Finite Group Databasebeta

← #577×#6923 #30625464

Subgroups — #577×#6923 #30625464

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
12−1+4×#6923C211yesmaximal, characteristic, complemented
2H(5,𝔽2)×#6923C211yesmaximal, characteristic, complemented
3#21462582C213yesmaximal, complemented
4#21462579C213yesmaximal, complemented
5#21462577C213yesmaximal, complemented
6#21462576C213yesmaximal, complemented
7#137×#6923C213yesmaximal, complemented
8AGL(1,ℤ/8)×#6923C213yesmaximal, complemented
9#135×#6923C213yesmaximal, complemented
10C2×SD16×#6923C213yesmaximal, complemented
11#21462473C211yesmaximal, characteristic, complemented
12#21462441C211yesmaximal, characteristic, complemented
13#21462440C211yesmaximal, characteristic, complemented
14#131×#6923C211yesmaximal, characteristic, complemented
15#577×D61C211yesmaximal, characteristic
16D61⋊#131C2211yescharacteristic
17#16840831—21no—
18#16840831—23no—
19#16840831C2213yes—
20#16840831C2211yescharacteristic
21#16840831C2211yescharacteristic
22#16840831C2213yescomplemented
23#16840830—21no—
24#16840830C2213yescomplemented
25#16840829—23no—
26#16840829C2213yes—
27#41×#6923—21no—
28#41×#6923—23no—
29#41×#6923C2213yes—
30#41×#6923C2211yescharacteristic
31#41×#6923C2213yescomplemented
32C2×Q8×#6923—21no—
33C2×Q8×#6923C2213yescomplemented
34C2×D4×#6923—23no—
35C2×D4×#6923C2213yes—
36#16840803C2216yescomplemented
37#16840802C2216yescomplemented
38#16840801C2216yescomplemented
39#16840801C2216yescomplemented
40Q16×#6923C2213yescomplemented
41Q16×#6923C2213yescomplemented
42SD16×#6923C2213yescomplemented
43SD16×#6923C2216yescomplemented
44SD16×#6923C2216yescomplemented
45SD16×#6923C2216yescomplemented
46SD16×#6923C2211yescharacteristic, complemented
47SD16×#6923C2213yescomplemented
48SD16×#6923C2213yescomplemented
49D8×#6923C2213yescomplemented
50D8×#6923C2213yescomplemented
51#16840773C2213yescomplemented
52#16840773C2213yescomplemented
53#16840772C2213yescomplemented
54C2×#14519845C2213yescomplemented
55#16840755C2213yescomplemented
56#16840754C2213yes—
57#16840753C2213yes—
58#16840753C2213yescomplemented
59#16840752C2213yes—
60#16840752C2213yescomplemented
61C2×#14519840C2213yescomplemented
62C2×#14519839C2213yes—
63#16840728C2213yescomplemented
64#16840725C2213yescomplemented
65M16×#6923C2213yescomplemented
66C2×C8×#6923C2213yescomplemented
672−1+4×D61C2211yescharacteristic
68H(5,𝔽2)×D61C2211yescharacteristic
69#16840574C411yescharacteristic, complemented
70#16840573C411yescharacteristic, complemented
71#16840572C413yescomplemented
72#16840571C413yescomplemented
73#16840570C411yescharacteristic, complemented
74#16840569C413yescomplemented
75#16840568C413yescomplemented
76#137×D61C2213yes—
77AGL(1,ℤ/8)×D61C2213yes—
78#135×D61C2213yes—
79C2×SD16×D61C2213yes—
80#131×D61C2211yescharacteristic
81C61×#577C411yescharacteristic, complemented
82C23×#6923—23no—
83#14519865—21no—
84#14519864—23no—
85D61⋊M16C2313yes—
86C2×D61⋊C8C2313yes—
87Q8×#6923—21no—
88Q8×#6923—21no—
89Q8×#6923—23no—
90Q8×#6923—23no—
91Q8×#6923—23no—
92Q8×#6923—23no—
93Q8×#6923D411yescharacteristic
94Q8×#6923D411yescharacteristic
95Q8×#6923C2313yes—
96Q8×#6923C2316yes—
97Q8×#6923C2311yescharacteristic
98Q8×#6923C2313yes—
99Q8×#6923C2313yes—
100D4×#6923—23no—
101D4×#6923—23no—
102D4×#6923—23no—
103D4×#6923—23no—
104D4×#6923—23no—
105D4×#6923—23no—
106D4×#6923—26no—
107D4×#6923—26no—
108D4×#6923—23no—
109D4×#6923—23no—
110D4×#6923—23no—
111D4×#6923—23no—
112D4×#6923D413yes—
113D4×#6923D413yes—
114D4×#6923C2311yescharacteristic
115D4×#6923C2313yes—
116D4×#6923C2313yes—
117D4×#6923C2313yes—
118D4×#6923C2316yes—
119#14519856—26no—
120#14519856—23no—
121#14519856—23no—
122#14519856—23no—
123#14519856—23no—
124#14519856C2313yes—
125#14519856C2313yes—
126#14519856C2313yes—
127C2×C4⋊#6923—23no—
128C2×C4⋊#6923—23no—
129C2×C4⋊#6923—23no—
130C2×C4⋊#6923C2313yes—
131C2×C4⋊#6923C2313yes—
132C2×C22⋊#6923—23no—
133C2×C22⋊#6923—26no—
134C2×C4×#6923—23no—
135C2×C4×#6923—23no—
136C2×C4×#6923—23no—
137C2×C4×#6923C2313yes—
138#14519846C2313yes—
139#14519846C2313yes—
140#14519845C2313yes—
141#14519845C2316yes—
142#14519845C2311yescharacteristic
143#14519840C2313yes—
144#14519840C2316yes—
145#14519840C2311yescharacteristic
146#14519840C2313yes—
147#14519840C2313yes—
148#14519839C2313yes—
149#14519839C2316yes—
150#14519839C2313yes—
151#14519839C2311yescharacteristic
152#14519839C2313yes—
153#14519831C2316yes—
154C8×#6923C2311yescharacteristic
155C8×#6923C2313yes—
156C8×#6923C2313yes—
157C8×#6923C2313yes—
158#14519825—21no—
159#14519825C2×C413yescomplemented
160#14519824—23no—
161#14519824C2×C413yescomplemented
162#14519824C2×C411yescharacteristic, complemented
163#14519823—21no—
164#14519823C2×C413yescomplemented
165#14519823C2×C411yescharacteristic, complemented
166#14519822—23no—
167#14519822C2×C413yescomplemented
168#41×D61—21no—
169#41×D61—23no—
170#41×D61C2313yes—
171#41×D61C2313yes—
172#41×D61C2311yescharacteristic
173C2×Q8×D61—21no—
174C2×Q8×D61C2313yes—
175C2×D4×D61—23no—
176C2×D4×D61C2313yes—
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#14519800C2×C413yescomplemented
188#14519799C2×C413yescomplemented
189#14519798C2×C413yescomplemented
190#14519798C2×C413yescomplemented
191#14519797C2×C413yescomplemented
192#14519797C2×C413yescomplemented
193#14519796C2×C413yescomplemented
194Q16×D61C2313yes—
195C2×#11758190C2×C413yescomplemented
196C2×#11758200C2×C413yescomplemented
197C2×#11758201C2×C413yescomplemented
198SD16×D61C2×C416yescomplemented
199SD16×D61C2×C416yescomplemented
200SD16×D61C2313yes—
201SD16×D61C2316yes—
202SD16×D61C2311yescharacteristic
203D8×D61C2313yes—
204#14519785C2×C413yescomplemented
205#14519784C2×C411yescharacteristic, complemented
206#14519783C2×C413yescomplemented
207M16×D61C2313yes—
208C2×C8×D61C2313yes—
2092−1+4×C61C2×C411yescharacteristic, complemented
210H(5,𝔽2)×C61C2×C411yescharacteristic, complemented
211#137×C61C2×C413yescomplemented
212AGL(1,ℤ/8)×C61C2×C413yescomplemented
213#135×C61C2×C413yescomplemented
214C2×SD16×C61C2×C413yescomplemented
215#131×C61C2×C411yescharacteristic, complemented
216C23×D61—23no—
217C22×#6923—23no—
218C22×#6923—23no—
219C22×#6923—21no—
220C22×#6923—23no—
221C22×#6923—23no—
222C22×#6923—23no—
223C22×#6923—26no—
224C22×#6923—86no—
225C22×#6923C2×D413yes—
226C22×#6923C2×D413yes—
227#41×C61—21no—
228#41×C61—23no—
229#41×C61C22×C413yes—
230#41×C61C22×C411yescharacteristic
231#41×C61C22×C413yescomplemented
232C2×Q8×C61—21no—
233C2×Q8×C61C22×C413yescomplemented
234C2×D4×C61—23no—
235C2×D4×C61C22×C413yes—
236C2×C22⋊D61—26no—
237C2×C22⋊D61—23no—
238#11758226—21no—
239#11758226—23no—
240#11758226C22×C413yes—
241#11758226C22×C413yescomplemented
242#11758226#4111yescharacteristic
243Q8×D61—21no—
244Q8×D61—23no—
245Q8×D61—23no—
246Q8×D61—23no—
247Q8×D61C22×C416yescomplemented
248Q8×D61C2×D411yescharacteristic
249Q8×D61C2413yes—
250Q8×D61C2411yescharacteristic
251#11758224—23no—
252#11758224—26no—
253#11758224—23no—
254#11758224—23no—
255#11758224—23no—
256#11758224C22×C413yes—
257#11758224C22×C413yescomplemented
258#11758224#4113yes—
259D4×D61—23no—
260D4×D61—23no—
261D4×D61—23no—
262D4×D61—26no—
263D4×D61—23no—
264D4×D61—23no—
265D4×D61—23no—
266D4×D61C22×C416yes—
267D4×D61C2×D413yes—
268D4×D61C2413yes—
269D4×D61C2411yescharacteristic
270#11758222—26no—
271#11758222—23no—
272#11758222—23no—
273#11758222—23no—
274#11758222—23no—
275#11758222C22×C413yes—
276#11758222C22×C413yes—
277#11758222C22×C413yescomplemented
278C2×D244—23no—
279C2×D244C22×C413yes—
280C2×C4×D61—23no—
281C2×C4×D61—23no—
282C2×C4×D61—23no—
283C2×C4×D61C2413yes—
284C2×Dic122—23no—
285C2×Dic122—23no—
286C2×Dic122C22×C413yescomplemented
287C22⋊#6923—23no—
288C22⋊#6923—23no—
289C22⋊#6923—23no—
290C22⋊#6923—26no—
291C22⋊#6923—23no—
292C22⋊#6923—21no—
293C22⋊#6923—23no—
294C22⋊#6923C2×D416yes—
295#11758217—23no—
296C2×#92420—23no—
297C4⋊#6923—23no—
298C4⋊#6923—26no—
299C4⋊#6923—23no—
300C4⋊#6923—21no—
301C4⋊#6923—23no—
302C4⋊#6923—23no—
303C4⋊#6923—23no—
304C4⋊#6923C2×D413yes—
305C4⋊#6923C2×D413yes—
306C4⋊#6923C2413yes—
307C4⋊#6923C2411yescharacteristic
308C4⋊#6923C2413yes—
309C4⋊#6923C2411yescharacteristic
310C4×#6923—21no—
311C4×#6923—23no—
312C4×#6923—23no—
313C4×#6923—23no—
314C4×#6923—26no—
315C4×#6923—23no—
316C4×#6923—23no—
317C4×#6923C2×D413yes—
318C4×#6923C2×D413yes—
319C4×#6923C2411yescharacteristic
320C4×#6923C2413yes—
321#11758213—23no—
322D61⋊C8—23no—
323D61⋊C8C2411yescharacteristic
324D61⋊C8C2413yes—
325Q16×C61C22×C413yescomplemented
326SD16×C61C22×C413yescomplemented
327SD16×C61C22×C416yescomplemented
328SD16×C61C22×C411yescharacteristic, complemented
329D8×C61C22×C413yescomplemented
330M16×C61C22×C413yescomplemented
331C2×C8×C61C22×C413yescomplemented
332#11758202C22×C413yescomplemented
333#11758202C22×C413yescomplemented
334#11758201C22×C416yescomplemented
335#11758201C22×C413yescomplemented
336#11758201C22×C411yescharacteristic, complemented
337#11758200C22×C413yescomplemented
338#11758200C22×C416yescomplemented
339#11758200C22×C411yescharacteristic, complemented
340#11758199C22×C413yescomplemented
341#11758199C22×C413yescomplemented
342#11758194C22×C413yescomplemented
343C2×#92418C22×C413yescomplemented
344Dic244C22×C413yescomplemented
345D488C22×C413yescomplemented
346#11758190C22×C416yescomplemented
347#11758190C22×C413yescomplemented
348#11758190C22×C411yescharacteristic, complemented
349#11758189C22×C416yescomplemented
350C8×D61C22×C413yescomplemented
351C8×D61C22×C413yescomplemented
352C8×D61C2411yescharacteristic
353C8×D61C2413yes—
354C23×C61—23no—
355C22×D61—23no—
356C22×D61—21no—
357C22×D61—23no—
358C22×D61—26no—
359C22×D61—83no—
360C22×D61—83no—
361C22×D61C22×D413yes—
362C2×#6923—26no—
363C2×#6923—21no—
364C2×#6923—23no—
365C2×#6923—21no—
366C2×#6923—23no—
367C2×#6923—43no—
368C2×#6923—42no—
369C2×#6923—46no—
370C2×#6923—83no—
371C2×#6923—83no—
372C2×#6923—86no—
373C2×#6923—83no—
374C2×#6923—83no—
375C2×#6923C22×D413yes—
376C2×#6923C22×D413yes—
377C2×#6923C22×D411yescharacteristic
378C2×#6923C22×D411yescharacteristic
379Q8×C61—23no—
380Q8×C61C4×D411yescharacteristic
381Q8×C61C23×C413yes—
382Q8×C61C23×C411yescharacteristic
383D4×C61—23no—
384D4×C61—23no—
385D4×C61—23no—
386D4×C61C4×D413yes—
387D4×C61C23×C411yescharacteristic
388D4×C61C23×C413yes—
389C2×C4×C61—23no—
390C2×C4×C61—23no—
391C2×C4×C61—23no—
392C2×C4×C61C23×C413yes—
393C22⋊D61—23no—
394C22⋊D61—23no—
395C22⋊D61—23no—
396C22⋊D61—23no—
397C22⋊D61—26no—
398C22⋊D61—21no—
399C22⋊D61—23no—
400C22⋊D61C4×D416yes—
401C2×Dic61—23no—
402C2×Dic61—23no—
403C2×Dic61—23no—
404C2×Dic61C2×#4113yes—
405D244—23no—
406D244—23no—
407D244—23no—
408D244C4×D413yes—
409D244C23×C413yes—
410D244C23×C411yescharacteristic
411C4×D61—26no—
412C4×D61—21no—
413C4×D61—23no—
414C4×D61—23no—
415C4×D61—23no—
416C4×D61—23no—
417C4×D61—23no—
418C4×D61C23×C413yes—
419C4×D61C22×D413yes—
420C4×D61C2×#4113yes—
421C4×D61C2511yescharacteristic
422Dic122—23no—
423Dic122—26no—
424Dic122—23no—
425Dic122—21no—
426Dic122C4×D413yes—
427Dic122C23×C413yes—
428Dic122C23×C411yescharacteristic
429#92420—21no—
430#92420—23no—
431C8×C61C23×C411yescharacteristic
432C8×C61C23×C413yes—
433#92418C23×C411yescharacteristic
434#92418C23×C413yes—
435C4×#577—611nomaximal, Sylow
436C22×C61—21no—
437C22×C61—23no—
438C22×C61—83no—
439C22×C61C2×C4×D413yes—
440C2×D61—23no—
441C2×D61—23no—
442C2×D61—21no—
443C2×D61—23no—
444C2×D61—41no—
445C2×D61—43no—
446C2×D61—43no—
447C2×D61—41no—
448C2×D61—86no—
449C2×D61—83no—
450C2×D61C2×C4×D413yes—
451C2×D61C23×D411yescharacteristic
452#6923—21no—
453#6923—23no—
454#6923—23no—
455#6923—43no—
456#6923—41no—
457#6923—41no—
458#6923—43no—
459#6923#57712yesdirect product factor
460C4×C61—23no—
461C4×C61—21no—
462C4×C61C2×C4×D413yes—
463C4×C61C24×C411yescharacteristic
464Dic61—23no—
465Dic61—21no—
466Dic61C2×C4×D413yes—
467Dic61C22×#4111yescharacteristic
468C2×#577—611no—
469C4×2−1+4—611no—
470C4×H(5,𝔽2)—611no—
471#2952—613no—
472#2949—613no—
473#2947—613no—
474#2946—613no—
475C4×#137—613no—
476C4×AGL(1,ℤ/8)—613no—
477C4×#135—613no—
478C2×C4×SD16—613no—
479#2912—611no—
480#2898—611no—
481#2897—611no—
482C4×#131—611no—
483C2×C61—23no—
484C2×C61—43no—
485C2×C61—41no—
486C2×C61C22×C4×D411yescharacteristic
487D61—23no—
488D61—41no—
489D61—43no—
490D61C2×#57711yescharacteristic
491D61#358411yescharacteristic
492C2×2−1+4—611no—
493C2×H(5,𝔽2)—611no—
494#577—611no—
495#577—611no—
496#577—613no—
497#577—613no—
498#577—613no—
499#577—613no—
500#577—611no—
501#577#692311yescharacteristic, direct product factor
502C2×#137—613no—
503C2×AGL(1,ℤ/8)—613no—
504C2×#135—613no—
505C22×SD16—613no—
506C2×#131—611no—
507C2×#131—611no—
508#520—611no—
509#520—611no—
510#520—613no—
511#520—613no—
512#520—1223no—
513#520—1221no—
514#519—613no—
515#519—1221no—
516#518—613no—
517#518—1223no—
518C4×#41—611no—
519C4×#41—613no—
520C4×#41—613no—
521C4×#41—1223no—
522C4×#41—1221no—
523C2×C4×Q8—613no—
524C2×C4×Q8—1221no—
525C2×C4×D4—613no—
526C2×C4×D4—1223no—
527#442—616no—
528#441—616no—
529#440—616no—
530#440—616no—
531C4×Q16—613no—
532C4×Q16—613no—
533C4×SD16—613no—
534C4×SD16—616no—
535C4×SD16—616no—
536C4×SD16—616no—
537C4×SD16—611no—
538C4×SD16—613no—
539C4×SD16—613no—
540C4×D8—613no—
541C4×D8—613no—
542#428—613no—
543#428—613no—
544#427—613no—
545C2×#106—613no—
546#419—613no—
547#418—613no—
548#417—613no—
549#417—613no—
550#416—613no—
551#416—613no—
552C2×#103—613no—
553C2×#102—613no—
554#405—613no—
555#405—613no—
556C4×M16—613no—
557C2×C4×C8—613no—
558C61C4×#57711yescharacteristic, complemented, Sylow
5592−1+4—611no—
5602−1+4—613no—
5612−1+4—613no—
5622−1+4—1221no—
5632−1+4—1223no—
5642−1+4C2×#692311yescharacteristic, complemented
565H(5,𝔽2)—613no—
566H(5,𝔽2)—611no—
567H(5,𝔽2)—613no—
568H(5,𝔽2)—1223no—
569H(5,𝔽2)—1221no—
570H(5,𝔽2)C2×#692311yescharacteristic, complemented
571C2×#41—611no—
572C2×#41—613no—
573C2×#41—613no—
574C2×#41—1223no—
575C2×#41—1221no—
576C22×Q8—613no—
577C22×Q8—1221no—
578C22×D4—613no—
579C22×D4—1223no—
580C23×C4—1223no—
581#137—613no—
582#137—613no—
583#137—616no—
584#137—616no—
585#137—613no—
586#137C2×#692313yescomplemented
587AGL(1,ℤ/8)—613no—
588AGL(1,ℤ/8)—613no—
589AGL(1,ℤ/8)—616no—
590AGL(1,ℤ/8)—616no—
591AGL(1,ℤ/8)—613no—
592AGL(1,ℤ/8)C2×#692313yescomplemented
593#135—613no—
594#135—613no—
595#135—613no—
596#135—613no—
597#135—613no—
598#135—613no—
599#135—613no—
600#135C2×#692313yescomplemented
601C2×Q16—613no—
602C2×SD16—613no—
603C2×SD16—613no—
604C2×SD16—613no—
605C2×SD16—616no—
606C2×SD16—616no—
607C2×SD16—616no—
608C2×SD16—611no—
609C2×SD16—613no—
610C2×SD16C2×#692313yescomplemented
611C2×D8—613no—
612#131—611no—
613#131—613no—
614#131—613no—
615#131—1223no—
616#131—1221no—
617#131C2×#692311yescharacteristic, complemented
618C2×M16—613no—
619C2×M16—613no—
620C22×C8—613no—
621C22×C8—613no—
622C4×Q8—611no—
623C4×Q8—611no—
624C4×Q8—613no—
625C4×Q8—616no—
626C4×Q8—611no—
627C4×Q8—613no—
628C4×Q8—613no—
629C4×Q8—1223no—
630C4×Q8—1223no—
631C4×Q8—1223no—
632C4×Q8—1223no—
633C4×Q8—1221no—
634C4×Q8—1221no—
635C4×D4—613no—
636C4×D4—613no—
637C4×D4—613no—
638C4×D4—616no—
639C4×D4—611no—
640C4×D4—613no—
641C4×D4—613no—
642C4×D4—1223no—
643C4×D4—1223no—
644C4×D4—1226no—
645C4×D4—1226no—
646C4×D4—1223no—
647C4×D4—1223no—
648C4×D4—1223no—
649C4×D4—1223no—
650C4×D4—1223no—
651C4×D4—1223no—
652C4×D4—1223no—
653C4×D4—1223no—
654#117—613no—
655#117—613no—
656#117—613no—
657#117—1223no—
658#117—1223no—
659#117—1226no—
660#117—1223no—
661#117—1223no—
662C2×C4⋊C4—613no—
663C2×C4⋊C4—613no—
664C2×C4⋊C4—1223no—
665C2×C4⋊C4—1223no—
666C2×C4⋊C4—1223no—
667C2×C22⋊C4—1226no—
668C2×C22⋊C4—1223no—
669C2×C42—613no—
670C2×C42—1223no—
671C2×C42—1223no—
672C2×C42—1223no—
673#107—613no—
674#107—613no—
675#106—613no—
676#106—616no—
677#106—611no—
678#103—613no—
679#103—616no—
680#103—611no—
681#103—613no—
682#103—613no—
683#102—613no—
684#102—616no—
685#102—611no—
686#102—613no—
687#102—613no—
688#97—616no—
689C4×C8—611no—
690C4×C8—613no—
691C4×C8—613no—
692C4×C8—613no—
693C24—1223no—
694#41—21no—
695#41—23no—
696#41—611no—
697#41—613no—
698#41—613no—
699#41—613no—
700#41—613no—
701#41—613no—
702#41—613no—
703#41—613no—
704#41—613no—
705#41—1223no—
706#41—1223no—
707#41—1226no—
708#41—1223no—
709#41—1223no—
710#41—1223no—
711#41—1223no—
712#41—1226no—
713#41—1223no—
714#41—1223no—
715#41—1221no—
716#41—1223no—
717#41C22×#692313yes—
718#41C22×#692311yescharacteristic
719#41C22×#692313yescomplemented
720C2×Q8—21no—
721C2×Q8—611no—
722C2×Q8—613no—
723C2×Q8—611no—
724C2×Q8—616no—
725C2×Q8—613no—
726C2×Q8—1223no—
727C2×Q8—1223no—
728C2×Q8—1223no—
729C2×Q8—1223no—
730C2×Q8—1223no—
731C2×Q8—1221no—
732C2×Q8C22×#692313yescomplemented
733C2×D4—23no—
734C2×D4—613no—
735C2×D4—611no—
736C2×D4—613no—
737C2×D4—616no—
738C2×D4—613no—
739C2×D4—1223no—
740C2×D4—1223no—
741C2×D4—1223no—
742C2×D4—1223no—
743C2×D4—1226no—
744C2×D4—1223no—
745C2×D4—1223no—
746C2×D4—1223no—
747C2×D4—1226no—
748C2×D4—1223no—
749C2×D4C22×#692313yes—
750C22×C4—613no—
751C22×C4—613no—
752C22×C4—613no—
753C22×C4—1223no—
754C22×C4—1223no—
755C22×C4—1223no—
756C22×C4—1223no—
757C22×C4—1223no—
758C22×C4—1226no—
759C22×C4—1221no—
760C22×C4—1223no—
761C22×C4—1223no—
762C22×C4—1223no—
763C22×C4—4886no—
764Q16—613no—
765Q16—613no—
766Q16—613no—
767Q16C22×#692313yescomplemented
768SD16—613no—
769SD16—616no—
770SD16—611no—
771SD16—613no—
772SD16—616no—
773SD16—611no—
774SD16—613no—
775SD16—616no—
776SD16—611no—
777SD16C22×#692313yescomplemented
778SD16C22×#692316yescomplemented
779SD16C22×#692311yescharacteristic, complemented
780D8—613no—
781D8—613no—
782D8—613no—
783D8C22×#692313yescomplemented
784M16—613no—
785M16—616no—
786M16—1223no—
787M16—1223no—
788M16C22×#692313yescomplemented
789C2×C8—613no—
790C2×C8—611no—
791C2×C8—613no—
792C2×C8—613no—
793C2×C8—613no—
794C2×C8—611no—
795C2×C8—613no—
796C2×C8—1223no—
797C2×C8—1223no—
798C2×C8C22×#692313yescomplemented
799C4⋊C4—613no—
800C4⋊C4—613no—
801C4⋊C4—613no—
802C4⋊C4—611no—
803C4⋊C4—613no—
804C4⋊C4—611no—
805C4⋊C4—1223no—
806C4⋊C4—1223no—
807C4⋊C4—1223no—
808C4⋊C4—1223no—
809C4⋊C4—1226no—
810C4⋊C4—1221no—
811C4⋊C4—1223no—
812C22⋊C4—616no—
813C22⋊C4—1223no—
814C22⋊C4—1223no—
815C22⋊C4—1226no—
816C22⋊C4—1221no—
817C22⋊C4—1223no—
818C22⋊C4—1223no—
819C22⋊C4—1223no—
820C42—611no—
821C42—613no—
822C42—613no—
823C42—613no—
824C42—1221no—
825C42—1223no—
826C42—1223no—
827C42—1223no—
828C42—1223no—
829C42—1223no—
830C42—1226no—
831C23—23no—
832C23—613no—
833C23—1226no—
834C23—1221no—
835C23—1223no—
836C23—1223no—
837C23—4883no—
838C23—4883no—
839Q8—23no—
840Q8—613no—
841Q8—613no—
842Q8—611no—
843Q8—1226no—
844Q8—1223no—
845Q8—1221no—
846Q8—1223no—
847Q8D4×#692311yescharacteristic
848Q8C23×#692313yes—
849Q8C23×#692311yescharacteristic
850D4—23no—
851D4—23no—
852D4—23no—
853D4—616no—
854D4—613no—
855D4—611no—
856D4—613no—
857D4—1223no—
858D4—1223no—
859D4—1226no—
860D4—1223no—
861D4—1221no—
862D4—1223no—
863D4—1223no—
864D4—1223no—
865D4—1223no—
866D4—1223no—
867D4D4×#692313yes—
868D4C23×#692311yescharacteristic
869D4C23×#692313yes—
870C2×C4—23no—
871C2×C4—23no—
872C2×C4—23no—
873C2×C4—611no—
874C2×C4—613no—
875C2×C4—613no—
876C2×C4—613no—
877C2×C4—613no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—613no—
881C2×C4—613no—
882C2×C4—1223no—
883C2×C4—1223no—
884C2×C4—1221no—
885C2×C4—1223no—
886C2×C4—1226no—
887C2×C4—1223no—
888C2×C4—1223no—
889C2×C4—1226no—
890C2×C4—1223no—
891C2×C4—1223no—
892C2×C4—1223no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1223no—
896C2×C4—1223no—
897C2×C4—4883no—
898C2×C4—4883no—
899C2×C4—4886no—
900C2×C4—4883no—
901C2×C4—4883no—
902C2×C4—2442no—
903C2×C4—2446no—
904C2×C4—2443no—
905C2×C4C23×#692313yes—
906C8—611no—
907C8—613no—
908C8—1221no—
909C8—1223no—
910C8C23×#692311yescharacteristic
911C8C23×#692313yes—
912C22—21no—
913C22—23no—
914C22—83no—
915C22—611no—
916C22—613no—
917C22—1223no—
918C22—1223no—
919C22—1221no—
920C22—1223no—
921C22—4883no—
922C22—4886no—
923C22—2441no—
924C22—2443no—
925C22—2443no—
926C22—2441no—
927C22C2×D4×#692313yes—
928C4—21no—
929C4—23no—
930C4—612no—
931C4—613no—
932C4—611no—
933C4—1223no—
934C4—1223no—
935C4—1221no—
936C4—1221no—
937C4—1223no—
938C4—2443no—
939C4—2441no—
940C4—2443no—
941C4—2441no—
942C4C2×D4×#692313yes—
943C4C24×#692311yescharacteristic
944C2—23no—
945C2—43no—
946C2—41no—
947C2—611no—
948C2—611no—
949C2—1223no—
950C2—2443no—
951C2—2441no—
952C2C22×D4×#692311yescharacteristic
subgroupG/H
centerC2C22×D4×#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC61×#577C4
socleC2×C61C22×C4×D4
prime radical#577×D61C2
cosocleC4×D61C25
hypercenter#577#6923
hypocenterC61C4×#577
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. 2−1+4×#6923C2semidirect
2. H(5,𝔽2)×#6923C2semidirect
3. #21462582C2semidirect
4. #21462579C2semidirect
5. #21462577C2semidirect
6. #21462576C2semidirect
7. #137×#6923C2semidirect
8. AGL(1,ℤ/8)×#6923C2semidirect
9. #135×#6923C2semidirect
10. C2×SD16×#6923C2semidirect
11. #21462473C2semidirect
12. #21462441C2semidirect
13. #21462440C2semidirect
14. #131×#6923C2semidirect
22. #16840831C22semidirect
24. #16840830C22semidirect
31. #41×#6923C22semidirect
33. C2×Q8×#6923C22semidirect
36. #16840803C22semidirect
37. #16840802C22semidirect
38. #16840801C22semidirect
39. #16840801C22semidirect
40. Q16×#6923C22semidirect
41. Q16×#6923C22semidirect
42. SD16×#6923C22semidirect
43. SD16×#6923C22semidirect
44. SD16×#6923C22semidirect
45. SD16×#6923C22semidirect
46. SD16×#6923C22semidirect
47. SD16×#6923C22semidirect
48. SD16×#6923C22semidirect
49. D8×#6923C22semidirect
50. D8×#6923C22semidirect
51. #16840773C22semidirect
52. #16840773C22semidirect
53. #16840772C22semidirect
54. C2×#14519845C22semidirect
55. #16840755C22semidirect
58. #16840753C22semidirect
60. #16840752C22semidirect
61. C2×#14519840C22semidirect
63. #16840728C22semidirect
64. #16840725C22semidirect
65. M16×#6923C22semidirect
66. C2×C8×#6923C22semidirect
69. #16840574C4semidirect
70. #16840573C4semidirect
71. #16840572C4semidirect
72. #16840571C4semidirect
73. #16840570C4semidirect
74. #16840569C4semidirect
75. #16840568C4semidirect
81. C61×#577C4semidirect
159. #14519825C2×C4semidirect
161. #14519824C2×C4semidirect
162. #14519824C2×C4semidirect
164. #14519823C2×C4semidirect
165. #14519823C2×C4semidirect
167. #14519822C2×C4semidirect
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
187. #14519800C2×C4semidirect
188. #14519799C2×C4semidirect
189. #14519798C2×C4semidirect
190. #14519798C2×C4semidirect
191. #14519797C2×C4semidirect
192. #14519797C2×C4semidirect
193. #14519796C2×C4semidirect
195. C2×#11758190C2×C4semidirect
196. C2×#11758200C2×C4semidirect
197. C2×#11758201C2×C4semidirect
198. SD16×D61C2×C4semidirect
199. SD16×D61C2×C4semidirect
204. #14519785C2×C4semidirect
205. #14519784C2×C4semidirect
206. #14519783C2×C4semidirect
209. 2−1+4×C61C2×C4semidirect
210. H(5,𝔽2)×C61C2×C4semidirect
211. #137×C61C2×C4semidirect
212. AGL(1,ℤ/8)×C61C2×C4semidirect
213. #135×C61C2×C4semidirect
214. C2×SD16×C61C2×C4semidirect
215. #131×C61C2×C4semidirect
231. #41×C61C22×C4semidirect
233. C2×Q8×C61C22×C4semidirect
241. #11758226C22×C4semidirect
247. Q8×D61C22×C4semidirect
257. #11758224C22×C4semidirect
277. #11758222C22×C4semidirect
286. C2×Dic122C22×C4semidirect
325. Q16×C61C22×C4semidirect
326. SD16×C61C22×C4semidirect
327. SD16×C61C22×C4semidirect
328. SD16×C61C22×C4semidirect
329. D8×C61C22×C4semidirect
330. M16×C61C22×C4semidirect
331. C2×C8×C61C22×C4semidirect
332. #11758202C22×C4semidirect
333. #11758202C22×C4semidirect
334. #11758201C22×C4semidirect
335. #11758201C22×C4semidirect
336. #11758201C22×C4semidirect
337. #11758200C22×C4semidirect
338. #11758200C22×C4semidirect
339. #11758200C22×C4semidirect
340. #11758199C22×C4semidirect
341. #11758199C22×C4semidirect
342. #11758194C22×C4semidirect
343. C2×#92418C22×C4semidirect
344. Dic244C22×C4semidirect
345. D488C22×C4semidirect
346. #11758190C22×C4semidirect
347. #11758190C22×C4semidirect
348. #11758190C22×C4semidirect
349. #11758189C22×C4semidirect
350. C8×D61C22×C4semidirect
351. C8×D61C22×C4semidirect
459. #6923#577direct (N × H)
501. #577#6923direct (N × H)
558. C61C4×#577semidirect
564. 2−1+4C2×#6923semidirect
570. H(5,𝔽2)C2×#6923semidirect
586. #137C2×#6923semidirect
592. AGL(1,ℤ/8)C2×#6923semidirect
600. #135C2×#6923semidirect
610. C2×SD16C2×#6923semidirect
617. #131C2×#6923semidirect
719. #41C22×#6923semidirect
732. C2×Q8C22×#6923semidirect
767. Q16C22×#6923semidirect
777. SD16C22×#6923semidirect
778. SD16C22×#6923semidirect
779. SD16C22×#6923semidirect
783. D8C22×#6923semidirect
788. M16C22×#6923semidirect
798. C2×C8C22×#6923semidirect

Maximal subgroups

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

subgroupindex
2−1+4×#69232
H(5,𝔽2)×#69232
#214625822
#214625792
#214625772
#214625762
#137×#69232
AGL(1,ℤ/8)×#69232
#135×#69232
C2×SD16×#69232
#214624732
#214624412
#214624402
#131×#69232
#577×D612
C4×#57761