473Dic43⋊C4—21no—
474Dic43⋊C4—21no—
475Dic43⋊C4C2×D411yescharacteristic
476Dic43⋊C4C2×D411yescharacteristic
477Dic43⋊C4C2×D411yescharacteristic
478Dic43⋊C4C2×D411yescharacteristic
479Dic43⋊C4C2×D411yescharacteristic
480Dic43⋊C4C2×D411yescharacteristic
481Dic43⋊C4C2×D411yescharacteristic
482Dic43⋊C4C2×D411yescharacteristic
483C4×Dic43—22no—
484C4×Dic43—22no—
485C4×Dic43—21no—
486C4×Dic43—21no—
487C4×Dic43—22no—
488C4×Dic43—22no—
489C4×Dic43—21no—
490C4×Dic43—21no—
491C4×Dic43—21no—
492C4×Dic43—21no—
493C4×Dic43C2×D411yescharacteristic
494C4×Dic43C2×D411yescharacteristic
495C4×Dic43C2×D411yescharacteristic
496C4×Dic43C2×D411yescharacteristic
497C4×Dic43C2411yescharacteristic
498C4×Dic43C2411yescharacteristic
499C4×Dic43C2411yescharacteristic
500C4×Dic43C2411yescharacteristic
501#10621877—22no—
502#10621877—22no—
503C2×C43⋊C8C2412yes—
504C2×C43⋊C8C2412yes—
505C23×C43—21no—
506C23×C43—22no—
507C23×C43—42no—
508C23×C43—42no—
509C23×C43—42no—
510C23×C43C22×D411yescharacteristic
511Q8×C43—21no—
512Q8×C43—22no—
513Q8×C43—22no—
514Q8×C43—42no—
515Q8×C43C2×#4112yes—
516D4×C43—24no—
517D4×C43—22no—
518D4×C43—21no—
519D4×C43—22no—
520D4×C43—42no—
521D4×C43C2×#4112yes—
522C2×C4×C43—21no—
523C2×C4×C43—24no—
524C2×C4×C43—22no—
525C2×C4×C43—21no—
526C2×C4×C43—21no—
527C2×C4×C43—41no—
528C2×C4×C43—41no—
529C2×C4×C43—42no—
530C2×C4×C43—42no—
531C2×C4×C43—81no—
532C2×C4×C43C22×D411yescharacteristic
533C2×C4×C43C22×D411yescharacteristic
534C2×C4×C43C22×D411yescharacteristic
535C2×C4×C43C22×D411yescharacteristic
536C2×C4×C43C22×D411yescharacteristic
537C2×C4×C43C2×#4112yes—
538C2×C4×C432−1+412yes—
539C2×C4×C43C2511yescharacteristic
540C2×Dic43—22no—
541C2×Dic43—22no—
542C2×Dic43—22no—
543C2×Dic43—21no—
544C2×Dic43—21no—
545C2×Dic43—21no—
546C2×Dic43—21no—
547C2×Dic43—41no—
548C2×Dic43—41no—
549C2×Dic43—41no—
550C2×Dic43—42no—
551C2×Dic43—44no—
552C2×Dic43—42no—
553C2×Dic43—42no—
554C2×Dic43—42no—
555C2×Dic43—44no—
556C2×Dic43—81no—
557C2×Dic43—81no—
558C2×Dic43C22×D411yescharacteristic
559C2×Dic43C22×D411yescharacteristic
560C2×Dic43C22×D411yescharacteristic
561C2×Dic43C22×D411yescharacteristic
562C2×Dic43C22×D411yescharacteristic
563C2×Dic43C22×D411yescharacteristic
564C2×Dic43C22×D411yescharacteristic
565C2×Dic43C22×D411yescharacteristic
566Dic86—22no—
567Dic86—22no—
568Dic86—22no—
569Dic86—22no—
570Dic86—41no—
571Dic86—41no—
572Dic86—42no—
573Dic86—42no—
574Dic86—42no—
575Dic86—42no—
576Dic86—81no—
577Dic86—81no—
578Dic86—81no—
579C8×C43—22no—
580C8×C43—22no—
581C43⋊C8—22no—
582C43⋊C8—22no—
583#61323—431nomaximal, Sylow
584C22×C43—21no—
585C22×C43—21no—
586C22×C43—22no—
587C22×C43—41no—
588C22×C43—41no—
589C22×C43—42no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—84no—
593C22×C43#54812yes—
594C22×C43C23×D411yescharacteristic
595C4×C43—21no—
596C4×C43—21no—
597C4×C43—22no—
598C4×C43—21no—
599C4×C43—21no—
600C4×C43—41no—
601C4×C43—42no—
602C4×C43—41no—
603C4×C43#54812yes—
604C4×C43C22×#4111yescharacteristic
605C4×C43C2×2−1+411yescharacteristic
606Dic43—21no—
607Dic43—21no—
608Dic43—21no—
609Dic43—21no—
610Dic43—21no—
611Dic43—21no—
612Dic43—21no—
613Dic43—41no—
614Dic43—41no—
615Dic43—42no—
616Dic43—41no—
617Dic43—41no—
618Dic43—42no—
619Dic43#57512yes—
620Q8×#41—431no—
621C2×#556—431no—
622#3377—432no—
623#3377—432no—
624#3376—432no—
625#3376—432no—
626#3369—432no—
627#3367—432no—
628#3364—432no—
629#3360—432no—
630#3140—431no—
631#3140—431no—
632#3139—431no—
633#3078—431no—
634#3078—431no—
635#3077—431no—
636#3040—431no—
637#3040D4311yescharacteristic
638#3039—431no—
639Q8×M16—431no—
640C4×#137—431no—
641C4×#137—431no—
642C4×AGL(1,ℤ/8)—431no—
643C2×C43—22no—
644C2×C43—42no—
645C2×C43—82no—
646C2×C43C2×#54811yescharacteristic
647C2×C43C2×#57511yescharacteristic
648C2×C43#358611yescharacteristic
649C2×#137—431no—
650C2×#137C2×D4311yescharacteristic
651C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
652Q82—431no—
653#557—431no—
654#557—431no—
655#557—431no—
656#556—432no—
657#556—432no—
658#556—432no—
659#556—432no—
660#556—861no—
661#556—861no—
662#556—861no—
663#556—861no—
664#554—431no—
665#554—431no—
666#554—431no—
667#554—861no—
668#554—861no—
669#554—861no—
670D4×Q8—431no—
671D4×Q8—861no—
672#533—431no—
673#533—431no—
674#533—431no—
675#533—861no—
676#533—861no—
677#533—861no—
678C2×C4⋊Q8—431no—
679C2×#126—861no—
680C2×#126—861no—
681C2×#124—431no—
682C2×#124C2×D4311yescharacteristic
683C2×C22⋊Q8—861no—
684C4×#41—431no—
685C4×#41—431no—
686C4×#41C2×D4311yescharacteristic
687C2×C4×Q8—431no—
688C2×C4×Q8—431no—
689C2×C4×Q8—431no—
690C2×C4×Q8—861no—
691C2×C4×D4—431no—
692C2×#117—861no—
693#491—432no—
694#491—432no—
695#489—432no—
696#489—432no—
697#489—432no—
698#489—432no—
699#488—432no—
700#488—432no—
701#488—432no—
702#488—432no—
703#487—432no—
704#487—432no—
705#479—432no—
706#479—432no—
707#479—432no—
708#479—432no—
709#478—432no—
710#478—432no—
711#477—432no—
712#477—432no—
713#476—432no—
714#475—432no—
715#475—432no—
716#474—432no—
717#464—432no—
718#464—432no—
719#464C2×D4312yes—
720#464C2×D4312yes—
721#463—432no—
722#463—432no—
723#463C2×D4312yes—
724#463C2×D4312yes—
725#462—432no—
726#462—432no—
727#461—432no—
728#461—432no—
729#446—432no—
730#446—432no—
731#446—432no—
732C8×Q8—432no—
733#442—432no—
734#441—432no—
735#441—432no—
736#440—432no—
737#440—432no—
738#440—432no—
739C4×Q16—432no—
740C4×Q16—432no—
741C4×SD16—432no—
742C4×SD16—432no—
743C4×SD16—432no—
744C4×D8—432no—
745#428—431no—
746#428—431no—
747#428—431no—
748#423—431no—
749#423—431no—
750#423C2×D4311yescharacteristic
751#419—431no—
752#419—431no—
753#419—431no—
754#419—431no—
755#419—431no—
756#419C2×D4311yescharacteristic
757#418—431no—
758#418—431no—
759#418C2×D4311yescharacteristic
760#417—431no—
761C4×M16—431no—
762C4×M16—431no—
763C4×M16—431no—
764C43#6132311yescharacteristic, complemented, Sylow
765C2×#41C22×D4311yescharacteristic
766C22×Q8—431no—
767C22×Q8—431no—
768C22×Q8—861no—
769C22×Q8C22×D4311yescharacteristic
770C22×D4C22×D4311yescharacteristic
771C23×C4—861no—
772#137—24no—
773#137—864no—
774AGL(1,ℤ/8)—24no—
775C2×Q16—432no—
776C2×Q16C22×D4312yes—
777C2×SD16—432no—
778C2×SD16C22×D4312yes—
779C2×SD16C22×D4312yes—
780C2×D8C22×D4312yes—
781C2×M16—431no—
782C2×M16—431no—
783C2×M16C22×D4311yescharacteristic
784C2×M16C22×D4311yescharacteristic
785C4⋊Q8—431no—
786C4⋊Q8—431no—
787C4⋊Q8—431no—
788C4⋊Q8—431no—
789C4⋊Q8—432no—
790C4⋊Q8—432no—
791C4⋊Q8—431no—
792C4⋊Q8—431no—
793C4⋊Q8—861no—
794C4⋊Q8—861no—
795C4⋊Q8—861no—
796C4⋊Q8—861no—
797C4⋊Q8—861no—
798C4⋊Q8—861no—
799C4⋊Q8—861no—
800C4⋊Q8—861no—
801#126—862no—
802#126—862no—
803#126—862no—
804#126—862no—
805#126—862no—
806#126—862no—
807#126—862no—
808#126—862no—
809#125—431no—
810#125—431no—
811#125—431no—
812#125—431no—
813#125—431no—
814#125—431no—
815#125—861no—
816#125—861no—
817#125—861no—
818#125—861no—
819#125—861no—
820#125—861no—
821#124—21no—
822#124—21no—
823#124—432no—
824#124—432no—
825#124—861no—
826#124—861no—
827#124C22×D4312yes—
828#124C22×D4312yes—
829C22⋊Q8—861no—
830C22⋊Q8—861no—
831C22⋊Q8—861no—
832C22⋊Q8—861no—
833C22⋊Q8—861no—
834C22⋊Q8—861no—
835C22⋊Q8—861no—
836C22⋊Q8—861no—
837C22⋊Q8—861no—
838C22⋊Q8—861no—
839C22⋊Q8—862no—
840C22⋊Q8—862no—
841C22⋊Q8—862no—
842C22⋊Q8—862no—
843C22⋊Q8—861no—
844C22⋊Q8—861no—
845C22⋊Q8—861no—
846C22⋊Q8—861no—
847C22⋊Q8—861no—
848C22⋊Q8—861no—
849C22⋊Q8—861no—
850C22⋊Q8—861no—
851C4×Q8—431no—
852C4×Q8—431no—
853C4×Q8—431no—
854C4×Q8—431no—
855C4×Q8—431no—
856C4×Q8—431no—
857C4×Q8—431no—
858C4×Q8—431no—
859C4×Q8—432no—
860C4×Q8—432no—
861C4×Q8—431no—
862C4×Q8—431no—
863C4×Q8—431no—
864C4×Q8—431no—
865C4×Q8—432no—
866C4×Q8—432no—
867C4×Q8—861no—
868C4×Q8—861no—
869C4×Q8—861no—
870C4×Q8—861no—
871C4×Q8—861no—
872C4×Q8—861no—
873C4×Q8—861no—
874C4×Q8—861no—
875C4×Q8—861no—
876C4×Q8—861no—
877C4×Q8—861no—
878C4×Q8—861no—
879C4×Q8—861no—
880C4×Q8—861no—
881C4×Q8C22×D4311yescharacteristic
882C4×Q8C22×D4311yescharacteristic
883C4×D4—21no—
884C4×D4—21no—
885C4×D4—432no—
886C4×D4—432no—
887C4×D4—431no—
888C4×D4—431no—
889C4×D4—431no—
890C4×D4—431no—
891C4×D4—861no—
892C4×D4—861no—
893C4×D4—861no—
894C4×D4—861no—
895C4×D4—861no—
896C4×D4—861no—
897C4×D4C22×D4311yescharacteristic
898C4×D4C22×D4311yescharacteristic
899#117—21no—
900#117—431no—
901#117—431no—
902#117—861no—
903#117—861no—
904#117—862no—
905#117—862no—
906#117—862no—
907#117—862no—
908#117C22×D4311yescharacteristic
909C2×C4⋊C4—431no—
910C2×C4⋊C4—431no—
911C2×C4⋊C4—431no—
912C2×C4⋊C4—431no—
913C2×C4⋊C4—861no—
914C2×C4⋊C4—861no—
915C2×C4⋊C4—861no—
916C2×C4⋊C4—861no—
917C2×C4⋊C4—861no—
918C2×C4⋊C4—861no—
919C2×C4⋊C4—861no—
920C2×C22⋊C4—21no—
921C2×C22⋊C4—21no—
922C2×C22⋊C4—861no—
923C2×C22⋊C4—861no—
924C2×C22⋊C4—861no—
925C2×C42—21no—
926C2×C42—431no—
927C2×C42—431no—
928C2×C42—861no—
929C2×C42—861no—
930C2×C42—861no—
931C2×C42—861no—
932C2×C42C22×D4311yescharacteristic
933#107—432no—
934#107—432no—
935#107—432no—
936#106—432no—
937#106—432no—
938#106—432no—
939C4⋊C8—432no—
940C4⋊C8—432no—
941C4⋊C8—432no—
942C4⋊C8—432no—
943C4⋊C8C22×D4312yes—
944C4⋊C8C22×D4312yes—
945#103—432no—
946#103—432no—
947#103—432no—
948#103—432no—
949#103—432no—
950#103—432no—
951#103—432no—
952#103—432no—
953#103—432no—
954#103—432no—
955#103—432no—
956#103C22×D4312yes—
957#103C22×D4312yes—
958#102—432no—
959#102—432no—
960#102—432no—
961#102—432no—
962#102—432no—
963#102C22×D4312yes—
964#102C22×D4312yes—
965#97—432no—
966#97—432no—
967#97—432no—
968C4×C8—432no—
969C4×C8—432no—
970C4×C8—432no—
971C24—21no—
972#41—22no—
973#41#1062190014yes—
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—431no—
978C2×Q8—431no—
979C2×Q8—431no—
980C2×Q8—431no—
981C2×Q8—432no—
982C2×Q8—861no—
983C2×Q8—861no—
984C2×Q8—861no—
985C2×Q8—861no—
986C2×Q8—861no—
987C2×Q8—861no—
988C2×Q8—861no—
989C2×Q8—862no—
990C2×Q8—862no—
991C2×Q8—1722no—
992C2×Q8—1724no—
993C2×Q8C23×D4312yes—
994C2×Q8C23×D4311yescharacteristic
995C2×D4—21no—
996C2×D4—21no—
997C2×D4—22no—
998C2×D4—22no—
999C2×D4C23×D4312yes—
1000C2×D4C23×D4311yescharacteristic
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—431no—
1006C22×C4—431no—
1007C22×C4—431no—
1008C22×C4—431no—
1009C22×C4—861no—
1010C22×C4—861no—
1011C22×C4—861no—
1012C22×C4—861no—
1013C22×C4—862no—
1014C22×C4—862no—
1015C22×C4—861no—
1016C22×C4—861no—
1017C22×C4—1724no—
1018C22×C4D4×D4311yescharacteristic
1019C22×C4D4×D4311yescharacteristic
1020C22×C4C23×D4311yescharacteristic
1021Q16—24no—
1022Q16—864no—
1023SD16—24no—
1024SD16—24no—
1025SD16—864no—
1026D8—24no—
1027M16—22no—
1028M16—22no—
1029M16—862no—
1030M16—862no—
1031C2×C8—432no—
1032C2×C8—432no—
1033C2×C8C23×D4312yes—
1034C2×C8C23×D4312yes—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—431no—
1038C4⋊C4—431no—
1039C4⋊C4—431no—
1040C4⋊C4—431no—
1041C4⋊C4—431no—
1042C4⋊C4—431no—
1043C4⋊C4—431no—
1044C4⋊C4—431no—
1045C4⋊C4—431no—
1046C4⋊C4—431no—
1047C4⋊C4—431no—
1048C4⋊C4—431no—
1049C4⋊C4—431no—
1050C4⋊C4—431no—
1051C4⋊C4—431no—
1052C4⋊C4—431no—
1053C4⋊C4—432no—
1054C4⋊C4—862no—
1055C4⋊C4—862no—
1056C4⋊C4—862no—
1057C4⋊C4—862no—
1058C4⋊C4—861no—
1059C4⋊C4—861no—
1060C4⋊C4—861no—
1061C4⋊C4—861no—
1062C4⋊C4—861no—
1063C4⋊C4—861no—
1064C4⋊C4—862no—
1065C4⋊C4—862no—
1066C4⋊C4—861no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—861no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—861no—
1073C4⋊C4—861no—
1074C4⋊C4—861no—
1075C4⋊C4—861no—
1076C4⋊C4—861no—
1077C4⋊C4—862no—
1078C4⋊C4—862no—
1079C4⋊C4—861no—
1080C4⋊C4—861no—
1081C4⋊C4—861no—
1082C4⋊C4—861no—
1083C4⋊C4—861no—
1084C4⋊C4—861no—
1085C4⋊C4C23×D4311yescharacteristic
1086C4⋊C4C23×D4311yescharacteristic
1087C22⋊C4—21no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—21no—
1093C22⋊C4—21no—
1094C22⋊C4—862no—
1095C22⋊C4—862no—
1096C22⋊C4—862no—
1097C22⋊C4—862no—
1098C22⋊C4—862no—
1099C22⋊C4—862no—
1100C22⋊C4—861no—
1101C22⋊C4—861no—
1102C22⋊C4—861no—
1103C22⋊C4—861no—
1104C22⋊C4—861no—
1105C22⋊C4—861no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—431no—
1110C42—431no—
1111C42—431no—
1112C42—431no—
1113C42—431no—
1114C42—431no—
1115C42—431no—
1116C42—431no—
1117C42—862no—
1118C42—862no—
1119C42—861no—
1120C42—861no—
1121C42—861no—
1122C42—861no—
1123C42—861no—
1124C42—861no—
1125C42—862no—
1126C42—862no—
1127C42D4×D4311yescharacteristic
1128C42D4×D4311yescharacteristic
1129C42C23×D4311yescharacteristic
1130C42C23×D4311yescharacteristic
1131C23—21no—
1132C23—22no—
1133C23—42no—
1134C23—42no—
1135C23—42no—
1136C23C2×D4×D4311yescharacteristic
1137Q8—21no—
1138Q8—22no—
1139Q8—22no—
1140Q8—42no—
1141Q8—862no—
1142Q8—862no—
1143Q8—862no—
1144Q8—862no—
1145Q8—3441no—
1146Q8—3441no—
1147Q8—3441no—
1148Q8—1721no—
1149Q8—1721no—
1150Q8—1722no—
1151Q8—1722no—
1152Q8—1722no—
1153Q8—1722no—
1154Q8C2×#1062190012yes—
1155D4—24no—
1156D4—22no—
1157D4—21no—
1158D4—22no—
1159D4—42no—
1160D4C2×#1062190012yes—
1161C2×C4—21no—
1162C2×C4—24no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—81no—
1171C2×C4—431no—
1172C2×C4—431no—
1173C2×C4—431no—
1174C2×C4—431no—
1175C2×C4—431no—
1176C2×C4—431no—
1177C2×C4—431no—
1178C2×C4—431no—
1179C2×C4—862no—
1180C2×C4—862no—
1181C2×C4—862no—
1182C2×C4—861no—
1183C2×C4—861no—
1184C2×C4—861no—
1185C2×C4—861no—
1186C2×C4—3441no—
1187C2×C4—3441no—
1188C2×C4—1724no—
1189C2×C4—1722no—
1190C2×C4—1721no—
1191C2×C4—1721no—
1192C2×C4—1721no—
1193C2×C4—1724no—
1194C2×C4—1722no—
1195C2×C4—1722no—
1196C2×C4—1722no—
1197C2×C4C2×D4×D4311yescharacteristic
1198C2×C4C2×D4×D4311yescharacteristic
1199C2×C4C2×D4×D4311yescharacteristic
1200C2×C4C2×D4×D4311yescharacteristic
1201C2×C4C2×D4×D4311yescharacteristic
1202C2×C4C2×#1062190012yes—
1203C2×C4#1306337212yes—
1204C2×C4C24×D4311yescharacteristic
1205C8—22no—
1206C8—22no—
1207C8—862no—
1208C8—862no—
1209C22—21no—
1210C22—21no—
1211C22—22no—
1212C22—41no—
1213C22—41no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—84no—
1218C22#1458355512yes—
1219C22C22×D4×D4311yescharacteristic
1220C4—21no—
1221C4—21no—
1222C4—22no—
1223C4—21no—
1224C4—21no—
1225C4—41no—
1226C4—42no—
1227C4—41no—
1228C4—432no—
1229C4—861no—
1230C4—861no—
1231C4—861no—
1232C4—861no—
1233C4—861no—
1234C4—861no—
1235C4—861no—
1236C4—1722no—
1237C4—1721no—
1238C4—1721no—
1239C4—1722no—
1240C4—1721no—
1241C4—1721no—
1242C4#1458355512yes—
1243C4C22×#1062190011yescharacteristic
1244C4C2×#1306337211yescharacteristic
1245C2—22no—
1246C2—42no—
1247C2—82no—
1248C2C2×#1458355511yescharacteristic
1249C2#575×D4311yescharacteristic
1250C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3040C2
socleC22×C43C23×D4
prime radicalC2×AGL(1,ℤ/8)×C43C22
hypercenter#3040D43
hypocenterC43#61323
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3040

Complements

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

NH ≅ G/Ntype
1. #41×Dic86C2semidirect
2. C2×#14583618C2semidirect
3. #19147441C2semidirect
4. #19147434C2semidirect
5. #19147426C2semidirect
6. #19147419C2semidirect
7. #19147330C2semidirect
8. #19147308C2semidirect
9. #19147275C2semidirect
10. #19147239C2semidirect
11. #19144981C2semidirect
12. #19144979C2semidirect
13. #19144973C2semidirect
14. #19144402C2semidirect
15. #19144397C2semidirect
16. #19144389C2semidirect
18. #19144080C2semidirect
19. #19143546C2semidirect
20. #137×Dic43C2semidirect
21. C4×#13063355C2semidirect
25. Q8×Dic86C22semidirect
26. #14583628C22semidirect
27. #14583625C22semidirect
28. #14583625C22semidirect
39. #14583608C22semidirect
40. #14583608C22semidirect
42. #14583606C22semidirect
44. D4×Dic86C22semidirect
64. #14583266C22semidirect
65. #14583266C22semidirect
74. #14583248C22semidirect
75. #14583248C22semidirect
76. #14583208C22semidirect
77. #14583207C22semidirect
78. #14583207C22semidirect
79. #14583204C22semidirect
82. #14583195C22semidirect
83. #14583192C22semidirect
85. #14583185C22semidirect
86. #14583182C22semidirect
92. #14583107C22semidirect
93. #14583107C22semidirect
94. #14583102C22semidirect
95. #14583102C22semidirect
96. #14583028C22semidirect
97. #14583028C22semidirect
98. #14583026C22semidirect
99. #14583023C22semidirect
101. #14583006C22semidirect
102. #14583004C22semidirect
104. #14583000C22semidirect
105. #14582999C22semidirect
106. Q16×Dic43C22semidirect
107. C4×#10621885C22semidirect
109. SD16×Dic43C22semidirect
110. C4×#10621883C22semidirect
764. C43#61323semidirect

Maximal subgroups

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

subgroupindex
#41×Dic862
C2×#145836182
#191474412
#191474342
#191474262
#191474192
#191473302
#191473082
#191472752
#191472392
#191449812
#191449792
#191449732
#191444022
#191443972
#191443892
#191440872
#191440802
#191435462
#137×Dic432
C4×#130633552
AGL(1,ℤ/8)×Dic432
C43×#30402
#6132343