Finite Group Databasebeta

← #30544228

Subgroups — #30544228

Order 15616.

2826 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840565C211yesmaximal, characteristic
2H(5,𝔽2)×Dic61C211yesmaximal, characteristic, complemented
3#21459025C211yesmaximal, characteristic, complemented
4#21454690C213yesmaximal, complemented
5#21454667C213yesmaximal, complemented
6#21454654C213yesmaximal, complemented
7#21454645C213yesmaximal, complemented
8#21454632C213yesmaximal, complemented
9#21454623C213yesmaximal, complemented
10#21454587C213yesmaximal, complemented
11C2×#16839842C213yesmaximal, complemented
12#21454417C211yesmaximal, characteristic, complemented
13#21454346C211yesmaximal, characteristic, complemented
14#131×Dic61C211yesmaximal, characteristic, complemented
15C61×#2897C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17#16840565C4116yescomplemented
18C2×#14519803C2213yes—
19C2×#14519802C2213yes—
20C2×#14519797C2213yes—
21C22×#11758199C2213yes—
22C2×#14519784C2211yescharacteristic
23#16840245—21no—
24#16840245C2211yescharacteristic
25#16840245C2213yescomplemented
26#16840244—21no—
27#16840243C2213yescomplemented
28#16840237—23no—
29#16840237C2213yescomplemented
30#16840236C2213yescomplemented
31#16840234—23no—
32#41×Dic61—21no—
33#41×Dic61C2211yescharacteristic
34#41×Dic61C2213yescomplemented
35C4×#11758226—21no—
36#16840230C2213yescomplemented
37C2×D4×Dic61—23no—
38C2×D4×Dic61C2213yescomplemented
39C2×#14519739C2213yescomplemented
40C4×D4×D61—23no—
41#16839871C2216yescomplemented
42#16839871C2216yescomplemented
43#16839865C2216yescomplemented
44#16839859C2216yescomplemented
45#16839854C2213yescomplemented
46#16839854C2211yescharacteristic, complemented
47#16839853C2213yescomplemented
48#16839853C2213yescomplemented
49#16839847C2213yescomplemented
50#16839847C2213yescomplemented
51#16839842C2216yescomplemented
52#16839842C2216yescomplemented
53#16839842C2213yescomplemented
54#16839842C2216yescomplemented
55#16839842C2213yescomplemented
56#16839805C2213yescomplemented
57#16839802C2213yescomplemented
58#16839798C2213yescomplemented
59C2×#14519710C2213yescomplemented
60#16839768C2213yescomplemented
61#16839764C2213yescomplemented
62#16839759C2213yescomplemented
63C2×#14519699C2213yescomplemented
64#16839720C2213yescomplemented
65#16839717C2213yescomplemented
66M16×Dic61C2213yescomplemented
67C2×C8×Dic61C2213yescomplemented
68C2×H(5,𝔽2)×C61C2211yescharacteristic
69C2×#131×C61C2211yescharacteristic
70C61×#520C2211yescharacteristic
71C61×#418C2213yescomplemented
72C61×#417C2213yescomplemented
73C61×#416C2213yescomplemented
74C2×#102×C61C2213yescomplemented
75#14519823—24no—
76#14519823C2×C418yescomplemented
77C2×#11758226—21no—
78C2×#11758222C2313yes—
79C22×D244C2313yes—
80C2×D4×D61—23no—
81C23×Dic61—23no—
82C22×C4×D61—23no—
83#14519803C2×C4124yescomplemented
84#14519802C2×C4124yescomplemented
85#14519797C2×C4124yescomplemented
86C2×#11758202C2311yescharacteristic
87C2×#11758200C2313yes—
88C2×#11758201C2313yes—
89C2×#11758199C2×C4124yescomplemented
90C2×#11758199C2313yes—
91C2×#11758199C2316yes—
92#14519784C2×C418yescomplemented
93C2×#11758194C2313yes—
94C22×#92418C2313yes—
95Q8×Dic61—21no—
96Q8×Dic61D411yescharacteristic
97Q8×Dic61D411yescharacteristic
98Q8×Dic61C2311yescharacteristic
99Q8×Dic61C2313yes—
100#14519742C2311yescharacteristic
101#14519742C2313yes—
102C4×D244—23no—
103C4×D244—23no—
104D4×Dic61—23no—
105D4×Dic61—23no—
106D4×Dic61—23no—
107D4×Dic61—26no—
108D4×Dic61—23no—
109D4×Dic61—23no—
110D4×Dic61—23no—
111D4×Dic61—23no—
112D4×Dic61D413yes—
113D4×Dic61D413yes—
114D4×Dic61C2313yes—
115D4×Dic61C2316yes—
116D4×Dic61C2313yes—
117#14519739—23no—
118#14519739—23no—
119#14519739C2313yes—
120#14519739C2316yes—
121#14519739C2313yes—
122C4×C22⋊D61—26no—
123#14519737—23no—
124#14519737—23no—
125#14519736—23no—
126#14519736—23no—
127#14519736C2313yes—
128#14519736C2313yes—
129#14519735—23no—
130#14519734—23no—
131C2×C4⋊Dic61—23no—
132C2×C4⋊Dic61C2313yes—
133C4⋊C4×D61—23no—
134C2×C22⋊Dic61—23no—
135C2×C22⋊Dic61—26no—
136C2×#11758198—23no—
137C22⋊C4×D61—26no—
138C2×C4×Dic61—23no—
139C2×C4×Dic61C2313yes—
140C42×D61—23no—
141#14519710C2313yes—
142#14519710C2316yes—
143#14519710C2311yescharacteristic
144#14519708C2313yes—
145#14519708C2313yes—
146#14519702C2311yescharacteristic
147#14519702C2313yes—
148#14519699C2313yes—
149#14519699C2316yes—
150#14519699C2313yes—
151#14519687C2316yes—
152C8×Dic61C2311yescharacteristic
153C8×Dic61C2313yes—
154C8×Dic61C2313yes—
155C8×Dic61C2313yes—
156H(5,𝔽2)×C61—24no—
157H(5,𝔽2)×C61C2×C418yescomplemented
158C2×#41×C61—21no—
159C2×#41×C61C2313yes—
160C2×#41×C61C2311yescharacteristic
161C22×D4×C61—23no—
162C22×D4×C61C2313yes—
163#131×C61—24no—
164C2×M16×C61C2313yes—
165C22×C8×C61C2313yes—
166C4×Q8×C61—21no—
167C4×D4×C61—23no—
168#117×C61C2313yes—
169C2×C4⋊C4×C61C2313yes—
170#103×C61C2311yescharacteristic
171#103×C61C2313yes—
172#102×C61C2313yes—
173#102×C61C2316yes—
174#102×C61C2313yes—
175C24×C61—23no—
176C23×D61—23no—
177#41×C61—28no—
178#41×C61—26no—
179#41×C61C22×C414yes—
180#41×C61C22×C4112yescomplemented
181#41×C61#4114yes—
182C2×Q8×C61C2×D411yescharacteristic
183C2×Q8×C61C2411yescharacteristic
184C2×D4×C61—23no—
185C2×D4×C61—224no—
186C2×D4×C61—23no—
187C2×D4×C61—26no—
188C2×D4×C61C22×C4112yescomplemented
189C2×D4×C61C2×D413yes—
190C2×D4×C61C2413yes—
191C22×C4×C61—23no—
192C22×C4×C61—23no—
193C22×C4×C61C2413yes—
194C2×C22⋊D61—23no—
195C22×Dic61—23no—
196C22×Dic61—23no—
197C22×Dic61—26no—
198C22×Dic61—23no—
199C22×Dic61—86no—
200C22×Dic61C2×D413yes—
201C22×Dic61C2×D413yes—
202#11758226—28no—
203D4×D61—224no—
204#11758222—26no—
205#11758222C22×C4112yescomplemented
206C2×D244—23no—
207C2×D244—26no—
208C2×D244C22×C4112yescomplemented
209C2×D244C2413yes—
210C2×C4×D61—23no—
211C2×C4×D61—23no—
212C2×C4×D61—26no—
213C2×C4×D61—23no—
214C2×C4×D61—86no—
215C2×Dic122C2411yescharacteristic
216M16×C61—26no—
217C2×C8×C61—26no—
218C2×C8×C61C2411yescharacteristic
219C2×C8×C61C2413yes—
220C4⋊C4×C61—23no—
221C4⋊C4×C61C2413yes—
222C4⋊C4×C61C2411yescharacteristic
223C22⋊C4×C61—23no—
224C42×C61—23no—
225C22⋊Dic61—23no—
226C22⋊Dic61—23no—
227C22⋊Dic61—26no—
228C22⋊Dic61—23no—
229C22⋊Dic61C2×D416yes—
230#11758202C22×C414yescomplemented
231#11758201C22×C4112yescomplemented
232#11758200C22×C4112yescomplemented
233#11758199C22×C4112yescomplemented
234#11758199C22×C4124yescomplemented
235#11758198—23no—
236#11758198—26no—
237#11758198—23no—
238C4⋊Dic61—23no—
239C4⋊Dic61—23no—
240C4⋊Dic61—21no—
241C4⋊Dic61C2×D413yes—
242C4⋊Dic61C2×D413yes—
243C4⋊Dic61C2411yescharacteristic
244C4⋊Dic61C2413yes—
245#11758196—23no—
246#11758196—21no—
247C4×Dic61—23no—
248C4×Dic61—21no—
249C4×Dic61—23no—
250C4×Dic61—21no—
251C4×Dic61—23no—
252C4×Dic61C2×D413yes—
253C4×Dic61C2×D413yes—
254C4×Dic61C2411yescharacteristic
255C4×Dic61C2413yes—
256#11758194C22×C4112yescomplemented
257C2×#92418C22×C4112yescomplemented
258C2×#92418C2411yescharacteristic
259C2×#92418C2413yes—
260C23×C61—23no—
261C23×C61—212no—
262C23×C61—83no—
263C23×C61—83no—
264C23×C61C22×D413yes—
265C22×D61—23no—
266C22×D61—212no—
267C22×D61—83no—
268C22×D61—83no—
269Q8×C61—21no—
270Q8×C61C4×D414yes—
271Q8×C61C23×C412yes—
272D4×C61—212no—
273D4×C61—212no—
274D4×C61—23no—
275D4×C61C4×D4112yes—
276D4×C61C23×C416yes—
277C2×C4×C61—21no—
278C2×C4×C61—212no—
279C2×C4×C61—21no—
280C2×C4×C61—23no—
281C2×C4×C61—83no—
282C2×C4×C61C23×C416yes—
283C2×C4×C61C22×D413yes—
284C2×C4×C61C2×#4116yes—
285C2×C4×C61C2511yescharacteristic
286C22⋊D61—212no—
287C2×Dic61—21no—
288C2×Dic61—26no—
289C2×Dic61—21no—
290C2×Dic61—23no—
291C2×Dic61—43no—
292C2×Dic61—46no—
293C2×Dic61—83no—
294C2×Dic61—86no—
295C2×Dic61—83no—
296C2×Dic61C22×D413yes—
297C2×Dic61C22×D411yescharacteristic
298C2×Dic61C22×D413yes—
299C2×Dic61C22×D411yescharacteristic
300D244—212no—
301D244—23no—
302D244C23×C416yes—
303C4×D61—212no—
304C4×D61—46no—
305C4×D61—83no—
306C4×D61—86no—
307Dic122—21no—
308Dic122C23×C412yes—
309C8×C61—21no—
310C8×C61—23no—
311#92418C23×C412yes—
312#92418C23×C416yes—
313C4×#576—611nomaximal, Sylow
314C22×C61—23no—
315C22×C61—23no—
316C22×C61—26no—
317C22×C61—43no—
318C22×C61—43no—
319C22×C61—812no—
320C22×C61C2×C4×D416yes—
321C22×C61C23×D411yescharacteristic
322C2×D61—26no—
323C2×D61—43no—
324C2×D61—43no—
325C2×D61—812no—
326C4×C61—22no—
327C4×C61—41no—
328C4×C61—43no—
329C4×C61C2×C4×D416yes—
330C4×C61C24×C411yescharacteristic
331C4×C61C22×#4111yescharacteristic
332Dic61—23no—
333Dic61—21no—
334Dic61—22no—
335Dic61—23no—
336Dic61—41no—
337Dic61—43no—
338Dic61#57612yescomplemented
339C2×#576—611no—
340C4×H(5,𝔽2)—611no—
341C4×H(5,𝔽2)—611no—
342#2951—613no—
343#2948—613no—
344#2946—613no—
345#2946—613no—
346C4×AGL(1,ℤ/8)—613no—
347C4×AGL(1,ℤ/8)—613no—
348C4×#135—613no—
349C2×C4×D8—613no—
350#2913—611no—
351#2897—611no—
352#2897D6111yescharacteristic, complemented
353C4×#131—611no—
354C2×C61—26no—
355C2×C61—46no—
356C2×C61C22×C4×D411yescharacteristic
357C2×C61C2×#57611yescharacteristic
358C2×C61#358411yescharacteristic
359D61—46no—
360C2×H(5,𝔽2)—611no—
361C2×H(5,𝔽2)C2×D6111yescharacteristic
362#576—6116no—
363C2×AGL(1,ℤ/8)—613no—
364C2×AGL(1,ℤ/8)—613no—
365C2×#135—613no—
366C22×D8—613no—
367C2×#131—611no—
368C2×#131C2×D6111yescharacteristic
369#520—611no—
370#520—613no—
371#520—613no—
372#520—1221no—
373#520—1221no—
374#520C2×D6111yescharacteristic
375#518—613no—
376#518—613no—
377#518—1223no—
378#518—1223no—
379C4×#41—611no—
380C4×#41—613no—
381C4×#41—613no—
382C4×#41—1221no—
383C4×#41—1221no—
384C2×C4×D4—613no—
385C2×C4×D4—613no—
386C2×C4×D4—1223no—
387C2×C4×D4—1223no—
388#442—616no—
389#442—616no—
390#440—616no—
391#440—616no—
392C4×Q16—611no—
393C4×Q16—613no—
394C4×SD16—613no—
395C4×SD16—613no—
396C4×SD16—613no—
397C4×SD16—613no—
398C4×D8—613no—
399C4×D8—616no—
400C4×D8—616no—
401C4×D8—616no—
402C4×D8—613no—
403#428—613no—
404#428—613no—
405#427—613no—
406C2×#107—613no—
407#418—613no—
408#418C2×D6113yescomplemented
409#417—613no—
410#417C2×D6113yescomplemented
411#416—613no—
412#416C2×D6113yescomplemented
413C2×#102—613no—
414C2×#102C2×D6113yescomplemented
415#405—613no—
416#405—613no—
417C4×M16—613no—
418C2×C4×C8—613no—
419C61C4×#57611yescharacteristic, complemented, Sylow
420H(5,𝔽2)—24no—
421H(5,𝔽2)—618no—
422H(5,𝔽2)—1224no—
423H(5,𝔽2)C4×D6118yescomplemented
424C2×#41—21no—
425C2×#41—613no—
426C2×#41—1221no—
427C2×#41C22×D6113yes—
428C2×#41C22×D6111yescharacteristic
429C22×D4—23no—
430C22×D4—613no—
431C22×D4—1223no—
432C22×D4C22×D6113yes—
433C23×C4—1223no—
434C23×C4—1223no—
435AGL(1,ℤ/8)—6124no—
436AGL(1,ℤ/8)—6124no—
437#135—6124no—
438C2×Q16—611no—
439C2×SD16—613no—
440C2×SD16—613no—
441C2×D8—6124no—
442C2×D8—613no—
443C2×D8—616no—
444#131—24no—
445#131—618no—
446C2×M16—613no—
447C2×M16C22×D6113yes—
448C22×C8—613no—
449C22×C8C22×D6113yes—
450C4×Q8—21no—
451C4×Q8—611no—
452C4×Q8—611no—
453C4×Q8—611no—
454C4×Q8—613no—
455C4×Q8—611no—
456C4×Q8—613no—
457C4×Q8—1221no—
458C4×D4—23no—
459C4×D4—613no—
460C4×D4—613no—
461C4×D4—613no—
462C4×D4—616no—
463C4×D4—613no—
464C4×D4—613no—
465C4×D4—616no—
466C4×D4—613no—
467C4×D4—1223no—
468C4×D4—1223no—
469C4×D4—1223no—
470C4×D4—1223no—
471C4×D4—1223no—
472C4×D4—1223no—
473C4×D4—1223no—
474C4×D4—1223no—
475C4×D4—1226no—
476C4×D4—1226no—
477C4×D4—1223no—
478C4×D4—1223no—
479C4×D4—1223no—
480C4×D4—1223no—
481C4×D4—1223no—
482#117—613no—
483#117—613no—
484#117—1223no—
485#117—1223no—
486#117—1223no—
487#117—1223no—
488#117C22×D6113yes—
489C2×C4⋊C4—613no—
490C2×C4⋊C4—1223no—
491C2×C4⋊C4—1223no—
492C2×C4⋊C4C22×D6113yes—
493C2×C22⋊C4—1226no—
494C2×C22⋊C4—1226no—
495C2×C22⋊C4—1223no—
496C2×C22⋊C4—1223no—
497C2×C42—613no—
498C2×C42—1223no—
499C2×C42—1223no—
500#107—613no—
501#107—616no—
502#107—611no—
503#106—613no—
504#106—613no—
505#103—611no—
506#103—613no—
507#103C22×D6111yescharacteristic
508#103C22×D6113yes—
509#102—613no—
510#102—616no—
511#102—613no—
512#102C22×D6113yes—
513#102C22×D6116yes—
514#102C22×D6113yes—
515#97—616no—
516C4×C8—611no—
517C4×C8—613no—
518C4×C8—613no—
519C4×C8—613no—
520C24—23no—
521C24—1223no—
522#41—28no—
523#41—26no—
524#41—6112no—
525#41—1228no—
526#41—1226no—
527#41C2×C4×D6114yes—
528#41C2×C4×D61112yescomplemented
529#41#1175822414yes—
530C2×Q8—611no—
531C2×Q8D4×D6111yescharacteristic
532C2×Q8C23×D6111yescharacteristic
533C2×D4—23no—
534C2×D4—224no—
535C2×D4—23no—
536C2×D4—26no—
537C2×D4—6112no—
538C2×D4—613no—
539C2×D4—1223no—
540C2×D4—12224no—
541C2×D4—1223no—
542C2×D4—1226no—
543C2×D4C2×C4×D61112yescomplemented
544C2×D4D4×D6113yes—
545C2×D4C23×D6113yes—
546C22×C4—23no—
547C22×C4—23no—
548C22×C4—613no—
549C22×C4—613no—
550C22×C4—1223no—
551C22×C4—1226no—
552C22×C4—1223no—
553C22×C4—1223no—
554C22×C4—1226no—
555C22×C4—1223no—
556C22×C4—1223no—
557C22×C4—1223no—
558C22×C4—4886no—
559C22×C4—4886no—
560C22×C4C23×D6113yes—
561Q16—614no—
562SD16—6112no—
563SD16—6112no—
564D8—6112no—
565D8—6124no—
566M16—26no—
567M16—6112no—
568C2×C8—26no—
569C2×C8—6112no—
570C2×C8—611no—
571C2×C8—613no—
572C2×C8C23×D6111yescharacteristic
573C2×C8C23×D6113yes—
574C4⋊C4—23no—
575C4⋊C4—613no—
576C4⋊C4—613no—
577C4⋊C4—611no—
578C4⋊C4—613no—
579C4⋊C4—1223no—
580C4⋊C4—1223no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1223no—
584C4⋊C4C23×D6111yescharacteristic
585C4⋊C4C23×D6113yes—
586C22⋊C4—23no—
587C22⋊C4—616no—
588C22⋊C4—1223no—
589C22⋊C4—1223no—
590C22⋊C4—1226no—
591C22⋊C4—1223no—
592C22⋊C4—1226no—
593C22⋊C4—1223no—
594C22⋊C4—1223no—
595C42—23no—
596C42—613no—
597C42—613no—
598C42—611no—
599C42—613no—
600C42—1221no—
601C42—1221no—
602C42—1223no—
603C42—1223no—
604C42—1223no—
605C23—23no—
606C23—212no—
607C23—83no—
608C23—83no—
609C23—12212no—
610C23—1223no—
611C23—4883no—
612C23—4883no—
613C23C2×D4×D6113yes—
614Q8—21no—
615Q8—612no—
616Q8—1221no—
617Q8#1451973714yes—
618Q8C22×C4×D6112yes—
619D4—212no—
620D4—212no—
621D4—23no—
622D4—616no—
623D4—12212no—
624D4—12212no—
625D4—1223no—
626D4#14519737112yes—
627D4C22×C4×D6116yes—
628C2×C4—21no—
629C2×C4—212no—
630C2×C4—21no—
631C2×C4—23no—
632C2×C4—83no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—613no—
636C2×C4—613no—
637C2×C4—1226no—
638C2×C4—1221no—
639C2×C4—12212no—
640C2×C4—1221no—
641C2×C4—1223no—
642C2×C4—4883no—
643C2×C4—4886no—
644C2×C4—4883no—
645C2×C4—4886no—
646C2×C4—4883no—
647C2×C4—2446no—
648C2×C4—2446no—
649C2×C4—2443no—
650C2×C4C22×C4×D6116yes—
651C2×C4C2×D4×D6113yes—
652C2×C4C2×#1175822416yes—
653C2×C4C24×D6111yescharacteristic
654C8—21no—
655C8—23no—
656C8—612no—
657C8—616no—
658C22—23no—
659C22—23no—
660C22—26no—
661C22—43no—
662C22—43no—
663C22—812no—
664C22—1226no—
665C22—48812no—
666C22—2443no—
667C22—2443no—
668C22C2×#1451973716yes—
669C22C22×D4×D6111yescharacteristic
670C4—22no—
671C4—43no—
672C4—41no—
673C4—612no—
674C4—1222no—
675C4—1223no—
676C4—1223no—
677C4—1221no—
678C4—2443no—
679C4—2441no—
680C4C2×#1451973716yes—
681C4C23×C4×D6111yescharacteristic
682C4C22×#1175822411yescharacteristic
683C2—26no—
684C2—46no—
685C2—2446no—
686C2C22×#1451973711yescharacteristic
687C2#576×D6111yescharacteristic
688C2#2146059111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC61×#2897C2
socleC22×C61C23×D4
prime radicalC2×#16840565C2
cosocleC2×C4×C61C25
hypercenter#2897D61
hypocenterC61C4×#576
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. H(5,𝔽2)×Dic61C2semidirect
3. #21459025C2semidirect
4. #21454690C2semidirect
5. #21454667C2semidirect
6. #21454654C2semidirect
7. #21454645C2semidirect
8. #21454632C2semidirect
9. #21454623C2semidirect
10. #21454587C2semidirect
11. C2×#16839842C2semidirect
12. #21454417C2semidirect
13. #21454346C2semidirect
14. #131×Dic61C2semidirect
15. C61×#2897C2semidirect
17. #16840565C4semidirect
25. #16840245C22semidirect
27. #16840243C22semidirect
29. #16840237C22semidirect
30. #16840236C22semidirect
34. #41×Dic61C22semidirect
36. #16840230C22semidirect
38. C2×D4×Dic61C22semidirect
39. C2×#14519739C22semidirect
41. #16839871C22semidirect
42. #16839871C22semidirect
43. #16839865C22semidirect
44. #16839859C22semidirect
45. #16839854C22semidirect
46. #16839854C22semidirect
47. #16839853C22semidirect
48. #16839853C22semidirect
49. #16839847C22semidirect
50. #16839847C22semidirect
51. #16839842C22semidirect
52. #16839842C22semidirect
53. #16839842C22semidirect
54. #16839842C22semidirect
55. #16839842C22semidirect
56. #16839805C22semidirect
57. #16839802C22semidirect
58. #16839798C22semidirect
59. C2×#14519710C22semidirect
60. #16839768C22semidirect
61. #16839764C22semidirect
62. #16839759C22semidirect
63. C2×#14519699C22semidirect
64. #16839720C22semidirect
65. #16839717C22semidirect
66. M16×Dic61C22semidirect
67. C2×C8×Dic61C22semidirect
71. C61×#418C22semidirect
72. C61×#417C22semidirect
73. C61×#416C22semidirect
74. C2×#102×C61C22semidirect
76. #14519823C2×C4semidirect
83. #14519803C2×C4semidirect
84. #14519802C2×C4semidirect
85. #14519797C2×C4semidirect
89. C2×#11758199C2×C4semidirect
92. #14519784C2×C4semidirect
157. H(5,𝔽2)×C61C2×C4semidirect
180. #41×C61C22×C4semidirect
188. C2×D4×C61C22×C4semidirect
205. #11758222C22×C4semidirect
208. C2×D244C22×C4semidirect
230. #11758202C22×C4semidirect
231. #11758201C22×C4semidirect
232. #11758200C22×C4semidirect
233. #11758199C22×C4semidirect
234. #11758199C22×C4semidirect
256. #11758194C22×C4semidirect
257. C2×#92418C22×C4semidirect
338. Dic61#576semidirect
352. #2897D61semidirect
408. #418C2×D61semidirect
410. #417C2×D61semidirect
412. #416C2×D61semidirect
414. C2×#102C2×D61semidirect
419. C61C4×#576semidirect
423. H(5,𝔽2)C4×D61semidirect
528. #41C2×C4×D61semidirect
543. C2×D4C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405652
H(5,𝔽2)×Dic612
#214590252
#214546902
#214546672
#214546542
#214546452
#214546322
#214546232
#214545872
C2×#168398422
#214544172
#214543462
#131×Dic612
C61×#28972
C4×#57661