Finite Group Databasebeta

← #30556270

Subgroups — #30556270

Order 15616.

2624 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460606C211yesmaximal, characteristic, complemented
2#21460596C211yesmaximal, characteristic, complemented
3#21460592C211yesmaximal, characteristic, complemented
4C2×#16840570C211yesmaximal, characteristic, complemented
5#21457609C214yesmaximal, complemented
6#21457598C214yesmaximal, complemented
7#21457589C214yesmaximal, complemented
8#21457587C214yesmaximal, complemented
9#21456297C211yesmaximal, characteristic, complemented
10#21455555C211yesmaximal, characteristic, complemented
11#21455549C211yesmaximal, characteristic, complemented
12#21455536C211yesmaximal, characteristic, complemented
13C2×#16840028C211yesmaximal, characteristic, complemented
14#21455197C211yesmaximal, characteristic, complemented
15#21455192C211yesmaximal, characteristic, complemented
16#21455178C211yesmaximal, characteristic, complemented
17#21454732C211yesmaximal, characteristic, complemented
18#21454718C211yesmaximal, characteristic, complemented
19C61×#3020C211yesmaximal, characteristic, complemented
20#16840598C2211yescharacteristic
21#16840598C2211yescharacteristic, complemented
22C2×#14519823C2211yescharacteristic, complemented
23#16840578—21no—
24#16840578C2212yescomplemented
25#16840577—22no—
26#16840577C2214yescomplemented
27#16840572—21no—
28#16840572C2212yescomplemented
29#16840571—21no—
30#16840571C2214yescomplemented
31#16840571C2212yescomplemented
32#16840570—22no—
33#16840570—22no—
34#16840570—22no—
35#16840570C2214yescomplemented
36#16840570C2214yescomplemented
37#16840570C2214yescomplemented
38#16840569—22no—
39#16840566—21no—
40#16840566C2214yescomplemented
41#16840566C2212yescomplemented
42#16840564—22no—
43#16840562C2211yescharacteristic
44#16840561—22no—
45#16840560—22no—
46#16840560C2211yescharacteristic
47#16840560C2211yescharacteristic, complemented
48#16840559—22no—
49C2×#14519808—21no—
50C2×#14519808—22no—
51C2×#14519808C2211yescharacteristic, complemented
52C2×#14519808C2211yescharacteristic, complemented
53C2×#14519808C2211yescharacteristic, complemented
54C2×#14519805C2211yescharacteristic
55C2×#14519802—21no—
56C2×#14519802C2211yescharacteristic, complemented
57C2×#14519802C2211yescharacteristic, complemented
58AGL(1,ℤ/8)×D61—22no—
59C2×#14519797—21no—
60C2×#14519797C2211yescharacteristic
61C2×#14519797C2211yescharacteristic, complemented
62#135×D61—22no—
63C22×#11758201—21no—
64C22×#11758201C2211yescharacteristic, complemented
65#16840529C2211yescharacteristic, complemented
66#16840528C2211yescharacteristic, complemented
67C2×#14519785C2211yescharacteristic, complemented
68C2×#14519784C2211yescharacteristic, complemented
69#16840331C2211yescharacteristic, complemented
70#16840154C2212yescomplemented
71#16840152C2212yescomplemented
72#16840144C2212yescomplemented
73#16840136C2212yescomplemented
74#16840036C2214yescomplemented
75#16840035C2212yescomplemented
76#16840030C2212yescomplemented
77#16840030C2214yescomplemented
78#16840028C2214yescomplemented
79#16840028C2214yescomplemented
80#16840028C2214yescomplemented
81#16840027C2212yescomplemented
82#16840027C2214yescomplemented
83#16840023C2212yescomplemented
84#16839944C2214yescomplemented
85#16839941C2214yescomplemented
86#16839939C2214yescomplemented
87#16839936C2214yescomplemented
88#16839931C2214yescomplemented
89#16839931C2214yescomplemented
90#16839881C2214yescomplemented
91#16839881C2214yescomplemented
92#16839876C2214yescomplemented
93#16839876C2214yescomplemented
94#16839810C2211yescharacteristic, complemented
95C2×#14519712C2211yescharacteristic, complemented
96#16839780C2211yescharacteristic, complemented
97#16839780C2211yescharacteristic, complemented
98#16839746C2211yescharacteristic, complemented
99#16839744C2211yescharacteristic, complemented
100C2×#14519693C2211yescharacteristic, complemented
101#16839718C2211yescharacteristic, complemented
102C2×2−1+4×C61C2211yescharacteristic, complemented
103C61×#575C2211yescharacteristic, complemented
104C61×#575C2211yescharacteristic, complemented
105C61×#536C2211yescharacteristic, complemented
106C61×#456C2214yescomplemented
107C61×#454C2214yescomplemented
108C61×#421C2211yescharacteristic, complemented
109C61×#421C2211yescharacteristic, complemented
110C2×#101×C61C2211yescharacteristic, complemented
111#14519825—21no—
112#14519825C2312yes—
113#14519824—21no—
114#14519824—21no—
115#14519824—21no—
116#14519824C2312yescomplemented
117#14519823—22no—
118#14519823—21no—
119#14519823—22no—
120#14519823—21no—
121#14519823—21no—
122#14519823—41no—
123#14519823C2314yes—
124#14519823C2312yescomplemented
125#14519822—21no—
126#14519822—41no—
127#14519822—41no—
128#14519822C2312yes—
129C2×#11758226—21no—
130C2×#11758222—22no—
131C2×#11758222—21no—
132C2×#11758222—41no—
133C2×#11758222C2311yescharacteristic
134C2×#11758222C2311yescharacteristic
135C2×#11758222C2311yescharacteristic
136#41×D61—22no—
137#41×D61—22no—
138#41×D61—22no—
139#41×D61—41no—
140C22×D244—21no—
141C22×D244C2311yescharacteristic
142C2×D4×D61—21no—
143C2×D4×D61—41no—
144#14519810—21no—
145#14519810C2312yes—
146#14519809—22no—
147#14519809—24no—
148#14519809—22no—
149#14519808—21no—
150#14519808—22no—
151#14519808—22no—
152#14519808—24no—
153#14519808—24no—
154#14519808—24no—
155#14519808—24no—
156#14519808—22no—
157#14519808—22no—
158#14519808D412yescomplemented
159#14519808C2314yes—
160#14519808C2314yescomplemented
161#14519807—24no—
162#14519807D412yescomplemented
163#14519807C2312yes—
164#14519806—22no—
165#14519806—22no—
166#14519805—22no—
167#14519805—21no—
168#14519805C2314yes—
169#14519805C2312yes—
170#14519804—22no—
171#14519804—24no—
172#14519804—24no—
173#14519804—22no—
174#14519803—21no—
175#14519803D412yescomplemented
176#14519802—22no—
177#14519802—24no—
178#14519802—24no—
179#14519802—24no—
180#14519802—22no—
181#14519802—22no—
182#14519802D412yescomplemented
183#14519802C2314yes—
184#14519802C2312yes—
185#14519801—24no—
186#14519801—22no—
187#14519801—22no—
188#14519800—22no—
189#14519800—24no—
190#14519799—22no—
191#14519798—22no—
192#14519798—24no—
193#14519798—22no—
194#14519797—22no—
195#14519797—24no—
196#14519797—24no—
197#14519797—24no—
198#14519797—24no—
199#14519797—21no—
200#14519797—21no—
201#14519797—21no—
202#14519797—21no—
203#14519797D412yescomplemented
204#14519797D412yescomplemented
205#14519797C2312yes—
206#14519797C2312yes—
207#14519797C2314yes—
208#14519796—22no—
209C2×#11758202—21no—
210C2×#11758202—21no—
211C2×#11758202—24no—
212C2×#11758202D411yescharacteristic, complemented
213C2×#11758202C2311yescharacteristic, complemented
214C2×#11758202C2312yescomplemented
215Q16×D61—22no—
216C2×#11758190—21no—
217C2×#11758200D411yescharacteristic, complemented
218C2×#11758200C2311yescharacteristic, complemented
219C2×#11758201—21no—
220C2×#11758201—21no—
221C2×#11758201—21no—
222C2×#11758201—24no—
223C2×#11758201—24no—
224C2×#11758201—24no—
225C2×#11758201—21no—
226C2×#11758201—21no—
227C2×#11758201—21no—
228C2×#11758201—21no—
229C2×#11758201D411yescharacteristic, complemented
230C2×#11758201C2312yes—
231C2×#11758201C2312yes—
232C2×#11758201C2312yes—
233C2×#11758201C2311yescharacteristic, complemented
234C2×#11758201C2312yescomplemented
235SD16×D61—22no—
236SD16×D61—22no—
237SD16×D61—24no—
238C2×D488—21no—
239C2×#11758199—21no—
240C2×#11758199D411yescharacteristic, complemented
241C2×#11758199C2312yes—
242C2×#11758199C2311yescharacteristic, complemented
243D8×D61—22no—
244D8×D61—24no—
245#14519785—21no—
246#14519785—21no—
247#14519785C2314yes—
248#14519785C2312yescomplemented
249#14519785C2312yescomplemented
250#14519784—22no—
251#14519784—21no—
252#14519784—21no—
253#14519784C2312yes—
254#14519784C2312yes—
255#14519784C2314yescomplemented
256#14519783—22no—
257C2×#11758194—22no—
258C2×#11758194—21no—
259C2×#11758194C2311yescharacteristic
260C2×#11758194C2311yescharacteristic
261C2×#11758194C2311yescharacteristic
262C2×#11758189—21no—
263M16×D61—22no—
264C22×#92418—21no—
265C22×#92418C2311yescharacteristic
266C2×C8×D61—21no—
267#14519774C2312yes—
268#14519765C2312yes—
269#14519752—41no—
270#14519747—41no—
271#14519712C2312yescomplemented
272#14519712C2314yescomplemented
273#14519712C2312yescomplemented
274#14519705C2314yes—
275#14519705C2314yescomplemented
276#14519696C2312yescomplemented
277#14519695C2312yescomplemented
278#14519694C2312yescomplemented
279#14519693C2314yes—
280#14519693C2312yescomplemented
281#14519688C2312yescomplemented
282C4×#92418C2312yescomplemented
2832−1+4×C61—22no—
2842−1+4×C61—22no—
2852−1+4×C61—41no—
2862−1+4×C61C2314yes—
287C2×#41×C61—21no—
288C2×#41×C61—21no—
289C2×#41×C61—41no—
290C2×#41×C61C2311yescharacteristic
291C2×#41×C61C2311yescharacteristic
292C2×#41×C61C2311yescharacteristic
293C22×Q8×C61—21no—
294C22×Q8×C61—21no—
295C22×Q8×C61C2311yescharacteristic
296#137×C61—21no—
297#137×C61—21no—
298#137×C61C2312yes—
299#137×C61C2312yescomplemented
300AGL(1,ℤ/8)×C61—21no—
301AGL(1,ℤ/8)×C61—21no—
302AGL(1,ℤ/8)×C61C2312yes—
303AGL(1,ℤ/8)×C61C2312yescomplemented
304#135×C61—22no—
305#135×C61—22no—
306C2×M16×C61C2311yescharacteristic
307C2×M16×C61C2311yescharacteristic
308C4⋊Q8×C61C2312yescomplemented
309#124×C61C2312yescomplemented
310#123×C61—41no—
311C22⋊Q8×C61—41no—
312#117×C61C2311yescharacteristic
313#104×C61C2314yes—
314#104×C61C2314yescomplemented
315#101×C61C2314yescomplemented
316C23×D61—21no—
317C23×D61—41no—
318#41×C61—21no—
319#41×C61—21no—
320#41×C61—21no—
321#41×C61—21no—
322#41×C61—24no—
323#41×C61—24no—
324#41×C61—21no—
325#41×C61—21no—
326#41×C61—21no—
327#41×C61—21no—
328#41×C61—44no—
329#41×C61—42no—
330#41×C61—42no—
331#41×C61—44no—
332#41×C61C2×D412yes—
333#41×C61C2×D412yes—
334#41×C61C2412yes—
335#41×C61C2412yes—
336C2×Q8×C61—21no—
337C2×Q8×C61—24no—
338C2×Q8×C61—24no—
339C2×Q8×C61—21no—
340C2×Q8×C61—21no—
341C2×Q8×C61—21no—
342C2×Q8×C61—21no—
343C2×Q8×C61—41no—
344C2×Q8×C61—42no—
345C2×Q8×C61—42no—
346C2×Q8×C61C2×D411yescharacteristic
347C2×Q8×C61C2×D411yescharacteristic
348C2×Q8×C61C2412yes—
349C2×Q8×C61C2411yescharacteristic
350C2×D4×C61—21no—
351C2×D4×C61—21no—
352C2×D4×C61—21no—
353C2×D4×C61—41no—
354C2×D4×C61C2×D411yescharacteristic
355C2×D4×C61C2×D411yescharacteristic
356C2×D4×C61C2411yescharacteristic
357C22×C4×C61—21no—
358C22×C4×C61—21no—
359C22×C4×C61—21no—
360C22×C4×C61—21no—
361C22×C4×C61—41no—
362C22×C4×C61—41no—
363C22×C4×C61C2411yescharacteristic
364C2×C22⋊D61—21no—
365C2×C22⋊D61—21no—
366C2×C22⋊D61—21no—
367C2×C22⋊D61—41no—
368C2×C22⋊D61—42no—
369C2×C22⋊D61—42no—
370#11758226—22no—
371#11758226—24no—
372#11758226—22no—
373#11758226—22no—
374#11758226—42no—
375#11758226—41no—
376Q8×D61—22no—
377Q8×D61—22no—
378Q8×D61—22no—
379Q8×D61—41no—
380#11758224—22no—
381#11758224—22no—
382#11758224—22no—
383#11758224—41no—
384#11758224—42no—
385#11758224—42no—
386#11758224—42no—
387#11758224—42no—
388D4×D61—24no—
389D4×D61—22no—
390D4×D61—22no—
391D4×D61—22no—
392D4×D61—42no—
393D4×D61—41no—
394D4×D61—44no—
395D4×D61—42no—
396D4×D61—44no—
397D4×D61—42no—
398D4×D61—42no—
399D4×D61—42no—
400#11758222—21no—
401#11758222—21no—
402#11758222—21no—
403#11758222—21no—
404#11758222—21no—
405#11758222—21no—
406#11758222—21no—
407#11758222—21no—
408#11758222—22no—
409#11758222—24no—
410#11758222—22no—
411#11758222—41no—
412#11758222—41no—
413#11758222—42no—
414#11758222—42no—
415#11758222—42no—
416#11758222—42no—
417#11758222—42no—
418#11758222C2×D412yes—
419#11758222C2×D412yes—
420#11758222C2412yes—
421#11758222C2412yes—
422C2×D244—21no—
423C2×D244—21no—
424C2×D244—21no—
425C2×D244—21no—
426C2×D244—24no—
427C2×D244—22no—
428C2×D244—21no—
429C2×D244—41no—
430C2×D244—42no—
431C2×D244—41no—
432C2×D244—42no—
433C2×D244C2×D411yescharacteristic
434C2×D244C2×D411yescharacteristic
435C2×D244C2412yes—
436C2×D244C2411yescharacteristic
437C2×C4×D61—21no—
438C2×C4×D61—21no—
439C2×C4×D61—21no—
440C2×C4×D61—42no—
441C2×C4×D61—42no—
442C2×C4×D61—41no—
443C2×Dic122—22no—
444C2×Dic122—41no—
445C2×Dic122C2×D411yescharacteristic
446C2×Dic122C2×D411yescharacteristic
447C2×Dic122C2411yescharacteristic
448Q16×C61—22no—
449Q16×C61—22no—
450SD16×C61—22no—
451SD16×C61—22no—
452SD16×C61—22no—
453SD16×C61—22no—
454D8×C61—22no—
455D8×C61—22no—
456M16×C61—21no—
457M16×C61—21no—
458M16×C61C2412yes—
459M16×C61C2412yes—
460C2×C8×C61—21no—
461C2×C8×C61—21no—
462C4⋊C4×C61—21no—
463C4⋊C4×C61—42no—
464C22⋊C4×C61—21no—
465C22⋊C4×C61—42no—
466C42×C61C2412yes—
467#11758202—22no—
468#11758202—24no—
469#11758202—24no—
470#11758202—24no—
471#11758202—21no—
472#11758202—21no—
473#11758202C2×D412yes—
474#11758202C2×D412yes—
475#11758202C2×D414yes—
476#11758201—22no—
477#11758201—24no—
478#11758201—24no—
479#11758201—24no—
480#11758201—24no—
481#11758201—22no—
482#11758201—22no—
483#11758201—21no—
484#11758201—24no—
485#11758201—21no—
486#11758201—22no—
487#11758201—22no—
488#11758201C2×D414yes—
489#11758201C2×D412yes—
490#11758201C2×D412yes—
491#11758200—22no—
492#11758200—21no—
493#11758200—21no—
494#11758200C2×D412yes—
495#11758200C2×D414yes—
496#11758200C2×D412yes—
497#11758199—24no—
498#11758199—22no—
499#11758199—21no—
500#11758199—24no—
501#11758199—21no—
502#11758199C2×D412yes—
503#11758199C2×D414yes—
504#11758199C2×D412yes—
505#11758198—42no—
506#11758194—21no—
507#11758194—21no—
508#11758194—22no—
509#11758194—22no—
510#11758194—24no—
511#11758194C2×D412yes—
512#11758194C2×D412yes—
513#11758194C2412yes—
514#11758194C2412yes—
515C2×#92418—21no—
516C2×#92418—21no—
517C2×#92418—22no—
518C2×#92418—22no—
519C2×#92418—24no—
520C2×#92418C2×D411yescharacteristic
521C2×#92418C2×D411yescharacteristic
522C2×#92418C2×D411yescharacteristic
523C2×#92418C2×D411yescharacteristic
524C2×#92418C2411yescharacteristic
525C2×#92418C2412yes—
526C2×#92418C2411yescharacteristic
527Dic244—22no—
528D488—24no—
529D488—22no—
530#11758190—22no—
531#11758190—22no—
532#11758190—24no—
533#11758189—24no—
534#11758189—22no—
535#11758189—22no—
536C8×D61—22no—
537C8×D61—22no—
538C8×D61—24no—
539C23×C61—21no—
540C23×C61—21no—
541C23×C61—21no—
542C23×C61H(5,𝔽2)11yescharacteristic
543C22×D61—21no—
544C22×D61—21no—
545C22×D61—22no—
546C22×D61—21no—
547C22×D61—42no—
548C22×D61—42no—
549C22×D61—44no—
550C22×D61—41no—
551C22×D61—41no—
552C22×D61—161no—
553C22×D61—162no—
554Q8×C61—21no—
555Q8×C61—21no—
556Q8×C61—22no—
557Q8×C61—22no—
558Q8×C61—21no—
559Q8×C61—21no—
560Q8×C61—44no—
561Q8×C61—41no—
562Q8×C61—41no—
563Q8×C61C22×D412yes—
564Q8×C61C22×D412yes—
565D4×C61—22no—
566D4×C61—22no—
567D4×C61—22no—
568D4×C61—22no—
569D4×C61—21no—
570D4×C61—21no—
571D4×C61—21no—
572D4×C61—21no—
573D4×C61—44no—
574D4×C61—41no—
575D4×C61—41no—
576D4×C61C22×D412yes—
577D4×C61C22×D412yes—
578C2×C4×C61—21no—
579C2×C4×C61—21no—
580C2×C4×C61—22no—
581C2×C4×C61—22no—
582C2×C4×C61—22no—
583C2×C4×C61—22no—
584C2×C4×C61—22no—
585C2×C4×C61—22no—
586C2×C4×C61—21no—
587C2×C4×C61—44no—
588C2×C4×C61—44no—
589C2×C4×C61—41no—
590C2×C4×C61—41no—
591C2×C4×C61—41no—
592C2×C4×C61—41no—
593C2×C4×C61C22×D411yescharacteristic
594C2×C4×C61C22×D411yescharacteristic
595C2×C4×C61C22×D411yescharacteristic
596C2×C4×C61C22×D411yescharacteristic
597C2×C4×C61H(5,𝔽2)11yescharacteristic
598C2×C4×C61C2511yescharacteristic
599C22⋊D61—22no—
600C22⋊D61—22no—
601C22⋊D61—22no—
602C22⋊D61—22no—
603C22⋊D61—42no—
604C22⋊D61—42no—
605C22⋊D61—44no—
606C22⋊D61—42no—
607C22⋊D61—42no—
608C22⋊D61—41no—
609C22⋊D61—41no—
610C2×Dic61—21no—
611C2×Dic61—21no—
612C2×Dic61—21no—
613C2×Dic61—42no—
614C2×Dic61—42no—
615D244—21no—
616D244—21no—
617D244—22no—
618D244—21no—
619D244—22no—
620D244—21no—
621D244—44no—
622D244—42no—
623D244—42no—
624D244—41no—
625D244—41no—
626D244—162no—
627D244C22×D412yes—
628D244C22×D412yes—
629C4×D61—22no—
630C4×D61—22no—
631C4×D61—22no—
632C4×D61—22no—
633C4×D61—44no—
634C4×D61—42no—
635C4×D61—42no—
636C4×D61—42no—
637C4×D61—42no—
638C4×D61—41no—
639C4×D61—41no—
640Dic122—21no—
641Dic122—21no—
642Dic122—21no—
643Dic122—21no—
644Dic122—42no—
645Dic122—42no—
646Dic122C22×D412yes—
647Dic122C22×D412yes—
648C8×C61—22no—
649C8×C61—22no—
650#92418—22no—
651#92418—22no—
652#92418C22×D411yescharacteristic
653#92418C22×D411yescharacteristic
654#92418C22×D414yes—
655#92418C22×D411yescharacteristic
656#92418C22×D411yescharacteristic
657#61107—611nomaximal, Sylow
658C22×C61—22no—
659C22×C61—22no—
660C22×C61—41no—
661C22×C61—42no—
662C22×C61—41no—
663C22×C61—81no—
664C22×C61—81no—
665C22×C61D4211yescharacteristic
666C22×C61D4211yescharacteristic
667C22×C61C2×H(5,𝔽2)11yescharacteristic
668C2×D61—22no—
669C2×D61—22no—
670C2×D61—41no—
671C2×D61—42no—
672C2×D61—81no—
673C2×D61—81no—
674C2×D61—82no—
675C2×D61—81no—
676C2×D61—82no—
677C2×D61—162no—
678C2×D61—162no—
679C2×D61—164no—
680C2×D61—161no—
681C4×C61—22no—
682C4×C61—22no—
683C4×C61—42no—
684C4×C61—41no—
685C4×C61—42no—
686C4×C61D4211yescharacteristic
687C4×C61D4211yescharacteristic
688C4×C61C23×D411yescharacteristic
689C4×C61C23×D411yescharacteristic
690Dic61—22no—
691Dic61—22no—
692Dic61—41no—
693#3586—611no—
694#3585—611no—
695#3584—611no—
696C2×#577—611no—
697#3291—614no—
698#3290—614no—
699#3289—614no—
700#3288—614no—
701#3154—611no—
702#3069—611no—
703#3068—611no—
704#3067—611no—
705C2×#471—611no—
706#3022—611no—
707#3021—611no—
708#3020D6111yescharacteristic, complemented
709#3019—611no—
710#2957—611no—
711#2955—611no—
712C2×C61—21no—
713C2×C61—21no—
714C2×C61—21no—
715C2×C61—42no—
716C2×C61—42no—
717C2×C61—81no—
718C2×C61C2×D4211yescharacteristic
719D61—42no—
720D61—42no—
721D61—82no—
722D61—81no—
723#585—611no—
724#585—611no—
725C2×2−1+4C2×D6111yescharacteristic, complemented
726C2×H(5,𝔽2)—611no—
727#578—614no—
728#578—612no—
729#578—1221no—
730#578—1222no—
731#577—614no—
732#577—614no—
733#577—614no—
734#577—614no—
735#577—612no—
736#577—612no—
737#577—1221no—
738#577—1221no—
739#577—1222no—
740#577—1222no—
741#577—1222no—
742#577—1222no—
743#576—614no—
744#576—612no—
745#576—1221no—
746#576—1222no—
747#575—611no—
748#575—611no—
749#575—611no—
750#575—1222no—
751#575—1222no—
752#575—1222no—
753#575C2×D6111yescharacteristic, complemented
754#575C2×D6111yescharacteristic, complemented
755C2×#137—611no—
756C2×#137—611no—
757C2×#137—611no—
758C2×#137—1221no—
759C2×#137—1222no—
760C2×AGL(1,ℤ/8)—611no—
761C2×AGL(1,ℤ/8)—611no—
762C2×AGL(1,ℤ/8)—611no—
763C2×AGL(1,ℤ/8)—1221no—
764C2×AGL(1,ℤ/8)—1222no—
765C2×#135—611no—
766C2×#135—611no—
767C2×#135—1221no—
768C2×#135—1222no—
769C22×SD16—611no—
770C22×SD16—1221no—
771#568—611no—
772#568—611no—
773C2×#131—611no—
774C2×#131—611no—
775#536C2×D6111yescharacteristic, complemented
776#535—611no—
777#497—612no—
778#496—612no—
779#495—612no—
780#492—612no—
781#473—612no—
782#473—614no—
783#472—612no—
784#472—614no—
785#471—612no—
786#471—614no—
787#471—612no—
788#471—614no—
789#471—614no—
790#471—614no—
791#456—614no—
792#456C2×D6114yescomplemented
793#455—614no—
794#455—614no—
795#454—614no—
796#454C2×D6114yescomplemented
797#453—614no—
798#453—614no—
799#444—614no—
800#444—614no—
801#443—614no—
802#443—614no—
803#430—611no—
804C2×#108—611no—
805#421—611no—
806#421—611no—
807#421C2×D6111yescharacteristic, complemented
808#421C2×D6111yescharacteristic, complemented
809#413—611no—
810#413—611no—
811C2×#101C2×D6111yescharacteristic, complemented
812C2×#100—611no—
813#405—611no—
814C61#6110711yescharacteristic, complemented, Sylow
8152−1+4—22no—
8162−1+4—22no—
8172−1+4—41no—
8182−1+4—612no—
8192−1+4—612no—
8202−1+4—1221no—
8212−1+4—1221no—
8222−1+4—1221no—
8232−1+4—1221no—
8242−1+4C22×D6114yes—
825H(5,𝔽2)—614no—
826H(5,𝔽2)—612no—
827H(5,𝔽2)—612no—
828H(5,𝔽2)—1221no—
829H(5,𝔽2)—1221no—
830H(5,𝔽2)—1221no—
831H(5,𝔽2)—1222no—
832H(5,𝔽2)—1222no—
833H(5,𝔽2)—1221no—
834H(5,𝔽2)—2441no—
835H(5,𝔽2)—2441no—
836H(5,𝔽2)—2441no—
837C2×#41—21no—
838C2×#41—21no—
839C2×#41—41no—
840C2×#41—611no—
841C2×#41—611no—
842C2×#41—611no—
843C2×#41—1221no—
844C2×#41—1222no—
845C2×#41—1222no—
846C2×#41—1222no—
847C2×#41—1222no—
848C2×#41—1221no—
849C2×#41—2441no—
850C2×#41—2441no—
851C2×#41C22×D6111yescharacteristic
852C2×#41C22×D6111yescharacteristic
853C2×#41C22×D6111yescharacteristic
854C22×Q8—21no—
855C22×Q8—21no—
856C22×Q8C22×D6111yescharacteristic
857C22×D4—611no—
858C22×D4—1221no—
859C22×D4—1221no—
860C22×D4—2441no—
861#137—21no—
862#137—21no—
863#137—612no—
864#137—612no—
865#137—612no—
866#137—614no—
867#137—614no—
868#137—612no—
869#137—1221no—
870#137—1222no—
871#137—1222no—
872#137—1222no—
873#137—1222no—
874#137—1222no—
875#137—1224no—
876#137—1224no—
877#137—1224no—
878#137—1222no—
879#137—1224no—
880#137—1224no—
881#137—1224no—
882#137—1222no—
883#137—1222no—
884#137—1221no—
885#137C22×D6112yes—
886#137C22×D6112yescomplemented
887AGL(1,ℤ/8)—21no—
888AGL(1,ℤ/8)—21no—
889AGL(1,ℤ/8)—612no—
890AGL(1,ℤ/8)—612no—
891AGL(1,ℤ/8)—614no—
892AGL(1,ℤ/8)—612no—
893AGL(1,ℤ/8)—614no—
894AGL(1,ℤ/8)—612no—
895AGL(1,ℤ/8)—1221no—
896AGL(1,ℤ/8)—1222no—
897AGL(1,ℤ/8)—1222no—
898AGL(1,ℤ/8)—1222no—
899AGL(1,ℤ/8)—1222no—
900AGL(1,ℤ/8)—1224no—
901AGL(1,ℤ/8)—1222no—
902AGL(1,ℤ/8)—1224no—
903AGL(1,ℤ/8)—1222no—
904AGL(1,ℤ/8)—1224no—
905AGL(1,ℤ/8)—1224no—
906AGL(1,ℤ/8)—1224no—
907AGL(1,ℤ/8)—1224no—
908AGL(1,ℤ/8)—1222no—
909AGL(1,ℤ/8)—1222no—
910AGL(1,ℤ/8)—1221no—
911AGL(1,ℤ/8)C22×D6112yes—
912AGL(1,ℤ/8)C22×D6112yescomplemented
913#135—22no—
914#135—22no—
915#135—612no—
916#135—612no—
917#135—612no—
918#135—612no—
919#135—614no—
920#135—1222no—
921#135—1221no—
922#135—1221no—
923#135—1221no—
924#135—1221no—
925#135—1222no—
926#135—1222no—
927#135—1224no—
928#135—1222no—
929#135—1224no—
930#135—1222no—
931#135—1224no—
932#135—1224no—
933#135—1224no—
934#135—1224no—
935#135—1222no—
936C2×Q16—611no—
937C2×Q16—611no—
938C2×Q16—612no—
939C2×Q16—1222no—
940C2×Q16—1224no—
941C2×Q16—1221no—
942C2×Q16—1221no—
943C2×SD16—611no—
944C2×SD16—611no—
945C2×SD16—612no—
946C2×SD16—612no—
947C2×SD16—611no—
948C2×SD16—612no—
949C2×SD16—612no—
950C2×SD16—611no—
951C2×SD16—1221no—
952C2×SD16—1221no—
953C2×SD16—1221no—
954C2×SD16—1221no—
955C2×SD16—1221no—
956C2×SD16—1222no—
957C2×SD16—1222no—
958C2×SD16—1224no—
959C2×SD16—1224no—
960C2×SD16—1224no—
961C2×SD16—1224no—
962C2×SD16—1221no—
963C2×SD16—1221no—
964C2×SD16—1221no—
965C2×D8—611no—
966C2×D8—611no—
967C2×D8—612no—
968C2×D8—1221no—
969C2×D8—1222no—
970C2×D8—1224no—
971C2×D8—1221no—
972#131—612no—
973#131—612no—
974#131—614no—
975#131—612no—
976#131—612no—
977#131—614no—
978#131—1222no—
979#131—1221no—
980#131—1221no—
981#131—1221no—
982#131—1221no—
983#131—1222no—
984C2×M16—611no—
985C2×M16—611no—
986C2×M16—611no—
987C2×M16—1221no—
988C2×M16—1221no—
989C2×M16—1222no—
990C2×M16—1222no—
991C2×M16C22×D6111yescharacteristic
992C2×M16C22×D6111yescharacteristic
993C22×C8—611no—
994C22×C8—1221no—
995C22×C8—1221no—
996C4⋊Q8C22×D6112yescomplemented
997#127—612no—
998#124—612no—
999#124C22×D6112yescomplemented
1000#123—41no—
1001C22⋊Q8—41no—
1002#121—2441no—
1003#120—2441no—
1004#117C22×D6111yescharacteristic
1005#108—612no—
1006#108—612no—
1007#108—614no—
1008#104—614no—
1009#104—614no—
1010#104C22×D6114yes—
1011#104C22×D6114yescomplemented
1012#101—612no—
1013#101—612no—
1014#101C22×D6114yescomplemented
1015#100—612no—
1016#100—614no—
1017#100—612no—
1018#97—612no—
1019C4×C8—612no—
1020C24—1221no—
1021C24—2441no—
1022#41—21no—
1023#41—21no—
1024#41—21no—
1025#41—21no—
1026#41—24no—
1027#41—24no—
1028#41—21no—
1029#41—21no—
1030#41—21no—
1031#41—21no—
1032#41—44no—
1033#41—42no—
1034#41—42no—
1035#41—44no—
1036#41—612no—
1037#41—612no—
1038#41—612no—
1039#41—612no—
1040#41—1222no—
1041#41—1224no—
1042#41—1222no—
1043#41—1221no—
1044#41—1221no—
1045#41—1221no—
1046#41—1221no—
1047#41—1222no—
1048#41—1222no—
1049#41—1222no—
1050#41—1222no—
1051#41—1224no—
1052#41—1222no—
1053#41—1222no—
1054#41—1221no—
1055#41—1221no—
1056#41—1221no—
1057#41—1221no—
1058#41—2442no—
1059#41—2442no—
1060#41—2442no—
1061#41—2442no—
1062#41—2442no—
1063#41—2441no—
1064#41—2441no—
1065#41—2442no—
1066#41—2442no—
1067#41—2442no—
1068#41—2442no—
1069#41—2442no—
1070#41—2441no—
1071#41—2441no—
1072#41D4×D6112yes—
1073#41D4×D6112yes—
1074#41C23×D6112yes—
1075#41C23×D6112yes—
1076C2×Q8—21no—
1077C2×Q8—24no—
1078C2×Q8—24no—
1079C2×Q8—21no—
1080C2×Q8—21no—
1081C2×Q8—21no—
1082C2×Q8—21no—
1083C2×Q8—41no—
1084C2×Q8—42no—
1085C2×Q8—42no—
1086C2×Q8—611no—
1087C2×Q8—611no—
1088C2×Q8—611no—
1089C2×Q8—1222no—
1090C2×Q8—1222no—
1091C2×Q8—1222no—
1092C2×Q8—1222no—
1093C2×Q8—2441no—
1094C2×Q8—2441no—
1095C2×Q8D4×D6111yescharacteristic
1096C2×Q8D4×D6111yescharacteristic
1097C2×Q8C23×D6111yescharacteristic
1098C2×Q8C23×D6112yes—
1099C2×D4—21no—
1100C2×D4—21no—
1101C2×D4—21no—
1102C2×D4—41no—
1103C2×D4—611no—
1104C2×D4—611no—
1105C2×D4—612no—
1106C2×D4—611no—
1107C2×D4—1224no—
1108C2×D4—1222no—
1109C2×D4—1222no—
1110C2×D4—1222no—
1111C2×D4—1221no—
1112C2×D4—1221no—
1113C2×D4—1224no—
1114C2×D4—1222no—
1115C2×D4—1221no—
1116C2×D4—1221no—
1117C2×D4—1221no—
1118C2×D4—1221no—
1119C2×D4—1221no—
1120C2×D4—1221no—
1121C2×D4—2442no—
1122C2×D4—2442no—
1123C2×D4—2441no—
1124C2×D4—2441no—
1125C2×D4—2442no—
1126C2×D4—2441no—
1127C2×D4—2444no—
1128C2×D4—2442no—
1129C2×D4—2444no—
1130C2×D4—2441no—
1131C2×D4—2442no—
1132C2×D4—2442no—
1133C2×D4—2442no—
1134C2×D4—2442no—
1135C2×D4—2442no—
1136C2×D4D4×D6111yescharacteristic
1137C2×D4D4×D6111yescharacteristic
1138C2×D4C23×D6111yescharacteristic
1139C22×C4—21no—
1140C22×C4—21no—
1141C22×C4—21no—
1142C22×C4—21no—
1143C22×C4—41no—
1144C22×C4—41no—
1145C22×C4—1221no—
1146C22×C4—1221no—
1147C22×C4—1221no—
1148C22×C4—2441no—
1149C22×C4—2442no—
1150C22×C4—2442no—
1151C22×C4C23×D6111yescharacteristic
1152Q16—22no—
1153Q16—22no—
1154Q16—612no—
1155Q16—612no—
1156Q16—614no—
1157Q16—1222no—
1158Q16—1221no—
1159Q16—1224no—
1160Q16—1221no—
1161Q16—1224no—
1162Q16—1224no—
1163Q16—1222no—
1164SD16—22no—
1165SD16—22no—
1166SD16—22no—
1167SD16—22no—
1168SD16—612no—
1169SD16—612no—
1170SD16—614no—
1171SD16—612no—
1172SD16—612no—
1173SD16—614no—
1174SD16—1222no—
1175SD16—1224no—
1176SD16—1222no—
1177SD16—1221no—
1178SD16—1221no—
1179SD16—1222no—
1180SD16—1222no—
1181SD16—1221no—
1182SD16—1222no—
1183SD16—1222no—
1184SD16—1224no—
1185SD16—1224no—
1186SD16—1221no—
1187SD16—1224no—
1188SD16—1224no—
1189SD16—1224no—
1190SD16—1222no—
1191SD16—1222no—
1192D8—22no—
1193D8—22no—
1194D8—612no—
1195D8—612no—
1196D8—614no—
1197D8—1224no—
1198D8—1222no—
1199D8—1221no—
1200D8—1224no—
1201D8—1221no—
1202D8—1224no—
1203D8—1222no—
1204M16—21no—
1205M16—21no—
1206M16—612no—
1207M16—612no—
1208M16—612no—
1209M16—612no—
1210M16—1224no—
1211M16—1222no—
1212M16—1222no—
1213M16—1222no—
1214M16—1222no—
1215M16—1224no—
1216M16—1221no—
1217M16—1221no—
1218M16C23×D6112yes—
1219M16C23×D6112yes—
1220C2×C8—21no—
1221C2×C8—21no—
1222C2×C8—611no—
1223C2×C8—611no—
1224C2×C8—611no—
1225C2×C8—611no—
1226C2×C8—611no—
1227C2×C8—612no—
1228C2×C8—611no—
1229C2×C8—1222no—
1230C2×C8—1222no—
1231C2×C8—1224no—
1232C2×C8—1222no—
1233C2×C8—1222no—
1234C2×C8—1224no—
1235C2×C8—1221no—
1236C2×C8—1221no—
1237C4⋊C4—21no—
1238C4⋊C4—42no—
1239C22⋊C4—21no—
1240C22⋊C4—42no—
1241C22⋊C4—2442no—
1242C42C23×D6112yes—
1243C23—21no—
1244C23—21no—
1245C23—21no—
1246C23—1221no—
1247C23—1221no—
1248C23—1222no—
1249C23—1221no—
1250C23—9762no—
1251C23—9761no—
1252C23—2442no—
1253C23—2444no—
1254C23—2442no—
1255C23—2441no—
1256C23—2441no—
1257C23#1451982211yescharacteristic
1258Q8—21no—
1259Q8—21no—
1260Q8—21no—
1261Q8—21no—
1262Q8—22no—
1263Q8—22no—
1264Q8—44no—
1265Q8—41no—
1266Q8—41no—
1267Q8—612no—
1268Q8—612no—
1269Q8—1221no—
1270Q8—1221no—
1271Q8—1221no—
1272Q8—1221no—
1273Q8—2442no—
1274Q8—2442no—
1275Q8C2×D4×D6112yes—
1276Q8C2×D4×D6112yes—
1277D4—22no—
1278D4—22no—
1279D4—22no—
1280D4—22no—
1281D4—21no—
1282D4—21no—
1283D4—21no—
1284D4—21no—
1285D4—44no—
1286D4—41no—
1287D4—41no—
1288D4—612no—
1289D4—612no—
1290D4—1222no—
1291D4—1222no—
1292D4—1222no—
1293D4—1222no—
1294D4—1222no—
1295D4—1221no—
1296D4—1222no—
1297D4—1221no—
1298D4—1221no—
1299D4—1221no—
1300D4—9762no—
1301D4—2444no—
1302D4—2442no—
1303D4—2442no—
1304D4—2444no—
1305D4—2442no—
1306D4—2442no—
1307D4—2442no—
1308D4—2442no—
1309D4—2441no—
1310D4—2441no—
1311D4—2441no—
1312D4—2441no—
1313D4C2×D4×D6112yes—
1314D4C2×D4×D6112yes—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—44no—
1325C2×C4—44no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—1221no—
1331C2×C4—1221no—
1332C2×C4—1222no—
1333C2×C4—1222no—
1334C2×C4—1222no—
1335C2×C4—1222no—
1336C2×C4—1221no—
1337C2×C4—2444no—
1338C2×C4—2442no—
1339C2×C4—2442no—
1340C2×C4—2442no—
1341C2×C4—2442no—
1342C2×C4—2442no—
1343C2×C4—2442no—
1344C2×C4—2441no—
1345C2×C4—2441no—
1346C2×C4C2×D4×D6111yescharacteristic
1347C2×C4C2×D4×D6111yescharacteristic
1348C2×C4C2×D4×D6111yescharacteristic
1349C2×C4C2×D4×D6111yescharacteristic
1350C2×C4#1451982211yescharacteristic
1351C2×C4C24×D6111yescharacteristic
1352C8—22no—
1353C8—22no—
1354C8—611no—
1355C8—611no—
1356C8—611no—
1357C8—611no—
1358C8—614no—
1359C8—1222no—
1360C8—1222no—
1361C22—22no—
1362C22—22no—
1363C22—41no—
1364C22—42no—
1365C22—41no—
1366C22—81no—
1367C22—81no—
1368C22—1222no—
1369C22—1222no—
1370C22—9761no—
1371C22—9764no—
1372C22—9762no—
1373C22—9762no—
1374C22—4881no—
1375C22—4882no—
1376C22—4882no—
1377C22—4881no—
1378C22—4881no—
1379C22—2441no—
1380C22—2442no—
1381C22#1684039411yescharacteristic
1382C22#1684039411yescharacteristic
1383C22C2×#1451982211yescharacteristic
1384C4—22no—
1385C4—22no—
1386C4—42no—
1387C4—42no—
1388C4—41no—
1389C4—1222no—
1390C4—1222no—
1391C4—2441no—
1392C4#1684039411yescharacteristic
1393C4#1684039411yescharacteristic
1394C4C22×D4×D6111yescharacteristic
1395C4C22×D4×D6111yescharacteristic
1396C2—21no—
1397C2—21no—
1398C2—21no—
1399C2—42no—
1400C2—42no—
1401C2—81no—
1402C2—4882no—
1403C2—4881no—
1404C2—2442no—
1405C2—2442no—
1406C2C2×#1684039411yescharacteristic
subgroupG/H
centerC2C2×#16840394
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3020C2
socleC2×C61C2×D42
hypercenter#3020D61
hypocenterC61#61107
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3020

Complements

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

NH ≅ G/Ntype
1. #21460606C2semidirect
2. #21460596C2semidirect
3. #21460592C2semidirect
4. C2×#16840570C2semidirect
5. #21457609C2semidirect
6. #21457598C2semidirect
7. #21457589C2semidirect
8. #21457587C2semidirect
9. #21456297C2semidirect
10. #21455555C2semidirect
11. #21455549C2semidirect
12. #21455536C2semidirect
13. C2×#16840028C2semidirect
14. #21455197C2semidirect
15. #21455192C2semidirect
16. #21455178C2semidirect
17. #21454732C2semidirect
18. #21454718C2semidirect
19. C61×#3020C2semidirect
21. #16840598C22semidirect
22. C2×#14519823C22semidirect
24. #16840578C22semidirect
26. #16840577C22semidirect
28. #16840572C22semidirect
30. #16840571C22semidirect
31. #16840571C22semidirect
35. #16840570C22semidirect
36. #16840570C22semidirect
37. #16840570C22semidirect
40. #16840566C22semidirect
41. #16840566C22semidirect
47. #16840560C22semidirect
51. C2×#14519808C22semidirect
52. C2×#14519808C22semidirect
53. C2×#14519808C22semidirect
56. C2×#14519802C22semidirect
57. C2×#14519802C22semidirect
61. C2×#14519797C22semidirect
64. C22×#11758201C22semidirect
65. #16840529C22semidirect
66. #16840528C22semidirect
67. C2×#14519785C22semidirect
68. C2×#14519784C22semidirect
69. #16840331C22semidirect
70. #16840154C22semidirect
71. #16840152C22semidirect
72. #16840144C22semidirect
73. #16840136C22semidirect
74. #16840036C22semidirect
75. #16840035C22semidirect
76. #16840030C22semidirect
77. #16840030C22semidirect
78. #16840028C22semidirect
79. #16840028C22semidirect
80. #16840028C22semidirect
81. #16840027C22semidirect
82. #16840027C22semidirect
83. #16840023C22semidirect
84. #16839944C22semidirect
85. #16839941C22semidirect
86. #16839939C22semidirect
87. #16839936C22semidirect
88. #16839931C22semidirect
89. #16839931C22semidirect
90. #16839881C22semidirect
91. #16839881C22semidirect
92. #16839876C22semidirect
93. #16839876C22semidirect
94. #16839810C22semidirect
95. C2×#14519712C22semidirect
96. #16839780C22semidirect
97. #16839780C22semidirect
98. #16839746C22semidirect
99. #16839744C22semidirect
100. C2×#14519693C22semidirect
101. #16839718C22semidirect
102. C2×2−1+4×C61C22semidirect
103. C61×#575C22semidirect
104. C61×#575C22semidirect
105. C61×#536C22semidirect
106. C61×#456C22semidirect
107. C61×#454C22semidirect
108. C61×#421C22semidirect
109. C61×#421C22semidirect
110. C2×#101×C61C22semidirect
116. #14519824C23semidirect
124. #14519823C23semidirect
158. #14519808D4semidirect
160. #14519808C23semidirect
162. #14519807D4semidirect
175. #14519803D4semidirect
182. #14519802D4semidirect
203. #14519797D4semidirect
204. #14519797D4semidirect
212. C2×#11758202D4semidirect
213. C2×#11758202C23semidirect
214. C2×#11758202C23semidirect
217. C2×#11758200D4semidirect
218. C2×#11758200C23semidirect
229. C2×#11758201D4semidirect
233. C2×#11758201C23semidirect
234. C2×#11758201C23semidirect
240. C2×#11758199D4semidirect
242. C2×#11758199C23semidirect
248. #14519785C23semidirect
249. #14519785C23semidirect
255. #14519784C23semidirect
271. #14519712C23semidirect
272. #14519712C23semidirect
273. #14519712C23semidirect
275. #14519705C23semidirect
276. #14519696C23semidirect
277. #14519695C23semidirect
278. #14519694C23semidirect
280. #14519693C23semidirect
281. #14519688C23semidirect
282. C4×#92418C23semidirect
299. #137×C61C23semidirect
303. AGL(1,ℤ/8)×C61C23semidirect
308. C4⋊Q8×C61C23semidirect
309. #124×C61C23semidirect
314. #104×C61C23semidirect
315. #101×C61C23semidirect
708. #3020D61semidirect
725. C2×2−1+4C2×D61semidirect
753. #575C2×D61semidirect
754. #575C2×D61semidirect
775. #536C2×D61semidirect
792. #456C2×D61semidirect
796. #454C2×D61semidirect
807. #421C2×D61semidirect
808. #421C2×D61semidirect
811. C2×#101C2×D61semidirect
814. C61#61107semidirect
886. #137C22×D61semidirect
912. AGL(1,ℤ/8)C22×D61semidirect
996. C4⋊Q8C22×D61semidirect
999. #124C22×D61semidirect
1011. #104C22×D61semidirect
1014. #101C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214606062
#214605962
#214605922
C2×#168405702
#214576092
#214575982
#214575892
#214575872
#214562972
#214555552
#214555492
#214555362
C2×#168400282
#214551972
#214551922
#214551782
#214547322
#214547182
C61×#30202
#6110761