Finite Group Databasebeta

← #30548534

Subgroups — #30548534

Order 15616.

2138 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840365C211yesmaximal, characteristic, complemented
2#21459022C211yesmaximal, characteristic, complemented
3#21456104C214yesmaximal, complemented
4#21456056C214yesmaximal, complemented
5#21456019C214yesmaximal, complemented
6#21456011C214yesmaximal, complemented
7#21455760C211yesmaximal, characteristic, complemented
8#21455755C211yesmaximal, characteristic, complemented
9#21455639C212yesmaximal, complemented
10#21455297C212yesmaximal, complemented
11#21455071C211yesmaximal, characteristic, complemented
12#21454632C212yesmaximal, complemented
13AGL(1,ℤ/8)×Dic61C212yesmaximal, complemented
14#21454454C211yesmaximal, characteristic, complemented
15C61×#3006C211yesmaximal, characteristic, complemented
16C2×#14519802C2212yes—
17#16840365—22no—
18#16840365—22no—
19#16840365C2214yes—
20#16840365C2214yescomplemented
21C2×#14519773C2211yescharacteristic, complemented
22C2×#14519768C2211yescharacteristic, complemented
23C2×#14519761—21no—
24C2×#14519759—21no—
25C2×#14519751C2211yescharacteristic
26C2×#14519749—21no—
27C2×#14519748—21no—
28#16840245—21no—
29#16840245—21no—
30#16840245C2212yescomplemented
31#16840245C2212yescomplemented
32#16840240C2212yescomplemented
33#16840237—21no—
34#16840237—21no—
35#16840237C2212yescomplemented
36#41×Dic61—22no—
37#41×Dic61C2212yes—
38#41×Dic61C2212yes—
39C2×D4×Dic61C2211yescharacteristic, complemented
40C2×#14519739C2211yescharacteristic, complemented
41C2×#14519736—22no—
42C2×#14519736C2211yescharacteristic
43C2×#14519736C2211yescharacteristic
44#16840087C2214yescomplemented
45#16840083C2214yescomplemented
46#16840081C2212yescomplemented
47#16840078C2212yescomplemented
48#16840076C2212yescomplemented
49#16840073C2212yescomplemented
50#16840071C2214yescomplemented
51#16840067C2214yescomplemented
52#16840064C2214yescomplemented
53#16840060C2214yescomplemented
54#16839960C2214yescomplemented
55#16839960C2214yescomplemented
56#16839955C2214yescomplemented
57#16839955C2214yescomplemented
58#16839907C2214yescomplemented
59#16839901C2212yescomplemented
60#16839896C2212yescomplemented
61#16839874C2214yescomplemented
62#16839871C2214yescomplemented
63#16839865C2214yescomplemented
64#16839863C2214yescomplemented
65SD16×Dic61C2214yescomplemented
66#16839847C2214yescomplemented
67D8×Dic61C2214yescomplemented
68#16839842C2214yescomplemented
69#16839820C2214yescomplemented
70#16839820C2214yescomplemented
71#16839804C2212yescomplemented
72#16839802C2212yescomplemented
73#16839785C2212yescomplemented
74#16839768C2212yescomplemented
75#16839767C2212yescomplemented
76#16839763C2212yes—
77#16839726C2211yescharacteristic
78M16×Dic61C2212yescomplemented
79C22×#41×C61C2211yescharacteristic
80C2×AGL(1,ℤ/8)×C61C2212yes—
81C2×#121×C61C2211yescharacteristic
82C61×#449C2214yescomplemented
83C61×#448C2212yescomplemented
84C61×#447C2212yescomplemented
85C61×#417C2212yes—
86C61×#407C2211yescharacteristic
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93#14519802—28no—
94C2×#11758201C2314yes—
95C2×#11758199C2314yes—
96C2×#11758194C2312yes—
97#14519773—22no—
98#14519773C2314yes—
99#14519768—22no—
100#14519768C2314yes—
101#14519761—24no—
102#14519761—24no—
103#14519759—24no—
104#14519759—24no—
105#14519751—21no—
106#14519751—21no—
107#14519751C2312yes—
108#14519751C2312yes—
109#14519749—24no—
110#14519749—24no—
111#14519748—24no—
112#14519748—24no—
113Q8×Dic61—22no—
114Q8×Dic61—22no—
115Q8×Dic61C2312yes—
116Q8×Dic61C2312yes—
117Q8×Dic61C2312yes—
118Q8×Dic61C2312yes—
119D4×Dic61—22no—
120D4×Dic61—22no—
121D4×Dic61—22no—
122D4×Dic61—22no—
123D4×Dic61—22no—
124D4×Dic61—22no—
125D4×Dic61—22no—
126D4×Dic61—22no—
127D4×Dic61—22no—
128D4×Dic61—22no—
129D4×Dic61—22no—
130D4×Dic61C2312yes—
131D4×Dic61C2312yes—
132D4×Dic61C2314yes—
133D4×Dic61C2312yes—
134D4×Dic61C2312yes—
135#14519739—22no—
136#14519739C2314yes—
137#14519736—21no—
138#14519736—21no—
139#14519736—22no—
140#14519736—22no—
141#14519736—22no—
142#14519736—22no—
143#14519736—22no—
144#14519736—22no—
145#14519736D412yes—
146#14519736D412yes—
147#14519736C2312yes—
148#14519736C2312yes—
149#14519736C2312yes—
150#14519736C2312yes—
151C2×C4⋊Dic61—21no—
152C2×C4⋊Dic61—22no—
153C2×C4⋊Dic61—22no—
154C2×C4⋊Dic61D411yescharacteristic
155C2×C4⋊Dic61D411yescharacteristic
156C2×C4⋊Dic61C2311yescharacteristic
157C2×C4⋊Dic61C2311yescharacteristic
158C2×C4⋊Dic61C2311yescharacteristic
159C2×#11758196—21no—
160C2×C22⋊Dic61—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61—22no—
163C2×C22⋊Dic61—22no—
164C2×C22⋊Dic61D411yescharacteristic
165C2×C22⋊Dic61D411yescharacteristic
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61—22no—
170C2×C4×Dic61—22no—
171C2×C4×Dic61C2311yescharacteristic
172C2×C4×Dic61C2311yescharacteristic
173#14519711C2314yes—
174#14519710C2314yes—
175#14519709C2314yes—
176#14519708C2314yes—
177#14519706C2314yes—
178#14519706C2314yes—
179#14519701C2314yes—
180#14519699C2314yes—
181#14519699C2314yes—
182#14519698C2314yes—
183#14519698C2314yes—
184#14519698C2314yes—
185C22⋊#92418C2312yes—
186C22⋊#92418C2312yes—
187#14519687C2314yes—
188C8×Dic61C2314yes—
189C2×#41×C61—28no—
190C2×#41×C61—21no—
191C2×#41×C61—21no—
192C2×#41×C61C2312yes—
193C2×#41×C61C2312yes—
194C22×Q8×C61C2311yescharacteristic
195C22×D4×C61—21no—
196C22×D4×C61—21no—
197C22×D4×C61C2311yescharacteristic
198C22×D4×C61C2311yescharacteristic
199C23×C4×C61—21no—
200C23×C4×C61C2311yescharacteristic
201AGL(1,ℤ/8)×C61—28no—
202C2×SD16×C61C2314yes—
203C2×D8×C61C2314yes—
204C2×M16×C61C2312yes—
205#121×C61—21no—
206#121×C61—21no—
207#121×C61C2312yes—
208#121×C61C2312yes—
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61—21no—
211#103×C61C2314yes—
212#102×C61C2314yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C24×C61—21no—
216C24×C61—21no—
217C24×C61C2×D411yescharacteristic
218C23×D61—21no—
219#41×C61—28no—
220#41×C61—28no—
221#41×C61—24no—
222#41×C61—24no—
223#41×C61—24no—
224#41×C61#4118yes—
225C2×Q8×C61—24no—
226C2×Q8×C61—21no—
227C2×Q8×C61C2412yes—
228C2×D4×C61—28no—
229C2×D4×C61—22no—
230C2×D4×C61—22no—
231C2×D4×C61—24no—
232C2×D4×C61—22no—
233C2×D4×C61—22no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—24no—
237C2×D4×C61—82no—
238C2×D4×C61C2412yes—
239C2×D4×C61C2412yes—
240C22×C4×C61—28no—
241C22×C4×C61—21no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—24no—
245C22×C4×C61—21no—
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2411yescharacteristic
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2411yescharacteristic
252C2×C22⋊D61—22no—
253C2×C22⋊D61—22no—
254C2×C22⋊D61—24no—
255C2×C22⋊D61—24no—
256C2×C22⋊D61—82no—
257C2×C22⋊D61—82no—
258C2×C22⋊D61—82no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—24no—
263C22×Dic61—22no—
264C22×Dic61—22no—
265C22×Dic61—22no—
266C22×Dic61—22no—
267C22×Dic61—82no—
268C22×Dic61C2×D411yescharacteristic
269C22×Dic61C2×D411yescharacteristic
270C22×Dic61C2×D411yescharacteristic
271C22×Dic61C2×D411yescharacteristic
272C2×D244—24no—
273C2×D244—21no—
274C2×D244C2412yes—
275C2×C4×D61—24no—
276C2×C4×D61—82no—
277SD16×C61—28no—
278D8×C61—28no—
279M16×C61—24no—
280C2×C8×C61C2414yes—
281C4⋊C4×C61—21no—
282C4⋊C4×C61C2412yes—
283C22⋊C4×C61—22no—
284C22⋊C4×C61—22no—
285C22⋊Dic61—22no—
286C22⋊Dic61—22no—
287C22⋊Dic61—22no—
288C22⋊Dic61—22no—
289C22⋊Dic61—22no—
290C22⋊Dic61—22no—
291C22⋊Dic61—24no—
292C22⋊Dic61C2×D412yes—
293C22⋊Dic61C2×D412yes—
294C22⋊Dic61C2×D412yes—
295C22⋊Dic61C2×D412yes—
296#11758201—28no—
297#11758199—28no—
298#11758198—22no—
299#11758198—22no—
300#11758198—24no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—22no—
305C4⋊Dic61—22no—
306C4⋊Dic61—22no—
307C4⋊Dic61—22no—
308C4⋊Dic61—24no—
309C4⋊Dic61C2×D412yes—
310C4⋊Dic61C2×D412yes—
311C4⋊Dic61C2×D412yes—
312C4⋊Dic61C2×D412yes—
313C4⋊Dic61C2412yes—
314C4⋊Dic61C2412yes—
315C4⋊Dic61C2412yes—
316#11758196—24no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323C4×Dic61C2×D412yes—
324C4×Dic61C2×D412yes—
325C4×Dic61C2412yes—
326C4×Dic61C2412yes—
327#11758194—24no—
328C2×#92418C2414yes—
329C23×C61—24no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—42no—
336C23×C61—42no—
337C23×C61—42no—
338C23×C61—81no—
339C23×C61—81no—
340C23×C61C22×D411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C22×D61—22no—
344C22×D61—42no—
345C22×D61—42no—
346C22×D61—42no—
347Q8×C61—24no—
348Q8×C61—22no—
349Q8×C61C2×#4114yes—
350D4×C61—28no—
351D4×C61—24no—
352D4×C61—28no—
353D4×C61—22no—
354D4×C61—24no—
355D4×C61—42no—
356D4×C61—82no—
357D4×C61—82no—
358D4×C61C2×#4114yes—
359C2×C4×C61—24no—
360C2×C4×C61—28no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—28no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—42no—
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C2×#4114yes—
374C2×C4×C61C2511yescharacteristic
375C22⋊D61—84no—
376C22⋊D61—84no—
377C22⋊D61—82no—
378C22⋊D61—82no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—42no—
387C2×Dic61—82no—
388C2×Dic61—82no—
389C2×Dic61—82no—
390C2×Dic61—82no—
391C2×Dic61—84no—
392C2×Dic61—81no—
393C2×Dic61—81no—
394C2×Dic61C22×D412yes—
395C2×Dic61C22×D412yes—
396C2×Dic61C22×D412yes—
397C2×Dic61C22×D412yes—
398D244—24no—
399D244—42no—
400C4×D61—84no—
401C8×C61—24no—
402#92418—24no—
403#60568—611nomaximal, Sylow
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—24no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—82no—
419C22×C61—84no—
420C22×C61—84no—
421C22×C61#52512yes—
422C22×C61C23×D411yescharacteristic
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—84no—
427C4×C61—21no—
428C4×C61—24no—
429C4×C61—21no—
430C4×C61—42no—
431C4×C61#52512yes—
432C4×C61C22×#4112yes—
433Dic61—22no—
434Dic61—22no—
435Dic61—22no—
436Dic61—22no—
437Dic61—42no—
438Dic61—42no—
439Dic61—42no—
440C2×#540—611no—
441#3428—611no—
442#3126—614no—
443#3122—614no—
444#3119—614no—
445#3119—614no—
446#3094—611no—
447#3094—611no—
448#3080—612no—
449#3038—612no—
450#3006—611no—
451#3006D6111yescharacteristic, complemented
452C4×AGL(1,ℤ/8)—612no—
453C4×AGL(1,ℤ/8)—612no—
454#2921—611no—
455C2×C61—22no—
456C2×C61—41no—
457C2×C61—41no—
458C2×C61—44no—
459C2×C61—82no—
460C2×C61C2×#52511yescharacteristic
461C2×C61#358511yescharacteristic
462C2×C61#358511yescharacteristic
463D61—82no—
464C22×#41C2×D6111yescharacteristic
465C2×AGL(1,ℤ/8)—612no—
466C2×AGL(1,ℤ/8)C2×D6112yes—
467#540—614no—
468#540—614no—
469#540—1222no—
470#540—1222no—
471C2×#127—611no—
472C2×#125—611no—
473C2×#123—1221no—
474C2×#123—1221no—
475C2×#121—611no—
476C2×#121—1221no—
477C2×#121—1221no—
478C2×#121C2×D6111yescharacteristic
479#520—612no—
480#520—612no—
481#520—1221no—
482#520—1221no—
483#519—612no—
484#518—612no—
485#518—1221no—
486#518—1221no—
487C4×#41—612no—
488C4×#41—612no—
489C4×#41—1222no—
490C2×C4×D4—611no—
491C2×C4×D4—611no—
492C2×#117—611no—
493C2×#117—611no—
494C2×#117—1222no—
495#482—614no—
496#482—614no—
497#481—612no—
498#481—612no—
499#480—612no—
500#480—612no—
501#479—614no—
502#479—614no—
503#478—614no—
504#478—614no—
505#460—614no—
506#460—614no—
507#459—614no—
508#459—614no—
509#449—614no—
510#449C2×D6114yescomplemented
511#448—612no—
512#448C2×D6112yescomplemented
513#447—612no—
514#447C2×D6112yescomplemented
515#442—614no—
516#442—614no—
517#440—614no—
518#440—614no—
519C4×SD16—614no—
520C4×SD16—614no—
521C4×D8—614no—
522C4×D8—614no—
523#433—614no—
524#433—614no—
525#428—612no—
526#428—612no—
527#423—612no—
528#418—612no—
529#418—612no—
530#417—612no—
531#417C2×D6112yes—
532#407—611no—
533#407C2×D6111yescharacteristic
534C4×M16—612no—
535C61#6056811yescharacteristic, complemented, Sylow
536C2×#41—28no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41C22×D6112yes—
540C2×#41C22×D6112yes—
541C22×Q8C22×D6111yescharacteristic
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—611no—
545C22×D4—1221no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4C22×D6111yescharacteristic
549C22×D4C22×D6111yescharacteristic
550C23×C4—21no—
551C23×C4—1221no—
552C23×C4—1221no—
553C23×C4C22×D6111yescharacteristic
554AGL(1,ℤ/8)—28no—
555AGL(1,ℤ/8)—1228no—
556C2×SD16—614no—
557C2×SD16C22×D6114yes—
558C2×D8—614no—
559C2×D8C22×D6114yes—
560C2×M16—612no—
561C2×M16C22×D6112yes—
562#127—614no—
563#127—1222no—
564#125—614no—
565#125—1222no—
566#123—1224no—
567#123—1224no—
568#123—1224no—
569#123—1224no—
570#121—21no—
571#121—21no—
572#121—612no—
573#121—612no—
574#121—1224no—
575#121—1224no—
576#121—1224no—
577#121—1224no—
578#121—1221no—
579#121—1221no—
580#121C22×D6112yes—
581#121C22×D6112yes—
582C4×Q8—612no—
583C4×Q8—612no—
584C4×Q8—612no—
585C4×Q8—612no—
586C4×Q8—1222no—
587C4×Q8—1222no—
588C4×D4—614no—
589C4×D4—612no—
590C4×D4—612no—
591C4×D4—612no—
592C4×D4—612no—
593C4×D4—614no—
594C4×D4—1222no—
595C4×D4—1222no—
596C4×D4—1222no—
597C4×D4—1222no—
598C4×D4—1222no—
599C4×D4—1222no—
600C4×D4—1222no—
601C4×D4—1222no—
602C4×D4—1222no—
603C4×D4—1222no—
604C4×D4—1222no—
605C4×D4—1222no—
606#117—612no—
607#117—612no—
608#117—612no—
609#117—612no—
610#117—612no—
611#117—612no—
612#117—1222no—
613#117—1222no—
614#117—1222no—
615#117—1222no—
616#117—1222no—
617#117—1222no—
618#117—1221no—
619#117—1221no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—1222no—
626C2×C4⋊C4—1222no—
627C2×C4⋊C4—1221no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4C22×D6111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—611no—
632C2×C22⋊C4—611no—
633C2×C22⋊C4—1222no—
634C2×C22⋊C4—1222no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C42—611no—
640C2×C42—611no—
641C2×C42—1222no—
642C2×C42—1222no—
643C2×C42—1221no—
644#107—614no—
645#107—614no—
646#106—614no—
647#106—614no—
648C4⋊C8—614no—
649C4⋊C8—614no—
650#103—614no—
651#103C22×D6114yes—
652#102—614no—
653#102—614no—
654#102—614no—
655#102—614no—
656#102—614no—
657#102C22×D6114yes—
658C22⋊C8—612no—
659C22⋊C8—612no—
660C22⋊C8C22×D6112yes—
661C22⋊C8C22×D6112yes—
662#97—614no—
663C4×C8—614no—
664C24—21no—
665C24—21no—
666C24—1221no—
667C24D4×D6111yescharacteristic
668#41—28no—
669#41—28no—
670#41—24no—
671#41—24no—
672#41—24no—
673#41#1175822418yes—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8C23×D6112yes—
677C2×D4—28no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—24no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—24no—
686C2×D4—82no—
687C2×D4—612no—
688C2×D4—1224no—
689C2×D4—1224no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1221no—
693C2×D4—1224no—
694C2×D4—4882no—
695C2×D4—4882no—
696C2×D4—4882no—
697C2×D4C23×D6112yes—
698C2×D4C23×D6112yes—
699C22×C4—28no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—24no—
704C22×C4—21no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—1224no—
710C22×C4—1222no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1224no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—4882no—
719C22×C4—4882no—
720C22×C4D4×D6111yescharacteristic
721C22×C4D4×D6111yescharacteristic
722C22×C4D4×D6111yescharacteristic
723C22×C4C23×D6111yescharacteristic
724C22×C4C23×D6111yescharacteristic
725C22×C4C23×D6111yescharacteristic
726SD16—28no—
727SD16—1228no—
728D8—28no—
729D8—1228no—
730M16—24no—
731M16—1224no—
732C2×C8—614no—
733C2×C8C23×D6114yes—
734C4⋊C4—21no—
735C4⋊C4—612no—
736C4⋊C4—612no—
737C4⋊C4—612no—
738C4⋊C4—612no—
739C4⋊C4—612no—
740C4⋊C4—612no—
741C4⋊C4—612no—
742C4⋊C4—1224no—
743C4⋊C4—1222no—
744C4⋊C4—1222no—
745C4⋊C4—1222no—
746C4⋊C4—1222no—
747C4⋊C4—1224no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4C23×D6112yes—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—612no—
755C22⋊C4—612no—
756C22⋊C4—612no—
757C22⋊C4—612no—
758C22⋊C4—1224no—
759C22⋊C4—1222no—
760C22⋊C4—1222no—
761C22⋊C4—1222no—
762C22⋊C4—1222no—
763C22⋊C4—1224no—
764C22⋊C4—1222no—
765C22⋊C4—1222no—
766C22⋊C4—1222no—
767C22⋊C4—1222no—
768C42—612no—
769C42—612no—
770C42—612no—
771C42—612no—
772C42—1222no—
773C42—1222no—
774C42—1222no—
775C42—1222no—
776C42—1222no—
777C42—1222no—
778C23—24no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—81no—
788C23—81no—
789C23—1222no—
790C23—2442no—
791C23—2442no—
792C23—2442no—
793C23C2×D4×D6111yescharacteristic
794C23C2×D4×D6111yescharacteristic
795C23C2×D4×D6111yescharacteristic
796Q8—24no—
797Q8—22no—
798Q8C2×#1175822414yes—
799D4—28no—
800D4—24no—
801D4—28no—
802D4—22no—
803D4—24no—
804D4—42no—
805D4—82no—
806D4—82no—
807D4—1224no—
808D4—4884no—
809D4—4884no—
810D4—4882no—
811D4—4882no—
812D4—2442no—
813D4C2×#1175822414yes—
814C2×C4—24no—
815C2×C4—28no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—28no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—42no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—612no—
828C2×C4—612no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—4884no—
833C2×C4—4882no—
834C2×C4—4882no—
835C2×C4—4882no—
836C2×C4—4882no—
837C2×C4—4884no—
838C2×C4—4881no—
839C2×C4—4881no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2442no—
845C2×C4C2×D4×D6111yescharacteristic
846C2×C4C2×D4×D6111yescharacteristic
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C2×#1175822414yes—
849C2×C4C24×D6111yescharacteristic
850C8—24no—
851C8—1224no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—24no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—82no—
867C22—84no—
868C22—84no—
869C22—4884no—
870C22—2442no—
871C22—2442no—
872C22—2442no—
873C22#1684026812yes—
874C22C22×D4×D6111yescharacteristic
875C4—21no—
876C4—24no—
877C4—21no—
878C4—42no—
879C4—1222no—
880C4—1222no—
881C4—1222no—
882C4—1222no—
883C4—2442no—
884C4—2442no—
885C4—2442no—
886C4#1684026812yes—
887C4C22×#1175822412yes—
888C2—22no—
889C2—41no—
890C2—41no—
891C2—44no—
892C2—82no—
893C2—4882no—
894C2C2×#1684026811yescharacteristic
895C2#2146059511yescharacteristic
896C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3006C2
socleC22×C61C23×D4
hypercenter#3006D61
hypocenterC61#60568
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. C2×#16840365C2semidirect
2. #21459022C2semidirect
3. #21456104C2semidirect
4. #21456056C2semidirect
5. #21456019C2semidirect
6. #21456011C2semidirect
7. #21455760C2semidirect
8. #21455755C2semidirect
9. #21455639C2semidirect
10. #21455297C2semidirect
11. #21455071C2semidirect
12. #21454632C2semidirect
13. AGL(1,ℤ/8)×Dic61C2semidirect
14. #21454454C2semidirect
15. C61×#3006C2semidirect
20. #16840365C22semidirect
21. C2×#14519773C22semidirect
22. C2×#14519768C22semidirect
30. #16840245C22semidirect
31. #16840245C22semidirect
32. #16840240C22semidirect
35. #16840237C22semidirect
39. C2×D4×Dic61C22semidirect
40. C2×#14519739C22semidirect
44. #16840087C22semidirect
45. #16840083C22semidirect
46. #16840081C22semidirect
47. #16840078C22semidirect
48. #16840076C22semidirect
49. #16840073C22semidirect
50. #16840071C22semidirect
51. #16840067C22semidirect
52. #16840064C22semidirect
53. #16840060C22semidirect
54. #16839960C22semidirect
55. #16839960C22semidirect
56. #16839955C22semidirect
57. #16839955C22semidirect
58. #16839907C22semidirect
59. #16839901C22semidirect
60. #16839896C22semidirect
61. #16839874C22semidirect
62. #16839871C22semidirect
63. #16839865C22semidirect
64. #16839863C22semidirect
65. SD16×Dic61C22semidirect
66. #16839847C22semidirect
67. D8×Dic61C22semidirect
68. #16839842C22semidirect
69. #16839820C22semidirect
70. #16839820C22semidirect
71. #16839804C22semidirect
72. #16839802C22semidirect
73. #16839785C22semidirect
74. #16839768C22semidirect
75. #16839767C22semidirect
78. M16×Dic61C22semidirect
82. C61×#449C22semidirect
83. C61×#448C22semidirect
84. C61×#447C22semidirect
451. #3006D61semidirect
510. #449C2×D61semidirect
512. #448C2×D61semidirect
514. #447C2×D61semidirect
535. C61#60568semidirect

Maximal subgroups

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

subgroupindex
C2×#168403652
#214590222
#214561042
#214560562
#214560192
#214560112
#214557602
#214557552
#214556392
#214552972
#214550712
#214546322
AGL(1,ℤ/8)×Dic612
#214544542
C61×#30062
#6056861