Finite Group Databasebeta

← #30549568

Subgroups — #30549568

Order 15616.

3178 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840577C211yesmaximal, characteristic, complemented
2C2×#16840574C211yesmaximal, characteristic, complemented
3C2×#16840565C211yesmaximal, characteristic, complemented
4#21459613C211yesmaximal, characteristic, complemented
5#21459607C211yesmaximal, characteristic, complemented
6#21456312C213yesmaximal, complemented
7#21456304C213yesmaximal, complemented
8#21456296C213yesmaximal, complemented
9#21456289C213yesmaximal, complemented
10#21456286C213yesmaximal, complemented
11#21456281C213yesmaximal, complemented
12#21456243C213yesmaximal, complemented
13C2×#16840143C213yesmaximal, complemented
14#131×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#577C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17C2×#14519823C2211yescharacteristic
18#16840577—28no—
19#16840574—28no—
20#16840565—28no—
21C2×#14519810C2213yescomplemented
22C2×#14519808C2213yescomplemented
23C2×#14519807C2213yescomplemented
24C2×#14519805C2213yescomplemented
25C2×#14519803C2213yes—
26C2×#14519802C2213yes—
27C2×#14519799C2213yescomplemented
28C2×#14519797C2213yes—
29C2×#14519797C2213yescomplemented
30C22×#11758202C2213yescomplemented
31C22×#11758190C2213yescomplemented
32C22×#11758199C2213yes—
33C2×#14519784C2211yescharacteristic
34#16840423—22no—
35#16840419—22no—
36#16840406—26no—
37#16840400—26no—
38#16840336C2213yescomplemented
39#16840333C2213yescomplemented
40#16840329C2213yescomplemented
41#16840326C2213yescomplemented
42#16840308C2213yescomplemented
43#16840308C2213yescomplemented
44C2×#14519766C2213yescomplemented
45C2×#14519764C2213yescomplemented
46#41×Dic61C2211yescharacteristic
47#16840155C2216yescomplemented
48#16840153C2216yescomplemented
49#16840150C2216yescomplemented
50#16840148C2216yescomplemented
51#16840147C2213yescomplemented
52#16840145C2213yescomplemented
53#16840143C2213yescomplemented
54#16840143C2216yescomplemented
55#16840143C2216yescomplemented
56#16840143C2216yescomplemented
57#16840143C2211yescharacteristic, complemented
58#16840140C2213yescomplemented
59#16840137C2213yescomplemented
60#16840133C2213yescomplemented
61#16840133C2213yescomplemented
62#16839720C2213yescomplemented
63#16839717C2213yescomplemented
64M16×Dic61C2213yescomplemented
65C2×C8×Dic61C2213yescomplemented
66C2×2−1+4×C61C2211yescharacteristic
67C2×H(5,𝔽2)×C61C2211yescharacteristic
68C61×#577—28no—
69C2×#137×C61C2213yescomplemented
70C2×AGL(1,ℤ/8)×C61C2213yescomplemented
71C2×#135×C61C2213yescomplemented
72C22×SD16×C61C2213yescomplemented
73C2×#131×C61C2211yescharacteristic
74#14519824—24no—
75#14519824—24no—
76#14519823—24no—
77#14519823—24no—
78C2×#11758226—21no—
79C2×#11758222C2313yes—
80C2×#11758222C2313yes—
81C2×#11758224—23no—
82C22×Dic122C2313yes—
83C2×Q8×D61—21no—
84C22×D244C2313yes—
85C2×D4×D61—23no—
86#14519810—212no—
87#14519808—212no—
88#14519807—212no—
89#14519805—212no—
90#14519803—212no—
91#14519802—212no—
92#14519799—212no—
93#14519797—212no—
94#14519797—212no—
95C2×Dic244C2313yes—
96C2×#11758202—212no—
97C2×#11758202C2313yes—
98C2×#11758202C2316yes—
99C2×#11758202C2311yescharacteristic
100C2×#11758190—212no—
101C2×#11758190C2313yes—
102C2×#11758190C2316yes—
103C2×#11758190C2311yescharacteristic
104C2×#11758200C2313yes—
105C2×#11758200C2313yes—
106C2×#11758201C2313yes—
107C2×#11758201C2313yes—
108C2×D488C2313yes—
109C2×#11758199—212no—
110C2×#11758199C2313yes—
111C2×#11758199C2316yes—
112C2×#11758199C2311yescharacteristic
113#14519784D418yescomplemented
114C2×#11758194C2313yes—
115C22×#92418C2313yes—
116#14519775C2313yes—
117#14519775C2313yes—
118#14519773C2313yes—
119#14519773C2313yes—
120#14519766—26no—
121#14519766C2313yes—
122#14519766C2316yes—
123#14519766C2311yescharacteristic
124#14519764—26no—
125#14519764C2313yes—
126#14519764C2316yes—
127#14519764C2311yescharacteristic
128#14519760—26no—
129#14519758—26no—
130#14519756—26no—
131#14519753—26no—
132#14519751—26no—
133#14519749—26no—
134#14519749—26no—
135#14519748—26no—
136#14519746—26no—
137#14519745—26no—
138Q8×Dic61D412yes—
139D4×Dic61D416yes—
140C4×C22⋊D61—26no—
141C4×C22⋊D61—26no—
142#14519736C2313yes—
143C2×C22⋊Dic61—26no—
144C2×#11758198—26no—
145C2×C4×Dic61C2313yes—
146#14519687C2316yes—
147C8×Dic61C2311yescharacteristic
148C8×Dic61C2313yes—
149C8×Dic61C2313yes—
150C8×Dic61C2313yes—
1512−1+4×C61—24no—
1522−1+4×C61—24no—
153H(5,𝔽2)×C61—24no—
154H(5,𝔽2)×C61—24no—
155C2×#41×C61—21no—
156C2×#41×C61—23no—
157C2×#41×C61C2313yes—
158C2×#41×C61C2313yes—
159C2×#41×C61C2311yescharacteristic
160C22×Q8×C61—21no—
161C22×Q8×C61C2313yes—
162C22×D4×C61—23no—
163C22×D4×C61C2313yes—
164#137×C61—212no—
165AGL(1,ℤ/8)×C61—212no—
166#135×C61—212no—
167C2×Q16×C61C2313yes—
168C2×SD16×C61—212no—
169C2×SD16×C61C2313yes—
170C2×SD16×C61C2316yes—
171C2×SD16×C61C2311yescharacteristic
172C2×D8×C61C2313yes—
173#131×C61D418yescomplemented
174C2×M16×C61C2313yes—
175C22×C8×C61C2313yes—
176C24×C61—23no—
177C23×D61—23no—
178#41×C61—26no—
179#41×C61—26no—
180#41×C61—26no—
181#41×C61—26no—
182#41×C61—44no—
183#41×C61—412no—
184#41×C61C2×D414yes—
185#41×C61C2×D414yes—
186C2×Q8×C61—23no—
187C2×Q8×C61—26no—
188C2×Q8×C61—26no—
189C2×Q8×C61—44no—
190C2×Q8×C61C2×D411yescharacteristic
191C2×Q8×C61C2413yes—
192C2×Q8×C61C2411yescharacteristic
193C2×D4×C61—23no—
194C2×D4×C61—23no—
195C2×D4×C61—26no—
196C2×D4×C61—26no—
197C2×D4×C61—23no—
198C2×D4×C61—412no—
199C2×D4×C61C2×D413yes—
200C2×D4×C61C2411yescharacteristic
201C2×D4×C61C2413yes—
202C22×C4×C61—23no—
203C22×C4×C61—23no—
204C22×C4×C61—23no—
205C22×C4×C61C2413yes—
206C2×C22⋊D61—23no—
207C2×C22⋊D61—23no—
208C2×C22⋊D61—26no—
209C2×C22⋊D61—26no—
210C22×Dic61—23no—
211C22×Dic61C2×D416yes—
212#11758226—44no—
213Q8×D61—44no—
214#11758224—412no—
215D4×D61—412no—
216#11758222—26no—
217#11758222—26no—
218#11758222—26no—
219#11758222—26no—
220C2×D244—26no—
221C2×D244—26no—
222C2×D244—23no—
223C2×D244C2413yes—
224C2×D244C2411yescharacteristic
225C2×C4×D61—23no—
226C2×C4×D61—23no—
227C2×Dic122—26no—
228C2×Dic122—26no—
229C2×Dic122—23no—
230C2×Dic122C2413yes—
231C2×Dic122C2411yescharacteristic
232Q16×C61—26no—
233SD16×C61—26no—
234SD16×C61—212no—
235SD16×C61—22no—
236D8×C61—26no—
237M16×C61C2×D4112yes—
238C2×C8×C61C2×D4112yes—
239C2×C8×C61C2411yescharacteristic
240C2×C8×C61C2413yes—
241C22⋊Dic61—26no—
242C22⋊Dic61—212no—
243C22⋊Dic61—22no—
244C22⋊Dic61C2×D416yes—
245#11758202—212no—
246#11758202—26no—
247#11758202—22no—
248#11758201—26no—
249#11758201—26no—
250#11758200—26no—
251#11758200—26no—
252#11758199—26no—
253#11758199—212no—
254#11758199—22no—
255#11758198—26no—
256#11758198—212no—
257#11758198—22no—
258C4⋊Dic61C2×D416yes—
259#11758196—26no—
260#11758196—26no—
261C4×Dic61C2×D416yes—
262C4×Dic61C2411yescharacteristic
263C4×Dic61C2413yes—
264#11758194C2×D4112yes—
265C2×#92418C2×D4112yes—
266C2×#92418C2411yescharacteristic
267C2×#92418C2413yes—
268Dic244—26no—
269D488—26no—
270#11758190—212no—
271#11758190—26no—
272#11758190—22no—
273C23×C61—23no—
274C23×C61—21no—
275C23×C61—46no—
276C23×C61—86no—
277C23×C61C22×D413yes—
278C22×D61—23no—
279C22×D61—21no—
280C22×D61—46no—
281C22×D61—86no—
282Q8×C61—21no—
283Q8×C61—23no—
284Q8×C61—23no—
285Q8×C61—21no—
286Q8×C61—46no—
287Q8×C61#12714yes—
288D4×C61—23no—
289D4×C61—21no—
290D4×C61—21no—
291D4×C61—23no—
292D4×C61—46no—
293D4×C61—46no—
294D4×C61—46no—
295D4×C61#127112yes—
296C2×C4×C61—21no—
297C2×C4×C61—23no—
298C2×C4×C61—46no—
299C2×C4×C61—46no—
300C2×C4×C61—46no—
301C2×C4×C61C22×D413yes—
302C2×C4×C61C22×D416yes—
303C2×C4×C61C22×D416yes—
304C2×C4×C61C2511yescharacteristic
305C22⋊D61—46no—
306C22⋊D61—46no—
307C22⋊D61—86no—
308C22⋊D61—86no—
309C2×Dic61—21no—
310C2×Dic61—23no—
311C2×Dic61—46no—
312C2×Dic61—46no—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D416yes—
315D244—23no—
316D244—21no—
317D244—23no—
318D244—21no—
319D244—46no—
320C4×D61—46no—
321C4×D61—46no—
322Dic122—23no—
323Dic122—21no—
324Dic122—21no—
325Dic122—23no—
326Dic122—46no—
327C8×C61C22×D412yes—
328C8×C61C22×D416yes—
329#92418C22×D412yes—
330#92418C22×D416yes—
331#60649—611nomaximal, Sylow
332C22×C61—26no—
333C22×C61—42no—
334C22×C61—46no—
335C22×C61—41no—
336C22×C61—43no—
337C22×C61—166no—
338C22×C61C2×#12716yes—
339C22×C61C23×D411yescharacteristic
340C2×D61—42no—
341C2×D61—46no—
342C2×D61—41no—
343C2×D61—43no—
344C2×D61—166no—
345C4×C61—41no—
346C4×C61—43no—
347C4×C61C2×#12716yes—
348C4×C61C23×D411yescharacteristic
349C4×C61C23×D411yescharacteristic
350Dic61—22no—
351Dic61—26no—
352Dic61—43no—
353Dic61—41no—
354C2×#578—611no—
355C2×#577—611no—
356C2×#577D6111yescharacteristic, complemented
357C2×#576—611no—
358#3500—611no—
359#3500—611no—
360#3156—613no—
361#3155—613no—
362#3154—613no—
363#3154—613no—
364#3153—613no—
365#3153—613no—
366#3147—613no—
367C2×#495—613no—
368C4×#131—611no—
369C2×C61—26no—
370C2×C61—81no—
371C2×C61—83no—
372C2×C61C22×#12711yescharacteristic
373C2×C61#358412yes—
374D61—81no—
375D61—83no—
376C2×2−1+4—611no—
377C2×2−1+4C2×D6111yescharacteristic
378C2×H(5,𝔽2)—611no—
379C2×H(5,𝔽2)C2×D6111yescharacteristic
380#578—1228no—
381#577—28no—
382#577—1228no—
383#576—1228no—
384C2×#137—613no—
385C2×#137—613no—
386C2×#137—613no—
387C2×#137C2×D6113yescomplemented
388C2×AGL(1,ℤ/8)—613no—
389C2×AGL(1,ℤ/8)—613no—
390C2×AGL(1,ℤ/8)—613no—
391C2×AGL(1,ℤ/8)C2×D6113yescomplemented
392C2×#135—613no—
393C2×#135—613no—
394C2×#135—613no—
395C2×#135C2×D6113yescomplemented
396C22×Q16—613no—
397C22×SD16—613no—
398C22×SD16C2×D6113yescomplemented
399C22×D8—613no—
400C2×#131—611no—
401C2×#131C2×D6111yescharacteristic
402#548—1222no—
403#548—1222no—
404#546—1226no—
405#546—1226no—
406#536—613no—
407#536—613no—
408#535—613no—
409#535—613no—
410#532—613no—
411#532—613no—
412C2×#124—613no—
413C2×#124—613no—
414C4×#41—611no—
415#497—616no—
416#497—616no—
417#496—616no—
418#496—616no—
419#495—613no—
420#495—613no—
421#495—616no—
422#495—616no—
423#495—616no—
424#495—611no—
425#495—613no—
426#494—613no—
427#493—613no—
428#492—613no—
429#492—613no—
430#405—613no—
431#405—613no—
432C4×M16—613no—
433C2×C4×C8—613no—
434C61#6064911yescharacteristic, complemented, Sylow
4352−1+4—24no—
4362−1+4—24no—
4372−1+4—1224no—
4382−1+4—1224no—
439H(5,𝔽2)—24no—
440H(5,𝔽2)—24no—
441H(5,𝔽2)—1224no—
442H(5,𝔽2)—1224no—
443C2×#41—21no—
444C2×#41—23no—
445C2×#41—613no—
446C2×#41—613no—
447C2×#41—1221no—
448C2×#41—1223no—
449C2×#41C22×D6113yes—
450C2×#41C22×D6113yes—
451C2×#41C22×D6111yescharacteristic
452C22×Q8—21no—
453C22×Q8—613no—
454C22×Q8—1221no—
455C22×Q8C22×D6113yes—
456C22×D4—23no—
457C22×D4—613no—
458C22×D4—1223no—
459C22×D4C22×D6113yes—
460#137—212no—
461#137—12212no—
462#137—12212no—
463#137—12212no—
464AGL(1,ℤ/8)—212no—
465AGL(1,ℤ/8)—12212no—
466AGL(1,ℤ/8)—12212no—
467AGL(1,ℤ/8)—12212no—
468#135—212no—
469#135—12212no—
470#135—12212no—
471#135—12212no—
472C2×Q16—613no—
473C2×Q16—616no—
474C2×Q16—611no—
475C2×Q16—613no—
476C2×Q16—12212no—
477C2×Q16C22×D6113yes—
478C2×SD16—212no—
479C2×SD16—613no—
480C2×SD16—613no—
481C2×SD16—613no—
482C2×SD16—613no—
483C2×SD16—613no—
484C2×SD16—616no—
485C2×SD16—611no—
486C2×SD16—12212no—
487C2×SD16C22×D6113yes—
488C2×SD16C22×D6116yes—
489C2×SD16C22×D6111yescharacteristic
490C2×D8—613no—
491C2×D8—616no—
492C2×D8—611no—
493C2×D8—613no—
494C2×D8—12212no—
495C2×D8C22×D6113yes—
496#131—618no—
497#131C22⋊D6118yescomplemented
498C2×M16—613no—
499C2×M16C22×D6113yes—
500C22×C8—613no—
501C22×C8C22×D6113yes—
502C4⋊Q8—613no—
503C4⋊Q8—613no—
504#127—613no—
505#127—613no—
506#124—613no—
507#124—616no—
508#124—611no—
509#124—613no—
510#124—616no—
511#124—611no—
512#124—1226no—
513#124—1226no—
514#123—1226no—
515#123—1226no—
516C22⋊Q8—1226no—
517C22⋊Q8—1226no—
518#121—1226no—
519#121—1226no—
520#121—1226no—
521#121—1226no—
522#120—1226no—
523#120—1226no—
524C4×Q8—612no—
525C4×D4—616no—
526C4×D4—1226no—
527C4×D4—1226no—
528#117—613no—
529C2×C22⋊C4—1226no—
530C2×C22⋊C4—1226no—
531C2×C42—613no—
532#97—616no—
533C4×C8—611no—
534C4×C8—613no—
535C4×C8—613no—
536C4×C8—613no—
537C24—23no—
538C24—1223no—
539#41—26no—
540#41—26no—
541#41—26no—
542#41—26no—
543#41—44no—
544#41—412no—
545#41—1226no—
546#41—1226no—
547#41—1226no—
548#41—1226no—
549#41—2444no—
550#41—24412no—
551#41D4×D6114yes—
552#41C2×C22⋊D6114yes—
553C2×Q8—23no—
554C2×Q8—26no—
555C2×Q8—26no—
556C2×Q8—44no—
557C2×Q8—613no—
558C2×Q8—611no—
559C2×Q8—1223no—
560C2×Q8—1226no—
561C2×Q8—1226no—
562C2×Q8—2444no—
563C2×Q8D4×D6111yescharacteristic
564C2×Q8C23×D6113yes—
565C2×Q8C23×D6111yescharacteristic
566C2×D4—23no—
567C2×D4—23no—
568C2×D4—26no—
569C2×D4—23no—
570C2×D4—26no—
571C2×D4—412no—
572C2×D4—613no—
573C2×D4—611no—
574C2×D4—1226no—
575C2×D4—1226no—
576C2×D4—1223no—
577C2×D4—1223no—
578C2×D4—1226no—
579C2×D4—1223no—
580C2×D4—1226no—
581C2×D4—24412no—
582C2×D4D4×D6113yes—
583C2×D4C23×D6113yes—
584C2×D4C23×D6111yescharacteristic
585C22×C4—23no—
586C22×C4—23no—
587C22×C4—23no—
588C22×C4—616no—
589C22×C4—1223no—
590C22×C4—1223no—
591C22×C4—1223no—
592C22×C4C23×D6113yes—
593Q16—26no—
594Q16—1226no—
595Q16—12212no—
596Q16—1222no—
597Q16—1226no—
598SD16—26no—
599SD16—212no—
600SD16—22no—
601SD16—1226no—
602SD16—1226no—
603SD16—1226no—
604SD16—1226no—
605SD16—1226no—
606SD16—12212no—
607SD16—1222no—
608D8—26no—
609D8—1226no—
610D8—12212no—
611D8—1222no—
612D8—1226no—
613M16—6112no—
614M16C2×C22⋊D61112yes—
615C2×C8—6112no—
616C2×C8—611no—
617C2×C8—613no—
618C2×C8C2×C22⋊D61112yes—
619C2×C8C23×D6111yescharacteristic
620C2×C8C23×D6113yes—
621C4⋊C4—616no—
622C4⋊C4—1226no—
623C4⋊C4—1226no—
624C22⋊C4—616no—
625C22⋊C4—1226no—
626C22⋊C4—12212no—
627C22⋊C4—1222no—
628C22⋊C4—1226no—
629C22⋊C4—12212no—
630C22⋊C4—1222no—
631C42—616no—
632C42—611no—
633C42—613no—
634C23—23no—
635C23—21no—
636C23—46no—
637C23—86no—
638C23—1223no—
639C23—1221no—
640C23—4886no—
641C23—2446no—
642C23C2×D4×D6113yes—
643Q8—21no—
644Q8—23no—
645Q8—23no—
646Q8—21no—
647Q8—46no—
648Q8—1221no—
649Q8—1223no—
650Q8—1223no—
651Q8—1221no—
652Q8—2446no—
653Q8#1451977314yes—
654D4—23no—
655D4—21no—
656D4—21no—
657D4—23no—
658D4—46no—
659D4—46no—
660D4—46no—
661D4—1223no—
662D4—1221no—
663D4—1221no—
664D4—1223no—
665D4—4886no—
666D4—4886no—
667D4—2446no—
668D4—2446no—
669D4—2446no—
670D4#14519773112yes—
671C2×C4—23no—
672C2×C4—21no—
673C2×C4—46no—
674C2×C4—46no—
675C2×C4—46no—
676C2×C4—612no—
677C2×C4—616no—
678C2×C4—1223no—
679C2×C4—1221no—
680C2×C4—2446no—
681C2×C4—2446no—
682C2×C4—2446no—
683C2×C4—2446no—
684C2×C4C2×D4×D6113yes—
685C2×C4C2×D4×D6116yes—
686C2×C4C22×C22⋊D6116yes—
687C2×C4C24×D6111yescharacteristic
688C8—612no—
689C8—616no—
690C8C22×C22⋊D6112yes—
691C8C22×C22⋊D6116yes—
692C22—26no—
693C22—42no—
694C22—46no—
695C22—41no—
696C22—43no—
697C22—166no—
698C22—9766no—
699C22—2442no—
700C22—2446no—
701C22—2441no—
702C22—2443no—
703C22C2×#1451977316yes—
704C22C22×D4×D6111yescharacteristic
705C4—41no—
706C4—43no—
707C4—1222no—
708C4—1226no—
709C4—2441no—
710C4—2443no—
711C4C2×#1451977316yes—
712C4C22×D4×D6111yescharacteristic
713C4C23×C22⋊D6111yescharacteristic
714C2—26no—
715C2—83no—
716C2—81no—
717C2—4883no—
718C2—4881no—
719C2C22×#1451977311yescharacteristic
720C2#2146059112yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#577C2
socleC22×C61C23×D4
hypercenterC2×#577D61
hypocenterC61#60649
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#16840577C2semidirect
2. C2×#16840574C2semidirect
3. C2×#16840565C2semidirect
4. #21459613C2semidirect
5. #21459607C2semidirect
6. #21456312C2semidirect
7. #21456304C2semidirect
8. #21456296C2semidirect
9. #21456289C2semidirect
10. #21456286C2semidirect
11. #21456281C2semidirect
12. #21456243C2semidirect
13. C2×#16840143C2semidirect
14. #131×Dic61C2semidirect
15. C2×C61×#577C2semidirect
21. C2×#14519810C22semidirect
22. C2×#14519808C22semidirect
23. C2×#14519807C22semidirect
24. C2×#14519805C22semidirect
27. C2×#14519799C22semidirect
29. C2×#14519797C22semidirect
30. C22×#11758202C22semidirect
31. C22×#11758190C22semidirect
38. #16840336C22semidirect
39. #16840333C22semidirect
40. #16840329C22semidirect
41. #16840326C22semidirect
42. #16840308C22semidirect
43. #16840308C22semidirect
44. C2×#14519766C22semidirect
45. C2×#14519764C22semidirect
47. #16840155C22semidirect
48. #16840153C22semidirect
49. #16840150C22semidirect
50. #16840148C22semidirect
51. #16840147C22semidirect
52. #16840145C22semidirect
53. #16840143C22semidirect
54. #16840143C22semidirect
55. #16840143C22semidirect
56. #16840143C22semidirect
57. #16840143C22semidirect
58. #16840140C22semidirect
59. #16840137C22semidirect
60. #16840133C22semidirect
61. #16840133C22semidirect
62. #16839720C22semidirect
63. #16839717C22semidirect
64. M16×Dic61C22semidirect
65. C2×C8×Dic61C22semidirect
69. C2×#137×C61C22semidirect
70. C2×AGL(1,ℤ/8)×C61C22semidirect
71. C2×#135×C61C22semidirect
72. C22×SD16×C61C22semidirect
113. #14519784D4semidirect
173. #131×C61D4semidirect
356. C2×#577D61semidirect
387. C2×#137C2×D61semidirect
391. C2×AGL(1,ℤ/8)C2×D61semidirect
395. C2×#135C2×D61semidirect
398. C22×SD16C2×D61semidirect
434. C61#60649semidirect
497. #131C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405772
C2×#168405742
C2×#168405652
#214596132
#214596072
#214563122
#214563042
#214562962
#214562892
#214562862
#214562812
#214562432
C2×#168401432
#131×Dic612
C2×C61×#5772
#6064961