Finite Group Databasebeta

← #25968859

Subgroups — #25968859

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2C22×#13063324C211yesmaximal, characteristic, complemented
3#19145828C212yesmaximal, complemented
4#19145823C212yesmaximal, complemented
5#19145819C212yesmaximal, complemented
6#19145814C212yesmaximal, complemented
7#19145744C212yesmaximal, complemented
8#19145737C212yesmaximal, complemented
9#19145721C212yesmaximal, complemented
10#19145714C212yesmaximal, complemented
11#19145139C212yesmaximal, complemented
12#19144986C212yesmaximal, complemented
13#19144520C211yesmaximal, characteristic, complemented
14#19144518C211yesmaximal, characteristic, complemented
15#19144515C211yesmaximal, characteristic, complemented
16#19144408C212yesmaximal, complemented
17#19144406C212yesmaximal, complemented
18#19143224C211yesmaximal, characteristic, complemented
19C43×#3092C211yesmaximal, characteristic, complemented
20C23×Dic86—21no—
21#14583452C2211yescharacteristic
22#14583451C2211yescharacteristic
23#14583451C2211yescharacteristic
24#14583445C2211yescharacteristic
25#14583444C2211yescharacteristic
26#14583444C2211yescharacteristic
27C2×#13063324—21no—
28C2×#13063324—21no—
29C2×#13063324—21no—
30C2×#13063324—21no—
31C2×#13063324—21no—
32C2×#13063324—21no—
33C2×#13063324C2212yes—
34C2×#13063324C2212yes—
35C2×#13063324C2212yes—
36C2×#13063324C2212yes—
37C2×#13063324C2212yes—
38C2×#13063324C2212yes—
39#14583435C2211yescharacteristic
40#14583435C2211yescharacteristic
41#14583430C2211yescharacteristic
42#14583430C2211yescharacteristic
43#14583429—21no—
44#14583429—21no—
45#14583426—21no—
46#14583426—21no—
47#14583410C2211yescharacteristic
48#14583405—21no—
49#14583405—21no—
50#41×Dic43C2211yescharacteristic
51#14583367C2211yescharacteristic
52C4×#10621900—21no—
53C4×#10621900—21no—
54C22×C4⋊Dic43C2211yescharacteristic
55C22×Dic43⋊C4—21no—
56C22×C4×Dic43C2211yescharacteristic
57#14583307C2214yescomplemented
58#14583306C2214yescomplemented
59#14583303C2214yescomplemented
60#14583296C2214yescomplemented
61#14583260C2214yescomplemented
62#14583257C2214yescomplemented
63#14583248C2214yescomplemented
64#14583244C2214yescomplemented
65#14583235C2212yes—
66#14583234C2212yes—
67#14583232C2212yes—
68#14583230C2212yes—
69#14583229C2212yes—
70#14583227C2212yes—
71#14583218C2212yes—
72#14583217C2212yes—
73#14583215C2212yes—
74#14583213C2212yes—
75#14583212C2212yes—
76#14583210C2212yes—
77#14583193C2214yescomplemented
78#14583192C2214yescomplemented
79#14583188C2214yescomplemented
80#14583187C2214yescomplemented
81#14583183C2214yescomplemented
82#14583182C2214yescomplemented
83#14583178C2214yescomplemented
84#14583177C2214yescomplemented
85#14582953C2212yes—
86#14582953C2212yes—
87#14582949C2212yes—
88#14582949C2212yes—
89#14582942C2212yes—
90#14582941C2212yes—
91#14582939C2212yes—
92#14582922C2212yes—
93#14582901C2212yes—
94#14582900C2212yes—
95#14582898C2212yes—
96#14582863C2211yescharacteristic
97M16×Dic43C2212yes—
98C43×#525C2211yescharacteristic
99C22×C4⋊C4×C43C2211yescharacteristic
100C43×#484C2212yes—
101C43×#483C2212yes—
102C43×#481C2212yes—
103C43×#480C2212yes—
104C43×#428C2212yes—
105C43×#417C2212yes—
106C43×#407C2211yescharacteristic
107C2×#10621898C2311yescharacteristic
108C2×#10621900—21no—
109C2×#10621900—21no—
110C22×Dic86—22no—
111C22×Dic86—22no—
112C22×Dic86—22no—
113C22×Dic86—22no—
114C22×Dic86—22no—
115C22×Dic86—22no—
116C22×Dic86—48no—
117C23×Dic43—21no—
118C23×Dic43D411yescharacteristic
119C23×Dic43D411yescharacteristic
120C2×#10621877C2312yes—
121#13063324—22no—
122#13063324—22no—
123#13063324—22no—
124#13063324—22no—
125#13063324—22no—
126#13063324—22no—
127#13063324—22no—
128#13063324—22no—
129#13063324—22no—
130#13063324—22no—
131#13063324—22no—
132#13063324—22no—
133#13063324C2311yescharacteristic
134#13063324C2314yes—
135#13063324C2311yescharacteristic
136#13063324C2314yes—
137#13063324C2314yes—
138#13063324C2314yes—
139#13063323C2311yescharacteristic
140#13063321C2311yescharacteristic
141#13063320—21no—
142#13063320—21no—
143#13063318—21no—
144#13063318—21no—
145#13063316C2311yescharacteristic
146#13063316C2311yescharacteristic
147#13063315—21no—
148#13063315—21no—
149#13063314C2311yescharacteristic
150#13063312C2311yescharacteristic
151#13063311—21no—
152#13063311—21no—
153#13063309—21no—
154#13063309—21no—
155#13063308—21no—
156#13063306—21no—
157#13063306—21no—
158#13063304C2311yescharacteristic
159#13063304C2311yescharacteristic
160#13063302—21no—
161#13063302—21no—
162#13063302—21no—
163#13063302—21no—
164#13063299C2311yescharacteristic
165#13063299C2311yescharacteristic
166#13063297—21no—
167#13063297—21no—
168#13063297—21no—
169#13063297—21no—
170#13063294—21no—
171Q8×Dic43C2311yescharacteristic
172Q8×Dic43C2311yescharacteristic
173C4×Dic86—21no—
174C4×Dic86—21no—
175#13063290—21no—
176#13063290—21no—
177#13063290C2311yescharacteristic
178#13063290C2311yescharacteristic
179D4×Dic43—21no—
180D4×Dic43—21no—
181D4×Dic43—21no—
182D4×Dic43—21no—
183D4×Dic43C2311yescharacteristic
184D4×Dic43C2311yescharacteristic
185#13063287C2311yescharacteristic
186#13063287C2311yescharacteristic
187C4×C22⋊D43—21no—
188C4×C22⋊D43—21no—
189C4×C22⋊D43—21no—
190C4×C22⋊D43—21no—
191(C22⋊D43)⋊C4—21no—
192(C22⋊D43)⋊C4—21no—
193(C22⋊D43)⋊C4—21no—
194(C22⋊D43)⋊C4—21no—
195(C22⋊D43)⋊C4—21no—
196(C22⋊D43)⋊C4—21no—
197#13063284—21no—
198#13063284C2311yescharacteristic
199#13063283—21no—
200#13063283—21no—
201#13063282—21no—
202#13063281—21no—
203#13063281—21no—
204#13063281—21no—
205#13063281—21no—
206C2×C4⋊Dic43—21no—
207C2×C4⋊Dic43—21no—
208C2×C4⋊Dic43—21no—
209C2×C4⋊Dic43C2312yes—
210C2×C4⋊Dic43C2312yes—
211C2×C4⋊Dic43C2312yes—
212C2×Dic43⋊C4—22no—
213C2×Dic43⋊C4—22no—
214C2×Dic43⋊C4—22no—
215C2×Dic43⋊C4—22no—
216C2×Dic43⋊C4—22no—
217C2×Dic43⋊C4—22no—
218C2×C4×Dic43—21no—
219C2×C4×Dic43D411yescharacteristic
220C2×C4×Dic43D411yescharacteristic
221C2×C4×Dic43D411yescharacteristic
222C2×C4×Dic43D411yescharacteristic
223C2×C4×Dic43D411yescharacteristic
224C2×C4×Dic43D411yescharacteristic
225C2×C4×Dic43C2311yescharacteristic
226C2×C4×Dic43C2311yescharacteristic
227C2×C4×Dic43C2311yescharacteristic
228C2×C4×Dic43C2311yescharacteristic
229C2×C4×Dic43C2311yescharacteristic
230C2×C4×Dic43C2311yescharacteristic
231C42×D43—21no—
232#13063259C2314yes—
233#13063258C2314yes—
234#13063258C2314yes—
235#13063257C2314yes—
236#13063256C2314yes—
237#13063256C2314yes—
238Dic43⋊C8C2314yes—
239Dic43⋊C8C2314yes—
240#13063250C2314yes—
241#13063249C2314yes—
242#13063248C2314yes—
243#13063247C2314yes—
244#13063246C2314yes—
245#13063245C2314yes—
246C22⋊(C43⋊C8)C2312yes—
247C22⋊(C43⋊C8)C2312yes—
248#13063235C2314yes—
249C8×Dic43C2314yes—
250C2×#41×C43C2311yescharacteristic
251C23×C4×C43—21no—
252C23×C4×C43C2311yescharacteristic
253C2×M16×C43C2312yes—
254#123×C43—21no—
255C22⋊Q8×C43C2311yescharacteristic
256C22⋊Q8×C43C2311yescharacteristic
257#121×C43C2311yescharacteristic
258#121×C43C2311yescharacteristic
259#120×C43—21no—
260C4×D4×C43—21no—
261C4×D4×C43—21no—
262#117×C43C2311yescharacteristic
263C2×C4⋊C4×C43—21no—
264C2×C4⋊C4×C43—21no—
265C2×C4⋊C4×C43—21no—
266C2×C4⋊C4×C43C2312yes—
267C2×C4⋊C4×C43C2312yes—
268C2×C4⋊C4×C43C2312yes—
269#107×C43C2314yes—
270#106×C43C2314yes—
271#103×C43C2314yes—
272#102×C43C2314yes—
273C22⋊C8×C43C2312yes—
274C22⋊C8×C43C2312yes—
275C24×C43C2×D411yescharacteristic
276#41×C43—24no—
277C2×Q8×C43C2411yescharacteristic
278C2×D4×C43—21no—
279C2×D4×C43—21no—
280C2×D4×C43—21no—
281C2×D4×C43C2411yescharacteristic
282C22×C4×C43—24no—
283C22×C4×C43—21no—
284C22×C4×C43—22no—
285C22×C4×C43—22no—
286C22×C4×C43—22no—
287C22×C4×C43—44no—
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2×D411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C2×C22⋊D43—21no—
295C2×C22⋊D43—21no—
296C2×C22⋊D43—21no—
297C2×C22⋊D43—21no—
298C2×C22⋊D43—21no—
299C22×Dic43—24no—
300C22×Dic43—24no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—22no—
304C22×Dic43—22no—
305C22×Dic43—22no—
306C22×Dic43—44no—
307C22×Dic43C2×D411yescharacteristic
308C22×Dic43C2×D411yescharacteristic
309C22×Dic43C2×D411yescharacteristic
310C22×Dic43C2×D411yescharacteristic
311C22×Dic43C2×D411yescharacteristic
312C22×Dic43C2×D411yescharacteristic
313C22×Dic43C2×D411yescharacteristic
314C22×Dic43C2×D411yescharacteristic
315C22×Dic43C2×D411yescharacteristic
316C22×Dic43C2×D411yescharacteristic
317C22×Dic43C2×D411yescharacteristic
318C22×Dic43C2×D411yescharacteristic
319#10621900—44no—
320#10621900—44no—
321#10621898—24no—
322C2×D172C2411yescharacteristic
323C2×C4×D43—21no—
324C2×C4×D43—21no—
325C2×C4×D43—21no—
326C2×Dic86—21no—
327C2×Dic86—21no—
328C2×Dic86—24no—
329C2×Dic86—24no—
330C2×Dic86—24no—
331C2×Dic86—24no—
332C2×Dic86—48no—
333C2×Dic86—48no—
334C2×Dic86—48no—
335C2×Dic86—48no—
336C2×Dic86—48no—
337C2×Dic86—48no—
338C2×Dic86C2411yescharacteristic
339M16×C43—24no—
340C2×C8×C43C2414yes—
341C4⋊C4×C43—22no—
342C4⋊C4×C43—22no—
343C4⋊C4×C43—22no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43—21no—
346C4⋊C4×C43C2414yes—
347C4⋊C4×C43C2411yescharacteristic
348C4⋊C4×C43C2411yescharacteristic
349C22⋊C4×C43—21no—
350C22⋊C4×C43—21no—
351C22⋊C4×C43—21no—
352C22⋊C4×C43—21no—
353C22⋊C4×C43—21no—
354C42×C43—21no—
355C22⋊Dic43—21no—
356C22⋊Dic43—21no—
357C22⋊Dic43—21no—
358C22⋊Dic43—21no—
359C22⋊Dic43—21no—
360C22⋊Dic43—21no—
361C22⋊Dic43—21no—
362(C2×D43)⋊C4—21no—
363(C2×D43)⋊C4—21no—
364(C2×D43)⋊C4—21no—
365(C2×D43)⋊C4—21no—
366(C2×D43)⋊C4—21no—
367(C2×D43)⋊C4—21no—
368C4⋊Dic43—22no—
369C4⋊Dic43—22no—
370C4⋊Dic43—22no—
371C4⋊Dic43—21no—
372C4⋊Dic43—21no—
373C4⋊Dic43—21no—
374C4⋊Dic43—21no—
375C4⋊Dic43C2414yes—
376C4⋊Dic43C2411yescharacteristic
377C4⋊Dic43C2411yescharacteristic
378Dic43⋊C4—21no—
379Dic43⋊C4—21no—
380Dic43⋊C4—24no—
381Dic43⋊C4—24no—
382Dic43⋊C4—24no—
383Dic43⋊C4—24no—
384Dic43⋊C4—21no—
385Dic43⋊C4—21no—
386Dic43⋊C4—21no—
387Dic43⋊C4—21no—
388Dic43⋊C4—21no—
389Dic43⋊C4—21no—
390Dic43⋊C4—21no—
391Dic43⋊C4—21no—
392C4×Dic43—21no—
393C4×Dic43—21no—
394C4×Dic43—21no—
395C4×Dic43—21no—
396C4×Dic43—21no—
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2×D411yescharacteristic
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2×D411yescharacteristic
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2×D411yescharacteristic
404C4×Dic43C2×D411yescharacteristic
405C4×Dic43C2×D411yescharacteristic
406C4×Dic43C2×D411yescharacteristic
407C4×Dic43C2×D411yescharacteristic
408C4×Dic43C2×D411yescharacteristic
409C4×Dic43C2411yescharacteristic
410C4×Dic43C2411yescharacteristic
411C4×Dic43C2411yescharacteristic
412C4×Dic43C2411yescharacteristic
413#10621877—24no—
414C2×C43⋊C8C2414yes—
415C23×C43—22no—
416C23×C43—22no—
417C23×C43—22no—
418C23×C43—21no—
419C23×C43C22×D411yescharacteristic
420C23×C43C22×D411yescharacteristic
421C23×C43C22×D411yescharacteristic
422C22×D43—21no—
423Q8×C43—22no—
424D4×C43—22no—
425D4×C43—42no—
426D4×C43—42no—
427D4×C43—42no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—21no—
434C2×C4×C43—21no—
435C2×C4×C43—21no—
436C2×C4×C43—24no—
437C2×C4×C43—44no—
438C2×C4×C43—44no—
439C2×C4×C43—44no—
440C2×C4×C43—42no—
441C2×C4×C43C22×D411yescharacteristic
442C2×C4×C43C22×D411yescharacteristic
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C432−1+414yes—
445C2×C4×C43C2511yescharacteristic
446C22⋊D43—42no—
447C22⋊D43—42no—
448C22⋊D43—42no—
449C22⋊D43—42no—
450C22⋊D43—42no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—21no—
462C2×Dic43—21no—
463C2×Dic43—21no—
464C2×Dic43—24no—
465C2×Dic43—44no—
466C2×Dic43—44no—
467C2×Dic43—44no—
468C2×Dic43—42no—
469C2×Dic43—42no—
470C2×Dic43AGL(1,ℤ/8)14yes—
471C2×Dic43#13714yes—
472C2×Dic43C22×D411yescharacteristic
473C2×Dic43C22×D411yescharacteristic
474C2×Dic43C22×D411yescharacteristic
475C2×Dic43C22×D411yescharacteristic
476C2×Dic43C22×D411yescharacteristic
477C2×Dic43C22×D411yescharacteristic
478C2×Dic43C22×D411yescharacteristic
479C2×Dic43C22×D411yescharacteristic
480D172—22no—
481C4×D43—42no—
482C4×D43—42no—
483C4×D43—42no—
484Dic86—22no—
485Dic86—48no—
486Dic86—48no—
487Dic86—48no—
488Dic86—48no—
489Dic86—42no—
490Dic86—42no—
491C8×C43—24no—
492C43⋊C8—24no—
493#60860—431nomaximal, Sylow
494C22×C43—28no—
495C22×C43—21no—
496C22×C43—21no—
497C22×C43—21no—
498C22×C43—21no—
499C22×C43—21no—
500C22×C43—21no—
501C22×C43—41no—
502C22×C43—41no—
503C22×C43—41no—
504C22×C43#53612yes—
505C22×C43C2×AGL(1,ℤ/8)12yes—
506C22×C43C2×#13712yes—
507C22×C43C23×D411yescharacteristic
508C2×D43—41no—
509C2×D43—41no—
510C2×D43—41no—
511C4×C43—21no—
512C4×C43—21no—
513C4×C43—41no—
514C4×C43—44no—
515C4×C43—41no—
516C4×C43—41no—
517C4×C43#53612yes—
518C4×C43C2×2−1+412yes—
519Dic43—21no—
520Dic43—21no—
521Dic43—21no—
522Dic43—21no—
523Dic43—41no—
524Dic43—44no—
525Dic43—41no—
526Dic43—41no—
527Dic43C2×AGL(1,ℤ/8)12yes—
528Dic43C2×AGL(1,ℤ/8)12yes—
529Dic43C2×#13712yes—
530Dic43C2×#13712yes—
531#3444—431no—
532C22×C4⋊Q8—431no—
533#3239—432no—
534#3239—432no—
535#3238—432no—
536#3238—432no—
537#3230—432no—
538#3229—432no—
539#3227—432no—
540#3226—432no—
541#3165—432no—
542#3141—432no—
543#3092—431no—
544#3092—431no—
545#3092—431no—
546#3092D4311yescharacteristic, complemented
547#3079—432no—
548#3079—432no—
549#2920—431no—
550C2×C43—22no—
551C2×C43—22no—
552C2×C43—22no—
553C2×C43—81no—
554C2×C43C2×#53611yescharacteristic
555C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
556C2×C43C22×#13711yescharacteristic
557D43—81no—
558C23×Q8—861no—
559#533—431no—
560#533—431no—
561#533—431no—
562#532—431no—
563#532—431no—
564#532—431no—
565C2×C4⋊Q8—432no—
566C2×C4⋊Q8—432no—
567C2×C4⋊Q8—432no—
568C2×C4⋊Q8—432no—
569C2×C4⋊Q8—432no—
570C2×C4⋊Q8—432no—
571C2×C4⋊Q8—861no—
572C2×C4⋊Q8—861no—
573C2×C4⋊Q8—861no—
574C2×C4⋊Q8—861no—
575C2×C4⋊Q8—861no—
576C2×C4⋊Q8—861no—
577#529—431no—
578#529—431no—
579#529—431no—
580#529—431no—
581#529—861no—
582#529—861no—
583#529—861no—
584#529—861no—
585#525—431no—
586#525—861no—
587#525—861no—
588#525C2×D4311yescharacteristic
589C4×#41—431no—
590C4×#41—431no—
591C4×#41—861no—
592C4×#41—861no—
593C22×C4⋊C4—431no—
594C22×C4⋊C4—861no—
595C22×C4⋊C4C2×D4311yescharacteristic
596C22×C42—431no—
597#501—434no—
598#501—434no—
599#500—434no—
600#498—434no—
601#489—434no—
602#489—434no—
603#487—434no—
604#486—434no—
605#484—432no—
606#484—432no—
607#484—432no—
608#484C2×D4312yes—
609#483—432no—
610#483—432no—
611#483—432no—
612#483C2×D4312yes—
613#481—432no—
614#481—432no—
615#481—432no—
616#481C2×D4312yes—
617#480—432no—
618#480—432no—
619#480—432no—
620#480C2×D4312yes—
621#477—434no—
622#477—434no—
623#476—434no—
624#476—434no—
625#475—434no—
626#475—434no—
627#474—434no—
628#474—434no—
629#432—432no—
630#432—432no—
631#431—432no—
632#431—432no—
633#428—432no—
634#428—432no—
635#428—432no—
636#428C2×D4312yes—
637#423—432no—
638#417—432no—
639#417—432no—
640#417—432no—
641#417C2×D4312yes—
642#407—431no—
643#407C2×D4311yescharacteristic
644C4×M16—432no—
645C43#6086011yescharacteristic, complemented, Sylow
646C2×#41—431no—
647C2×#41—861no—
648C2×#41—861no—
649C2×#41C22×D4311yescharacteristic
650C22×Q8—862no—
651C22×Q8—862no—
652C22×Q8—862no—
653C22×Q8—862no—
654C22×Q8—862no—
655C22×Q8—862no—
656C22×Q8—1728no—
657C23×C4—21no—
658C23×C4—431no—
659C23×C4—431no—
660C23×C4—861no—
661C23×C4C22×D4311yescharacteristic
662C2×M16—432no—
663C2×M16C22×D4312yes—
664C4⋊Q8—434no—
665C4⋊Q8—434no—
666C4⋊Q8—434no—
667C4⋊Q8—434no—
668C4⋊Q8—431no—
669C4⋊Q8—431no—
670C4⋊Q8—431no—
671C4⋊Q8—862no—
672C4⋊Q8—862no—
673C4⋊Q8—862no—
674C4⋊Q8—862no—
675C4⋊Q8—862no—
676C4⋊Q8—862no—
677C4⋊Q8—862no—
678C4⋊Q8—862no—
679C4⋊Q8—862no—
680C4⋊Q8—862no—
681C4⋊Q8—862no—
682C4⋊Q8—862no—
683#127—431no—
684#126—861no—
685#126—861no—
686#126—861no—
687#126—861no—
688#125—431no—
689#125—431no—
690#125—861no—
691#125—861no—
692#124—431no—
693#124—431no—
694#124—861no—
695#124—861no—
696#123—21no—
697#123—861no—
698#123—861no—
699#123—861no—
700#123—861no—
701#123—861no—
702C22⋊Q8—431no—
703C22⋊Q8—431no—
704C22⋊Q8—861no—
705C22⋊Q8—861no—
706C22⋊Q8—861no—
707C22⋊Q8—861no—
708C22⋊Q8C22×D4311yescharacteristic
709C22⋊Q8C22×D4311yescharacteristic
710#121—431no—
711#121—431no—
712#121—861no—
713#121—861no—
714#121—861no—
715#121—861no—
716#121C22×D4311yescharacteristic
717#121C22×D4311yescharacteristic
718#120—21no—
719#120—861no—
720C4×Q8—431no—
721C4×Q8—431no—
722C4×Q8—431no—
723C4×Q8—431no—
724C4×Q8—861no—
725C4×Q8—861no—
726C4×Q8—861no—
727C4×Q8—861no—
728C4×D4—21no—
729C4×D4—21no—
730C4×D4—431no—
731C4×D4—431no—
732C4×D4—431no—
733C4×D4—431no—
734C4×D4—861no—
735C4×D4—861no—
736C4×D4—861no—
737C4×D4—861no—
738C4×D4—861no—
739C4×D4—861no—
740C4×D4—861no—
741C4×D4—861no—
742C4×D4—861no—
743C4×D4—861no—
744C4×D4—861no—
745C4×D4—861no—
746C4×D4—861no—
747C4×D4—861no—
748#117—431no—
749#117—861no—
750#117—861no—
751#117—861no—
752#117—861no—
753#117—861no—
754#117—861no—
755#117—861no—
756#117—861no—
757#117C22×D4311yescharacteristic
758C2×C4⋊C4—21no—
759C2×C4⋊C4—21no—
760C2×C4⋊C4—21no—
761C2×C4⋊C4—432no—
762C2×C4⋊C4—432no—
763C2×C4⋊C4—432no—
764C2×C4⋊C4—862no—
765C2×C4⋊C4—862no—
766C2×C4⋊C4—862no—
767C2×C4⋊C4—862no—
768C2×C4⋊C4—862no—
769C2×C4⋊C4—862no—
770C2×C4⋊C4—861no—
771C2×C4⋊C4—861no—
772C2×C4⋊C4—861no—
773C2×C4⋊C4C22×D4312yes—
774C2×C4⋊C4C22×D4312yes—
775C2×C4⋊C4C22×D4312yes—
776C2×C42—431no—
777C2×C42—431no—
778C2×C42—431no—
779C2×C42—431no—
780C2×C42—431no—
781C2×C42—431no—
782C2×C42—431no—
783C2×C42—431no—
784C2×C42—431no—
785C2×C42—431no—
786C2×C42—431no—
787C2×C42—431no—
788C2×C42—861no—
789C2×C42—861no—
790#107—434no—
791#107—434no—
792#107—434no—
793#107C22×D4314yes—
794#106—434no—
795#106—434no—
796#106—434no—
797#106C22×D4314yes—
798C4⋊C8—434no—
799C4⋊C8—434no—
800#103—434no—
801#103—434no—
802#103—434no—
803#103C22×D4314yes—
804#102—434no—
805#102—434no—
806#102—434no—
807#102C22×D4314yes—
808C22⋊C8—432no—
809C22⋊C8—432no—
810C22⋊C8C22×D4312yes—
811C22⋊C8C22×D4312yes—
812#97—434no—
813C4×C8—434no—
814C24D4×D4311yescharacteristic
815#41—24no—
816#41—864no—
817#41—1724no—
818#41—1724no—
819C2×Q8—431no—
820C2×Q8—861no—
821C2×Q8—861no—
822C2×Q8—864no—
823C2×Q8—864no—
824C2×Q8—864no—
825C2×Q8—864no—
826C2×Q8—1728no—
827C2×Q8—1728no—
828C2×Q8—1728no—
829C2×Q8—1728no—
830C2×Q8—1728no—
831C2×Q8—1728no—
832C2×Q8C23×D4311yescharacteristic
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—431no—
837C2×D4—861no—
838C2×D4—861no—
839C2×D4—861no—
840C2×D4—861no—
841C2×D4—861no—
842C2×D4C23×D4311yescharacteristic
843C22×C4—24no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—44no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—864no—
864C22×C4—864no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—862no—
868C22×C4—862no—
869C22×C4—862no—
870C22×C4—861no—
871C22×C4—1724no—
872C22×C4D4×D4311yescharacteristic
873C22×C4D4×D4311yescharacteristic
874C22×C4D4×D4311yescharacteristic
875C22×C4C23×D4311yescharacteristic
876C22×C4C23×D4311yescharacteristic
877C22×C4C23×D4311yescharacteristic
878M16—24no—
879M16—864no—
880C2×C8—434no—
881C2×C8C23×D4314yes—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—434no—
888C4⋊C4—431no—
889C4⋊C4—431no—
890C4⋊C4—864no—
891C4⋊C4—864no—
892C4⋊C4—864no—
893C4⋊C4—864no—
894C4⋊C4—861no—
895C4⋊C4—861no—
896C4⋊C4—861no—
897C4⋊C4—861no—
898C4⋊C4—861no—
899C4⋊C4—861no—
900C4⋊C4—861no—
901C4⋊C4—861no—
902C4⋊C4—861no—
903C4⋊C4—861no—
904C4⋊C4—861no—
905C4⋊C4—861no—
906C4⋊C4—862no—
907C4⋊C4—862no—
908C4⋊C4—862no—
909C4⋊C4—861no—
910C4⋊C4—861no—
911C4⋊C4C23×D4314yes—
912C4⋊C4C23×D4311yescharacteristic
913C4⋊C4C23×D4311yescharacteristic
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—21no—
918C22⋊C4—21no—
919C22⋊C4—861no—
920C22⋊C4—861no—
921C22⋊C4—861no—
922C22⋊C4—861no—
923C22⋊C4—861no—
924C22⋊C4—861no—
925C22⋊C4—861no—
926C22⋊C4—861no—
927C22⋊C4—861no—
928C22⋊C4—861no—
929C22⋊C4—861no—
930C22⋊C4—861no—
931C22⋊C4—861no—
932C42—21no—
933C42—431no—
934C42—431no—
935C42—431no—
936C42—431no—
937C42—431no—
938C42—431no—
939C42—431no—
940C42—431no—
941C42—431no—
942C42—431no—
943C42—431no—
944C42—431no—
945C42—431no—
946C42—431no—
947C42—431no—
948C42—431no—
949C42—861no—
950C42—861no—
951C42—861no—
952C42—861no—
953C42—861no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—21no—
958C23—861no—
959C23C2×D4×D4311yescharacteristic
960C23C2×D4×D4311yescharacteristic
961C23C2×D4×D4311yescharacteristic
962Q8—22no—
963Q8—862no—
964Q8—1728no—
965Q8—1728no—
966Q8—1722no—
967Q8—1722no—
968Q8—1728no—
969Q8—1728no—
970D4—22no—
971D4—42no—
972D4—42no—
973D4—42no—
974D4—862no—
975D4—1722no—
976D4—1722no—
977D4—1722no—
978D4—1722no—
979D4—1722no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—24no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—44no—
992C2×C4—42no—
993C2×C4—434no—
994C2×C4—434no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—431no—
998C2×C4—431no—
999C2×C4—431no—
1000C2×C4—431no—
1001C2×C4—431no—
1002C2×C4—431no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—862no—
1012C2×C4—862no—
1013C2×C4—861no—
1014C2×C4—861no—
1015C2×C4—861no—
1016C2×C4—864no—
1017C2×C4—1722no—
1018C2×C4—1722no—
1019C2×C4—1722no—
1020C2×C4—1722no—
1021C2×C4—1724no—
1022C2×C4—1724no—
1023C2×C4—1724no—
1024C2×C4—1722no—
1025C2×C4C2×D4×D4311yescharacteristic
1026C2×C4C2×D4×D4311yescharacteristic
1027C2×C4C2×D4×D4311yescharacteristic
1028C2×C4#1306337214yes—
1029C2×C4C24×D4311yescharacteristic
1030C8—24no—
1031C8—864no—
1032C22—28no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—21no—
1038C22—21no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—1721no—
1043C22—1721no—
1044C22—1721no—
1045C22#1458347112yes—
1046C22AGL(1,ℤ/8)×D4312yes—
1047C22#137×D4312yes—
1048C22C22×D4×D4311yescharacteristic
1049C4—21no—
1050C4—21no—
1051C4—44no—
1052C4—41no—
1053C4—41no—
1054C4—41no—
1055C4—432no—
1056C4—432no—
1057C4—432no—
1058C4—432no—
1059C4—861no—
1060C4—861no—
1061C4—861no—
1062C4—861no—
1063C4—1724no—
1064C4—1721no—
1065C4—1721no—
1066C4—1721no—
1067C4#1458347112yes—
1068C4C2×#1306337212yes—
1069C2—22no—
1070C2—22no—
1071C2—22no—
1072C2—81no—
1073C2—3441no—
1074C2C2×#1458347111yescharacteristic
1075C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1076C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3092C2
socleC22×C43C23×D4
prime radical#19147887C2
hypercenter#3092D43
hypocenterC43#60860
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
2. C22×#13063324C2semidirect
3. #19145828C2semidirect
4. #19145823C2semidirect
5. #19145819C2semidirect
6. #19145814C2semidirect
7. #19145744C2semidirect
8. #19145737C2semidirect
9. #19145721C2semidirect
10. #19145714C2semidirect
11. #19145139C2semidirect
12. #19144986C2semidirect
13. #19144520C2semidirect
14. #19144518C2semidirect
15. #19144515C2semidirect
16. #19144408C2semidirect
17. #19144406C2semidirect
18. #19143224C2semidirect
19. C43×#3092C2semidirect
57. #14583307C22semidirect
58. #14583306C22semidirect
59. #14583303C22semidirect
60. #14583296C22semidirect
61. #14583260C22semidirect
62. #14583257C22semidirect
63. #14583248C22semidirect
64. #14583244C22semidirect
77. #14583193C22semidirect
78. #14583192C22semidirect
79. #14583188C22semidirect
80. #14583187C22semidirect
81. #14583183C22semidirect
82. #14583182C22semidirect
83. #14583178C22semidirect
84. #14583177C22semidirect
546. #3092D43semidirect
645. C43#60860semidirect

Maximal subgroups

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

subgroupindex
#191478872
C22×#130633242
#191458282
#191458232
#191458192
#191458142
#191457442
#191457372
#191457212
#191457142
#191451392
#191449862
#191445202
#191445182
#191445152
#191444082
#191444062
#191432242
C43×#30922
#6086043