Finite Group Databasebeta

← #30561095

Subgroups — #30561095

Order 15616.

1900 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459412C211yesmaximal, characteristic
2C2×#16840490C211yesmaximal, characteristic, complemented
3#21458873C214yesmaximal, complemented
4#21458870C212yesmaximal, complemented
5#21458851C214yesmaximal, complemented
6#21458848C212yesmaximal, complemented
7#21458824C212yesmaximal, complemented
8#21458798C212yesmaximal, complemented
9#21456278C211yesmaximal, characteristic, complemented
10#21456274C212yesmaximal, complemented
11#21455306C211yesmaximal, characteristic, complemented
12#21455305C212yesmaximal, complemented
13#21455291C211yesmaximal, characteristic, complemented
14#21455290C212yesmaximal, complemented
15M16×Dic122C211yesmaximal, characteristic, complemented
16#21454637C212yesmaximal, complemented
17C4×#137×C61C211yesmaximal, characteristic, complemented
18C2×#14519810C2212yes—
19C2×#14519810C2212yes—
20C2×#14519808C2212yes—
21C2×#14519807C2212yes—
22#16840497C2211yescharacteristic
23#16840495C2212yes—
24#16840490—21no—
25#16840490—22no—
26#16840490—21no—
27#16840490C2212yes—
28#16840490C2211yescharacteristic
29#16840490C2212yes—
30#16840490C2214yes—
31#16840484C2212yes—
32#16840482C2211yescharacteristic
33#16840461—22no—
34#16840458—21no—
35#16840433C2211yescharacteristic
36#16840421—21no—
37#16840312C2211yescharacteristic
38#16840308C2212yes—
39C2×#14519777C2211yescharacteristic
40C2×#14519775C2212yes—
41#16840296—21no—
42#16840290—22no—
43C2×#14519769—21no—
44C2×#14519767—22no—
45C4×#11758222—21no—
46#16840230C2212yes—
47C2×C4×Dic122—21no—
48C2×C4×Dic122C2211yescharacteristic
49C2×#14519742C2212yes—
50#16840156C2214yes—
51#16840155C2214yes—
52#16840153C2214yes—
53#16840142C2212yes—
54#16840140C2214yes—
55#16840135C2212yes—
56#16840133C2214yes—
57#16839987C2214yes—
58#16839984C2214yes—
59#16839983C2214yes—
60#16839972C2212yes—
61#16839972C2212yes—
62#16839972C2212yes—
63#16839971C2214yes—
64#16839971C2214yes—
65#16839971C2214yes—
66#16839967C2212yes—
67#16839967C2212yes—
68#16839966C2214yes—
69#16839966C2214yes—
70#16839962C2212yes—
71#16839961C2214yes—
72#16839892C2212yes—
73#16839890C2214yes—
74C8×Dic122C2212yes—
75#16839868C2214yes—
76#16839861C2214yes—
77#16839856C2214yes—
78#16839849C2214yes—
79#16839786C2211yescharacteristic
80#16839785C2212yes—
81#16839770C2212yes—
82#16839761C2212yes—
83M16×Dic61C2212yes—
84C2×#137×C61C2211yescharacteristic
85C4×#41×C61C2211yescharacteristic
86C2×C4×Q8×C61C2211yescharacteristic
87C61×#441C2212yes—
88C61×#440C2212yes—
89C4×Q16×C61C2212yes—
90C4×SD16×C61C2212yes—
91C61×#428C2211yescharacteristic
92C61×#419C2211yescharacteristic
93C61×#417C2211yescharacteristic
94C4×M16×C61C2211yescharacteristic
95C2×#11758222—21no—
96C2×#11758222C2312yes—
97C22×Dic122D411yescharacteristic
98C22×Dic122C2312yes—
99#14519810—28no—
100#14519810—44no—
101#14519808—44no—
102#14519807—44no—
103C2×Dic244C2314yes—
104C2×Dic244C2314yes—
105C2×#11758202C2314yes—
106C2×#11758202C2314yes—
107C2×#11758190C2314yes—
108C2×#11758190C2314yes—
109C2×#11758200C2314yes—
110C2×#11758201C2314yes—
111C2×#11758194C2312yes—
112#14519777—21no—
113#14519777—21no—
114#14519777C2312yes—
115#14519777C2312yes—
116#14519777C2311yescharacteristic
117#14519775—22no—
118#14519775—22no—
119#14519775C2314yes—
120#14519775C2314yes—
121#14519775C2312yes—
122#14519774C2311yescharacteristic
123#14519773C2312yes—
124#14519772—22no—
125#14519771—22no—
126#14519770—22no—
127#14519769—21no—
128#14519769—22no—
129#14519769—22no—
130#14519769—24no—
131#14519767—22no—
132#14519767—24no—
133#14519767—24no—
134#14519767—24no—
135#14519767—24no—
136#14519766C2312yes—
137#14519765—21no—
138#14519765C2312yes—
139#14519764C2312yes—
140#14519763—22no—
141#14519762—22no—
142#14519760—22no—
143#14519759—22no—
144#14519756—21no—
145#14519755—22no—
146#14519751—21no—
147#14519751—21no—
148#14519751—21no—
149#14519750—22no—
150#14519749—22no—
151#14519749—22no—
152C4×Dic122—24no—
153C4×Dic122—22no—
154C4×Dic122—22no—
155C4×Dic122—21no—
156C4×Dic122D411yescharacteristic
157C4×Dic122D412yes—
158C4×Dic122D411yescharacteristic
159C4×Dic122C2311yescharacteristic
160C4×Dic122C2312yes—
161C4×Dic122C2311yescharacteristic
162#14519742—22no—
163#14519742—22no—
164#14519742C2314yes—
165#14519742C2314yes—
166#14519742C2312yes—
167#14519742C2312yes—
168C4×D244—21no—
169C4×D244—21no—
170C4×D244—21no—
171#14519739C2312yes—
172#14519739C2312yes—
173C4×C22⋊D61—22no—
174C4×C22⋊D61—22no—
175C4×C22⋊D61—22no—
176#14519737—22no—
177#14519737—22no—
178#14519736—21no—
179#14519734—22no—
180#14519734—22no—
181C2×C4⋊Dic61—21no—
182C2×C4⋊Dic61—21no—
183C2×C4⋊Dic61D411yescharacteristic
184C2×#11758196—22no—
185C2×#11758196—22no—
186C2×#11758196—22no—
187C2×#11758196D412yes—
188C2×C4×Dic61—22no—
189C2×C4×Dic61C2312yes—
190C42×D61—22no—
191C4⋊#92418C2312yes—
192C4⋊#92418C2312yes—
193#14519706C2314yes—
194#14519706C2314yes—
195#14519700C2314yes—
196#14519700C2314yes—
197#14519700C2314yes—
198#14519697C2314yes—
199#14519687C2314yes—
200C8×Dic61C2314yes—
201C2×#41×C61C2311yescharacteristic
202C22×Q8×C61C2311yescharacteristic
203#137×C61—24no—
204C2×Q16×C61C2312yes—
205C2×SD16×C61C2312yes—
206C2×M16×C61C2311yescharacteristic
207C2×M16×C61C2311yescharacteristic
208C4×Q8×C61—21no—
209C4×Q8×C61—21no—
210C4×Q8×C61C2312yes—
211C4×Q8×C61C2311yescharacteristic
212C4×Q8×C61C2311yescharacteristic
213C4×Q8×C61C2312yes—
214C4×D4×C61—21no—
215C4×D4×C61—21no—
216C4×D4×C61C2311yescharacteristic
217C4×D4×C61C2311yescharacteristic
218#117×C61—21no—
219#117×C61C2311yescharacteristic
220C2×C4⋊C4×C61—21no—
221C2×C4⋊C4×C61C2311yescharacteristic
222C2×C42×C61—21no—
223C2×C42×C61—21no—
224C2×C42×C61C2311yescharacteristic
225#107×C61C2312yes—
226#106×C61C2312yes—
227#103×C61C2312yes—
228#103×C61C2312yes—
229#103×C61C2312yes—
230#102×C61C2312yes—
231#97×C61C2312yes—
232C4×C8×C61C2312yes—
233#41×C61—22no—
234#41×C61—22no—
235C2×Q8×C61—21no—
236C2×Q8×C61—22no—
237C2×Q8×C61—22no—
238C2×Q8×C61C2412yes—
239C2×Q8×C61C2411yescharacteristic
240C2×D4×C61—21no—
241C2×D4×C61C2411yescharacteristic
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2411yescharacteristic
250C2×C22⋊D61—22no—
251C2×C22⋊D61—22no—
252C2×C22⋊D61—22no—
253C22×Dic61—22no—
254C22×Dic61C2×D412yes—
255C22×Dic61C2×D412yes—
256#11758222—24no—
257#11758222—24no—
258#11758222—44no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244C2412yes—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×C4×D61—22no—
265C2×Dic122—24no—
266C2×Dic122—24no—
267C2×Dic122—24no—
268C2×Dic122—22no—
269C2×Dic122C2×D412yes—
270C2×Dic122C2×D411yescharacteristic
271C2×Dic122C2×D411yescharacteristic
272C2×Dic122C2414yes—
273C2×Dic122C2412yes—
274Q16×C61—24no—
275SD16×C61—24no—
276M16×C61—22no—
277M16×C61#4114yescomplemented
278C2×C8×C61C2412yes—
279C2×C8×C61C2412yes—
280C4⋊C4×C61—22no—
281C4⋊C4×C61—22no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61C2412yes—
286C4⋊C4×C61C2411yescharacteristic
287C4⋊C4×C61C2411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C42×C61—21no—
292C42×C61—21no—
293C42×C61—21no—
294C42×C61—22no—
295C42×C61—22no—
296C42×C61C2×D411yescharacteristic
297C42×C61C2×D411yescharacteristic
298C42×C61C2411yescharacteristic
299C42×C61C2411yescharacteristic
300C22⋊Dic61—22no—
301C22⋊Dic61—22no—
302#11758202—44no—
303#11758202—44no—
304#11758201—44no—
305#11758200—44no—
306#11758198—22no—
307#11758198—22no—
308#11758198—22no—
309#11758198—22no—
310#11758198—22no—
311#11758198—22no—
312C4⋊Dic61—22no—
313C4⋊Dic61—22no—
314C4⋊Dic61—22no—
315C4⋊Dic61—22no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61C2×D411yescharacteristic
319C4⋊Dic61C2×D411yescharacteristic
320C4⋊Dic61C2×D412yes—
321#11758196—24no—
322#11758196—24no—
323#11758196—24no—
324#11758196—24no—
325#11758196—24no—
326#11758196—24no—
327#11758196—22no—
328#11758196—22no—
329#11758196—22no—
330#11758196—22no—
331#11758196C2×D412yes—
332#11758196C2×D412yes—
333#11758196C2×D412yes—
334#11758196C2×D412yes—
335C4×Dic61—22no—
336C4×Dic61—22no—
337C4×Dic61—24no—
338C4×Dic61—24no—
339C4×Dic61C2×D412yes—
340C4×Dic61C2×D412yes—
341C4×Dic61C2412yes—
342C4×Dic61C2412yes—
343#11758194—24no—
344C2×#92418C2414yes—
345Dic244—28no—
346Dic244—44no—
347#11758190—28no—
348#11758190—44no—
349C23×C61—21no—
350C23×C61C22×D411yescharacteristic
351C22×D61—22no—
352Q8×C61—22no—
353Q8×C61—21no—
354Q8×C61—22no—
355Q8×C61—21no—
356Q8×C61—42no—
357D4×C61—21no—
358D4×C61—21no—
359D4×C61—42no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—22no—
365C2×C4×C61—21no—
366C2×C4×C61—41no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61—42no—
371C2×C4×C61—81no—
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C2×#4112yes—
378C2×C4×C61H(5,𝔽2)12yes—
379C2×C4×C61C2511yescharacteristic
380C22⋊D61—44no—
381C22⋊D61—44no—
382C22⋊D61—82no—
383C2×Dic61—24no—
384C2×Dic61—24no—
385C2×Dic61—22no—
386C2×Dic61—42no—
387C2×Dic61—44no—
388C2×Dic61C22×D412yes—
389C2×Dic61C22×D412yes—
390C2×Dic61C22×D412yes—
391C2×Dic61C22×D412yes—
392D244—22no—
393D244—22no—
394D244—42no—
395D244—81no—
396C4×D61—44no—
397C4×D61—44no—
398C4×D61—82no—
399Dic122—22no—
400Dic122—24no—
401Dic122—24no—
402Dic122—22no—
403Dic122—24no—
404Dic122—22no—
405Dic122—44no—
406Dic122#13714yescomplemented
407C8×C61—22no—
408C8×C61C2×#4114yes—
409#92418—24no—
410#61404—611nomaximal, Sylow
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61#55012yes—
417C22×C61C23×D411yescharacteristic
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C4×C61—21no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—41no—
425C4×C61—42no—
426C4×C61—41no—
427C4×C61—42no—
428C4×C61—41no—
429C4×C61#55012yes—
430C4×C61C2×#13712yes—
431C4×C61C22×#4111yescharacteristic
432C4×C61C2×H(5,𝔽2)11yescharacteristic
433Dic61—22no—
434Dic61—22no—
435Dic61—22no—
436Dic61—44no—
437Dic61—42no—
438Dic61C2×#13714yes—
439#3480—611no—
440C2×#557—611no—
441#3400—614no—
442#3400—612no—
443#3398—614no—
444#3398—612no—
445#3395—612no—
446#3392—612no—
447#3152—611no—
448#3152—612no—
449#3039—612no—
450#3039—611no—
451#3037—612no—
452#3037—611no—
453Q8×M16—611no—
454C4×#137—612no—
455C4×#137D6111yescharacteristic, complemented
456C2×C61—22no—
457C2×C61—81no—
458C2×C61C2×#55011yescharacteristic
459C2×C61C22×#13711yescharacteristic
460C2×C61#358611yescharacteristic
461D61—82no—
462C2×#137—612no—
463C2×#137—612no—
464C2×#137—612no—
465C2×#137—612no—
466C2×#137C2×D6111yescharacteristic
467#559—611no—
468#559—612no—
469#557—612no—
470#557—611no—
471#557—614no—
472#557—612no—
473#557—1221no—
474#557—1221no—
475#557—1222no—
476#556—612no—
477#556—611no—
478#553—1221no—
479#553—1222no—
480#550—611no—
481#548—1221no—
482#532—612no—
483#532—611no—
484C2×C4⋊Q8—612no—
485C2×C4⋊Q8—611no—
486#529—1221no—
487#529—1222no—
488C2×#125—1221no—
489C2×#125—1222no—
490C4×#41—612no—
491C4×#41—1221no—
492C4×#41C2×D6111yescharacteristic
493C2×C4×Q8—611no—
494C2×C4×Q8—612no—
495C2×C4×Q8—1221no—
496C2×C4×Q8C2×D6111yescharacteristic
497#497—614no—
498#497—614no—
499#497—614no—
500#494—614no—
501#494—612no—
502#492—614no—
503#492—612no—
504#464—614no—
505#464—614no—
506#464—614no—
507#462—612no—
508#462—612no—
509#462—612no—
510#462—614no—
511#462—614no—
512#462—614no—
513#461—612no—
514#461—612no—
515#461—614no—
516#461—614no—
517#460—612no—
518#460—614no—
519#446—614no—
520#446—612no—
521C8×Q8—612no—
522#441—614no—
523#441C2×D6112yes—
524#440—614no—
525#440C2×D6112yes—
526C4×Q16—614no—
527C4×Q16C2×D6112yes—
528C4×SD16—614no—
529C4×SD16C2×D6112yes—
530#428C2×D6111yescharacteristic
531#423—612no—
532#423—611no—
533#419—612no—
534#419C2×D6111yescharacteristic
535#417—612no—
536#417C2×D6111yescharacteristic
537C4×M16—612no—
538C4×M16C2×D6111yescharacteristic
539C61#6140411yescharacteristic, complemented, Sylow
540C2×#41—612no—
541C2×#41—1221no—
542C2×#41C22×D6111yescharacteristic
543C22×Q8—611no—
544C22×Q8—612no—
545C22×Q8C22×D6111yescharacteristic
546#137—24no—
547#137—1228no—
548#137—2444no—
549#137—2444no—
550#137—2444no—
551C2×Q16—614no—
552C2×Q16—614no—
553C2×Q16—614no—
554C2×Q16—614no—
555C2×Q16C22×D6112yes—
556C2×SD16—614no—
557C2×SD16—614no—
558C2×SD16—614no—
559C2×SD16—614no—
560C2×SD16C22×D6112yes—
561C2×M16—612no—
562C2×M16C22×D6111yescharacteristic
563C2×M16C22×D6111yescharacteristic
564C4⋊Q8—614no—
565C4⋊Q8—614no—
566C4⋊Q8—612no—
567C4⋊Q8—612no—
568C4⋊Q8—612no—
569C4⋊Q8—611no—
570C4⋊Q8—1222no—
571C4⋊Q8—1222no—
572C4⋊Q8—1221no—
573C4⋊Q8—1221no—
574#127—612no—
575#127—611no—
576#126—1222no—
577#126—1222no—
578#126—1222no—
579#125—1222no—
580#125—1222no—
581#125—1224no—
582#125—1221no—
583#125—1224no—
584#125—1224no—
585#125—1224no—
586#125—1224no—
587#125—1222no—
588#124—612no—
589#124—612no—
590#124—612no—
591#124—1221no—
592#124—1222no—
593#123—1222no—
594#123—1222no—
595#123—1222no—
596C22⋊Q8—1222no—
597C22⋊Q8—1221no—
598#121—1222no—
599#121—1221no—
600#121—1222no—
601#121—1222no—
602#121—1221no—
603#121—1221no—
604C4×Q8—21no—
605C4×Q8—21no—
606C4×Q8—611no—
607C4×Q8—612no—
608C4×Q8—611no—
609C4×Q8—611no—
610C4×Q8—612no—
611C4×Q8—611no—
612C4×Q8—614no—
613C4×Q8—614no—
614C4×Q8—612no—
615C4×Q8—612no—
616C4×Q8—1222no—
617C4×Q8—1224no—
618C4×Q8—1222no—
619C4×Q8—1221no—
620C4×Q8—1222no—
621C4×Q8—1222no—
622C4×Q8C22×D6112yes—
623C4×Q8C22×D6112yes—
624C4×Q8C22×D6111yescharacteristic
625C4×Q8C22×D6111yescharacteristic
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—612no—
629C4×D4—612no—
630C4×D4—1221no—
631C4×D4—1222no—
632C4×D4—1222no—
633C4×D4—1222no—
634C4×D4—1222no—
635C4×D4—1222no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4C22×D6111yescharacteristic
639C4×D4C22×D6111yescharacteristic
640#117—21no—
641#117—1222no—
642#117—1222no—
643#117—1221no—
644#117C22×D6111yescharacteristic
645C2×C4⋊C4—21no—
646C2×C4⋊C4—612no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—1222no—
649C2×C4⋊C4—1222no—
650C2×C4⋊C4—1222no—
651C2×C4⋊C4—1221no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4C22×D6111yescharacteristic
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—612no—
657C2×C42—1222no—
658C2×C42—1222no—
659C2×C42C22×D6111yescharacteristic
660#107C22×D6112yes—
661#106C22×D6112yes—
662C4⋊C8—614no—
663C4⋊C8—614no—
664C4⋊C8—612no—
665C4⋊C8—612no—
666#103—614no—
667#103—614no—
668#103—614no—
669#103C22×D6112yes—
670#103C22×D6112yes—
671#103C22×D6112yes—
672#102—614no—
673#102C22×D6112yes—
674#97—614no—
675#97C22×D6112yes—
676C4×C8—614no—
677C4×C8C22×D6112yes—
678#41—22no—
679#41—22no—
680#41—1224no—
681#41—1224no—
682#41—2444no—
683C2×Q8—21no—
684C2×Q8—22no—
685C2×Q8—22no—
686C2×Q8—611no—
687C2×Q8—612no—
688C2×Q8—611no—
689C2×Q8—612no—
690C2×Q8—614no—
691C2×Q8—1224no—
692C2×Q8—1222no—
693C2×Q8—1224no—
694C2×Q8—1224no—
695C2×Q8C23×D6111yescharacteristic
696C2×Q8C23×D6112yes—
697C2×D4—21no—
698C2×D4—612no—
699C2×D4—1222no—
700C2×D4—1222no—
701C2×D4—1222no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4C23×D6111yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—612no—
711C22×C4—612no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—1222no—
716C22×C4D4×D6111yescharacteristic
717C22×C4D4×D6111yescharacteristic
718C22×C4C23×D6111yescharacteristic
719Q16—24no—
720Q16—1228no—
721Q16—2444no—
722Q16—2444no—
723Q16—2444no—
724SD16—24no—
725SD16—1228no—
726SD16—2444no—
727SD16—2444no—
728SD16—2444no—
729M16—22no—
730M16—1224no—
731M16#1175822214yescomplemented
732C2×C8—614no—
733C2×C8C23×D6112yes—
734C2×C8C23×D6112yes—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—612no—
741C4⋊C4—612no—
742C4⋊C4—612no—
743C4⋊C4—612no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—612no—
747C4⋊C4—1224no—
748C4⋊C4—1224no—
749C4⋊C4—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1224no—
752C4⋊C4—1224no—
753C4⋊C4—1222no—
754C4⋊C4—1222no—
755C4⋊C4—1222no—
756C4⋊C4—1222no—
757C4⋊C4—1222no—
758C4⋊C4—1222no—
759C4⋊C4—1222no—
760C4⋊C4—1222no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4C23×D6112yes—
764C4⋊C4C23×D6111yescharacteristic
765C4⋊C4C23×D6111yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—1222no—
770C22⋊C4—1222no—
771C22⋊C4—1222no—
772C22⋊C4—1222no—
773C22⋊C4—1222no—
774C22⋊C4—1222no—
775C22⋊C4—1222no—
776C22⋊C4—1222no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—22no—
781C42—22no—
782C42—612no—
783C42—612no—
784C42—612no—
785C42—612no—
786C42—1222no—
787C42—1222no—
788C42—1224no—
789C42—1224no—
790C42D4×D6111yescharacteristic
791C42D4×D6111yescharacteristic
792C42C23×D6111yescharacteristic
793C42C23×D6111yescharacteristic
794C23—21no—
795C23—1222no—
796C23C2×D4×D6111yescharacteristic
797Q8—22no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—42no—
802Q8—614no—
803Q8—1224no—
804Q8—1222no—
805Q8—1224no—
806Q8—1222no—
807Q8—1224no—
808Q8—1222no—
809Q8—2444no—
810D4—21no—
811D4—21no—
812D4—42no—
813D4—1222no—
814D4—1222no—
815D4—4881no—
816D4—4882no—
817D4—2444no—
818D4—2444no—
819D4—2442no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—81no—
832C2×C4—612no—
833C2×C4—612no—
834C2×C4—612no—
835C2×C4—612no—
836C2×C4—1224no—
837C2×C4—1222no—
838C2×C4—1224no—
839C2×C4—4882no—
840C2×C4—2444no—
841C2×C4—2442no—
842C2×C4—2444no—
843C2×C4—2444no—
844C2×C4C2×D4×D6111yescharacteristic
845C2×C4C2×D4×D6111yescharacteristic
846C2×C4C2×D4×D6111yescharacteristic
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4C2×#1175822212yes—
850C2×C4#1451982312yes—
851C2×C4C24×D6111yescharacteristic
852C8—22no—
853C8—1224no—
854C8C2×#1175822214yes—
855C22—21no—
856C22—21no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—2442no—
861C22—2442no—
862C22—2442no—
863C22#1684043312yes—
864C22C22×D4×D6111yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—41no—
869C4—41no—
870C4—42no—
871C4—42no—
872C4—41no—
873C4—614no—
874C4—1222no—
875C4—1222no—
876C4—1222no—
877C4—2442no—
878C4—2444no—
879C4#1684043312yes—
880C4#137×D6112yes—
881C4C22×#1175822211yescharacteristic
882C4C2×#1451982311yescharacteristic
883C2—22no—
884C2—81no—
885C2—4882no—
886C2C2×#1684043311yescharacteristic
887C2C2×#137×D6111yescharacteristic
888C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC4×#137×C61C2
socleC22×C61C23×D4
prime radical#21459412C2
hypercenterC4×#137D61
hypocenterC61#61404
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#16840490C2semidirect
3. #21458873C2semidirect
4. #21458870C2semidirect
5. #21458851C2semidirect
6. #21458848C2semidirect
7. #21458824C2semidirect
8. #21458798C2semidirect
9. #21456278C2semidirect
10. #21456274C2semidirect
11. #21455306C2semidirect
12. #21455305C2semidirect
13. #21455291C2semidirect
14. #21455290C2semidirect
15. M16×Dic122C2semidirect
16. #21454637C2semidirect
17. C4×#137×C61C2semidirect
277. M16×C61#41semidirect
406. Dic122#137semidirect
455. C4×#137D61semidirect
539. C61#61404semidirect
731. M16#11758222semidirect

Maximal subgroups

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

subgroupindex
#214594122
C2×#168404902
#214588732
#214588702
#214588512
#214588482
#214588242
#214587982
#214562782
#214562742
#214553062
#214553052
#214552912
#214552902
M16×Dic1222
#214546372
C4×#137×C612
#6140461