Finite Group Databasebeta

← #29748640

Subgroups — #29748640

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448888C211yesmaximal, characteristic
2#21447233C211yesmaximal, characteristic
3#21447190C211yesmaximal, characteristic
4#21447060C211yesmaximal, characteristic
5#21447060C211yesmaximal, characteristic
6#21446494C211yesmaximal, characteristic, complemented
7#21446453C211yesmaximal, characteristic, complemented
8#21446401C211yesmaximal, characteristic, complemented
9#21446394C211yesmaximal, characteristic, complemented
10#21446378C211yesmaximal, characteristic, complemented
11#21446086C211yesmaximal, characteristic, complemented
12#21446079C211yesmaximal, characteristic
13#21445831C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic
15C61×#2508C211yesmaximal, characteristic, complemented
16C2×#14519765C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519700C2211yescharacteristic
23C2×#14519700C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31#16839668C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839652—21no—
34#16839651—21no—
35#16839633—21no—
36C4×C4⋊Dic61C2211yescharacteristic
37#16839609—21no—
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C61×#400—21no—
49C61×#398—21no—
50C61×#389C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#387—21no—
55C61×#382—21no—
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519765—22no—
67#14519765—22no—
68C4×Dic122—22no—
69C4×Dic122—41no—
70C4×D244—22no—
71C4×D244—41no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82#14519708—22no—
83#14519708—22no—
84C4⋊#92418—41no—
85#14519700—22no—
86#14519700—22no—
87#14519700—22no—
88#14519700—41no—
89#14519697—22no—
90#14519697—22no—
91#14519697—22no—
92#14519697—41no—
93C4×#92418—41no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61D411yescharacteristic
102C2×C4⋊C4×C61D411yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C42×C61—21no—
108C2×C42×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110C2×C42×C61C2311yescharacteristic
111#95×C61—21no—
112#95×C61—21no—
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C23×D61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244#4112yes—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C2×C4×D61—81no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122#4112yes—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61—42no—
160C4⋊C4×C61—81no—
161C4⋊C4×C61—81no—
162C4⋊C4×C61—81no—
163C4⋊C4×C61#4112yes—
164C42×C61—21no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—42no—
171#11758198—24no—
172#11758198—24no—
173#11758198—42no—
174#11758198—42no—
175#11758198—81no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61#4112yes—
180#11758196—42no—
181C4×Dic61—42no—
182C4×Dic61—81no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C23×C61C22×D411yescharacteristic
196C22×D61—22no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—22no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61#13512yes—
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61H(5,𝔽2)11yescharacteristic
238C2×C4×C612−1+411yescharacteristic
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248D244—22no—
249D244—22no—
250D244—41no—
251D244—41no—
252C4×D61—84no—
253Dic122—22no—
254Dic122—22no—
255Dic122—41no—
256Dic122—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#26760—611nomaximal, Sylow
262C22×C61#52511yescharacteristic
263C22×C61#54611yescharacteristic
264C22×C61#54811yescharacteristic
265C22×C61C2×#13511yescharacteristic
266C22×C61#57511yescharacteristic
267C22×C61#57711yescharacteristic
268C22×C61#57711yescharacteristic
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—81no—
275C2×D61—81no—
276C4×C61—22no—
277C4×C61—41no—
278C4×C61—42no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61#52911yescharacteristic
287C4×C61#53911yescharacteristic
288C4×C61#55211yescharacteristic
289C4×C61#55311yescharacteristic
290Dic61—42no—
291Dic61—42no—
292Dic61—81no—
293#2508D6111yescharacteristic, complemented
294#2367—611no—
295#2073—611no—
296#2065—611no—
297#2042—611no—
298#2042—611no—
299#1933—611no—
300#1927—611no—
301#1920—611no—
302#1919—611no—
303#1916—611no—
304#1865—611no—
305#1864—611no—
306#1805—611no—
307C4×#102—611no—
308C2×C61#246011yescharacteristic
309C2×C61#310211yescharacteristic
310C2×C61#312511yescharacteristic
311C2×C61#329611yescharacteristic
312C2×C61#332111yescharacteristic
313C2×C61#336011yescharacteristic
314C2×C61#337111yescharacteristic
315D61—82no—
316C2×#124—611no—
317C2×C4×Q8—611no—
318C2×C4×D4—611no—
319C2×#106—611no—
320C2×#106—611no—
321C2×C4⋊C8—611no—
322C2×#103—611no—
323C2×#103—611no—
324C2×#103—611no—
325C2×#103—611no—
326C2×#102—611no—
327C2×#102—611no—
328C2×#102—611no—
329C2×#102—611no—
330C2×C4×C8—611no—
331#400—21no—
332#398—21no—
333#391—611no—
334#390—611no—
335#389C2×D6111yescharacteristic
336#389C2×D6111yescharacteristic
337#389C2×D6111yescharacteristic
338#389C2×D6111yescharacteristic
339#388—1221no—
340#388—1221no—
341#387—21no—
342#385—1221no—
343#382—21no—
344#382C2×D6111yescharacteristic
345C4×C4⋊C4—611no—
346C4×C4⋊C4C2×D6111yescharacteristic
347C4×C4⋊C4C2×D6111yescharacteristic
348C4×C22⋊C4—1221no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#336—611no—
356#336—611no—
357#336—611no—
358#336—611no—
359C61#2676011yescharacteristic, complemented, Sylow
360C22×Q8—611no—
361C22×D4—611no—
362C23×C4—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—611no—
367#124—1222no—
368#124—1222no—
369C4×Q8—1222no—
370C4×Q8—2441no—
371C4×D4—1222no—
372C4×D4—2441no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4C22⋊D6111yescharacteristic
381C2×C4⋊C4C22⋊D6111yescharacteristic
382C2×C4⋊C4C22×D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—21no—
392C2×C42—1221no—
393C2×C42—1221no—
394C2×C42C22×D6111yescharacteristic
395C2×C42C22×D6111yescharacteristic
396C2×C42C22×D6111yescharacteristic
397#106—1222no—
398#106—1222no—
399C4⋊C8—2441no—
400#103—1222no—
401#103—1222no—
402#103—1222no—
403#103—2441no—
404#102—1222no—
405#102—1222no—
406#102—1222no—
407#102—2441no—
408C4×C8—2441no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95C22⋊D6111yescharacteristic
420#95C22⋊D6111yescharacteristic
421C24—1221no—
422C2×Q8—612no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×D4—612no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1221no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—4881no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4C2×C22⋊D6111yescharacteristic
445C22×C4C2×C22⋊D6111yescharacteristic
446C22×C4C2×C22⋊D6111yescharacteristic
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450C22×C4C23×D6111yescharacteristic
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—42no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—612no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—2442no—
481C4⋊C4#1175822612yes—
482C22⋊C4—1224no—
483C22⋊C4—1224no—
484C22⋊C4—4881no—
485C22⋊C4—2442no—
486C22⋊C4—2442no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—4881no—
495C42—2442no—
496C23—1222no—
497C23—2441no—
498C23—2441no—
499C23—2441no—
500C23—2441no—
501C23—2441no—
502C23—2441no—
503C23C22×C22⋊D6111yescharacteristic
504Q8—1222no—
505Q8—1222no—
506Q8—2441no—
507Q8—2441no—
508D4—1222no—
509D4—1222no—
510D4—2441no—
511D4—2441no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—4884no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4#1451979712yes—
552C2×C4#41×D6111yescharacteristic
553C2×C4#41×D6111yescharacteristic
554C2×C4#41×D6111yescharacteristic
555C2×C4C2×#1175822611yescharacteristic
556C2×C4#1451982311yescharacteristic
557C2×C4#1451982511yescharacteristic
558C8—2441no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C22—4881no—
563C22—4881no—
564C22—4881no—
565C22—4881no—
566C22—2442no—
567C22—2442no—
568C22—2442no—
569C22#1684026911yescharacteristic
570C22#1684040011yescharacteristic
571C22#1684042311yescharacteristic
572C22C2×#1451979711yescharacteristic
573C22#1684056011yescharacteristic
574C22#1684057011yescharacteristic
575C22#1684057311yescharacteristic
576C4—22no—
577C4—42no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—4881no—
587C4—2442no—
588C4—2442no—
589C4#1684029711yescharacteristic
590C4#1684036011yescharacteristic
591C4#1684044411yescharacteristic
592C4#1684046511yescharacteristic
593C2—4882no—
594C2#2144976711yescharacteristic
595C2#2145583111yescharacteristic
596C2#2145609011yescharacteristic
597C2#2145764811yescharacteristic
598C2#2145799911yescharacteristic
599C2#2145846811yescharacteristic
600C2#2145858711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2508C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2508D61
hypocenterC61#26760
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2508

Complements

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

NH ≅ G/Ntype
6. #21446494C2semidirect
7. #21446453C2semidirect
8. #21446401C2semidirect
9. #21446394C2semidirect
10. #21446378C2semidirect
11. #21446086C2semidirect
13. #21445831C2semidirect
15. C61×#2508C2semidirect
293. #2508D61semidirect
359. C61#26760semidirect

Maximal subgroups

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

subgroupindex
#214488882
#214472332
#214471902
#214470602
#214464942
#214464532
#214464012
#214463942
#214463782
#214460862
#214460792
#214458312
C4×#145196972
C61×#25082
#2676061