Finite Group Databasebeta

← #30549545

Subgroups — #30549545

Order 15616.

3250 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840574C211yesmaximal, characteristic, complemented
2C2×#16840573C211yesmaximal, characteristic, complemented
3C2×#16840570C211yesmaximal, characteristic, complemented
4#21459600C211yesmaximal, characteristic, complemented
5#21459593C211yesmaximal, characteristic, complemented
6#21456298C213yesmaximal, complemented
7#21456296C213yesmaximal, complemented
8#21456293C213yesmaximal, complemented
9#21456289C213yesmaximal, complemented
10#21456274C213yesmaximal, complemented
11#21456267C213yesmaximal, complemented
12#21456243C213yesmaximal, complemented
13C2×#16840133C213yesmaximal, complemented
14#131×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#577C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17C2×#14519823C2211yescharacteristic
18#16840574—28no—
19#16840573—28no—
20#16840570—28no—
21C2×#14519810C2213yescomplemented
22C2×#14519808C2213yescomplemented
23C2×#14519807C2213yescomplemented
24C2×#14519805C2213yescomplemented
25C2×#14519803C2213yescomplemented
26C2×#14519802C2213yescomplemented
27C2×#14519799C2213yescomplemented
28C2×#14519797C2213yescomplemented
29C2×#14519797C2213yescomplemented
30C22×#11758190C2213yescomplemented
31C22×#11758200C2213yescomplemented
32C22×#11758201C2213yescomplemented
33C2×#14519784C2211yescharacteristic
34#16840431—22no—
35Q8×C22⋊D61—22no—
36#16840411—26no—
37D4×C22⋊D61—26no—
38#16840336C2213yescomplemented
39#16840333C2213yescomplemented
40#16840329C2213yes—
41#16840326C2213yes—
42#16840308C2213yes—
43#16840308C2213yescomplemented
44C2×#14519775C2213yescomplemented
45C2×#14519773C2213yes—
46#41×Dic61C2211yescharacteristic
47#16840155C2216yescomplemented
48#16840153C2216yescomplemented
49#16840150C2216yescomplemented
50#16840148C2216yescomplemented
51#16840147C2213yescomplemented
52#16840145C2213yescomplemented
53#16840143C2213yescomplemented
54#16840143C2213yescomplemented
55#16840140C2213yescomplemented
56#16840137C2213yescomplemented
57#16840133C2213yescomplemented
58#16840133C2216yescomplemented
59#16840133C2216yescomplemented
60#16840133C2216yescomplemented
61#16840133C2211yescharacteristic, complemented
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—
85C22×C22⋊D61—26no—
86C2×D4×D61—23no—
87#14519810—212no—
88#14519808—212no—
89#14519807—212no—
90#14519805—212no—
91#14519803—212no—
92#14519802—212no—
93#14519799—212no—
94#14519797—212no—
95#14519797—212no—
96C2×Dic244C2313yes—
97C2×#11758202C2313yes—
98C2×#11758202C2313yes—
99C2×#11758190—212no—
100C2×#11758190C2313yes—
101C2×#11758190C2316yes—
102C2×#11758190C2311yescharacteristic
103C2×#11758200—212no—
104C2×#11758200C2313yes—
105C2×#11758200C2316yes—
106C2×#11758200C2311yescharacteristic
107C2×#11758201—212no—
108C2×#11758201C2313yes—
109C2×#11758201C2316yes—
110C2×#11758201C2311yescharacteristic
111C2×D488C2313yes—
112C2×#11758199C2313yes—
113C2×#11758199C2313yes—
114#14519784D418yescomplemented
115C2×#11758194C2313yes—
116C22×#92418C2313yes—
117#14519775—26no—
118#14519775C2313yes—
119#14519775C2316yes—
120#14519775C2311yescharacteristic
121#14519773—26no—
122#14519773C2313yes—
123#14519773C2316yes—
124#14519773C2311yescharacteristic
125#14519766C2313yes—
126#14519766C2313yes—
127#14519764C2313yes—
128#14519764C2313yes—
129#14519760—26no—
130#14519758—26no—
131#14519756—26no—
132#14519753—26no—
133#14519751—26no—
134#14519749—26no—
135#14519749—26no—
136#14519748—26no—
137#14519746—26no—
138#14519745—26no—
139Q8×Dic61D412yes—
140D4×Dic61D416yes—
141C4×C22⋊D61—26no—
142C4×C22⋊D61—26no—
143#14519736C2313yes—
144C2×#11758196—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—22no—
210C2×C22⋊D61—212no—
211C2×C22⋊D61—812no—
212C22×Dic61—23no—
213C22×Dic61C2×D416yes—
214#11758226—44no—
215Q8×D61—44no—
216#11758224—412no—
217D4×D61—412no—
218#11758222—26no—
219#11758222—26no—
220#11758222—26no—
221#11758222—26no—
222C2×D244—26no—
223C2×D244—26no—
224C2×D244—23no—
225C2×D244C2413yes—
226C2×D244C2411yescharacteristic
227C2×C4×D61—23no—
228C2×C4×D61—23no—
229C2×Dic122—26no—
230C2×Dic122—26no—
231C2×Dic122—23no—
232C2×Dic122C2413yes—
233C2×Dic122C2411yescharacteristic
234Q16×C61—26no—
235SD16×C61—26no—
236SD16×C61—212no—
237SD16×C61—22no—
238D8×C61—26no—
239M16×C61C2×D4112yescomplemented
240C2×C8×C61C2×D4112yescomplemented
241C2×C8×C61C2411yescharacteristic
242C2×C8×C61C2413yes—
243C22⋊Dic61—26no—
244C22⋊Dic61—26no—
245C22⋊Dic61C2×D416yes—
246#11758202—26no—
247#11758202—26no—
248#11758201—212no—
249#11758201—26no—
250#11758201—22no—
251#11758200—26no—
252#11758200—212no—
253#11758200—22no—
254#11758199—26no—
255#11758199—26no—
256#11758198—26no—
257#11758198—26no—
258C4⋊Dic61C2×D416yes—
259#11758196—26no—
260#11758196—212no—
261#11758196—22no—
262C4×Dic61C2×D416yes—
263C4×Dic61C2411yescharacteristic
264C4×Dic61C2413yes—
265#11758194C2×D4112yescomplemented
266C2×#92418C2×D4112yescomplemented
267C2×#92418C2411yescharacteristic
268C2×#92418C2413yes—
269Dic244—26no—
270D488—26no—
271#11758190—212no—
272#11758190—26no—
273#11758190—22no—
274C23×C61—21no—
275C23×C61—23no—
276C23×C61—46no—
277C23×C61—86no—
278C23×C61C22×D413yes—
279C22×D61—21no—
280C22×D61—23no—
281C22×D61—46no—
282C22×D61—86no—
283Q8×C61—23no—
284Q8×C61—21no—
285Q8×C61—23no—
286Q8×C61—21no—
287Q8×C61—46no—
288Q8×C61#12714yes—
289D4×C61—21no—
290D4×C61—23no—
291D4×C61—21no—
292D4×C61—23no—
293D4×C61—46no—
294D4×C61—46no—
295D4×C61—46no—
296D4×C61#127112yes—
297C2×C4×C61—23no—
298C2×C4×C61—21no—
299C2×C4×C61—46no—
300C2×C4×C61—46no—
301C2×C4×C61—46no—
302C2×C4×C61C22×D413yes—
303C2×C4×C61C22×D416yes—
304C2×C4×C61C22×D416yes—
305C2×C4×C61C2511yescharacteristic
306C22⋊D61—46no—
307C22⋊D61—46no—
308C22⋊D61—44no—
309C22⋊D61—412no—
310C22⋊D61—812no—
311C2×Dic61—212no—
312C2×Dic61—23no—
313C2×Dic61—21no—
314C2×Dic61—46no—
315C2×Dic61C22×D416yes—
316C2×Dic61C22×D412yes—
317D244—23no—
318D244—21no—
319D244—21no—
320D244—23no—
321D244—46no—
322C4×D61—46no—
323C4×D61—46no—
324Dic122—23no—
325Dic122—21no—
326Dic122—23no—
327Dic122—21no—
328Dic122—46no—
329C8×C61C22×D412yes—
330C8×C61C22×D416yes—
331#92418C22×D412yes—
332#92418C22×D416yes—
333#60646—611nomaximal, Sylow
334C22×C61—26no—
335C22×C61—41no—
336C22×C61—43no—
337C22×C61—46no—
338C22×C61—42no—
339C22×C61—166no—
340C22×C61C2×#12716yes—
341C22×C61C23×D411yescharacteristic
342C2×D61—41no—
343C2×D61—43no—
344C2×D61—46no—
345C2×D61—42no—
346C2×D61—166no—
347C4×C61—41no—
348C4×C61—43no—
349C4×C61C2×#12716yes—
350C4×C61C23×D411yescharacteristic
351C4×C61C23×D411yescharacteristic
352Dic61—26no—
353Dic61—43no—
354Dic61—41no—
355Dic61#57714yescomplemented
356C2×#577—611no—
357C2×#577—611no—
358C2×#577—611no—
359C2×#577D6111yescharacteristic, complemented
360#3499—611no—
361#3498—611no—
362#3154—613no—
363#3154—613no—
364#3154—613no—
365#3154—613no—
366#3152—613no—
367#3151—613no—
368#3147—613no—
369C2×#492—613no—
370C4×#131—611no—
371C2×C61—26no—
372C2×C61—81no—
373C2×C61—83no—
374C2×C61C22×#12711yescharacteristic
375C2×C61C2×#57712yes—
376D61—81no—
377D61—83no—
378C2×2−1+4—611no—
379C2×2−1+4C2×D6111yescharacteristic
380C2×H(5,𝔽2)—611no—
381C2×H(5,𝔽2)C2×D6111yescharacteristic
382#577—28no—
383#577—1228no—
384#577—1228no—
385#577—1228no—
386C2×#137—613no—
387C2×#137—613no—
388C2×#137—613no—
389C2×#137C2×D6113yescomplemented
390C2×AGL(1,ℤ/8)—613no—
391C2×AGL(1,ℤ/8)—613no—
392C2×AGL(1,ℤ/8)—613no—
393C2×AGL(1,ℤ/8)C2×D6113yescomplemented
394C2×#135—613no—
395C2×#135—613no—
396C2×#135—613no—
397C2×#135C2×D6113yescomplemented
398C22×SD16—613no—
399C22×SD16—613no—
400C22×SD16—613no—
401C22×SD16C2×D6113yescomplemented
402C2×#131—611no—
403C2×#131C2×D6111yescharacteristic
404#550—1222no—
405D4×Q8—1222no—
406#547—1226no—
407D42—1226no—
408#536—613no—
409#536—613no—
410#535—613no—
411#535—613no—
412#532—613no—
413#532—613no—
414C2×C4⋊Q8—613no—
415C2×#127—613no—
416C4×#41—611no—
417#497—616no—
418#497—616no—
419#496—616no—
420#496—616no—
421#495—613no—
422#495—613no—
423#495—613no—
424#495—613no—
425#494—613no—
426#493—613no—
427#492—613no—
428#492—616no—
429#492—616no—
430#492—616no—
431#492—611no—
432#405—613no—
433#405—613no—
434C4×M16—613no—
435C2×C4×C8—613no—
436C61#6064611yescharacteristic, complemented, Sylow
4372−1+4—24no—
4382−1+4—24no—
4392−1+4—1224no—
4402−1+4—1224no—
441H(5,𝔽2)—24no—
442H(5,𝔽2)—24no—
443H(5,𝔽2)—1224no—
444H(5,𝔽2)—1224no—
445C2×#41—21no—
446C2×#41—23no—
447C2×#41—613no—
448C2×#41—613no—
449C2×#41—1221no—
450C2×#41—1223no—
451C2×#41C22×D6113yes—
452C2×#41C22×D6113yes—
453C2×#41C22×D6111yescharacteristic
454C22×Q8—21no—
455C22×Q8—613no—
456C22×Q8—1221no—
457C22×Q8C22×D6113yes—
458C22×D4—23no—
459C22×D4—613no—
460C22×D4—1226no—
461C22×D4—1223no—
462C22×D4C22×D6113yes—
463#137—212no—
464#137—12212no—
465#137—12212no—
466#137—12212no—
467AGL(1,ℤ/8)—212no—
468AGL(1,ℤ/8)—12212no—
469AGL(1,ℤ/8)—12212no—
470AGL(1,ℤ/8)—12212no—
471#135—212no—
472#135—12212no—
473#135—12212no—
474#135—12212no—
475C2×Q16—613no—
476C2×Q16—613no—
477C2×Q16—613no—
478C2×Q16C22×D6113yes—
479C2×SD16—212no—
480C2×SD16—613no—
481C2×SD16—616no—
482C2×SD16—611no—
483C2×SD16—613no—
484C2×SD16—616no—
485C2×SD16—611no—
486C2×SD16—613no—
487C2×SD16—616no—
488C2×SD16—611no—
489C2×SD16—12212no—
490C2×SD16—12212no—
491C2×SD16—12212no—
492C2×SD16C22×D6113yes—
493C2×SD16C22×D6116yes—
494C2×SD16C22×D6111yescharacteristic
495C2×D8—613no—
496C2×D8—613no—
497C2×D8—613no—
498C2×D8C22×D6113yes—
499#131—618no—
500#131C22⋊D6118yescomplemented
501C2×M16—613no—
502C2×M16C22×D6113yes—
503C22×C8—613no—
504C22×C8C22×D6113yes—
505C4⋊Q8—613no—
506C4⋊Q8—616no—
507C4⋊Q8—611no—
508C4⋊Q8—1226no—
509#127—613no—
510#127—616no—
511#127—611no—
512#127—1226no—
513#124—613no—
514#124—613no—
515#124—613no—
516#124—613no—
517#123—1226no—
518#123—1226no—
519C22⋊Q8—1226no—
520C22⋊Q8—1226no—
521#121—1226no—
522#121—1226no—
523#121—1226no—
524#121—1226no—
525#120—1226no—
526#120—1226no—
527C4×Q8—612no—
528C4×D4—616no—
529C4×D4—1226no—
530C4×D4—1226no—
531#117—613no—
532C2×C4⋊C4—1226no—
533C2×C42—613no—
534#97—616no—
535C4×C8—611no—
536C4×C8—613no—
537C4×C8—613no—
538C4×C8—613no—
539C24—23no—
540C24—1223no—
541#41—26no—
542#41—26no—
543#41—26no—
544#41—26no—
545#41—44no—
546#41—412no—
547#41—1226no—
548#41—1226no—
549#41—1226no—
550#41—1226no—
551#41—2444no—
552#41—24412no—
553#41D4×D6114yes—
554#41C2×C22⋊D6114yes—
555C2×Q8—23no—
556C2×Q8—26no—
557C2×Q8—26no—
558C2×Q8—44no—
559C2×Q8—611no—
560C2×Q8—613no—
561C2×Q8—1223no—
562C2×Q8—1226no—
563C2×Q8—1226no—
564C2×Q8—2444no—
565C2×Q8D4×D6111yescharacteristic
566C2×Q8C23×D6111yescharacteristic
567C2×Q8C23×D6113yes—
568C2×D4—23no—
569C2×D4—23no—
570C2×D4—26no—
571C2×D4—23no—
572C2×D4—26no—
573C2×D4—412no—
574C2×D4—611no—
575C2×D4—613no—
576C2×D4—12212no—
577C2×D4—1222no—
578C2×D4—1226no—
579C2×D4—1223no—
580C2×D4—1223no—
581C2×D4—1226no—
582C2×D4—1223no—
583C2×D4—1226no—
584C2×D4—48812no—
585C2×D4—24412no—
586C2×D4D4×D6113yes—
587C2×D4C23×D6111yescharacteristic
588C2×D4C23×D6113yes—
589C22×C4—23no—
590C22×C4—23no—
591C22×C4—23no—
592C22×C4—616no—
593C22×C4—1223no—
594C22×C4—1223no—
595C22×C4—1223no—
596C22×C4C23×D6113yes—
597Q16—26no—
598Q16—1226no—
599Q16—1226no—
600Q16—1226no—
601SD16—26no—
602SD16—212no—
603SD16—22no—
604SD16—1226no—
605SD16—12212no—
606SD16—1222no—
607SD16—1226no—
608SD16—12212no—
609SD16—1222no—
610SD16—1226no—
611SD16—12212no—
612SD16—1222no—
613D8—26no—
614D8—1226no—
615D8—1226no—
616D8—1226no—
617M16—6112no—
618M16C2×C22⋊D61112yescomplemented
619C2×C8—6112no—
620C2×C8—611no—
621C2×C8—613no—
622C2×C8C2×C22⋊D61112yescomplemented
623C2×C8C23×D6111yescharacteristic
624C2×C8C23×D6113yes—
625C4⋊C4—616no—
626C4⋊C4—1226no—
627C4⋊C4—12212no—
628C4⋊C4—1222no—
629C22⋊C4—616no—
630C22⋊C4—1226no—
631C22⋊C4—1226no—
632C22⋊C4—1226no—
633C22⋊C4—1226no—
634C42—616no—
635C42—611no—
636C42—613no—
637C23—21no—
638C23—23no—
639C23—46no—
640C23—86no—
641C23—1221no—
642C23—1223no—
643C23—4886no—
644C23—2446no—
645C23C2×D4×D6113yes—
646Q8—23no—
647Q8—21no—
648Q8—23no—
649Q8—21no—
650Q8—46no—
651Q8—1223no—
652Q8—1221no—
653Q8—1223no—
654Q8—1221no—
655Q8—2446no—
656Q8#1451977314yes—
657D4—21no—
658D4—23no—
659D4—21no—
660D4—23no—
661D4—46no—
662D4—46no—
663D4—46no—
664D4—1221no—
665D4—1223no—
666D4—1221no—
667D4—1223no—
668D4—48812no—
669D4—2444no—
670D4—24412no—
671D4—2446no—
672D4—2446no—
673D4—2446no—
674D4#14519773112yes—
675C2×C4—21no—
676C2×C4—23no—
677C2×C4—46no—
678C2×C4—46no—
679C2×C4—46no—
680C2×C4—612no—
681C2×C4—616no—
682C2×C4—12212no—
683C2×C4—1221no—
684C2×C4—1223no—
685C2×C4—2446no—
686C2×C4—2446no—
687C2×C4—2446no—
688C2×C4C2×D4×D6113yes—
689C2×C4C2×D4×D6116yes—
690C2×C4C22×C22⋊D6116yes—
691C2×C4C24×D6111yescharacteristic
692C8—612no—
693C8—616no—
694C8C22×C22⋊D6112yes—
695C8C22×C22⋊D6116yes—
696C22—26no—
697C22—46no—
698C22—42no—
699C22—41no—
700C22—43no—
701C22—166no—
702C22—9766no—
703C22—2446no—
704C22—2442no—
705C22—2441no—
706C22—2443no—
707C22C2×#1451977316yes—
708C22C22×D4×D6111yescharacteristic
709C4—41no—
710C4—43no—
711C4—614no—
712C4—1226no—
713C4—2441no—
714C4—2443no—
715C4C2×#1451977316yes—
716C4C22×D4×D6111yescharacteristic
717C4C23×C22⋊D6111yescharacteristic
718C2—26no—
719C2—83no—
720C2—81no—
721C2—4883no—
722C2—4881no—
723C2C22×#1451977311yescharacteristic
724C2#577×D6112yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#577C2
socleC22×C61C23×D4
hypercenterC2×#577D61
hypocenterC61#60646
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×#16840574C2semidirect
2. C2×#16840573C2semidirect
3. C2×#16840570C2semidirect
4. #21459600C2semidirect
5. #21459593C2semidirect
6. #21456298C2semidirect
7. #21456296C2semidirect
8. #21456293C2semidirect
9. #21456289C2semidirect
10. #21456274C2semidirect
11. #21456267C2semidirect
12. #21456243C2semidirect
13. C2×#16840133C2semidirect
14. #131×Dic61C2semidirect
15. C2×C61×#577C2semidirect
21. C2×#14519810C22semidirect
22. C2×#14519808C22semidirect
23. C2×#14519807C22semidirect
24. C2×#14519805C22semidirect
25. C2×#14519803C22semidirect
26. C2×#14519802C22semidirect
27. C2×#14519799C22semidirect
28. C2×#14519797C22semidirect
29. C2×#14519797C22semidirect
30. C22×#11758190C22semidirect
31. C22×#11758200C22semidirect
32. C22×#11758201C22semidirect
38. #16840336C22semidirect
39. #16840333C22semidirect
43. #16840308C22semidirect
44. C2×#14519775C22semidirect
47. #16840155C22semidirect
48. #16840153C22semidirect
49. #16840150C22semidirect
50. #16840148C22semidirect
51. #16840147C22semidirect
52. #16840145C22semidirect
53. #16840143C22semidirect
54. #16840143C22semidirect
55. #16840140C22semidirect
56. #16840137C22semidirect
57. #16840133C22semidirect
58. #16840133C22semidirect
59. #16840133C22semidirect
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
114. #14519784D4semidirect
173. #131×C61D4semidirect
239. M16×C61C2×D4semidirect
240. C2×C8×C61C2×D4semidirect
265. #11758194C2×D4semidirect
266. C2×#92418C2×D4semidirect
355. Dic61#577semidirect
359. C2×#577D61semidirect
389. C2×#137C2×D61semidirect
393. C2×AGL(1,ℤ/8)C2×D61semidirect
397. C2×#135C2×D61semidirect
401. C22×SD16C2×D61semidirect
436. C61#60646semidirect
500. #131C22⋊D61semidirect
618. M16C2×C22⋊D61semidirect
622. C2×C8C2×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405742
C2×#168405732
C2×#168405702
#214596002
#214595932
#214562982
#214562962
#214562932
#214562892
#214562742
#214562672
#214562432
C2×#168401332
#131×Dic612
C2×C61×#5772
#6064661