Finite Group Databasebeta

← #30548539

Subgroups — #30548539

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×#16840366C211yesmaximal, characteristic, complemented
2#21459018C211yesmaximal, characteristic, complemented
3#21456108C214yesmaximal, complemented
4#21456060C214yesmaximal, complemented
5#21456017C214yesmaximal, complemented
6#21456015C214yesmaximal, complemented
7#21455757C212yesmaximal, complemented
8#21455642C211yesmaximal, characteristic, complemented
9#21455641C211yesmaximal, characteristic, complemented
10#21455295C211yesmaximal, characteristic, complemented
11#21455067C212yesmaximal, complemented
12AGL(1,ℤ/8)×Dic61C212yesmaximal, complemented
13#21454623C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3038C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519803C2212yes—
18#16840366—21no—
19#16840366—21no—
20#16840366—21no—
21#16840366—21no—
22#16840366C2214yes—
23#16840366C2214yescomplemented
24C2×#14519769C2211yescharacteristic, complemented
25C2×#14519758—22no—
26C2×#14519749—22no—
27C2×#14519748C2212yes—
28#16840244C2212yescomplemented
29#16840241—22no—
30#16840241C2212yescomplemented
31#16840238C2212yescomplemented
32#16840234—22no—
33#16840234C2212yescomplemented
34#41×Dic61C2211yescharacteristic
35C4×#11758222—21no—
36C4×#11758222C2211yescharacteristic
37#16840230—21no—
38#16840230C2211yescharacteristic
39C2×D4×Dic61C2212yescomplemented
40C2×#14519734—21no—
41C2×#14519734C2211yescharacteristic
42#117×D61—21no—
43#117×D61C2211yescharacteristic
44#16840085C2214yescomplemented
45#16840084C2214yescomplemented
46#16840079C2214yescomplemented
47#16840074C2214yescomplemented
48#16840070C2214yescomplemented
49#16840069C2214yescomplemented
50#16840063C2214yescomplemented
51#16840062C2214yescomplemented
52#16839959C2214yescomplemented
53#16839954C2214yescomplemented
54#16839906C2214yescomplemented
55#16839904C2214yescomplemented
56#16839899C2214yescomplemented
57#16839894C2214yescomplemented
58#16839874C2214yescomplemented
59#16839871C2214yescomplemented
60#16839863C2214yescomplemented
61#16839859C2214yescomplemented
62#16839853C2214yescomplemented
63SD16×Dic61C2214yescomplemented
64D8×Dic61C2214yescomplemented
65#16839842C2214yescomplemented
66#16839822C2214yescomplemented
67#16839822C2214yescomplemented
68#16839805C2212yescomplemented
69#16839804C2212yescomplemented
70#16839786C2211yescharacteristic, complemented
71#16839767C2212yescomplemented
72#16839764C2212yes—
73#16839763C2212yes—
74#16839725C2212yes—
75M16×Dic61C2212yescomplemented
76C2×AGL(1,ℤ/8)×C61C2212yes—
77C2×#127×C61C2211yescharacteristic, complemented
78C4×#41×C61C2211yescharacteristic
79C61×#460C2214yescomplemented
80C61×#459C2214yescomplemented
81C61×#423C2211yescharacteristic, complemented
82C61×#418C2212yescomplemented
83C2×#11758226C2311yescharacteristic
84C2×#11758222—21no—
85C2×#11758222C2311yescharacteristic
86C2×#11758224—21no—
87C2×#11758224C2311yescharacteristic
88#41×D61—24no—
89#41×D61—24no—
90C2×Q8×D61C2311yescharacteristic
91C22×C22⋊D61—22no—
92C2×D4×D61—21no—
93C2×D4×D61C2311yescharacteristic
94C23×Dic61—22no—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97#14519803—28no—
98C2×#11758200C2314yes—
99C2×#11758199C2314yes—
100C2×#11758194C2312yes—
101#14519769—21no—
102#14519769—21no—
103#14519769C2314yes—
104#14519758—24no—
105#14519758—24no—
106#14519758—24no—
107#14519758—24no—
108#14519749—24no—
109#14519749—24no—
110#14519749—24no—
111#14519749—24no—
112#14519748—22no—
113#14519748—22no—
114#14519748C2314yes—
115#14519748C2314yes—
116Q8×Dic61C2312yes—
117C4×Dic122—22no—
118C4×Dic122C2312yes—
119#14519742—22no—
120#14519742C2312yes—
121C4×D244—22no—
122C4×D244C2312yes—
123D4×Dic61—22no—
124D4×Dic61—22no—
125D4×Dic61—22no—
126D4×Dic61C2314yes—
127D4×Dic61C2314yes—
128D4×Dic61C2312yes—
129#14519739—22no—
130#14519739C2312yes—
131C4×C22⋊D61—22no—
132C4×C22⋊D61—22no—
133C4×C22⋊D61—22no—
134#14519737—22no—
135#14519737—22no—
136#14519737—22no—
137#14519736—21no—
138#14519736C2311yescharacteristic
139#14519735—22no—
140#14519735C2312yes—
141#14519734—21no—
142#14519734—21no—
143#14519734—22no—
144#14519734—22no—
145#14519734—21no—
146#14519734D411yescharacteristic
147#14519734D411yescharacteristic
148#14519734D411yescharacteristic
149#14519734D411yescharacteristic
150#14519734C2312yes—
151#14519734C2312yes—
152#14519733—21no—
153#14519733—22no—
154C2×C4⋊Dic61C2312yes—
155C2×#11758196—22no—
156C2×#11758196—22no—
157C2×#11758196D412yes—
158C4⋊C4×D61—22no—
159C4⋊C4×D61C2312yes—
160C2×C22⋊Dic61—22no—
161C2×C22⋊Dic61—22no—
162C2×#11758198—22no—
163C2×#11758198D412yes—
164C22⋊C4×D61—21no—
165C22⋊C4×D61—22no—
166C2×C4×Dic61—21no—
167C2×C4×Dic61C2311yescharacteristic
168C42×D61—21no—
169C42×D61—21no—
170C42×D61—21no—
171#14519711C2314yes—
172#14519710C2314yes—
173#14519709C2314yes—
174#14519708C2314yes—
175C4⋊#92418C2314yes—
176#14519702C2314yes—
177#14519701C2314yes—
178#14519699C2314yes—
179#14519698C2314yes—
180#14519698C2314yes—
181#14519698C2314yes—
182#14519689C2314yes—
183#14519689C2314yes—
184#14519687C2314yes—
185C8×Dic61C2314yes—
186C2×#41×C61C2311yescharacteristic
187C22×D4×C61—22no—
188C22×D4×C61C2312yes—
189AGL(1,ℤ/8)×C61—28no—
190C2×SD16×C61C2314yes—
191C2×D8×C61C2314yes—
192C2×M16×C61C2312yes—
193#127×C61—21no—
194#127×C61—21no—
195#127×C61C2314yes—
196C4×Q8×C61C2312yes—
197C4×D4×C61—22no—
198C4×D4×C61C2312yes—
199#117×C61—21no—
200#117×C61C2311yescharacteristic
201C2×C42×C61—21no—
202C2×C42×C61C2311yescharacteristic
203C4⋊C8×C61C2314yes—
204#102×C61C2314yes—
205#102×C61C2314yes—
206C24×C61—22no—
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209#41×C61—22no—
210#41×C61#4114yes—
211C2×Q8×C61C2411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61—22no—
214C2×D4×C61—24no—
215C2×D4×C61—24no—
216C2×D4×C61—24no—
217C2×D4×C61—24no—
218C2×D4×C61—84no—
219C2×D4×C61C2414yes—
220C2×D4×C61C2411yescharacteristic
221C22×C4×C61—21no—
222C22×C4×C61—22no—
223C22×C4×C61C2×D412yes—
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—84no—
231C22×Dic61—21no—
232C22×Dic61—22no—
233C22×Dic61—24no—
234C22×Dic61—24no—
235C22×Dic61—22no—
236C22×Dic61—84no—
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D412yes—
239#11758226—22no—
240#11758226—22no—
241Q8×D61—22no—
242Q8×D61—22no—
243#11758224—28no—
244#11758224—22no—
245#11758224—22no—
246D4×D61—28no—
247D4×D61—22no—
248D4×D61—22no—
249#11758222—28no—
250#11758222—22no—
251#11758222#4114yes—
252C2×D244—21no—
253C2×D244C2411yescharacteristic
254C2×C4×D61—28no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—21no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2411yescharacteristic
266C2×C4×D61C2411yescharacteristic
267C2×Dic122—21no—
268C2×Dic122C2411yescharacteristic
269SD16×C61—28no—
270D8×C61—28no—
271M16×C61—24no—
272C2×C8×C61C2414yes—
273C4⋊C4×C61—22no—
274C4⋊C4×C61C2412yes—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—22no—
277C42×C61—21no—
278C42×C61—22no—
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2412yes—
282C22⋊Dic61—21no—
283C22⋊Dic61—22no—
284C22⋊Dic61—24no—
285C22⋊Dic61—24no—
286C22⋊Dic61—24no—
287C22⋊Dic61—24no—
288#11758200—28no—
289#11758199—28no—
290#11758198—22no—
291#11758198—22no—
292#11758198—22no—
293#11758198C2×D412yes—
294#11758198C2×D412yes—
295#11758198C2×D412yes—
296#11758198C2×D412yes—
297C4⋊Dic61—22no—
298C4⋊Dic61—22no—
299C4⋊Dic61C2412yes—
300C4⋊Dic61C2414yes—
301#11758196—22no—
302#11758196—24no—
303#11758196—24no—
304#11758196—22no—
305#11758196—22no—
306#11758196C2×D412yes—
307#11758196C2×D412yes—
308#11758196C2×D412yes—
309#11758196C2×D412yes—
310C4×Dic61—21no—
311C4×Dic61—22no—
312C4×Dic61—22no—
313C4×Dic61—22no—
314C4×Dic61—22no—
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2412yes—
318#11758194—24no—
319C2×#92418C2414yes—
320C23×C61—21no—
321C23×C61—24no—
322C23×C61—44no—
323C23×C61—44no—
324C23×C61—44no—
325C23×C61C22×D411yescharacteristic
326C22×D61—21no—
327C22×D61—24no—
328C22×D61—22no—
329C22×D61—42no—
330C22×D61—82no—
331C22×D61C22×D411yescharacteristic
332C22×D61C22×D411yescharacteristic
333Q8×C61—21no—
334Q8×C61C2×#4112yes—
335D4×C61—24no—
336D4×C61—21no—
337D4×C61—24no—
338D4×C61—24no—
339D4×C61—44no—
340D4×C61—84no—
341D4×C61—84no—
342D4×C61C2×#4112yes—
343C2×C4×C61—21no—
344C2×C4×C61—24no—
345C2×C4×C61—22no—
346C2×C4×C61—42no—
347C2×C4×C61—82no—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D412yes—
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2×#4112yes—
352C2×C4×C61C2×#4112yes—
353C2×C4×C61C2511yescharacteristic
354C22⋊D61—24no—
355C22⋊D61—24no—
356C22⋊D61—24no—
357C22⋊D61—84no—
358C22⋊D61—84no—
359C2×Dic61—24no—
360C2×Dic61—22no—
361C2×Dic61—21no—
362C2×Dic61—22no—
363C2×Dic61—24no—
364C2×Dic61—42no—
365C2×Dic61—44no—
366C2×Dic61—82no—
367C2×Dic61—84no—
368C2×Dic61—84no—
369C2×Dic61C22×D411yescharacteristic
370C2×Dic61C22×D412yes—
371C2×Dic61C22×D412yes—
372C2×Dic61C22×D411yescharacteristic
373D244—24no—
374D244—21no—
375D244C2×#4112yes—
376C4×D61—24no—
377C4×D61—24no—
378C4×D61—22no—
379C4×D61—24no—
380C4×D61—22no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—82no—
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—44no—
398C22×C61—44no—
399C22×C61—44no—
400C22×C61—88no—
401C22×C61#52512yes—
402C22×C61C23×D411yescharacteristic
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—22no—
408C2×D61—42no—
409C2×D61—82no—
410C2×D61—84no—
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—42no—
415C4×C61#52512yes—
416C4×C61C22×#4111yescharacteristic
417C4×C61C22×#4111yescharacteristic
418Dic61—22no—
419Dic61—22no—
420Dic61—21no—
421Dic61—22no—
422Dic61—21no—
423Dic61—42no—
424Dic61—44no—
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#3080—611no—
434#3038—611no—
435#3038D6111yescharacteristic, complemented
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×C61—84no—
443C2×C61C2×#52511yescharacteristic
444C2×C61#358512yes—
445D61—41no—
446D61—41no—
447D61—42no—
448C22×#41—611no—
449C2×AGL(1,ℤ/8)—612no—
450C2×AGL(1,ℤ/8)C2×D6112yes—
451#540—614no—
452#540—614no—
453#540—1221no—
454#540—1221no—
455#540—1221no—
456#540—1221no—
457C2×#127C2×D6111yescharacteristic, complemented
458C2×#125—611no—
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#479—614no—
485#478—614no—
486#478—614no—
487#460—614no—
488#460C2×D6114yescomplemented
489#459—614no—
490#459C2×D6114yescomplemented
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#428—612no—
507#423—611no—
508#423C2×D6111yescharacteristic, complemented
509#418—612no—
510#418C2×D6112yescomplemented
511#417—612no—
512#417—612no—
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—22no—
526C22×D4—611no—
527C22×D4—1221no—
528C22×D4—1222no—
529C22×D4C22×D6112yes—
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1222no—
533AGL(1,ℤ/8)—28no—
534AGL(1,ℤ/8)—1228no—
535C2×SD16—614no—
536C2×SD16C22×D6114yes—
537C2×D8—614no—
538C2×D8C22×D6114yes—
539C2×M16—612no—
540C2×M16C22×D6112yes—
541#127—21no—
542#127—21no—
543#127C22×D6114yes—
544#125—614no—
545#125—1221no—
546#125—1221no—
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—614no—
567C4×D4—614no—
568C4×D4—612no—
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—612no—
603C2×C4⋊C4—612no—
604C2×C4⋊C4—612no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
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#107—614no—
623#106—614no—
624#106—614no—
625C4⋊C8—614no—
626C4⋊C8C22×D6114yes—
627#103—614no—
628#103—614no—
629#102—614no—
630#102—614no—
631#102—614no—
632#102—614no—
633#102C22×D6114yes—
634#102C22×D6114yes—
635C22⋊C8—614no—
636C22⋊C8—614no—
637#97—614no—
638C4×C8—614no—
639C24—22no—
640C24—611no—
641C24—1221no—
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#1175822414yes—
652C2×Q8—611no—
653C2×Q8—1221no—
654C2×Q8—1222no—
655C2×Q8—1222no—
656C2×Q8C23×D6111yescharacteristic
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—84no—
664C2×D4—611no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1222no—
668C2×D4—1228no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1222no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—4884no—
675C2×D4C23×D6114yes—
676C2×D4C23×D6111yescharacteristic
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—611no—
680C22×C4—612no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—1221no—
686C22×C4—1222no—
687C22×C4—1221no—
688C22×C4—1228no—
689C22×C4—1222no—
690C22×C4—1221no—
691C22×C4—1222no—
692C22×C4—1224no—
693C22×C4—1224no—
694C22×C4—1221no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—4884no—
700C22×C4D4×D6112yes—
701C22×C4C23×D6111yescharacteristic
702SD16—28no—
703SD16—1228no—
704D8—28no—
705D8—1228no—
706M16—24no—
707M16—1224no—
708C2×C8—614no—
709C2×C8C23×D6114yes—
710C4⋊C4—22no—
711C4⋊C4—612no—
712C4⋊C4—612no—
713C4⋊C4—612no—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—614no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1224no—
723C4⋊C4—1224no—
724C4⋊C4C23×D6112yes—
725C22⋊C4—21no—
726C22⋊C4—22no—
727C22⋊C4—612no—
728C22⋊C4—612no—
729C22⋊C4—612no—
730C22⋊C4—612no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—1224no—
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—24no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—611no—
759C23—611no—
760C23—1224no—
761C23—1222no—
762C23—1221no—
763C23—4882no—
764C23—2442no—
765C23C2×D4×D6111yescharacteristic
766Q8—21no—
767Q8—612no—
768Q8—1224no—
769Q8—1221no—
770Q8C2×#1175822412yes—
771D4—24no—
772D4—21no—
773D4—24no—
774D4—24no—
775D4—44no—
776D4—84no—
777D4—84no—
778D4—612no—
779D4—1224no—
780D4—1224no—
781D4—1224no—
782D4—1224no—
783D4—1221no—
784D4—4884no—
785D4—4884no—
786D4C2×#1175822412yes—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—42no—
791C2×C4—82no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—1224no—
797C2×C4—1224no—
798C2×C4—1224no—
799C2×C4—1222no—
800C2×C4—1221no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1224no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1222no—
809C2×C4—1224no—
810C2×C4—4882no—
811C2×C4—4882no—
812C2×C4—4882no—
813C2×C4—4882no—
814C2×C4—4884no—
815C2×C4—4884no—
816C2×C4—2442no—
817C2×C4—2444no—
818C2×C4C2×D4×D6112yes—
819C2×C4C2×D4×D6112yes—
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4#41×D6112yes—
822C2×C4C2×#1175822412yes—
823C2×C4C24×D6111yescharacteristic
824C8—24no—
825C8—1224no—
826C22—22no—
827C22—22no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—88no—
833C22—1222no—
834C22—1222no—
835C22—1221no—
836C22—1222no—
837C22—1221no—
838C22—4882no—
839C22—4884no—
840C22—2442no—
841C22#1684027212yes—
842C22C22×D4×D6111yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—42no—
847C4—1222no—
848C4—1222no—
849C4—1221no—
850C4—1221no—
851C4—1222no—
852C4—2442no—
853C4—2444no—
854C4#1684027212yes—
855C4C2×#41×D6111yescharacteristic
856C4C22×#1175822411yescharacteristic
857C2—22no—
858C2—42no—
859C2—84no—
860C2—2441no—
861C2—2441no—
862C2—2442no—
863C2C2×#1684027211yescharacteristic
864C2#2146059512yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3038C2
socleC22×C61C23×D4
hypercenter#3038D61
hypocenterC61#60568
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. C2×#16840366C2semidirect
2. #21459018C2semidirect
3. #21456108C2semidirect
4. #21456060C2semidirect
5. #21456017C2semidirect
6. #21456015C2semidirect
7. #21455757C2semidirect
8. #21455642C2semidirect
9. #21455641C2semidirect
10. #21455295C2semidirect
11. #21455067C2semidirect
12. AGL(1,ℤ/8)×Dic61C2semidirect
13. #21454623C2semidirect
14. #21454456C2semidirect
15. C61×#3038C2semidirect
23. #16840366C22semidirect
24. C2×#14519769C22semidirect
28. #16840244C22semidirect
30. #16840241C22semidirect
31. #16840238C22semidirect
33. #16840234C22semidirect
39. C2×D4×Dic61C22semidirect
44. #16840085C22semidirect
45. #16840084C22semidirect
46. #16840079C22semidirect
47. #16840074C22semidirect
48. #16840070C22semidirect
49. #16840069C22semidirect
50. #16840063C22semidirect
51. #16840062C22semidirect
52. #16839959C22semidirect
53. #16839954C22semidirect
54. #16839906C22semidirect
55. #16839904C22semidirect
56. #16839899C22semidirect
57. #16839894C22semidirect
58. #16839874C22semidirect
59. #16839871C22semidirect
60. #16839863C22semidirect
61. #16839859C22semidirect
62. #16839853C22semidirect
63. SD16×Dic61C22semidirect
64. D8×Dic61C22semidirect
65. #16839842C22semidirect
66. #16839822C22semidirect
67. #16839822C22semidirect
68. #16839805C22semidirect
69. #16839804C22semidirect
70. #16839786C22semidirect
71. #16839767C22semidirect
75. M16×Dic61C22semidirect
77. C2×#127×C61C22semidirect
79. C61×#460C22semidirect
80. C61×#459C22semidirect
81. C61×#423C22semidirect
82. C61×#418C22semidirect
435. #3038D61semidirect
457. C2×#127C2×D61semidirect
488. #460C2×D61semidirect
490. #459C2×D61semidirect
508. #423C2×D61semidirect
510. #418C2×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×#168403662
#214590182
#214561082
#214560602
#214560172
#214560152
#214557572
#214556422
#214556412
#214552952
#214550672
AGL(1,ℤ/8)×Dic612
#214546232
#214544562
C61×#30382
#6056861