Finite Group Databasebeta

← #30548543

Subgroups — #30548543

Order 15616.

2138 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840368C211yesmaximal, characteristic, complemented
2#21459018C211yesmaximal, characteristic, complemented
3#21456112C214yesmaximal, complemented
4#21456064C214yesmaximal, complemented
5#21456025C214yesmaximal, complemented
6#21456023C214yesmaximal, complemented
7#21455761C212yesmaximal, complemented
8#21455637C211yesmaximal, characteristic, complemented
9#21455300C211yesmaximal, characteristic, complemented
10#21455299C211yesmaximal, characteristic, complemented
11#21455072C212yesmaximal, complemented
12#21454632C212yesmaximal, complemented
13#21454626C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3080C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519805C2212yes—
18C2×#14519802C2212yes—
19#16840368—21no—
20#16840368—21no—
21#16840368—21no—
22#16840368—21no—
23#16840368C2214yes—
24#16840368C2214yescomplemented
25C2×#14519774C2211yescharacteristic, complemented
26C2×#14519762—22no—
27C2×#14519752—22no—
28C2×#14519752C2212yes—
29#16840244C2212yescomplemented
30#16840241—22no—
31#16840241C2212yescomplemented
32#16840238C2212yescomplemented
33#16840234—22no—
34#16840234C2212yescomplemented
35#41×Dic61C2211yescharacteristic
36C4×#11758222—21no—
37C4×#11758222C2211yescharacteristic
38#16840230—21no—
39#16840230C2211yescharacteristic
40C2×#14519739C2212yescomplemented
41C2×#14519734—21no—
42C2×#14519734C2211yescharacteristic
43#117×D61—21no—
44#117×D61C2211yescharacteristic
45#16840089C2214yescomplemented
46#16840088C2214yescomplemented
47#16840082C2214yescomplemented
48#16840077C2214yescomplemented
49#16840066C2214yescomplemented
50#16840059C2214yescomplemented
51#16839963C2214yescomplemented
52#16839962C2214yescomplemented
53#16839958C2214yescomplemented
54#16839957C2214yescomplemented
55#16839910C2214yescomplemented
56#16839908C2214yescomplemented
57#16839902C2214yescomplemented
58#16839897C2214yescomplemented
59#16839873C2214yescomplemented
60#16839871C2214yescomplemented
61#16839865C2214yescomplemented
62#16839861C2214yescomplemented
63#16839849C2214yescomplemented
64#16839847C2214yescomplemented
65#16839844C2214yescomplemented
66#16839842C2214yescomplemented
67#16839822C2214yescomplemented
68#16839822C2214yescomplemented
69#16839802C2212yescomplemented
70#16839786C2211yescharacteristic, complemented
71#16839768C2212yescomplemented
72#16839766C2212yescomplemented
73#16839761C2212yes—
74#16839725C2212yes—
75M16×Dic61C2212yescomplemented
76C2×#125×C61C2211yescharacteristic, complemented
77C4×#41×C61C2211yescharacteristic
78C61×#479C2214yescomplemented
79C61×#478C2214yescomplemented
80C61×#428C2212yescomplemented
81C61×#423C2211yescharacteristic, complemented
82C61×#417C2212yes—
83C2×#11758226C2311yescharacteristic
84C2×#11758222—21no—
85C2×#11758222C2311yescharacteristic
86C2×#11758224—21no—
87C2×#11758224C2311yescharacteristic
88#41×D61—24no—
89#41×D61—24no—
90C2×Q8×D61C2311yescharacteristic
91C22×D244—22no—
92C22×D244—22no—
93C22×D244C2312yes—
94C2×D4×D61—21no—
95C2×D4×D61C2311yescharacteristic
96C22×C4×D61—21no—
97C22×C4×D61—22no—
98C22×C4×D61C2311yescharacteristic
99#14519805—28no—
100#14519802—28no—
101C2×#11758190C2314yes—
102C2×#11758201C2314yes—
103C2×D488C2314yes—
104C2×#11758199C2314yes—
105C2×#11758194C2312yes—
106#14519774—21no—
107#14519774—21no—
108#14519774C2314yes—
109#14519762—24no—
110#14519762—24no—
111#14519762—24no—
112#14519762—24no—
113#14519752—22no—
114#14519752—22no—
115#14519752—24no—
116#14519752—24no—
117#14519752—24no—
118#14519752—24no—
119#14519752C2314yes—
120#14519752C2314yes—
121Q8×Dic61C2312yes—
122C4×Dic122—22no—
123C4×Dic122C2312yes—
124#14519742—22no—
125#14519742C2312yes—
126C4×D244—22no—
127C4×D244C2312yes—
128D4×Dic61—22no—
129D4×Dic61C2312yes—
130#14519739—22no—
131#14519739—22no—
132#14519739—22no—
133#14519739C2314yes—
134#14519739C2314yes—
135#14519739C2312yes—
136C4×C22⋊D61—22no—
137C4×C22⋊D61—22no—
138C4×C22⋊D61—22no—
139#14519737—22no—
140#14519737—22no—
141#14519737—22no—
142#14519736—21no—
143#14519736C2311yescharacteristic
144#14519735—22no—
145#14519735C2312yes—
146#14519734—21no—
147#14519734—21no—
148#14519734—22no—
149#14519734—22no—
150#14519734—21no—
151#14519734D411yescharacteristic
152#14519734D411yescharacteristic
153#14519734D411yescharacteristic
154#14519734D411yescharacteristic
155#14519734C2312yes—
156#14519734C2312yes—
157#14519733—21no—
158#14519733—22no—
159C2×#11758196—22no—
160C2×#11758196D412yes—
161C4⋊C4×D61—22no—
162C4⋊C4×D61C2312yes—
163C2×#11758198—22no—
164C2×#11758198—22no—
165C2×#11758198—22no—
166C2×#11758198D412yes—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—22no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61C2311yescharacteristic
171C42×D61—21no—
172C42×D61—21no—
173C42×D61—21no—
174#14519710C2314yes—
175#14519708C2314yes—
176C4⋊#92418C2314yes—
177#14519700C2314yes—
178#14519699C2314yes—
179#14519699C2314yes—
180#14519697C2314yes—
181#14519697C2314yes—
182#14519697C2314yes—
183#14519689C2314yes—
184#14519689C2314yes—
185#14519687C2314yes—
186C8×Dic61C2314yes—
187C2×#41×C61C2311yescharacteristic
188C2×M16×C61C2312yes—
189#125×C61—21no—
190#125×C61—21no—
191#125×C61C2314yes—
192C4×Q8×C61C2312yes—
193C4×D4×C61—22no—
194C4×D4×C61C2312yes—
195#117×C61—21no—
196#117×C61C2311yescharacteristic
197C2×C4⋊C4×C61—22no—
198C2×C4⋊C4×C61C2312yes—
199C2×C42×C61—21no—
200C2×C42×C61C2311yescharacteristic
201#107×C61C2314yes—
202#106×C61C2314yes—
203C4⋊C8×C61C2314yes—
204#103×C61C2314yes—
205#102×C61C2314yes—
206C23×D61—21no—
207C23×D61—22no—
208C23×D61C2×D411yescharacteristic
209#41×C61—22no—
210#41×C61#4114yes—
211C2×Q8×C61C2411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61C2411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C22×Dic61—21no—
223C22×Dic61—22no—
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D412yes—
226#11758226—22no—
227#11758226—22no—
228Q8×D61—22no—
229Q8×D61—22no—
230#11758224—28no—
231#11758224—22no—
232#11758224—22no—
233D4×D61—28no—
234D4×D61—22no—
235D4×D61—22no—
236#11758222—28no—
237#11758222—22no—
238#11758222#4114yes—
239C2×D244—21no—
240C2×D244—24no—
241C2×D244—24no—
242C2×D244—22no—
243C2×D244—24no—
244C2×D244—24no—
245C2×D244—24no—
246C2×D244—24no—
247C2×D244—84no—
248C2×D244—84no—
249C2×D244C2414yes—
250C2×D244C2411yescharacteristic
251C2×C4×D61—28no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—21no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—24no—
260C2×C4×D61—24no—
261C2×C4×D61—22no—
262C2×C4×D61—84no—
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2411yescharacteristic
266C2×C4×D61C2411yescharacteristic
267C2×Dic122—21no—
268C2×Dic122C2411yescharacteristic
269M16×C61—24no—
270C2×C8×C61C2414yes—
271C4⋊C4×C61—24no—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—22no—
275C4⋊C4×C61C2414yes—
276C4⋊C4×C61C2412yes—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—22no—
279C42×C61—21no—
280C42×C61—22no—
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2412yes—
284C22⋊Dic61—21no—
285C22⋊Dic61—22no—
286#11758201—28no—
287#11758199—28no—
288#11758198—22no—
289#11758198—22no—
290#11758198—22no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295#11758198C2×D412yes—
296#11758198C2×D412yes—
297#11758198C2×D412yes—
298#11758198C2×D412yes—
299C4⋊Dic61—22no—
300C4⋊Dic61C2412yes—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304#11758196C2×D412yes—
305#11758196C2×D412yes—
306#11758196C2×D412yes—
307#11758196C2×D412yes—
308C4×Dic61—21no—
309C4×Dic61—22no—
310C4×Dic61—22no—
311C4×Dic61—22no—
312C4×Dic61—22no—
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2412yes—
316#11758194—24no—
317C2×#92418C2414yes—
318D488—28no—
319#11758190—28no—
320C23×C61—21no—
321C23×C61C22×D411yescharacteristic
322C22×D61—21no—
323C22×D61—24no—
324C22×D61—22no—
325C22×D61—24no—
326C22×D61—42no—
327C22×D61—44no—
328C22×D61—44no—
329C22×D61—44no—
330C22×D61—82no—
331C22×D61C22×D411yescharacteristic
332C22×D61C22×D411yescharacteristic
333Q8×C61—21no—
334Q8×C61C2×#4112yes—
335D4×C61—24no—
336D4×C61—21no—
337D4×C61C2×#4112yes—
338C2×C4×C61—21no—
339C2×C4×C61—24no—
340C2×C4×C61—22no—
341C2×C4×C61—24no—
342C2×C4×C61—42no—
343C2×C4×C61—44no—
344C2×C4×C61—82no—
345C2×C4×C61C22×D412yes—
346C2×C4×C61C22×D412yes—
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4112yes—
349C2×C4×C61C2×#4112yes—
350C2×C4×C61C2511yescharacteristic
351C22⋊D61—24no—
352C22⋊D61—24no—
353C22⋊D61—24no—
354C2×Dic61—24no—
355C2×Dic61—22no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—42no—
359C2×Dic61—82no—
360C2×Dic61C22×D411yescharacteristic
361C2×Dic61C22×D412yes—
362C2×Dic61C22×D412yes—
363C2×Dic61C22×D411yescharacteristic
364D244—24no—
365D244—21no—
366D244—24no—
367D244—24no—
368D244—44no—
369D244—84no—
370D244—84no—
371D244—84no—
372D244—84no—
373D244C2×#4112yes—
374C4×D61—24no—
375C4×D61—24no—
376C4×D61—22no—
377C4×D61—24no—
378C4×D61—22no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—82no—
384C4×D61—84no—
385C4×D61—84no—
386C4×D61—82no—
387C4×D61—82no—
388Dic122—24no—
389Dic122—21no—
390Dic122C2×#4112yes—
391C8×C61—24no—
392#92418—24no—
393#60568—611nomaximal, Sylow
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—42no—
397C22×C61#52512yes—
398C22×C61C23×D411yescharacteristic
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—22no—
404C2×D61—42no—
405C2×D61—44no—
406C2×D61—44no—
407C2×D61—44no—
408C2×D61—82no—
409C2×D61—84no—
410C2×D61—88no—
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—44no—
415C4×C61—42no—
416C4×C61#52512yes—
417C4×C61C22×#4111yescharacteristic
418C4×C61C22×#4111yescharacteristic
419Dic61—22no—
420Dic61—22no—
421Dic61—21no—
422Dic61—22no—
423Dic61—21no—
424Dic61—42no—
425C2×#540—611no—
426#3428—611no—
427#3126—614no—
428#3122—614no—
429#3119—614no—
430#3119—614no—
431#3094—612no—
432#3080—611no—
433#3080D6111yescharacteristic, complemented
434#3038—611no—
435#3038—611no—
436#3006—612no—
437C4×AGL(1,ℤ/8)—612no—
438C4×AGL(1,ℤ/8)—612no—
439#2921—611no—
440C2×C61—22no—
441C2×C61—42no—
442C2×C61C2×#52511yescharacteristic
443C2×C61#358512yes—
444D61—41no—
445D61—41no—
446D61—42no—
447D61—84no—
448C22×#41—611no—
449C2×AGL(1,ℤ/8)—612no—
450C2×AGL(1,ℤ/8)—612no—
451#540—614no—
452#540—614no—
453#540—1221no—
454#540—1221no—
455#540—1221no—
456#540—1221no—
457C2×#127—611no—
458C2×#125C2×D6111yescharacteristic, complemented
459C2×#123—1222no—
460C2×#121—612no—
461C2×#121—1222no—
462#520—612no—
463#520—612no—
464#520—1222no—
465#519—612no—
466#518—612no—
467#518—1222no—
468C4×#41—611no—
469C4×#41—611no—
470C4×#41—611no—
471C4×#41—1221no—
472C4×#41—1221no—
473C4×#41C2×D6111yescharacteristic
474C2×C4×D4—612no—
475C2×#117—611no—
476C2×#117—611no—
477C2×#117—1221no—
478C2×#117—1221no—
479#482—614no—
480#482—614no—
481#481—614no—
482#480—614no—
483#479—614no—
484#479C2×D6114yescomplemented
485#478—614no—
486#478C2×D6114yescomplemented
487#460—614no—
488#460—614no—
489#459—614no—
490#459—614no—
491#449—614no—
492#449—614no—
493#448—614no—
494#447—614no—
495#442—614no—
496#442—614no—
497#440—614no—
498#440—614no—
499C4×SD16—614no—
500C4×SD16—614no—
501C4×D8—614no—
502C4×D8—614no—
503#433—614no—
504#433—614no—
505#428—612no—
506#428C2×D6112yescomplemented
507#423—611no—
508#423C2×D6111yescharacteristic, complemented
509#418—612no—
510#418—612no—
511#417—612no—
512#417C2×D6112yes—
513#407—612no—
514C4×M16—612no—
515C61#6056811yescharacteristic, complemented, Sylow
516C2×#41—611no—
517C2×#41—611no—
518C2×#41—611no—
519C2×#41—1221no—
520C2×#41—1221no—
521C2×#41—1224no—
522C2×#41—1224no—
523C2×#41C22×D6111yescharacteristic
524C22×Q8—611no—
525C22×D4—611no—
526C22×D4—612no—
527C22×D4—1222no—
528C22×D4—1221no—
529C22×D4—1222no—
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1222no—
533AGL(1,ℤ/8)—1228no—
534AGL(1,ℤ/8)—1228no—
535C2×SD16—614no—
536C2×SD16—614no—
537C2×D8—614no—
538C2×D8—614no—
539C2×M16—612no—
540C2×M16C22×D6112yes—
541#127—614no—
542#127—1221no—
543#127—1221no—
544#125—21no—
545#125—21no—
546#125C22×D6114yes—
547#123—1224no—
548#123—1224no—
549#123—1224no—
550#123—1224no—
551#121—614no—
552#121—614no—
553#121—1224no—
554#121—1224no—
555#121—1224no—
556#121—1224no—
557#121—1222no—
558#121—1222no—
559C4×Q8—612no—
560C4×Q8—612no—
561C4×Q8—612no—
562C4×Q8—1222no—
563C4×Q8—1222no—
564C4×Q8C22×D6112yes—
565C4×D4—22no—
566C4×D4—612no—
567C4×D4—614no—
568C4×D4—614no—
569C4×D4—612no—
570C4×D4—612no—
571C4×D4—1222no—
572C4×D4—1222no—
573C4×D4—1222no—
574C4×D4—1222no—
575C4×D4—1222no—
576C4×D4—1222no—
577C4×D4—1222no—
578C4×D4—1222no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4C22×D6112yes—
583#117—21no—
584#117—611no—
585#117—611no—
586#117—611no—
587#117—611no—
588#117—612no—
589#117—612no—
590#117—611no—
591#117—612no—
592#117—1221no—
593#117—1222no—
594#117—1222no—
595#117—1221no—
596#117—1221no—
597#117—1222no—
598#117—1221no—
599#117—1222no—
600#117—1221no—
601#117C22×D6111yescharacteristic
602C2×C4⋊C4—22no—
603C2×C4⋊C4—612no—
604C2×C4⋊C4—612no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4C22×D6112yes—
608C2×C22⋊C4—612no—
609C2×C22⋊C4—1222no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1222no—
612C2×C22⋊C4—1222no—
613C2×C22⋊C4—1222no—
614C2×C42—21no—
615C2×C42—611no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619C2×C42—1221no—
620C2×C42C22×D6111yescharacteristic
621#107—614no—
622#107C22×D6114yes—
623#106—614no—
624#106C22×D6114yes—
625C4⋊C8—614no—
626C4⋊C8C22×D6114yes—
627#103—614no—
628#103C22×D6114yes—
629#102—614no—
630#102—614no—
631#102—614no—
632#102—614no—
633#102—614no—
634#102C22×D6114yes—
635C22⋊C8—614no—
636C22⋊C8—614no—
637#97—614no—
638C4×C8—614no—
639C24—611no—
640C24—1221no—
641C24—1222no—
642#41—22no—
643#41—614no—
644#41—1228no—
645#41—1222no—
646#41—1228no—
647#41—1222no—
648#41—1222no—
649#41—1222no—
650#41—1222no—
651#41#1175822614yes—
652C2×Q8—611no—
653C2×Q8—1221no—
654C2×Q8—1222no—
655C2×Q8—1222no—
656C2×Q8C23×D6111yescharacteristic
657C2×D4—21no—
658C2×D4—611no—
659C2×D4—614no—
660C2×D4—1221no—
661C2×D4—1224no—
662C2×D4—1224no—
663C2×D4—1221no—
664C2×D4—1222no—
665C2×D4—1228no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1222no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1222no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—4884no—
675C2×D4—4884no—
676C2×D4C23×D6111yescharacteristic
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—611no—
681C22×C4—612no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—1221no—
687C22×C4—1222no—
688C22×C4—1224no—
689C22×C4—1224no—
690C22×C4—1221no—
691C22×C4—1228no—
692C22×C4—1222no—
693C22×C4—1221no—
694C22×C4—1222no—
695C22×C4—1221no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—4884no—
700C22×C4D4×D6112yes—
701C22×C4C23×D6111yescharacteristic
702SD16—1228no—
703SD16—1228no—
704D8—1228no—
705D8—1228no—
706M16—24no—
707M16—1224no—
708C2×C8—614no—
709C2×C8C23×D6114yes—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—612no—
717C4⋊C4—612no—
718C4⋊C4—612no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4C23×D6112yes—
724C4⋊C4C23×D6114yes—
725C22⋊C4—21no—
726C22⋊C4—22no—
727C22⋊C4—612no—
728C22⋊C4—612no—
729C22⋊C4—612no—
730C22⋊C4—612no—
731C22⋊C4—1222no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C22⋊C4—1221no—
739C22⋊C4—1222no—
740C42—21no—
741C42—22no—
742C42—611no—
743C42—611no—
744C42—612no—
745C42—1222no—
746C42—1222no—
747C42—1222no—
748C42—1221no—
749C42—1222no—
750C42D4×D6111yescharacteristic
751C42D4×D6111yescharacteristic
752C42C23×D6112yes—
753C23—21no—
754C23—611no—
755C23—611no—
756C23—1224no—
757C23—1222no—
758C23—1221no—
759C23—1224no—
760C23—4882no—
761C23—2442no—
762C23—2444no—
763C23—2444no—
764C23—2444no—
765C23C2×D4×D6111yescharacteristic
766Q8—21no—
767Q8—612no—
768Q8—1224no—
769Q8—1221no—
770Q8C2×#1175822612yes—
771D4—24no—
772D4—21no—
773D4—612no—
774D4—1224no—
775D4—1224no—
776D4—1224no—
777D4—1224no—
778D4—1224no—
779D4—1221no—
780D4—1224no—
781D4—4884no—
782D4—4884no—
783D4—4884no—
784D4—4884no—
785D4—2444no—
786D4C2×#1175822612yes—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—82no—
794C2×C4—612no—
795C2×C4—612no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—1224no—
799C2×C4—1224no—
800C2×C4—1224no—
801C2×C4—1222no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1224no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1222no—
811C2×C4—4882no—
812C2×C4—4882no—
813C2×C4—4884no—
814C2×C4—4884no—
815C2×C4—4882no—
816C2×C4—4882no—
817C2×C4—2442no—
818C2×C4C2×D4×D6112yes—
819C2×C4C2×D4×D6112yes—
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4#41×D6112yes—
822C2×C4C2×#1175822612yes—
823C2×C4C24×D6111yescharacteristic
824C8—24no—
825C8—1224no—
826C22—22no—
827C22—22no—
828C22—42no—
829C22—1222no—
830C22—1222no—
831C22—1221no—
832C22—1222no—
833C22—1221no—
834C22—4888no—
835C22—4882no—
836C22—4884no—
837C22—2444no—
838C22—2444no—
839C22—2444no—
840C22—2442no—
841C22#1684027512yes—
842C22C22×D4×D6111yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—44no—
847C4—42no—
848C4—1222no—
849C4—1222no—
850C4—1221no—
851C4—1221no—
852C4—1222no—
853C4—2442no—
854C4#1684027512yes—
855C4C2×#41×D6111yescharacteristic
856C4C22×#1175822611yescharacteristic
857C2—22no—
858C2—42no—
859C2—4884no—
860C2—2441no—
861C2—2441no—
862C2—2442no—
863C2C2×#1684027511yescharacteristic
864C2#2146059612yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3080C2
socleC22×C61C23×D4
hypercenter#3080D61
hypocenterC61#60568
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#16840368C2semidirect
2. #21459018C2semidirect
3. #21456112C2semidirect
4. #21456064C2semidirect
5. #21456025C2semidirect
6. #21456023C2semidirect
7. #21455761C2semidirect
8. #21455637C2semidirect
9. #21455300C2semidirect
10. #21455299C2semidirect
11. #21455072C2semidirect
12. #21454632C2semidirect
13. #21454626C2semidirect
14. #21454456C2semidirect
15. C61×#3080C2semidirect
24. #16840368C22semidirect
25. C2×#14519774C22semidirect
29. #16840244C22semidirect
31. #16840241C22semidirect
32. #16840238C22semidirect
34. #16840234C22semidirect
40. C2×#14519739C22semidirect
45. #16840089C22semidirect
46. #16840088C22semidirect
47. #16840082C22semidirect
48. #16840077C22semidirect
49. #16840066C22semidirect
50. #16840059C22semidirect
51. #16839963C22semidirect
52. #16839962C22semidirect
53. #16839958C22semidirect
54. #16839957C22semidirect
55. #16839910C22semidirect
56. #16839908C22semidirect
57. #16839902C22semidirect
58. #16839897C22semidirect
59. #16839873C22semidirect
60. #16839871C22semidirect
61. #16839865C22semidirect
62. #16839861C22semidirect
63. #16839849C22semidirect
64. #16839847C22semidirect
65. #16839844C22semidirect
66. #16839842C22semidirect
67. #16839822C22semidirect
68. #16839822C22semidirect
69. #16839802C22semidirect
70. #16839786C22semidirect
71. #16839768C22semidirect
72. #16839766C22semidirect
75. M16×Dic61C22semidirect
76. C2×#125×C61C22semidirect
78. C61×#479C22semidirect
79. C61×#478C22semidirect
80. C61×#428C22semidirect
81. C61×#423C22semidirect
433. #3080D61semidirect
458. C2×#125C2×D61semidirect
484. #479C2×D61semidirect
486. #478C2×D61semidirect
506. #428C2×D61semidirect
508. #423C2×D61semidirect
515. C61#60568semidirect

Maximal subgroups

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

subgroupindex
C2×#168403682
#214590182
#214561122
#214560642
#214560252
#214560232
#214557612
#214556372
#214553002
#214552992
#214550722
#214546322
#214546262
#214544562
C61×#30802
#6056861