Finite Group Databasebeta

← #30564932

Subgroups — #30564932

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459671C211yesmaximal, characteristic, complemented
2C2×#16840408C211yesmaximal, characteristic, complemented
3#21457977C214yesmaximal, complemented
4#21457857C214yesmaximal, complemented
5#21457364C214yesmaximal, complemented
6#21457349C214yesmaximal, complemented
7#21456824C211yesmaximal, characteristic, complemented
8#21456808C211yesmaximal, characteristic, complemented
9#21456651C212yesmaximal, complemented
10#21456586C212yesmaximal, complemented
11#21455919C211yesmaximal, characteristic, complemented
12#21455911C211yesmaximal, characteristic, complemented
13#21455049C212yesmaximal, complemented
14#21455041C212yesmaximal, complemented
15C61×#2973C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C2×#14519805C2214yescomplemented
19C2×#14519799C2214yescomplemented
20#16840495—22no—
21#16840482C2212yescomplemented
22#16840477C2212yescomplemented
23#16840462—22no—
24#16840433C2212yescomplemented
25#16840417C2212yescomplemented
26#16840408—22no—
27#16840408—22no—
28#16840408C2214yes—
29#16840408C2214yes—
30#16840350—21no—
31#16840350—21no—
32#16840329—21no—
33#16840319C2211yescharacteristic, complemented
34#16840312C2211yescharacteristic, complemented
35C2×#14519765C2211yescharacteristic
36#16840273C2212yes—
37#16840273C2212yescomplemented
38C2×#14519762—21no—
39C2×#14519756C2211yescharacteristic
40C2×#14519751C2211yescharacteristic
41C2×#14519750—21no—
42C2×#14519745—21no—
43#16840243—21no—
44C2×C4×D244C2211yescharacteristic
45C2×C22⋊C4×D61—21no—
46#16840156C2212yescomplemented
47#16840151C2212yescomplemented
48#16840122C2212yescomplemented
49#16840122C2212yescomplemented
50#16840104C2214yescomplemented
51#16840098C2212yescomplemented
52#16840087C2214yescomplemented
53#16840081C2212yescomplemented
54#16840053C2212yescomplemented
55#16840043C2212yescomplemented
56#16840020C2214yescomplemented
57#16840008C2214yescomplemented
58#16839998C2214yescomplemented
59#16839991C2214yescomplemented
60#16839985C2214yescomplemented
61#16839978C2214yescomplemented
62#16839968C2212yescomplemented
63#16839958C2212yescomplemented
64#16839926C2214yescomplemented
65#16839926C2214yescomplemented
66#16839920C2212yescomplemented
67#16839915C2212yes—
68#16839915C2212yes—
69#16839915C2214yescomplemented
70#16839909C2214yescomplemented
71#16839909C2214yescomplemented
72#16839903C2212yescomplemented
73#16839898C2212yes—
74#16839898C2212yes—
75#16839898C2214yescomplemented
76#16839875C2214yescomplemented
77#16839864C2214yescomplemented
78#16839768C2214yescomplemented
79#16839759C2214yescomplemented
80C2×C4×D4×C61C2211yescharacteristic
81C61×#435C2214yescomplemented
82C61×#435C2214yescomplemented
83C61×#432C2211yescharacteristic, complemented
84C61×#432C2211yescharacteristic, complemented
85C61×#407C2212yes—
86C2×C22⋊C8×C61C2212yescomplemented
87C24×D61—21no—
88C2×#11758222—21no—
89C2×#11758222—22no—
90C2×#11758222—44no—
91C2×#11758222C2314yes—
92C2×#11758222C2312yes—
93C2×#11758222C2312yescomplemented
94C22×Dic122C2311yescharacteristic
95C22×D244—21no—
96C22×D244—22no—
97C22×D244—44no—
98C22×D244C2311yescharacteristic
99C22×D244C2314yes—
100C22×D244C2311yescharacteristic
101C22×C22⋊D61—21no—
102C22×C22⋊D61—21no—
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105#14519805—48no—
106#14519799—48no—
107C2×Dic244C2314yescomplemented
108C2×#11758190C2314yes—
109C2×#11758190C2314yes—
110C2×#11758190C2314yescomplemented
111C2×D488C2314yes—
112C2×D488C2314yes—
113#14519777C2311yescharacteristic, complemented
114#14519777C2311yescharacteristic, complemented
115#14519777C2311yescharacteristic, complemented
116#14519774C2311yescharacteristic, complemented
117#14519773—22no—
118#14519770—22no—
119#14519770—22no—
120#14519769—21no—
121#14519765—21no—
122#14519765—21no—
123#14519765—21no—
124#14519765C2312yes—
125#14519765C2312yes—
126#14519764—22no—
127#14519763—22no—
128#14519763—22no—
129#14519762—24no—
130#14519762—24no—
131#14519760—22no—
132#14519760—22no—
133#14519759—22no—
134#14519759—22no—
135#14519756—22no—
136#14519756—21no—
137#14519756C2312yes—
138#14519756C2314yes—
139#14519756C2312yes—
140#14519756C2312yescomplemented
141#14519751—22no—
142#14519751—21no—
143#14519751C2312yes—
144#14519751C2314yes—
145#14519751C2312yes—
146#14519751C2312yescomplemented
147#14519750—22no—
148#14519750—22no—
149#14519750—24no—
150#14519750—24no—
151#14519748—22no—
152#14519748—22no—
153#14519746—22no—
154#14519746—22no—
155#14519745—24no—
156#14519745—24no—
157C4×Dic122—21no—
158C4×Dic122C2312yescomplemented
159#14519742—22no—
160C4×D244—21no—
161C4×D244—21no—
162C4×D244—21no—
163C4×D244C2312yes—
164C4×D244C2312yes—
165C4×D244C2312yescomplemented
166#14519739—22no—
167C4×C22⋊D61—22no—
168C4×C22⋊D61—22no—
169C4×C22⋊D61—22no—
170C4×C22⋊D61—22no—
171#14519736—21no—
172#14519736C2312yes—
173#14519736C2312yescomplemented
174#14519735—22no—
175C2×C4⋊Dic61C2311yescharacteristic
176C2×#11758196—21no—
177C4⋊C4×D61—22no—
178C2×C22⋊Dic61—21no—
179C2×#11758198—21no—
180C2×#11758198—21no—
181C2×#11758198—21no—
182C2×#11758198—21no—
183C22⋊C4×D61—24no—
184C22⋊C4×D61—24no—
185#14519711C2314yescomplemented
186#14519709C2314yescomplemented
187#14519702C2314yescomplemented
188#14519702C2314yescomplemented
189#14519702C2314yescomplemented
190#14519699C2314yes—
191#14519699C2314yes—
192#14519699C2314yes—
193#14519699C2314yes—
194#14519699C2314yescomplemented
195C22×D4×C61D411yescharacteristic
196C23×C4×C61C2311yescharacteristic
197C23×C4×C61C2311yescharacteristic
198C2×M16×C61C2314yes—
199C22×C8×C61C2314yescomplemented
200C4×D4×C61D412yes—
201C4×D4×C61D412yes—
202C4×D4×C61C2312yes—
203C4×D4×C61C2312yes—
204C2×C4⋊C4×C61D411yescharacteristic
205C2×C22⋊C4×C61D411yescharacteristic
206C2×C22⋊C4×C61D411yescharacteristic
207C2×C42×C61C2311yescharacteristic
208C4⋊C8×C61C2312yescomplemented
209C4⋊C8×C61C2312yescomplemented
210C22⋊C8×C61C2312yes—
211C22⋊C8×C61C2312yes—
212C22⋊C8×C61C2314yes—
213C22⋊C8×C61C2314yescomplemented
214#97×C61C2312yescomplemented
215#97×C61C2312yescomplemented
216C24×C61C2×D411yescharacteristic
217C24×C61C2×D411yescharacteristic
218C23×D61—21no—
219C23×D61—21no—
220C23×D61—24no—
221C23×D61—44no—
222C23×D61—44no—
223C23×D61—82no—
224C2×D4×C61—42no—
225C2×D4×C61C2×D412yes—
226C2×D4×C61C2×D412yes—
227C22×C4×C61—42no—
228C22×C4×C61—42no—
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2411yescharacteristic
236C22×C4×C61C2412yes—
237C22×C4×C61C2412yes—
238C2×C22⋊D61—24no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—24no—
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—22no—
245C2×C22⋊D61—44no—
246C2×C22⋊D61—82no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249#11758222—28no—
250#11758222—44no—
251#11758222—44no—
252#11758222—44no—
253#11758222—48no—
254#11758222—44no—
255C2×D244—21no—
256C2×D244—24no—
257C2×D244—28no—
258C2×D244—24no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—44no—
263C2×D244—42no—
264C2×D244—48no—
265C2×D244—44no—
266C2×D244C2412yes—
267C2×D244C2412yes—
268C2×D244C2412yes—
269C2×C4×D61—24no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—22no—
273C2×C4×D61—22no—
274C2×C4×D61—22no—
275C2×C4×D61—44no—
276C2×C4×D61—82no—
277C2×Dic122—21no—
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—42no—
281C2×Dic122C2412yes—
282C2×Dic122C2412yes—
283M16×C61—44no—
284C2×C8×C61—44no—
285C2×C8×C61C2414yes—
286C2×C8×C61C2414yes—
287C4⋊C4×C61C2×D412yes—
288C4⋊C4×C61C2×D412yes—
289C22⋊C4×C61C2×D412yes—
290C22⋊C4×C61C2×D412yes—
291C22⋊C4×C61C2×D412yes—
292C22⋊C4×C61C2×D412yes—
293C42×C61C2×D411yescharacteristic
294C42×C61C2×D411yescharacteristic
295C42×C61C2411yescharacteristic
296C42×C61C2411yescharacteristic
297C22⋊Dic61—24no—
298C22⋊Dic61—22no—
299C22⋊Dic61—22no—
300C22⋊Dic61—22no—
301C22⋊Dic61—22no—
302C22⋊Dic61—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—24no—
306#11758198—22no—
307#11758198—22no—
308#11758198—22no—
309#11758198—22no—
310#11758198—22no—
311#11758198—22no—
312#11758198—22no—
313#11758198—22no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61C2412yes—
320C4⋊Dic61C2412yes—
321C4⋊Dic61C2412yes—
322#11758196—22no—
323#11758196—22no—
324#11758196—24no—
325#11758196—22no—
326#11758196—22no—
327C4×Dic61—22no—
328C4×Dic61—22no—
329C4×Dic61—22no—
330Dic244—44no—
331D488—28no—
332D488—44no—
333#11758190—28no—
334#11758190—44no—
335#11758190—44no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61C22×D412yes—
343C23×C61C22×D412yes—
344C23×C61C22×D411yescharacteristic
345C22×D61—24no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—48no—
350C22×D61—42no—
351C22×D61—42no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—48no—
355C22×D61—42no—
356C22×D61—84no—
357C22×D61—816no—
358D4×C61—42no—
359D4×C61—42no—
360C2×C4×C61—22no—
361C2×C4×C61—24no—
362C2×C4×C61—24no—
363C2×C4×C61—22no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—42no—
367C2×C4×C61—41no—
368C2×C4×C61—42no—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D412yes—
371C2×C4×C61C22×D412yes—
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C2511yescharacteristic
377C22⋊D61—48no—
378C22⋊D61—44no—
379C22⋊D61—82no—
380C22⋊D61—82no—
381C22⋊D61—82no—
382C22⋊D61—82no—
383C22⋊D61—84no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391D244—24no—
392D244—22no—
393D244—24no—
394D244—24no—
395D244—48no—
396D244—42no—
397D244—42no—
398D244—81no—
399D244H(5,𝔽2)14yes—
400C4×D61—48no—
401C4×D61—44no—
402C4×D61—82no—
403C4×D61—82no—
404C4×D61—82no—
405C4×D61—82no—
406Dic122—24no—
407Dic122—24no—
408Dic122—42no—
409Dic122—42no—
410Dic122—81no—
411C8×C61—24no—
412C8×C61—24no—
413#61576—611nomaximal, Sylow
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—44no—
423C22×C61—82no—
424C22×C61#57512yes—
425C22×C61C23×D411yescharacteristic
426C2×D61—24no—
427C2×D61—48no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—816no—
437C2×D61—84no—
438C4×C61—21no—
439C4×C61—21no—
440C4×C61—21no—
441C4×C61—22no—
442C4×C61—22no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61C2×H(5,𝔽2)12yes—
446Dic61—42no—
447Dic61—42no—
448Dic61—42no—
449Dic61—42no—
450Dic61—42no—
451#3506—611no—
452C2×#546—611no—
453#3319—614no—
454#3311—614no—
455#3268—614no—
456#3267—614no—
457#3215—611no—
458#3213—611no—
459#3196—612no—
460#3188—612no—
461#3110—611no—
462#3109—611no—
463#3003—612no—
464#3002—612no—
465#2973D6111yescharacteristic, complemented
466C2×C61—22no—
467C2×C61—42no—
468C2×C61—42no—
469C2×C61#348411yescharacteristic
470C2×C61C2×#57511yescharacteristic
471C2×C61#358511yescharacteristic
472D61—44no—
473D61—82no—
474D61—82no—
475C22×#41—611no—
476C23×D4—611no—
477C2×AGL(1,ℤ/8)—614no—
478C2×#135—614no—
479#559—1222no—
480#556—612no—
481#555—612no—
482#553—1222no—
483#550—612no—
484#547—612no—
485#546—614no—
486#546—614no—
487#546—1222no—
488#546—1222no—
489#538—1221no—
490#538—1221no—
491#535—1221no—
492#533—611no—
493#532—611no—
494C2×#124—611no—
495#525—612no—
496#525—612no—
497C2×#123—1221no—
498C2×C22⋊Q8—611no—
499C2×#121—611no—
500C2×#121—1221no—
501C2×#120—1221no—
502#520—1221no—
503C2×C4×D4—611no—
504C2×C4×D4C2×D6111yescharacteristic
505C22×C22⋊C4—1221no—
506#497—612no—
507#496—612no—
508#489—612no—
509#489—612no—
510#485—614no—
511#484—612no—
512#482—614no—
513#481—612no—
514#476—612no—
515#474—612no—
516#470—614no—
517#468—614no—
518#466—614no—
519#465—614no—
520#464—614no—
521#463—614no—
522#461—612no—
523#459—612no—
524#452—614no—
525#452—614no—
526#451—612no—
527#450—612no—
528#450—612no—
529#450—614no—
530#449—614no—
531#449—614no—
532#448—612no—
533#447—612no—
534#447—612no—
535#447—614no—
536#442—614no—
537#440—614no—
538#435C2×D6114yescomplemented
539#435C2×D6114yescomplemented
540#432C2×D6111yescharacteristic, complemented
541#432C2×D6111yescharacteristic, complemented
542#418—614no—
543#416—614no—
544#407C2×D6112yes—
545C2×C22⋊C8C2×D6112yescomplemented
546C61#6157611yescharacteristic, complemented, Sylow
547C25—1221no—
548C2×#41—614no—
549C2×#41—612no—
550C2×#41—612no—
551C2×#41—1221no—
552C2×#41—1222no—
553C2×#41—2444no—
554C22×Q8—611no—
555C22×D4—611no—
556C22×D4—614no—
557C22×D4—611no—
558C22×D4—1221no—
559C22×D4—1221no—
560C22×D4—1221no—
561C22×D4—1222no—
562C22×D4—2444no—
563C22×D4D24411yescharacteristic
564C23×C4—1221no—
565C23×C4—1221no—
566C23×C4C22×D6111yescharacteristic
567C23×C4C22×D6111yescharacteristic
568AGL(1,ℤ/8)—2448no—
569#135—2448no—
570C2×Q16—614no—
571C2×SD16—614no—
572C2×SD16—614no—
573C2×SD16—614no—
574C2×D8—614no—
575C2×D8—614no—
576C2×M16C22×D6114yes—
577C22×C8C22×D6114yescomplemented
578C4⋊Q8—611no—
579C4⋊Q8—611no—
580C4⋊Q8—611no—
581#127—611no—
582#127—1222no—
583#126—1222no—
584#126—1222no—
585#125—1221no—
586#124—612no—
587#124—612no—
588#124—1222no—
589#124—1222no—
590#124—1222no—
591#124—1221no—
592#124—1221no—
593#124—1221no—
594#123—1222no—
595#123—1222no—
596#123—1224no—
597#123—1224no—
598#123—1222no—
599#123—1222no—
600C22⋊Q8—614no—
601C22⋊Q8—612no—
602C22⋊Q8—612no—
603C22⋊Q8—612no—
604C22⋊Q8—1222no—
605C22⋊Q8—1221no—
606#121—614no—
607#121—612no—
608#121—612no—
609#121—612no—
610#121—1222no—
611#121—1222no—
612#121—1222no—
613#121—1221no—
614#121—1224no—
615#121—1224no—
616#121—1222no—
617#121—1222no—
618#120—1222no—
619#120—1222no—
620#120—1224no—
621#120—1224no—
622C4×Q8—612no—
623C4×Q8—1222no—
624C4×Q8—1221no—
625C4×D4—612no—
626C4×D4—612no—
627C4×D4—612no—
628C4×D4—1222no—
629C4×D4—1222no—
630C4×D4—1222no—
631C4×D4—1222no—
632C4×D4—1222no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4D24412yes—
637C4×D4D24412yes—
638C4×D4C22×D6112yes—
639C4×D4C22×D6112yes—
640#117—612no—
641#117—612no—
642#117—1221no—
643#117—1222no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4—1222no—
647C2×C4⋊C4D24411yescharacteristic
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1224no—
654C2×C22⋊C4—1224no—
655C2×C22⋊C4D24411yescharacteristic
656C2×C22⋊C4D24411yescharacteristic
657C2×C42C22×D6111yescharacteristic
658#107—614no—
659#106—614no—
660C4⋊C8C22×D6112yescomplemented
661C4⋊C8C22×D6112yescomplemented
662#103—614no—
663#103—614no—
664#103—614no—
665#102—614no—
666#102—614no—
667#102—614no—
668#102—614no—
669#102—614no—
670C22⋊C8C22×D6112yes—
671C22⋊C8C22×D6112yes—
672C22⋊C8C22×D6114yes—
673C22⋊C8C22×D6114yescomplemented
674#97C22×D6112yescomplemented
675#97C22×D6112yescomplemented
676C24—1221no—
677C24—1224no—
678C24—1221no—
679C24—4882no—
680C24—2444no—
681C24—2444no—
682C24C2×D24411yescharacteristic
683C24C2×D24411yescharacteristic
684#41—1228no—
685#41—2444no—
686#41—2444no—
687#41—2444no—
688#41—2444no—
689#41—2448no—
690C2×Q8—612no—
691C2×Q8—612no—
692C2×Q8—1221no—
693C2×Q8—1221no—
694C2×Q8—1221no—
695C2×Q8—2442no—
696C2×D4—42no—
697C2×D4—612no—
698C2×D4—612no—
699C2×D4—612no—
700C2×D4—1224no—
701C2×D4—1228no—
702C2×D4—1222no—
703C2×D4—1222no—
704C2×D4—1224no—
705C2×D4—1222no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—1224no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1224no—
713C2×D4—1221no—
714C2×D4—4882no—
715C2×D4—2444no—
716C2×D4—2442no—
717C2×D4—2448no—
718C2×D4—2444no—
719C2×D4—2444no—
720C2×D4C2×D24412yes—
721C2×D4C2×D24412yes—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1222no—
727C22×C4—1222no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1224no—
731C22×C4—1222no—
732C22×C4—4882no—
733C22×C4—2444no—
734C22×C4C2×D24411yescharacteristic
735C22×C4C2×D24411yescharacteristic
736C22×C4C2×D24411yescharacteristic
737C22×C4C2×D24411yescharacteristic
738C22×C4C2×D24412yes—
739C22×C4C2×D24412yes—
740C22×C4C23×D6111yescharacteristic
741C22×C4C23×D6112yes—
742C22×C4C23×D6112yes—
743Q16—2444no—
744SD16—1228no—
745SD16—2444no—
746SD16—2444no—
747D8—1228no—
748D8—2444no—
749M16—44no—
750C2×C8—44no—
751C2×C8C23×D6114yes—
752C2×C8C23×D6114yes—
753C4⋊C4—612no—
754C4⋊C4—612no—
755C4⋊C4—612no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1222no—
759C4⋊C4—1222no—
760C4⋊C4—1224no—
761C4⋊C4—1222no—
762C4⋊C4—1222no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4C2×D24412yes—
767C4⋊C4C2×D24412yes—
768C22⋊C4—1224no—
769C22⋊C4—1222no—
770C22⋊C4—1222no—
771C22⋊C4—1222no—
772C22⋊C4—1222no—
773C22⋊C4—1222no—
774C22⋊C4—1224no—
775C22⋊C4—1222no—
776C22⋊C4—1222no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—1222no—
783C22⋊C4—1222no—
784C22⋊C4—1222no—
785C22⋊C4C2×D24412yes—
786C22⋊C4C2×D24412yes—
787C22⋊C4C2×D24412yes—
788C22⋊C4C2×D24412yes—
789C42—1222no—
790C42—1222no—
791C42—1222no—
792C42C2×D24411yescharacteristic
793C42C2×D24411yescharacteristic
794C42C23×D6111yescharacteristic
795C42C23×D6111yescharacteristic
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—1224no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—4884no—
807C23—48816no—
808C23—2448no—
809C23—2442no—
810C23—2442no—
811C23—2448no—
812C23—2442no—
813C23—2442no—
814C23—2442no—
815C23C22×D24412yes—
816C23C22×D24412yes—
817C23C22×D24411yescharacteristic
818Q8—1224no—
819Q8—1224no—
820Q8—4881no—
821Q8—2442no—
822Q8—2442no—
823D4—42no—
824D4—42no—
825D4—614no—
826D4—1224no—
827D4—1222no—
828D4—1224no—
829D4—1224no—
830D4—4881no—
831D4—4882no—
832D4—4882no—
833D4—4884no—
834D4—4882no—
835D4—4882no—
836D4—2448no—
837D4—2442no—
838D4—2442no—
839D4—2448no—
840D4—2444no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—4882no—
856C2×C4—4882no—
857C2×C4—4882no—
858C2×C4—4882no—
859C2×C4—2448no—
860C2×C4—2444no—
861C2×C4—2442no—
862C2×C4—2442no—
863C2×C4C22×D24411yescharacteristic
864C2×C4C22×D24412yes—
865C2×C4C22×D24412yes—
866C2×C4C22×D24411yescharacteristic
867C2×C4C22×D24411yescharacteristic
868C2×C4C22×D24411yescharacteristic
869C2×C4C22×D24411yescharacteristic
870C2×C4C24×D6111yescharacteristic
871C8—24no—
872C8—24no—
873C22—21no—
874C22—21no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—44no—
882C22—82no—
883C22—1224no—
884C22—4884no—
885C22—48816no—
886C22—2448no—
887C22—2442no—
888C22—2442no—
889C22—2442no—
890C22—2442no—
891C22—2442no—
892C22—2442no—
893C22—2442no—
894C22—2442no—
895C22#1684056212yes—
896C22C23×D24411yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—22no—
903C4—22no—
904C4—2442no—
905C4—2442no—
906C4—2442no—
907C4—2442no—
908C4—2442no—
909C4H(5,𝔽2)×D6112yes—
910C2—22no—
911C2—42no—
912C2—42no—
913C2—4882no—
914C2—4882no—
915C2—2444no—
916C2#2145945511yescharacteristic
917C2C2×#1684056211yescharacteristic
918C2#2146060011yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2973C2
socleC22×C61C23×D4
hypercenter#2973D61
hypocenterC61#61576
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. #21459671C2semidirect
2. C2×#16840408C2semidirect
3. #21457977C2semidirect
4. #21457857C2semidirect
5. #21457364C2semidirect
6. #21457349C2semidirect
7. #21456824C2semidirect
8. #21456808C2semidirect
9. #21456651C2semidirect
10. #21456586C2semidirect
11. #21455919C2semidirect
12. #21455911C2semidirect
13. #21455049C2semidirect
14. #21455041C2semidirect
15. C61×#2973C2semidirect
18. C2×#14519805C22semidirect
19. C2×#14519799C22semidirect
21. #16840482C22semidirect
22. #16840477C22semidirect
24. #16840433C22semidirect
25. #16840417C22semidirect
33. #16840319C22semidirect
34. #16840312C22semidirect
37. #16840273C22semidirect
46. #16840156C22semidirect
47. #16840151C22semidirect
48. #16840122C22semidirect
49. #16840122C22semidirect
50. #16840104C22semidirect
51. #16840098C22semidirect
52. #16840087C22semidirect
53. #16840081C22semidirect
54. #16840053C22semidirect
55. #16840043C22semidirect
56. #16840020C22semidirect
57. #16840008C22semidirect
58. #16839998C22semidirect
59. #16839991C22semidirect
60. #16839985C22semidirect
61. #16839978C22semidirect
62. #16839968C22semidirect
63. #16839958C22semidirect
64. #16839926C22semidirect
65. #16839926C22semidirect
66. #16839920C22semidirect
69. #16839915C22semidirect
70. #16839909C22semidirect
71. #16839909C22semidirect
72. #16839903C22semidirect
75. #16839898C22semidirect
76. #16839875C22semidirect
77. #16839864C22semidirect
78. #16839768C22semidirect
79. #16839759C22semidirect
81. C61×#435C22semidirect
82. C61×#435C22semidirect
83. C61×#432C22semidirect
84. C61×#432C22semidirect
86. C2×C22⋊C8×C61C22semidirect
93. C2×#11758222C23semidirect
107. C2×Dic244C23semidirect
110. C2×#11758190C23semidirect
113. #14519777C23semidirect
114. #14519777C23semidirect
115. #14519777C23semidirect
116. #14519774C23semidirect
140. #14519756C23semidirect
146. #14519751C23semidirect
158. C4×Dic122C23semidirect
165. C4×D244C23semidirect
173. #14519736C23semidirect
185. #14519711C23semidirect
186. #14519709C23semidirect
187. #14519702C23semidirect
188. #14519702C23semidirect
189. #14519702C23semidirect
194. #14519699C23semidirect
199. C22×C8×C61C23semidirect
208. C4⋊C8×C61C23semidirect
209. C4⋊C8×C61C23semidirect
213. C22⋊C8×C61C23semidirect
214. #97×C61C23semidirect
215. #97×C61C23semidirect
465. #2973D61semidirect
538. #435C2×D61semidirect
539. #435C2×D61semidirect
540. #432C2×D61semidirect
541. #432C2×D61semidirect
545. C2×C22⋊C8C2×D61semidirect
546. C61#61576semidirect
577. C22×C8C22×D61semidirect
660. C4⋊C8C22×D61semidirect
661. C4⋊C8C22×D61semidirect
673. C22⋊C8C22×D61semidirect
674. #97C22×D61semidirect
675. #97C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214596712
C2×#168404082
#214579772
#214578572
#214573642
#214573492
#214568242
#214568082
#214566512
#214565862
#214559192
#214559112
#214550492
#214550412
C61×#29732
#6157661