Finite Group Databasebeta

← #30548554

Subgroups — #30548554

Order 15616.

2010 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840375C211yesmaximal, characteristic, complemented
2#21459018C211yesmaximal, characteristic
3#21456121C214yesmaximal, complemented
4#21456073C214yesmaximal, complemented
5#21456040C214yesmaximal, complemented
6#21456038C214yesmaximal, complemented
7#21455769C212yesmaximal, complemented
8#21455637C211yesmaximal, characteristic, complemented
9#21455307C211yesmaximal, characteristic, complemented
10#21455306C211yesmaximal, characteristic, complemented
11#21455080C212yesmaximal
12#21454643C212yesmaximal, complemented
13#21454637C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3080C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519810C2212yes—
18C2×#14519807C2212yes—
19#16840375—21no—
20#16840375—21no—
21#16840375—21no—
22#16840375—21no—
23#16840375C2214yes—
24#16840375C2214yescomplemented
25C2×#14519777C2211yescharacteristic, complemented
26C2×#14519772—22no—
27C2×#14519768—22no—
28C2×#14519757C2212yes—
29#16840244C2212yes—
30#16840241—22no—
31#16840241C2212yes—
32#16840238C2212yes—
33#16840234—22no—
34#16840234C2212yes—
35#41×Dic61C2211yescharacteristic
36C4×#11758222—21no—
37C4×#11758222C2211yescharacteristic
38#16840230—21no—
39#16840230C2211yescharacteristic
40C2×#14519742C2212yescomplemented
41C2×#14519734—21no—
42C2×#14519734C2211yescharacteristic
43#117×D61—21no—
44#117×D61C2211yescharacteristic
45#16840106C2214yes—
46#16840105C2214yes—
47#16840099C2214yescomplemented
48#16840094C2214yescomplemented
49#16840066C2214yescomplemented
50#16840059C2214yescomplemented
51#16839973C2214yescomplemented
52#16839972C2214yescomplemented
53#16839968C2214yescomplemented
54#16839967C2214yescomplemented
55#16839927C2214yes—
56#16839925C2214yes—
57#16839919C2214yes—
58#16839914C2214yes—
59#16839868C2214yescomplemented
60#16839866C2214yescomplemented
61#16839861C2214yescomplemented
62#16839859C2214yescomplemented
63#16839856C2214yescomplemented
64#16839854C2214yescomplemented
65#16839853C2214yescomplemented
66#16839849C2214yescomplemented
67#16839822C2214yes—
68#16839822C2214yescomplemented
69#16839802C2212yescomplemented
70#16839786C2211yescharacteristic, complemented
71#16839772C2212yescomplemented
72#16839770C2212yescomplemented
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—
90C22×Dic122C2312yes—
91C2×Q8×D61C2311yescharacteristic
92C2×D4×D61—21no—
93C2×D4×D61C2311yescharacteristic
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96#14519810—28no—
97#14519807—28no—
98C2×Dic244C2314yes—
99C2×#11758202C2314yes—
100C2×#11758190C2314yes—
101C2×#11758200C2314yes—
102C2×#11758194C2312yes—
103#14519777—21no—
104#14519777—21no—
105#14519777C2314yes—
106#14519772—24no—
107#14519772—24no—
108#14519772—24no—
109#14519772—24no—
110#14519768—24no—
111#14519768—24no—
112#14519768—24no—
113#14519768—24no—
114#14519757—22no—
115#14519757—22no—
116#14519757C2314yes—
117#14519757C2314yes—
118Q8×Dic61C2312yes—
119C4×Dic122—22no—
120C4×Dic122C2312yes—
121#14519742—22no—
122#14519742—22no—
123#14519742—22no—
124#14519742C2314yes—
125#14519742C2314yes—
126#14519742C2312yes—
127C4×D244—22no—
128C4×D244C2312yes—
129D4×Dic61—22no—
130D4×Dic61C2312yes—
131#14519739—22no—
132#14519739C2312yes—
133C4×C22⋊D61—22no—
134C4×C22⋊D61—22no—
135C4×C22⋊D61—22no—
136#14519737—22no—
137#14519737—22no—
138#14519737—22no—
139#14519736—21no—
140#14519736C2311yescharacteristic
141#14519735—22no—
142#14519735C2312yes—
143#14519734—21no—
144#14519734—21no—
145#14519734—22no—
146#14519734—22no—
147#14519734—21no—
148#14519734D411yescharacteristic
149#14519734D411yescharacteristic
150#14519734D411yescharacteristic
151#14519734D411yescharacteristic
152#14519734C2312yes—
153#14519734C2312yes—
154#14519733—21no—
155#14519733—22no—
156C2×C4⋊Dic61—22no—
157C2×C4⋊Dic61—22no—
158C2×#11758196—22no—
159C2×#11758196—22no—
160C2×#11758196D412yes—
161C4⋊C4×D61—22no—
162C4⋊C4×D61C2312yes—
163C2×#11758198—22no—
164C2×#11758198—22no—
165C2×#11758198D412yes—
166C22⋊C4×D61—21no—
167C22⋊C4×D61—22no—
168C2×C4×Dic61—22no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61C2311yescharacteristic
171C42×D61—21no—
172C42×D61—21no—
173C42×D61—21no—
174#14519710C2314yes—
175#14519708C2314yes—
176C4⋊#92418C2314yes—
177#14519702C2314yes—
178#14519702C2314yes—
179#14519700C2314yes—
180#14519700C2314yes—
181#14519700C2314yes—
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×D61C2×D411yescharacteristic
208#41×C61—22no—
209#41×C61#4114yes—
210C2×Q8×C61C2411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61C2411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C22×Dic61—21no—
222C22×Dic61—22no—
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×D244C2411yescharacteristic
241C2×C4×D61—28no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—21no—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2411yescharacteristic
253C2×C4×D61C2411yescharacteristic
254C2×Dic122—21no—
255C2×Dic122—24no—
256C2×Dic122—24no—
257C2×Dic122—22no—
258C2×Dic122C2414yes—
259C2×Dic122C2411yescharacteristic
260M16×C61—24no—
261C2×C8×C61C2414yes—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61—22no—
265C4⋊C4×C61—22no—
266C4⋊C4×C61C2414yes—
267C4⋊C4×C61C2412yes—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—22no—
270C42×C61—21no—
271C42×C61—22no—
272C42×C61C2×D411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C42×C61C2412yes—
275C22⋊Dic61—21no—
276C22⋊Dic61—22no—
277#11758202—28no—
278#11758200—28no—
279#11758198—22no—
280#11758198—24no—
281#11758198—24no—
282#11758198—22no—
283#11758198—22no—
284#11758198C2×D412yes—
285#11758198C2×D412yes—
286#11758198C2×D412yes—
287#11758198C2×D412yes—
288C4⋊Dic61—24no—
289C4⋊Dic61—24no—
290C4⋊Dic61—22no—
291C4⋊Dic61—24no—
292C4⋊Dic61—24no—
293C4⋊Dic61C2412yes—
294#11758196—22no—
295#11758196—22no—
296#11758196—22no—
297#11758196—24no—
298#11758196—24no—
299#11758196C2×D412yes—
300#11758196C2×D412yes—
301#11758196C2×D412yes—
302#11758196C2×D412yes—
303C4×Dic61—21no—
304C4×Dic61—22no—
305C4×Dic61—22no—
306C4×Dic61—22no—
307C4×Dic61—22no—
308C4×Dic61—24no—
309C4×Dic61—24no—
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2412yes—
313#11758194—24no—
314C2×#92418C2414yes—
315Dic244—28no—
316#11758190—28no—
317C23×C61—21no—
318C23×C61C22×D411yescharacteristic
319C22×D61—21no—
320C22×D61—24no—
321C22×D61—22no—
322C22×D61—42no—
323C22×D61—82no—
324C22×D61C22×D411yescharacteristic
325C22×D61C22×D411yescharacteristic
326Q8×C61—21no—
327Q8×C61C2×#4112yes—
328D4×C61—24no—
329D4×C61—21no—
330D4×C61C2×#4112yes—
331C2×C4×C61—21no—
332C2×C4×C61—24no—
333C2×C4×C61—24no—
334C2×C4×C61—22no—
335C2×C4×C61—42no—
336C2×C4×C61—44no—
337C2×C4×C61—82no—
338C2×C4×C61C22×D412yes—
339C2×C4×C61C22×D412yes—
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4112yes—
342C2×C4×C61C2×#4112yes—
343C2×C4×C61C2511yescharacteristic
344C22⋊D61—24no—
345C22⋊D61—24no—
346C22⋊D61—24no—
347C2×Dic61—24no—
348C2×Dic61—22no—
349C2×Dic61—21no—
350C2×Dic61—22no—
351C2×Dic61—24no—
352C2×Dic61—42no—
353C2×Dic61—44no—
354C2×Dic61—82no—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D411yescharacteristic
358C2×Dic61C22×D411yescharacteristic
359D244—24no—
360D244—21no—
361D244C2×#4112yes—
362C4×D61—24no—
363C4×D61—24no—
364C4×D61—22no—
365C4×D61—24no—
366C4×D61—22no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—82no—
372C4×D61—82no—
373C4×D61—82no—
374Dic122—24no—
375Dic122—21no—
376Dic122—24no—
377Dic122—24no—
378Dic122—44no—
379Dic122C2×#4112yes—
380C8×C61—24no—
381#92418—24no—
382#60569—611nomaximal, Sylow
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—42no—
386C22×C61#52512yes—
387C22×C61C23×D411yescharacteristic
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—22no—
393C2×D61—42no—
394C2×D61—82no—
395C2×D61—84no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—42no—
400C4×C61—44no—
401C4×C61#52512yes—
402C4×C61C22×#4111yescharacteristic
403C4×C61C22×#4111yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—21no—
407Dic61—22no—
408Dic61—21no—
409Dic61—42no—
410Dic61—44no—
411C2×#541—611no—
412#3428—611no—
413#3127—614no—
414#3123—614no—
415#3120—614no—
416#3120—614no—
417#3095—612no—
418#3080—611no—
419#3080D6111yescharacteristic, complemented
420#3039—611no—
421#3039—611no—
422#3007—612no—
423C4×#137—612no—
424C4×#137—612no—
425#2921—611no—
426C2×C61—22no—
427C2×C61—42no—
428C2×C61C2×#52511yescharacteristic
429C2×C61#358612yes—
430D61—41no—
431D61—41no—
432D61—42no—
433C22×#41—611no—
434C2×#137—612no—
435C2×#137—612no—
436#541—614no—
437#541—614no—
438#541—1221no—
439#541—1221no—
440#541—1221no—
441#541—1221no—
442C2×C4⋊Q8—611no—
443C2×#126—1222no—
444C2×#125—1222no—
445C2×#125C2×D6111yescharacteristic, complemented
446C2×C22⋊Q8—612no—
447#520—612no—
448#520—612no—
449#520—1222no—
450#519—612no—
451#518—612no—
452#518—1222no—
453C4×#41—611no—
454C4×#41—611no—
455C4×#41—611no—
456C4×#41—1221no—
457C4×#41—1221no—
458C4×#41C2×D6111yescharacteristic
459C2×C4×Q8—612no—
460C2×#117—611no—
461C2×#117—611no—
462C2×#117—1221no—
463C2×#117—1221no—
464#485—614no—
465#485—614no—
466#484—614no—
467#483—614no—
468#479—614no—
469#479C2×D6114yescomplemented
470#478—614no—
471#478C2×D6114yescomplemented
472#462—614no—
473#462—614no—
474#461—614no—
475#461—614no—
476#452—614no—
477#452—614no—
478#451—614no—
479#450—614no—
480#441—614no—
481#441—614no—
482#440—614no—
483#440—614no—
484C4×Q16—614no—
485C4×Q16—614no—
486C4×SD16—614no—
487C4×SD16—614no—
488#433—614no—
489#433—614no—
490#428—612no—
491#428C2×D6112yescomplemented
492#423—611no—
493#423C2×D6111yescharacteristic, complemented
494#419—612no—
495#419—612no—
496#417—612no—
497#417C2×D6112yes—
498#407—612no—
499C4×M16—612no—
500C61#6056911yescharacteristic, complemented, Sylow
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41—1224no—
507C2×#41—1224no—
508C2×#41C22×D6111yescharacteristic
509C22×Q8—611no—
510C22×Q8—612no—
511C22×D4—611no—
512C22×D4—1221no—
513C23×C4—611no—
514C23×C4—1221no—
515#137—1228no—
516#137—1228no—
517C2×Q16—614no—
518C2×Q16—614no—
519C2×SD16—614no—
520C2×SD16—614no—
521C2×M16—612no—
522C2×M16C22×D6112yes—
523C4⋊Q8—614no—
524C4⋊Q8—1221no—
525C4⋊Q8—1221no—
526#126—1224no—
527#126—1224no—
528#126—1224no—
529#126—1224no—
530#125—21no—
531#125—21no—
532#125—1224no—
533#125—1224no—
534#125—1224no—
535#125—1224no—
536#125C22×D6114yes—
537C22⋊Q8—614no—
538C22⋊Q8—614no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C4×Q8—612no—
542C4×Q8—614no—
543C4×Q8—614no—
544C4×Q8—612no—
545C4×Q8—612no—
546C4×Q8—1222no—
547C4×Q8—1222no—
548C4×Q8—1222no—
549C4×Q8—1222no—
550C4×Q8C22×D6112yes—
551C4×D4—22no—
552C4×D4—612no—
553C4×D4—612no—
554C4×D4—612no—
555C4×D4—1222no—
556C4×D4—1222no—
557C4×D4—1222no—
558C4×D4—1222no—
559C4×D4—1222no—
560C4×D4—1222no—
561C4×D4—1222no—
562C4×D4—1222no—
563C4×D4—1222no—
564C4×D4C22×D6112yes—
565#117—21no—
566#117—611no—
567#117—611no—
568#117—611no—
569#117—611no—
570#117—612no—
571#117—612no—
572#117—611no—
573#117—612no—
574#117—1221no—
575#117—1222no—
576#117—1222no—
577#117—1221no—
578#117—1221no—
579#117—1222no—
580#117—1221no—
581#117—1222no—
582#117—1221no—
583#117C22×D6111yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—612no—
586C2×C4⋊C4—612no—
587C2×C4⋊C4—1222no—
588C2×C4⋊C4—1222no—
589C2×C4⋊C4—1222no—
590C2×C4⋊C4—1222no—
591C2×C4⋊C4—1222no—
592C2×C4⋊C4C22×D6112yes—
593C2×C22⋊C4—612no—
594C2×C22⋊C4—1222no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1222no—
597C2×C22⋊C4—1222no—
598C2×C42—21no—
599C2×C42—611no—
600C2×C42—1221no—
601C2×C42—1221no—
602C2×C42—1221no—
603C2×C42—1222no—
604C2×C42—1221no—
605C2×C42C22×D6111yescharacteristic
606#107—614no—
607#107C22×D6114yes—
608#106—614no—
609#106C22×D6114yes—
610C4⋊C8—614no—
611C4⋊C8C22×D6114yes—
612#103—614no—
613#103—614no—
614#103—614no—
615#103—614no—
616#103—614no—
617#103C22×D6114yes—
618#102—614no—
619#102C22×D6114yes—
620C22⋊C8—614no—
621C22⋊C8—614no—
622#97—614no—
623C4×C8—614no—
624C24—611no—
625C24—1221no—
626#41—22no—
627#41—614no—
628#41—1228no—
629#41—1222no—
630#41—1228no—
631#41—1222no—
632#41—1222no—
633#41—1222no—
634#41—1222no—
635#41#1175822614yes—
636C2×Q8—611no—
637C2×Q8—614no—
638C2×Q8—1221no—
639C2×Q8—1222no—
640C2×Q8—1222no—
641C2×Q8—1222no—
642C2×Q8—1224no—
643C2×Q8—1224no—
644C2×Q8C23×D6111yescharacteristic
645C2×D4—21no—
646C2×D4—611no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1222no—
650C2×D4—1228no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1222no—
654C2×D4C23×D6111yescharacteristic
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—611no—
659C22×C4—612no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—1221no—
665C22×C4—1222no—
666C22×C4—1221no—
667C22×C4—1228no—
668C22×C4—1222no—
669C22×C4—1221no—
670C22×C4—1222no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4D4×D6112yes—
677C22×C4C23×D6111yescharacteristic
678Q16—1228no—
679Q16—1228no—
680SD16—1228no—
681SD16—1228no—
682M16—24no—
683M16—1224no—
684C2×C8—614no—
685C2×C8C23×D6114yes—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—612no—
693C4⋊C4—612no—
694C4⋊C4—612no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1224no—
698C4⋊C4—1224no—
699C4⋊C4—1222no—
700C4⋊C4—1224no—
701C4⋊C4—1224no—
702C4⋊C4—1222no—
703C4⋊C4—1224no—
704C4⋊C4—1224no—
705C4⋊C4C23×D6114yes—
706C4⋊C4C23×D6112yes—
707C22⋊C4—21no—
708C22⋊C4—22no—
709C22⋊C4—612no—
710C22⋊C4—612no—
711C22⋊C4—612no—
712C22⋊C4—612no—
713C22⋊C4—1222no—
714C22⋊C4—1222no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1222no—
718C22⋊C4—1221no—
719C22⋊C4—1222no—
720C42—21no—
721C42—22no—
722C42—611no—
723C42—611no—
724C42—612no—
725C42—1222no—
726C42—1222no—
727C42—1222no—
728C42—1224no—
729C42—1224no—
730C42—1221no—
731C42—1222no—
732C42D4×D6111yescharacteristic
733C42D4×D6111yescharacteristic
734C42C23×D6112yes—
735C23—21no—
736C23—611no—
737C23—611no—
738C23—1224no—
739C23—1222no—
740C23—1221no—
741C23—4882no—
742C23—2442no—
743C23C2×D4×D6111yescharacteristic
744Q8—21no—
745Q8—612no—
746Q8—1224no—
747Q8—1221no—
748Q8—1224no—
749Q8—1224no—
750Q8—2444no—
751Q8C2×#1175822612yes—
752D4—24no—
753D4—21no—
754D4—612no—
755D4—1224no—
756D4—1224no—
757D4—1224no—
758D4—1224no—
759D4—1221no—
760D4C2×#1175822612yes—
761C2×C4—21no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—82no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—1224no—
773C2×C4—1224no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1221no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1224no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1224no—
786C2×C4—4882no—
787C2×C4—4882no—
788C2×C4—4882no—
789C2×C4—4882no—
790C2×C4—2442no—
791C2×C4—2444no—
792C2×C4C2×D4×D6112yes—
793C2×C4C2×D4×D6112yes—
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4#41×D6112yes—
796C2×C4C2×#1175822612yes—
797C2×C4C24×D6111yescharacteristic
798C8—24no—
799C8—1224no—
800C22—22no—
801C22—22no—
802C22—42no—
803C22—1221no—
804C22—1222no—
805C22—1221no—
806C22—1222no—
807C22—1222no—
808C22—4882no—
809C22—4884no—
810C22—2442no—
811C22#1684027512yes—
812C22C22×D4×D6111yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—44no—
817C4—42no—
818C4—1221no—
819C4—1221no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4—2444no—
824C4—2442no—
825C4#1684027512yes—
826C4C2×#41×D6111yescharacteristic
827C4C22×#1175822611yescharacteristic
828C2—22no—
829C2—42no—
830C2—2441no—
831C2—2441no—
832C2—2442no—
833C2C2×#1684027511yescharacteristic
834C2#2146060312yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3080C2
socleC22×C61C23×D4
prime radicalC2×#41×D61C22
hypercenter#3080D61
hypocenterC61#60569
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×#16840375C2semidirect
3. #21456121C2semidirect
4. #21456073C2semidirect
5. #21456040C2semidirect
6. #21456038C2semidirect
7. #21455769C2semidirect
8. #21455637C2semidirect
9. #21455307C2semidirect
10. #21455306C2semidirect
12. #21454643C2semidirect
13. #21454637C2semidirect
14. #21454456C2semidirect
15. C61×#3080C2semidirect
24. #16840375C22semidirect
25. C2×#14519777C22semidirect
40. C2×#14519742C22semidirect
47. #16840099C22semidirect
48. #16840094C22semidirect
49. #16840066C22semidirect
50. #16840059C22semidirect
51. #16839973C22semidirect
52. #16839972C22semidirect
53. #16839968C22semidirect
54. #16839967C22semidirect
59. #16839868C22semidirect
60. #16839866C22semidirect
61. #16839861C22semidirect
62. #16839859C22semidirect
63. #16839856C22semidirect
64. #16839854C22semidirect
65. #16839853C22semidirect
66. #16839849C22semidirect
68. #16839822C22semidirect
69. #16839802C22semidirect
70. #16839786C22semidirect
71. #16839772C22semidirect
72. #16839770C22semidirect
75. M16×Dic61C22semidirect
76. C2×#125×C61C22semidirect
78. C61×#479C22semidirect
79. C61×#478C22semidirect
80. C61×#428C22semidirect
81. C61×#423C22semidirect
419. #3080D61semidirect
445. C2×#125C2×D61semidirect
469. #479C2×D61semidirect
471. #478C2×D61semidirect
491. #428C2×D61semidirect
493. #423C2×D61semidirect
500. C61#60569semidirect

Maximal subgroups

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

subgroupindex
C2×#168403752
#214590182
#214561212
#214560732
#214560402
#214560382
#214557692
#214556372
#214553072
#214553062
#214550802
#214546432
#214546372
#214544562
C61×#30802
#6056961