Finite Group Databasebeta

← #30593885

Subgroups — #30593885

Order 15616.

10698 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460632C211yesmaximal, characteristic, complemented
2#21460631C211yesmaximal, characteristic, complemented
3#21460607C211yesmaximal, characteristic, complemented
4#21460604C218yesmaximal, complemented
5#21460603C216yesmaximal, complemented
6#21460602C216yesmaximal, complemented
7#21460601C218yesmaximal, complemented
8#21460592C216yesmaximal, complemented
9#21460591C218yesmaximal, complemented
10#21460590C211yesmaximal, characteristic, complemented
11C2×#16840578C216yesmaximal, complemented
12C2×#16840577C211yesmaximal, characteristic, complemented
13#578×D61C218yesmaximal, complemented
14#21460532C211yesmaximal, characteristic, complemented
15C61×#3586C211yesmaximal, characteristic, complemented
16#16840599—24no—
17#16840599C2218yescomplemented
18#16840598—24no—
19#16840598—26no—
20#16840598C2211yescharacteristic
21#16840598C2211yescharacteristic, complemented
22#16840598C2216yescomplemented
23#16840598C2216yescomplemented
24#16840597—26no—
25#16840597C2218yescomplemented
26C2×#14519825—22no—
27C2×#14519825C2216yescomplemented
28C2×#14519824—24no—
29C2×#14519824C2211yescharacteristic, complemented
30C2×#14519824C2216yescomplemented
312−1+4×D61—22no—
322−1+4×D61—24no—
332−1+4×D61C2218yescomplemented
342−1+4×D61C2218yescomplemented
35#16840579C2218yescomplemented
36#16840578C22112yescomplemented
37#16840578C22124yescomplemented
38#16840578C22112yescomplemented
39#16840578C22124yescomplemented
40#16840578C22124yescomplemented
41#16840577C2214yescomplemented
42#16840577C2218yescomplemented
43#16840577C2218yescomplemented
44#16840576C22124yescomplemented
45#16840575C22124yescomplemented
46#16840574C2218yescomplemented
47#16840573C2214yescomplemented
48#16840572C22112yescomplemented
49#16840572C22112yescomplemented
50#16840571C22112yescomplemented
51#16840571C22112yescomplemented
52#16840570C2214yescomplemented
53#16840569C22124yescomplemented
54#16840568C22124yescomplemented
55#16840566C22112yescomplemented
56#16840566C2214yescomplemented
57#16840565C2214yescomplemented
58#16840562C2216yescomplemented
59#16840561C22124yescomplemented
60#16840560C2216yescomplemented
61#16840559C22124yescomplemented
62#16840558C22124yescomplemented
63C2×#14519810C2216yescomplemented
64C2×#14519809C22112yescomplemented
65C2×#14519808C2213yescomplemented
66C2×#14519807C2213yescomplemented
67C2×#14519806C22112yescomplemented
68#137×D61C22124yescomplemented
69#137×D61C22124yescomplemented
70C2×#14519798C22112yescomplemented
71C2×#14519797C2213yescomplemented
72C2×#14519797C2216yescomplemented
73#135×D61C22124yescomplemented
74C22×#11758202C2213yescomplemented
75C2×Q16×D61C22112yescomplemented
76#16840528C2216yescomplemented
77#16840527C2218yescomplemented
78C2×#14519785C2216yescomplemented
79C2×#14519784C2211yescharacteristic, complemented
80#131×D61C2218yescomplemented
81C61×#585C2211yescharacteristic, complemented
82C2×2−1+4×C61C2211yescharacteristic, complemented
83C61×#578C2218yescomplemented
84C61×#577C2218yescomplemented
85C61×#575C2216yescomplemented
86C2×#137×C61C2216yescomplemented
87C61×#568C2211yescharacteristic, complemented
88#14519825—21no—
89#14519825—28no—
90#14519825—28no—
91#14519825—28no—
92#14519825—212no—
93#14519825—212no—
94#14519825D412yes—
95#14519825C23124yes—
96#14519825C23112yes—
97#14519825C23112yes—
98#14519824—24no—
99#14519824—28no—
100#14519824—224no—
101#14519824—224no—
102#14519824—212no—
103#14519824—212no—
104#14519824—26no—
105#14519824—26no—
106#14519824D414yes—
107#14519824C23124yes—
108#14519824C23112yes—
109#14519824C23112yes—
110#14519824C2314yes—
111#14519824C2318yes—
112#14519823—224no—
113#14519823—26no—
114#14519823—26no—
115#14519823D414yes—
116#14519823C23112yes—
117#14519823C2314yes—
118#14519823C2314yes—
119#14519822—23no—
120#14519822—212no—
121#14519822—212no—
122#14519822—224no—
123#14519822D416yes—
124#14519822C23112yes—
125#14519822C2314yes—
126C2×#11758226—28no—
127C2×#11758226—26no—
128C2×#11758226C23112yes—
129C2×#11758222—212no—
130C2×#11758222—212no—
131C2×#11758222—212no—
132C2×#11758222—26no—
133C2×#11758222C2316yes—
134C2×#11758222C2313yes—
135C2×#11758222C2316yes—
136C2×#11758224—23no—
137C2×#11758224—212no—
138C2×#11758224—224no—
139C2×#11758224C23112yes—
140#41×D61—24no—
141#41×D61—28no—
142#41×D61—224no—
143#41×D61—224no—
144#41×D61—224no—
145#41×D61—212no—
146#41×D61—212no—
147#41×D61C23124yes—
148#41×D61C23124yes—
149#41×D61C2318yes—
150C22×Dic122—26no—
151C22×Dic122C2313yes—
152C2×Q8×D61—21no—
153C2×Q8×D61—28no—
154C2×Q8×D61—28no—
155C2×Q8×D61—26no—
156C2×Q8×D61C23112yes—
157C2×Q8×D61C23112yes—
158#14519810C23112yes—
159#14519810C23124yes—
160#14519810C23112yes—
161#14519809C23124yes—
162#14519809C23148yes—
163#14519809C23124yes—
164#14519808C23112yes—
165#14519808C23124yes—
166#14519807C23112yes—
167#14519807C23124yes—
168#14519806C23124yes—
169#14519806C23148yes—
170#14519806C23124yes—
171#14519805C23112yes—
172#14519805C2314yes—
173#14519804C2318yes—
174#14519804C23124yes—
175#14519803C23112yes—
176#14519802C23112yes—
177#14519801C23124yes—
178#14519801C2318yes—
179#14519800C23124yes—
180#14519799C23124yes—
181#14519798C2318yes—
182#14519798C23124yes—
183#14519798C23148yes—
184#14519797C23112yes—
185#14519797C23112yes—
186#14519797C2314yes—
187#14519797C23112yes—
188#14519797C23112yes—
189#14519797C23112yes—
190#14519796C23124yes—
191C2×Dic244C23112yes—
192C2×#11758202C2316yes—
193C2×#11758202C23112yes—
194C2×#11758202C2313yes—
195C2×#11758202C23112yes—
196C2×#11758202C2316yes—
197Q16×D61C23124yes—
198Q16×D61C23148yes—
199C2×#11758190C23112yes—
200C2×#11758200C2316yes—
201C2×#11758200C2313yes—
202C2×#11758201C2313yes—
203C2×#11758201C2316yes—
204SD16×D61C23124yes—
205SD16×D61C23124yes—
206C2×#11758199C2311yescharacteristic
207C2×#11758199C2316yes—
208D8×D61C2318yes—
209#14519785C23112yes—
210#14519785C2314yes—
211#14519785C23112yes—
212#14519785C23112yes—
213#14519784C2314yes—
214#14519784C2314yes—
215#14519783C23124yes—
216C2×#11758194C2313yes—
217C2×#11758189C23112yes—
218M16×D61C23124yes—
219C22×#92418C2313yes—
220C2×C8×D61C23112yes—
2212−1+4×C61—24no—
2222−1+4×C61—21no—
2232−1+4×C61C2318yes—
2242−1+4×C61C2314yes—
225H(5,𝔽2)×C61—23no—
226H(5,𝔽2)×C61C2314yes—
227C2×#41×C61—24no—
228C2×#41×C61—23no—
229C2×#41×C61C2316yes—
230C2×#41×C61C2313yes—
231C2×#41×C61C2311yescharacteristic
232C22×Q8×C61—21no—
233C22×Q8×C61C2313yes—
234#137×C61C23112yes—
235#137×C61C23124yes—
236#137×C61C23112yes—
237AGL(1,ℤ/8)×C61C2314yes—
238AGL(1,ℤ/8)×C61C23112yes—
239#135×C61C23124yes—
240C2×Q16×C61C23112yes—
241C2×SD16×C61C23112yes—
242#131×C61C2318yes—
243C2×M16×C61C2316yes—
244#41×C61—24no—
245#41×C61—224no—
246#41×C61—212no—
247#41×C61—26no—
248#41×C61—26no—
249#41×C61—26no—
250#41×C61C2×D414yes—
251#41×C61C24112yes—
252#41×C61C24112yes—
253#41×C61C2414yes—
254#41×C61C2414yes—
255C2×Q8×C61—24no—
256C2×Q8×C61—28no—
257C2×Q8×C61—26no—
258C2×Q8×C61—23no—
259C2×Q8×C61C2×D411yescharacteristic
260C2×Q8×C61C2416yes—
261C2×Q8×C61C24112yes—
262C2×Q8×C61C2413yes—
263C2×D4×C61—26no—
264C2×D4×C61—23no—
265C2×D4×C61—212no—
266C2×D4×C61C2×D413yes—
267C2×D4×C61C2416yes—
268C2×D4×C61C2411yescharacteristic
269C22×C4×C61—23no—
270C22×C4×C61—26no—
271C22×C4×C61—23no—
272C22×C4×C61C2413yes—
273C2×C22⋊D61—23no—
274C2×C22⋊D61—26no—
275C2×C22⋊D61—212no—
276C2×C22⋊D61—224no—
277C2×C22⋊D61—28no—
278C2×C22⋊D61C2×D4112yes—
279C22×Dic61—23no—
280C22×Dic61—212no—
281#11758226—24no—
282#11758226—212no—
283#11758226—212no—
284#11758226—224no—
285#11758226—224no—
286#11758226C2×D418yes—
287#11758226C2418yes—
288#11758226C24124yes—
289Q8×D61—28no—
290Q8×D61—24no—
291Q8×D61—224no—
292Q8×D61—224no—
293Q8×D61—212no—
294Q8×D61—212no—
295Q8×D61—224no—
296Q8×D61C2×D418yes—
297Q8×D61C24124yes—
298Q8×D61C24124yes—
299#11758224—212no—
300#11758224—224no—
301#11758224—224no—
302#11758224—224no—
303#11758224—248no—
304#11758224—224no—
305#11758224—224no—
306#11758224—224no—
307#11758224—24no—
308#11758224—212no—
309#11758224C2×D4124yes—
310#11758224C2418yes—
311#11758224C24124yes—
312D4×D61—224no—
313D4×D61—224no—
314D4×D61—212no—
315D4×D61—28no—
316D4×D61—224no—
317D4×D61—212no—
318D4×D61—24no—
319D4×D61C2×D4124yes—
320D4×D61C2418yes—
321D4×D61C2418yes—
322#11758222—26no—
323#11758222—26no—
324#11758222—26no—
325#11758222—224no—
326#11758222—248no—
327#11758222—224no—
328#11758222—224no—
329#11758222—212no—
330#11758222—212no—
331#11758222—224no—
332#11758222—224no—
333#11758222—212no—
334#11758222—24no—
335#11758222C2×D4112yes—
336#11758222C2×D4112yes—
337#11758222C24112yes—
338#11758222C2414yes—
339#11758222C24112yes—
340#11758222C24112yes—
341#11758222C2414yes—
342C2×D244—212no—
343C2×D244—24no—
344C2×D244—212no—
345C2×D244C2×D416yes—
346C2×D244C2411yescharacteristic
347C2×D244C2416yes—
348C2×C4×D61—212no—
349C2×C4×D61—212no—
350C2×C4×D61—23no—
351C2×C4×D61—26no—
352C2×C4×D61—212no—
353C2×C4×D61—224no—
354C2×C4×D61—224no—
355C2×C4×D61C24112yes—
356C2×Dic122—23no—
357C2×Dic122—26no—
358C2×Dic122—212no—
359C2×Dic122—212no—
360C2×Dic122—212no—
361C2×Dic122—224no—
362C2×Dic122—212no—
363C2×Dic122C2×D416yes—
364C2×Dic122C2413yes—
365C2×Dic122C2416yes—
366C2×Dic122C24112yes—
367Q16×C61C24124yes—
368SD16×C61C24124yes—
369SD16×C61C2418yes—
370D8×C61C2418yes—
371M16×C61C2414yes—
372M16×C61C24112yes—
373C2×C8×C61C24112yes—
374#11758202C24112yes—
375#11758202C24124yes—
376#11758202C2416yes—
377#11758202C2414yes—
378#11758202C2416yes—
379#11758201C24112yes—
380#11758201C24112yes—
381#11758201C2414yes—
382#11758200C24112yes—
383#11758200C24112yes—
384#11758200C2414yes—
385#11758199C2412yes—
386#11758199C2414yes—
387#11758199C2412yes—
388#11758199C24112yes—
389#11758194C24112yes—
390C2×#92418C2416yes—
391C2×#92418C2411yescharacteristic
392C2×#92418C2416yes—
393C2×#92418C2413yes—
394Dic244C24124yes—
395D488C2418yes—
396#11758190C2418yes—
397#11758190C24124yes—
398#11758189C24124yes—
399#11758189C2418yes—
400C8×D61C2418yes—
401C8×D61C24124yes—
402C23×C61—26no—
403C23×C61—21no—
404C23×C61C22×D413yes—
405C22×D61—26no—
406C22×D61—21no—
407C22×D61—28no—
408C22×D61—28no—
409C22×D61C22×D4112yes—
410Q8×C61—26no—
411Q8×C61—23no—
412Q8×C61—212no—
413Q8×C61C22×D414yes—
414Q8×C61C2514yes—
415Q8×C61C2516yes—
416D4×C61—212no—
417D4×C61—212no—
418D4×C61—24no—
419D4×C61—21no—
420D4×C61—26no—
421D4×C61C22×D4112yes—
422D4×C61C2514yes—
423D4×C61C2512yes—
424C2×C4×C61—26no—
425C2×C4×C61—212no—
426C2×C4×C61—23no—
427C2×C4×C61—24no—
428C2×C4×C61—212no—
429C2×C4×C61—212no—
430C2×C4×C61C22×D416yes—
431C2×C4×C61C22×D413yes—
432C2×C4×C61C2511yescharacteristic
433C2×C4×C61C2516yes—
434C22⋊D61—24no—
435C22⋊D61—212no—
436C22⋊D61—212no—
437C22⋊D61—28no—
438C22⋊D61—224no—
439C22⋊D61—28no—
440C22⋊D61—28no—
441C22⋊D61C22×D418yes—
442C22⋊D61C22×D4124yes—
443C2×Dic61—26no—
444C2×Dic61—212no—
445C2×Dic61—23no—
446C2×Dic61—28no—
447C2×Dic61—224no—
448C2×Dic61C22×D4112yes—
449D244—224no—
450D244—28no—
451D244—21no—
452D244—26no—
453D244C22×D414yes—
454D244C22×D4112yes—
455D244C2514yes—
456D244C2512yes—
457C4×D61—224no—
458C4×D61—224no—
459C4×D61—212no—
460C4×D61—24no—
461C4×D61—212no—
462C4×D61—28no—
463C4×D61—224no—
464C4×D61C22×D4124yes—
465C4×D61C2518yes—
466Dic122—23no—
467Dic122—212no—
468Dic122—26no—
469Dic122—224no—
470Dic122—224no—
471Dic122C22×D414yes—
472Dic122C22×D4112yes—
473Dic122C2516yes—
474Dic122C2514yes—
475C8×C61C2518yes—
476#92418C2511yescharacteristic
477#92418C2516yes—
478#92418C2511yescharacteristic
479#63093—611nomaximal, Sylow
480C22×C61—24no—
481C22×C61—22no—
482C22×C61—43no—
483C22×C61—86no—
484C22×C61—81no—
485C22×C61C23×D416yes—
486C22×C61C23×D411yescharacteristic
487C2×D61—24no—
488C2×D61—22no—
489C2×D61—412no—
490C2×D61—88no—
491C2×D61—88no—
492C2×D61—86no—
493C2×D61—81no—
494C2×D61C23×D418yes—
495C4×C61—24no—
496C4×C61—26no—
497C4×C61C23×D411yescharacteristic
498C4×C61C23×D416yes—
499C4×C61C2611yescharacteristic
500Dic61—24no—
501Dic61—26no—
502Dic61C23×D418yes—
5032−1+6—611no—
5042−1+6—611no—
505#3586—618no—
506#3586—618no—
507#3586—616no—
508#3586—616no—
509#3586—611no—
510#3586D6111yescharacteristic, complemented
511#3584—611no—
512#3584—618no—
513#3584—616no—
514C2×#578—611no—
515C2×#578—618no—
516C2×#578—616no—
517#3573—611no—
518C2×C61—26no—
519C2×C61—21no—
520C2×C61—42no—
521C2×C61—44no—
522C2×C61C24×D411yescharacteristic
523D61—28no—
524D61—44no—
525D61—42no—
526#585—611no—
527#585—618no—
528#585—618no—
529#585—616no—
530#585—616no—
531#585—611no—
532#585—1224no—
533#585—1226no—
534#585—1226no—
535#585—1224no—
536#585C2×D6111yescharacteristic, complemented
537C2×2−1+4—618no—
538C2×2−1+4—618no—
539C2×2−1+4—616no—
540C2×2−1+4—611no—
541C2×2−1+4—616no—
542C2×2−1+4—1222no—
543C2×2−1+4—1224no—
544C2×2−1+4—1224no—
545C2×2−1+4—1222no—
546C2×2−1+4C2×D6111yescharacteristic, complemented
547#578—614no—
548#578—618no—
549#578—618no—
550#578—6112no—
551#578—6124no—
552#578—6112no—
553#578—6124no—
554#578—6124no—
555#578—6124no—
556#578—6124no—
557#578—618no—
558#578C2×D6118yescomplemented
559#577—614no—
560#577—614no—
561#577—6112no—
562#577—6112no—
563#577—6112no—
564#577—6112no—
565#577—6124no—
566#577—6124no—
567#577—618no—
568#577C2×D6118yescomplemented
569#576—614no—
570#576—6112no—
571#576—614no—
572#575—616no—
573#575—6124no—
574#575—6124no—
575#575—6124no—
576#575—616no—
577#575C2×D6116yescomplemented
578C2×#137—613no—
579C2×#137—613no—
580C2×#137—6124no—
581C2×#137—6124no—
582C2×#137—6112no—
583C2×#137—6112no—
584C2×#137—616no—
585C2×#137C2×D6116yescomplemented
586C2×#135—613no—
587C2×#135—616no—
588C2×#135—6124no—
589C2×#135—6112no—
590C22×Q16—613no—
591C22×Q16—6112no—
592#568—618no—
593#568—616no—
594#568C2×D6111yescharacteristic, complemented
595C2×#131—611no—
596C2×#131—618no—
597C2×#131—616no—
598C61#6309311yescharacteristic, complemented, Sylow
5992−1+4—24no—
6002−1+4—21no—
6012−1+4—614no—
6022−1+4—612no—
6032−1+4—6112no—
6042−1+4—6124no—
6052−1+4—6112no—
6062−1+4—614no—
6072−1+4—618no—
6082−1+4—6112no—
6092−1+4—6112no—
6102−1+4—6124no—
6112−1+4—1228no—
6122−1+4—1228no—
6132−1+4—1228no—
6142−1+4—12212no—
6152−1+4—12212no—
6162−1+4—1228no—
6172−1+4—1226no—
6182−1+4—1226no—
6192−1+4—12224no—
6202−1+4—12224no—
6212−1+4—12212no—
6222−1+4—12212no—
6232−1+4—1224no—
6242−1+4—1221no—
6252−1+4C22×D6114yes—
6262−1+4C22×D6118yes—
627H(5,𝔽2)—23no—
628H(5,𝔽2)—614no—
629H(5,𝔽2)—616no—
630H(5,𝔽2)—614no—
631H(5,𝔽2)—6112no—
632H(5,𝔽2)—614no—
633H(5,𝔽2)—614no—
634H(5,𝔽2)—6112no—
635H(5,𝔽2)—12212no—
636H(5,𝔽2)—12212no—
637H(5,𝔽2)—12224no—
638H(5,𝔽2)—12224no—
639H(5,𝔽2)—1226no—
640H(5,𝔽2)—1226no—
641H(5,𝔽2)—1223no—
642H(5,𝔽2)C22×D6114yes—
643C2×#41—24no—
644C2×#41—23no—
645C2×#41—618no—
646C2×#41—616no—
647C2×#41—6124no—
648C2×#41—6124no—
649C2×#41—6112no—
650C2×#41—6112no—
651C2×#41—613no—
652C2×#41—616no—
653C2×#41—12212no—
654C2×#41—1226no—
655C2×#41—12212no—
656C2×#41—12212no—
657C2×#41—12212no—
658C2×#41—12224no—
659C2×#41—1226no—
660C2×#41—12224no—
661C2×#41—12224no—
662C2×#41—1228no—
663C2×#41—1228no—
664C2×#41—12224no—
665C2×#41—12212no—
666C2×#41—12212no—
667C2×#41—1224no—
668C2×#41—1223no—
669C2×#41C22×D6113yes—
670C2×#41C22×D6116yes—
671C2×#41C22×D6111yescharacteristic
672C22×Q8—21no—
673C22×Q8—6112no—
674C22×Q8—6112no—
675C22×Q8—613no—
676C22×Q8—1226no—
677C22×Q8—1228no—
678C22×Q8—1228no—
679C22×Q8—1226no—
680C22×Q8—1221no—
681C22×Q8C22×D6113yes—
682#137—6112no—
683#137—6124no—
684#137—6112no—
685#137—6124no—
686#137—6124no—
687#137—6148no—
688#137—6124no—
689#137—6124no—
690#137—6148no—
691#137—6124no—
692#137—6112no—
693#137—6124no—
694#137—6112no—
695#137C22×D61112yes—
696#137C22×D61124yes—
697#137C22×D61112yes—
698AGL(1,ℤ/8)—6112no—
699AGL(1,ℤ/8)—6112no—
700AGL(1,ℤ/8)—618no—
701AGL(1,ℤ/8)—6124no—
702AGL(1,ℤ/8)—6124no—
703AGL(1,ℤ/8)—618no—
704AGL(1,ℤ/8)—6112no—
705AGL(1,ℤ/8)—614no—
706AGL(1,ℤ/8)C22×D61112yes—
707AGL(1,ℤ/8)C22×D6114yes—
708#135—614no—
709#135—6112no—
710#135—6112no—
711#135—6112no—
712#135—6112no—
713#135—6112no—
714#135—6124no—
715#135—618no—
716#135—6124no—
717#135—6148no—
718#135—6124no—
719#135—6124no—
720#135C22×D61124yes—
721C2×Q16—613no—
722C2×Q16—616no—
723C2×Q16—6112no—
724C2×Q16—616no—
725C2×Q16—6112no—
726C2×Q16—6124no—
727C2×Q16—6148no—
728C2×Q16—6112no—
729C2×Q16C22×D61112yes—
730C2×SD16—613no—
731C2×SD16—616no—
732C2×SD16—613no—
733C2×SD16—616no—
734C2×SD16—6124no—
735C2×SD16—6124no—
736C2×SD16—6112no—
737C2×SD16C22×D61112yes—
738C2×D8—611no—
739C2×D8—616no—
740C2×D8—618no—
741#131—614no—
742#131—614no—
743#131—6112no—
744#131—614no—
745#131—6112no—
746#131—6112no—
747#131—6124no—
748#131C22×D6118yes—
749C2×M16—613no—
750C2×M16—6124no—
751C2×M16—6112no—
752C2×M16C22×D6116yes—
753C22×C8—613no—
754C22×C8—6112no—
755#41—24no—
756#41—212no—
757#41—224no—
758#41—26no—
759#41—26no—
760#41—26no—
761#41—618no—
762#41—6124no—
763#41—6112no—
764#41—6112no—
765#41—614no—
766#41—6112no—
767#41—618no—
768#41—6124no—
769#41—6124no—
770#41—618no—
771#41—614no—
772#41—6112no—
773#41—6112no—
774#41—12224no—
775#41—12224no—
776#41—12224no—
777#41—12224no—
778#41—12248no—
779#41—12212no—
780#41—12224no—
781#41—12212no—
782#41—1224no—
783#41—12212no—
784#41—12224no—
785#41—12224no—
786#41—12224no—
787#41—12224no—
788#41—12224no—
789#41—12248no—
790#41—12224no—
791#41—12212no—
792#41—1224no—
793#41—12212no—
794#41—12224no—
795#41—12212no—
796#41—1224no—
797#41—12224no—
798#41—12212no—
799#41—1226no—
800#41—1226no—
801#41—1226no—
802#41D4×D6114yes—
803#41C23×D6114yes—
804#41C23×D61112yes—
805#41C23×D61112yes—
806#41C23×D6114yes—
807C2×Q8—28no—
808C2×Q8—24no—
809C2×Q8—23no—
810C2×Q8—26no—
811C2×Q8—618no—
812C2×Q8—616no—
813C2×Q8—6124no—
814C2×Q8—6124no—
815C2×Q8—613no—
816C2×Q8—616no—
817C2×Q8—6112no—
818C2×Q8—12212no—
819C2×Q8—12212no—
820C2×Q8—12212no—
821C2×Q8—12224no—
822C2×Q8—12212no—
823C2×Q8—12224no—
824C2×Q8—12224no—
825C2×Q8—12224no—
826C2×Q8—12212no—
827C2×Q8—12212no—
828C2×Q8—1224no—
829C2×Q8—1228no—
830C2×Q8—1226no—
831C2×Q8—1223no—
832C2×Q8D4×D6111yescharacteristic
833C2×Q8C23×D6113yes—
834C2×Q8C23×D6116yes—
835C2×Q8C23×D61112yes—
836C2×D4—23no—
837C2×D4—26no—
838C2×D4—212no—
839C2×D4—6112no—
840C2×D4—6124no—
841C2×D4—618no—
842C2×D4—618no—
843C2×D4—616no—
844C2×D4—611no—
845C2×D4—616no—
846C2×D4—1224no—
847C2×D4—12212no—
848C2×D4—12212no—
849C2×D4—1228no—
850C2×D4—12224no—
851C2×D4—12212no—
852C2×D4—1224no—
853C2×D4—12224no—
854C2×D4—12224no—
855C2×D4—1228no—
856C2×D4—12224no—
857C2×D4—12212no—
858C2×D4—1226no—
859C2×D4—1223no—
860C2×D4—12212no—
861C2×D4D4×D6113yes—
862C2×D4C23×D6111yescharacteristic
863C2×D4C23×D6116yes—
864C22×C4—23no—
865C22×C4—23no—
866C22×C4—26no—
867C22×C4—6112no—
868C22×C4—12212no—
869C22×C4—12224no—
870C22×C4—12224no—
871C22×C4—12212no—
872C22×C4—12212no—
873C22×C4—12212no—
874C22×C4—1223no—
875C22×C4—1226no—
876C22×C4—1223no—
877C22×C4C23×D6113yes—
878Q16—614no—
879Q16—616no—
880Q16—6112no—
881Q16—6124no—
882Q16—616no—
883Q16—6124no—
884Q16C23×D61124yes—
885SD16—6112no—
886SD16—614no—
887SD16—6112no—
888SD16—6112no—
889SD16—614no—
890SD16—6112no—
891SD16—618no—
892SD16—6124no—
893SD16C23×D6118yes—
894SD16C23×D61124yes—
895D8—614no—
896D8—612no—
897D8—6112no—
898D8—612no—
899D8—618no—
900D8C23×D6118yes—
901M16—6112no—
902M16—6124no—
903M16—618no—
904M16C23×D61112yes—
905M16C23×D6114yes—
906C2×C8—611no—
907C2×C8—616no—
908C2×C8—613no—
909C2×C8—616no—
910C2×C8—618no—
911C2×C8—6124no—
912C2×C8C23×D61112yes—
913C23—21no—
914C23—26no—
915C23—6112no—
916C23—1228no—
917C23—1228no—
918C23—1226no—
919C23—1221no—
920C23C2×D4×D6113yes—
921Q8—212no—
922Q8—23no—
923Q8—26no—
924Q8—6112no—
925Q8—614no—
926Q8—616no—
927Q8—614no—
928Q8—12224no—
929Q8—12224no—
930Q8—12212no—
931Q8—1226no—
932Q8—1223no—
933Q8C2×D4×D6114yes—
934Q8C24×D6114yes—
935Q8C24×D6116yes—
936D4—212no—
937D4—24no—
938D4—212no—
939D4—26no—
940D4—21no—
941D4—6124no—
942D4—618no—
943D4—6112no—
944D4—614no—
945D4—614no—
946D4—612no—
947D4—1228no—
948D4—12224no—
949D4—1228no—
950D4—1228no—
951D4—1228no—
952D4—12224no—
953D4—12212no—
954D4—12212no—
955D4—1224no—
956D4—1226no—
957D4—1221no—
958D4C2×D4×D61112yes—
959D4C24×D6114yes—
960D4C24×D6112yes—
961C2×C4—23no—
962C2×C4—26no—
963C2×C4—212no—
964C2×C4—24no—
965C2×C4—212no—
966C2×C4—212no—
967C2×C4—6112no—
968C2×C4—6124no—
969C2×C4—618no—
970C2×C4—1228no—
971C2×C4—12224no—
972C2×C4—12224no—
973C2×C4—12224no—
974C2×C4—1228no—
975C2×C4—12224no—
976C2×C4—1226no—
977C2×C4—12212no—
978C2×C4—1223no—
979C2×C4—12212no—
980C2×C4—12212no—
981C2×C4—1224no—
982C2×C4C2×D4×D6116yes—
983C2×C4C2×D4×D6113yes—
984C2×C4C24×D6111yescharacteristic
985C2×C4C24×D6116yes—
986C8—611no—
987C8—616no—
988C8—611no—
989C8C24×D6118yes—
990C22—22no—
991C22—24no—
992C22—43no—
993C22—81no—
994C22—86no—
995C22—618no—
996C22—1224no—
997C22—1222no—
998C22—4881no—
999C22—4886no—
1000C22—4888no—
1001C22—4888no—
1002C22—24412no—
1003C22C22×D4×D6116yes—
1004C22C22×D4×D6111yescharacteristic
1005C4—24no—
1006C4—26no—
1007C4—618no—
1008C4—1224no—
1009C4—1226no—
1010C4C22×D4×D6116yes—
1011C4C22×D4×D6111yescharacteristic
1012C4C25×D6111yescharacteristic
1013C2—21no—
1014C2—26no—
1015C2—44no—
1016C2—42no—
1017C2—1228no—
1018C2—2444no—
1019C2—2442no—
1020C2C23×D4×D6111yescharacteristic
subgroupG/H
centerC2C23×D4×D61
commutator, cosocleC4×C61C26
FrattiniC4C25×D61
FittingC61×#3586C2
socleC2×C61C24×D4
hypercenter#3586D61
hypocenterC61#63093
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×#41 ◁ #3586

Complements

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

NH ≅ G/Ntype
1. #21460632C2semidirect
2. #21460631C2semidirect
3. #21460607C2semidirect
4. #21460604C2semidirect
5. #21460603C2semidirect
6. #21460602C2semidirect
7. #21460601C2semidirect
8. #21460592C2semidirect
9. #21460591C2semidirect
10. #21460590C2semidirect
11. C2×#16840578C2semidirect
12. C2×#16840577C2semidirect
13. #578×D61C2semidirect
14. #21460532C2semidirect
15. C61×#3586C2semidirect
17. #16840599C22semidirect
21. #16840598C22semidirect
22. #16840598C22semidirect
23. #16840598C22semidirect
25. #16840597C22semidirect
27. C2×#14519825C22semidirect
29. C2×#14519824C22semidirect
30. C2×#14519824C22semidirect
33. 2−1+4×D61C22semidirect
34. 2−1+4×D61C22semidirect
35. #16840579C22semidirect
36. #16840578C22semidirect
37. #16840578C22semidirect
38. #16840578C22semidirect
39. #16840578C22semidirect
40. #16840578C22semidirect
41. #16840577C22semidirect
42. #16840577C22semidirect
43. #16840577C22semidirect
44. #16840576C22semidirect
45. #16840575C22semidirect
46. #16840574C22semidirect
47. #16840573C22semidirect
48. #16840572C22semidirect
49. #16840572C22semidirect
50. #16840571C22semidirect
51. #16840571C22semidirect
52. #16840570C22semidirect
53. #16840569C22semidirect
54. #16840568C22semidirect
55. #16840566C22semidirect
56. #16840566C22semidirect
57. #16840565C22semidirect
58. #16840562C22semidirect
59. #16840561C22semidirect
60. #16840560C22semidirect
61. #16840559C22semidirect
62. #16840558C22semidirect
63. C2×#14519810C22semidirect
64. C2×#14519809C22semidirect
65. C2×#14519808C22semidirect
66. C2×#14519807C22semidirect
67. C2×#14519806C22semidirect
68. #137×D61C22semidirect
69. #137×D61C22semidirect
70. C2×#14519798C22semidirect
71. C2×#14519797C22semidirect
72. C2×#14519797C22semidirect
73. #135×D61C22semidirect
74. C22×#11758202C22semidirect
75. C2×Q16×D61C22semidirect
76. #16840528C22semidirect
77. #16840527C22semidirect
78. C2×#14519785C22semidirect
79. C2×#14519784C22semidirect
80. #131×D61C22semidirect
81. C61×#585C22semidirect
82. C2×2−1+4×C61C22semidirect
83. C61×#578C22semidirect
84. C61×#577C22semidirect
85. C61×#575C22semidirect
86. C2×#137×C61C22semidirect
87. C61×#568C22semidirect
510. #3586D61semidirect
536. #585C2×D61semidirect
546. C2×2−1+4C2×D61semidirect
558. #578C2×D61semidirect
568. #577C2×D61semidirect
577. #575C2×D61semidirect
585. C2×#137C2×D61semidirect
594. #568C2×D61semidirect
598. C61#63093semidirect

Maximal subgroups

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

subgroupindex
#214606322
#214606312
#214606072
#214606042
#214606032
#214606022
#214606012
#214605922
#214605912
#214605902
C2×#168405782
C2×#168405772
#578×D612
#214605322
C61×#35862
#6309361