Finite Group Databasebeta

← #30548536

Subgroups — #30548536

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#21459020C211yesmaximal, characteristic, complemented
3#21456106C214yesmaximal, complemented
4#21456058C214yesmaximal, complemented
5#21456021C214yesmaximal, complemented
6#21456013C214yesmaximal, complemented
7#21455759C211yesmaximal, characteristic, complemented
8#21455640C212yesmaximal, complemented
9#21455298C212yesmaximal, complemented
10#21455073C211yesmaximal, characteristic, complemented
11#21455069C211yesmaximal, characteristic, complemented
12#21454626C212yesmaximal, complemented
13#21454623C212yesmaximal, complemented
14#21454454C211yesmaximal, characteristic, complemented
15C61×#3094C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519805C2212yes—
18C2×#14519803C2212yes—
19#16840365—22no—
20#16840365—22no—
21#16840365C2214yes—
22#16840365C2214yescomplemented
23C2×#14519773C2211yescharacteristic, complemented
24C2×#14519768C2211yescharacteristic, complemented
25C2×#14519761—21no—
26C2×#14519759—21no—
27C2×#14519751C2211yescharacteristic
28C2×#14519749—21no—
29C2×#14519748—21no—
30#16840243C2212yescomplemented
31#16840243C2212yescomplemented
32#16840242—21no—
33#16840242—21no—
34#16840239C2212yescomplemented
35#16840236C2212yescomplemented
36#16840235—21no—
37#16840235—21no—
38C4×#11758222—22no—
39#16840230C2212yes—
40#16840230C2212yes—
41C2×D4×Dic61C2211yescharacteristic, complemented
42C2×#14519739C2211yescharacteristic, complemented
43C2×#14519736C2211yescharacteristic
44#117×D61—22no—
45#16840086C2214yescomplemented
46#16840080C2212yescomplemented
47#16840075C2212yescomplemented
48#16840072C2214yescomplemented
49#16840068C2214yescomplemented
50#16840065C2214yescomplemented
51#16840061C2214yescomplemented
52#16839961C2214yescomplemented
53#16839961C2214yescomplemented
54#16839956C2214yescomplemented
55#16839956C2214yescomplemented
56#16839909C2214yescomplemented
57#16839905C2214yescomplemented
58#16839903C2212yescomplemented
59#16839900C2212yescomplemented
60#16839898C2212yescomplemented
61#16839895C2212yescomplemented
62#16839873C2214yescomplemented
63#16839871C2214yescomplemented
64#16839861C2214yescomplemented
65#16839859C2214yescomplemented
66#16839853C2214yescomplemented
67#16839849C2214yescomplemented
68#16839844C2214yescomplemented
69#16839842C2214yescomplemented
70#16839820C2214yescomplemented
71#16839820C2214yescomplemented
72#16839805C2212yescomplemented
73#16839785C2212yescomplemented
74#16839766C2212yescomplemented
75#16839764C2212yes—
76#16839761C2212yes—
77#16839726C2211yescharacteristic
78M16×Dic61C2212yescomplemented
79C2×#121×C61C2211yescharacteristic
80C2×#117×C61C2211yescharacteristic
81C61×#482C2214yescomplemented
82C61×#481C2212yescomplemented
83C61×#480C2212yescomplemented
84C61×#428C2212yescomplemented
85C61×#418C2212yescomplemented
86C61×#407C2211yescharacteristic
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—28no—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C22×Dic122C2311yescharacteristic
93C22×D244C2311yescharacteristic
94C22×D244C2311yescharacteristic
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C23×Dic61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102#14519805—28no—
103#14519803—28no—
104C2×#11758190C2314yes—
105C2×#11758200C2314yes—
106C2×D488C2314yes—
107C2×#11758199C2314yes—
108C2×#11758194C2312yes—
109#14519773—22no—
110#14519773C2314yes—
111#14519768—22no—
112#14519768C2314yes—
113#14519761—24no—
114#14519761—24no—
115#14519759—24no—
116#14519759—24no—
117#14519751—21no—
118#14519751—21no—
119#14519751C2312yes—
120#14519751C2312yes—
121#14519749—24no—
122#14519749—24no—
123#14519748—24no—
124#14519748—24no—
125C4×Dic122—22no—
126C4×Dic122—22no—
127#14519742C2312yes—
128#14519742C2312yes—
129#14519742C2312yes—
130#14519742C2312yes—
131C4×D244—22no—
132C4×D244—22no—
133D4×Dic61—22no—
134D4×Dic61C2314yes—
135#14519739—22no—
136#14519739C2312yes—
137#14519739C2312yes—
138#14519739C2314yes—
139#14519739C2312yes—
140#14519739C2312yes—
141C4×C22⋊D61—22no—
142C4×C22⋊D61—22no—
143C4×C22⋊D61—22no—
144C4×C22⋊D61—22no—
145#14519737—22no—
146#14519737—22no—
147#14519737—22no—
148#14519737—22no—
149#14519736D412yes—
150#14519736D412yes—
151#14519736C2312yes—
152#14519736C2312yes—
153#14519735—22no—
154#14519735—22no—
155#14519734—22no—
156#14519734—22no—
157#14519733—22no—
158#14519733—22no—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61D411yescharacteristic
161C2×C4⋊Dic61D411yescharacteristic
162C2×C4⋊Dic61C2311yescharacteristic
163C2×#11758196—21no—
164C4⋊C4×D61—22no—
165C4⋊C4×D61—22no—
166C2×C22⋊Dic61—21no—
167C2×C22⋊Dic61D411yescharacteristic
168C2×C22⋊Dic61D411yescharacteristic
169C2×#11758198—21no—
170C2×#11758198—21no—
171C22⋊C4×D61—22no—
172C22⋊C4×D61—22no—
173C2×C4×Dic61C2311yescharacteristic
174C2×C4×Dic61C2311yescharacteristic
175C42×D61—22no—
176C42×D61—22no—
177#14519710C2314yes—
178#14519708C2314yes—
179#14519706C2314yes—
180#14519706C2314yes—
181#14519702C2314yes—
182#14519700C2314yes—
183#14519699C2314yes—
184#14519697C2314yes—
185#14519697C2314yes—
186#14519697C2314yes—
187C22⋊#92418C2312yes—
188C22⋊#92418C2312yes—
189#14519687C2314yes—
190C8×Dic61C2314yes—
191C22×D4×C61—21no—
192C22×D4×C61C2311yescharacteristic
193C23×C4×C61C2311yescharacteristic
194C2×M16×C61C2312yes—
195#121×C61—21no—
196#121×C61—21no—
197#121×C61C2312yes—
198#121×C61C2312yes—
199#117×C61—21no—
200#117×C61—21no—
201#117×C61C2312yes—
202#117×C61C2312yes—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C42×C61—21no—
209#107×C61C2314yes—
210#106×C61C2314yes—
211#102×C61C2314yes—
212#102×C61C2314yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C24×C61—21no—
216C24×C61C2×D411yescharacteristic
217C23×D61—21no—
218C23×D61—21no—
219C2×D4×C61—22no—
220C2×D4×C61—22no—
221C2×D4×C61—21no—
222C2×D4×C61—24no—
223C2×D4×C61—82no—
224C2×D4×C61C2412yes—
225C22×C4×C61—24no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C2×C22⋊D61—28no—
236C2×C22⋊D61—22no—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—24no—
241C2×C22⋊D61—24no—
242C2×C22⋊D61—82no—
243C2×C22⋊D61—82no—
244C2×C22⋊D61—82no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—24no—
248C22×Dic61—82no—
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251C22×Dic61C2×D411yescharacteristic
252C22×Dic61C2×D411yescharacteristic
253#11758222—28no—
254#11758222—28no—
255#11758222—24no—
256#11758222—24no—
257#11758222—24no—
258#11758222#4118yes—
259C2×D244—21no—
260C2×D244—24no—
261C2×D244—24no—
262C2×D244—21no—
263C2×D244C2412yes—
264C2×D244C2412yes—
265C2×C4×D61—28no—
266C2×C4×D61—22no—
267C2×C4×D61—22no—
268C2×C4×D61—24no—
269C2×C4×D61—22no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—22no—
273C2×C4×D61—82no—
274C2×Dic122—21no—
275C2×Dic122—24no—
276C2×Dic122C2412yes—
277M16×C61—24no—
278C2×C8×C61C2414yes—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61C2412yes—
283C4⋊C4×C61C2412yes—
284C4⋊C4×C61C2412yes—
285C22⋊C4×C61—22no—
286C22⋊C4×C61—22no—
287C22⋊C4×C61—22no—
288C22⋊C4×C61—22no—
289C42×C61—22no—
290C42×C61—22no—
291C22⋊Dic61—24no—
292C22⋊Dic61C2×D412yes—
293C22⋊Dic61C2×D412yes—
294C22⋊Dic61C2×D412yes—
295C22⋊Dic61C2×D412yes—
296#11758200—28no—
297#11758199—28no—
298#11758198—22no—
299#11758198—22no—
300#11758198—22no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304#11758198—24no—
305C4⋊Dic61—21no—
306C4⋊Dic61—24no—
307C4⋊Dic61C2×D412yes—
308C4⋊Dic61C2×D412yes—
309C4⋊Dic61C2×D412yes—
310C4⋊Dic61C2×D412yes—
311C4⋊Dic61C2412yes—
312#11758196—22no—
313#11758196—22no—
314#11758196—22no—
315#11758196—22no—
316#11758196—24no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C4×Dic61C2×D412yes—
322C4×Dic61C2×D412yes—
323C4×Dic61C2412yes—
324C4×Dic61C2412yes—
325#11758194—24no—
326C2×#92418C2414yes—
327D488—28no—
328#11758190—28no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—42no—
334C23×C61—42no—
335C23×C61—42no—
336C23×C61C22×D411yescharacteristic
337C23×C61C22×D411yescharacteristic
338C23×C61C22×D411yescharacteristic
339C22×D61—22no—
340C22×D61—24no—
341C22×D61—22no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—81no—
346C22×D61—81no—
347D4×C61—24no—
348D4×C61—42no—
349D4×C61—82no—
350D4×C61—82no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—42no—
360C2×C4×C61—81no—
361C2×C4×C61—81no—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C2×#4114yes—
366C2×C4×C61C2511yescharacteristic
367C22⋊D61—28no—
368C22⋊D61—28no—
369C22⋊D61—84no—
370C22⋊D61—84no—
371C22⋊D61—82no—
372C22⋊D61—82no—
373C2×Dic61—24no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—42no—
381C2×Dic61—84no—
382C2×Dic61C22×D412yes—
383C2×Dic61C22×D412yes—
384C2×Dic61C22×D412yes—
385C2×Dic61C22×D412yes—
386D244—24no—
387D244—22no—
388D244—24no—
389D244—42no—
390D244C2×#4114yes—
391C4×D61—28no—
392C4×D61—28no—
393C4×D61—82no—
394C4×D61—82no—
395C4×D61—82no—
396C4×D61—82no—
397C4×D61—84no—
398Dic122—24no—
399Dic122—22no—
400Dic122C2×#4114yes—
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—42no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—82no—
416C22×C61—84no—
417C22×C61#52512yes—
418C22×C61C23×D411yescharacteristic
419C2×D61—24no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—84no—
426C2×D61—84no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—42no—
430C4×C61—42no—
431C4×C61—42no—
432C4×C61#52512yes—
433C4×C61C22×#4112yes—
434Dic61—22no—
435Dic61—22no—
436Dic61—22no—
437Dic61—22no—
438Dic61—24no—
439Dic61—42no—
440C2×#540—611no—
441#3428—611no—
442#3126—614no—
443#3122—614no—
444#3119—614no—
445#3119—614no—
446#3094—611no—
447#3094D6111yescharacteristic, complemented
448#3080—612no—
449#3038—612no—
450#3006—611no—
451#3006—611no—
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—82no—
459C2×C61C2×#52511yescharacteristic
460C2×C61#358511yescharacteristic
461C2×C61#358511yescharacteristic
462D61—44no—
463D61—82no—
464C22×#41—611no—
465C2×AGL(1,ℤ/8)—612no—
466C2×AGL(1,ℤ/8)—612no—
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—1222no—
494C2×#117C2×D6111yescharacteristic
495#482—614no—
496#482C2×D6114yescomplemented
497#481—612no—
498#481C2×D6112yescomplemented
499#480—612no—
500#480C2×D6112yescomplemented
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#449—614no—
511#448—612no—
512#448—612no—
513#447—612no—
514#447—612no—
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#428C2×D6112yescomplemented
527#423—612no—
528#418—612no—
529#418C2×D6112yescomplemented
530#417—612no—
531#417—612no—
532#407—611no—
533#407C2×D6111yescharacteristic
534C4×M16—612no—
535C61#6056811yescharacteristic, complemented, Sylow
536C2×#41—612no—
537C2×#41—612no—
538C2×#41—1228no—
539C2×#41—1221no—
540C2×#41—1221no—
541C22×Q8—611no—
542C22×D4—21no—
543C22×D4—611no—
544C22×D4—611no—
545C22×D4—1221no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—1221no—
549C22×D4C22×D6111yescharacteristic
550C23×C4—1221no—
551C23×C4—1221no—
552C23×C4—1221no—
553C23×C4C22×D6111yescharacteristic
554AGL(1,ℤ/8)—1228no—
555AGL(1,ℤ/8)—1228no—
556C2×SD16—614no—
557C2×SD16—614no—
558C2×D8—614no—
559C2×D8—614no—
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—614no—
590C4×D4—612no—
591C4×D4—612no—
592C4×D4—612no—
593C4×D4—612no—
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—21no—
607#117—21no—
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#117C22×D6112yes—
619#117C22×D6112yes—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—1222no—
624C2×C4⋊C4—1222no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4C22×D6111yescharacteristic
628C2×C4⋊C4C22×D6111yescharacteristic
629C2×C4⋊C4C22×D6111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—611no—
633C2×C22⋊C4—611no—
634C2×C22⋊C4—1222no—
635C2×C22⋊C4—1222no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C42—21no—
640C2×C42—611no—
641C2×C42—611no—
642C2×C42—1222no—
643C2×C42—1222no—
644#107—614no—
645#107C22×D6114yes—
646#106—614no—
647#106C22×D6114yes—
648C4⋊C8—614no—
649C4⋊C8—614no—
650#103—614no—
651#103—614no—
652#102—614no—
653#102—614no—
654#102—614no—
655#102—614no—
656#102C22×D6114yes—
657#102C22×D6114yes—
658C22⋊C8—612no—
659C22⋊C8—612no—
660C22⋊C8C22×D6112yes—
661C22⋊C8C22×D6112yes—
662#97—614no—
663C4×C8—614no—
664C24—21no—
665C24—1221no—
666C24—1221no—
667C24D4×D6111yescharacteristic
668#41—618no—
669#41—1224no—
670#41—1224no—
671#41—1228no—
672#41—1228no—
673#41—1224no—
674C2×Q8—612no—
675C2×Q8—1224no—
676C2×Q8—1221no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—24no—
681C2×D4—82no—
682C2×D4—612no—
683C2×D4—612no—
684C2×D4—1224no—
685C2×D4—1224no—
686C2×D4—1224no—
687C2×D4—1228no—
688C2×D4—1222no—
689C2×D4—1222no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1224no—
695C2×D4—4882no—
696C2×D4—4882no—
697C2×D4—4882no—
698C2×D4C23×D6112yes—
699C22×C4—24no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1224no—
712C22×C4—1228no—
713C22×C4—1224no—
714C22×C4—1221no—
715C22×C4—1222no—
716C22×C4—1222no—
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—1228no—
727SD16—1228no—
728D8—1228no—
729D8—1228no—
730M16—24no—
731M16—1224no—
732C2×C8—614no—
733C2×C8C23×D6114yes—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—612no—
738C4⋊C4—612no—
739C4⋊C4—612no—
740C4⋊C4—612no—
741C4⋊C4—612no—
742C4⋊C4—1222no—
743C4⋊C4—1222no—
744C4⋊C4—1222no—
745C4⋊C4—1222no—
746C4⋊C4—1224no—
747C4⋊C4—1224no—
748C4⋊C4—1221no—
749C4⋊C4C23×D6112yes—
750C4⋊C4C23×D6112yes—
751C4⋊C4C23×D6112yes—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—612no—
757C22⋊C4—612no—
758C22⋊C4—612no—
759C22⋊C4—612no—
760C22⋊C4—1222no—
761C22⋊C4—1222no—
762C22⋊C4—1222no—
763C22⋊C4—1222no—
764C22⋊C4—1224no—
765C22⋊C4—1224no—
766C22⋊C4—1222no—
767C22⋊C4—1222no—
768C42—22no—
769C42—22no—
770C42—612no—
771C42—612no—
772C42—612no—
773C42—612no—
774C42—1222no—
775C42—1222no—
776C42—1222no—
777C42—1222no—
778C23—22no—
779C23—22no—
780C23—41no—
781C23—41no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—1224no—
786C23—1222no—
787C23—1222no—
788C23—4881no—
789C23—4881no—
790C23—2442no—
791C23—2442no—
792C23—2442no—
793C23C2×D4×D6111yescharacteristic
794C23C2×D4×D6111yescharacteristic
795C23C2×D4×D6111yescharacteristic
796Q8—614no—
797Q8—1224no—
798Q8—1222no—
799D4—24no—
800D4—42no—
801D4—82no—
802D4—82no—
803D4—614no—
804D4—1224no—
805D4—1228no—
806D4—1228no—
807D4—1222no—
808D4—1224no—
809D4—4884no—
810D4—4884no—
811D4—4882no—
812D4—4882no—
813D4—2442no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—612no—
828C2×C4—612no—
829C2×C4—1228no—
830C2×C4—1224no—
831C2×C4—1222no—
832C2×C4—1228no—
833C2×C4—1222no—
834C2×C4—4882no—
835C2×C4—4882no—
836C2×C4—4882no—
837C2×C4—4882no—
838C2×C4—4884no—
839C2×C4—4884no—
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×C4#41×D6114yes—
849C2×C4C24×D6111yescharacteristic
850C8—24no—
851C8—1224no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—82no—
864C22—84no—
865C22—1224no—
866C22—4884no—
867C22—4884no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22—2442no—
872C22—2442no—
873C22#1684027012yes—
874C22C22×D4×D6111yescharacteristic
875C4—21no—
876C4—21no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—1224no—
881C4—1222no—
882C4—1222no—
883C4—1222no—
884C4—1222no—
885C4—2442no—
886C4#1684027012yes—
887C4C2×#41×D6112yes—
888C2—22no—
889C2—41no—
890C2—41no—
891C2—82no—
892C2—4882no—
893C2—2444no—
894C2C2×#1684027011yescharacteristic
895C2#2146059511yescharacteristic
896C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3094C2
socleC22×C61C23×D4
hypercenter#3094D61
hypocenterC61#60568
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. C2×#16840365C2semidirect
2. #21459020C2semidirect
3. #21456106C2semidirect
4. #21456058C2semidirect
5. #21456021C2semidirect
6. #21456013C2semidirect
7. #21455759C2semidirect
8. #21455640C2semidirect
9. #21455298C2semidirect
10. #21455073C2semidirect
11. #21455069C2semidirect
12. #21454626C2semidirect
13. #21454623C2semidirect
14. #21454454C2semidirect
15. C61×#3094C2semidirect
22. #16840365C22semidirect
23. C2×#14519773C22semidirect
24. C2×#14519768C22semidirect
30. #16840243C22semidirect
31. #16840243C22semidirect
34. #16840239C22semidirect
35. #16840236C22semidirect
41. C2×D4×Dic61C22semidirect
42. C2×#14519739C22semidirect
45. #16840086C22semidirect
46. #16840080C22semidirect
47. #16840075C22semidirect
48. #16840072C22semidirect
49. #16840068C22semidirect
50. #16840065C22semidirect
51. #16840061C22semidirect
52. #16839961C22semidirect
53. #16839961C22semidirect
54. #16839956C22semidirect
55. #16839956C22semidirect
56. #16839909C22semidirect
57. #16839905C22semidirect
58. #16839903C22semidirect
59. #16839900C22semidirect
60. #16839898C22semidirect
61. #16839895C22semidirect
62. #16839873C22semidirect
63. #16839871C22semidirect
64. #16839861C22semidirect
65. #16839859C22semidirect
66. #16839853C22semidirect
67. #16839849C22semidirect
68. #16839844C22semidirect
69. #16839842C22semidirect
70. #16839820C22semidirect
71. #16839820C22semidirect
72. #16839805C22semidirect
73. #16839785C22semidirect
74. #16839766C22semidirect
78. M16×Dic61C22semidirect
81. C61×#482C22semidirect
82. C61×#481C22semidirect
83. C61×#480C22semidirect
84. C61×#428C22semidirect
85. C61×#418C22semidirect
447. #3094D61semidirect
496. #482C2×D61semidirect
498. #481C2×D61semidirect
500. #480C2×D61semidirect
526. #428C2×D61semidirect
529. #418C2×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
#214590202
#214561062
#214560582
#214560212
#214560132
#214557592
#214556402
#214552982
#214550732
#214550692
#214546262
#214546232
#214544542
C61×#30942
#6056861