Finite Group Databasebeta

← #30548763

Subgroups — #30548763

Order 15616.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459561C211yesmaximal, characteristic, complemented
2#518×D61C211yesmaximal, characteristic, complemented
3#21456070C212yesmaximal, complemented
4#21456068C212yesmaximal, complemented
5#21456009C212yesmaximal, complemented
6#21456007C212yesmaximal, complemented
7#21455961C212yesmaximal, complemented
8#21455916C212yesmaximal, complemented
9#21455870C212yesmaximal, complemented
10#21455825C212yesmaximal, complemented
11#21455765C211yesmaximal, characteristic, complemented
12#21455736C211yesmaximal, characteristic, complemented
13#21455653C211yesmaximal, characteristic, complemented
14#21455652C211yesmaximal, characteristic, complemented
15#21455330C211yesmaximal, characteristic, complemented
16#21455328C211yesmaximal, characteristic, complemented
17#21455048C211yesmaximal, characteristic
18C2×#16839911C211yesmaximal, characteristic, complemented
19#21454678C211yesmaximal, characteristic, complemented
20#21454653C211yesmaximal, characteristic, complemented
21#21454651C211yesmaximal, characteristic, complemented
22#21454474C211yesmaximal, characteristic, complemented
23C61×#2949C211yesmaximal, characteristic, complemented
24C22×D4×D61C2211yescharacteristic
25C2×#14519805C2211yescharacteristic
26C2×#14519803C2211yescharacteristic
27C22×#11758201C2211yescharacteristic
28#16840485—21no—
29#16840472—21no—
30#16840453—21no—
31#16840453—21no—
32#16840445—22no—
33#16840436—22no—
34#16840390C2211yescharacteristic, complemented
35#16840384C2212yescomplemented
36#16840370C2212yescomplemented
37#16840336C2211yescharacteristic, complemented
38#16840316C2212yescomplemented
39#16840299C2212yescomplemented
40#16840274C2211yescharacteristic
41C2×#14519753C2211yescharacteristic
42#16840242C2211yescharacteristic, complemented
43#16840237C2211yescharacteristic
44#16840236C2211yescharacteristic
45#16840236C2211yescharacteristic
46#16840235—22no—
47#16840234—21no—
48#16840234—21no—
49#16840234C2212yes—
50#16840234C2212yes—
51C4×D4×D61—21no—
52C4×D4×D61—21no—
53C4×D4×D61C2212yes—
54C4×D4×D61C2212yes—
55#117×D61C2211yescharacteristic
56#117×D61C2211yescharacteristic
57C2×C22⋊C4×D61—22no—
58#16840106C2211yescharacteristic, complemented
59#16840105C2211yescharacteristic, complemented
60#16840102C2212yescomplemented
61#16840101C2212yescomplemented
62#16840099C2211yescharacteristic, complemented
63#16840096C2212yescomplemented
64#16840094C2211yescharacteristic, complemented
65#16840091C2212yescomplemented
66#16840089C2211yescharacteristic, complemented
67#16840088C2211yescharacteristic, complemented
68#16840082C2211yescharacteristic, complemented
69#16840077C2211yescharacteristic, complemented
70#16840065C2212yescomplemented
71#16840064C2212yescomplemented
72#16840061C2212yescomplemented
73#16840060C2212yescomplemented
74#16840051C2212yescomplemented
75#16840050C2212yescomplemented
76#16840041C2212yescomplemented
77#16840040C2212yescomplemented
78#16839980C2212yescomplemented
79#16839980C2212yescomplemented
80#16839979C2212yescomplemented
81#16839979C2212yescomplemented
82#16839966C2212yescomplemented
83#16839966C2212yescomplemented
84#16839965C2212yescomplemented
85#16839965C2212yescomplemented
86#16839914C2212yes—
87#16839914C2212yes—
88#16839911C2212yes—
89#16839911C2212yes—
90#16839911C2212yes—
91#16839911C2212yes—
92#16839897C2212yes—
93#16839897C2212yes—
94#16839875C2212yescomplemented
95#16839872C2212yescomplemented
96#16839864C2212yescomplemented
97#16839862C2212yescomplemented
98#16839860C2212yescomplemented
99#16839860C2212yescomplemented
100C4×#11758190C2212yescomplemented
101C4×#11758201C2212yescomplemented
102C4×#11758201C2212yescomplemented
103C4×#11758200C2212yescomplemented
104C4×D488C2212yescomplemented
105C4×#11758199C2212yescomplemented
106#16839824C2212yescomplemented
107#16839821C2212yescomplemented
108#16839817C2212yescomplemented
109#16839813C2212yescomplemented
110#16839805C2211yescharacteristic, complemented
111#16839804C2211yescharacteristic, complemented
112#16839798C2211yescharacteristic, complemented
113#16839790C2211yescharacteristic, complemented
114#16839788C2211yescharacteristic, complemented
115#16839771C2211yescharacteristic, complemented
116#16839766C2211yescharacteristic
117#16839759C2211yescharacteristic, complemented
118#16839756C2211yescharacteristic, complemented
119C2×#14519699C2211yescharacteristic
120C2×#14519698C2211yescharacteristic
121#16839725C2211yescharacteristic
122C2×#14519689C2211yescharacteristic
123#16839718C2211yescharacteristic, complemented
124C22×SD16×C61C2211yescharacteristic
125C61×#519C2211yescharacteristic, complemented
126C61×#518C2211yescharacteristic
127C61×#440C2212yescomplemented
128C61×#440C2212yescomplemented
129C4×SD16×C61C2212yescomplemented
130C4×SD16×C61C2212yescomplemented
131C61×#427C2211yescharacteristic, complemented
132C61×#419C2211yescharacteristic, complemented
133C61×#418C2211yescharacteristic
134C61×#405C2211yescharacteristic, complemented
135C24×D61—21no—
136C2×#11758222C2311yescharacteristic
137C22×D244C2311yescharacteristic
138C22×C22⋊D61—21no—
139C2×D4×D61—24no—
140C2×D4×D61—24no—
141C2×D4×D61—21no—
142C2×D4×D61—21no—
143C2×D4×D61C2312yes—
144C2×D4×D61C2312yes—
145C22×C4×D61—22no—
146C22×C4×D61—22no—
147C22×C4×D61C2311yescharacteristic
148#14519805—24no—
149#14519803—24no—
150C2×#11758190C2312yes—
151C2×#11758200C2312yes—
152C2×#11758201—24no—
153C2×#11758201C2312yes—
154C2×#11758201C2312yes—
155C2×D488C2312yes—
156C2×#11758199C2312yes—
157C2×#11758194C2311yescharacteristic
158C22×#92418C2311yescharacteristic
159#14519777—21no—
160#14519776C2312yescomplemented
161#14519775C2312yescomplemented
162#14519772—22no—
163#14519772—22no—
164#14519771—22no—
165#14519771—22no—
166#14519769—21no—
167#14519769—22no—
168#14519768C2312yescomplemented
169#14519767—22no—
170#14519767—22no—
171#14519766C2312yescomplemented
172#14519765—22no—
173#14519762—22no—
174#14519762—22no—
175#14519761—21no—
176#14519760—22no—
177#14519757C2311yescharacteristic
178#14519757C2311yescharacteristic
179#14519755—22no—
180#14519755—22no—
181#14519754—22no—
182#14519753—21no—
183#14519753—21no—
184#14519753—21no—
185#14519753—21no—
186#14519753C2312yes—
187#14519753C2312yes—
188#14519752C2311yescharacteristic
189#14519752C2311yescharacteristic
190#14519747—21no—
191C4×Dic122—22no—
192C4×Dic122C2312yescomplemented
193C4×D244—21no—
194C4×D244—21no—
195C4×D244—22no—
196C4×D244—21no—
197C4×D244—21no—
198C4×D244C2312yes—
199C4×D244C2312yes—
200C4×D244C2312yescomplemented
201D4×Dic61—21no—
202D4×Dic61—21no—
203D4×Dic61C2312yes—
204D4×Dic61C2312yes—
205#14519739—21no—
206#14519739—21no—
207#14519739C2312yes—
208#14519739C2312yes—
209C4×C22⋊D61—22no—
210C4×C22⋊D61—22no—
211C4×C22⋊D61—22no—
212C4×C22⋊D61—22no—
213#14519737—22no—
214#14519737—22no—
215#14519737—22no—
216#14519737—22no—
217#14519737—22no—
218#14519736C2311yescharacteristic
219#14519736C2311yescharacteristic
220#14519735—21no—
221#14519735D411yescharacteristic
222#14519735D411yescharacteristic
223#14519735C2311yescharacteristic
224#14519735C2311yescharacteristic
225#14519734—22no—
226#14519734—21no—
227#14519734—22no—
228#14519734C2312yes—
229#14519733—21no—
230#14519733D412yes—
231C2×C4⋊Dic61C2311yescharacteristic
232C2×#11758196—21no—
233C4⋊C4×D61—21no—
234C4⋊C4×D61D411yescharacteristic
235C4⋊C4×D61D411yescharacteristic
236C4⋊C4×D61C2311yescharacteristic
237C4⋊C4×D61C2311yescharacteristic
238C2×C22⋊Dic61—22no—
239C2×#11758198—21no—
240C2×#11758198—22no—
241C2×#11758198—22no—
242C22⋊C4×D61—21no—
243C22⋊C4×D61—22no—
244C22⋊C4×D61—22no—
245C22⋊C4×D61—22no—
246C22⋊C4×D61—22no—
247C22⋊C4×D61—22no—
248C22⋊C4×D61—22no—
249C22⋊C4×D61D412yes—
250C42×D61—21no—
251C42×D61C2312yes—
252#14519711C2312yescomplemented
253#14519710C2311yescharacteristic, complemented
254#14519710C2312yescomplemented
255#14519710C2311yescharacteristic, complemented
256#14519709C2312yescomplemented
257#14519708C2311yescharacteristic, complemented
258#14519708C2312yescomplemented
259#14519708C2311yescharacteristic, complemented
260#14519706C2312yescomplemented
261#14519706C2312yescomplemented
262#14519706C2312yescomplemented
263#14519706C2312yescomplemented
264#14519702C2311yescharacteristic, complemented
265#14519702C2311yescharacteristic, complemented
266#14519701C2312yescomplemented
267#14519701C2312yescomplemented
268#14519700C2311yescharacteristic, complemented
269#14519700C2311yescharacteristic, complemented
270#14519699C2312yes—
271#14519699C2312yes—
272#14519699C2311yescharacteristic, complemented
273#14519699C2311yescharacteristic, complemented
274#14519698C2312yes—
275#14519698C2312yes—
276#14519697C2312yes—
277#14519697C2312yes—
278#14519697C2311yescharacteristic, complemented
279#14519697C2311yescharacteristic, complemented
280#14519689C2311yescharacteristic
281#14519689C2311yescharacteristic
282#14519689C2311yescharacteristic
283#14519689C2311yescharacteristic
284#14519689C2312yes—
285#14519689C2312yes—
286#14519688C2312yescomplemented
287C4×#92418C2312yescomplemented
288C22×Q8×C61C2311yescharacteristic
289C22×D4×C61C2311yescharacteristic
290C2×SD16×C61—24no—
291C2×SD16×C61C2312yes—
292C2×SD16×C61C2312yes—
293C2×M16×C61C2311yescharacteristic
294C22×C8×C61C2311yescharacteristic
295C4×Q8×C61—21no—
296C4×Q8×C61—21no—
297C4×Q8×C61C2312yescomplemented
298C4×Q8×C61C2312yescomplemented
299C4×D4×C61—21no—
300C4×D4×C61—21no—
301C4×D4×C61C2312yes—
302C4×D4×C61C2312yes—
303#117×C61—22no—
304#117×C61C2311yescharacteristic
305#117×C61C2311yescharacteristic
306#117×C61C2311yescharacteristic
307C2×C22⋊C4×C61—22no—
308#107×C61C2311yescharacteristic, complemented
309#107×C61C2311yescharacteristic, complemented
310#106×C61C2311yescharacteristic, complemented
311#106×C61C2311yescharacteristic, complemented
312#103×C61C2312yescomplemented
313#103×C61C2312yescomplemented
314#102×C61C2312yes—
315#102×C61C2312yes—
316#97×C61C2312yescomplemented
317C4×C8×C61C2312yescomplemented
318C24×C61—21no—
319C23×D61—28no—
320C23×D61—21no—
321C23×D61—22no—
322C23×D61—22no—
323C23×D61—82no—
324C23×D61—82no—
325C23×D61C2×D411yescharacteristic
326C2×Q8×C61—21no—
327C2×Q8×C61—22no—
328C2×Q8×C61—22no—
329C2×Q8×C61C2412yes—
330C2×D4×C61—21no—
331C2×D4×C61—22no—
332C2×D4×C61#4114yes—
333C2×D4×C61C2412yes—
334C22×C4×C61—21no—
335C22×C4×C61—22no—
336C22×C4×C61—22no—
337C22×C4×C61C2411yescharacteristic
338C2×C22⋊D61—28no—
339C2×C22⋊D61—21no—
340C2×C22⋊D61—22no—
341C2×C22⋊D61—22no—
342C22×Dic61—21no—
343C22×Dic61—22no—
344C22×Dic61—22no—
345C22×Dic61C2×D411yescharacteristic
346D4×D61—28no—
347D4×D61—28no—
348D4×D61—24no—
349D4×D61—24no—
350D4×D61—24no—
351D4×D61—24no—
352#11758222—22no—
353#11758222—22no—
354C2×D244—21no—
355C2×D244—22no—
356C2×D244—21no—
357C2×D244—21no—
358C2×D244#4114yes—
359C2×D244C2411yescharacteristic
360C2×D244C2412yes—
361C2×C4×D61—22no—
362C2×C4×D61—22no—
363C2×C4×D61—21no—
364C2×C4×D61—21no—
365C2×C4×D61—21no—
366C2×C4×D61—22no—
367C2×C4×D61—22no—
368C2×C4×D61—22no—
369C2×C4×D61—22no—
370C2×C4×D61—22no—
371C2×C4×D61—84no—
372C2×C4×D61—84no—
373C2×C4×D61C2×D412yes—
374C2×C4×D61C2×D411yescharacteristic
375C2×C4×D61C2×D411yescharacteristic
376C2×C4×D61C2×D412yes—
377C2×C4×D61C2411yescharacteristic
378C2×C4×D61C2411yescharacteristic
379C2×Dic122—22no—
380C2×Dic122C2411yescharacteristic
381SD16×C61—24no—
382SD16×C61—24no—
383M16×C61—22no—
384C2×C8×C61—22no—
385C2×C8×C61C2411yescharacteristic
386C2×C8×C61C2412yes—
387C2×C8×C61C2411yescharacteristic
388C4⋊C4×C61—22no—
389C4⋊C4×C61—22no—
390C4⋊C4×C61C2×D411yescharacteristic
391C4⋊C4×C61C2×D411yescharacteristic
392C4⋊C4×C61C2411yescharacteristic
393C4⋊C4×C61C2411yescharacteristic
394C4⋊C4×C61C2411yescharacteristic
395C4⋊C4×C61C2411yescharacteristic
396C22⋊C4×C61—21no—
397C22⋊C4×C61—21no—
398C22⋊C4×C61—22no—
399C22⋊C4×C61—22no—
400C22⋊C4×C61C2×D412yes—
401C42×C61—22no—
402C42×C61—22no—
403C42×C61—21no—
404C42×C61—21no—
405C42×C61C2412yes—
406C22⋊Dic61—21no—
407C22⋊Dic61—22no—
408C22⋊Dic61—22no—
409C22⋊Dic61C2×D412yes—
410#11758201—24no—
411#11758201—24no—
412#11758200—24no—
413#11758199—24no—
414#11758198—21no—
415#11758198—21no—
416#11758198—22no—
417#11758198—22no—
418#11758198—21no—
419#11758198—21no—
420#11758198—22no—
421#11758198—22no—
422#11758198—22no—
423#11758198—22no—
424#11758198—22no—
425#11758198—21no—
426#11758198—22no—
427#11758198—21no—
428#11758198—22no—
429#11758198C2×D412yes—
430#11758198C2×D412yes—
431C4⋊Dic61—21no—
432C4⋊Dic61—21no—
433C4⋊Dic61—22no—
434C4⋊Dic61—21no—
435C4⋊Dic61C2×D411yescharacteristic
436C4⋊Dic61C2×D411yescharacteristic
437C4⋊Dic61C2412yes—
438C4⋊Dic61C2411yescharacteristic
439C4⋊Dic61C2411yescharacteristic
440#11758196—22no—
441#11758196—21no—
442#11758196—21no—
443#11758196—22no—
444#11758196—22no—
445#11758196—22no—
446#11758196—22no—
447#11758196—22no—
448#11758196—22no—
449#11758196C2×D412yes—
450#11758196C2×D412yes—
451C4×Dic61—21no—
452C4×Dic61—22no—
453C4×Dic61—21no—
454C4×Dic61—21no—
455C4×Dic61C2×D412yes—
456C4×Dic61C2×D412yes—
457C4×Dic61C2412yes—
458#11758194—22no—
459C2×#92418—22no—
460C2×#92418C2411yescharacteristic
461C2×#92418C2412yes—
462C2×#92418C2411yescharacteristic
463D488—24no—
464#11758190—24no—
465C23×C61—22no—
466C23×C61—24no—
467C23×C61—81no—
468C23×C61—81no—
469C23×C61C22×D411yescharacteristic
470C22×D61—28no—
471C22×D61—22no—
472C22×D61—22no—
473C22×D61—28no—
474C22×D61—24no—
475C22×D61—22no—
476C22×D61—21no—
477C22×D61—41no—
478C22×D61—44no—
479C22×D61—44no—
480C22×D61—82no—
481C22×D61—82no—
482C22×D61—816no—
483C22×D61—81no—
484C22×D61—81no—
485C22×D61C22×D411yescharacteristic
486C22×D61C22×D411yescharacteristic
487Q8×C61—22no—
488Q8×C61—22no—
489Q8×C61—42no—
490D4×C61—24no—
491D4×C61—22no—
492D4×C61C2×#4114yes—
493C2×C4×C61—21no—
494C2×C4×C61—21no—
495C2×C4×C61—22no—
496C2×C4×C61—21no—
497C2×C4×C61—21no—
498C2×C4×C61—42no—
499C2×C4×C61—82no—
500C2×C4×C61—82no—
501C2×C4×C61C22×D412yes—
502C2×C4×C61C22×D412yes—
503C2×C4×C61C22×D411yescharacteristic
504C2×C4×C61C2×#4112yes—
505C2×C4×C61C2×#4112yes—
506C2×C4×C61C2511yescharacteristic
507C22⋊D61—28no—
508C22⋊D61—28no—
509C22⋊D61—42no—
510C2×Dic61—22no—
511C2×Dic61—21no—
512C2×Dic61—21no—
513C2×Dic61—21no—
514C2×Dic61—22no—
515C2×Dic61—82no—
516C2×Dic61—82no—
517C2×Dic61—81no—
518C2×Dic61C22×D411yescharacteristic
519C2×Dic61C22×D411yescharacteristic
520C2×Dic61C22×D412yes—
521C2×Dic61C22×D412yes—
522D244—24no—
523D244—22no—
524D244—21no—
525D244—21no—
526D244—42no—
527D244—81no—
528D244C2×#4114yes—
529C4×D61—24no—
530C4×D61—22no—
531C4×D61—22no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—21no—
535C4×D61—21no—
536C4×D61—42no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—82no—
541C4×D61—82no—
542C4×D61—82no—
543C4×D61—82no—
544C4×D61—82no—
545Dic122—21no—
546Dic122—21no—
547Dic122—82no—
548C8×C61—22no—
549C8×C61—21no—
550C8×C61—21no—
551#92418—21no—
552#92418—21no—
553#92418—22no—
554#60579—611nomaximal, Sylow
555C22×C61—21no—
556C22×C61—21no—
557C22×C61—24no—
558C22×C61—42no—
559C22×C61—42no—
560C22×C61—84no—
561C22×C61#52512yes—
562C22×C61C23×D411yescharacteristic
563C2×D61—21no—
564C2×D61—21no—
565C2×D61—21no—
566C2×D61—21no—
567C2×D61—24no—
568C2×D61—21no—
569C2×D61—44no—
570C2×D61—416no—
571C2×D61—42no—
572C2×D61—42no—
573C2×D61—41no—
574C2×D61—41no—
575C2×D61—41no—
576C2×D61—84no—
577C2×D61—88no—
578C2×D61#57712yes—
579C4×C61—22no—
580C4×C61—22no—
581C4×C61—41no—
582C4×C61—41no—
583C4×C61—42no—
584C4×C61—41no—
585C4×C61—41no—
586C4×C61#52512yes—
587C4×C61C22×#4111yescharacteristic
588C4×C61C22×#4111yescharacteristic
589Dic61—22no—
590Dic61—21no—
591Dic61—21no—
592Dic61—22no—
593Dic61—42no—
594Dic61—41no—
595Dic61—41no—
596Dic61—41no—
597#3495—611no—
598C2×#518—611no—
599#3123—612no—
600#3123—612no—
601#3118—612no—
602#3118—612no—
603#3114—612no—
604#3110—612no—
605#3105—612no—
606#3101—612no—
607#3095—611no—
608#3091—611no—
609#3081—611no—
610#3081—611no—
611#3042—611no—
612#3042—611no—
613#3003—611no—
614C2×#450—611no—
615#2949—611no—
616#2949D6111yescharacteristic, complemented
617#2946—611no—
618#2946—611no—
619#2924—611no—
620C2×C61—22no—
621C2×C61—44no—
622C2×C61C2×#52511yescharacteristic
623C2×C61C2×#57711yescharacteristic
624C2×C61#358511yescharacteristic
625D61—22no—
626D61—41no—
627D61—44no—
628D61—81no—
629C23×D4—611no—
630C2×AGL(1,ℤ/8)—611no—
631C2×AGL(1,ℤ/8)—611no—
632C22×SD16—611no—
633C22×SD16C2×D6111yescharacteristic
634#556—1221no—
635#554—1221no—
636#552—1221no—
637#552—1222no—
638#552—1221no—
639#551—1222no—
640#544—611no—
641#542—612no—
642#541—612no—
643#536—611no—
644#533—612no—
645#529—612no—
646#525—611no—
647C2×C22⋊Q8—611no—
648#520—611no—
649#519C2×D6111yescharacteristic, complemented
650#518—611no—
651#518—612no—
652#518—612no—
653#518—611no—
654#518—611no—
655#518—1222no—
656#518—1221no—
657#518—1221no—
658#518C2×D6111yescharacteristic
659C2×C4×D4—612no—
660C2×C4×D4—612no—
661C2×C4×D4—1221no—
662C2×C4×D4—1221no—
663C2×#117—611no—
664C2×#117—611no—
665C22×C22⋊C4—1222no—
666#485—611no—
667#485—611no—
668#485—612no—
669#485—612no—
670#484—611no—
671#484—612no—
672#483—611no—
673#483—612no—
674#482—611no—
675#482—611no—
676#481—611no—
677#480—611no—
678#478—612no—
679#478—612no—
680#478—612no—
681#478—612no—
682#476—612no—
683#476—612no—
684#474—612no—
685#474—612no—
686#463—612no—
687#463—612no—
688#463—612no—
689#463—612no—
690#461—612no—
691#461—612no—
692#461—612no—
693#461—612no—
694#450—612no—
695#450—612no—
696#450—612no—
697#450—612no—
698#450—612no—
699#450—612no—
700#447—612no—
701#447—612no—
702#442—612no—
703#442—612no—
704#440—612no—
705#440—612no—
706#440—612no—
707#440—612no—
708#440C2×D6112yescomplemented
709#440C2×D6112yescomplemented
710C4×SD16—612no—
711C4×SD16—612no—
712C4×SD16—612no—
713C4×SD16—612no—
714C4×SD16C2×D6112yescomplemented
715C4×SD16C2×D6112yescomplemented
716C4×D8—612no—
717C4×D8—612no—
718#433—612no—
719#433—612no—
720#432—612no—
721#431—612no—
722#428—611no—
723#428—611no—
724#427—611no—
725#427C2×D6111yescharacteristic, complemented
726#424—611no—
727#424—611no—
728#419—611no—
729#419C2×D6111yescharacteristic, complemented
730#418—611no—
731#418C2×D6111yescharacteristic
732#416—611no—
733#416—611no—
734C2×#102—611no—
735C2×#102—611no—
736#407—611no—
737C2×C22⋊C8—611no—
738#405—611no—
739#405C2×D6111yescharacteristic, complemented
740C61#6057911yescharacteristic, complemented, Sylow
741C25—1221no—
742C2×#41—611no—
743C22×Q8C22×D6111yescharacteristic
744C22×D4—612no—
745C22×D4—612no—
746C22×D4—611no—
747C22×D4—1221no—
748C22×D4—1221no—
749C22×D4—1221no—
750C22×D4—1224no—
751C22×D4—1224no—
752C22×D4C22×D6111yescharacteristic
753C23×C4—611no—
754C23×C4—1222no—
755C23×C4—1222no—
756AGL(1,ℤ/8)—1224no—
757AGL(1,ℤ/8)—1224no—
758C2×SD16—24no—
759C2×SD16—612no—
760C2×SD16—612no—
761C2×SD16—612no—
762C2×SD16—612no—
763C2×SD16—1224no—
764C2×SD16C22×D6112yes—
765C2×SD16C22×D6112yes—
766C2×D8—612no—
767C2×D8—612no—
768C2×M16—611no—
769C2×M16C22×D6111yescharacteristic
770C22×C8—611no—
771C22×C8C22×D6111yescharacteristic
772C4⋊Q8—612no—
773C4⋊Q8—612no—
774C4⋊Q8—1221no—
775#126—1222no—
776#126—1222no—
777#126—1222no—
778#126—1222no—
779#125—612no—
780#125—1222no—
781#125—1221no—
782#125—1222no—
783#125—1222no—
784#124—612no—
785#124—1222no—
786#123—1221no—
787#123—1222no—
788#123—1222no—
789#123—1222no—
790C22⋊Q8—612no—
791C22⋊Q8—612no—
792C22⋊Q8—611no—
793C22⋊Q8—611no—
794C22⋊Q8—1222no—
795C22⋊Q8—1222no—
796C22⋊Q8—1222no—
797C22⋊Q8—1221no—
798C22⋊Q8—1221no—
799C22⋊Q8—1221no—
800C22⋊Q8—1221no—
801#121—611no—
802#121—611no—
803#120—1221no—
804C4×Q8—21no—
805C4×Q8—21no—
806C4×Q8—612no—
807C4×Q8—1222no—
808C4×Q8C22×D6112yescomplemented
809C4×Q8C22×D6112yescomplemented
810C4×D4—21no—
811C4×D4—21no—
812C4×D4—612no—
813C4×D4—612no—
814C4×D4—612no—
815C4×D4—612no—
816C4×D4—612no—
817C4×D4—612no—
818C4×D4—612no—
819C4×D4—1221no—
820C4×D4—1221no—
821C4×D4—1221no—
822C4×D4—1221no—
823C4×D4—1222no—
824C4×D4—1222no—
825C4×D4—1222no—
826C4×D4—1222no—
827C4×D4—1222no—
828C4×D4—1222no—
829C4×D4—1222no—
830C4×D4—1222no—
831C4×D4—1222no—
832C4×D4—1221no—
833C4×D4—1221no—
834C4×D4—1221no—
835C4×D4—1221no—
836C4×D4—1222no—
837C4×D4C22×D6112yes—
838C4×D4C22×D6112yes—
839#117—22no—
840#117—611no—
841#117—611no—
842#117—611no—
843#117—612no—
844#117—612no—
845#117—611no—
846#117—611no—
847#117—611no—
848#117—1222no—
849#117—1221no—
850#117—1222no—
851#117—1221no—
852#117—1221no—
853#117C22×D6111yescharacteristic
854#117C22×D6111yescharacteristic
855#117C22×D6111yescharacteristic
856C2×C4⋊C4—611no—
857C2×C4⋊C4—611no—
858C2×C4⋊C4—611no—
859C2×C4⋊C4—611no—
860C2×C4⋊C4—611no—
861C2×C4⋊C4—1221no—
862C2×C4⋊C4—1221no—
863C2×C22⋊C4—22no—
864C2×C22⋊C4—612no—
865C2×C22⋊C4—1222no—
866C2×C22⋊C4—1222no—
867C2×C22⋊C4—1222no—
868C2×C22⋊C4—1222no—
869C2×C22⋊C4—1222no—
870C2×C22⋊C4—1221no—
871C2×C22⋊C4—1222no—
872C2×C22⋊C4—1222no—
873C2×C22⋊C4—1222no—
874C2×C22⋊C4—1221no—
875C2×C22⋊C4—1222no—
876C2×C42—612no—
877C2×C42—1221no—
878#107—612no—
879#107—611no—
880#107—611no—
881#107—612no—
882#107C22×D6111yescharacteristic, complemented
883#107C22×D6111yescharacteristic, complemented
884#106—612no—
885#106—611no—
886#106—611no—
887#106—612no—
888#106C22×D6111yescharacteristic, complemented
889#106C22×D6111yescharacteristic, complemented
890C4⋊C8—612no—
891C4⋊C8—612no—
892C4⋊C8—612no—
893C4⋊C8—612no—
894#103—612no—
895#103—612no—
896#103—611no—
897#103—611no—
898#103—611no—
899#103—611no—
900#103C22×D6112yescomplemented
901#103C22×D6112yescomplemented
902#102—612no—
903#102—612no—
904#102—612no—
905#102—612no—
906#102—611no—
907#102—611no—
908#102—612no—
909#102—612no—
910#102—611no—
911#102—611no—
912#102C22×D6112yes—
913#102C22×D6112yes—
914C22⋊C8—611no—
915C22⋊C8—611no—
916C22⋊C8—611no—
917C22⋊C8—611no—
918C22⋊C8—612no—
919C22⋊C8—612no—
920#97—612no—
921#97C22×D6112yescomplemented
922C4×C8—612no—
923C4×C8C22×D6112yescomplemented
924C24—21no—
925C24—611no—
926C24—1222no—
927C24—1222no—
928C24—1228no—
929C24—1221no—
930C24—4882no—
931C24—4882no—
932#41—1222no—
933#41—1222no—
934C2×Q8—21no—
935C2×Q8—22no—
936C2×Q8—22no—
937C2×Q8—611no—
938C2×Q8—1222no—
939C2×Q8C23×D6112yes—
940C2×D4—21no—
941C2×D4—22no—
942C2×D4—614no—
943C2×D4—612no—
944C2×D4—611no—
945C2×D4—1221no—
946C2×D4—1221no—
947C2×D4—1222no—
948C2×D4—1222no—
949C2×D4—1224no—
950C2×D4—1224no—
951C2×D4—1228no—
952C2×D4—1228no—
953C2×D4—1228no—
954C2×D4—1224no—
955C2×D4—1224no—
956C2×D4—1221no—
957C2×D4—1221no—
958C2×D4—1222no—
959C2×D4#1175822214yes—
960C2×D4C23×D6112yes—
961C22×C4—21no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—611no—
965C22×C4—612no—
966C22×C4—611no—
967C22×C4—611no—
968C22×C4—611no—
969C22×C4—611no—
970C22×C4—612no—
971C22×C4—1222no—
972C22×C4—1222no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1222no—
976C22×C4—1222no—
977C22×C4—1222no—
978C22×C4—1222no—
979C22×C4—1221no—
980C22×C4—1222no—
981C22×C4—1222no—
982C22×C4—1222no—
983C22×C4—1221no—
984C22×C4—4884no—
985C22×C4—4884no—
986C22×C4C23×D6111yescharacteristic
987SD16—24no—
988SD16—24no—
989SD16—1224no—
990SD16—1224no—
991SD16—1224no—
992SD16—1224no—
993D8—1224no—
994D8—1224no—
995M16—22no—
996M16—1222no—
997C2×C8—22no—
998C2×C8—611no—
999C2×C8—612no—
1000C2×C8—611no—
1001C2×C8—1222no—
1002C2×C8C23×D6111yescharacteristic
1003C2×C8C23×D6112yes—
1004C2×C8C23×D6111yescharacteristic
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—612no—
1008C4⋊C4—612no—
1009C4⋊C4—611no—
1010C4⋊C4—611no—
1011C4⋊C4—612no—
1012C4⋊C4—611no—
1013C4⋊C4—611no—
1014C4⋊C4—1221no—
1015C4⋊C4—1221no—
1016C4⋊C4—1222no—
1017C4⋊C4—1222no—
1018C4⋊C4—1222no—
1019C4⋊C4—1222no—
1020C4⋊C4—1222no—
1021C4⋊C4—1222no—
1022C4⋊C4—1221no—
1023C4⋊C4—1221no—
1024C4⋊C4—1222no—
1025C4⋊C4—1221no—
1026C4⋊C4—1222no—
1027C4⋊C4D4×D6111yescharacteristic
1028C4⋊C4D4×D6111yescharacteristic
1029C4⋊C4C23×D6111yescharacteristic
1030C4⋊C4C23×D6111yescharacteristic
1031C4⋊C4C23×D6111yescharacteristic
1032C4⋊C4C23×D6111yescharacteristic
1033C22⋊C4—21no—
1034C22⋊C4—21no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—612no—
1038C22⋊C4—612no—
1039C22⋊C4—612no—
1040C22⋊C4—1222no—
1041C22⋊C4—1222no—
1042C22⋊C4—1221no—
1043C22⋊C4—1222no—
1044C22⋊C4—1221no—
1045C22⋊C4—1222no—
1046C22⋊C4—1221no—
1047C22⋊C4—1221no—
1048C22⋊C4—1222no—
1049C22⋊C4—1222no—
1050C22⋊C4—1221no—
1051C22⋊C4—1221no—
1052C22⋊C4—1222no—
1053C22⋊C4—1222no—
1054C22⋊C4—1221no—
1055C22⋊C4—1222no—
1056C22⋊C4—1222no—
1057C22⋊C4—1222no—
1058C22⋊C4D4×D6112yes—
1059C42—21no—
1060C42—22no—
1061C42—22no—
1062C42—21no—
1063C42—612no—
1064C42—612no—
1065C42—612no—
1066C42—1221no—
1067C42—1221no—
1068C42—1221no—
1069C42—1222no—
1070C42C23×D6112yes—
1071C23—22no—
1072C23—24no—
1073C23—81no—
1074C23—81no—
1075C23—611no—
1076C23—611no—
1077C23—1222no—
1078C23—1228no—
1079C23—1228no—
1080C23—1224no—
1081C23—1222no—
1082C23—1222no—
1083C23—1221no—
1084C23—4881no—
1085C23—4881no—
1086C23—4882no—
1087C23—4882no—
1088C23—48816no—
1089C23—2441no—
1090C23—2444no—
1091C23—2444no—
1092C23C2×D4×D6111yescharacteristic
1093Q8—22no—
1094Q8—22no—
1095Q8—42no—
1096Q8—1221no—
1097Q8—1221no—
1098Q8—4882no—
1099D4—24no—
1100D4—22no—
1101D4—614no—
1102D4—1228no—
1103D4—1228no—
1104D4—1224no—
1105D4—1221no—
1106D4—1222no—
1107D4—1221no—
1108D4—4881no—
1109D4—2442no—
1110D4—2442no—
1111D4C2×#1175822214yes—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—42no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—611no—
1121C2×C4—612no—
1122C2×C4—612no—
1123C2×C4—611no—
1124C2×C4—1224no—
1125C2×C4—1222no—
1126C2×C4—1222no—
1127C2×C4—1222no—
1128C2×C4—1221no—
1129C2×C4—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1222no—
1136C2×C4—4882no—
1137C2×C4—4882no—
1138C2×C4—4882no—
1139C2×C4—4882no—
1140C2×C4—4882no—
1141C2×C4—4882no—
1142C2×C4—4882no—
1143C2×C4—4881no—
1144C2×C4—2442no—
1145C2×C4—2442no—
1146C2×C4—2442no—
1147C2×C4—2442no—
1148C2×C4C2×D4×D6112yes—
1149C2×C4C2×D4×D6112yes—
1150C2×C4C2×D4×D6111yescharacteristic
1151C2×C4#41×D6112yes—
1152C2×C4C2×#1175822212yes—
1153C2×C4C24×D6111yescharacteristic
1154C8—22no—
1155C8—21no—
1156C8—21no—
1157C8—1221no—
1158C8—1221no—
1159C8—1222no—
1160C22—21no—
1161C22—21no—
1162C22—24no—
1163C22—42no—
1164C22—42no—
1165C22—84no—
1166C22—612no—
1167C22—1221no—
1168C22—1221no—
1169C22—1221no—
1170C22—1221no—
1171C22—1224no—
1172C22—1221no—
1173C22—4884no—
1174C22—4888no—
1175C22—2444no—
1176C22—24416no—
1177C22—2441no—
1178C22—2441no—
1179C22—2441no—
1180C22—2442no—
1181C22—2442no—
1182C22#1684027112yes—
1183C22C22×D4×D6111yescharacteristic
1184C4—22no—
1185C4—22no—
1186C4—41no—
1187C4—41no—
1188C4—42no—
1189C4—41no—
1190C4—41no—
1191C4—1222no—
1192C4—1221no—
1193C4—1221no—
1194C4—1222no—
1195C4—2441no—
1196C4—2441no—
1197C4—2441no—
1198C4—2442no—
1199C4#1684027112yes—
1200C4C2×#41×D6111yescharacteristic
1201C4C22×#1175822211yescharacteristic
1202C2—22no—
1203C2—44no—
1204C2—1222no—
1205C2—4881no—
1206C2—2441no—
1207C2—2444no—
1208C2C2×#1684027111yescharacteristic
1209C2#577×D6111yescharacteristic
1210C2#2146059711yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2949C2
socleC22×C61C23×D4
prime radical#21455048C2
hypercenter#2949D61
hypocenterC61#60579
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #2949

Complements

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

NH ≅ G/Ntype
1. #21459561C2semidirect
2. #518×D61C2semidirect
3. #21456070C2semidirect
4. #21456068C2semidirect
5. #21456009C2semidirect
6. #21456007C2semidirect
7. #21455961C2semidirect
8. #21455916C2semidirect
9. #21455870C2semidirect
10. #21455825C2semidirect
11. #21455765C2semidirect
12. #21455736C2semidirect
13. #21455653C2semidirect
14. #21455652C2semidirect
15. #21455330C2semidirect
16. #21455328C2semidirect
18. C2×#16839911C2semidirect
19. #21454678C2semidirect
20. #21454653C2semidirect
21. #21454651C2semidirect
22. #21454474C2semidirect
23. C61×#2949C2semidirect
34. #16840390C22semidirect
35. #16840384C22semidirect
36. #16840370C22semidirect
37. #16840336C22semidirect
38. #16840316C22semidirect
39. #16840299C22semidirect
42. #16840242C22semidirect
58. #16840106C22semidirect
59. #16840105C22semidirect
60. #16840102C22semidirect
61. #16840101C22semidirect
62. #16840099C22semidirect
63. #16840096C22semidirect
64. #16840094C22semidirect
65. #16840091C22semidirect
66. #16840089C22semidirect
67. #16840088C22semidirect
68. #16840082C22semidirect
69. #16840077C22semidirect
70. #16840065C22semidirect
71. #16840064C22semidirect
72. #16840061C22semidirect
73. #16840060C22semidirect
74. #16840051C22semidirect
75. #16840050C22semidirect
76. #16840041C22semidirect
77. #16840040C22semidirect
78. #16839980C22semidirect
79. #16839980C22semidirect
80. #16839979C22semidirect
81. #16839979C22semidirect
82. #16839966C22semidirect
83. #16839966C22semidirect
84. #16839965C22semidirect
85. #16839965C22semidirect
94. #16839875C22semidirect
95. #16839872C22semidirect
96. #16839864C22semidirect
97. #16839862C22semidirect
98. #16839860C22semidirect
99. #16839860C22semidirect
100. C4×#11758190C22semidirect
101. C4×#11758201C22semidirect
102. C4×#11758201C22semidirect
103. C4×#11758200C22semidirect
104. C4×D488C22semidirect
105. C4×#11758199C22semidirect
106. #16839824C22semidirect
107. #16839821C22semidirect
108. #16839817C22semidirect
109. #16839813C22semidirect
110. #16839805C22semidirect
111. #16839804C22semidirect
112. #16839798C22semidirect
113. #16839790C22semidirect
114. #16839788C22semidirect
115. #16839771C22semidirect
117. #16839759C22semidirect
118. #16839756C22semidirect
123. #16839718C22semidirect
125. C61×#519C22semidirect
127. C61×#440C22semidirect
128. C61×#440C22semidirect
129. C4×SD16×C61C22semidirect
130. C4×SD16×C61C22semidirect
131. C61×#427C22semidirect
132. C61×#419C22semidirect
134. C61×#405C22semidirect
160. #14519776C23semidirect
161. #14519775C23semidirect
168. #14519768C23semidirect
171. #14519766C23semidirect
192. C4×Dic122C23semidirect
200. C4×D244C23semidirect
252. #14519711C23semidirect
253. #14519710C23semidirect
254. #14519710C23semidirect
255. #14519710C23semidirect
256. #14519709C23semidirect
257. #14519708C23semidirect
258. #14519708C23semidirect
259. #14519708C23semidirect
260. #14519706C23semidirect
261. #14519706C23semidirect
262. #14519706C23semidirect
263. #14519706C23semidirect
264. #14519702C23semidirect
265. #14519702C23semidirect
266. #14519701C23semidirect
267. #14519701C23semidirect
268. #14519700C23semidirect
269. #14519700C23semidirect
272. #14519699C23semidirect
273. #14519699C23semidirect
278. #14519697C23semidirect
279. #14519697C23semidirect
286. #14519688C23semidirect
287. C4×#92418C23semidirect
297. C4×Q8×C61C23semidirect
298. C4×Q8×C61C23semidirect
308. #107×C61C23semidirect
309. #107×C61C23semidirect
310. #106×C61C23semidirect
311. #106×C61C23semidirect
312. #103×C61C23semidirect
313. #103×C61C23semidirect
316. #97×C61C23semidirect
317. C4×C8×C61C23semidirect
616. #2949D61semidirect
649. #519C2×D61semidirect
708. #440C2×D61semidirect
709. #440C2×D61semidirect
714. C4×SD16C2×D61semidirect
715. C4×SD16C2×D61semidirect
725. #427C2×D61semidirect
729. #419C2×D61semidirect
739. #405C2×D61semidirect
740. C61#60579semidirect
808. C4×Q8C22×D61semidirect
809. C4×Q8C22×D61semidirect
882. #107C22×D61semidirect
883. #107C22×D61semidirect
888. #106C22×D61semidirect
889. #106C22×D61semidirect
900. #103C22×D61semidirect
901. #103C22×D61semidirect
921. #97C22×D61semidirect
923. C4×C8C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214595612
#518×D612
#214560702
#214560682
#214560092
#214560072
#214559612
#214559162
#214558702
#214558252
#214557652
#214557362
#214556532
#214556522
#214553302
#214553282
#214550482
C2×#168399112
#214546782
#214546532
#214546512
#214544742
C61×#29492
#6057961