Finite Group Databasebeta

← #30551451

Subgroups — #30551451

Order 15616.

2262 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic, complemented
2C2×#124×D61C211yesmaximal, characteristic, complemented
3#21456818C211yesmaximal, characteristic, complemented
4#21456817C212yesmaximal, complemented
5#21456808C211yesmaximal, characteristic, complemented
6#21456807C212yesmaximal, complemented
7#21456806C211yesmaximal, characteristic, complemented
8#21456789C212yesmaximal, complemented
9#21456788C214yesmaximal, complemented
10#21456787C212yesmaximal, complemented
11#21456282C212yesmaximal, complemented
12#21456204C212yesmaximal, complemented
13#21455310C214yesmaximal, complemented
14#21455054C212yesmaximal, complemented
15#21455047C212yesmaximal, complemented
16#21454449C211yesmaximal, characteristic, complemented
17C61×#3215C211yesmaximal, characteristic, complemented
18C22×Q8×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C2×#14519809C2214yescomplemented
21C2×#14519804C2214yes—
22#16840317C2211yescharacteristic, complemented
23#16840317C2211yescharacteristic, complemented
24#16840313C2211yescharacteristic, complemented
25#16840313C2211yescharacteristic, complemented
26#16840312C2211yescharacteristic, complemented
27#16840299—21no—
28#16840299C2212yescomplemented
29#16840298—21no—
30#16840298C2212yescomplemented
31#16840297—21no—
32#16840297—21no—
33C2×#14519766C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35C2×#14519764C2211yescharacteristic
36C2×#14519763—21no—
37C2×#14519763—21no—
38#124×D61—21no—
39#124×D61—21no—
40#124×D61—21no—
41#124×D61—21no—
42#124×D61C2212yes—
43#124×D61C2212yes—
44#124×D61C2212yes—
45#124×D61C2212yes—
46#16840275—21no—
47#16840275C2212yes—
48#16840274—21no—
49C4×#11758226—21no—
50C4×#11758226C2212yescomplemented
51#16840230—21no—
52C2×C22⋊C4×D61—21no—
53C2×C22⋊C4×D61—21no—
54C2×C42×D61C2211yescharacteristic
55#16840154C2212yescomplemented
56#16840152C2212yescomplemented
57#16840151C2212yescomplemented
58#16840147C2214yescomplemented
59#16840143C2214yescomplemented
60#16840124C2212yescomplemented
61#16840122C2212yescomplemented
62#16840121C2212yescomplemented
63#16840118C2214yescomplemented
64#16840115C2214yescomplemented
65#16839986C2214yescomplemented
66#16839984C2214yescomplemented
67#16839982C2214yescomplemented
68#16839980C2214yescomplemented
69#16839978C2214yescomplemented
70#16839976C2214yescomplemented
71#16839974C2214yescomplemented
72#16839917C2212yescomplemented
73#16839916C2214yescomplemented
74#16839912C2212yes—
75#16839911C2214yes—
76#16839903C2212yescomplemented
77#16839902C2214yescomplemented
78#16839901C2212yescomplemented
79#16839898C2212yes—
80#16839897C2214yes—
81#16839896C2212yes—
82#16839819C2211yescharacteristic, complemented
83#16839817C2212yescomplemented
84#16839814C2212yescomplemented
85#16839812C2212yescomplemented
86#16839784C2212yescomplemented
87#16839769C2214yescomplemented
88#16839765C2214yes—
89#16839724C2212yes—
90#16839714C2212yescomplemented
91C61×#533C2211yescharacteristic, complemented
92C2×#124×C61C2211yescharacteristic
93C61×#497C2212yescomplemented
94C61×#489C2212yescomplemented
95C61×#464C2214yescomplemented
96C61×#451C2212yescomplemented
97C61×#450C2212yes—
98C61×#432C2211yescharacteristic, complemented
99C24×D61—21no—
100C2×#11758226—21no—
101C2×#11758226C2312yes—
102C2×#11758222—21no—
103C22×Dic122—21no—
104C22×Dic122C2311yescharacteristic
105C2×Q8×D61—21no—
106C2×Q8×D61—21no—
107C2×Q8×D61—44no—
108C2×Q8×D61C2312yes—
109C2×Q8×D61C2312yes—
110C22×D244C2311yescharacteristic
111C22×C22⋊D61—21no—
112C2×D4×D61—21no—
113C2×D4×D61—21no—
114C2×D4×D61—44no—
115C2×D4×D61C2312yes—
116C2×D4×D61C2312yes—
117C22×C4×D61—21no—
118C22×C4×D61D411yescharacteristic
119C22×C4×D61D411yescharacteristic
120C22×C4×D61C2311yescharacteristic
121#14519809—48no—
122#14519804—48no—
123C2×#11758202C2314yescomplemented
124C2×#11758190C2314yescomplemented
125C2×#11758201C2314yes—
126C2×#11758201C2314yescomplemented
127C2×D488C2314yes—
128C2×#11758199C2314yes—
129C2×#11758189C2314yes—
130#14519777C2311yescharacteristic, complemented
131#14519774C2311yescharacteristic, complemented
132#14519772—22no—
133#14519772—22no—
134#14519768—21no—
135#14519768C2312yescomplemented
136#14519766—21no—
137#14519766—21no—
138#14519766—21no—
139#14519766C2312yes—
140#14519766C2312yes—
141#14519766C2312yescomplemented
142#14519765—21no—
143#14519765—21no—
144#14519765—21no—
145#14519765C2312yes—
146#14519765C2312yes—
147#14519764—21no—
148#14519764—21no—
149#14519764C2312yes—
150#14519764C2312yes—
151#14519763—22no—
152#14519763—22no—
153#14519763—22no—
154#14519763—22no—
155#14519763—22no—
156#14519763—22no—
157#14519763—22no—
158#14519763—22no—
159#14519762—22no—
160#14519762—22no—
161#14519761—22no—
162#14519757—21no—
163#14519757—21no—
164#14519753—21no—
165#14519753C2312yes—
166#14519752—21no—
167#14519752—21no—
168#14519752—21no—
169#14519752C2312yes—
170#14519751—21no—
171#14519751C2312yes—
172#14519747—22no—
173Q8×Dic61—21no—
174Q8×Dic61C2312yescomplemented
175#14519742—21no—
176#14519742—21no—
177C4×D244—22no—
178C4×D244—22no—
179C4×D244—21no—
180C4×D244C2312yescomplemented
181#14519739—22no—
182#14519739—22no—
183#14519739—21no—
184#14519739—21no—
185#14519739—21no—
186#14519739C2312yescomplemented
187#14519737—22no—
188#14519737—22no—
189#14519735—21no—
190#14519735—22no—
191#14519735—22no—
192#14519735C2312yes—
193#14519734—22no—
194C2×C22⋊Dic61—21no—
195C2×C22⋊Dic61—21no—
196C2×#11758198—21no—
197C2×#11758198—21no—
198C2×#11758198—21no—
199C2×#11758198—21no—
200C22⋊C4×D61—22no—
201C22⋊C4×D61—22no—
202C22⋊C4×D61—22no—
203C22⋊C4×D61—22no—
204C22⋊C4×D61—22no—
205C22⋊C4×D61—22no—
206C22⋊C4×D61—22no—
207C22⋊C4×D61—22no—
208C2×C4×Dic61D411yescharacteristic
209C2×C4×Dic61D411yescharacteristic
210C2×C4×Dic61C2311yescharacteristic
211C42×D61—22no—
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61D411yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219C42×D61C2311yescharacteristic
220C4⋊#92418C2312yescomplemented
221#14519706C2314yescomplemented
222#14519702C2314yescomplemented
223#14519701C2314yescomplemented
224#14519700C2314yescomplemented
225#14519699C2314yes—
226#14519698C2314yes—
227#14519697C2314yes—
228C22⋊#92418C2312yes—
229#14519689C2314yes—
230#14519688C2312yescomplemented
231C8×Dic61C2314yescomplemented
232C22×Q8×C61C2311yescharacteristic
233C22×D4×C61C2311yescharacteristic
234C2×Q16×C61C2314yescomplemented
235C2×SD16×C61C2314yes—
236C4⋊Q8×C61C2311yescharacteristic, complemented
237C4⋊Q8×C61C2311yescharacteristic, complemented
238#125×C61—21no—
239#124×C61—21no—
240#124×C61—21no—
241#124×C61C2312yes—
242#124×C61C2312yes—
243C22⋊Q8×C61—21no—
244C22⋊Q8×C61C2312yes—
245C4×Q8×C61—21no—
246C4×Q8×C61C2312yescomplemented
247#117×C61—21no—
248C2×C22⋊C4×C61—21no—
249C2×C22⋊C4×C61—21no—
250C2×C42×C61C2311yescharacteristic
251C4⋊C8×C61C2312yescomplemented
252#103×C61C2314yescomplemented
253#102×C61C2314yes—
254C22⋊C8×C61C2312yes—
255#97×C61C2312yescomplemented
256C24×C61—21no—
257C23×D61—21no—
258C23×D61—22no—
259C23×D61—22no—
260C23×D61—44no—
261C23×D61—44no—
262C23×D61—44no—
263C23×D61C2×D411yescharacteristic
264C2×Q8×C61—21no—
265C2×Q8×C61—21no—
266C2×Q8×C61—42no—
267C2×Q8×C61C2412yes—
268C2×Q8×C61C2412yes—
269C2×D4×C61—21no—
270C2×D4×C61—42no—
271C2×D4×C61C2412yes—
272C22×C4×C61—21no—
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2411yescharacteristic
276C2×C22⋊D61—22no—
277C2×C22⋊D61—22no—
278C2×C22⋊D61—22no—
279C2×C22⋊D61—44no—
280C22×Dic61—21no—
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283C22×Dic61C2×D411yescharacteristic
284#11758226—28no—
285#11758226—44no—
286Q8×D61—28no—
287Q8×D61—44no—
288Q8×D61—44no—
289Q8×D61—44no—
290D4×D61—28no—
291D4×D61—44no—
292D4×D61—44no—
293D4×D61—44no—
294#11758222—44no—
295C2×D244—22no—
296C2×D244—22no—
297C2×D244—21no—
298C2×D244—21no—
299C2×D244—21no—
300C2×D244—42no—
301C2×D244C2412yes—
302C2×D244C2412yes—
303C2×C4×D61—24no—
304C2×C4×D61—22no—
305C2×C4×D61—22no—
306C2×C4×D61—22no—
307C2×C4×D61—22no—
308C2×C4×D61—22no—
309C2×C4×D61—42no—
310C2×C4×D61—42no—
311C2×C4×D61—44no—
312C2×C4×D61C2×D411yescharacteristic
313C2×C4×D61C2×D411yescharacteristic
314C2×C4×D61C2×D411yescharacteristic
315C2×C4×D61C2×D411yescharacteristic
316C2×C4×D61C2×D411yescharacteristic
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2×D411yescharacteristic
321C2×C4×D61C2×D411yescharacteristic
322C2×C4×D61C2411yescharacteristic
323C2×C4×D61C2411yescharacteristic
324C2×Dic122—21no—
325C2×Dic122—21no—
326C2×Dic122—22no—
327C2×Dic122—22no—
328C2×Dic122—42no—
329C2×Dic122—44no—
330C2×Dic122C2412yes—
331Q16×C61—44no—
332SD16×C61—44no—
333C2×C8×C61C2414yes—
334C4⋊C4×C61—21no—
335C4⋊C4×C61—21no—
336C4⋊C4×C61—21no—
337C4⋊C4×C61—22no—
338C4⋊C4×C61—22no—
339C4⋊C4×C61C2412yes—
340C22⋊C4×C61—22no—
341C22⋊C4×C61—22no—
342C22⋊C4×C61—22no—
343C22⋊C4×C61—22no—
344C22⋊C4×C61—22no—
345C42×C61—22no—
346C42×C61C2×D411yescharacteristic
347C42×C61C2×D411yescharacteristic
348C42×C61C2411yescharacteristic
349C42×C61C2411yescharacteristic
350C22⋊Dic61—22no—
351C22⋊Dic61—22no—
352C22⋊Dic61—22no—
353C22⋊Dic61—22no—
354#11758202—44no—
355#11758201—44no—
356#11758201—44no—
357#11758199—44no—
358#11758198—22no—
359#11758198—22no—
360#11758198—22no—
361#11758198—22no—
362#11758198—22no—
363#11758198—22no—
364#11758198—22no—
365#11758198—22no—
366#11758198—22no—
367#11758198—22no—
368#11758198—22no—
369#11758198—22no—
370#11758198—22no—
371#11758198—22no—
372#11758198—22no—
373#11758198—22no—
374C4⋊Dic61—21no—
375C4⋊Dic61—22no—
376C4⋊Dic61—22no—
377C4⋊Dic61C2412yes—
378#11758196—22no—
379#11758196—22no—
380C4×Dic61—22no—
381C4×Dic61—22no—
382C4×Dic61C2×D411yescharacteristic
383C4×Dic61C2×D411yescharacteristic
384C4×Dic61C2×D411yescharacteristic
385C4×Dic61C2×D411yescharacteristic
386C4×Dic61C2×D411yescharacteristic
387C4×Dic61C2×D411yescharacteristic
388C4×Dic61C2×D411yescharacteristic
389C4×Dic61C2×D411yescharacteristic
390C4×Dic61C2×D411yescharacteristic
391C4×Dic61C2×D411yescharacteristic
392C4×Dic61C2411yescharacteristic
393C4×Dic61C2411yescharacteristic
394C2×#92418C2414yes—
395D488—44no—
396#11758190—44no—
397#11758189—28no—
398C23×C61—22no—
399C23×C61—42no—
400C23×C61—42no—
401C23×C61—42no—
402C23×C61C22×D411yescharacteristic
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—44no—
409C22×D61—44no—
410C22×D61—44no—
411C22×D61—44no—
412C22×D61—42no—
413C22×D61—42no—
414C22×D61—42no—
415C22×D61—44no—
416C22×D61—44no—
417C22×D61—816no—
418C22×D61C22×D411yescharacteristic
419C22×D61C22×D411yescharacteristic
420Q8×C61—24no—
421Q8×C61—24no—
422Q8×C61—42no—
423Q8×C61—42no—
424D4×C61—24no—
425D4×C61—42no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—41no—
432C2×C4×C61—42no—
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C22×D411yescharacteristic
435C2×C4×C61C22×D411yescharacteristic
436C2×C4×C61C22×D411yescharacteristic
437C2×C4×C61C22×D411yescharacteristic
438C2×C4×C61C2511yescharacteristic
439C22⋊D61—44no—
440C22⋊D61—44no—
441C22⋊D61—44no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—41no—
447C2×Dic61—42no—
448C2×Dic61C22×D411yescharacteristic
449C2×Dic61C22×D411yescharacteristic
450C2×Dic61C22×D411yescharacteristic
451C2×Dic61C22×D411yescharacteristic
452C2×Dic61C22×D411yescharacteristic
453C2×Dic61C22×D411yescharacteristic
454D244—24no—
455D244—24no—
456D244—42no—
457D244—42no—
458D244—42no—
459D244—44no—
460D244—44no—
461C4×D61—22no—
462C4×D61—22no—
463C4×D61—22no—
464C4×D61—22no—
465C4×D61—22no—
466C4×D61—41no—
467C4×D61—41no—
468C4×D61—41no—
469C4×D61—41no—
470C4×D61—41no—
471C4×D61—41no—
472C4×D61—44no—
473C4×D61—44no—
474C4×D61—44no—
475C4×D61—44no—
476C4×D61—44no—
477C4×D61H(5,𝔽2)14yes—
478Dic122—24no—
479Dic122—44no—
480Dic122—42no—
481Dic122—42no—
482Dic122—44no—
483C8×C61—24no—
484#92418—24no—
485#60799—611nomaximal, Sylow
486C22×C61—21no—
487C22×C61—21no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—84no—
492C22×C61#57512yes—
493C22×C61C23×D411yescharacteristic
494C2×D61—28no—
495C2×D61—21no—
496C2×D61—21no—
497C2×D61—21no—
498C2×D61—21no—
499C2×D61—42no—
500C2×D61—42no—
501C2×D61—42no—
502C2×D61—42no—
503C2×D61—42no—
504C2×D61—42no—
505C2×D61—88no—
506C2×D61—88no—
507C2×D61—84no—
508C2×D61#53512yes—
509C2×D61#57512yes—
510C4×C61—21no—
511C4×C61—21no—
512C4×C61—21no—
513C4×C61—21no—
514C4×C61—21no—
515C4×C61—42no—
516C4×C61—42no—
517C4×C61—42no—
518C4×C61C2×H(5,𝔽2)12yes—
519Dic61—21no—
520Dic61—21no—
521Dic61—21no—
522Dic61—21no—
523Dic61—21no—
524Dic61—42no—
525Dic61—42no—
526Dic61#53512yes—
527#3444—611no—
528C22×#124—611no—
529#3215—612no—
530#3215—611no—
531#3215D6111yescharacteristic, complemented
532#3213—612no—
533#3213—611no—
534#3213—611no—
535#3211—614no—
536#3211—612no—
537#3211—612no—
538#3153—612no—
539#3140—612no—
540#3040—614no—
541#3004—612no—
542#3003—612no—
543#2920—611no—
544C2×C61—22no—
545C2×C61—82no—
546C2×C61C2×#53511yescharacteristic
547C2×C61C2×#57511yescharacteristic
548C2×C61C2×#57511yescharacteristic
549D61—22no—
550D61—22no—
551D61—82no—
552D61—82no—
553C23×Q8—611no—
554C23×D4—611no—
555C2×#137—614no—
556C2×AGL(1,ℤ/8)—614no—
557#533—611no—
558#533—611no—
559#533C2×D6111yescharacteristic, complemented
560#532—611no—
561#532—611no—
562#532—611no—
563#529—612no—
564#529—612no—
565#529—1221no—
566#529—1221no—
567#529—1221no—
568#529—1221no—
569C2×#124—611no—
570C2×#124—611no—
571C2×#124—612no—
572C2×#124—612no—
573C2×#124—612no—
574C2×#124—612no—
575C2×#124—611no—
576C2×#124—1221no—
577C2×#124—1221no—
578C2×#124—1221no—
579C2×#124—1221no—
580C2×#124—1221no—
581C2×#124—1221no—
582C2×#124C2×D6111yescharacteristic
583#525—612no—
584#525—1221no—
585#525—1221no—
586C4×#41—612no—
587C4×#41—1221no—
588C4×#41—1221no—
589C22×C22⋊C4—1221no—
590C22×C22⋊C4—1221no—
591C22×C42—611no—
592#497—612no—
593#497C2×D6112yescomplemented
594#496—612no—
595#496—612no—
596#495—614no—
597#495—614no—
598#489—612no—
599#489—612no—
600#489—612no—
601#489C2×D6112yescomplemented
602#488—614no—
603#488—614no—
604#464—614no—
605#464—614no—
606#464—614no—
607#464C2×D6114yescomplemented
608#463—614no—
609#463—614no—
610#463—614no—
611#463—614no—
612#451—614no—
613#451—612no—
614#451C2×D6112yescomplemented
615#450—614no—
616#450—612no—
617#450C2×D6112yes—
618#448—612no—
619#448—614no—
620#448—612no—
621#447—612no—
622#447—614no—
623#447—612no—
624#432—611no—
625#432—612no—
626#432C2×D6111yescharacteristic, complemented
627#431—612no—
628#431—612no—
629#423—612no—
630#419—614no—
631#418—614no—
632#407—612no—
633C4×M16—612no—
634C61#6079911yescharacteristic, complemented, Sylow
635C25—1221no—
636C2×#41—612no—
637C2×#41—1221no—
638C2×#41—1221no—
639C22×Q8—612no—
640C22×Q8—612no—
641C22×Q8—611no—
642C22×Q8—1221no—
643C22×Q8—1221no—
644C22×Q8—1221no—
645C22×Q8—2444no—
646C22×Q8C22×D6111yescharacteristic
647C22×D4—612no—
648C22×D4—612no—
649C22×D4—611no—
650C22×D4—1221no—
651C22×D4—1221no—
652C22×D4—1221no—
653C22×D4—2444no—
654C22×D4C22×D6111yescharacteristic
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—1221no—
659#137—2448no—
660AGL(1,ℤ/8)—2448no—
661C2×Q16—614no—
662C2×Q16C22×D6114yescomplemented
663C2×SD16—614no—
664C2×SD16—614no—
665C2×SD16—614no—
666C2×SD16C22×D6114yes—
667C2×D8—614no—
668C2×D8—614no—
669C2×M16—614no—
670C4⋊Q8—611no—
671C4⋊Q8C22×D6111yescharacteristic, complemented
672C4⋊Q8C22×D6111yescharacteristic, complemented
673#127—611no—
674#126—1222no—
675#126—1222no—
676#125—21no—
677#125—612no—
678#125—1221no—
679#124—21no—
680#124—21no—
681#124—612no—
682#124—612no—
683#124—612no—
684#124—612no—
685#124—612no—
686#124—612no—
687#124—612no—
688#124—1222no—
689#124—1222no—
690#124—1222no—
691#124—1222no—
692#124—1222no—
693#124—1222no—
694#124—1222no—
695#124—1222no—
696#124—1221no—
697#124—1221no—
698#124—1221no—
699#124—1221no—
700#124—1221no—
701#124—1221no—
702#124—1221no—
703#124—1221no—
704#124C22×D6112yes—
705#124C22×D6112yes—
706#123—1222no—
707#123—1222no—
708#123—1222no—
709C22⋊Q8—21no—
710C22⋊Q8—612no—
711C22⋊Q8—1221no—
712C22⋊Q8—1221no—
713C22⋊Q8—1221no—
714C22⋊Q8C22×D6112yes—
715#121—612no—
716#121—612no—
717#121—1221no—
718#121—1221no—
719#121—1221no—
720#121—1221no—
721#120—1222no—
722C4×Q8—21no—
723C4×Q8—612no—
724C4×Q8—1221no—
725C4×Q8—1221no—
726C4×Q8—1221no—
727C4×Q8C22×D6112yescomplemented
728C4×D4—612no—
729C4×D4—612no—
730C4×D4—1222no—
731C4×D4—1222no—
732C4×D4—1221no—
733C4×D4—1221no—
734C4×D4—1221no—
735C4×D4—1222no—
736C4×D4—1222no—
737C4×D4—1222no—
738C4×D4—1222no—
739C4×D4—1221no—
740#117—21no—
741#117—612no—
742#117—1222no—
743#117—1222no—
744#117—1222no—
745#117—1221no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—1222no—
749C2×C22⋊C4—1222no—
750C2×C22⋊C4—1222no—
751C2×C22⋊C4—1222no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1221no—
757C2×C22⋊C4—1221no—
758C2×C22⋊C4—1221no—
759C2×C22⋊C4—1221no—
760C2×C22⋊C4—1221no—
761C2×C22⋊C4—1221no—
762C2×C42—611no—
763C2×C42—611no—
764C2×C42—611no—
765C2×C42—611no—
766C2×C42—611no—
767C2×C42—611no—
768C2×C42—611no—
769C2×C42—611no—
770C2×C42—611no—
771C2×C42—611no—
772C2×C42—611no—
773C2×C42—1222no—
774C2×C42C22×D6111yescharacteristic
775C4⋊C8—614no—
776C4⋊C8—612no—
777C4⋊C8C22×D6112yescomplemented
778#103—614no—
779#103—614no—
780#103—614no—
781#103C22×D6114yescomplemented
782#102—614no—
783#102—614no—
784#102—614no—
785#102C22×D6114yes—
786C22⋊C8—612no—
787C22⋊C8—614no—
788C22⋊C8C22×D6112yes—
789#97—612no—
790#97C22×D6112yescomplemented
791C4×C8—614no—
792C24—21no—
793C24—611no—
794C24—1222no—
795C24—1222no—
796C24—1221no—
797C24—2444no—
798C24—2444no—
799C24—2444no—
800#41—1228no—
801#41—2444no—
802#41—2444no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—42no—
806C2×Q8—612no—
807C2×Q8—1222no—
808C2×Q8—1222no—
809C2×Q8—1228no—
810C2×Q8—1221no—
811C2×Q8—1221no—
812C2×Q8—2442no—
813C2×Q8—2444no—
814C2×Q8—2444no—
815C2×Q8—2444no—
816C2×Q8—2444no—
817C2×Q8C23×D6112yes—
818C2×Q8C23×D6112yes—
819C2×D4—21no—
820C2×D4—42no—
821C2×D4—612no—
822C2×D4—612no—
823C2×D4—1222no—
824C2×D4—1222no—
825C2×D4—1228no—
826C2×D4—1222no—
827C2×D4—1222no—
828C2×D4—1222no—
829C2×D4—1221no—
830C2×D4—1221no—
831C2×D4—1221no—
832C2×D4—2442no—
833C2×D4—2444no—
834C2×D4—2444no—
835C2×D4—2444no—
836C2×D4—2444no—
837C2×D4C23×D6112yes—
838C22×C4—21no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—611no—
843C22×C4—611no—
844C22×C4—611no—
845C22×C4—611no—
846C22×C4—611no—
847C22×C4—611no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—1224no—
855C22×C4—1222no—
856C22×C4—1222no—
857C22×C4—1222no—
858C22×C4—1222no—
859C22×C4—1221no—
860C22×C4—1222no—
861C22×C4—2442no—
862C22×C4—2442no—
863C22×C4—2444no—
864C22×C4D4×D6111yescharacteristic
865C22×C4D4×D6111yescharacteristic
866C22×C4C23×D6111yescharacteristic
867Q16—44no—
868Q16—2444no—
869SD16—44no—
870SD16—2444no—
871SD16—2444no—
872SD16—2444no—
873D8—2444no—
874D8—2444no—
875M16—1228no—
876C2×C8—614no—
877C2×C8C23×D6114yes—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—612no—
884C4⋊C4—1222no—
885C4⋊C4—1222no—
886C4⋊C4—1222no—
887C4⋊C4—1222no—
888C4⋊C4—1221no—
889C4⋊C4C23×D6112yes—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—1222no—
896C22⋊C4—1222no—
897C22⋊C4—1222no—
898C22⋊C4—1222no—
899C22⋊C4—1222no—
900C22⋊C4—1222no—
901C22⋊C4—1222no—
902C22⋊C4—1222no—
903C22⋊C4—1222no—
904C22⋊C4—1222no—
905C22⋊C4—1222no—
906C22⋊C4—1222no—
907C22⋊C4—1222no—
908C22⋊C4—1222no—
909C22⋊C4—1222no—
910C22⋊C4—1222no—
911C22⋊C4—1222no—
912C22⋊C4—1222no—
913C22⋊C4—1222no—
914C22⋊C4—1222no—
915C42—22no—
916C42—611no—
917C42—611no—
918C42—611no—
919C42—611no—
920C42—611no—
921C42—611no—
922C42—611no—
923C42—611no—
924C42—611no—
925C42—611no—
926C42—611no—
927C42—611no—
928C42—1222no—
929C42—1222no—
930C42D4×D6111yescharacteristic
931C42D4×D6111yescharacteristic
932C42C23×D6111yescharacteristic
933C42C23×D6111yescharacteristic
934C23—22no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—611no—
939C23—611no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—48816no—
946C23—2442no—
947C23—2442no—
948C23—2444no—
949C23—2444no—
950C23—2444no—
951C23—2444no—
952C23—2444no—
953C23—2444no—
954C23—2442no—
955C23C2×D4×D6111yescharacteristic
956Q8—24no—
957Q8—24no—
958Q8—42no—
959Q8—42no—
960Q8—1224no—
961Q8—2442no—
962Q8—2442no—
963Q8—2444no—
964Q8—2444no—
965D4—24no—
966D4—42no—
967D4—1224no—
968D4—1224no—
969D4—2442no—
970D4—2442no—
971D4—2442no—
972D4—2444no—
973D4—2444no—
974D4—2444no—
975D4—2444no—
976D4—2444no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—41no—
983C2×C4—42no—
984C2×C4—611no—
985C2×C4—614no—
986C2×C4—611no—
987C2×C4—611no—
988C2×C4—611no—
989C2×C4—611no—
990C2×C4—611no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2444no—
1007C2×C4—2444no—
1008C2×C4—2444no—
1009C2×C4—2444no—
1010C2×C4—2444no—
1011C2×C4—2441no—
1012C2×C4—2442no—
1013C2×C4C2×D4×D6111yescharacteristic
1014C2×C4C2×D4×D6111yescharacteristic
1015C2×C4C2×D4×D6111yescharacteristic
1016C2×C4C2×D4×D6111yescharacteristic
1017C2×C4C2×D4×D6111yescharacteristic
1018C2×C4C24×D6111yescharacteristic
1019C8—24no—
1020C8—1224no—
1021C22—21no—
1022C22—21no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—84no—
1027C22—612no—
1028C22—612no—
1029C22—1228no—
1030C22—1221no—
1031C22—1221no—
1032C22—1221no—
1033C22—1221no—
1034C22—4884no—
1035C22—4888no—
1036C22—4888no—
1037C22—2442no—
1038C22—2442no—
1039C22—2442no—
1040C22—2442no—
1041C22—2442no—
1042C22—2442no—
1043C22#1684056112yes—
1044C22C22×D4×D6111yescharacteristic
1045C4—21no—
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—42no—
1051C4—42no—
1052C4—42no—
1053C4—612no—
1054C4—1221no—
1055C4—1221no—
1056C4—1221no—
1057C4—1221no—
1058C4—1221no—
1059C4—2442no—
1060C4—2442no—
1061C4H(5,𝔽2)×D6112yes—
1062C2—22no—
1063C2—82no—
1064C2—1222no—
1065C2—1222no—
1066C2—4882no—
1067C2—4882no—
1068C2#535×D6111yescharacteristic
1069C2#575×D6111yescharacteristic
1070C2C2×#1684056111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3215C2
socleC22×C61C23×D4
hypercenter#3215D61
hypocenterC61#60799
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3215

Complements

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

NH ≅ G/Ntype
1. #21459116C2semidirect
2. C2×#124×D61C2semidirect
3. #21456818C2semidirect
4. #21456817C2semidirect
5. #21456808C2semidirect
6. #21456807C2semidirect
7. #21456806C2semidirect
8. #21456789C2semidirect
9. #21456788C2semidirect
10. #21456787C2semidirect
11. #21456282C2semidirect
12. #21456204C2semidirect
13. #21455310C2semidirect
14. #21455054C2semidirect
15. #21455047C2semidirect
16. #21454449C2semidirect
17. C61×#3215C2semidirect
20. C2×#14519809C22semidirect
22. #16840317C22semidirect
23. #16840317C22semidirect
24. #16840313C22semidirect
25. #16840313C22semidirect
26. #16840312C22semidirect
28. #16840299C22semidirect
30. #16840298C22semidirect
50. C4×#11758226C22semidirect
55. #16840154C22semidirect
56. #16840152C22semidirect
57. #16840151C22semidirect
58. #16840147C22semidirect
59. #16840143C22semidirect
60. #16840124C22semidirect
61. #16840122C22semidirect
62. #16840121C22semidirect
63. #16840118C22semidirect
64. #16840115C22semidirect
65. #16839986C22semidirect
66. #16839984C22semidirect
67. #16839982C22semidirect
68. #16839980C22semidirect
69. #16839978C22semidirect
70. #16839976C22semidirect
71. #16839974C22semidirect
72. #16839917C22semidirect
73. #16839916C22semidirect
76. #16839903C22semidirect
77. #16839902C22semidirect
78. #16839901C22semidirect
82. #16839819C22semidirect
83. #16839817C22semidirect
84. #16839814C22semidirect
85. #16839812C22semidirect
86. #16839784C22semidirect
87. #16839769C22semidirect
90. #16839714C22semidirect
91. C61×#533C22semidirect
93. C61×#497C22semidirect
94. C61×#489C22semidirect
95. C61×#464C22semidirect
96. C61×#451C22semidirect
98. C61×#432C22semidirect
123. C2×#11758202C23semidirect
124. C2×#11758190C23semidirect
126. C2×#11758201C23semidirect
130. #14519777C23semidirect
131. #14519774C23semidirect
135. #14519768C23semidirect
141. #14519766C23semidirect
174. Q8×Dic61C23semidirect
180. C4×D244C23semidirect
186. #14519739C23semidirect
220. C4⋊#92418C23semidirect
221. #14519706C23semidirect
222. #14519702C23semidirect
223. #14519701C23semidirect
224. #14519700C23semidirect
230. #14519688C23semidirect
231. C8×Dic61C23semidirect
234. C2×Q16×C61C23semidirect
236. C4⋊Q8×C61C23semidirect
237. C4⋊Q8×C61C23semidirect
246. C4×Q8×C61C23semidirect
251. C4⋊C8×C61C23semidirect
252. #103×C61C23semidirect
255. #97×C61C23semidirect
531. #3215D61semidirect
559. #533C2×D61semidirect
593. #497C2×D61semidirect
601. #489C2×D61semidirect
607. #464C2×D61semidirect
614. #451C2×D61semidirect
626. #432C2×D61semidirect
634. C61#60799semidirect
662. C2×Q16C22×D61semidirect
671. C4⋊Q8C22×D61semidirect
672. C4⋊Q8C22×D61semidirect
727. C4×Q8C22×D61semidirect
777. C4⋊C8C22×D61semidirect
781. #103C22×D61semidirect
790. #97C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214591162
C2×#124×D612
#214568182
#214568172
#214568082
#214568072
#214568062
#214567892
#214567882
#214567872
#214562822
#214562042
#214553102
#214550542
#214550472
#214544492
C61×#32152
#6079961