Finite Group Databasebeta

← #28604682

Subgroups — #28604682

Order 15104.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837524C211yesmaximal, characteristic, complemented
2#21432972C211yesmaximal, characteristic, complemented
3#21432629C211yesmaximal, characteristic, complemented
4#21432622C211yesmaximal, characteristic, complemented
5#21425001C211yesmaximal, characteristic, complemented
6#21424979C211yesmaximal, characteristic, complemented
7#21424613C211yesmaximal, characteristic, complemented
8#21424606C211yesmaximal, characteristic, complemented
9#21424474C211yesmaximal, characteristic, complemented
10#21424467C211yesmaximal, characteristic, complemented
11#21424160C211yesmaximal, characteristic, complemented
12#21424055C211yesmaximal, characteristic, complemented
13#21424050C211yesmaximal, characteristic, complemented
14#21423938C211yesmaximal, characteristic, complemented
15C2×C59×#577C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C2×#14273734C2211yescharacteristic, complemented
18#16837885C2211yescharacteristic
19#16837885C2211yescharacteristic, complemented
20#16837524—24no—
21#16837503—21no—
22#16837503—21no—
23Q16×Dic59—21no—
24D8×Dic59—21no—
25C2×#14273663C2211yescharacteristic, complemented
26C2×#14273661C2211yescharacteristic, complemented
27C2×#14273654C2211yescharacteristic
28C2×#14273654C2211yescharacteristic
29C2×#14273654C2211yescharacteristic, complemented
30#16837411—21no—
31#16837411C2211yescharacteristic, complemented
32#16837407—21no—
33#16837407C2211yescharacteristic
34#16837403—21no—
35#16837403—21no—
36#16837403C2211yescharacteristic
37#16837403C2211yescharacteristic
38#16837403C2211yescharacteristic
39#16837403C2211yescharacteristic, complemented
40#16837398—21no—
41#16837398—21no—
42#16837398C2211yescharacteristic
43C2×#14273651—21no—
44C2×#14273651C2211yescharacteristic, complemented
45C2×#14273648—21no—
46C2×#14273648C2211yescharacteristic
47C2×#14273646C2211yescharacteristic, complemented
48C2×#14273644C2211yescharacteristic
49#16837357C2211yescharacteristic, complemented
50C2×#14273637C2211yescharacteristic, complemented
51#16837309C2211yescharacteristic, complemented
52#16837305C2211yescharacteristic
53#16837170C2211yescharacteristic, complemented
54#16837170C2211yescharacteristic, complemented
55#16837166C2211yescharacteristic, complemented
56#16837163C2211yescharacteristic, complemented
57C2×2−1+4×C59C2211yescharacteristic
58C2×H(5,𝔽2)×C59C2211yescharacteristic
59C59×#577—24no—
60C59×#577C418yescomplemented
61C2×#137×C59—21no—
62C2×#137×C59C2211yescharacteristic
63C2×AGL(1,ℤ/8)×C59—21no—
64C2×AGL(1,ℤ/8)×C59C2211yescharacteristic
65C2×#135×C59—21no—
66C2×#135×C59C2211yescharacteristic
67C22×SD16×C59—21no—
68C22×SD16×C59C2211yescharacteristic
69C2×#131×C59C2211yescharacteristic
70#14273734—22no—
71#14273734—22no—
72#14273734—41no—
73#14273734—41no—
74C2×#11745664—21no—
75C2×#11745664—21no—
76C2×#11745664C2311yescharacteristic
77C2×#11745664C2311yescharacteristic
78C2×#11745664C2311yescharacteristic
79C22×C59⋊C8—21no—
80C22×C59⋊C8—21no—
81C22×C59⋊C8C2311yescharacteristic
82Q8×Dic59—21no—
83Q8×Dic59—21no—
84D4×Dic59—21no—
85D4×Dic59—21no—
86D4×Dic59—41no—
87D4×Dic59—41no—
88#14273686—21no—
89#14273686—21no—
90#14273686C2311yescharacteristic
91C2×C4⋊Dic59—21no—
92C2×C4⋊Dic59—21no—
93C2×C4⋊Dic59C2311yescharacteristic
94C2×C4⋊Dic59C2311yescharacteristic
95C2×C22⋊Dic59—41no—
96C2×C4×Dic59C2311yescharacteristic
97#14273663—22no—
98#14273661—21no—
99#14273661—21no—
100#14273654—22no—
101#14273654—22no—
102#14273654—22no—
103#14273651—21no—
104#14273651—21no—
105#14273651—21no—
106#14273651—21no—
107#14273651—21no—
108#14273651—21no—
109#14273651—21no—
110#14273651—21no—
111#14273651D411yescharacteristic
112#14273651D411yescharacteristic
113#14273648—21no—
114#14273648—21no—
115#14273648—21no—
116#14273648—21no—
117#14273648—21no—
118#14273648—21no—
119#14273648—21no—
120#14273648—21no—
121#14273648D411yescharacteristic
122#14273648D411yescharacteristic
123#14273646—41no—
124#14273644—41no—
125#14273637—21no—
126#14273637—22no—
127C8×Dic59—21no—
128C59⋊#95—41no—
1292−1+4×C59—22no—
1302−1+4×C59—22no—
1312−1+4×C59—41no—
1322−1+4×C59C2×C414yescomplemented
133H(5,𝔽2)×C59—22no—
134H(5,𝔽2)×C59—22no—
135H(5,𝔽2)×C59—41no—
136H(5,𝔽2)×C59C2×C414yescomplemented
137C2×#41×C59—21no—
138C2×#41×C59—21no—
139C2×#41×C59—21no—
140C2×#41×C59—21no—
141C2×#41×C59—41no—
142C2×#41×C59C2311yescharacteristic
143C2×#41×C59C2311yescharacteristic
144C2×#41×C59C2311yescharacteristic
145C22×Q8×C59—21no—
146C22×Q8×C59—21no—
147C22×Q8×C59C2311yescharacteristic
148C22×D4×C59—21no—
149C22×D4×C59—21no—
150C22×D4×C59—41no—
151C22×D4×C59C2311yescharacteristic
152#137×C59—22no—
153#137×C59—28no—
154#137×C59C2×C414yescomplemented
155AGL(1,ℤ/8)×C59—22no—
156AGL(1,ℤ/8)×C59—28no—
157AGL(1,ℤ/8)×C59C2×C414yescomplemented
158#135×C59—28no—
159#135×C59C2×C414yes—
160#135×C59D414yes—
161C2×Q16×C59—21no—
162C2×Q16×C59D411yescharacteristic
163C2×SD16×C59—21no—
164C2×SD16×C59—21no—
165C2×SD16×C59—28no—
166C2×SD16×C59—21no—
167C2×SD16×C59—21no—
168C2×SD16×C59—22no—
169C2×SD16×C59C2×C414yescomplemented
170C2×SD16×C59D411yescharacteristic
171C2×SD16×C59D411yescharacteristic
172C2×D8×C59—21no—
173C2×D8×C59D411yescharacteristic
174#131×C59—22no—
175#131×C59C2×C414yescomplemented
176C2×M16×C59—21no—
177C2×M16×C59C2311yescharacteristic
178C22×C8×C59—21no—
179C22×C8×C59C2311yescharacteristic
180C24×C59—21no—
181C24×C59—41no—
182#41×C59—21no—
183#41×C59—21no—
184#41×C59—21no—
185#41×C59—21no—
186#41×C59—21no—
187#41×C59—21no—
188#41×C59—24no—
189#41×C59—24no—
190#41×C59—24no—
191#41×C59—24no—
192#41×C59—44no—
193#41×C59—42no—
194#41×C59—42no—
195#41×C59—42no—
196#41×C59—42no—
197#41×C59—44no—
198#41×C59C22×C412yes—
199#41×C59C22×C412yes—
200#41×C59C22×C412yes—
201#41×C59C2×D412yes—
202#41×C59C2×D412yes—
203#41×C59#4112yes—
204C2×Q8×C59—21no—
205C2×Q8×C59—24no—
206C2×Q8×C59—24no—
207C2×Q8×C59—21no—
208C2×Q8×C59—21no—
209C2×Q8×C59—21no—
210C2×Q8×C59—21no—
211C2×Q8×C59—41no—
212C2×Q8×C59—42no—
213C2×Q8×C59—42no—
214C2×Q8×C59C22×C412yes—
215C2×Q8×C59C2×D411yescharacteristic
216C2×Q8×C59C2×D411yescharacteristic
217C2×Q8×C59C2×D411yescharacteristic
218C2×D4×C59—21no—
219C2×D4×C59—21no—
220C2×D4×C59—21no—
221C2×D4×C59—24no—
222C2×D4×C59—24no—
223C2×D4×C59—21no—
224C2×D4×C59—21no—
225C2×D4×C59—21no—
226C2×D4×C59—21no—
227C2×D4×C59—21no—
228C2×D4×C59—42no—
229C2×D4×C59—42no—
230C2×D4×C59—41no—
231C2×D4×C59—41no—
232C2×D4×C59—44no—
233C2×D4×C59—44no—
234C2×D4×C59—41no—
235C2×D4×C59C22×C412yes—
236C2×D4×C59C2×D411yescharacteristic
237C2×D4×C59C2×D411yescharacteristic
238C2×D4×C59C2×D411yescharacteristic
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—41no—
244C22×C4×C59—41no—
245C22×C4×C59—41no—
246C22×C4×C59C2411yescharacteristic
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—41no—
251C22×Dic59—41no—
252Q16×C59—24no—
253Q16×C59C22⋊C414yescomplemented
254SD16×C59—24no—
255SD16×C59—24no—
256SD16×C59—24no—
257SD16×C59—24no—
258SD16×C59C22⋊C414yescomplemented
259SD16×C59C22⋊C414yescomplemented
260D8×C59—24no—
261D8×C59C22⋊C414yescomplemented
262M16×C59—21no—
263M16×C59—24no—
264M16×C59C22×C412yes—
265C2×C8×C59—21no—
266C2×C8×C59—24no—
267C2×C8×C59C22×C412yes—
268C2×C8×C59C2×D411yescharacteristic
269C2×C8×C59C2×D411yescharacteristic
270C2×C8×C59C2×D412yes—
271C22⋊Dic59—21no—
272C22⋊Dic59—41no—
273C22⋊Dic59—41no—
274C22⋊Dic59—82no—
275C4⋊Dic59—21no—
276C4⋊Dic59—21no—
277C4⋊Dic59—21no—
278C4⋊Dic59—21no—
279C4⋊Dic59—41no—
280C4⋊Dic59—41no—
281C4⋊Dic59C2×D411yescharacteristic
282C4⋊Dic59C2×D411yescharacteristic
283C4×Dic59—21no—
284C4×Dic59—21no—
285C4×Dic59—21no—
286C4×Dic59—41no—
287C4×Dic59—41no—
288#11745664—21no—
289#11745664—21no—
290#11745664—21no—
291#11745664—21no—
292#11745664—21no—
293#11745664—21no—
294#11745664—42no—
295#11745664—42no—
296C2×C59⋊C8—21no—
297C2×C59⋊C8—21no—
298C2×C59⋊C8—21no—
299C2×C59⋊C8—21no—
300C2×C59⋊C8—21no—
301C2×C59⋊C8—42no—
302C2×C59⋊C8—42no—
303C2×C59⋊C8C2×D411yescharacteristic
304C2×C59⋊C8C2×D411yescharacteristic
305C23×C59—21no—
306C23×C59—21no—
307C23×C59—21no—
308C23×C59—22no—
309C23×C59—44no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—81no—
313C23×C59—81no—
314C23×C59—161no—
315C23×C59—161no—
316C23×C59H(5,𝔽2)11yescharacteristic
317Q8×C59—21no—
318Q8×C59—21no—
319Q8×C59—21no—
320Q8×C59—22no—
321Q8×C59—22no—
322Q8×C59—44no—
323Q8×C59—41no—
324Q8×C59—41no—
325Q8×C59C2×C22⋊C412yes—
326Q8×C59C2×C22⋊C412yes—
327Q8×C59C4×D412yes—
328D4×C59—22no—
329D4×C59—22no—
330D4×C59—22no—
331D4×C59—22no—
332D4×C59—22no—
333D4×C59—22no—
334D4×C59—22no—
335D4×C59—22no—
336D4×C59—21no—
337D4×C59—21no—
338D4×C59—21no—
339D4×C59—44no—
340D4×C59—44no—
341D4×C59—44no—
342D4×C59—41no—
343D4×C59—41no—
344D4×C59C2×C22⋊C412yes—
345D4×C59C2×C22⋊C412yes—
346D4×C59C4×D412yes—
347C2×C4×C59—21no—
348C2×C4×C59—21no—
349C2×C4×C59—21no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—44no—
358C2×C4×C59—44no—
359C2×C4×C59—44no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59C23×C411yescharacteristic
363C2×C4×C59C22×D411yescharacteristic
364C2×C4×C59C22×D411yescharacteristic
365C2×C4×C59C22×D411yescharacteristic
366C2×C4×C59C2×#4111yescharacteristic
367C2×C4×C59H(5,𝔽2)11yescharacteristic
368C2×Dic59—21no—
369C2×Dic59—21no—
370C2×Dic59—41no—
371C2×Dic59—41no—
372C2×Dic59—41no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C2×Dic59—81no—
376C2×Dic59—81no—
377C2×Dic59—161no—
378C2×Dic59—161no—
379C8×C59—22no—
380C8×C59C2×C22⋊C412yes—
381C8×C59C2×C22⋊C412yes—
382C59⋊C8—21no—
383C59⋊C8—21no—
384C59⋊C8—41no—
385C59⋊C8—41no—
386C59⋊C8—41no—
387#22464—591nomaximal, Sylow
388C22×C59—21no—
389C22×C59—21no—
390C22×C59—22no—
391C22×C59—22no—
392C22×C59—22no—
393C22×C59—41no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59—42no—
400C22×C59—82no—
401C22×C59—81no—
402C22×C59—81no—
403C22×C59—161no—
404C22×C59—164no—
405C22×C59#51811yescharacteristic
406C22×C59D4211yescharacteristic
407C22×C59#54611yescharacteristic
408C4×C59—22no—
409C4×C59—22no—
410C4×C59—22no—
411C4×C59—42no—
412C4×C59C22×C22⋊C411yescharacteristic
413C4×C59C2×C4×D411yescharacteristic
414C4×C59D4211yescharacteristic
415C4×C59#54611yescharacteristic
416Dic59—41no—
417Dic59—41no—
418Dic59—81no—
419Dic59—81no—
420Dic59—81no—
421C2×#577D5911yescharacteristic
422C2×#444—591no—
423#2951—591no—
424#2898—591no—
425#2897—591no—
426#1977—591no—
427#1973—591no—
428#1908—591no—
429#1907—591no—
430#1883—591no—
431#1882—591no—
432#1816—591no—
433#1793—591no—
434#1792—591no—
435#1765—591no—
436C2×C59—21no—
437C2×C59—21no—
438C2×C59—42no—
439C2×C59—42no—
440C2×C59—42no—
441C2×C59—82no—
442C2×C59D4×C22⋊C411yescharacteristic
443C2×C59#328811yescharacteristic
444C2×C59#328911yescharacteristic
445C2×2−1+4C2×D5911yescharacteristic
446C2×H(5,𝔽2)C2×D5911yescharacteristic
447#577—24no—
448#577Dic5918yescomplemented
449C2×#137—21no—
450C2×#137C2×D5911yescharacteristic
451C2×AGL(1,ℤ/8)—21no—
452C2×AGL(1,ℤ/8)C2×D5911yescharacteristic
453C2×#135—21no—
454C2×#135C2×D5911yescharacteristic
455C22×SD16—21no—
456C22×SD16C2×D5911yescharacteristic
457C2×#131—591no—
458C2×#131—591no—
459C2×#131C2×D5911yescharacteristic
460#520—591no—
461#520—591no—
462#444—1184no—
463#440—1181no—
464#440—1181no—
465C4×Q16—1181no—
466C4×D8—1181no—
467C2×#108—591no—
468C2×#107—591no—
469C2×#104—591no—
470C2×#104—591no—
471C2×#104—591no—
472#419—591no—
473#419—1181no—
474#418—591no—
475#418—1181no—
476#417—591no—
477#417—591no—
478#417—591no—
479#417—591no—
480#417—1181no—
481#417—1181no—
482#416—591no—
483#416—1181no—
484#416—1181no—
485C2×#103—591no—
486C2×#103—1181no—
487C2×#102—591no—
488C2×#102—1181no—
489C2×#101—591no—
490C2×#100—591no—
491#405—591no—
492C2×#97—591no—
493#391—591no—
494#390—591no—
495#343—591no—
496#343—591no—
497#341—591no—
498#339—591no—
499C59#2246411yescharacteristic, complemented, Sylow
5002−1+4—22no—
5012−1+4—22no—
5022−1+4—41no—
5032−1+4C2×Dic5914yescomplemented
504H(5,𝔽2)—22no—
505H(5,𝔽2)—22no—
506H(5,𝔽2)—41no—
507H(5,𝔽2)C2×Dic5914yescomplemented
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—41no—
513C2×#41C22×D5911yescharacteristic
514C2×#41C22×D5911yescharacteristic
515C2×#41C22×D5911yescharacteristic
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C22×D5911yescharacteristic
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4C22×D5911yescharacteristic
523#137—22no—
524#137—28no—
525#137C2×Dic5914yescomplemented
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—28no—
528AGL(1,ℤ/8)C2×Dic5914yescomplemented
529#135—28no—
530#135C2×Dic5914yes—
531#135C22⋊D5914yes—
532C2×Q16—21no—
533C2×Q16C22⋊D5911yescharacteristic
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—28no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—22no—
540C2×SD16C2×Dic5914yescomplemented
541C2×SD16C22⋊D5911yescharacteristic
542C2×SD16C22⋊D5911yescharacteristic
543C2×D8—21no—
544C2×D8C22⋊D5911yescharacteristic
545#131—22no—
546#131—1182no—
547#131—1182no—
548#131—2361no—
549#131—2361no—
550#131C2×Dic5914yescomplemented
551C2×M16—21no—
552C2×M16—591no—
553C2×M16—591no—
554C2×M16—591no—
555C2×M16—1181no—
556C2×M16—1181no—
557C2×M16C22×D5911yescharacteristic
558C22×C8—21no—
559C22×C8—591no—
560C22×C8—1181no—
561C22×C8—1181no—
562C22×C8C22×D5911yescharacteristic
563C4×Q8—1181no—
564C4×Q8—1181no—
565C4×D4—1181no—
566C4×D4—1181no—
567C4×D4—2361no—
568C4×D4—2361no—
569#117—591no—
570#117—1181no—
571#117—1181no—
572C2×C4⋊C4—591no—
573C2×C4⋊C4—591no—
574C2×C4⋊C4—1181no—
575C2×C4⋊C4—1181no—
576C2×C22⋊C4—2361no—
577C2×C42—591no—
578#108—1182no—
579#107—1181no—
580#107—1181no—
581#104—1182no—
582#104—1182no—
583#104—1182no—
584#103—591no—
585#103—591no—
586#103—1181no—
587#103—1181no—
588#103—1181no—
589#103—1181no—
590#103—1181no—
591#103—1181no—
592#103—1181no—
593#103—1181no—
594#102—591no—
595#102—591no—
596#102—1181no—
597#102—1181no—
598#102—1181no—
599#102—1181no—
600#102—1181no—
601#102—1181no—
602#102—1181no—
603#102—1181no—
604#101—2361no—
605#100—2361no—
606#97—1182no—
607#97—1181no—
608C4×C8—1181no—
609#95—2361no—
610C24—21no—
611C24—41no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—24no—
619#41—24no—
620#41—24no—
621#41—24no—
622#41—44no—
623#41—42no—
624#41—42no—
625#41—42no—
626#41—42no—
627#41—44no—
628#41#1174568712yes—
629#41C22×Dic5912yes—
630#41C22×Dic5912yes—
631#41C22×Dic5912yes—
632#41C2×C22⋊D5912yes—
633#41C2×C22⋊D5912yes—
634C2×Q8—21no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—41no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8D4×D5911yescharacteristic
645C2×Q8C22×Dic5912yes—
646C2×Q8C2×C22⋊D5911yescharacteristic
647C2×Q8C2×C22⋊D5911yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—41no—
661C2×D4—41no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—41no—
665C2×D4D4×D5911yescharacteristic
666C2×D4C22×Dic5912yes—
667C2×D4C2×C22⋊D5911yescharacteristic
668C2×D4C2×C22⋊D5911yescharacteristic
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—1181no—
677C22×C4—1181no—
678C22×C4—1181no—
679C22×C4—2361no—
680C22×C4—2361no—
681C22×C4C23×D5911yescharacteristic
682Q16—24no—
683Q16C22⋊Dic5914yescomplemented
684SD16—24no—
685SD16—24no—
686SD16—24no—
687SD16—24no—
688SD16C22⋊Dic5914yescomplemented
689SD16C22⋊Dic5914yescomplemented
690D8—24no—
691D8C22⋊Dic5914yescomplemented
692M16—21no—
693M16—24no—
694M16—1181no—
695M16—1181no—
696M16—1181no—
697M16—1181no—
698M16—1181no—
699M16—1181no—
700M16—2362no—
701M16—2362no—
702M16C22×Dic5912yes—
703C2×C8—21no—
704C2×C8—24no—
705C2×C8—591no—
706C2×C8—591no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—1181no—
710C2×C8—1181no—
711C2×C8—1181no—
712C2×C8—2362no—
713C2×C8—2362no—
714C2×C8C22×Dic5912yes—
715C2×C8C2×C22⋊D5911yescharacteristic
716C2×C8C2×C22⋊D5911yescharacteristic
717C2×C8C2×C22⋊D5912yes—
718C4⋊C4—591no—
719C4⋊C4—591no—
720C4⋊C4—1181no—
721C4⋊C4—1181no—
722C4⋊C4—1181no—
723C4⋊C4—1181no—
724C4⋊C4—2361no—
725C4⋊C4—2361no—
726C22⋊C4—1181no—
727C22⋊C4—4722no—
728C22⋊C4—2361no—
729C22⋊C4—2361no—
730C42—1181no—
731C42—1181no—
732C42—1181no—
733C42—2361no—
734C42—2361no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—44no—
740C23—41no—
741C23—41no—
742C23—81no—
743C23—81no—
744C23—161no—
745C23—161no—
746C23#1427377211yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—22no—
751Q8—22no—
752Q8—44no—
753Q8—41no—
754Q8—41no—
755Q8C2×C22⋊Dic5912yes—
756Q8C2×C22⋊Dic5912yes—
757Q8D4×Dic5912yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—21no—
765D4—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—44no—
770D4—44no—
771D4—44no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊Dic5912yes—
775D4C2×C22⋊Dic5912yes—
776D4D4×Dic5912yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—1181no—
793C2×C4—1181no—
794C2×C4—9441no—
795C2×C4—9441no—
796C2×C4—4721no—
797C2×C4—4721no—
798C2×C4—2361no—
799C2×C4—2361no—
800C2×C4—2361no—
801C2×C4—2361no—
802C2×C4—2361no—
803C2×C4C23×Dic5911yescharacteristic
804C2×C4C2×D4×D5911yescharacteristic
805C2×C4C22×C22⋊D5911yescharacteristic
806C2×C4C22×C22⋊D5911yescharacteristic
807C2×C4C2×#1174568711yescharacteristic
808C2×C4#1427377211yescharacteristic
809C8—22no—
810C8—1181no—
811C8—1181no—
812C8—2361no—
813C8—2361no—
814C8—2361no—
815C8C2×C22⋊Dic5912yes—
816C8C2×C22⋊Dic5912yes—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—82no—
830C22—81no—
831C22—81no—
832C22—161no—
833C22—164no—
834C22#1683787711yescharacteristic
835C22D4×C22⋊D5911yescharacteristic
836C22#1683804611yescharacteristic
837C4—22no—
838C4—22no—
839C4—22no—
840C4—42no—
841C4—4721no—
842C4—4721no—
843C4—4721no—
844C4—2361no—
845C4—2361no—
846C4C22×C22⋊Dic5911yescharacteristic
847C4C2×D4×Dic5911yescharacteristic
848C4D4×C22⋊D5911yescharacteristic
849C4#1683804611yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—42no—
855C2—82no—
856C2D4×C22⋊Dic5911yescharacteristic
857C2#2143585811yescharacteristic
858C2#2143586911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#577C2
socleC22×C59D42
cosocleC22×C4×C59C24
hypercenterC2×#577D59
hypocenterC59#22464
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#16837524C2semidirect
2. #21432972C2semidirect
3. #21432629C2semidirect
4. #21432622C2semidirect
5. #21425001C2semidirect
6. #21424979C2semidirect
7. #21424613C2semidirect
8. #21424606C2semidirect
9. #21424474C2semidirect
10. #21424467C2semidirect
11. #21424160C2semidirect
12. #21424055C2semidirect
13. #21424050C2semidirect
14. #21423938C2semidirect
17. C2×#14273734C22semidirect
19. #16837885C22semidirect
25. C2×#14273663C22semidirect
26. C2×#14273661C22semidirect
29. C2×#14273654C22semidirect
31. #16837411C22semidirect
39. #16837403C22semidirect
44. C2×#14273651C22semidirect
47. C2×#14273646C22semidirect
49. #16837357C22semidirect
50. C2×#14273637C22semidirect
51. #16837309C22semidirect
53. #16837170C22semidirect
54. #16837170C22semidirect
55. #16837166C22semidirect
56. #16837163C22semidirect
60. C59×#577C4semidirect
132. 2−1+4×C59C2×C4semidirect
136. H(5,𝔽2)×C59C2×C4semidirect
154. #137×C59C2×C4semidirect
157. AGL(1,ℤ/8)×C59C2×C4semidirect
169. C2×SD16×C59C2×C4semidirect
175. #131×C59C2×C4semidirect
253. Q16×C59C22⋊C4semidirect
258. SD16×C59C22⋊C4semidirect
259. SD16×C59C22⋊C4semidirect
261. D8×C59C22⋊C4semidirect
448. #577Dic59semidirect
499. C59#22464semidirect
503. 2−1+4C2×Dic59semidirect
507. H(5,𝔽2)C2×Dic59semidirect
525. #137C2×Dic59semidirect
528. AGL(1,ℤ/8)C2×Dic59semidirect
540. C2×SD16C2×Dic59semidirect
550. #131C2×Dic59semidirect
683. Q16C22⋊Dic59semidirect
688. SD16C22⋊Dic59semidirect
689. SD16C22⋊Dic59semidirect
691. D8C22⋊Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375242
#214329722
#214326292
#214326222
#214250012
#214249792
#214246132
#214246062
#214244742
#214244672
#214241602
#214240552
#214240502
#214239382
C2×C59×#5772
#2246459