Finite Group Databasebeta

← #25963098

Subgroups — #25963098

Order 11008.

4938 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583735C211yesmaximal, characteristic, complemented
2C2×AGL(1,ℤ/8)×D43C212yesmaximal, complemented
3C2×#14583465C211yesmaximal, characteristic, complemented
4#19143878C214yesmaximal, complemented
5#19143876C214yesmaximal, complemented
6#19143860C214yesmaximal, complemented
7#19143858C214yesmaximal, complemented
8#19143849C211yesmaximal, characteristic, complemented
9#19143848C212yesmaximal, complemented
10#19143847C211yesmaximal, characteristic, complemented
11#19143845C211yesmaximal, characteristic, complemented
12#19143843C212yesmaximal, complemented
13#19143111C212yesmaximal, complemented
14#19143038C211yesmaximal, characteristic, complemented
15C43×#3006C211yesmaximal, characteristic, complemented
16#14583735—216no—
17C2×#13063373C2212yescomplemented
18C2×#13063372—21no—
19C2×#13063372C2212yescomplemented
20C2×#13063371—21no—
21C2×#13063371C2212yescomplemented
22C2×#13063370—21no—
23C2×#13063370—21no—
24C2×#13063370C2212yescomplemented
25C22×#10621898—22no—
26C22×#10621898C2211yescharacteristic
27C22×#10621898C2211yescharacteristic, complemented
28C2×#41×D43—22no—
29C2×#41×D43C2212yes—
30C2×#41×D43C2212yescomplemented
31C22×D4×D43C2211yescharacteristic, complemented
32C2×#13063353C2212yescomplemented
33C2×#13063352C2214yescomplemented
34C2×#13063351C2212yescomplemented
35C2×#13063350C2212yescomplemented
36C2×#13063349C2214yescomplemented
37AGL(1,ℤ/8)×D43—216no—
38C2×SD16×D43C2214yescomplemented
39C2×D8×D43C2214yescomplemented
40C2×M16×D43C2212yescomplemented
41#14583465—22no—
42#14583465—22no—
43#14583465C2214yescomplemented
44#14583465C2214yescomplemented
45C2×#13063321—21no—
46C2×#13063311—21no—
47C2×#13063300C2211yescharacteristic, complemented
48C2×#13063299C2211yescharacteristic, complemented
49C2×#13063296C2211yescharacteristic, complemented
50C2×#13063295—21no—
51C2×#13063293—21no—
52C2×#13063283C2211yescharacteristic, complemented
53#14583047C2214yescomplemented
54#14583046C2214yescomplemented
55#14583045C2214yescomplemented
56#14583044C2214yescomplemented
57#14583043C2214yescomplemented
58#14583042C2214yescomplemented
59#14583041C2214yescomplemented
60#14583040C2212yescomplemented
61#14583039C2214yescomplemented
62#14583038C2212yescomplemented
63#14583037C2212yescomplemented
64#14583036C2214yescomplemented
65#14583035C2212yescomplemented
66#14583034C2214yescomplemented
67#14583033C2212yescomplemented
68#14583032C2212yescomplemented
69#14583031C2214yescomplemented
70#14582906C2214yescomplemented
71#14582902C2214yescomplemented
72#14582901C2212yescomplemented
73#14582900C2212yescomplemented
74#14582898C2212yescomplemented
75#14582894C2214yescomplemented
76#14582892C2214yescomplemented
77#14582864C2214yescomplemented
78#14582864C2214yescomplemented
79#14582863C2211yescharacteristic, complemented
80#14582862C2212yescomplemented
81C22×#41×C43C2211yescharacteristic, complemented
82C2×AGL(1,ℤ/8)×C43C2212yescomplemented
83C2×#121×C43C2211yescharacteristic, complemented
84C43×#449C2214yescomplemented
85C43×#448C2212yescomplemented
86C43×#447C2212yescomplemented
87C43×#417C2212yescomplemented
88C43×#407C2211yescharacteristic, complemented
89C24×D43—21no—
90#13063373—28no—
91#13063373—28no—
92#13063372—216no—
93#13063372—28no—
94#13063372—28no—
95#13063371—216no—
96#13063371—28no—
97#13063371—28no—
98#13063370—216no—
99#13063370—216no—
100#13063370—28no—
101#13063370—28no—
102C2×#10621902—22no—
103C2×#10621902C2312yes—
104C2×#10621902C2312yescomplemented
105C2×#10621898—232no—
106C2×#10621898—21no—
107C2×#10621898—21no—
108C2×#10621898—22no—
109C2×#10621898—22no—
110C2×#10621898—28no—
111C2×#10621898—22no—
112C2×#10621898—22no—
113C2×#10621898—22no—
114C2×#10621898—28no—
115C2×#10621898—22no—
116C2×#10621898D412yes—
117C2×#10621898D412yes—
118C2×#10621898C2312yes—
119C2×#10621898C2312yes—
120C2×#10621898C2312yes—
121C2×#10621898C2312yescomplemented
122C2×#10621900—22no—
123C2×#10621900—22no—
124C2×#10621900—22no—
125C2×#10621900—22no—
126C2×#10621900—22no—
127C2×#10621900C2312yes—
128C2×#10621900C2312yescomplemented
129#41×D43—232no—
130#41×D43—28no—
131#41×D43—28no—
132#41×D43—28no—
133#41×D43D4116yescomplemented
134C22×Dic86—22no—
135C22×Dic86D411yescharacteristic
136C22×Dic86C2311yescharacteristic, complemented
137C2×Q8×D43—22no—
138C2×Q8×D43C2312yes—
139C2×Q8×D43C2312yescomplemented
140C22×D172—22no—
141C22×D172—21no—
142C22×D172D411yescharacteristic
143C22×D172C2311yescharacteristic
144C22×D172C2311yescharacteristic, complemented
145C22×C22⋊D43—21no—
146C22×C22⋊D43—22no—
147C22×C22⋊D43—22no—
148C22×C22⋊D43—21no—
149C22×C22⋊D43—21no—
150C22×C22⋊D43—21no—
151C22×C22⋊D43D411yescharacteristic
152C22×C22⋊D43D411yescharacteristic
153C2×D4×D43—22no—
154C2×D4×D43—22no—
155C2×D4×D43—22no—
156C2×D4×D43—22no—
157C2×D4×D43—22no—
158C2×D4×D43—28no—
159C2×D4×D43—22no—
160C2×D4×D43C2314yes—
161C2×D4×D43C2312yes—
162C2×D4×D43C2312yescomplemented
163C22×C4×D43—21no—
164C22×C4×D43—22no—
165C22×C4×D43—22no—
166C22×C4×D43C2311yescharacteristic
167C22×C4×D43C2311yescharacteristic
168#13063353—28no—
169#13063352—216no—
170#13063351—28no—
171#13063350—28no—
172#13063349—216no—
173C2×#10621873C2314yes—
174C2×#10621883C2314yes—
175C2×#10621884C2314yes—
176SD16×D43—216no—
177C2×D344C2314yes—
178C2×#10621882C2314yes—
179C2×#10621882C2314yes—
180D8×D43—216no—
181C2×#10621877C2312yes—
182C2×#10621872C2314yes—
183M16×D43—28no—
184C2×C8×D43C2314yes—
185#13063321—24no—
186#13063321—24no—
187#13063311—24no—
188#13063311—24no—
189#13063300—22no—
190#13063300C2314yes—
191#13063299—21no—
192#13063299—21no—
193#13063299C2312yes—
194#13063299C2312yes—
195#13063296—22no—
196#13063296C2314yes—
197#13063295—24no—
198#13063295—24no—
199#13063293—24no—
200#13063293—24no—
201#13063283—22no—
202#13063283C2314yes—
203C2×C4⋊Dic43C2311yescharacteristic
204C2×C22⋊Dic43—21no—
205C2×(C2×D43)⋊C4—21no—
206C2×(C2×D43)⋊C4—21no—
207C2×(C2×D43)⋊C4—21no—
208C2×C4×Dic43—21no—
209#13063250C2314yescomplemented
210#13063249C2314yescomplemented
211#13063248C2314yescomplemented
212#13063247C2314yescomplemented
213#13063246C2314yescomplemented
214#13063245C2314yescomplemented
215C22⋊(C43⋊C8)C2312yescomplemented
216C22⋊(C43⋊C8)C2312yescomplemented
217(C2×D43)⋊C8C2314yescomplemented
218(C2×D43)⋊C8C2314yescomplemented
219C2×#41×C43—28no—
220C2×#41×C43—21no—
221C2×#41×C43—21no—
222C2×#41×C43C2312yes—
223C2×#41×C43C2312yescomplemented
224C22×Q8×C43C2311yescharacteristic, complemented
225C22×D4×C43—21no—
226C22×D4×C43—21no—
227C22×D4×C43C2311yescharacteristic
228C22×D4×C43C2311yescharacteristic, complemented
229C23×C4×C43—21no—
230C23×C4×C43C2311yescharacteristic
231AGL(1,ℤ/8)×C43—28no—
232C2×SD16×C43C2314yes—
233C2×D8×C43C2314yes—
234C2×M16×C43C2312yes—
235#121×C43—21no—
236#121×C43—21no—
237#121×C43C2312yes—
238#121×C43C2312yes—
239C2×C4⋊C4×C43C2311yescharacteristic
240C2×C22⋊C4×C43—21no—
241#103×C43C2314yescomplemented
242#102×C43C2314yescomplemented
243C22⋊C8×C43C2312yescomplemented
244C22⋊C8×C43C2312yescomplemented
245C24×C43—21no—
246C24×C43—21no—
247C24×C43C2×D411yescharacteristic
248C23×D43—21no—
249C23×D43—22no—
250C23×D43—22no—
251C23×D43—21no—
252C23×D43—24no—
253C23×D43—44no—
254C23×D43—82no—
255C23×D43—82no—
256C23×D43C2×D411yescharacteristic
257C23×D43C2×D411yescharacteristic
258#41×C43—28no—
259#41×C43—28no—
260#41×C43—24no—
261#41×C43—24no—
262#41×C43—24no—
263#41×C43C2×D418yes—
264C2×Q8×C43—24no—
265C2×Q8×C43—21no—
266C2×Q8×C43C2412yes—
267C2×D4×C43—28no—
268C2×D4×C43—24no—
269C2×D4×C43—21no—
270C2×D4×C43—21no—
271C2×D4×C43—22no—
272C2×D4×C43—22no—
273C2×D4×C43—22no—
274C2×D4×C43—22no—
275C2×D4×C43—24no—
276C2×D4×C43—82no—
277C2×D4×C43C2412yes—
278C2×D4×C43C2412yes—
279C22×C4×C43—28no—
280C22×C4×C43—22no—
281C22×C4×C43—22no—
282C22×C4×C43—24no—
283C22×C4×C43—21no—
284C22×C4×C43—21no—
285C22×C4×C43C2×D411yescharacteristic
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C22×C4×C43C2411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C2×C22⋊D43—216no—
292C2×C22⋊D43—28no—
293C2×C22⋊D43—216no—
294C2×C22⋊D43—24no—
295C2×C22⋊D43—22no—
296C2×C22⋊D43—22no—
297C2×C22⋊D43—24no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C2×C22⋊D43—22no—
301C2×C22⋊D43—22no—
302C2×C22⋊D43—24no—
303C2×C22⋊D43—22no—
304C2×C22⋊D43—22no—
305C2×C22⋊D43—24no—
306C2×C22⋊D43—44no—
307C2×C22⋊D43—82no—
308C2×C22⋊D43—82no—
309C2×C22⋊D43C2×D412yes—
310C2×C22⋊D43C2×D412yes—
311C2×C22⋊D43C2×D412yes—
312C2×C22⋊D43C2×D412yes—
313C22×Dic43—22no—
314C22×Dic43—22no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43C2×D411yescharacteristic
318C22×Dic43C2×D411yescharacteristic
319#10621902—216no—
320#10621902—24no—
321#10621902—24no—
322#10621902—24no—
323#10621902C2×D418yescomplemented
324Q8×D43—216no—
325Q8×D43—24no—
326Q8×D43—24no—
327Q8×D43—24no—
328Q8×D43C2×D418yescomplemented
329#10621900—216no—
330#10621900—216no—
331#10621900—216no—
332#10621900—216no—
333#10621900—24no—
334#10621900—216no—
335#10621900—24no—
336#10621900—24no—
337#10621900C2×D418yescomplemented
338D4×D43—216no—
339D4×D43—216no—
340D4×D43—216no—
341D4×D43—216no—
342D4×D43—24no—
343D4×D43—24no—
344D4×D43—24no—
345D4×D43—216no—
346D4×D43—28no—
347D4×D43—28no—
348D4×D43—48no—
349D4×D43C2×D418yescomplemented
350#10621898—216no—
351#10621898—28no—
352#10621898—216no—
353#10621898—216no—
354#10621898—28no—
355#10621898—216no—
356#10621898—216no—
357#10621898—24no—
358#10621898—24no—
359#10621898—28no—
360#10621898—216no—
361#10621898—28no—
362#10621898—24no—
363#10621898—24no—
364#10621898—24no—
365#10621898—24no—
366#10621898—24no—
367#10621898C2×D418yes—
368C2×D172—216no—
369C2×D172—21no—
370C2×D172—24no—
371C2×D172—21no—
372C2×D172—24no—
373C2×D172—22no—
374C2×D172—22no—
375C2×D172—24no—
376C2×D172—24no—
377C2×D172—82no—
378C2×D172C2×D412yes—
379C2×D172C2×D412yes—
380C2×D172C2412yes—
381C2×D172C2412yes—
382C2×C4×D43—28no—
383C2×C4×D43—216no—
384C2×C4×D43—22no—
385C2×C4×D43—22no—
386C2×C4×D43—24no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—216no—
390C2×C4×D43—22no—
391C2×C4×D43—22no—
392C2×C4×D43C2×D418yes—
393C2×C4×D43C2×D412yes—
394C2×C4×D43C2×D412yes—
395C2×C4×D43C2412yes—
396C2×C4×D43C2412yes—
397C2×Dic86—216no—
398C2×Dic86—21no—
399C2×Dic86—24no—
400C2×Dic86—22no—
401C2×Dic86—22no—
402C2×Dic86—24no—
403C2×Dic86C2×D412yes—
404C2×Dic86C2×D412yes—
405C2×Dic86C2412yes—
406SD16×C43—28no—
407D8×C43—28no—
408M16×C43—24no—
409C2×C8×C43C2414yes—
410C4⋊C4×C43—21no—
411C4⋊C4×C43C2412yes—
412C22⋊C4×C43—22no—
413C22⋊C4×C43—22no—
414C22⋊Dic43—24no—
415#10621884—28no—
416#10621883—28no—
417#10621882—28no—
418#10621882—28no—
419(C2×D43)⋊C4—22no—
420(C2×D43)⋊C4—22no—
421(C2×D43)⋊C4—24no—
422(C2×D43)⋊C4—24no—
423C4⋊Dic43—21no—
424C4⋊Dic43C2412yes—
425C4×Dic43—24no—
426#10621877—24no—
427C2×C43⋊C8C2414yes—
428D344—28no—
429#10621873—28no—
430#10621872—28no—
431C8×D43—28no—
432C23×C43—24no—
433C23×C43—22no—
434C23×C43—22no—
435C23×C43—22no—
436C23×C43—41no—
437C23×C43—41no—
438C23×C43—42no—
439C23×C43—42no—
440C23×C43—42no—
441C23×C43—81no—
442C23×C43—81no—
443C23×C43C22×D411yescharacteristic
444C23×C43C22×D411yescharacteristic
445C23×C43C22×D411yescharacteristic
446C22×D43—22no—
447C22×D43—24no—
448C22×D43—28no—
449C22×D43—22no—
450C22×D43—28no—
451C22×D43—22no—
452C22×D43—41no—
453C22×D43—41no—
454C22×D43—41no—
455C22×D43—41no—
456C22×D43—42no—
457C22×D43—42no—
458C22×D43—42no—
459C22×D43—48no—
460C22×D43—82no—
461C22×D43—82no—
462C22×D43—82no—
463C22×D43—82no—
464C22×D43—84no—
465C22×D43—84no—
466C22×D43—81no—
467C22×D43—81no—
468C22×D43—816no—
469C22×D43#12014yes—
470C22×D43C22×D412yes—
471C22×D43C22×D412yes—
472Q8×C43—24no—
473Q8×C43—22no—
474Q8×C43C22×D414yes—
475D4×C43—28no—
476D4×C43—24no—
477D4×C43—28no—
478D4×C43—22no—
479D4×C43—24no—
480D4×C43—42no—
481D4×C43—82no—
482D4×C43—82no—
483D4×C43C22×D414yes—
484C2×C4×C43—28no—
485C2×C4×C43—24no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—28no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—42no—
495C2×C4×C43C22×D411yescharacteristic
496C2×C4×C43C22×D411yescharacteristic
497C2×C4×C43C22×D411yescharacteristic
498C2×C4×C43C22×D414yes—
499C2×C4×C43C2511yescharacteristic
500C22⋊D43—28no—
501C22⋊D43—28no—
502C22⋊D43—28no—
503C22⋊D43—28no—
504C22⋊D43—24no—
505C22⋊D43—24no—
506C22⋊D43—28no—
507C22⋊D43—24no—
508C22⋊D43—24no—
509C22⋊D43—28no—
510C22⋊D43—48no—
511C22⋊D43—84no—
512C22⋊D43—82no—
513C22⋊D43—82no—
514C2×Dic43—28no—
515C2×Dic43—24no—
516C2×Dic43—22no—
517C2×Dic43—22no—
518C2×Dic43—28no—
519C2×Dic43—22no—
520C2×Dic43—42no—
521C2×Dic43#12014yes—
522C2×Dic43C22×D412yes—
523C2×Dic43C22×D412yes—
524D172—24no—
525D172—28no—
526D172—24no—
527D172—28no—
528D172—24no—
529D172—22no—
530D172—24no—
531D172—42no—
532D172—84no—
533D172C22×D414yes—
534C4×D43—28no—
535C4×D43—28no—
536C4×D43—28no—
537C4×D43—28no—
538C4×D43—28no—
539C4×D43—24no—
540C4×D43—22no—
541C4×D43—22no—
542C4×D43—28no—
543C4×D43#12018yes—
544C4×D43C22×D414yes—
545C4×D43C22×D414yes—
546Dic86—24no—
547Dic86—28no—
548Dic86—22no—
549Dic86—24no—
550Dic86—28no—
551Dic86—24no—
552Dic86C22×D414yes—
553C8×C43—24no—
554C43⋊C8—24no—
555#60369—431nomaximal, Sylow
556C22×C43—21no—
557C22×C43—21no—
558C22×C43—21no—
559C22×C43—21no—
560C22×C43—21no—
561C22×C43—21no—
562C22×C43—24no—
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—42no—
566C22×C43—42no—
567C22×C43—42no—
568C22×C43—42no—
569C22×C43—42no—
570C22×C43—82no—
571C22×C43—84no—
572C22×C43—84no—
573C22×C43C2×#12012yes—
574C22×C43C23×D411yescharacteristic
575C2×D43—22no—
576C2×D43—22no—
577C2×D43—22no—
578C2×D43—22no—
579C2×D43—24no—
580C2×D43—22no—
581C2×D43—44no—
582C2×D43—42no—
583C2×D43—42no—
584C2×D43—42no—
585C2×D43—42no—
586C2×D43—42no—
587C2×D43—88no—
588C2×D43—816no—
589C2×D43—82no—
590C2×D43—88no—
591C2×D43—84no—
592C2×D43—84no—
593C2×D43C2×#12014yes—
594C4×C43—21no—
595C4×C43—24no—
596C4×C43—21no—
597C4×C43—42no—
598C4×C43C2×#12012yes—
599C4×C43C23×D412yes—
600Dic43—22no—
601Dic43—24no—
602Dic43—42no—
603Dic43C2×#12014yes—
604C2×#585—431no—
605C22×AGL(1,ℤ/8)—432no—
606C2×#535—431no—
607#3010—434no—
608#3010—434no—
609#3008—434no—
610#3008—434no—
611#3006—432no—
612#3006—431no—
613#3006—431no—
614#3006—432no—
615#3006—431no—
616#3006D4311yescharacteristic, complemented
617#2896—432no—
618#2879—431no—
619C2×C43—22no—
620C2×C43—41no—
621C2×C43—44no—
622C2×C43—41no—
623C2×C43—82no—
624C2×C43C22×#12011yescharacteristic
625C2×C43#358511yescharacteristic
626C2×C43#358511yescharacteristic
627D43—24no—
628D43—42no—
629D43—44no—
630D43—82no—
631#585—8616no—
632C2×2−1+4—432no—
633C2×2−1+4—432no—
634C2×2−1+4—861no—
635C2×H(5,𝔽2)—432no—
636C2×H(5,𝔽2)—432no—
637C2×H(5,𝔽2)—861no—
638C2×H(5,𝔽2)—861no—
639C2×H(5,𝔽2)—861no—
640C22×#41—431no—
641C22×#41—432no—
642C22×#41—432no—
643C22×#41—431no—
644C22×#41—862no—
645C22×#41—862no—
646C22×#41C2×D4311yescharacteristic, complemented
647C23×D4—431no—
648C2×AGL(1,ℤ/8)—432no—
649C2×AGL(1,ℤ/8)—432no—
650C2×AGL(1,ℤ/8)—434no—
651C2×AGL(1,ℤ/8)—434no—
652C2×AGL(1,ℤ/8)—432no—
653C2×AGL(1,ℤ/8)—8616no—
654C2×AGL(1,ℤ/8)C2×D4312yescomplemented
655C22×SD16—434no—
656C22×D8—434no—
657C22×M16—432no—
658#535—434no—
659#535—434no—
660#535—862no—
661#535—862no—
662C2×#127—861no—
663C2×#124—861no—
664C2×#121—431no—
665C2×#121—431no—
666C2×#121—431no—
667C2×#121C2×D4311yescharacteristic, complemented
668C2×#120—861no—
669C2×#120—861no—
670C2×#117—431no—
671#449—434no—
672#449—434no—
673#449—434no—
674#449—434no—
675#449—434no—
676#449—434no—
677#449—434no—
678#449C2×D4314yescomplemented
679#448—432no—
680#448—434no—
681#448—432no—
682#448—434no—
683#448—432no—
684#448C2×D4312yescomplemented
685#447—432no—
686#447—434no—
687#447—432no—
688#447—434no—
689#447—432no—
690#447C2×D4312yescomplemented
691#419—434no—
692#418—434no—
693#417—432no—
694#417—432no—
695#417—432no—
696#417C2×D4312yescomplemented
697#416—434no—
698#416—434no—
699#408—434no—
700#408—434no—
701#407—431no—
702#407—432no—
703#407C2×D4311yescharacteristic, complemented
704C43#6036911yescharacteristic, complemented, Sylow
705C25—861no—
7062−1+4—868no—
7072−1+4—868no—
7082−1+4—868no—
7092−1+4—868no—
7102−1+4—8616no—
711H(5,𝔽2)—868no—
712H(5,𝔽2)—868no—
713H(5,𝔽2)—8616no—
714H(5,𝔽2)—8616no—
715H(5,𝔽2)—868no—
716H(5,𝔽2)—868no—
717H(5,𝔽2)—8616no—
718C2×#41—28no—
719C2×#41—21no—
720C2×#41—21no—
721C2×#41—432no—
722C2×#41—432no—
723C2×#41—432no—
724C2×#41—432no—
725C2×#41—4316no—
726C2×#41—432no—
727C2×#41—432no—
728C2×#41—432no—
729C2×#41—432no—
730C2×#41—432no—
731C2×#41—432no—
732C2×#41—862no—
733C2×#41—862no—
734C2×#41—868no—
735C2×#41—862no—
736C2×#41—862no—
737C2×#41—862no—
738C2×#41—862no—
739C2×#41—868no—
740C2×#41—8632no—
741C2×#41—862no—
742C2×#41—862no—
743C2×#41—868no—
744C2×#41—862no—
745C2×#41—862no—
746C2×#41—862no—
747C2×#41—862no—
748C2×#41—868no—
749C2×#41—8632no—
750C2×#41—868no—
751C2×#41—861no—
752C2×#41—861no—
753C2×#41C22×D4312yes—
754C2×#41C22×D4312yescomplemented
755C22×Q8—431no—
756C22×Q8—432no—
757C22×Q8—432no—
758C22×Q8—431no—
759C22×Q8—862no—
760C22×Q8—862no—
761C22×Q8C22×D4311yescharacteristic, complemented
762C22×D4—21no—
763C22×D4—21no—
764C22×D4—432no—
765C22×D4—431no—
766C22×D4—431no—
767C22×D4—434no—
768C22×D4—432no—
769C22×D4—431no—
770C22×D4—431no—
771C22×D4—431no—
772C22×D4—862no—
773C22×D4—861no—
774C22×D4—868no—
775C22×D4—862no—
776C22×D4—861no—
777C22×D4—862no—
778C22×D4—862no—
779C22×D4—862no—
780C22×D4—862no—
781C22×D4—862no—
782C22×D4—862no—
783C22×D4—862no—
784C22×D4—861no—
785C22×D4—861no—
786C22×D4—861no—
787C22×D4C22×D4311yescharacteristic
788C22×D4C22×D4311yescharacteristic, complemented
789C23×C4—21no—
790C23×C4—431no—
791C23×C4—431no—
792C23×C4—862no—
793C23×C4—862no—
794C23×C4—861no—
795C23×C4C22×D4311yescharacteristic
796AGL(1,ℤ/8)—28no—
797AGL(1,ℤ/8)—868no—
798AGL(1,ℤ/8)—8616no—
799AGL(1,ℤ/8)—8616no—
800AGL(1,ℤ/8)—868no—
801AGL(1,ℤ/8)—868no—
802C2×SD16—434no—
803C2×SD16—434no—
804C2×SD16—434no—
805C2×SD16—8616no—
806C2×SD16C22×D4314yes—
807C2×D8—434no—
808C2×D8—434no—
809C2×D8—434no—
810C2×D8—8616no—
811C2×D8C22×D4314yes—
812C2×M16—432no—
813C2×M16—434no—
814C2×M16—868no—
815C2×M16C22×D4312yes—
816C22×C8—434no—
817#127—864no—
818#127—864no—
819#124—864no—
820#124—864no—
821#121—21no—
822#121—21no—
823#121—434no—
824#121—432no—
825#121—432no—
826#121—434no—
827#121—862no—
828#121—862no—
829#121—861no—
830#121—861no—
831#121C22×D4312yes—
832#121C22×D4312yes—
833#120—864no—
834#120—864no—
835#120—864no—
836#120—864no—
837#117—434no—
838#117—862no—
839C2×C4⋊C4—431no—
840C2×C4⋊C4C22×D4311yescharacteristic
841C2×C22⋊C4—21no—
842C2×C22⋊C4—861no—
843C2×C22⋊C4—861no—
844C2×C22⋊C4—861no—
845C2×C22⋊C4—861no—
846C2×C42—861no—
847#103—434no—
848#103—434no—
849#103—434no—
850#103C22×D4314yescomplemented
851#102—434no—
852#102—434no—
853#102—434no—
854#102C22×D4314yescomplemented
855C22⋊C8—432no—
856C22⋊C8—432no—
857C22⋊C8—434no—
858C22⋊C8—434no—
859C22⋊C8C22×D4312yescomplemented
860C22⋊C8C22×D4312yescomplemented
861C24—21no—
862C24—21no—
863C24—431no—
864C24—431no—
865C24—862no—
866C24—862no—
867C24—864no—
868C24—861no—
869C24—861no—
870C24—3442no—
871C24—3442no—
872C24—1724no—
873C24D4×D4311yescharacteristic
874#41—28no—
875#41—28no—
876#41—24no—
877#41—24no—
878#41—24no—
879#41—438no—
880#41—438no—
881#41—438no—
882#41—868no—
883#41—8616no—
884#41—868no—
885#41—864no—
886#41—864no—
887#41—864no—
888#41—864no—
889#41—864no—
890#41—864no—
891#41—868no—
892#41—8616no—
893#41—8616no—
894#41—8616no—
895#41—8616no—
896#41—8616no—
897#41—868no—
898#41—8616no—
899#41—864no—
900#41—864no—
901#41—864no—
902#41—8616no—
903#41—8616no—
904#41—8616no—
905#41—8616no—
906#41—864no—
907#41—8616no—
908#41—864no—
909#41—864no—
910#41—864no—
911#41D4×D4318yes—
912C2×Q8—24no—
913C2×Q8—21no—
914C2×Q8—432no—
915C2×Q8—432no—
916C2×Q8—438no—
917C2×Q8—432no—
918C2×Q8—862no—
919C2×Q8—862no—
920C2×Q8—864no—
921C2×Q8—864no—
922C2×Q8—8616no—
923C2×Q8—864no—
924C2×Q8—864no—
925C2×Q8—8616no—
926C2×Q8—864no—
927C2×Q8—861no—
928C2×Q8C23×D4312yes—
929C2×D4—28no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—24no—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4—21no—
936C2×D4—24no—
937C2×D4—21no—
938C2×D4—82no—
939C2×D4—438no—
940C2×D4—432no—
941C2×D4—432no—
942C2×D4—432no—
943C2×D4—432no—
944C2×D4—432no—
945C2×D4—432no—
946C2×D4—432no—
947C2×D4—432no—
948C2×D4—864no—
949C2×D4—864no—
950C2×D4—862no—
951C2×D4—862no—
952C2×D4—8616no—
953C2×D4—864no—
954C2×D4—864no—
955C2×D4—868no—
956C2×D4—868no—
957C2×D4—862no—
958C2×D4—862no—
959C2×D4—864no—
960C2×D4—864no—
961C2×D4—864no—
962C2×D4—8616no—
963C2×D4—8616no—
964C2×D4—8616no—
965C2×D4—8616no—
966C2×D4—8616no—
967C2×D4—864no—
968C2×D4—862no—
969C2×D4—862no—
970C2×D4—8616no—
971C2×D4—8616no—
972C2×D4—868no—
973C2×D4—862no—
974C2×D4—862no—
975C2×D4—864no—
976C2×D4—864no—
977C2×D4—862no—
978C2×D4—862no—
979C2×D4—861no—
980C2×D4—864no—
981C2×D4—861no—
982C2×D4—3442no—
983C2×D4—3442no—
984C2×D4—3442no—
985C2×D4—1728no—
986C2×D4—1724no—
987C2×D4C23×D4312yes—
988C2×D4C23×D4312yes—
989C22×C4—28no—
990C22×C4—21no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—24no—
994C22×C4—21no—
995C22×C4—431no—
996C22×C4—432no—
997C22×C4—438no—
998C22×C4—432no—
999C22×C4—431no—
1000C22×C4—432no—
1001C22×C4—432no—
1002C22×C4—862no—
1003C22×C4—862no—
1004C22×C4—8616no—
1005C22×C4—862no—
1006C22×C4—862no—
1007C22×C4—8616no—
1008C22×C4—868no—
1009C22×C4—862no—
1010C22×C4—862no—
1011C22×C4—861no—
1012C22×C4—864no—
1013C22×C4—862no—
1014C22×C4—862no—
1015C22×C4—861no—
1016C22×C4D4×D4311yescharacteristic
1017C22×C4D4×D4311yescharacteristic
1018C22×C4D4×D4311yescharacteristic
1019C22×C4C23×D4311yescharacteristic
1020C22×C4C23×D4311yescharacteristic
1021C22×C4C23×D4311yescharacteristic
1022SD16—28no—
1023SD16—868no—
1024SD16—868no—
1025SD16—868no—
1026D8—28no—
1027D8—868no—
1028D8—868no—
1029D8—868no—
1030M16—24no—
1031M16—868no—
1032M16—864no—
1033C2×C8—434no—
1034C2×C8—868no—
1035C2×C8C23×D4314yes—
1036C4⋊C4—21no—
1037C4⋊C4—432no—
1038C4⋊C4—861no—
1039C4⋊C4C23×D4312yes—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—864no—
1043C22⋊C4—864no—
1044C22⋊C4—864no—
1045C22⋊C4—862no—
1046C22⋊C4—862no—
1047C42—864no—
1048C23—24no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—41no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—81no—
1058C23—81no—
1059C23—432no—
1060C23—434no—
1061C23—432no—
1062C23—868no—
1063C23—864no—
1064C23—868no—
1065C23—862no—
1066C23—862no—
1067C23—862no—
1068C23—3441no—
1069C23—3441no—
1070C23—3442no—
1071C23—3442no—
1072C23—3442no—
1073C23—3442no—
1074C23—3444no—
1075C23—3444no—
1076C23—34416no—
1077C23—1721no—
1078C23—1721no—
1079C23—1721no—
1080C23—1721no—
1081C23—1722no—
1082C23—1722no—
1083C23—1728no—
1084C23—1722no—
1085C23C2×D4×D4311yescharacteristic
1086C23C2×D4×D4311yescharacteristic
1087C23C2×D4×D4311yescharacteristic
1088Q8—24no—
1089Q8—22no—
1090Q8—434no—
1091Q8—864no—
1092Q8—868no—
1093Q8—864no—
1094Q8—864no—
1095Q8—868no—
1096Q8—862no—
1097Q8C2×D4×D4314yes—
1098D4—28no—
1099D4—24no—
1100D4—28no—
1101D4—22no—
1102D4—24no—
1103D4—42no—
1104D4—82no—
1105D4—82no—
1106D4—434no—
1107D4—864no—
1108D4—864no—
1109D4—868no—
1110D4—864no—
1111D4—868no—
1112D4—864no—
1113D4—864no—
1114D4—868no—
1115D4—864no—
1116D4—864no—
1117D4—868no—
1118D4—868no—
1119D4—868no—
1120D4—868no—
1121D4—868no—
1122D4—862no—
1123D4—864no—
1124D4—3444no—
1125D4—3442no—
1126D4—3442no—
1127D4—3444no—
1128D4—1728no—
1129D4—1722no—
1130D4C2×D4×D4314yes—
1131C2×C4—24no—
1132C2×C4—28no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—28no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—42no—
1142C2×C4—434no—
1143C2×C4—432no—
1144C2×C4—438no—
1145C2×C4—434no—
1146C2×C4—434no—
1147C2×C4—432no—
1148C2×C4—868no—
1149C2×C4—868no—
1150C2×C4—868no—
1151C2×C4—868no—
1152C2×C4—868no—
1153C2×C4—868no—
1154C2×C4—868no—
1155C2×C4—864no—
1156C2×C4—862no—
1157C2×C4—862no—
1158C2×C4—864no—
1159C2×C4—868no—
1160C2×C4—862no—
1161C2×C4—862no—
1162C2×C4—862no—
1163C2×C4—1722no—
1164C2×C4C2×D4×D4311yescharacteristic
1165C2×C4C2×D4×D4311yescharacteristic
1166C2×C4C2×D4×D4311yescharacteristic
1167C2×C4C2×D4×D4314yes—
1168C2×C4C24×D4311yescharacteristic
1169C8—24no—
1170C8—864no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—21no—
1175C22—24no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—21no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—82no—
1186C22—84no—
1187C22—84no—
1188C22—434no—
1189C22—862no—
1190C22—862no—
1191C22—864no—
1192C22—862no—
1193C22—862no—
1194C22—862no—
1195C22—3444no—
1196C22—3442no—
1197C22—3448no—
1198C22—3444no—
1199C22—3448no—
1200C22—34416no—
1201C22—1724no—
1202C22—1722no—
1203C22—1722no—
1204C22—1722no—
1205C22—1722no—
1206C22—1722no—
1207C22#120×D4312yes—
1208C22C22×D4×D4311yescharacteristic
1209C4—21no—
1210C4—24no—
1211C4—21no—
1212C4—42no—
1213C4—434no—
1214C4—862no—
1215C4—864no—
1216C4—1722no—
1217C4#120×D4312yes—
1218C4C22×D4×D4312yes—
1219C2—22no—
1220C2—41no—
1221C2—41no—
1222C2—44no—
1223C2—82no—
1224C2—864no—
1225C2—3442no—
1226C2—1722no—
1227C2—1724no—
1228C2C2×#120×D4311yescharacteristic
1229C2#1914937111yescharacteristic
1230C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3006C2
socleC22×C43C23×D4
hypercenter#3006D43
hypocenterC43#60369
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. C2×#14583735C2semidirect
2. C2×AGL(1,ℤ/8)×D43C2semidirect
3. C2×#14583465C2semidirect
4. #19143878C2semidirect
5. #19143876C2semidirect
6. #19143860C2semidirect
7. #19143858C2semidirect
8. #19143849C2semidirect
9. #19143848C2semidirect
10. #19143847C2semidirect
11. #19143845C2semidirect
12. #19143843C2semidirect
13. #19143111C2semidirect
14. #19143038C2semidirect
15. C43×#3006C2semidirect
17. C2×#13063373C22semidirect
19. C2×#13063372C22semidirect
21. C2×#13063371C22semidirect
24. C2×#13063370C22semidirect
27. C22×#10621898C22semidirect
30. C2×#41×D43C22semidirect
31. C22×D4×D43C22semidirect
32. C2×#13063353C22semidirect
33. C2×#13063352C22semidirect
34. C2×#13063351C22semidirect
35. C2×#13063350C22semidirect
36. C2×#13063349C22semidirect
38. C2×SD16×D43C22semidirect
39. C2×D8×D43C22semidirect
40. C2×M16×D43C22semidirect
43. #14583465C22semidirect
44. #14583465C22semidirect
47. C2×#13063300C22semidirect
48. C2×#13063299C22semidirect
49. C2×#13063296C22semidirect
52. C2×#13063283C22semidirect
53. #14583047C22semidirect
54. #14583046C22semidirect
55. #14583045C22semidirect
56. #14583044C22semidirect
57. #14583043C22semidirect
58. #14583042C22semidirect
59. #14583041C22semidirect
60. #14583040C22semidirect
61. #14583039C22semidirect
62. #14583038C22semidirect
63. #14583037C22semidirect
64. #14583036C22semidirect
65. #14583035C22semidirect
66. #14583034C22semidirect
67. #14583033C22semidirect
68. #14583032C22semidirect
69. #14583031C22semidirect
70. #14582906C22semidirect
71. #14582902C22semidirect
72. #14582901C22semidirect
73. #14582900C22semidirect
74. #14582898C22semidirect
75. #14582894C22semidirect
76. #14582892C22semidirect
77. #14582864C22semidirect
78. #14582864C22semidirect
79. #14582863C22semidirect
80. #14582862C22semidirect
81. C22×#41×C43C22semidirect
82. C2×AGL(1,ℤ/8)×C43C22semidirect
83. C2×#121×C43C22semidirect
84. C43×#449C22semidirect
85. C43×#448C22semidirect
86. C43×#447C22semidirect
87. C43×#417C22semidirect
88. C43×#407C22semidirect
104. C2×#10621902C23semidirect
121. C2×#10621898C23semidirect
128. C2×#10621900C23semidirect
133. #41×D43D4semidirect
136. C22×Dic86C23semidirect
139. C2×Q8×D43C23semidirect
144. C22×D172C23semidirect
162. C2×D4×D43C23semidirect
209. #13063250C23semidirect
210. #13063249C23semidirect
211. #13063248C23semidirect
212. #13063247C23semidirect
213. #13063246C23semidirect
214. #13063245C23semidirect
215. C22⋊(C43⋊C8)C23semidirect
216. C22⋊(C43⋊C8)C23semidirect
217. (C2×D43)⋊C8C23semidirect
218. (C2×D43)⋊C8C23semidirect
223. C2×#41×C43C23semidirect
224. C22×Q8×C43C23semidirect
228. C22×D4×C43C23semidirect
241. #103×C43C23semidirect
242. #102×C43C23semidirect
243. C22⋊C8×C43C23semidirect
244. C22⋊C8×C43C23semidirect
323. #10621902C2×D4semidirect
328. Q8×D43C2×D4semidirect
337. #10621900C2×D4semidirect
349. D4×D43C2×D4semidirect
616. #3006D43semidirect
646. C22×#41C2×D43semidirect
654. C2×AGL(1,ℤ/8)C2×D43semidirect
667. C2×#121C2×D43semidirect
678. #449C2×D43semidirect
684. #448C2×D43semidirect
690. #447C2×D43semidirect
696. #417C2×D43semidirect
703. #407C2×D43semidirect
704. C43#60369semidirect
754. C2×#41C22×D43semidirect
761. C22×Q8C22×D43semidirect
788. C22×D4C22×D43semidirect
850. #103C22×D43semidirect
854. #102C22×D43semidirect
859. C22⋊C8C22×D43semidirect
860. C22⋊C8C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837352
C2×AGL(1,ℤ/8)×D432
C2×#145834652
#191438782
#191438762
#191438602
#191438582
#191438492
#191438482
#191438472
#191438452
#191438432
#191431112
#191430382
C43×#30062
#6036943