Finite Group Databasebeta

← #30553010

Subgroups — #30553010

Order 15616.

2168 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459112C211yesmaximal, characteristic, complemented
2C2×#16840310C211yesmaximal, characteristic, complemented
3#21457204C212yesmaximal, complemented
4#21457198C212yesmaximal, complemented
5#21457179C212yesmaximal, complemented
6#21457177C212yesmaximal, complemented
7#21457143C212yesmaximal, complemented
8#21457141C212yesmaximal, complemented
9#21457133C212yesmaximal, complemented
10#21457127C212yesmaximal, complemented
11#21455635C211yesmaximal, characteristic, complemented
12#21455634C211yesmaximal, characteristic, complemented
13#21455613C212yesmaximal, complemented
14#21455436C212yesmaximal, complemented
15#21455432C212yesmaximal, complemented
16#21455295C211yesmaximal, characteristic, complemented
17#21455280C212yesmaximal, complemented
18#423×D61C211yesmaximal, characteristic, complemented
19C61×#3038C211yesmaximal, characteristic, complemented
20C22×#11758224—21no—
21C2×#14519803C2212yes—
22C2×M16×D61C2212yes—
23#16840316C2211yescharacteristic, complemented
24#16840316C2211yescharacteristic, complemented
25#16840315C2211yescharacteristic
26#16840310—21no—
27#16840310—21no—
28#16840310—21no—
29#16840310—21no—
30#16840310C2212yes—
31#16840310C2212yes—
32#16840310C2212yes—
33#16840310C2212yes—
34#16840309C2211yescharacteristic, complemented
35#16840309C2211yescharacteristic, complemented
36#16840308C2211yescharacteristic
37C2×#14519777C2211yescharacteristic
38#16840299C2211yescharacteristic, complemented
39#16840299C2211yescharacteristic, complemented
40#16840294C2211yescharacteristic, complemented
41#16840294C2211yescharacteristic, complemented
42#16840292—21no—
43#16840292—21no—
44#16840290—21no—
45#16840290—21no—
46C2×#14519764—21no—
47#16840274C2211yescharacteristic
48#16840271—21no—
49#16840271—21no—
50#16840269C2211yescharacteristic
51C2×#14519748—21no—
52C2×#14519748C2212yes—
53C4×#11758222—21no—
54C4×#11758222—21no—
55C4×#11758222C2211yescharacteristic
56C2×D4×Dic61—21no—
57C2×D4×Dic61C2212yes—
58C2×C42×D61C2211yescharacteristic
59#16840064C2214yescomplemented
60#16840060C2214yescomplemented
61#16840058C2212yescomplemented
62#16840057C2212yescomplemented
63#16840053C2212yescomplemented
64#16840052C2212yescomplemented
65#16840050C2214yescomplemented
66#16840048C2212yescomplemented
67#16840047C2212yescomplemented
68#16840043C2212yescomplemented
69#16840042C2212yescomplemented
70#16840040C2214yescomplemented
71#16840014C2214yescomplemented
72#16840012C2214yescomplemented
73#16840007C2214yescomplemented
74#16840005C2214yescomplemented
75#16839997C2214yescomplemented
76#16839995C2214yescomplemented
77#16839990C2214yescomplemented
78#16839988C2214yescomplemented
79#16839979C2214yescomplemented
80#16839975C2214yescomplemented
81#16839965C2214yescomplemented
82#16839959C2212yescomplemented
83#16839959C2212yescomplemented
84#16839955C2214yescomplemented
85#16839954C2212yescomplemented
86#16839954C2212yescomplemented
87#16839805C2212yes—
88#16839804C2212yes—
89#16839786C2211yescharacteristic
90#16839785C2212yes—
91#16839784C2212yescomplemented
92#16839784C2212yescomplemented
93C4⋊C8×D61C2212yescomplemented
94C4⋊C8×D61C2212yescomplemented
95#16839767C2212yes—
96#16839764C2212yes—
97#16839763C2212yes—
98C2×AGL(1,ℤ/8)×C61C2212yes—
99C2×#127×C61C2211yescharacteristic
100C4×#41×C61C2211yescharacteristic
101C61×#460C2212yescomplemented
102C61×#460C2212yescomplemented
103C61×#459C2212yescomplemented
104C61×#459C2212yescomplemented
105C61×#423C2211yescharacteristic
106C61×#418C2212yes—
107C2×#11758222—21no—
108C2×#11758222—21no—
109C2×#11758222C2311yescharacteristic
110C2×#11758224—22no—
111C2×#11758224—22no—
112C2×#11758224—22no—
113C2×#11758224—22no—
114C2×#11758224—48no—
115C22×Dic122—21no—
116C22×C22⋊D61—22no—
117C23×Dic61—22no—
118C22×C4×D61D411yescharacteristic
119C22×C4×D61D411yescharacteristic
120C22×C4×D61C2311yescharacteristic
121#14519803—44no—
122C2×#11758200C2314yes—
123C2×#11758199C2314yes—
124C2×#11758194C2312yes—
125C2×#11758189C2314yes—
126M16×D61—44no—
127C2×C8×D61C2314yes—
128#14519777—21no—
129#14519777—21no—
130#14519777C2312yes—
131#14519777C2312yes—
132#14519776C2311yescharacteristic
133#14519776C2311yescharacteristic
134#14519775C2311yescharacteristic
135#14519773C2311yescharacteristic
136#14519772—21no—
137#14519772—21no—
138#14519770—21no—
139#14519770—21no—
140#14519768C2311yescharacteristic
141#14519768C2311yescharacteristic
142#14519767—21no—
143#14519767—21no—
144#14519766C2311yescharacteristic
145#14519764—22no—
146#14519764—22no—
147#14519764—22no—
148#14519764—22no—
149#14519764C2311yescharacteristic
150#14519763—21no—
151#14519763—21no—
152#14519762—21no—
153#14519762—21no—
154#14519761—21no—
155#14519759—21no—
156#14519759—21no—
157#14519758—21no—
158#14519757C2311yescharacteristic
159#14519757C2311yescharacteristic
160#14519755—21no—
161#14519755—21no—
162#14519754—21no—
163#14519754—21no—
164#14519753C2311yescharacteristic
165#14519753C2311yescharacteristic
166#14519752C2311yescharacteristic
167#14519752C2311yescharacteristic
168#14519750—21no—
169#14519750—21no—
170#14519749—21no—
171#14519749—21no—
172#14519748—22no—
173#14519748—22no—
174#14519748—22no—
175#14519748—22no—
176#14519748—22no—
177#14519748—22no—
178#14519748C2314yes—
179#14519748C2311yescharacteristic
180#14519748C2314yes—
181#14519748C2311yescharacteristic
182#14519747—21no—
183#14519745—21no—
184C4×Dic122—21no—
185C4×Dic122—21no—
186C4×Dic122—21no—
187C4×Dic122—21no—
188C4×Dic122C2311yescharacteristic
189C4×Dic122C2311yescharacteristic
190C4×D244—21no—
191C4×D244—21no—
192C4×D244—21no—
193C4×D244—21no—
194C4×D244C2311yescharacteristic
195C4×D244C2311yescharacteristic
196D4×Dic61—22no—
197D4×Dic61—22no—
198D4×Dic61—22no—
199D4×Dic61—22no—
200D4×Dic61—22no—
201D4×Dic61—22no—
202D4×Dic61C2314yes—
203D4×Dic61C2314yes—
204C4×C22⋊D61—21no—
205C4×C22⋊D61—21no—
206C4×C22⋊D61—21no—
207C4×C22⋊D61—21no—
208C4×C22⋊D61—21no—
209C4×C22⋊D61—21no—
210C4×C22⋊D61—21no—
211C4×C22⋊D61—21no—
212C4×C22⋊D61—21no—
213C4×C22⋊D61—21no—
214#14519736—21no—
215#14519736—21no—
216#14519736C2311yescharacteristic
217#14519734—21no—
218#14519734—21no—
219#14519734—21no—
220#14519734—21no—
221#14519734—21no—
222C2×C4⋊Dic61—21no—
223C2×C4⋊Dic61C2312yes—
224C2×C22⋊Dic61—22no—
225C2×C22⋊Dic61—22no—
226C2×C4×Dic61D411yescharacteristic
227C2×C4×Dic61D411yescharacteristic
228C2×C4×Dic61C2311yescharacteristic
229C42×D61—21no—
230C42×D61D411yescharacteristic
231C42×D61D411yescharacteristic
232C42×D61D411yescharacteristic
233C42×D61D411yescharacteristic
234C42×D61C2311yescharacteristic
235C42×D61C2311yescharacteristic
236C42×D61C2311yescharacteristic
237C42×D61C2311yescharacteristic
238#14519711C2314yes—
239#14519710C2314yes—
240#14519709C2314yes—
241#14519708C2314yes—
242C4⋊#92418C2312yes—
243C4⋊#92418C2312yes—
244#14519706C2314yes—
245#14519706C2314yes—
246#14519702C2314yes—
247#14519701C2314yes—
248#14519699C2314yes—
249#14519698C2314yes—
250#14519698C2314yes—
251#14519698C2314yes—
252C2×#41×C61C2311yescharacteristic
253C22×D4×C61—21no—
254C22×D4×C61—21no—
255C22×D4×C61C2312yes—
256AGL(1,ℤ/8)×C61—44no—
257C2×SD16×C61C2314yes—
258C2×D8×C61C2314yes—
259C2×M16×C61C2312yes—
260#127×C61—21no—
261#127×C61—21no—
262#127×C61C2312yes—
263#127×C61C2312yes—
264C4×Q8×C61C2311yescharacteristic
265C4×Q8×C61C2311yescharacteristic
266C4×D4×C61—21no—
267C4×D4×C61—21no—
268C4×D4×C61C2311yescharacteristic
269C4×D4×C61C2311yescharacteristic
270#117×C61—21no—
271#117×C61C2311yescharacteristic
272C2×C42×C61—21no—
273C2×C42×C61C2311yescharacteristic
274C4⋊C8×C61C2312yes—
275C4⋊C8×C61C2312yes—
276#102×C61C2314yes—
277#102×C61C2314yes—
278C24×C61—22no—
279C23×D61C2×D411yescharacteristic
280#41×C61—22no—
281#41×C61—22no—
282C2×Q8×C61C2411yescharacteristic
283C2×D4×C61—21no—
284C2×D4×C61—22no—
285C2×D4×C61—22no—
286C2×D4×C61—22no—
287C2×D4×C61—22no—
288C2×D4×C61—22no—
289C2×D4×C61—24no—
290C2×D4×C61—24no—
291C2×D4×C61—44no—
292C2×D4×C61—44no—
293C2×D4×C61C2414yes—
294C2×D4×C61C2411yescharacteristic
295C22×C4×C61—21no—
296C22×C4×C61—21no—
297C22×C4×C61—21no—
298C22×C4×C61C2×D411yescharacteristic
299C22×C4×C61C2×D411yescharacteristic
300C22×C4×C61C2411yescharacteristic
301C2×C22⋊D61—21no—
302C2×C22⋊D61—24no—
303C2×C22⋊D61—24no—
304C2×C22⋊D61—21no—
305C2×C22⋊D61—21no—
306C2×C22⋊D61—21no—
307C2×C22⋊D61—21no—
308C2×C22⋊D61—48no—
309C22×Dic61—22no—
310C22×Dic61—24no—
311C22×Dic61—24no—
312C22×Dic61—48no—
313C22×Dic61C2×D411yescharacteristic
314C22×Dic61C2×D411yescharacteristic
315C22×Dic61C2×D411yescharacteristic
316#11758224—48no—
317#11758224—48no—
318#11758224—48no—
319#11758224—48no—
320#11758222—22no—
321#11758222—22no—
322#11758222—44no—
323#11758222—44no—
324C2×D244—21no—
325C2×D244—21no—
326C2×D244C2411yescharacteristic
327C2×C4×D61—22no—
328C2×C4×D61—22no—
329C2×C4×D61—24no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—42no—
334C2×C4×D61C2×D411yescharacteristic
335C2×C4×D61C2×D411yescharacteristic
336C2×C4×D61C2×D411yescharacteristic
337C2×C4×D61C2×D411yescharacteristic
338C2×C4×D61C2×D411yescharacteristic
339C2×C4×D61C2×D411yescharacteristic
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×C4×D61C2×D411yescharacteristic
344C2×C4×D61C2411yescharacteristic
345C2×C4×D61C2411yescharacteristic
346C2×Dic122—22no—
347C2×Dic122—22no—
348C2×Dic122—21no—
349C2×Dic122—21no—
350C2×Dic122—44no—
351C2×Dic122C2411yescharacteristic
352SD16×C61—44no—
353D8×C61—44no—
354M16×C61—24no—
355C2×C8×C61C2414yes—
356C4⋊C4×C61—21no—
357C4⋊C4×C61—21no—
358C4⋊C4×C61C2411yescharacteristic
359C4⋊C4×C61C2411yescharacteristic
360C22⋊C4×C61—21no—
361C22⋊C4×C61—21no—
362C22⋊C4×C61—21no—
363C42×C61—21no—
364C42×C61—21no—
365C42×C61—21no—
366C42×C61C2×D411yescharacteristic
367C42×C61C2×D411yescharacteristic
368C42×C61C2411yescharacteristic
369C42×C61C2411yescharacteristic
370C22⋊Dic61—21no—
371C22⋊Dic61—24no—
372C22⋊Dic61—24no—
373C22⋊Dic61—24no—
374C22⋊Dic61—24no—
375C22⋊Dic61—21no—
376C22⋊Dic61—21no—
377C22⋊Dic61—21no—
378C22⋊Dic61—21no—
379#11758200—44no—
380#11758199—44no—
381#11758198—21no—
382#11758198—21no—
383#11758198—21no—
384#11758198—21no—
385#11758198—21no—
386#11758198—21no—
387#11758198—21no—
388#11758198—21no—
389#11758198—21no—
390#11758198—21no—
391C4⋊Dic61—22no—
392C4⋊Dic61—22no—
393C4⋊Dic61—22no—
394C4⋊Dic61—21no—
395C4⋊Dic61—21no—
396C4⋊Dic61—21no—
397C4⋊Dic61—21no—
398C4⋊Dic61C2411yescharacteristic
399C4⋊Dic61C2411yescharacteristic
400C4⋊Dic61C2414yes—
401#11758196—21no—
402#11758196—21no—
403#11758196—21no—
404#11758196—21no—
405#11758196—21no—
406#11758196—21no—
407#11758196—21no—
408#11758196—21no—
409#11758196—21no—
410#11758196—21no—
411C4×Dic61—21no—
412C4×Dic61—21no—
413C4×Dic61—21no—
414C4×Dic61C2×D411yescharacteristic
415C4×Dic61C2×D411yescharacteristic
416C4×Dic61C2×D411yescharacteristic
417C4×Dic61C2×D411yescharacteristic
418C4×Dic61C2×D411yescharacteristic
419C4×Dic61C2×D411yescharacteristic
420C4×Dic61C2×D411yescharacteristic
421C4×Dic61C2×D411yescharacteristic
422C4×Dic61C2×D411yescharacteristic
423C4×Dic61C2×D411yescharacteristic
424C4×Dic61C2411yescharacteristic
425C4×Dic61C2411yescharacteristic
426#11758194—24no—
427C2×#92418C2414yes—
428#11758189—44no—
429C8×D61—44no—
430C23×C61—21no—
431C23×C61—24no—
432C23×C61—44no—
433C23×C61—44no—
434C23×C61—44no—
435C23×C61C22×D411yescharacteristic
436C22×D61—22no—
437C22×D61—22no—
438C22×D61—21no—
439C22×D61—41no—
440C22×D61C22×D411yescharacteristic
441C22×D61C22×D411yescharacteristic
442Q8×C61—21no—
443Q8×C61—21no—
444D4×C61—24no—
445D4×C61—21no—
446D4×C61—24no—
447D4×C61—21no—
448D4×C61—44no—
449D4×C61—44no—
450D4×C61—42no—
451D4×C61—44no—
452D4×C61—44no—
453D4×C61—44no—
454C2×C4×C61—22no—
455C2×C4×C61—22no—
456C2×C4×C61—21no—
457C2×C4×C61—21no—
458C2×C4×C61—21no—
459C2×C4×C61—42no—
460C2×C4×C61—42no—
461C2×C4×C61—42no—
462C2×C4×C61C22×D411yescharacteristic
463C2×C4×C61C22×D411yescharacteristic
464C2×C4×C61C22×D411yescharacteristic
465C2×C4×C61C22×D411yescharacteristic
466C2×C4×C61C22×D411yescharacteristic
467C2×C4×C61H(5,𝔽2)12yes—
468C2×C4×C612−1+412yes—
469C2×C4×C61C2511yescharacteristic
470C22⋊D61—42no—
471C22⋊D61—42no—
472C22⋊D61—48no—
473C22⋊D61—42no—
474C22⋊D61—42no—
475C22⋊D61—48no—
476C22⋊D61—42no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—21no—
480C2×Dic61—21no—
481C2×Dic61—21no—
482C2×Dic61—24no—
483C2×Dic61—41no—
484C2×Dic61—48no—
485C2×Dic61—44no—
486C2×Dic61—48no—
487C2×Dic61C22×D411yescharacteristic
488C2×Dic61C22×D411yescharacteristic
489C2×Dic61C22×D411yescharacteristic
490C2×Dic61C22×D411yescharacteristic
491C2×Dic61C22×D411yescharacteristic
492C2×Dic61C22×D411yescharacteristic
493D244—21no—
494D244—21no—
495D244—42no—
496D244—42no—
497C4×D61—22no—
498C4×D61—22no—
499C4×D61—22no—
500C4×D61—22no—
501C4×D61—22no—
502C4×D61—22no—
503C4×D61—21no—
504C4×D61—21no—
505C4×D61—21no—
506C4×D61—21no—
507C4×D61—22no—
508C4×D61—41no—
509C4×D61—41no—
510C4×D61—42no—
511C4×D61—42no—
512C4×D61—42no—
513C4×D61AGL(1,ℤ/8)14yescomplemented
514Dic122—21no—
515Dic122—21no—
516Dic122—42no—
517Dic122—44no—
518Dic122—44no—
519Dic122—42no—
520C8×C61—24no—
521#92418—24no—
522#60916—611nomaximal, Sylow
523C22×C61—21no—
524C22×C61—21no—
525C22×C61—41no—
526C22×C61—44no—
527C22×C61—44no—
528C22×C61—41no—
529C22×C61—41no—
530C22×C61—44no—
531C22×C61—88no—
532C22×C61#53712yes—
533C22×C61C23×D411yescharacteristic
534C2×D61—21no—
535C2×D61—21no—
536C2×D61—21no—
537C2×D61—21no—
538C2×D61—21no—
539C2×D61—44no—
540C2×D61—41no—
541C2×D61—41no—
542C2×D61—41no—
543C2×D61C2×AGL(1,ℤ/8)12yes—
544C4×C61—21no—
545C4×C61—21no—
546C4×C61—41no—
547C4×C61—41no—
548C4×C61—41no—
549C4×C61#53712yes—
550C4×C61C2×AGL(1,ℤ/8)12yes—
551C4×C61#57512yes—
552C4×C61C2×H(5,𝔽2)11yescharacteristic
553C4×C61C2×2−1+411yescharacteristic
554Dic61—21no—
555Dic61—21no—
556Dic61—21no—
557Dic61—21no—
558Dic61—21no—
559Dic61—41no—
560Dic61—44no—
561Dic61—41no—
562Dic61—41no—
563Dic61C2×AGL(1,ℤ/8)12yes—
564#3444—611no—
565C2×#532—611no—
566#3254—612no—
567#3253—612no—
568#3251—612no—
569#3251—612no—
570#3247—612no—
571#3247—612no—
572#3246—612no—
573#3245—612no—
574#3079—611no—
575#3079—611no—
576#3077—612no—
577#3055—612no—
578#3055—612no—
579#3038—611no—
580#3038D6111yescharacteristic, complemented
581#3036—612no—
582C2×#423—611no—
583C2×C61—22no—
584C2×C61—81no—
585C2×C61—84no—
586C2×C61C2×#53711yescharacteristic
587C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
588C2×C61C2×#57511yescharacteristic
589D61—22no—
590D61—41no—
591D61—81no—
592C22×#41—1221no—
593C2×AGL(1,ℤ/8)—612no—
594C2×AGL(1,ℤ/8)C2×D6112yes—
595C22×M16—612no—
596#533—611no—
597#533—611no—
598#533—611no—
599#532—612no—
600#532—612no—
601#532—612no—
602#532—612no—
603#532—611no—
604#532—611no—
605#532—611no—
606#532—1221no—
607#532—1221no—
608#532—1221no—
609#532—1221no—
610C2×C4⋊Q8—611no—
611C2×#127C2×D6111yescharacteristic
612#529—611no—
613#529—611no—
614#529—611no—
615#529—611no—
616#529—1221no—
617#529—1221no—
618#529—1221no—
619#529—1221no—
620C2×#124—1221no—
621#525—611no—
622#525—611no—
623#525—1221no—
624#525—1221no—
625C2×#121—612no—
626C2×#121—1221no—
627C4×#41—611no—
628C4×#41—1221no—
629C4×#41—1221no—
630C4×#41C2×D6111yescharacteristic
631C2×C4×D4—612no—
632C2×C4×D4—1221no—
633C22×C42—611no—
634#478—614no—
635#478—614no—
636#477—612no—
637#477—612no—
638#476—612no—
639#476—612no—
640#476—614no—
641#475—612no—
642#475—612no—
643#474—612no—
644#474—612no—
645#474—614no—
646#469—614no—
647#469—614no—
648#468—614no—
649#468—614no—
650#466—614no—
651#466—614no—
652#465—614no—
653#465—614no—
654#463—614no—
655#463—614no—
656#461—614no—
657#460—612no—
658#460—612no—
659#460C2×D6112yescomplemented
660#460C2×D6112yescomplemented
661#459—614no—
662#459—612no—
663#459—612no—
664#459C2×D6112yescomplemented
665#459C2×D6112yescomplemented
666#428—612no—
667#428—612no—
668#423—612no—
669#423—611no—
670#423—612no—
671#423—612no—
672#423C2×D6111yescharacteristic
673C2×C4⋊C8—612no—
674C2×C4⋊C8—612no—
675#418—612no—
676#418C2×D6112yes—
677#417—612no—
678#417—612no—
679C61#6091611yescharacteristic, complemented, Sylow
680C2×#41—611no—
681C2×#41—1221no—
682C2×#41—1221no—
683C2×#41—1222no—
684C2×#41—1222no—
685C2×#41—1222no—
686C2×#41—1222no—
687C2×#41—2448no—
688C2×#41C22×D6111yescharacteristic
689C22×Q8—1221no—
690C22×D4—21no—
691C22×D4—21no—
692C22×D4—1222no—
693C22×D4C22×D6112yes—
694C23×C4—611no—
695C23×C4—611no—
696C23×C4—611no—
697C23×C4—1222no—
698AGL(1,ℤ/8)—44no—
699AGL(1,ℤ/8)—2444no—
700C2×SD16—614no—
701C2×SD16C22×D6114yes—
702C2×D8—614no—
703C2×D8C22×D6114yes—
704C2×M16—612no—
705C2×M16—614no—
706C2×M16—2444no—
707C2×M16C22×D6112yes—
708C22×C8—614no—
709C4⋊Q8—611no—
710C4⋊Q8—611no—
711C4⋊Q8—611no—
712C4⋊Q8—612no—
713C4⋊Q8—612no—
714C4⋊Q8—1221no—
715C4⋊Q8—1221no—
716#127—21no—
717#127—21no—
718#127—611no—
719#127C22×D6112yes—
720#127C22×D6112yes—
721#126—1221no—
722#126—1221no—
723#126—1221no—
724#126—1221no—
725#125—611no—
726#125—611no—
727#125—1221no—
728#125—1221no—
729#124—611no—
730#124—611no—
731#124—1221no—
732#124—1221no—
733#124—1222no—
734#124—1222no—
735#124—1222no—
736#124—1222no—
737#123—1221no—
738#123—1221no—
739#123—1221no—
740#123—1221no—
741#123—1221no—
742#123—1221no—
743C22⋊Q8—611no—
744C22⋊Q8—611no—
745C22⋊Q8—611no—
746C22⋊Q8—611no—
747C22⋊Q8—1221no—
748C22⋊Q8—1221no—
749C22⋊Q8—1221no—
750C22⋊Q8—1221no—
751#121—614no—
752#121—614no—
753#121—611no—
754#121—611no—
755#121—611no—
756#121—611no—
757#121—1221no—
758#121—1221no—
759#121—1222no—
760#121—1222no—
761#121—1222no—
762#121—1222no—
763#121—1222no—
764#121—1222no—
765#121—1221no—
766#121—1221no—
767#120—1221no—
768#120—1221no—
769C4×Q8—611no—
770C4×Q8—611no—
771C4×Q8—1221no—
772C4×Q8—1221no—
773C4×Q8—1221no—
774C4×Q8—1221no—
775C4×Q8C22×D6111yescharacteristic
776C4×Q8C22×D6111yescharacteristic
777C4×D4—21no—
778C4×D4—21no—
779C4×D4—614no—
780C4×D4—614no—
781C4×D4—611no—
782C4×D4—611no—
783C4×D4—1221no—
784C4×D4—1221no—
785C4×D4—1221no—
786C4×D4—1221no—
787C4×D4—1221no—
788C4×D4—1221no—
789C4×D4—1221no—
790C4×D4—1221no—
791C4×D4—1222no—
792C4×D4—1222no—
793C4×D4—1222no—
794C4×D4—1222no—
795C4×D4—1222no—
796C4×D4—1222no—
797C4×D4—1221no—
798C4×D4—1221no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4C22×D6111yescharacteristic
804C4×D4C22×D6111yescharacteristic
805#117—21no—
806#117—611no—
807#117—1221no—
808#117—1221no—
809#117—1221no—
810#117—1221no—
811#117—1221no—
812#117—1221no—
813#117—1221no—
814#117C22×D6111yescharacteristic
815C2×C4⋊C4—612no—
816C2×C4⋊C4—1221no—
817C2×C22⋊C4—1222no—
818C2×C22⋊C4—1222no—
819C2×C42—21no—
820C2×C42—611no—
821C2×C42—611no—
822C2×C42—611no—
823C2×C42—611no—
824C2×C42—611no—
825C2×C42—611no—
826C2×C42—611no—
827C2×C42—611no—
828C2×C42—611no—
829C2×C42—611no—
830C2×C42—611no—
831C2×C42—1221no—
832C2×C42C22×D6111yescharacteristic
833#107—614no—
834#107—614no—
835#106—614no—
836#106—614no—
837C4⋊C8—614no—
838C4⋊C8—614no—
839C4⋊C8—612no—
840C4⋊C8—612no—
841C4⋊C8C22×D6112yes—
842C4⋊C8C22×D6112yes—
843#103—614no—
844#103—614no—
845#102—614no—
846#102—614no—
847#102—614no—
848#102—614no—
849#102C22×D6114yes—
850#102C22×D6114yes—
851C24—22no—
852C24—611no—
853#41—22no—
854#41—22no—
855#41—1222no—
856#41—1222no—
857#41—2444no—
858#41—2444no—
859#41—2448no—
860#41—2448no—
861#41—2448no—
862#41—2448no—
863C2×Q8—611no—
864C2×Q8—1221no—
865C2×Q8—1221no—
866C2×Q8—1222no—
867C2×Q8—1222no—
868C2×Q8—2444no—
869C2×Q8C23×D6111yescharacteristic
870C2×D4—21no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—611no—
881C2×D4—1221no—
882C2×D4—1221no—
883C2×D4—1221no—
884C2×D4—1221no—
885C2×D4—1221no—
886C2×D4—1221no—
887C2×D4—1224no—
888C2×D4—1224no—
889C2×D4—1221no—
890C2×D4—2448no—
891C2×D4C23×D6111yescharacteristic
892C2×D4C23×D6114yes—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—611no—
897C22×C4—611no—
898C22×C4—611no—
899C22×C4—611no—
900C22×C4—611no—
901C22×C4—611no—
902C22×C4—611no—
903C22×C4—611no—
904C22×C4—611no—
905C22×C4—611no—
906C22×C4—611no—
907C22×C4—611no—
908C22×C4—611no—
909C22×C4—611no—
910C22×C4—611no—
911C22×C4—1224no—
912C22×C4—1224no—
913C22×C4—1224no—
914C22×C4—1222no—
915C22×C4—1222no—
916C22×C4—1222no—
917C22×C4—1221no—
918C22×C4—1221no—
919C22×C4—1221no—
920C22×C4—2442no—
921C22×C4—2448no—
922C22×C4D4×D6111yescharacteristic
923C22×C4D4×D6111yescharacteristic
924C22×C4C23×D6111yescharacteristic
925SD16—44no—
926SD16—2444no—
927D8—44no—
928D8—2444no—
929M16—24no—
930M16—1224no—
931M16—2444no—
932C2×C8—614no—
933C2×C8—2444no—
934C2×C8C23×D6114yes—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—611no—
938C4⋊C4—611no—
939C4⋊C4—614no—
940C4⋊C4—1221no—
941C4⋊C4—1221no—
942C4⋊C4—1221no—
943C4⋊C4—1221no—
944C4⋊C4—1221no—
945C4⋊C4—1221no—
946C4⋊C4—1221no—
947C4⋊C4—1221no—
948C4⋊C4—1221no—
949C4⋊C4—1221no—
950C4⋊C4—1221no—
951C4⋊C4—1221no—
952C4⋊C4—1222no—
953C4⋊C4—1222no—
954C4⋊C4—1222no—
955C4⋊C4—1221no—
956C4⋊C4—1221no—
957C4⋊C4C23×D6111yescharacteristic
958C4⋊C4C23×D6111yescharacteristic
959C22⋊C4—21no—
960C22⋊C4—21no—
961C22⋊C4—21no—
962C22⋊C4—1221no—
963C22⋊C4—1221no—
964C22⋊C4—1221no—
965C22⋊C4—1221no—
966C22⋊C4—1221no—
967C22⋊C4—1221no—
968C22⋊C4—1221no—
969C22⋊C4—1221no—
970C22⋊C4—1224no—
971C22⋊C4—1224no—
972C22⋊C4—1224no—
973C22⋊C4—1224no—
974C22⋊C4—1221no—
975C22⋊C4—1221no—
976C22⋊C4—1221no—
977C22⋊C4—1221no—
978C22⋊C4—1221no—
979C22⋊C4—1221no—
980C22⋊C4—1221no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—611no—
985C42—611no—
986C42—611no—
987C42—611no—
988C42—611no—
989C42—611no—
990C42—611no—
991C42—611no—
992C42—611no—
993C42—611no—
994C42—611no—
995C42—611no—
996C42—1221no—
997C42—1221no—
998C42—1221no—
999C42D4×D6111yescharacteristic
1000C42D4×D6111yescharacteristic
1001C42C23×D6111yescharacteristic
1002C42C23×D6111yescharacteristic
1003C23—21no—
1004C23—24no—
1005C23—44no—
1006C23—44no—
1007C23—44no—
1008C23—611no—
1009C23—611no—
1010C23—1222no—
1011C23—1222no—
1012C23—1221no—
1013C23—2441no—
1014C23C2×D4×D6111yescharacteristic
1015Q8—21no—
1016Q8—21no—
1017Q8—1221no—
1018Q8—1221no—
1019Q8—2444no—
1020Q8—2442no—
1021Q8—2442no—
1022Q8—2444no—
1023D4—21no—
1024D4—24no—
1025D4—24no—
1026D4—21no—
1027D4—44no—
1028D4—44no—
1029D4—42no—
1030D4—44no—
1031D4—44no—
1032D4—44no—
1033D4—1221no—
1034D4—1221no—
1035D4—2442no—
1036D4—2442no—
1037D4—2442no—
1038D4—2442no—
1039D4—2448no—
1040D4—2442no—
1041D4—2448no—
1042D4—2442no—
1043D4—2442no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—611no—
1053C2×C4—614no—
1054C2×C4—611no—
1055C2×C4—611no—
1056C2×C4—611no—
1057C2×C4—611no—
1058C2×C4—611no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1222no—
1065C2×C4—1222no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1221no—
1069C2×C4—1221no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1221no—
1073C2×C4—1221no—
1074C2×C4—1221no—
1075C2×C4—1224no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2448no—
1079C2×C4—2441no—
1080C2×C4—2448no—
1081C2×C4—2444no—
1082C2×C4—2442no—
1083C2×C4—2442no—
1084C2×C4—2442no—
1085C2×C4C2×D4×D6111yescharacteristic
1086C2×C4C2×D4×D6111yescharacteristic
1087C2×C4C2×D4×D6111yescharacteristic
1088C2×C4C2×D4×D6111yescharacteristic
1089C2×C4C2×D4×D6111yescharacteristic
1090C2×C4#1451982212yes—
1091C2×C4#1451982412yes—
1092C2×C4C24×D6111yescharacteristic
1093C8—24no—
1094C8—1224no—
1095C22—21no—
1096C22—21no—
1097C22—41no—
1098C22—44no—
1099C22—41no—
1100C22—44no—
1101C22—41no—
1102C22—44no—
1103C22—88no—
1104C22—612no—
1105C22—1221no—
1106C22—1221no—
1107C22—1221no—
1108C22—1221no—
1109C22—1221no—
1110C22—2444no—
1111C22—2441no—
1112C22—2441no—
1113C22—2441no—
1114C22#1684034112yes—
1115C22C22×D4×D6111yescharacteristic
1116C4—21no—
1117C4—21no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—612no—
1122C4—1221no—
1123C4—1221no—
1124C4—1221no—
1125C4—1221no—
1126C4—1221no—
1127C4—2444no—
1128C4—2441no—
1129C4—2441no—
1130C4—2441no—
1131C4#1684034112yes—
1132C4AGL(1,ℤ/8)×D6112yes—
1133C4#1684055812yes—
1134C4C2×#1451982211yescharacteristic
1135C4C2×#1451982411yescharacteristic
1136C2—22no—
1137C2—84no—
1138C2—81no—
1139C2—1222no—
1140C2—4881no—
1141C2—2441no—
1142C2C2×#1684034111yescharacteristic
1143C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
1144C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3038C2
socleC22×C61C23×D4
hypercenter#3038D61
hypocenterC61#60916
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #21459112C2semidirect
2. C2×#16840310C2semidirect
3. #21457204C2semidirect
4. #21457198C2semidirect
5. #21457179C2semidirect
6. #21457177C2semidirect
7. #21457143C2semidirect
8. #21457141C2semidirect
9. #21457133C2semidirect
10. #21457127C2semidirect
11. #21455635C2semidirect
12. #21455634C2semidirect
13. #21455613C2semidirect
14. #21455436C2semidirect
15. #21455432C2semidirect
16. #21455295C2semidirect
17. #21455280C2semidirect
18. #423×D61C2semidirect
19. C61×#3038C2semidirect
23. #16840316C22semidirect
24. #16840316C22semidirect
34. #16840309C22semidirect
35. #16840309C22semidirect
38. #16840299C22semidirect
39. #16840299C22semidirect
40. #16840294C22semidirect
41. #16840294C22semidirect
59. #16840064C22semidirect
60. #16840060C22semidirect
61. #16840058C22semidirect
62. #16840057C22semidirect
63. #16840053C22semidirect
64. #16840052C22semidirect
65. #16840050C22semidirect
66. #16840048C22semidirect
67. #16840047C22semidirect
68. #16840043C22semidirect
69. #16840042C22semidirect
70. #16840040C22semidirect
71. #16840014C22semidirect
72. #16840012C22semidirect
73. #16840007C22semidirect
74. #16840005C22semidirect
75. #16839997C22semidirect
76. #16839995C22semidirect
77. #16839990C22semidirect
78. #16839988C22semidirect
79. #16839979C22semidirect
80. #16839975C22semidirect
81. #16839965C22semidirect
82. #16839959C22semidirect
83. #16839959C22semidirect
84. #16839955C22semidirect
85. #16839954C22semidirect
86. #16839954C22semidirect
91. #16839784C22semidirect
92. #16839784C22semidirect
93. C4⋊C8×D61C22semidirect
94. C4⋊C8×D61C22semidirect
101. C61×#460C22semidirect
102. C61×#460C22semidirect
103. C61×#459C22semidirect
104. C61×#459C22semidirect
513. C4×D61AGL(1,ℤ/8)semidirect
580. #3038D61semidirect
659. #460C2×D61semidirect
660. #460C2×D61semidirect
664. #459C2×D61semidirect
665. #459C2×D61semidirect
679. C61#60916semidirect

Maximal subgroups

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

subgroupindex
#214591122
C2×#168403102
#214572042
#214571982
#214571792
#214571772
#214571432
#214571412
#214571332
#214571272
#214556352
#214556342
#214556132
#214554362
#214554322
#214552952
#214552802
#423×D612
C61×#30382
#6091661