Finite Group Databasebeta

← D61×#3586 #30593856

Subgroups — D61×#3586 #30593856

Order 15616.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#585×D61C211yesmaximal, characteristic, complemented
2C2×2−1+4×D61C211yesmaximal, characteristic, complemented
3#21460607C211yesmaximal, characteristic, complemented
4#21460606C211yesmaximal, characteristic, complemented
5#21460605C211yesmaximal, characteristic, complemented
6#21460604C218yesmaximal, complemented
7#21460603C216yesmaximal, complemented
8#21460602C216yesmaximal, complemented
9#21460601C218yesmaximal, complemented
10#578×D61C218yesmaximal, complemented
11#577×D61C218yesmaximal, complemented
12#575×D61C216yesmaximal, complemented
13C2×#137×D61C216yesmaximal, complemented
14#568×D61C211yesmaximal, characteristic, complemented
15C61×#3586C211yesmaximal, characteristic, complemented
16#16840599—21no—
17#16840599C2214yescomplemented
18#16840598—24no—
19#16840598C2211yescharacteristic, complemented
20#16840598C2216yescomplemented
21#16840597—23no—
22#16840597C2214yescomplemented
23C2×#14519825—21no—
24C2×#14519825C2213yescomplemented
25C2×#14519824—23no—
26C2×#14519824C2211yescharacteristic, complemented
27C2×#14519824C2213yescomplemented
282−1+4×D61—24no—
292−1+4×D61—24no—
302−1+4×D61—21no—
312−1+4×D61C2218yescomplemented
322−1+4×D61C2214yescomplemented
332−1+4×D61C2218yescomplemented
34H(5,𝔽2)×D61—23no—
35H(5,𝔽2)×D61C2214yescomplemented
36C2×#41×D61—24no—
37C2×#41×D61—23no—
38C2×#41×D61C2216yes—
39C2×#41×D61C2211yescharacteristic
40C2×#41×D61C2213yescomplemented
41C22×Q8×D61—21no—
42C22×Q8×D61C2213yescomplemented
43#16840579C2218yescomplemented
44#16840578C22124yescomplemented
45#16840578C22124yescomplemented
46#16840577C2218yescomplemented
47#16840577C2218yescomplemented
48#16840576C22124yescomplemented
49#16840575C22124yescomplemented
50#16840574C2218yescomplemented
51#16840573C2218yescomplemented
52#16840572C22124yescomplemented
53#16840571C22124yescomplemented
54#16840570C2218yescomplemented
55#16840569C22124yescomplemented
56#16840568C22124yescomplemented
57#16840562C2216yescomplemented
58#16840561C22112yescomplemented
59#16840561C22112yescomplemented
60#16840560C2216yescomplemented
61#16840560C2216yescomplemented
62#16840559C22124yescomplemented
63#16840558C22112yescomplemented
64#16840558C22112yescomplemented
65C2×#14519810C2216yescomplemented
66C2×#14519809C22112yescomplemented
67C2×#14519808C2216yescomplemented
68C2×#14519807C2216yescomplemented
69C2×#14519806C22112yescomplemented
70#137×D61C22112yescomplemented
71#137×D61C22124yescomplemented
72#137×D61C22112yescomplemented
73#137×D61C22124yescomplemented
74#137×D61C22124yescomplemented
75AGL(1,ℤ/8)×D61C2214yescomplemented
76AGL(1,ℤ/8)×D61C22112yescomplemented
77#135×D61C22124yescomplemented
78C2×Q16×D61C22112yescomplemented
79C2×SD16×D61C22112yescomplemented
80#16840529C2211yescharacteristic, complemented
81#16840528C2216yescomplemented
82#16840527C2218yescomplemented
83#131×D61C2218yescomplemented
84C2×M16×D61C2216yescomplemented
85C61×#585C2211yescharacteristic, complemented
86C2×2−1+4×C61C2211yescharacteristic, complemented
87C61×#578C2218yescomplemented
88C61×#577C2218yescomplemented
89C61×#575C2216yescomplemented
90C2×#137×C61C2216yescomplemented
91C61×#568C2211yescharacteristic, complemented
92#14519825—21no—
93#14519825—28no—
94#14519825—28no—
95#14519825—24no—
96#14519825—24no—
97#14519825—212no—
98#14519825C23124yescomplemented
99#14519825C23112yescomplemented
100#14519824—24no—
101#14519824—24no—
102#14519824—224no—
103#14519824—224no—
104#14519824—212no—
105#14519824—212no—
106#14519824—26no—
107#14519824C23124yescomplemented
108#14519824C23112yescomplemented
109#14519824C2318yescomplemented
110#14519824C2314yescomplemented
111#14519823—24no—
112#14519823—212no—
113#14519823—26no—
114#14519823C23112yescomplemented
115#14519823C2314yescomplemented
116#14519822—23no—
117#14519822—212no—
118#14519822—212no—
119#14519822—212no—
120#14519822C23112yescomplemented
121C2×#11758226—24no—
122C2×#11758226—23no—
123C2×#11758226D411yescharacteristic
124C2×#11758226C2316yes—
125C2×#11758226C2313yescomplemented
126C2×#11758222—26no—
127C2×#11758222—212no—
128C2×#11758222—23no—
129C2×#11758222—26no—
130C2×#11758222—23no—
131C2×#11758222C2313yes—
132C2×#11758222C2316yes—
133C2×#11758222C2313yescomplemented
134C2×#11758224—23no—
135C2×#11758224—26no—
136C2×#11758224—26no—
137C2×#11758224—23no—
138C2×#11758224—212no—
139C2×#11758224D413yes—
140C2×#11758224C2316yes—
141C2×#11758224C2313yescomplemented
142#41×D61—24no—
143#41×D61—24no—
144#41×D61—24no—
145#41×D61—212no—
146#41×D61—212no—
147#41×D61—224no—
148#41×D61—224no—
149#41×D61—212no—
150#41×D61—26no—
151#41×D61—26no—
152#41×D61—26no—
153#41×D61—26no—
154#41×D61—26no—
155#41×D61—26no—
156#41×D61D414yes—
157#41×D61D414yes—
158#41×D61C23112yes—
159#41×D61C23112yes—
160#41×D61C2314yes—
161#41×D61C23112yes—
162#41×D61C23112yes—
163#41×D61C2314yes—
164#41×D61C2314yes—
165#41×D61C23112yescomplemented
166C22×Dic122—23no—
167C22×Dic122—23no—
168C22×Dic122C2313yescomplemented
169C2×Q8×D61—21no—
170C2×Q8×D61—28no—
171C2×Q8×D61—28no—
172C2×Q8×D61—24no—
173C2×Q8×D61—23no—
174C2×Q8×D61—26no—
175C2×Q8×D61—26no—
176C2×Q8×D61—23no—
177C2×Q8×D61—23no—
178C2×Q8×D61D411yescharacteristic
179C2×Q8×D61C23112yes—
180C2×Q8×D61C2316yes—
181C2×Q8×D61C2313yes—
182C2×Q8×D61C2316yescomplemented
183C2×Q8×D61C23112yescomplemented
184C2×D4×D61—23no—
185C2×D4×D61—26no—
186C2×D4×D61—212no—
187C2×D4×D61D413yes—
188C2×D4×D61C2316yes—
189C2×D4×D61C2311yescharacteristic
190C22×C4×D61—23no—
191C22×C4×D61—23no—
192C22×C4×D61—26no—
193C22×C4×D61C2313yes—
194#14519810C23112yescomplemented
195#14519810C23124yescomplemented
196#14519810C23112yescomplemented
197#14519809C23124yescomplemented
198#14519809C23148yescomplemented
199#14519809C23124yescomplemented
200#14519808C23112yescomplemented
201#14519808C23124yescomplemented
202#14519808C23112yescomplemented
203#14519807C23112yescomplemented
204#14519807C23124yescomplemented
205#14519807C23112yescomplemented
206#14519806C23124yescomplemented
207#14519806C23148yescomplemented
208#14519806C23124yescomplemented
209#14519805C2314yescomplemented
210#14519805C23112yescomplemented
211#14519804C2318yescomplemented
212#14519804C23124yescomplemented
213#14519803C2314yescomplemented
214#14519803C23112yescomplemented
215#14519802C2314yescomplemented
216#14519802C23112yescomplemented
217#14519801C2318yescomplemented
218#14519801C23124yescomplemented
219#14519800C23124yescomplemented
220#14519799C23124yescomplemented
221#14519798C23124yescomplemented
222#14519798C23124yescomplemented
223#14519797C23124yescomplemented
224#14519797C23124yescomplemented
225#14519796C23124yescomplemented
226C2×Dic244C23112yescomplemented
227C2×#11758202C23112yescomplemented
228C2×#11758202C23112yescomplemented
229Q16×D61C23124yes—
230Q16×D61C23148yescomplemented
231C2×#11758190C23112yescomplemented
232C2×#11758200C23112yescomplemented
233C2×#11758201C23112yescomplemented
234SD16×D61C23124yes—
235SD16×D61C2318yes—
236SD16×D61C23148yescomplemented
237D8×D61C2318yes—
238#14519785C23124yescomplemented
239#14519784C2318yescomplemented
240#14519783C23124yescomplemented
241C2×#11758194C2316yescomplemented
242C2×#11758189C23112yescomplemented
243M16×D61C2314yes—
244M16×D61C23112yes—
245M16×D61C23112yescomplemented
246M16×D61C23112yescomplemented
247C2×C8×D61C23112yes—
2482−1+4×C61—24no—
2492−1+4×C61—21no—
2502−1+4×C61C2318yescomplemented
2512−1+4×C61C2314yescomplemented
252H(5,𝔽2)×C61—23no—
253H(5,𝔽2)×C61C2314yescomplemented
254C2×#41×C61—24no—
255C2×#41×C61—23no—
256C2×#41×C61C2316yes—
257C2×#41×C61C2311yescharacteristic
258C2×#41×C61C2313yescomplemented
259C22×Q8×C61—21no—
260C22×Q8×C61C2313yescomplemented
261#137×C61C23112yescomplemented
262#137×C61C23124yescomplemented
263#137×C61C23112yescomplemented
264AGL(1,ℤ/8)×C61C2314yescomplemented
265AGL(1,ℤ/8)×C61C23112yescomplemented
266#135×C61C23124yescomplemented
267C2×Q16×C61C23112yescomplemented
268C2×SD16×C61C23112yescomplemented
269#131×C61C2318yescomplemented
270C2×M16×C61C2316yescomplemented
271C23×D61—21no—
272C23×D61—26no—
273C23×D61C2×D413yes—
274#41×C61—24no—
275#41×C61—212no—
276#41×C61—224no—
277#41×C61—26no—
278#41×C61—26no—
279#41×C61—26no—
280#41×C61C2×D414yes—
281#41×C61C2414yes—
282#41×C61C24112yes—
283#41×C61C24112yes—
284#41×C61C2414yes—
285C2×Q8×C61—28no—
286C2×Q8×C61—24no—
287C2×Q8×C61—23no—
288C2×Q8×C61—26no—
289C2×Q8×C61C2×D411yescharacteristic
290C2×Q8×C61C2413yes—
291C2×Q8×C61C24112yes—
292C2×Q8×C61C2416yes—
293C2×D4×C61—23no—
294C2×D4×C61—26no—
295C2×D4×C61—212no—
296C2×D4×C61C2×D413yes—
297C2×D4×C61C2416yes—
298C2×D4×C61C2411yescharacteristic
299C22×C4×C61—23no—
300C22×C4×C61—23no—
301C22×C4×C61—26no—
302C22×C4×C61C2413yes—
303C2×C22⋊D61—23no—
304C2×C22⋊D61—26no—
305C2×C22⋊D61—23no—
306C2×C22⋊D61—26no—
307C2×C22⋊D61—224no—
308C2×C22⋊D61—21no—
309C2×C22⋊D61—26no—
310C2×C22⋊D61C2×D416yes—
311C22×Dic61—23no—
312C22×Dic61—23no—
313C22×Dic61—26no—
314C22×Dic61C2×D413yes—
315#11758226—24no—
316#11758226—212no—
317#11758226—224no—
318#11758226—26no—
319#11758226—26no—
320#11758226—26no—
321#11758226C2×D414yes—
322#11758226C2×D414yes—
323#11758226C2414yes—
324#11758226C24112yes—
325#11758226C24112yes—
326Q8×D61—28no—
327Q8×D61—24no—
328Q8×D61—23no—
329Q8×D61—212no—
330Q8×D61—23no—
331Q8×D61—212no—
332Q8×D61—26no—
333Q8×D61—212no—
334Q8×D61—212no—
335Q8×D61—212no—
336Q8×D61—26no—
337Q8×D61—224no—
338Q8×D61—212no—
339Q8×D61C2×D414yes—
340Q8×D61C2×D414yes—
341Q8×D61C2416yes—
342Q8×D61C24124yes—
343Q8×D61C24112yes—
344Q8×D61C2416yes—
345Q8×D61C2414yes—
346#11758224—212no—
347#11758224—224no—
348#11758224—224no—
349#11758224—248no—
350#11758224—24no—
351#11758224—212no—
352#11758224—212no—
353#11758224—212no—
354#11758224—212no—
355#11758224—212no—
356#11758224—26no—
357#11758224—26no—
358#11758224—26no—
359#11758224—212no—
360#11758224C2×D4112yes—
361#11758224C2×D4112yes—
362#11758224C2414yes—
363#11758224C24112yes—
364#11758224C24112yes—
365D4×D61—24no—
366D4×D61—212no—
367D4×D61—212no—
368D4×D61—212no—
369D4×D61—212no—
370D4×D61—212no—
371D4×D61—212no—
372D4×D61—224no—
373D4×D61—212no—
374D4×D61—26no—
375D4×D61—21no—
376D4×D61—21no—
377D4×D61—26no—
378D4×D61C2×D4112yes—
379D4×D61C2×D4112yes—
380D4×D61C2414yes—
381D4×D61C2412yes—
382D4×D61C24112yes—
383D4×D61C2412yes—
384#11758222—26no—
385#11758222—26no—
386#11758222—26no—
387#11758222—224no—
388#11758222—248no—
389#11758222—212no—
390#11758222—224no—
391#11758222—212no—
392#11758222—24no—
393#11758222—212no—
394#11758222—212no—
395#11758222—212no—
396#11758222—212no—
397#11758222—212no—
398#11758222C2×D4112yes—
399#11758222C24112yes—
400#11758222C2414yes—
401#11758222C24112yes—
402#11758222C24112yes—
403C2×D244—23no—
404C2×D244—26no—
405C2×D244—212no—
406C2×D244C2×D413yes—
407C2×D244C2416yes—
408C2×D244C2411yescharacteristic
409C2×C4×D61—23no—
410C2×C4×D61—26no—
411C2×C4×D61—212no—
412C2×C4×D61—212no—
413C2×C4×D61—26no—
414C2×C4×D61—23no—
415C2×C4×D61—26no—
416C2×C4×D61—23no—
417C2×C4×D61—26no—
418C2×C4×D61—24no—
419C2×C4×D61—212no—
420C2×C4×D61—212no—
421C2×C4×D61—212no—
422C2×C4×D61—212no—
423C2×C4×D61—212no—
424C2×C4×D61C2×D413yes—
425C2×C4×D61C2×D416yes—
426C2×C4×D61C2×D416yes—
427C2×C4×D61C2×D413yes—
428C2×C4×D61C2411yescharacteristic
429C2×C4×D61C2416yes—
430C2×C4×D61C2416yes—
431C2×C4×D61C2413yes—
432C2×Dic122—23no—
433C2×Dic122—26no—
434C2×Dic122—23no—
435C2×Dic122—26no—
436C2×Dic122—212no—
437C2×Dic122—212no—
438C2×Dic122—26no—
439C2×Dic122—224no—
440C2×Dic122—212no—
441C2×Dic122C2×D413yes—
442C2×Dic122C2413yes—
443C2×Dic122C24112yes—
444C2×Dic122C2416yes—
445Q16×C61C24124yes—
446SD16×C61C24124yes—
447SD16×C61C2418yes—
448D8×C61C2418yes—
449M16×C61C2414yes—
450M16×C61C24112yes—
451C2×C8×C61C24112yes—
452#11758202C24124yes—
453#11758202C24124yes—
454#11758201C24124yes—
455#11758201C2418yes—
456#11758200C24124yes—
457#11758200C2418yes—
458#11758199C2418yes—
459#11758199C2418yes—
460#11758194C2414yes—
461#11758194C24112yes—
462C2×#92418C24112yes—
463Dic244C24124yes—
464D488C2418yes—
465#11758190C24124yes—
466#11758190C2418yes—
467#11758189C2418yes—
468#11758189C24124yes—
469C8×D61C2418yes—
470C8×D61C24124yes—
471C23×C61—21no—
472C23×C61—26no—
473C23×C61C22×D413yes—
474C22×D61—21no—
475C22×D61—26no—
476C22×D61—22no—
477C22×D61—22no—
478C22×D61—24no—
479C22×D61—212no—
480C22×D61—46no—
481C22×D61—44no—
482C22×D61—812no—
483C22×D61C22×D411yescharacteristic
484C22×D61C22×D416yes—
485C22×D61C22×D413yes—
486C22×D61C22×D416yes—
487Q8×C61—212no—
488Q8×C61—23no—
489Q8×C61—26no—
490Q8×C61C22×D414yes—
491Q8×C61C2516yes—
492Q8×C61C2514yes—
493D4×C61—24no—
494D4×C61—212no—
495D4×C61—212no—
496D4×C61—26no—
497D4×C61—21no—
498D4×C61C22×D4112yes—
499D4×C61C2512yes—
500D4×C61C2514yes—
501C2×C4×C61—23no—
502C2×C4×C61—212no—
503C2×C4×C61—26no—
504C2×C4×C61—212no—
505C2×C4×C61—212no—
506C2×C4×C61—24no—
507C2×C4×C61C22×D413yes—
508C2×C4×C61C22×D416yes—
509C2×C4×C61C2516yes—
510C2×C4×C61C2511yescharacteristic
511C22⋊D61—212no—
512C22⋊D61—24no—
513C22⋊D61—212no—
514C22⋊D61—212no—
515C22⋊D61—24no—
516C22⋊D61—212no—
517C22⋊D61—22no—
518C22⋊D61—22no—
519C22⋊D61—24no—
520C22⋊D61—212no—
521C22⋊D61C22×D4124yes—
522C2×Dic61—23no—
523C2×Dic61—212no—
524C2×Dic61—26no—
525C2×Dic61—212no—
526C2×Dic61—212no—
527C2×Dic61—24no—
528C2×Dic61C22×D411yescharacteristic
529C2×Dic61C22×D416yes—
530C2×Dic61C22×D413yes—
531C2×Dic61C22×D416yes—
532D244—24no—
533D244—212no—
534D244—212no—
535D244—26no—
536D244—21no—
537D244C22×D4112yes—
538D244C2514yes—
539D244C2512yes—
540C4×D61—24no—
541C4×D61—26no—
542C4×D61—26no—
543C4×D61—212no—
544C4×D61—224no—
545C4×D61—24no—
546C4×D61—212no—
547C4×D61—212no—
548C4×D61—24no—
549C4×D61—212no—
550C4×D61—212no—
551C4×D61C22×D411yescharacteristic
552C4×D61C22×D416yes—
553C4×D61C22×D416yes—
554C4×D61C22×D416yes—
555C4×D61C22×D416yes—
556C4×D61C22×D411yescharacteristic
557C4×D61C22×D416yes—
558C4×D61C2511yescharacteristic
559C4×D61C2516yes—
560C4×D61C2511yescharacteristic
561Dic122—212no—
562Dic122—23no—
563Dic122—26no—
564Dic122—26no—
565Dic122—224no—
566Dic122—26no—
567Dic122—24no—
568Dic122—212no—
569Dic122C22×D4112yes—
570Dic122C2516yes—
571Dic122C2514yes—
572C8×C61C2518yes—
573#92418C2518yes—
574C2×#3586—611nomaximal, Sylow
575C22×C61—22no—
576C22×C61—24no—
577C22×C61—43no—
578C22×C61—42no—
579C22×C61—86no—
580C22×C61C23×D411yescharacteristic
581C22×C61C23×D416yes—
582C2×D61—22no—
583C2×D61—212no—
584C2×D61—22no—
585C2×D61—24no—
586C2×D61—46no—
587C2×D61—43no—
588C2×D61—44no—
589C2×D61—42no—
590C2×D61—44no—
591C2×D61—48no—
592C2×D61—812no—
593C2×D61—86no—
594C2×D61C23×D411yescharacteristic
595C2×D61C23×D416yes—
596C2×D61C23×D411yescharacteristic
597C4×C61—26no—
598C4×C61—24no—
599C4×C61C23×D416yes—
600C4×C61C23×D411yescharacteristic
601C4×C61C2611yescharacteristic
602Dic61—26no—
603Dic61—24no—
604Dic61C23×D411yescharacteristic
605Dic61C23×D416yes—
606Dic61C23×D411yescharacteristic
607C2×#585—611no—
608C22×2−1+4—611no—
609#3586—611no—
610#3586—611no—
611#3586—618no—
612#3586—618no—
613#3586—616no—
614#3586—616no—
615#3586—611no—
616#3586D6111yescharacteristic, direct product factor
617C2×#578—618no—
618C2×#577—618no—
619C2×#575—616no—
620C22×#137—616no—
621C2×#568—611no—
622C2×C61—21no—
623C2×C61—26no—
624C2×C61—42no—
625C2×C61—44no—
626C2×C61C24×D411yescharacteristic
627D61—21no—
628D61—26no—
629D61—42no—
630D61—44no—
631D61#358612yesdirect product factor
632#585—614no—
633#585—614no—
634#585—616no—
635#585—611no—
636#585—1224no—
637#585—1223no—
638#585—1221no—
639#585C2×D6111yescharacteristic, complemented
640C2×2−1+4—618no—
641C2×2−1+4—618no—
642C2×2−1+4—614no—
643C2×2−1+4—611no—
644C2×2−1+4—613no—
645C2×2−1+4—613no—
646C2×2−1+4—1221no—
647C2×2−1+4—1221no—
648C2×2−1+4—1223no—
649C2×2−1+4—1224no—
650C2×2−1+4—1224no—
651C2×2−1+4C2×D6111yescharacteristic, complemented
652C2×H(5,𝔽2)—614no—
653C2×H(5,𝔽2)—1223no—
654C22×#41—611no—
655C22×#41—616no—
656C22×#41—613no—
657C22×#41—1223no—
658C22×#41—1224no—
659C23×Q8—613no—
660C23×Q8—1221no—
661#578—618no—
662#578—618no—
663#578—6124no—
664#578—6124no—
665#578—6124no—
666#578—6124no—
667#578—618no—
668#578C2×D6118yescomplemented
669#577—618no—
670#577—618no—
671#577—6124no—
672#577—6124no—
673#577—6124no—
674#577—6124no—
675#577—618no—
676#577C2×D6118yescomplemented
677#575—616no—
678#575—616no—
679#575—6112no—
680#575—6112no—
681#575—6112no—
682#575—6112no—
683#575—6124no—
684#575—616no—
685#575C2×D6116yescomplemented
686C2×#137—616no—
687C2×#137—616no—
688C2×#137—6124no—
689C2×#137—6124no—
690C2×#137—6112no—
691C2×#137—6124no—
692C2×#137—6112no—
693C2×#137—6112no—
694C2×#137—6112no—
695C2×#137—616no—
696C2×#137C2×D6116yescomplemented
697C2×AGL(1,ℤ/8)—614no—
698C2×AGL(1,ℤ/8)—6112no—
699C2×#135—6124no—
700C22×Q16—6112no—
701C22×SD16—6112no—
702#568—611no—
703#568—618no—
704#568—616no—
705#568C2×D6111yescharacteristic, complemented
706C2×#131—618no—
707C22×M16—616no—
708C61C2×#358611yescharacteristic, complemented, Sylow
7092−1+4—24no—
7102−1+4—21no—
7112−1+4—6124no—
7122−1+4—618no—
7132−1+4—6112no—
7142−1+4—614no—
7152−1+4—6124no—
7162−1+4—6112no—
7172−1+4—1224no—
7182−1+4—1228no—
7192−1+4—1228no—
7202−1+4—12212no—
7212−1+4—1224no—
7222−1+4—1224no—
7232−1+4—1226no—
7242−1+4—12224no—
7252−1+4—12224no—
7262−1+4—12212no—
7272−1+4—12212no—
7282−1+4—1224no—
7292−1+4—1221no—
7302−1+4C22×D6118yescomplemented
7312−1+4C22×D6114yescomplemented
732H(5,𝔽2)—23no—
733H(5,𝔽2)—6112no—
734H(5,𝔽2)—614no—
735H(5,𝔽2)—6112no—
736H(5,𝔽2)—12212no—
737H(5,𝔽2)—12212no—
738H(5,𝔽2)—12212no—
739H(5,𝔽2)—12212no—
740H(5,𝔽2)—1226no—
741H(5,𝔽2)—1224no—
742H(5,𝔽2)—1223no—
743H(5,𝔽2)C22×D6114yescomplemented
744C2×#41—24no—
745C2×#41—23no—
746C2×#41—614no—
747C2×#41—614no—
748C2×#41—614no—
749C2×#41—614no—
750C2×#41—611no—
751C2×#41—613no—
752C2×#41—613no—
753C2×#41—6112no—
754C2×#41—6112no—
755C2×#41—614no—
756C2×#41—6112no—
757C2×#41—6112no—
758C2×#41—6112no—
759C2×#41—616no—
760C2×#41—613no—
761C2×#41—616no—
762C2×#41—613no—
763C2×#41—616no—
764C2×#41—613no—
765C2×#41—1223no—
766C2×#41—1226no—
767C2×#41—1226no—
768C2×#41—1223no—
769C2×#41—12212no—
770C2×#41—1223no—
771C2×#41—1226no—
772C2×#41—1226no—
773C2×#41—1226no—
774C2×#41—1226no—
775C2×#41—1226no—
776C2×#41—1226no—
777C2×#41—1226no—
778C2×#41—1226no—
779C2×#41—12212no—
780C2×#41—1223no—
781C2×#41—12212no—
782C2×#41—12224no—
783C2×#41—12224no—
784C2×#41—1224no—
785C2×#41—1224no—
786C2×#41—1224no—
787C2×#41—12212no—
788C2×#41—12212no—
789C2×#41—1224no—
790C2×#41—1223no—
791C2×#41C22×D6116yes—
792C2×#41C22×D6111yescharacteristic
793C2×#41C22×D6113yescomplemented
794C22×Q8—21no—
795C22×Q8—611no—
796C22×Q8—6112no—
797C22×Q8—616no—
798C22×Q8—613no—
799C22×Q8—616no—
800C22×Q8—6112no—
801C22×Q8—613no—
802C22×Q8—1223no—
803C22×Q8—1223no—
804C22×Q8—1223no—
805C22×Q8—1226no—
806C22×Q8—1223no—
807C22×Q8—1226no—
808C22×Q8—1228no—
809C22×Q8—1228no—
810C22×Q8—1223no—
811C22×Q8—1224no—
812C22×Q8—1221no—
813C22×Q8C22×D6113yescomplemented
814C22×D4—613no—
815C22×D4—616no—
816C22×D4—611no—
817C22×D4—12212no—
818C22×D4—1223no—
819C22×D4—1226no—
820C23×C4—613no—
821C23×C4—1223no—
822C23×C4—1226no—
823C23×C4—1223no—
824#137—6112no—
825#137—6124no—
826#137—6112no—
827#137—6112no—
828#137—6124no—
829#137—6112no—
830#137—6124no—
831#137—6148no—
832#137—6124no—
833#137—6124no—
834#137—6148no—
835#137—6124no—
836#137—6112no—
837#137—6124no—
838#137—6112no—
839#137C22×D61112yescomplemented
840#137C22×D61124yescomplemented
841#137C22×D61112yescomplemented
842AGL(1,ℤ/8)—614no—
843AGL(1,ℤ/8)—6112no—
844AGL(1,ℤ/8)—614no—
845AGL(1,ℤ/8)—6112no—
846AGL(1,ℤ/8)—618no—
847AGL(1,ℤ/8)—6124no—
848AGL(1,ℤ/8)—618no—
849AGL(1,ℤ/8)—6124no—
850AGL(1,ℤ/8)—614no—
851AGL(1,ℤ/8)—6112no—
852AGL(1,ℤ/8)C22×D6114yescomplemented
853AGL(1,ℤ/8)C22×D61112yescomplemented
854#135—6124no—
855#135—6124no—
856#135—6124no—
857#135—6124no—
858#135—6124no—
859#135—6124no—
860#135—6124no—
861#135C22×D61124yescomplemented
862C2×Q16—6112no—
863C2×Q16—6112no—
864C2×Q16—6124no—
865C2×Q16—6148no—
866C2×Q16—6112no—
867C2×Q16C22×D61112yescomplemented
868C2×SD16—6112no—
869C2×SD16—6112no—
870C2×SD16—6124no—
871C2×SD16—6148no—
872C2×SD16—618no—
873C2×SD16—6112no—
874C2×SD16C22×D61112yescomplemented
875C2×D8—618no—
876#131—618no—
877#131—6124no—
878#131—6124no—
879#131C22×D6118yescomplemented
880C2×M16—616no—
881C2×M16—614no—
882C2×M16—6112no—
883C2×M16—6112no—
884C2×M16—6112no—
885C2×M16—6112no—
886C2×M16C22×D6116yescomplemented
887C22×C8—6112no—
888C24—613no—
889C24—1226no—
890C24—1221no—
891#41—24no—
892#41—212no—
893#41—224no—
894#41—26no—
895#41—26no—
896#41—26no—
897#41—614no—
898#41—614no—
899#41—6112no—
900#41—6112no—
901#41—6112no—
902#41—6112no—
903#41—6112no—
904#41—6112no—
905#41—614no—
906#41—6112no—
907#41—6112no—
908#41—614no—
909#41—6112no—
910#41—6112no—
911#41—614no—
912#41—1224no—
913#41—12212no—
914#41—12212no—
915#41—12212no—
916#41—12212no—
917#41—12212no—
918#41—12224no—
919#41—12212no—
920#41—12248no—
921#41—12224no—
922#41—12212no—
923#41—1224no—
924#41—12212no—
925#41—1226no—
926#41—12212no—
927#41—12212no—
928#41—1226no—
929#41—12212no—
930#41—12212no—
931#41—1226no—
932#41—1226no—
933#41—1226no—
934#41—1226no—
935#41—12224no—
936#41—12248no—
937#41—12212no—
938#41—12212no—
939#41—12224no—
940#41—1224no—
941#41—12212no—
942#41—12224no—
943#41—1226no—
944#41—1226no—
945#41—1226no—
946#41D4×D6114yes—
947#41C23×D61112yes—
948#41C23×D61112yes—
949#41C23×D6114yes—
950#41C23×D6114yes—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—23no—
954C2×Q8—26no—
955C2×Q8—614no—
956C2×Q8—614no—
957C2×Q8—613no—
958C2×Q8—616no—
959C2×Q8—614no—
960C2×Q8—6124no—
961C2×Q8—6112no—
962C2×Q8—616no—
963C2×Q8—6112no—
964C2×Q8—616no—
965C2×Q8—613no—
966C2×Q8—1223no—
967C2×Q8—1226no—
968C2×Q8—12212no—
969C2×Q8—12212no—
970C2×Q8—1226no—
971C2×Q8—12224no—
972C2×Q8—12212no—
973C2×Q8—1223no—
974C2×Q8—1223no—
975C2×Q8—12212no—
976C2×Q8—12212no—
977C2×Q8—1226no—
978C2×Q8—12212no—
979C2×Q8—12212no—
980C2×Q8—12212no—
981C2×Q8—1226no—
982C2×Q8—12224no—
983C2×Q8—12212no—
984C2×Q8—1228no—
985C2×Q8—1224no—
986C2×Q8—1223no—
987C2×Q8—1226no—
988C2×Q8D4×D6111yescharacteristic
989C2×Q8C23×D61112yes—
990C2×Q8C23×D6116yes—
991C2×Q8C23×D6113yes—
992C2×D4—23no—
993C2×D4—26no—
994C2×D4—212no—
995C2×D4—616no—
996C2×D4—6112no—
997C2×D4—6112no—
998C2×D4—612no—
999C2×D4—614no—
1000C2×D4—6112no—
1001C2×D4—612no—
1002C2×D4—613no—
1003C2×D4—616no—
1004C2×D4—611no—
1005C2×D4—12212no—
1006C2×D4—1223no—
1007C2×D4—1226no—
1008C2×D4—1226no—
1009C2×D4—1221no—
1010C2×D4—1221no—
1011C2×D4—1226no—
1012C2×D4—1221no—
1013C2×D4—1226no—
1014C2×D4—12224no—
1015C2×D4—12212no—
1016C2×D4—1224no—
1017C2×D4—12212no—
1018C2×D4—12212no—
1019C2×D4—12212no—
1020C2×D4—12212no—
1021C2×D4—12212no—
1022C2×D4—12224no—
1023C2×D4—1223no—
1024C2×D4—1226no—
1025C2×D4—1223no—
1026C2×D4—1226no—
1027C2×D4—12212no—
1028C2×D4D4×D6113yes—
1029C2×D4C23×D6116yes—
1030C2×D4C23×D6111yescharacteristic
1031C22×C4—23no—
1032C22×C4—23no—
1033C22×C4—26no—
1034C22×C4—613no—
1035C22×C4—613no—
1036C22×C4—616no—
1037C22×C4—613no—
1038C22×C4—616no—
1039C22×C4—616no—
1040C22×C4—611no—
1041C22×C4—613no—
1042C22×C4—616no—
1043C22×C4—1224no—
1044C22×C4—12212no—
1045C22×C4—1223no—
1046C22×C4—12212no—
1047C22×C4—12212no—
1048C22×C4—1226no—
1049C22×C4—12212no—
1050C22×C4—12212no—
1051C22×C4—1223no—
1052C22×C4—1226no—
1053C22×C4—1226no—
1054C22×C4—12212no—
1055C22×C4—12212no—
1056C22×C4—1223no—
1057C22×C4—1226no—
1058C22×C4—1223no—
1059C22×C4—1223no—
1060C22×C4—1226no—
1061C22×C4C23×D6113yes—
1062Q16—6124no—
1063Q16—6124no—
1064Q16—6124no—
1065Q16C23×D61124yes—
1066SD16—6124no—
1067SD16—618no—
1068SD16—6124no—
1069SD16—618no—
1070SD16—6124no—
1071SD16—618no—
1072SD16C23×D61124yes—
1073SD16C23×D6118yes—
1074D8—618no—
1075D8—618no—
1076D8—618no—
1077D8C23×D6118yes—
1078M16—614no—
1079M16—6112no—
1080M16—618no—
1081M16—6124no—
1082M16C23×D6114yes—
1083M16C23×D61112yes—
1084C2×C8—6112no—
1085C2×C8—618no—
1086C2×C8—6124no—
1087C2×C8C23×D61112yes—
1088C23—21no—
1089C23—26no—
1090C23—611no—
1091C23—616no—
1092C23—616no—
1093C23—613no—
1094C23—12212no—
1095C23—1222no—
1096C23—1222no—
1097C23—1224no—
1098C23—1226no—
1099C23—1221no—
1100C23—48812no—
1101C23—2446no—
1102C23—2444no—
1103C23C2×D4×D6113yes—
1104Q8—23no—
1105Q8—212no—
1106Q8—26no—
1107Q8—6112no—
1108Q8—616no—
1109Q8—614no—
1110Q8—1226no—
1111Q8—1226no—
1112Q8—12224no—
1113Q8—1224no—
1114Q8—12212no—
1115Q8—1223no—
1116Q8—12212no—
1117Q8—1226no—
1118Q8C2×D4×D6114yes—
1119Q8C24×D6116yes—
1120Q8C24×D6114yes—
1121D4—24no—
1122D4—212no—
1123D4—212no—
1124D4—26no—
1125D4—21no—
1126D4—6124no—
1127D4—6112no—
1128D4—612no—
1129D4—614no—
1130D4—1224no—
1131D4—12212no—
1132D4—12212no—
1133D4—1224no—
1134D4—12212no—
1135D4—1222no—
1136D4—1222no—
1137D4—1224no—
1138D4—12212no—
1139D4—12212no—
1140D4—1224no—
1141D4—12212no—
1142D4—12212no—
1143D4—1226no—
1144D4—1221no—
1145D4C2×D4×D61112yes—
1146D4C24×D6112yes—
1147D4C24×D6114yes—
1148C2×C4—23no—
1149C2×C4—26no—
1150C2×C4—212no—
1151C2×C4—24no—
1152C2×C4—212no—
1153C2×C4—212no—
1154C2×C4—611no—
1155C2×C4—613no—
1156C2×C4—616no—
1157C2×C4—616no—
1158C2×C4—611no—
1159C2×C4—611no—
1160C2×C4—616no—
1161C2×C4—616no—
1162C2×C4—616no—
1163C2×C4—616no—
1164C2×C4—616no—
1165C2×C4—611no—
1166C2×C4—616no—
1167C2×C4—611no—
1168C2×C4—1224no—
1169C2×C4—12212no—
1170C2×C4—12212no—
1171C2×C4—1224no—
1172C2×C4—1226no—
1173C2×C4—1226no—
1174C2×C4—12212no—
1175C2×C4—12224no—
1176C2×C4—1224no—
1177C2×C4—12212no—
1178C2×C4—12212no—
1179C2×C4—1223no—
1180C2×C4—1226no—
1181C2×C4—12212no—
1182C2×C4—1224no—
1183C2×C4—12212no—
1184C2×C4—12212no—
1185C2×C4C2×D4×D6113yes—
1186C2×C4C2×D4×D6116yes—
1187C2×C4C24×D6116yes—
1188C2×C4C24×D6111yescharacteristic
1189C8—618no—
1190C8C24×D6118yes—
1191C22—22no—
1192C22—24no—
1193C22—43no—
1194C22—42no—
1195C22—86no—
1196C22—611no—
1197C22—611no—
1198C22—616no—
1199C22—12212no—
1200C22—1222no—
1201C22—1222no—
1202C22—1224no—
1203C22—4886no—
1204C22—48812no—
1205C22—2443no—
1206C22—2446no—
1207C22—2442no—
1208C22—2448no—
1209C22—2444no—
1210C22—2444no—
1211C22C22×D4×D6111yescharacteristic
1212C22C22×D4×D6116yes—
1213C4—24no—
1214C4—26no—
1215C4—611no—
1216C4—611no—
1217C4—616no—
1218C4—1224no—
1219C4—1226no—
1220C4C22×D4×D6111yescharacteristic
1221C4C22×D4×D6116yes—
1222C4C25×D6111yescharacteristic
1223C2—21no—
1224C2—26no—
1225C2—42no—
1226C2—44no—
1227C2—612no—
1228C2—1226no—
1229C2—1221no—
1230C2—2444no—
1231C2—2442no—
1232C2C23×D4×D6111yescharacteristic
subgroupG/H
centerC2C23×D4×D61
commutator, cosocleC4×C61C26
FrattiniC4C25×D61
FittingC61×#3586C2
socleC2×C61C24×D4
hypercenter#3586D61
hypocenterC61C2×#3586
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. #585×D61C2semidirect
2. C2×2−1+4×D61C2semidirect
3. #21460607C2semidirect
4. #21460606C2semidirect
5. #21460605C2semidirect
6. #21460604C2semidirect
7. #21460603C2semidirect
8. #21460602C2semidirect
9. #21460601C2semidirect
10. #578×D61C2semidirect
11. #577×D61C2semidirect
12. #575×D61C2semidirect
13. C2×#137×D61C2semidirect
14. #568×D61C2semidirect
15. C61×#3586C2semidirect
17. #16840599C22semidirect
19. #16840598C22semidirect
20. #16840598C22semidirect
22. #16840597C22semidirect
24. C2×#14519825C22semidirect
26. C2×#14519824C22semidirect
27. C2×#14519824C22semidirect
31. 2−1+4×D61C22semidirect
32. 2−1+4×D61C22semidirect
33. 2−1+4×D61C22semidirect
35. H(5,𝔽2)×D61C22semidirect
40. C2×#41×D61C22semidirect
42. C22×Q8×D61C22semidirect
43. #16840579C22semidirect
44. #16840578C22semidirect
45. #16840578C22semidirect
46. #16840577C22semidirect
47. #16840577C22semidirect
48. #16840576C22semidirect
49. #16840575C22semidirect
50. #16840574C22semidirect
51. #16840573C22semidirect
52. #16840572C22semidirect
53. #16840571C22semidirect
54. #16840570C22semidirect
55. #16840569C22semidirect
56. #16840568C22semidirect
57. #16840562C22semidirect
58. #16840561C22semidirect
59. #16840561C22semidirect
60. #16840560C22semidirect
61. #16840560C22semidirect
62. #16840559C22semidirect
63. #16840558C22semidirect
64. #16840558C22semidirect
65. C2×#14519810C22semidirect
66. C2×#14519809C22semidirect
67. C2×#14519808C22semidirect
68. C2×#14519807C22semidirect
69. C2×#14519806C22semidirect
70. #137×D61C22semidirect
71. #137×D61C22semidirect
72. #137×D61C22semidirect
73. #137×D61C22semidirect
74. #137×D61C22semidirect
75. AGL(1,ℤ/8)×D61C22semidirect
76. AGL(1,ℤ/8)×D61C22semidirect
77. #135×D61C22semidirect
78. C2×Q16×D61C22semidirect
79. C2×SD16×D61C22semidirect
80. #16840529C22semidirect
81. #16840528C22semidirect
82. #16840527C22semidirect
83. #131×D61C22semidirect
84. C2×M16×D61C22semidirect
85. C61×#585C22semidirect
86. C2×2−1+4×C61C22semidirect
87. C61×#578C22semidirect
88. C61×#577C22semidirect
89. C61×#575C22semidirect
90. C2×#137×C61C22semidirect
91. C61×#568C22semidirect
98. #14519825C23semidirect
99. #14519825C23semidirect
107. #14519824C23semidirect
108. #14519824C23semidirect
109. #14519824C23semidirect
110. #14519824C23semidirect
114. #14519823C23semidirect
115. #14519823C23semidirect
120. #14519822C23semidirect
125. C2×#11758226C23semidirect
133. C2×#11758222C23semidirect
141. C2×#11758224C23semidirect
165. #41×D61C23semidirect
168. C22×Dic122C23semidirect
182. C2×Q8×D61C23semidirect
183. C2×Q8×D61C23semidirect
194. #14519810C23semidirect
195. #14519810C23semidirect
196. #14519810C23semidirect
197. #14519809C23semidirect
198. #14519809C23semidirect
199. #14519809C23semidirect
200. #14519808C23semidirect
201. #14519808C23semidirect
202. #14519808C23semidirect
203. #14519807C23semidirect
204. #14519807C23semidirect
205. #14519807C23semidirect
206. #14519806C23semidirect
207. #14519806C23semidirect
208. #14519806C23semidirect
209. #14519805C23semidirect
210. #14519805C23semidirect
211. #14519804C23semidirect
212. #14519804C23semidirect
213. #14519803C23semidirect
214. #14519803C23semidirect
215. #14519802C23semidirect
216. #14519802C23semidirect
217. #14519801C23semidirect
218. #14519801C23semidirect
219. #14519800C23semidirect
220. #14519799C23semidirect
221. #14519798C23semidirect
222. #14519798C23semidirect
223. #14519797C23semidirect
224. #14519797C23semidirect
225. #14519796C23semidirect
226. C2×Dic244C23semidirect
227. C2×#11758202C23semidirect
228. C2×#11758202C23semidirect
230. Q16×D61C23semidirect
231. C2×#11758190C23semidirect
232. C2×#11758200C23semidirect
233. C2×#11758201C23semidirect
236. SD16×D61C23semidirect
238. #14519785C23semidirect
239. #14519784C23semidirect
240. #14519783C23semidirect
241. C2×#11758194C23semidirect
242. C2×#11758189C23semidirect
245. M16×D61C23semidirect
246. M16×D61C23semidirect
250. 2−1+4×C61C23semidirect
251. 2−1+4×C61C23semidirect
253. H(5,𝔽2)×C61C23semidirect
258. C2×#41×C61C23semidirect
260. C22×Q8×C61C23semidirect
261. #137×C61C23semidirect
262. #137×C61C23semidirect
263. #137×C61C23semidirect
264. AGL(1,ℤ/8)×C61C23semidirect
265. AGL(1,ℤ/8)×C61C23semidirect
266. #135×C61C23semidirect
267. C2×Q16×C61C23semidirect
268. C2×SD16×C61C23semidirect
269. #131×C61C23semidirect
270. C2×M16×C61C23semidirect
616. #3586D61direct (N × H)
631. D61#3586direct (N × H)
639. #585C2×D61semidirect
651. C2×2−1+4C2×D61semidirect
668. #578C2×D61semidirect
676. #577C2×D61semidirect
685. #575C2×D61semidirect
696. C2×#137C2×D61semidirect
705. #568C2×D61semidirect
708. C61C2×#3586semidirect
730. 2−1+4C22×D61semidirect
731. 2−1+4C22×D61semidirect
743. H(5,𝔽2)C22×D61semidirect
793. C2×#41C22×D61semidirect
813. C22×Q8C22×D61semidirect
839. #137C22×D61semidirect
840. #137C22×D61semidirect
841. #137C22×D61semidirect
852. AGL(1,ℤ/8)C22×D61semidirect
853. AGL(1,ℤ/8)C22×D61semidirect
861. #135C22×D61semidirect
867. C2×Q16C22×D61semidirect
874. C2×SD16C22×D61semidirect
879. #131C22×D61semidirect
886. C2×M16C22×D61semidirect

Maximal subgroups

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

subgroupindex
#585×D612
C2×2−1+4×D612
#214606072
#214606062
#214606052
#214606042
#214606032
#214606022
#214606012
#578×D612
#577×D612
#575×D612
C2×#137×D612
#568×D612
C61×#35862
C2×#358661