Finite Group Databasebeta

← #30547052

Subgroups — #30547052

Order 15616.

2762 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840573C211yesmaximal, characteristic, complemented
2C2×#16840565C211yesmaximal, characteristic, complemented
3#21459612C211yesmaximal, characteristic, complemented
4#21455369C213yesmaximal, complemented
5#21455358C213yesmaximal, complemented
6#21455331C213yesmaximal, complemented
7#21455322C213yesmaximal, complemented
8#21455313C213yesmaximal, complemented
9#21455283C213yesmaximal, complemented
10#21455274C213yesmaximal, complemented
11C2×#16839977C213yesmaximal, complemented
12#21454387C211yesmaximal, characteristic, complemented
13#21454349C211yesmaximal, characteristic, complemented
14#21454342C211yesmaximal, characteristic, complemented
15C4×H(5,𝔽2)×C61C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17C2×#14519823C2211yescharacteristic
18#16840573—28no—
19#16840565—28no—
20C2×#14519807C2213yescomplemented
21C2×#14519803C2213yes—
22C2×#14519803C2213yescomplemented
23C2×#14519802C2213yes—
24C2×#14519797C2213yes—
25C2×#14519797C2213yescomplemented
26C22×#11758200C2213yescomplemented
27C22×#11758199C2213yes—
28C2×#14519784C2211yescharacteristic
29C2×#14519784C2211yescharacteristic
30#16840424—21no—
31#16840424—21no—
32#16840407—23no—
33#16840407—23no—
34#16840338C2213yescomplemented
35#16840331C2213yescomplemented
36#16840312C2213yescomplemented
37C2×#14519765C2213yescomplemented
38#16839984C2216yescomplemented
39#16839984C2211yescharacteristic, complemented
40#16839984C2213yescomplemented
41#16839977C2216yescomplemented
42#16839977C2213yescomplemented
43#16839977C2216yescomplemented
44#16839977C2216yescomplemented
45#16839977C2213yescomplemented
46#16839977C2216yescomplemented
47#16839972C2213yescomplemented
48#16839967C2216yescomplemented
49#16839967C2213yescomplemented
50#16839962C2213yescomplemented
51#16839957C2213yescomplemented
52#16839957C2216yescomplemented
53#16839789C2213yescomplemented
54#16839789C2213yescomplemented
55#16839786C2213yescomplemented
56C2×C4⋊#92418C2213yescomplemented
57#16839770C2213yescomplemented
58#16839766C2213yescomplemented
59#16839761C2213yescomplemented
60#16839761C2213yescomplemented
61#16839756C2213yescomplemented
62#16839756C2213yescomplemented
63C2×#14519700C2213yescomplemented
64C2×#14519697C2213yescomplemented
65C2×H(5,𝔽2)×C61C2211yescharacteristic
66C61×#520—21no—
67C61×#520C2211yescharacteristic
68C61×#520C2213yescomplemented
69C61×#518—23no—
70C61×#518C2213yescomplemented
71C4×#41×C61—21no—
72C4×#41×C61C2211yescharacteristic
73C4×#41×C61C2213yescomplemented
74C2×C4×D4×C61—23no—
75C2×C4×D4×C61C2213yescomplemented
76#14519824—24no—
77#14519824—24no—
78#14519823—24no—
79#14519823—24no—
80C2×#11758226—21no—
81C2×#11758222C2313yes—
82C2×#11758222C2313yes—
83C2×#11758224—23no—
84C22×Dic122C2313yes—
85C2×Q8×D61—21no—
86C22×D244C2313yes—
87C2×D4×D61—23no—
88#14519807—212no—
89#14519803—212no—
90#14519803—212no—
91#14519802—212no—
92#14519797—212no—
93#14519797—212no—
94C2×#11758202C2311yescharacteristic
95C2×#11758202C2313yes—
96C2×#11758200—212no—
97C2×#11758200C2313yes—
98C2×#11758200C2313yes—
99C2×#11758200C2316yes—
100C2×#11758201C2311yescharacteristic
101C2×#11758201C2313yes—
102C2×#11758199—212no—
103C2×#11758199C2313yes—
104C2×#11758199C2313yes—
105C2×#11758199C2316yes—
106#14519784—24no—
107#14519784—24no—
108C2×#11758194C2313yes—
109C2×#11758194C2313yes—
110C22×#92418C2313yes—
111C22×#92418C2313yes—
112#14519777C2313yes—
113#14519774C2313yes—
114#14519765—23no—
115#14519765—23no—
116#14519765C2313yes—
117#14519765C2316yes—
118#14519765C2311yescharacteristic
119#14519761—26no—
120#14519757—23no—
121#14519757—23no—
122#14519752—23no—
123#14519752—23no—
124#14519751—23no—
125#14519751—23no—
126#14519747—26no—
127C4×D244—23no—
128C4×D244—23no—
129C2×#11758198—23no—
130C2×#11758198—23no—
131C4⋊#92418C2316yes—
132C4⋊#92418C2313yes—
133C4⋊#92418C2313yes—
134C4⋊#92418C2311yescharacteristic
135C4⋊#92418C2313yes—
136#14519700C2311yescharacteristic
137#14519700C2313yes—
138#14519700C2316yes—
139#14519700C2313yes—
140#14519700C2313yes—
141#14519697C2311yescharacteristic
142#14519697C2313yes—
143#14519697C2316yes—
144#14519697C2313yes—
145#14519697C2313yes—
146H(5,𝔽2)×C61—24no—
147H(5,𝔽2)×C61D418yescomplemented
148C2×#41×C61—21no—
149C2×#41×C61C2313yes—
150C2×#41×C61C2311yescharacteristic
151C22×D4×C61—23no—
152C22×D4×C61C2313yes—
153C23×C4×C61—23no—
154C4×Q8×C61—21no—
155C4×Q8×C61D411yescharacteristic
156C4×Q8×C61D411yescharacteristic
157C4×Q8×C61C2313yes—
158C4×Q8×C61C2311yescharacteristic
159C4×D4×C61—23no—
160C4×D4×C61—23no—
161C4×D4×C61—23no—
162C4×D4×C61—23no—
163C4×D4×C61—23no—
164C4×D4×C61—26no—
165C4×D4×C61—23no—
166C4×D4×C61—23no—
167C4×D4×C61D413yes—
168C4×D4×C61D413yes—
169C4×D4×C61C2316yes—
170C4×D4×C61C2313yes—
171C4×D4×C61C2313yes—
172#117×C61—23no—
173#117×C61—23no—
174#117×C61C2313yes—
175#117×C61C2313yes—
176C2×C4⋊C4×C61—23no—
177C2×C4⋊C4×C61C2313yes—
178C2×C22⋊C4×C61—23no—
179C2×C22⋊C4×C61—26no—
180C2×C42×C61—23no—
181C2×C42×C61C2313yes—
182C24×C61—23no—
183C23×D61—23no—
184#41×C61—28no—
185#41×C61—26no—
186#41×C61C2×D4112yes—
187#41×C61C2×D414yes—
188#41×C61#4114yes—
189C2×Q8×C61C2×D411yescharacteristic
190C2×Q8×C61C2411yescharacteristic
191C2×D4×C61—23no—
192C2×D4×C61—224no—
193C2×D4×C61—23no—
194C2×D4×C61—26no—
195C2×D4×C61C2×D4112yes—
196C2×D4×C61C2×D413yes—
197C2×D4×C61C2413yes—
198C22×C4×C61—23no—
199C22×C4×C61—23no—
200C22×C4×C61—23no—
201C22×C4×C61—23no—
202C22×C4×C61—26no—
203C22×C4×C61—86no—
204C22×C4×C61C2×D413yes—
205C22×C4×C61C2×D413yes—
206C22×C4×C61C2413yes—
207C2×C22⋊D61—23no—
208C2×C22⋊D61—23no—
209C22×Dic61—23no—
210#11758226—44no—
211Q8×D61—44no—
212#11758224—412no—
213D4×D61—412no—
214#11758222—26no—
215#11758222—26no—
216#11758222—26no—
217#11758222—26no—
218C2×D244—26no—
219C2×D244—26no—
220C2×D244—23no—
221C2×D244—23no—
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
232C4⋊C4×C61—23no—
233C4⋊C4×C61—23no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2×D413yes—
236C4⋊C4×C61C2×D413yes—
237C4⋊C4×C61C2413yes—
238C4⋊C4×C61C2411yescharacteristic
239C22⋊C4×C61—23no—
240C22⋊C4×C61—23no—
241C22⋊C4×C61—26no—
242C22⋊C4×C61—23no—
243C22⋊C4×C61C2×D416yes—
244C42×C61—21no—
245C42×C61—23no—
246C42×C61—23no—
247C42×C61C2×D413yes—
248C42×C61C2×D413yes—
249C42×C61C2411yescharacteristic
250C42×C61C2413yes—
251#11758202—22no—
252#11758202—26no—
253#11758201—22no—
254#11758201—26no—
255#11758200—26no—
256#11758200—212no—
257#11758200—26no—
258#11758199—26no—
259#11758199—212no—
260#11758199—26no—
261#11758198—23no—
262#11758198—23no—
263#11758198—26no—
264#11758198—26no—
265#11758198—21no—
266#11758198—21no—
267C4⋊Dic61—23no—
268C4⋊Dic61—23no—
269#11758194—26no—
270#11758194—26no—
271C2×#92418—26no—
272C2×#92418—26no—
273C2×#92418C2411yescharacteristic
274C2×#92418C2413yes—
275C2×#92418C2411yescharacteristic
276C2×#92418C2413yes—
277C23×C61—23no—
278C23×C61—212no—
279C23×C61—83no—
280C23×C61—83no—
281C23×C61C22×D413yes—
282C22×D61—23no—
283C22×D61—21no—
284C22×D61—46no—
285C22×D61—83no—
286C22×D61—83no—
287Q8×C61—21no—
288Q8×C61#12114yes—
289Q8×C61C22×D412yes—
290D4×C61—212no—
291D4×C61—212no—
292D4×C61—23no—
293D4×C61#121112yes—
294D4×C61C22×D416yes—
295C2×C4×C61—21no—
296C2×C4×C61—212no—
297C2×C4×C61—21no—
298C2×C4×C61—23no—
299C2×C4×C61—43no—
300C2×C4×C61—43no—
301C2×C4×C61—46no—
302C2×C4×C61—83no—
303C2×C4×C61—86no—
304C2×C4×C61—83no—
305C2×C4×C61C22×D413yes—
306C2×C4×C61C22×D413yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D413yes—
310C2×C4×C61C22×D416yes—
311C2×C4×C61C2×#4116yes—
312C2×C4×C61C2511yescharacteristic
313C22⋊D61—46no—
314C22⋊D61—46no—
315C2×Dic61—21no—
316C2×Dic61—23no—
317C2×Dic61—46no—
318D244—23no—
319D244—21no—
320D244—23no—
321D244—21no—
322D244—46no—
323D244—83no—
324D244—83no—
325C4×D61—46no—
326C4×D61—46no—
327Dic122—23no—
328Dic122—21no—
329Dic122—23no—
330Dic122—21no—
331Dic122—46no—
332#92418—21no—
333#92418—21no—
334#92418—23no—
335#92418—23no—
336#60430—611nomaximal, Sylow
337C22×C61—23no—
338C22×C61—23no—
339C22×C61—26no—
340C22×C61—43no—
341C22×C61—43no—
342C22×C61—812no—
343C22×C61C2×#12116yes—
344C22×C61C23×D411yescharacteristic
345C2×D61—41no—
346C2×D61—43no—
347C2×D61—41no—
348C2×D61—43no—
349C2×D61—41no—
350C2×D61—43no—
351C2×D61—166no—
352C4×C61—23no—
353C4×C61—21no—
354C4×C61—23no—
355C4×C61—21no—
356C4×C61—22no—
357C4×C61—41no—
358C4×C61—43no—
359C4×C61C2×#12116yes—
360C4×C61C23×D411yescharacteristic
361C4×C61C22×#4111yescharacteristic
362Dic61—43no—
363Dic61—41no—
364C2×#577—611no—
365C2×#576—611no—
366#3500—611no—
367C4×H(5,𝔽2)D6111yescharacteristic, complemented
368#3046—613no—
369#3045—613no—
370#3042—613no—
371#3041—613no—
372#3040—613no—
373#3036—613no—
374#3035—613no—
375C2×#463—613no—
376#2906—611no—
377#2898—611no—
378#2897—611no—
379C2×C61—26no—
380C2×C61—46no—
381C2×C61C22×#12111yescharacteristic
382C2×C61#358411yescharacteristic
383C2×C61#358511yescharacteristic
384D61—81no—
385D61—83no—
386C2×2−1+4—611no—
387C2×H(5,𝔽2)—611no—
388C2×H(5,𝔽2)C2×D6111yescharacteristic
389#577—1228no—
390#576—1228no—
391C2×#137—613no—
392C2×AGL(1,ℤ/8)—613no—
393C2×AGL(1,ℤ/8)—613no—
394C2×AGL(1,ℤ/8)—613no—
395C2×#135—613no—
396C2×#135—613no—
397C22×SD16—613no—
398C22×D8—613no—
399C2×#131—611no—
400C2×#131—611no—
401#548—1221no—
402#548—1221no—
403#546—1223no—
404#546—1223no—
405#536—613no—
406#535—613no—
407#532—613no—
408C2×#124—613no—
409#520—21no—
410#520C2×D6111yescharacteristic
411#520C2×D6113yescomplemented
412#518—23no—
413#518C2×D6113yescomplemented
414C4×#41—21no—
415C4×#41C2×D6111yescharacteristic
416C4×#41C2×D6113yescomplemented
417C2×C4×D4—23no—
418C2×C4×D4C2×D6113yescomplemented
419#464—611no—
420#464—613no—
421#464—616no—
422#463—613no—
423#463—616no—
424#463—616no—
425#463—616no—
426#463—613no—
427#463—616no—
428#462—613no—
429#461—613no—
430#461—616no—
431#460—613no—
432#459—613no—
433#459—616no—
434#424—613no—
435#424—613no—
436#423—613no—
437C2×C4⋊C8—613no—
438#419—613no—
439#418—613no—
440#417—613no—
441#417—613no—
442#416—613no—
443#416—613no—
444C2×#103—613no—
445C2×#102—613no—
446C61#6043011yescharacteristic, complemented, Sylow
4472−1+4—1224no—
4482−1+4—1224no—
449H(5,𝔽2)—24no—
450H(5,𝔽2)—1224no—
451H(5,𝔽2)—1224no—
452H(5,𝔽2)D24418yescomplemented
453C2×#41—21no—
454C2×#41—613no—
455C2×#41—613no—
456C2×#41—1221no—
457C2×#41—1223no—
458C2×#41C22×D6113yes—
459C2×#41C22×D6111yescharacteristic
460C22×Q8—613no—
461C22×Q8—1221no—
462C22×D4—23no—
463C22×D4—613no—
464C22×D4—1223no—
465C22×D4C22×D6113yes—
466C23×C4—23no—
467#137—12212no—
468AGL(1,ℤ/8)—12212no—
469AGL(1,ℤ/8)—12212no—
470AGL(1,ℤ/8)—12212no—
471#135—12212no—
472#135—12212no—
473C2×Q16—611no—
474C2×Q16—613no—
475C2×SD16—611no—
476C2×SD16—613no—
477C2×SD16—613no—
478C2×SD16—616no—
479C2×SD16—613no—
480C2×SD16—12212no—
481C2×D8—613no—
482C2×D8—616no—
483C2×D8—613no—
484C2×D8—12212no—
485#131—1224no—
486#131—1224no—
487C2×M16—613no—
488C2×M16—613no—
489C22×C8—613no—
490C22×C8—613no—
491C4⋊Q8—613no—
492#127—613no—
493#124—613no—
494#124—616no—
495#124—611no—
496#124—1223no—
497#124—1223no—
498#123—1226no—
499C22⋊Q8—1223no—
500C22⋊Q8—1223no—
501#121—1223no—
502#121—1223no—
503#121—1223no—
504#121—1223no—
505#120—1226no—
506C4×Q8—21no—
507C4×Q8C22⋊D6111yescharacteristic
508C4×Q8C22⋊D6111yescharacteristic
509C4×Q8C22×D6111yescharacteristic
510C4×Q8C22×D6113yes—
511C4×D4—23no—
512C4×D4—23no—
513C4×D4—23no—
514C4×D4—23no—
515C4×D4—23no—
516C4×D4—26no—
517C4×D4—23no—
518C4×D4—23no—
519C4×D4—1223no—
520C4×D4—1223no—
521C4×D4C22⋊D6113yes—
522C4×D4C22⋊D6113yes—
523C4×D4C22×D6113yes—
524C4×D4C22×D6116yes—
525C4×D4C22×D6113yes—
526#117—23no—
527#117—23no—
528#117C22×D6113yes—
529#117C22×D6113yes—
530C2×C4⋊C4—23no—
531C2×C4⋊C4C22×D6113yes—
532C2×C22⋊C4—23no—
533C2×C22⋊C4—26no—
534C2×C22⋊C4—1223no—
535C2×C22⋊C4—1223no—
536C2×C42—23no—
537C2×C42C22×D6113yes—
538C4⋊C8—611no—
539C4⋊C8—613no—
540C4⋊C8—613no—
541C4⋊C8—613no—
542C4⋊C8—616no—
543#103—613no—
544#103—616no—
545#103—611no—
546#103—613no—
547#103—613no—
548#102—613no—
549#102—616no—
550#102—611no—
551#102—613no—
552#102—613no—
553C24—23no—
554C24—1223no—
555#41—28no—
556#41—26no—
557#41—1226no—
558#41—1226no—
559#41—1226no—
560#41—1226no—
561#41—2444no—
562#41—24412no—
563#41C2×D244112yes—
564#41C2×D24414yes—
565#41#1175822214yes—
566C2×Q8—613no—
567C2×Q8—611no—
568C2×Q8—1223no—
569C2×Q8—1226no—
570C2×Q8—1226no—
571C2×Q8—2444no—
572C2×Q8C2×C22⋊D6111yescharacteristic
573C2×Q8C23×D6111yescharacteristic
574C2×D4—23no—
575C2×D4—224no—
576C2×D4—23no—
577C2×D4—26no—
578C2×D4—613no—
579C2×D4—611no—
580C2×D4—1223no—
581C2×D4—1223no—
582C2×D4—1223no—
583C2×D4—1223no—
584C2×D4—1223no—
585C2×D4—1226no—
586C2×D4—1226no—
587C2×D4—24412no—
588C2×D4C2×D244112yes—
589C2×D4C2×C22⋊D6113yes—
590C2×D4C23×D6113yes—
591C22×C4—23no—
592C22×C4—23no—
593C22×C4—23no—
594C22×C4—23no—
595C22×C4—26no—
596C22×C4—86no—
597C22×C4—1223no—
598C22×C4—1223no—
599C22×C4—1223no—
600C22×C4C2×C22⋊D6113yes—
601C22×C4C2×C22⋊D6113yes—
602C22×C4C23×D6113yes—
603Q16—1222no—
604Q16—1226no—
605SD16—1222no—
606SD16—1226no—
607SD16—1226no—
608SD16—12212no—
609SD16—1226no—
610D8—1226no—
611D8—12212no—
612D8—1226no—
613M16—1226no—
614M16—1226no—
615C2×C8—611no—
616C2×C8—613no—
617C2×C8—611no—
618C2×C8—613no—
619C2×C8—1226no—
620C2×C8—1226no—
621C4⋊C4—23no—
622C4⋊C4—23no—
623C4⋊C4—21no—
624C4⋊C4—1223no—
625C4⋊C4—1223no—
626C4⋊C4C2×C22⋊D6113yes—
627C4⋊C4C2×C22⋊D6113yes—
628C4⋊C4C23×D6113yes—
629C4⋊C4C23×D6111yescharacteristic
630C22⋊C4—23no—
631C22⋊C4—23no—
632C22⋊C4—26no—
633C22⋊C4—23no—
634C22⋊C4—1223no—
635C22⋊C4—1223no—
636C22⋊C4—1226no—
637C22⋊C4—1226no—
638C22⋊C4—1221no—
639C22⋊C4—1221no—
640C22⋊C4C2×C22⋊D6116yes—
641C42—21no—
642C42—23no—
643C42—23no—
644C42C2×C22⋊D6113yes—
645C42C2×C22⋊D6113yes—
646C42C23×D6111yescharacteristic
647C42C23×D6113yes—
648C23—23no—
649C23—212no—
650C23—83no—
651C23—83no—
652C23—1223no—
653C23—1221no—
654C23—4883no—
655C23—4883no—
656C23—2446no—
657C23C22×C22⋊D6113yes—
658Q8—21no—
659Q8—1223no—
660Q8—1221no—
661Q8—1223no—
662Q8—1221no—
663Q8—2446no—
664Q8#1451975114yes—
665Q8C22×D24412yes—
666D4—212no—
667D4—212no—
668D4—23no—
669D4—1223no—
670D4—1221no—
671D4—1223no—
672D4—1221no—
673D4—4883no—
674D4—4883no—
675D4—2446no—
676D4—2446no—
677D4—2446no—
678D4#14519751112yes—
679D4C22×D24416yes—
680C2×C4—21no—
681C2×C4—212no—
682C2×C4—21no—
683C2×C4—23no—
684C2×C4—43no—
685C2×C4—43no—
686C2×C4—46no—
687C2×C4—83no—
688C2×C4—86no—
689C2×C4—83no—
690C2×C4—1223no—
691C2×C4—1221no—
692C2×C4—2446no—
693C2×C4—2446no—
694C2×C4—2446no—
695C2×C4C22×C22⋊D6111yescharacteristic
696C2×C4C22×C22⋊D6113yes—
697C2×C4C22×C22⋊D6111yescharacteristic
698C2×C4C22×C22⋊D6113yes—
699C2×C4C22×C22⋊D6113yes—
700C2×C4C22×D24416yes—
701C2×C4C2×#1175822216yes—
702C2×C4C24×D6111yescharacteristic
703C8—1221no—
704C8—1221no—
705C8—1223no—
706C8—1223no—
707C22—23no—
708C22—23no—
709C22—26no—
710C22—43no—
711C22—43no—
712C22—812no—
713C22—9766no—
714C22—2441no—
715C22—2443no—
716C22—2441no—
717C22—2443no—
718C22—2441no—
719C22—2443no—
720C22C2×#1451975116yes—
721C22C23×C22⋊D6111yescharacteristic
722C4—22no—
723C4—21no—
724C4—23no—
725C4—21no—
726C4—23no—
727C4—41no—
728C4—43no—
729C4—2441no—
730C4—2443no—
731C4C2×#1451975116yes—
732C4C23×D24411yescharacteristic
733C4C22×#1175822211yescharacteristic
734C2—26no—
735C2—46no—
736C2—4883no—
737C2—4881no—
738C2C22×#1451975111yescharacteristic
739C2#2146059011yescharacteristic
740C2#2146059911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC4×H(5,𝔽2)×C61C2
socleC22×C61C23×D4
hypercenterC4×H(5,𝔽2)D61
hypocenterC61#60430
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#16840573C2semidirect
2. C2×#16840565C2semidirect
3. #21459612C2semidirect
4. #21455369C2semidirect
5. #21455358C2semidirect
6. #21455331C2semidirect
7. #21455322C2semidirect
8. #21455313C2semidirect
9. #21455283C2semidirect
10. #21455274C2semidirect
11. C2×#16839977C2semidirect
12. #21454387C2semidirect
13. #21454349C2semidirect
14. #21454342C2semidirect
15. C4×H(5,𝔽2)×C61C2semidirect
20. C2×#14519807C22semidirect
22. C2×#14519803C22semidirect
25. C2×#14519797C22semidirect
26. C22×#11758200C22semidirect
34. #16840338C22semidirect
35. #16840331C22semidirect
36. #16840312C22semidirect
37. C2×#14519765C22semidirect
38. #16839984C22semidirect
39. #16839984C22semidirect
40. #16839984C22semidirect
41. #16839977C22semidirect
42. #16839977C22semidirect
43. #16839977C22semidirect
44. #16839977C22semidirect
45. #16839977C22semidirect
46. #16839977C22semidirect
47. #16839972C22semidirect
48. #16839967C22semidirect
49. #16839967C22semidirect
50. #16839962C22semidirect
51. #16839957C22semidirect
52. #16839957C22semidirect
53. #16839789C22semidirect
54. #16839789C22semidirect
55. #16839786C22semidirect
56. C2×C4⋊#92418C22semidirect
57. #16839770C22semidirect
58. #16839766C22semidirect
59. #16839761C22semidirect
60. #16839761C22semidirect
61. #16839756C22semidirect
62. #16839756C22semidirect
63. C2×#14519700C22semidirect
64. C2×#14519697C22semidirect
68. C61×#520C22semidirect
70. C61×#518C22semidirect
73. C4×#41×C61C22semidirect
75. C2×C4×D4×C61C22semidirect
147. H(5,𝔽2)×C61D4semidirect
367. C4×H(5,𝔽2)D61semidirect
411. #520C2×D61semidirect
413. #518C2×D61semidirect
416. C4×#41C2×D61semidirect
418. C2×C4×D4C2×D61semidirect
446. C61#60430semidirect
452. H(5,𝔽2)D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168405732
C2×#168405652
#214596122
#214553692
#214553582
#214553312
#214553222
#214553132
#214552832
#214552742
C2×#168399772
#214543872
#214543492
#214543422
C4×H(5,𝔽2)×C612
#6043061