Finite Group Databasebeta

← #30564947

Subgroups — #30564947

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459658C211yesmaximal, characteristic, complemented
2C2×#16840433C211yesmaximal, characteristic, complemented
3#21457947C214yesmaximal, complemented
4#21457827C214yesmaximal, complemented
5#21457409C214yesmaximal, complemented
6#21457364C214yesmaximal, complemented
7#21456839C212yesmaximal, complemented
8#21456626C211yesmaximal, characteristic, complemented
9#21456619C211yesmaximal, characteristic, complemented
10#21456586C212yesmaximal, complemented
11#21455992C212yesmaximal, complemented
12#21455081C211yesmaximal, characteristic, complemented
13#21455073C211yesmaximal, characteristic, complemented
14#21455041C212yesmaximal, complemented
15C61×#2973C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758222C2211yescharacteristic, complemented
18C2×#14519810C2212yescomplemented
19C2×#14519805C2212yescomplemented
20C2×#14519799C2214yescomplemented
21#16840461—22no—
22#16840458C2212yescomplemented
23#16840452C2212yescomplemented
24#16840441—22no—
25#16840433—22no—
26#16840433—22no—
27#16840433C2214yes—
28#16840433C2214yescomplemented
29#16840421C2212yescomplemented
30#16840408C2212yescomplemented
31#16840359—21no—
32#16840350—21no—
33#16840321—21no—
34C2×#14519774C2211yescharacteristic, complemented
35C2×#14519773—21no—
36#16840296C2212yes—
37#16840273C2212yes—
38C2×#14519756C2211yescharacteristic
39C2×#14519751C2211yescharacteristic
40C2×#14519751C2211yescharacteristic
41C2×#14519751C2211yescharacteristic, complemented
42C2×#14519750—21no—
43C2×#14519750—21no—
44#16840235—21no—
45C2×C4×Dic122C2211yescharacteristic, complemented
46C2×#14519739—21no—
47#16840151C2214yescomplemented
48#16840127C2214yescomplemented
49#16840098C2212yescomplemented
50#16840087C2214yescomplemented
51#16840081C2212yes—
52#16840081C2212yescomplemented
53#16840076C2212yescomplemented
54#16840070C2214yescomplemented
55#16840015C2214yescomplemented
56#16840008C2214yescomplemented
57#16839998C2214yescomplemented
58#16839991C2214yescomplemented
59#16839985C2214yescomplemented
60#16839963C2214yescomplemented
61#16839958C2214yescomplemented
62#16839926C2214yescomplemented
63#16839926C2214yescomplemented
64#16839920C2212yescomplemented
65#16839915C2212yescomplemented
66#16839915C2212yescomplemented
67#16839909C2214yescomplemented
68#16839909C2214yescomplemented
69#16839909C2214yescomplemented
70#16839903C2212yes—
71#16839903C2212yescomplemented
72#16839898C2212yes—
73#16839898C2212yes—
74#16839898C2212yescomplemented
75#16839870C2214yescomplemented
76#16839864C2214yescomplemented
77#16839764C2212yescomplemented
78#16839764C2212yescomplemented
79#16839759C2214yescomplemented
80C2×C4×D4×C61C2211yescharacteristic
81C61×#435C2214yescomplemented
82C61×#435C2214yescomplemented
83C61×#432C2212yescomplemented
84C61×#407C2211yescharacteristic
85C61×#407C2211yescharacteristic
86C2×C22⋊C8×C61C2212yescomplemented
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—22no—
90C2×#11758222—44no—
91C2×#11758222—44no—
92C2×#11758222C2314yes—
93C2×#11758222C2312yes—
94C2×#11758222C2312yes—
95C2×#11758222C2312yes—
96C22×Dic122C2311yescharacteristic
97C22×Dic122C2311yescharacteristic
98C22×D244—21no—
99C22×D244—21no—
100C22×D244C2311yescharacteristic
101C22×D244C2311yescharacteristic
102C22×D244C2311yescharacteristic
103C22×C22⋊D61—21no—
104C22×C22⋊D61—21no—
105C22×C22⋊D61—21no—
106C22×C22⋊D61—21no—
107C22×C22⋊D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61—21no—
110#14519810—44no—
111#14519805—44no—
112#14519799—48no—
113C2×Dic244C2314yes—
114C2×#11758190C2314yes—
115C2×#11758190C2314yes—
116C2×#11758190C2314yes—
117C2×D488C2314yes—
118C2×D488C2314yes—
119#14519774—22no—
120#14519774C2314yes—
121#14519773—24no—
122#14519773—24no—
123#14519772—22no—
124#14519771—22no—
125#14519770—22no—
126#14519769C2312yes—
127#14519767—22no—
128#14519765C2312yes—
129#14519763—22no—
130#14519762—22no—
131#14519760—22no—
132#14519760—22no—
133#14519759—22no—
134#14519758—22no—
135#14519756—21no—
136#14519756—21no—
137#14519756C2312yes—
138#14519756C2312yes—
139#14519756C2312yes—
140#14519755—22no—
141#14519751—21no—
142#14519751—21no—
143#14519751—21no—
144#14519751—21no—
145#14519751—22no—
146#14519751C2312yes—
147#14519751C2312yes—
148#14519751C2314yes—
149#14519751C2312yes—
150#14519751C2312yes—
151#14519751C2312yes—
152#14519750—22no—
153#14519750—24no—
154#14519750—24no—
155#14519750—24no—
156#14519750—24no—
157#14519749—22no—
158#14519749—22no—
159#14519746—22no—
160#14519745—22no—
161C4×Dic122—22no—
162C4×Dic122C2312yes—
163C4×Dic122C2314yes—
164C4×D244C2312yes—
165#14519739—24no—
166#14519739—24no—
167C4×C22⋊D61—22no—
168C4×C22⋊D61—22no—
169C4×C22⋊D61—22no—
170#14519737—22no—
171#14519737—22no—
172#14519736C2312yes—
173#14519734—22no—
174#14519733—22no—
175C2×C4⋊Dic61C2311yescharacteristic
176C2×C4⋊Dic61C2311yescharacteristic
177C2×C4⋊Dic61C2311yescharacteristic
178C2×#11758196—21no—
179C2×#11758196—21no—
180C2×C22⋊Dic61—21no—
181C2×#11758198—21no—
182C2×#11758198—21no—
183C2×#11758198—21no—
184C22⋊C4×D61—22no—
185C2×C4×Dic61—21no—
186#14519711C2314yes—
187#14519709C2314yes—
188#14519702C2314yes—
189#14519702C2314yes—
190#14519702C2314yes—
191#14519699C2314yes—
192#14519699C2314yes—
193#14519699C2314yes—
194#14519699C2314yes—
195#14519699C2314yes—
196C22×D4×C61D411yescharacteristic
197C23×C4×C61C2311yescharacteristic
198C23×C4×C61C2311yescharacteristic
199C2×M16×C61C2312yes—
200C2×M16×C61C2312yes—
201C22×C8×C61C2314yes—
202C4×D4×C61D412yes—
203C4×D4×C61D412yes—
204C4×D4×C61C2312yes—
205C4×D4×C61C2312yes—
206C2×C4⋊C4×C61D411yescharacteristic
207C2×C22⋊C4×C61D411yescharacteristic
208C2×C22⋊C4×C61D411yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C4⋊C8×C61C2314yes—
211C22⋊C8×C61C2312yes—
212C22⋊C8×C61C2312yes—
213C22⋊C8×C61C2314yes—
214C22⋊C8×C61C2312yes—
215C22⋊C8×C61C2312yes—
216#97×C61C2314yes—
217C24×C61C2×D411yescharacteristic
218C24×C61C2×D411yescharacteristic
219C23×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C2×D4×C61—42no—
223C2×D4×C61C2×D412yes—
224C2×D4×C61C2×D412yes—
225C22×C4×C61—42no—
226C22×C4×C61—42no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C22×C4×C61C2412yes—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—24no—
240C2×C22⋊D61—22no—
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—24no—
245C2×C22⋊D61—22no—
246C2×C22⋊D61—22no—
247C2×C22⋊D61—22no—
248C2×C22⋊D61—44no—
249C2×C22⋊D61—44no—
250C2×C22⋊D61—44no—
251C2×C22⋊D61—82no—
252C2×C22⋊D61—82no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258#11758222—24no—
259#11758222—28no—
260#11758222—24no—
261#11758222—42no—
262#11758222—44no—
263#11758222—42no—
264#11758222—44no—
265#11758222—44no—
266#11758222—48no—
267#11758222—44no—
268C2×D244—24no—
269C2×D244—21no—
270C2×D244—21no—
271C2×D244—24no—
272C2×D244—21no—
273C2×D244—42no—
274C2×D244—42no—
275C2×D244—42no—
276C2×D244—44no—
277C2×D244—82no—
278C2×D244C2412yes—
279C2×D244C2412yes—
280C2×D244C2412yes—
281C2×C4×D61—24no—
282C2×C4×D61—22no—
283C2×C4×D61—22no—
284C2×C4×D61—22no—
285C2×C4×D61—22no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×Dic122—21no—
289C2×Dic122—24no—
290C2×Dic122—21no—
291C2×Dic122—42no—
292C2×Dic122C2412yes—
293C2×Dic122C2412yes—
294M16×C61—42no—
295M16×C61—42no—
296C2×C8×C61—44no—
297C2×C8×C61C2414yes—
298C2×C8×C61C2414yes—
299C4⋊C4×C61C2×D412yes—
300C4⋊C4×C61C2×D412yes—
301C22⋊C4×C61C2×D412yes—
302C22⋊C4×C61C2×D412yes—
303C22⋊C4×C61C2×D412yes—
304C22⋊C4×C61C2×D412yes—
305C42×C61C2×D412yes—
306C42×C61C2412yes—
307C22⋊Dic61—22no—
308C22⋊Dic61—22no—
309C22⋊Dic61—22no—
310C22⋊Dic61—22no—
311#11758198—22no—
312#11758198—22no—
313#11758198—22no—
314#11758198—24no—
315#11758198—22no—
316#11758198—22no—
317#11758198—22no—
318#11758198—22no—
319#11758198—22no—
320C4⋊Dic61—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61C2412yes—
324C4⋊Dic61C2412yes—
325C4⋊Dic61C2412yes—
326#11758196—22no—
327#11758196—24no—
328#11758196—22no—
329#11758196—22no—
330#11758196—22no—
331#11758196—22no—
332#11758196—22no—
333C4×Dic61—24no—
334C4×Dic61—22no—
335C4×Dic61—22no—
336Dic244—28no—
337D488—44no—
338D488—44no—
339#11758190—28no—
340#11758190—44no—
341#11758190—44no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61C22×D411yescharacteristic
349C23×C61C22×D412yes—
350C23×C61C22×D411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—42no—
360C22×D61—42no—
361C22×D61—42no—
362C22×D61—81no—
363C22×D61—81no—
364D4×C61—42no—
365D4×C61—42no—
366C2×C4×C61—22no—
367C2×C4×C61—24no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—42no—
376C2×C4×C61—41no—
377C2×C4×C61C22×D412yes—
378C2×C4×C61C22×D412yes—
379C2×C4×C61C22×D412yes—
380C2×C4×C61C22×D411yescharacteristic
381C2×C4×C61C22×D411yescharacteristic
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C2511yescharacteristic
384C22⋊D61—44no—
385C22⋊D61—48no—
386C22⋊D61—44no—
387C22⋊D61—44no—
388C22⋊D61—44no—
389C22⋊D61—82no—
390C22⋊D61—82no—
391C22⋊D61—82no—
392C22⋊D61—84no—
393C22⋊D61—82no—
394C2×Dic61—24no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—42no—
401C2×Dic61—42no—
402C2×Dic61—81no—
403C2×Dic61—81no—
404D244—24no—
405D244—22no—
406D244—24no—
407D244—22no—
408D244—48no—
409D244—42no—
410D244—42no—
411D244—81no—
412D244—84no—
413C4×D61—44no—
414C4×D61—48no—
415C4×D61—44no—
416C4×D61—82no—
417C4×D61—82no—
418Dic122—24no—
419Dic122—22no—
420Dic122—24no—
421Dic122—81no—
422Dic122H(5,𝔽2)14yes—
423C8×C61—24no—
424C8×C61—24no—
425#61577—611nomaximal, Sylow
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—22no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—22no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—22no—
437C22×C61—82no—
438C22×C61—82no—
439C22×C61#57512yes—
440C22×C61C23×D411yescharacteristic
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—84no—
451C2×D61—84no—
452C2×D61—162no—
453C4×C61—22no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—22no—
457C4×C61—21no—
458C4×C61—22no—
459C4×C61C2×H(5,𝔽2)12yes—
460Dic61—24no—
461Dic61—42no—
462Dic61—42no—
463Dic61—42no—
464Dic61—42no—
465#3505—611no—
466C2×#550—611no—
467#3317—614no—
468#3309—614no—
469#3271—614no—
470#3268—614no—
471#3217—612no—
472#3193—611no—
473#3192—611no—
474#3188—612no—
475#3117—612no—
476#3007—611no—
477#3006—611no—
478#3002—612no—
479#2973D6111yescharacteristic, complemented
480C2×C61—22no—
481C2×C61—41no—
482C2×C61—41no—
483C2×C61—42no—
484C2×C61#348411yescharacteristic
485C2×C61C2×#57511yescharacteristic
486C2×C61#358511yescharacteristic
487D61—82no—
488D61—82no—
489D61—82no—
490C22×#41—611no—
491C22×#41—611no—
492C2×#137—612no—
493C2×AGL(1,ℤ/8)—612no—
494C2×#135—614no—
495#553—612no—
496#553—1222no—
497#552—612no—
498#551—1222no—
499#550—614no—
500#550—614no—
501#550—1222no—
502#550—1222no—
503#548—612no—
504#546—612no—
505#539—1221no—
506#538—1221no—
507#534—1221no—
508C2×#127—611no—
509C2×#127—1221no—
510#529—612no—
511#525—612no—
512C2×C22⋊Q8—611no—
513C2×#121—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#121—1221no—
517C2×#121—1221no—
518#518—1221no—
519C2×C4×Q8—611no—
520C2×C4×D4—1221no—
521C2×C4×D4C2×D6111yescharacteristic
522#496—614no—
523#490—614no—
524#484—612no—
525#482—614no—
526#481—612no—
527#481—612no—
528#480—612no—
529#479—614no—
530#469—614no—
531#468—614no—
532#466—614no—
533#465—614no—
534#464—614no—
535#460—614no—
536#459—614no—
537#452—614no—
538#452—614no—
539#451—612no—
540#450—612no—
541#450—612no—
542#449—614no—
543#449—614no—
544#449—614no—
545#448—612no—
546#448—612no—
547#447—612no—
548#447—612no—
549#447—612no—
550#441—614no—
551#440—614no—
552#435C2×D6114yescomplemented
553#435C2×D6114yescomplemented
554#432C2×D6112yescomplemented
555#417—612no—
556#417—612no—
557#416—614no—
558#407C2×D6111yescharacteristic
559#407C2×D6111yescharacteristic
560C2×C22⋊C8C2×D6112yescomplemented
561C61#6157711yescharacteristic, complemented, Sylow
562C2×#41—614no—
563C2×#41—612no—
564C2×#41—612no—
565C2×#41—612no—
566C2×#41—1221no—
567C2×#41—1221no—
568C2×#41—1222no—
569C2×#41—2444no—
570C2×#41—2444no—
571C22×Q8—611no—
572C22×Q8—611no—
573C22×D4—611no—
574C22×D4—611no—
575C22×D4—611no—
576C22×D4—1221no—
577C22×D4—1221no—
578C22×D4—1221no—
579C22×D4—1221no—
580C22×D4—1221no—
581C22×D4—1221no—
582C22×D4—1221no—
583C22×D4D24411yescharacteristic
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588#137—2444no—
589AGL(1,ℤ/8)—2444no—
590#135—2448no—
591C2×Q16—614no—
592C2×SD16—614no—
593C2×SD16—614no—
594C2×SD16—614no—
595C2×D8—614no—
596C2×D8—614no—
597C2×M16C22×D6112yes—
598C2×M16C22×D6112yes—
599C22×C8C22×D6114yes—
600#127—614no—
601#127—1224no—
602#127—1224no—
603#127—1222no—
604#126—1222no—
605#126—1222no—
606#126—1222no—
607#125—612no—
608#125—1222no—
609#124—612no—
610#124—1222no—
611#123—1222no—
612#123—1222no—
613#123—1222no—
614#123—1222no—
615#123—1222no—
616C22⋊Q8—612no—
617C22⋊Q8—612no—
618C22⋊Q8—612no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8—1222no—
622#121—612no—
623#121—612no—
624#121—612no—
625#121—612no—
626#121—614no—
627#121—612no—
628#121—1222no—
629#121—1222no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1222no—
634#121—1221no—
635#121—1224no—
636#121—1224no—
637#121—1224no—
638#121—1224no—
639#121—1222no—
640#120—1222no—
641#120—1222no—
642C4×Q8—614no—
643C4×Q8—612no—
644C4×Q8—1222no—
645C4×D4—612no—
646C4×D4—1222no—
647C4×D4—1222no—
648C4×D4—1222no—
649C4×D4—1224no—
650C4×D4—1224no—
651C4×D4—1222no—
652C4×D4—1222no—
653C4×D4D24412yes—
654C4×D4D24412yes—
655C4×D4C22×D6112yes—
656C4×D4C22×D6112yes—
657#117—612no—
658#117—1222no—
659#117—1222no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—611no—
663C2×C4⋊C4—1221no—
664C2×C4⋊C4—1221no—
665C2×C4⋊C4D24411yescharacteristic
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C22⋊C4—1222no—
671C2×C22⋊C4D24411yescharacteristic
672C2×C22⋊C4D24411yescharacteristic
673C2×C42—1221no—
674C2×C42C22×D6111yescharacteristic
675#107—614no—
676#106—614no—
677C4⋊C8C22×D6114yes—
678#103—614no—
679#103—614no—
680#103—614no—
681#102—614no—
682#102—614no—
683#102—614no—
684#102—614no—
685#102—614no—
686C22⋊C8C22×D6112yes—
687C22⋊C8C22×D6112yes—
688C22⋊C8C22×D6114yes—
689C22⋊C8C22×D6112yes—
690C22⋊C8C22×D6112yes—
691#97C22×D6114yes—
692C24—1221no—
693C24—1221no—
694C24—1221no—
695C24C2×D24411yescharacteristic
696C24C2×D24411yescharacteristic
697#41—1228no—
698#41—1224no—
699#41—1224no—
700#41—2444no—
701#41—2444no—
702#41—2442no—
703#41—2442no—
704#41—2448no—
705#41—2444no—
706#41—2444no—
707C2×Q8—612no—
708C2×Q8—612no—
709C2×Q8—1224no—
710C2×Q8—1221no—
711C2×Q8—1221no—
712C2×Q8—2442no—
713C2×D4—42no—
714C2×D4—612no—
715C2×D4—612no—
716C2×D4—612no—
717C2×D4—1222no—
718C2×D4—1222no—
719C2×D4—1222no—
720C2×D4—1224no—
721C2×D4—1222no—
722C2×D4—1222no—
723C2×D4—1222no—
724C2×D4—1222no—
725C2×D4—1224no—
726C2×D4—1222no—
727C2×D4—1221no—
728C2×D4—1224no—
729C2×D4—1224no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—4882no—
733C2×D4—4882no—
734C2×D4—4882no—
735C2×D4—2442no—
736C2×D4—2442no—
737C2×D4—2442no—
738C2×D4—2444no—
739C2×D4—2444no—
740C2×D4—2444no—
741C2×D4—2444no—
742C2×D4C2×D24412yes—
743C2×D4C2×D24412yes—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1222no—
752C22×C4—1222no—
753C22×C4—1224no—
754C22×C4—1222no—
755C22×C4—1222no—
756C22×C4—2444no—
757C22×C4—2444no—
758C22×C4C2×D24411yescharacteristic
759C22×C4C2×D24411yescharacteristic
760C22×C4C2×D24411yescharacteristic
761C22×C4C2×D24411yescharacteristic
762C22×C4C2×D24411yescharacteristic
763C22×C4C2×D24411yescharacteristic
764C22×C4C2×D24412yes—
765C22×C4C23×D6111yescharacteristic
766C22×C4C23×D6111yescharacteristic
767C22×C4C23×D6111yescharacteristic
768C22×C4C23×D6112yes—
769Q16—1228no—
770SD16—1228no—
771SD16—2444no—
772SD16—2444no—
773D8—2444no—
774D8—2444no—
775M16—42no—
776M16—42no—
777C2×C8—44no—
778C2×C8C23×D6114yes—
779C2×C8C23×D6114yes—
780C4⋊C4—612no—
781C4⋊C4—612no—
782C4⋊C4—612no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1222no—
787C4⋊C4—1224no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1222no—
793C4⋊C4C2×D24412yes—
794C4⋊C4C2×D24412yes—
795C22⋊C4—1222no—
796C22⋊C4—1222no—
797C22⋊C4—1222no—
798C22⋊C4—1222no—
799C22⋊C4—1222no—
800C22⋊C4—1224no—
801C22⋊C4—1222no—
802C22⋊C4—1222no—
803C22⋊C4—1222no—
804C22⋊C4—1222no—
805C22⋊C4—1222no—
806C22⋊C4—1222no—
807C22⋊C4—1222no—
808C22⋊C4C2×D24412yes—
809C22⋊C4C2×D24412yes—
810C22⋊C4C2×D24412yes—
811C22⋊C4C2×D24412yes—
812C42—1224no—
813C42—1222no—
814C42—1222no—
815C42C2×D24412yes—
816C42C23×D6112yes—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—1222no—
824C23—1222no—
825C23—1222no—
826C23—4881no—
827C23—4881no—
828C23—2442no—
829C23—2442no—
830C23—2442no—
831C23—2442no—
832C23—2442no—
833C23—2442no—
834C23—2442no—
835C23C22×D24411yescharacteristic
836C23C22×D24412yes—
837C23C22×D24411yescharacteristic
838C23C22×D24411yescharacteristic
839Q8—614no—
840Q8—1224no—
841Q8—1222no—
842Q8—1224no—
843Q8—4881no—
844D4—42no—
845D4—42no—
846D4—1224no—
847D4—1222no—
848D4—1224no—
849D4—1222no—
850D4—4884no—
851D4—4881no—
852D4—4882no—
853D4—4882no—
854D4—4884no—
855D4—4882no—
856D4—4882no—
857D4—2448no—
858D4—2442no—
859D4—2442no—
860D4—2444no—
861D4—2448no—
862D4—2444no—
863D4—2444no—
864D4—2444no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—42no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—1224no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—4882no—
883C2×C4—4882no—
884C2×C4—4881no—
885C2×C4—4881no—
886C2×C4—2448no—
887C2×C4—2444no—
888C2×C4—2444no—
889C2×C4—2442no—
890C2×C4—2442no—
891C2×C4C22×D24412yes—
892C2×C4C22×D24412yes—
893C2×C4C22×D24412yes—
894C2×C4C22×D24411yescharacteristic
895C2×C4C22×D24411yescharacteristic
896C2×C4C22×D24411yescharacteristic
897C2×C4C24×D6111yescharacteristic
898C8—24no—
899C8—24no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—22no—
905C22—21no—
906C22—22no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—21no—
911C22—82no—
912C22—82no—
913C22—9762no—
914C22—4884no—
915C22—4884no—
916C22—2442no—
917C22—2442no—
918C22—2442no—
919C22—2442no—
920C22—2442no—
921C22—2442no—
922C22—2442no—
923C22—2442no—
924C22—2442no—
925C22#1684056212yes—
926C22C23×D24411yescharacteristic
927C4—22no—
928C4—22no—
929C4—21no—
930C4—22no—
931C4—21no—
932C4—21no—
933C4—1224no—
934C4—2442no—
935C4—2442no—
936C4—2442no—
937C4—2442no—
938C4H(5,𝔽2)×D6112yes—
939C2—22no—
940C2—41no—
941C2—41no—
942C2—42no—
943C2—4882no—
944C2—4882no—
945C2—4882no—
946C2#2145945511yescharacteristic
947C2C2×#1684056211yescharacteristic
948C2#2146060011yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2973C2
socleC22×C61C23×D4
hypercenter#2973D61
hypocenterC61#61577
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
1. #21459658C2semidirect
2. C2×#16840433C2semidirect
3. #21457947C2semidirect
4. #21457827C2semidirect
5. #21457409C2semidirect
6. #21457364C2semidirect
7. #21456839C2semidirect
8. #21456626C2semidirect
9. #21456619C2semidirect
10. #21456586C2semidirect
11. #21455992C2semidirect
12. #21455081C2semidirect
13. #21455073C2semidirect
14. #21455041C2semidirect
15. C61×#2973C2semidirect
17. C22×#11758222C22semidirect
18. C2×#14519810C22semidirect
19. C2×#14519805C22semidirect
20. C2×#14519799C22semidirect
22. #16840458C22semidirect
23. #16840452C22semidirect
28. #16840433C22semidirect
29. #16840421C22semidirect
30. #16840408C22semidirect
34. C2×#14519774C22semidirect
41. C2×#14519751C22semidirect
45. C2×C4×Dic122C22semidirect
47. #16840151C22semidirect
48. #16840127C22semidirect
49. #16840098C22semidirect
50. #16840087C22semidirect
52. #16840081C22semidirect
53. #16840076C22semidirect
54. #16840070C22semidirect
55. #16840015C22semidirect
56. #16840008C22semidirect
57. #16839998C22semidirect
58. #16839991C22semidirect
59. #16839985C22semidirect
60. #16839963C22semidirect
61. #16839958C22semidirect
62. #16839926C22semidirect
63. #16839926C22semidirect
64. #16839920C22semidirect
65. #16839915C22semidirect
66. #16839915C22semidirect
67. #16839909C22semidirect
68. #16839909C22semidirect
69. #16839909C22semidirect
71. #16839903C22semidirect
74. #16839898C22semidirect
75. #16839870C22semidirect
76. #16839864C22semidirect
77. #16839764C22semidirect
78. #16839764C22semidirect
79. #16839759C22semidirect
81. C61×#435C22semidirect
82. C61×#435C22semidirect
83. C61×#432C22semidirect
86. C2×C22⋊C8×C61C22semidirect
479. #2973D61semidirect
552. #435C2×D61semidirect
553. #435C2×D61semidirect
554. #432C2×D61semidirect
560. C2×C22⋊C8C2×D61semidirect
561. C61#61577semidirect

Maximal subgroups

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

subgroupindex
#214596582
C2×#168404332
#214579472
#214578272
#214574092
#214573642
#214568392
#214566262
#214566192
#214565862
#214559922
#214550812
#214550732
#214550412
C61×#29732
#6157761