Finite Group Databasebeta

← #30625495

Subgroups — #30625495

Order 15616.

2604 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462815C211yesmaximal, characteristic, complemented
2#21462814C211yesmaximal, characteristic, complemented
3#21462597C213yesmaximal, complemented
4#21462596C213yesmaximal, complemented
5#21462594C213yesmaximal, complemented
6#21462593C213yesmaximal, complemented
7#21462592C213yesmaximal, complemented
8#21462591C213yesmaximal, complemented
9D61⋊#444C213yesmaximal, complemented
10C2×#16840807C213yesmaximal, complemented
11#21462481C211yesmaximal, characteristic, complemented
12#21462450C211yesmaximal, characteristic, complemented
13#21462449C211yesmaximal, characteristic, complemented
14#21462389C211yesmaximal, characteristic, complemented
15#21460591C211yesmaximal, characteristic
16#16840842—21no—
17#16840842C2213yescomplemented
18#16840841—21no—
19#16840841—23no—
20#16840841C2211yescharacteristic
21#16840841C2211yescharacteristic
22#16840841C2213yescomplemented
23#16840841C2213yescomplemented
24#16840840—23no—
25#16840840C2213yescomplemented
26C2×#14519865—21no—
27C2×#14519865C2213yescomplemented
28D61⋊#131—21no—
29D61⋊#131—23no—
30D61⋊#131C2211yescharacteristic
31D61⋊#131C2213yescomplemented
32D61⋊#131C2213yescomplemented
33C2×#14519864—23no—
34C2×#14519864C2213yescomplemented
35#41×#6923C2211yescharacteristic
36#16840809C2213yescomplemented
37#16840809C2213yescomplemented
38#16840808C2213yescomplemented
39#16840808C2213yescomplemented
40#16840807C2213yescomplemented
41#16840807C2216yescomplemented
42#16840807C2216yescomplemented
43#16840807C2216yescomplemented
44#16840807C2211yescharacteristic, complemented
45#16840807C2213yescomplemented
46#16840807C2213yescomplemented
47#16840806C2216yescomplemented
48#16840805C2216yescomplemented
49#16840805C2216yescomplemented
50#16840804C2216yescomplemented
51#16840777C2213yescomplemented
52#16840777C2213yescomplemented
53C2×#14519848C2213yescomplemented
54D61⋊#108C2213yescomplemented
55#16840761C2213yescomplemented
56#16840760C2213yescomplemented
57#16840759C2213yescomplemented
58#16840759C2213yescomplemented
59C2×#14519842C2213yescomplemented
60D61⋊#104C2213yescomplemented
61D61⋊#104C2213yescomplemented
62C2×#14519841C2213yescomplemented
63#16840728C2213yescomplemented
64#16840725C2213yescomplemented
65M16×#6923C2213yescomplemented
66C2×#14519831C2213yescomplemented
67#16840599C2211yescharacteristic
68#16840597C2211yescharacteristic
69#16840578C413yescomplemented
70#16840577C411yescharacteristic, complemented
71#16840574C411yescharacteristic, complemented
72#16840569C413yescomplemented
73#16840568C413yescomplemented
74#16840566C413yescomplemented
75#16840565C411yescharacteristic, complemented
76#16840561C2213yes—
77#16840558C2213yes—
78C2×#14519798C2213yes—
79#135×D61C2213yes—
80#131×D61C2211yescharacteristic
81C61×#577C411yescharacteristic, complemented
82#14519865—21no—
83#14519865—21no—
84#14519865—23no—
85#14519865—23no—
86#14519865—23no—
87#14519865—23no—
88#14519865D411yescharacteristic
89#14519865D411yescharacteristic
90#14519865C2313yes—
91#14519865C2316yes—
92#14519865C2313yes—
93#14519865C2313yes—
94#14519865C2311yescharacteristic
95#14519864—23no—
96#14519864—23no—
97#14519864—26no—
98#14519864—26no—
99#14519864—23no—
100#14519864—23no—
101#14519864—23no—
102#14519864—23no—
103#14519864—23no—
104#14519864—23no—
105#14519864—23no—
106#14519864—23no—
107#14519864D413yes—
108#14519864D413yes—
109#14519864C2313yes—
110#14519864C2316yes—
111#14519864C2313yes—
112#14519864C2313yes—
113#14519864C2311yescharacteristic
114C2×#11758213—23no—
115C2×#11758213—23no—
116C2×#11758213—23no—
117C2×#11758213C2313yes—
118C2×#11758213C2313yes—
119D61⋊M16—26no—
120D61⋊M16—23no—
121D61⋊M16—23no—
122D61⋊M16—23no—
123D61⋊M16—23no—
124D61⋊M16C2313yes—
125D61⋊M16C2313yes—
126D61⋊M16C2313yes—
127C2×#11758217—26no—
128C2×#11758217—23no—
129C2×D61⋊C8—23no—
130C2×D61⋊C8—23no—
131C2×D61⋊C8—23no—
132C2×D61⋊C8C2313yes—
133C22×#92420—23no—
134Q8×#6923—21no—
135D4×#6923—23no—
136#14519856C2313yes—
137C2×C4×#6923C2313yes—
138#14519848C2311yescharacteristic
139#14519848C2313yes—
140#14519848C2316yes—
141#14519847C2313yes—
142#14519847C2313yes—
143#14519842C2311yescharacteristic
144#14519842C2313yes—
145#14519842C2313yes—
146#14519842C2313yes—
147#14519842C2316yes—
148#14519841C2313yes—
149#14519841C2316yes—
150#14519841C2311yescharacteristic
151#14519841C2313yes—
152#14519841C2313yes—
153#14519831C2311yescharacteristic
154#14519831C2313yes—
155#14519831C2313yes—
156#14519831C2313yes—
157C8×#6923C2316yes—
158#14519825—21no—
159#14519825C2×C413yes—
160#14519824—21no—
161#14519824C2×C413yes—
162#14519824C2×C411yescharacteristic
163#14519823—23no—
164#14519823C2×C413yes—
165#14519823C2×C411yescharacteristic
166#14519822—23no—
167#14519822C2×C413yes—
168C2×#11758226—21no—
169C2×#11758226C2313yes—
170C2×#11758224—23no—
171C2×#11758224C2313yes—
172#41×D61—21no—
173#41×D61—23no—
174#41×D61C2313yes—
175#41×D61C2313yes—
176#41×D61C2311yescharacteristic
177#14519810C2×C413yescomplemented
178#14519809C2×C416yescomplemented
179#14519808C2×C413yescomplemented
180#14519807C2×C413yescomplemented
181#14519806C2×C416yescomplemented
182#14519805C2×C413yescomplemented
183#14519804C2×C416yescomplemented
184#14519803C2×C413yescomplemented
185#14519802C2×C413yescomplemented
186#14519801C2×C416yescomplemented
187#14519800C2313yes—
188#14519799C2×C413yescomplemented
189#14519798C2×C416yescomplemented
190#14519798C2×C416yescomplemented
191#14519798C2311yescharacteristic
192#14519798C2313yes—
193#14519798C2316yes—
194#14519797C2×C413yescomplemented
195#14519797C2×C413yescomplemented
196#14519796C2313yes—
197C2×#11758202C2×C413yescomplemented
198Q16×D61C2×C413yescomplemented
199C2×#11758190C2×C413yescomplemented
200SD16×D61C2×C413yescomplemented
201SD16×D61C2×C413yescomplemented
202C2×#11758199C2×C413yescomplemented
203D8×D61C2×C413yescomplemented
204#14519785C2×C413yes—
205#14519784C2×C411yescharacteristic
206#14519783C2×C413yes—
207M16×D61C2313yes—
208C2×C8×D61C2313yes—
2092−1+4×C61C2×C411yescharacteristic
210H(5,𝔽2)×C61C2×C411yescharacteristic
211#137×C61C2×C413yescomplemented
212AGL(1,ℤ/8)×C61C2×C413yescomplemented
213#135×C61C2×C413yescomplemented
214C2×SD16×C61C2×C413yescomplemented
215#131×C61C2×C411yescharacteristic
216C22×#6923—23no—
217#41×C61—21no—
218#41×C61—23no—
219#41×C61C22×C413yes—
220#41×C61C22×C413yes—
221#41×C61C22×C411yescharacteristic
222C2×Q8×C61—21no—
223C2×Q8×C61C22×C413yes—
224C2×D4×C61—23no—
225C2×D4×C61C22×C413yes—
226C2×C22⋊D61—23no—
227C2×C22⋊D61—26no—
228C22×Dic61—23no—
229#11758226—21no—
230#11758226—23no—
231#11758226—23no—
232#11758226—23no—
233#11758226C22×C416yes—
234#11758226C2×D411yescharacteristic
235#11758226C2411yescharacteristic
236#11758226C2413yes—
237Q8×D61—21no—
238Q8×D61—23no—
239Q8×D61C22×C413yes—
240Q8×D61C22×C413yes—
241Q8×D61#4111yescharacteristic
242#11758224—23no—
243#11758224—26no—
244#11758224—23no—
245#11758224—23no—
246#11758224—23no—
247#11758224—23no—
248#11758224—23no—
249#11758224C22×C416yes—
250#11758224C2×D413yes—
251#11758224C2411yescharacteristic
252#11758224C2413yes—
253D4×D61—23no—
254D4×D61—23no—
255D4×D61—23no—
256D4×D61—26no—
257D4×D61—23no—
258D4×D61C22×C413yes—
259D4×D61C22×C413yes—
260D4×D61#4113yes—
261#11758222—26no—
262#11758222—23no—
263#11758222—23no—
264#11758222—23no—
265#11758222—23no—
266#11758222C22×C413yes—
267#11758222C22×C413yes—
268#11758222C22×C413yes—
269C2×D244—23no—
270C2×D244—23no—
271C2×D244C22×C413yes—
272C2×C4×D61—23no—
273C2×C4×D61—23no—
274C2×C4×D61—23no—
275C2×C4×D61C2413yes—
276C2×Dic122—23no—
277C2×Dic122C22×C413yes—
278C22⋊#6923—23no—
279#11758217—23no—
280#11758217—23no—
281#11758217—23no—
282#11758217—23no—
283#11758217—26no—
284#11758217—21no—
285#11758217—23no—
286#11758217C2×D416yes—
287C2×#92420—23no—
288C2×#92420—23no—
289C2×#92420—23no—
290C2×#92420—26no—
291C2×#92420—21no—
292C2×#92420—23no—
293C2×#92420—23no—
294C2×#92420C2×D413yes—
295C2×#92420C2×D413yes—
296C4⋊#6923—23no—
297C4×#6923—23no—
298C4×#6923C2413yes—
299C4×#6923C2411yescharacteristic
300#11758213—23no—
301#11758213—23no—
302#11758213—21no—
303#11758213—23no—
304#11758213—23no—
305#11758213—23no—
306#11758213—26no—
307#11758213C2×D413yes—
308#11758213C2×D413yes—
309#11758213C2411yescharacteristic
310#11758213C2413yes—
311#11758213C2411yescharacteristic
312#11758213C2413yes—
313D61⋊C8—23no—
314D61⋊C8—23no—
315D61⋊C8—21no—
316D61⋊C8—23no—
317D61⋊C8—23no—
318D61⋊C8—23no—
319D61⋊C8—26no—
320D61⋊C8C2×D413yes—
321D61⋊C8C2×D413yes—
322D61⋊C8C2413yes—
323D61⋊C8C2411yescharacteristic
324Q16×C61C22×C413yes—
325SD16×C61C22×C413yes—
326SD16×C61C22×C416yes—
327SD16×C61C22×C411yescharacteristic
328D8×C61C22×C413yes—
329M16×C61C22×C413yes—
330C2×C8×C61C22×C413yes—
331#11758202C22×C416yes—
332#11758202C22×C411yescharacteristic
333#11758202C22×C413yes—
334#11758201C22×C413yes—
335#11758201C22×C413yes—
336#11758200C22×C413yes—
337#11758200C22×C413yes—
338#11758199C22×C411yescharacteristic
339#11758199C22×C413yes—
340#11758199C22×C416yes—
341#11758194C22×C413yes—
342C2×#92418C22×C413yes—
343Dic244C22×C413yes—
344D488C22×C413yes—
345#11758190C22×C416yes—
346#11758190C22×C411yescharacteristic
347#11758190C22×C413yes—
348#11758189C22×C416yes—
349C8×D61C22×C413yes—
350C8×D61C22×C413yes—
351C8×D61C2413yes—
352C8×D61C2411yescharacteristic
353C23×C61—23no—
354C22×D61—23no—
355C22×D61—23no—
356C22×D61—23no—
357C22×D61C2×#4113yes—
358C2×#6923—21no—
359C2×#6923—23no—
360C2×#6923—83no—
361Q8×C61—23no—
362Q8×C61C4×D411yescharacteristic
363Q8×C61C23×C411yescharacteristic
364Q8×C61C23×C413yes—
365D4×C61—23no—
366D4×C61—23no—
367D4×C61—23no—
368D4×C61C4×D413yes—
369D4×C61C23×C413yes—
370D4×C61C23×C411yescharacteristic
371C2×C4×C61—23no—
372C2×C4×C61—23no—
373C2×C4×C61—23no—
374C2×C4×C61C23×C413yes—
375C22⋊D61—23no—
376C22⋊D61—23no—
377C22⋊D61—26no—
378C22⋊D61—21no—
379C22⋊D61—23no—
380C22⋊D61—23no—
381C22⋊D61—23no—
382C22⋊D61C4×D416yes—
383C2×Dic61—23no—
384C2×Dic61—26no—
385C2×Dic61—21no—
386C2×Dic61—23no—
387C2×Dic61C22×D413yes—
388D244—26no—
389D244—23no—
390D244—21no—
391D244—23no—
392D244C4×D413yes—
393D244C23×C413yes—
394D244C23×C411yescharacteristic
395C4×D61—23no—
396C4×D61—23no—
397C4×D61—23no—
398C4×D61—23no—
399C4×D61—26no—
400C4×D61—21no—
401C4×D61—23no—
402C4×D61C23×C413yes—
403C4×D61C22×D413yes—
404C4×D61C2×#4113yes—
405C4×D61C2511yescharacteristic
406Dic122—23no—
407Dic122—23no—
408Dic122—23no—
409Dic122C4×D413yes—
410Dic122C23×C413yes—
411Dic122C23×C411yescharacteristic
412#92420—21no—
413#92420—23no—
414#92420—21no—
415#92420—23no—
416#92420C22×D411yescharacteristic
417#92420C22×D413yes—
418#92420C22×D411yescharacteristic
419#92420C22×D413yes—
420C8×C61C23×C411yescharacteristic
421C8×C61C23×C413yes—
422#92418C23×C411yescharacteristic
423#92418C23×C413yes—
424#60184—611nomaximal, Sylow
425C22×C61—23no—
426C22×C61—21no—
427C22×C61—83no—
428C22×C61C2×C4×D413yes—
429C2×D61—23no—
430C2×D61—21no—
431C2×D61—43no—
432C2×D61—83no—
433C2×D61—83no—
434C2×D61—83no—
435C2×D61C2×C4×D413yes—
436C2×D61C22×#4111yescharacteristic
437#6923—43no—
438#6923—41no—
439C4×C61—21no—
440C4×C61—23no—
441C4×C61C2×C4×D413yes—
442C4×C61C24×C411yescharacteristic
443Dic61—21no—
444Dic61—23no—
445Dic61C2×C4×D413yes—
446Dic61C23×D411yescharacteristic
447#3584—611no—
448#3573—611no—
449#3573—611no—
450#2957—613no—
451#2957—613no—
452#2956—613no—
453#2956—613no—
454#2955—613no—
455#2955—613no—
456C2×#444—613no—
457C2×#444—613no—
458#2916—611no—
459#2901—611no—
460#2901—611no—
461#2875—611no—
462C2×C61—23no—
463C2×C61—41no—
464C2×C61—43no—
465C2×C61C22×C4×D411yescharacteristic
466D61—21no—
467D61—23no—
468D61—43no—
469D61—41no—
470#585—611no—
471#585—611no—
472#578—611no—
473#578—613no—
474#577—613no—
475#577—613no—
476#577—611no—
477#577#692311yescharacteristic, complemented
478#576—611no—
479#576—613no—
480#575—613no—
481#575—613no—
482C2×#135—613no—
483C2×#135—613no—
484#568—611no—
485#568—611no—
486#568—613no—
487#568—613no—
488#568—613no—
489#568—613no—
490#568—1223no—
491#568—1221no—
492#568—1223no—
493#568—1221no—
494C2×#131—611no—
495C2×#131—611no—
496C2×#131—613no—
497C2×#131—613no—
498C2×#131—613no—
499C2×#131—613no—
500C2×#131—1223no—
501C2×#131—1223no—
502C2×#131—1221no—
503C2×#131—1221no—
504C4×#41—611no—
505#444—613no—
506#444—611no—
507#444—616no—
508#444—616no—
509#444—616no—
510#444—613no—
511#444—613no—
512#444—613no—
513#444—613no—
514#444—613no—
515#444—613no—
516#443—616no—
517#443—616no—
518#443—616no—
519#443—616no—
520#430—613no—
521#430—613no—
522C2×#108—613no—
523C2×#108—613no—
524#421—613no—
525#421—613no—
526#421—613no—
527#421—613no—
528C2×#104—613no—
529C2×#104—613no—
530C2×#104—613no—
531C2×#104—613no—
532#405—613no—
533#405—613no—
534C4×M16—613no—
535C2×#97—613no—
536C61#6018411yescharacteristic, complemented, Sylow
5372−1+4—613no—
5382−1+4—611no—
5392−1+4—613no—
5402−1+4—1221no—
5412−1+4—1221no—
5422−1+4C2×#692311yescharacteristic
543H(5,𝔽2)—613no—
544H(5,𝔽2)—611no—
545H(5,𝔽2)—613no—
546H(5,𝔽2)—1223no—
547H(5,𝔽2)—1223no—
548H(5,𝔽2)C2×#692311yescharacteristic
549C2×#41—611no—
550C2×#41—613no—
551C2×#41—613no—
552C2×#41—613no—
553C2×#41—613no—
554C2×#41—1223no—
555C2×#41—1221no—
556C2×#41—1221no—
557C2×#41—1223no—
558#137—613no—
559#137—613no—
560#137—616no—
561#137—616no—
562#137—613no—
563#137C2×#692313yescomplemented
564AGL(1,ℤ/8)—613no—
565AGL(1,ℤ/8)—613no—
566AGL(1,ℤ/8)—616no—
567AGL(1,ℤ/8)—616no—
568AGL(1,ℤ/8)—613no—
569AGL(1,ℤ/8)C2×#692313yescomplemented
570#135—613no—
571#135—613no—
572#135—613no—
573#135—611no—
574#135—613no—
575#135—616no—
576#135—616no—
577#135—616no—
578#135—613no—
579#135—613no—
580#135C2×#692313yescomplemented
581C2×Q16—613no—
582C2×Q16—613no—
583C2×SD16—613no—
584C2×SD16—613no—
585C2×SD16—613no—
586C2×SD16C2×#692313yescomplemented
587C2×D8—613no—
588C2×D8—613no—
589#131—613no—
590#131—613no—
591#131—611no—
592#131—611no—
593#131—611no—
594#131—613no—
595#131—613no—
596#131—613no—
597#131—611no—
598#131—611no—
599#131—613no—
600#131—616no—
601#131—613no—
602#131—613no—
603#131—613no—
604#131—613no—
605#131—616no—
606#131—1223no—
607#131—1223no—
608#131—1223no—
609#131—1223no—
610#131—1223no—
611#131—1223no—
612#131—1223no—
613#131—1223no—
614#131—1226no—
615#131—1226no—
616#131—1223no—
617#131—1223no—
618#131—1223no—
619#131—1223no—
620#131—1223no—
621#131—1223no—
622#131—1221no—
623#131—1221no—
624#131C2×#692311yescharacteristic
625C2×M16—613no—
626C2×M16—613no—
627C2×M16—613no—
628C2×M16—613no—
629C2×M16—613no—
630C2×M16—613no—
631C2×M16—1223no—
632C2×M16—1223no—
633C2×M16—1223no—
634C2×M16—1223no—
635C2×M16—1226no—
636C2×M16—1223no—
637C2×M16—1223no—
638C2×M16—1226no—
639C2×M16—1223no—
640C2×M16—1223no—
641C22×C8—613no—
642C22×C8—613no—
643C22×C8—1223no—
644C22×C8—1223no—
645C22×C8—1223no—
646C22×C8—1223no—
647C4×Q8—1221no—
648C4×D4—1223no—
649#117—613no—
650C2×C42—613no—
651#108—613no—
652#108—613no—
653#108—611no—
654#108—613no—
655#108—616no—
656#104—613no—
657#104—611no—
658#104—616no—
659#104—613no—
660#104—613no—
661#104—611no—
662#104—613no—
663#104—613no—
664#104—613no—
665#104—616no—
666#97—611no—
667#97—613no—
668#97—613no—
669#97—613no—
670C4×C8—616no—
671#41—21no—
672#41—23no—
673#41—611no—
674#41—613no—
675#41—613no—
676#41—611no—
677#41—613no—
678#41—616no—
679#41—613no—
680#41—611no—
681#41—616no—
682#41—613no—
683#41—613no—
684#41—1223no—
685#41—1223no—
686#41—1226no—
687#41—1223no—
688#41—1223no—
689#41—1223no—
690#41—1223no—
691#41—1223no—
692#41—1223no—
693#41—1223no—
694#41—1223no—
695#41—1226no—
696#41—1223no—
697#41—1223no—
698#41—1221no—
699#41—1223no—
700#41C22×#692313yes—
701#41C22×#692313yes—
702#41C22×#692311yescharacteristic
703C2×Q8—21no—
704C2×Q8—611no—
705C2×Q8—613no—
706C2×Q8—613no—
707C2×Q8—613no—
708C2×Q8—1223no—
709C2×Q8—1223no—
710C2×Q8—1221no—
711C2×Q8C22×#692313yes—
712C2×D4—23no—
713C2×D4—613no—
714C2×D4—613no—
715C2×D4—613no—
716C2×D4—613no—
717C2×D4—1223no—
718C2×D4—1223no—
719C2×D4—1226no—
720C2×D4—1223no—
721C2×D4—1223no—
722C2×D4—1223no—
723C2×D4—1226no—
724C2×D4—1223no—
725C2×D4—1223no—
726C2×D4C22×#692313yes—
727C22×C4—613no—
728C22×C4—1223no—
729C22×C4—1223no—
730C22×C4—1223no—
731C22×C4—1223no—
732C22×C4—1223no—
733Q16—611no—
734Q16—613no—
735Q16—616no—
736Q16—613no—
737Q16C22×#692313yes—
738SD16—613no—
739SD16—613no—
740SD16—613no—
741SD16—613no—
742SD16—611no—
743SD16—613no—
744SD16—616no—
745SD16C22×#692311yescharacteristic
746SD16C22×#692313yes—
747SD16C22×#692316yes—
748D8—613no—
749D8—611no—
750D8—616no—
751D8—613no—
752D8C22×#692313yes—
753M16—613no—
754M16—613no—
755M16—616no—
756M16—613no—
757M16—616no—
758M16—613no—
759M16—611no—
760M16—611no—
761M16—613no—
762M16—1221no—
763M16—1223no—
764M16—1223no—
765M16—1223no—
766M16—1226no—
767M16—1223no—
768M16—1221no—
769M16—1226no—
770M16—1223no—
771M16—1223no—
772M16—1223no—
773M16—1223no—
774M16—1223no—
775M16—1223no—
776M16C22×#692313yes—
777C2×C8—613no—
778C2×C8—611no—
779C2×C8—613no—
780C2×C8—613no—
781C2×C8—613no—
782C2×C8—613no—
783C2×C8—613no—
784C2×C8—613no—
785C2×C8—611no—
786C2×C8—613no—
787C2×C8—613no—
788C2×C8—1221no—
789C2×C8—1223no—
790C2×C8—1223no—
791C2×C8—1221no—
792C2×C8—1223no—
793C2×C8—1223no—
794C2×C8—1226no—
795C2×C8—1226no—
796C2×C8—1223no—
797C2×C8—1223no—
798C2×C8—1223no—
799C2×C8—1223no—
800C2×C8—1223no—
801C2×C8—1223no—
802C2×C8C22×#692313yes—
803C4⋊C4—1223no—
804C22⋊C4—1223no—
805C42—613no—
806C42—611no—
807C42—1223no—
808C23—23no—
809C23—613no—
810C23—1223no—
811C23—1223no—
812C23—1223no—
813Q8—23no—
814Q8—613no—
815Q8—613no—
816Q8—611no—
817Q8—1223no—
818Q8—1223no—
819Q8—1223no—
820Q8D4×#692311yescharacteristic
821Q8C23×#692311yescharacteristic
822Q8C23×#692313yes—
823D4—23no—
824D4—23no—
825D4—23no—
826D4—616no—
827D4—613no—
828D4—613no—
829D4—611no—
830D4—1221no—
831D4—1223no—
832D4—1226no—
833D4—1223no—
834D4—1223no—
835D4—1221no—
836D4—1223no—
837D4—1226no—
838D4—1223no—
839D4—1223no—
840D4—1223no—
841D4D4×#692313yes—
842D4C23×#692313yes—
843D4C23×#692311yescharacteristic
844C2×C4—23no—
845C2×C4—23no—
846C2×C4—23no—
847C2×C4—613no—
848C2×C4—613no—
849C2×C4—613no—
850C2×C4—613no—
851C2×C4—611no—
852C2×C4—1221no—
853C2×C4—1223no—
854C2×C4—1226no—
855C2×C4—1223no—
856C2×C4—1223no—
857C2×C4—1221no—
858C2×C4—1223no—
859C2×C4—1226no—
860C2×C4—1223no—
861C2×C4—1223no—
862C2×C4—1223no—
863C2×C4—1221no—
864C2×C4—1223no—
865C2×C4—4883no—
866C2×C4C23×#692313yes—
867C8—611no—
868C8—611no—
869C8—613no—
870C8—613no—
871C8—611no—
872C8—613no—
873C8—1221no—
874C8—1223no—
875C8—1221no—
876C8—1223no—
877C8C23×#692311yescharacteristic
878C8C23×#692313yes—
879C22—21no—
880C22—23no—
881C22—83no—
882C22—611no—
883C22—613no—
884C22—1223no—
885C22—1221no—
886C22—4883no—
887C22—4883no—
888C22—4883no—
889C22—2443no—
890C22C2×D4×#692313yes—
891C4—21no—
892C4—23no—
893C4—613no—
894C4—611no—
895C4—1221no—
896C4—1223no—
897C4—2441no—
898C4—2443no—
899C4C2×D4×#692313yes—
900C4C24×#692311yescharacteristic
901C2—23no—
902C2—43no—
903C2—41no—
904C2—1221no—
905C2—1223no—
906C2—2443no—
907C2—2441no—
908C2C22×D4×#692311yescharacteristic
subgroupG/H
centerC2C22×D4×#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC61×#577C4
socleC2×C61C22×C4×D4
prime radical#21460591C2
cosocleC4×D61C25
hypercenter#577#6923
hypocenterC61#60184
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ #41 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #21462815C2semidirect
2. #21462814C2semidirect
3. #21462597C2semidirect
4. #21462596C2semidirect
5. #21462594C2semidirect
6. #21462593C2semidirect
7. #21462592C2semidirect
8. #21462591C2semidirect
9. D61⋊#444C2semidirect
10. C2×#16840807C2semidirect
11. #21462481C2semidirect
12. #21462450C2semidirect
13. #21462449C2semidirect
14. #21462389C2semidirect
17. #16840842C22semidirect
22. #16840841C22semidirect
23. #16840841C22semidirect
25. #16840840C22semidirect
27. C2×#14519865C22semidirect
31. D61⋊#131C22semidirect
32. D61⋊#131C22semidirect
34. C2×#14519864C22semidirect
36. #16840809C22semidirect
37. #16840809C22semidirect
38. #16840808C22semidirect
39. #16840808C22semidirect
40. #16840807C22semidirect
41. #16840807C22semidirect
42. #16840807C22semidirect
43. #16840807C22semidirect
44. #16840807C22semidirect
45. #16840807C22semidirect
46. #16840807C22semidirect
47. #16840806C22semidirect
48. #16840805C22semidirect
49. #16840805C22semidirect
50. #16840804C22semidirect
51. #16840777C22semidirect
52. #16840777C22semidirect
53. C2×#14519848C22semidirect
54. D61⋊#108C22semidirect
55. #16840761C22semidirect
56. #16840760C22semidirect
57. #16840759C22semidirect
58. #16840759C22semidirect
59. C2×#14519842C22semidirect
60. D61⋊#104C22semidirect
61. D61⋊#104C22semidirect
62. C2×#14519841C22semidirect
63. #16840728C22semidirect
64. #16840725C22semidirect
65. M16×#6923C22semidirect
66. C2×#14519831C22semidirect
69. #16840578C4semidirect
70. #16840577C4semidirect
71. #16840574C4semidirect
72. #16840569C4semidirect
73. #16840568C4semidirect
74. #16840566C4semidirect
75. #16840565C4semidirect
81. C61×#577C4semidirect
177. #14519810C2×C4semidirect
178. #14519809C2×C4semidirect
179. #14519808C2×C4semidirect
180. #14519807C2×C4semidirect
181. #14519806C2×C4semidirect
182. #14519805C2×C4semidirect
183. #14519804C2×C4semidirect
184. #14519803C2×C4semidirect
185. #14519802C2×C4semidirect
186. #14519801C2×C4semidirect
188. #14519799C2×C4semidirect
189. #14519798C2×C4semidirect
190. #14519798C2×C4semidirect
194. #14519797C2×C4semidirect
195. #14519797C2×C4semidirect
197. C2×#11758202C2×C4semidirect
198. Q16×D61C2×C4semidirect
199. C2×#11758190C2×C4semidirect
200. SD16×D61C2×C4semidirect
201. SD16×D61C2×C4semidirect
202. C2×#11758199C2×C4semidirect
203. D8×D61C2×C4semidirect
211. #137×C61C2×C4semidirect
212. AGL(1,ℤ/8)×C61C2×C4semidirect
213. #135×C61C2×C4semidirect
214. C2×SD16×C61C2×C4semidirect
477. #577#6923semidirect
536. C61#60184semidirect
563. #137C2×#6923semidirect
569. AGL(1,ℤ/8)C2×#6923semidirect
580. #135C2×#6923semidirect
586. C2×SD16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214628152
#214628142
#214625972
#214625962
#214625942
#214625932
#214625922
#214625912
D61⋊#4442
C2×#168408072
#214624812
#214624502
#214624492
#214623892
#214605912
#6018461