Finite Group Databasebeta

← #29739118

Subgroups — #29739118

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448766C211yesmaximal, characteristic
2#21447348C211yesmaximal, characteristic
3#21447343C211yesmaximal, characteristic
4#21447204C211yesmaximal, characteristic
5#21447190C211yesmaximal, characteristic
6#21446585C211yesmaximal, characteristic, complemented
7#21446577C211yesmaximal, characteristic, complemented
8#21446575C211yesmaximal, characteristic, complemented
9#21446543C211yesmaximal, characteristic, complemented
10#21446408C211yesmaximal, characteristic, complemented
11#21446401C211yesmaximal, characteristic, complemented
12#21445988C211yesmaximal, characteristic, complemented
13#21445826C211yesmaximal, characteristic
14#21445647C211yesmaximal, characteristic
15C61×#2570C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17C2×#14519735—21no—
18C2×#14519710C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839654—21no—
35#16839654—21no—
36#16839632C2211yescharacteristic
37#16839619—21no—
38C4×C4⋊Dic61C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C61×#400—21no—
49C61×#398—21no—
50C61×#389C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#387—21no—
53C61×#387—21no—
54C61×#384C2211yescharacteristic
55C61×#382C2211yescharacteristic
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C4×D244—22no—
66C4×D244Q814yes—
67#14519735—44no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80#14519710—22no—
81#14519710—41no—
82#14519710—41no—
83#14519710—41no—
84#14519708—22no—
85#14519708—41no—
86C4⋊#92418—22no—
87C4⋊#92418—22no—
88C4⋊#92418—22no—
89#14519697—22no—
90#14519697—22no—
91#14519697—41no—
92#14519697—41no—
93#14519688—22no—
94#14519684—21no—
95#14519684—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61D411yescharacteristic
101C2×C4⋊C4×C61D411yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C42×C61—21no—
107C2×C42×C61C2311yescharacteristic
108C2×C42×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110#95×C61—21no—
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×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119C23×D61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244C2×Q812yes—
140C2×C4×D61—24no—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—42no—
154C4⋊C4×C61—42no—
155C4⋊C4×C61—81no—
156C4⋊C4×C61—81no—
157C42×C61—21no—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—81no—
162C42×C61C2×Q812yes—
163C42×C61#4112yes—
164#11758198—24no—
165#11758198—42no—
166#11758198—42no—
167#11758198—81no—
168#11758198—81no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—42no—
175C4⋊Dic61—81no—
176C4⋊Dic61C2×Q812yes—
177C4×Dic61—42no—
178C4×Dic61—42no—
179C2×#92418—21no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418#4112yes—
190C2×#92418#4112yes—
191C23×C61C22×D411yescharacteristic
192C22×D61—22no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
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—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C22⋊Q812yes—
227C2×C4×C61C22⋊Q812yes—
228C2×C4×C61AGL(1,ℤ/8)12yes—
229C2×C4×C61C22×Q811yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61H(5,𝔽2)11yescharacteristic
234C2×C4×C612−1+411yescharacteristic
235C2×Dic61—22no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244D244—22no—
245D244—22no—
246D244—41no—
247D244—41no—
248C4×D61—48no—
249#92418—22no—
250#92418—22no—
251#92418—41no—
252#92418—41no—
253#26098—611nomaximal, Sylow
254C22×C61C2×C22⋊Q811yescharacteristic
255C22×C61#54711yescharacteristic
256C22×C61#55011yescharacteristic
257C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C61#57511yescharacteristic
259C22×C61#57611yescharacteristic
260C22×C61#57811yescharacteristic
261C2×D61—42no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—81no—
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C4×C61—22no—
269C4×C61—22no—
270C4×C61—22no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61#53311yescharacteristic
279C4×C61#54411yescharacteristic
280C4×C61#55211yescharacteristic
281C4×C61#55311yescharacteristic
282Dic61—42no—
283Dic61—81no—
284Dic61—81no—
285#2570D6111yescharacteristic, complemented
286#2354—611no—
287#2093—611no—
288#2092—611no—
289#2067—611no—
290#2065—611no—
291#1949—611no—
292#1947—611no—
293#1947—611no—
294#1940—611no—
295#1921—611no—
296#1920—611no—
297#1847—611no—
298#1804—611no—
299#1762—611no—
300C2×C61#244111yescharacteristic
301C2×C61#307711yescharacteristic
302C2×C61#308311yescharacteristic
303C2×C61#334311yescharacteristic
304C2×C61#334711yescharacteristic
305C2×C61#339911yescharacteristic
306C2×C61#340211yescharacteristic
307D61—82no—
308C2×C4×D4—611no—
309C2×#117—1221no—
310C2×#107—611no—
311C2×#107—611no—
312C2×#107—611no—
313C2×#107—611no—
314C2×#106—611no—
315C2×#106—611no—
316C2×C4⋊C8—611no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×#102—611no—
320C2×#102—611no—
321C2×#102—611no—
322C2×#102—611no—
323C2×#97—611no—
324#400—21no—
325#398—21no—
326#390—611no—
327#390—611no—
328#389C2×D6111yescharacteristic
329#389C2×D6111yescharacteristic
330#388—1221no—
331#388—1221no—
332#387—21no—
333#387—21no—
334#384—611no—
335#384C2×D6111yescharacteristic
336#382C2×D6111yescharacteristic
337#382C2×D6111yescharacteristic
338#380—1221no—
339C4×C4⋊C4—611no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4C2×D6111yescharacteristic
342C4×C4⋊C4C2×D6111yescharacteristic
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#336—611no—
350#336—611no—
351C61#2609811yescharacteristic, complemented, Sylow
352C22×D4—611no—
353C23×C4—1221no—
354C22×C8—611no—
355C22×C8—611no—
356C22×C8—611no—
357C22×C8—611no—
358C4×D4—614no—
359C4×D4—1222no—
360#117—2444no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—1221no—
369C2×C4⋊C4—1221no—
370C2×C4⋊C4C22⋊D6111yescharacteristic
371C2×C4⋊C4C22⋊D6111yescharacteristic
372C2×C4⋊C4C22×D6111yescharacteristic
373C2×C4⋊C4C22×D6111yescharacteristic
374C2×C4⋊C4C22×D6111yescharacteristic
375C2×C4⋊C4C22×D6111yescharacteristic
376C2×C22⋊C4—1221no—
377C2×C22⋊C4—1221no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C42—21no—
382C2×C42—1221no—
383C2×C42—1221no—
384C2×C42C22×D6111yescharacteristic
385C2×C42C22×D6111yescharacteristic
386C2×C42C22×D6111yescharacteristic
387#107—1222no—
388#107—2441no—
389#107—2441no—
390#107—2441no—
391#106—1222no—
392#106—2441no—
393C4⋊C8—1222no—
394C4⋊C8—1222no—
395C4⋊C8—1222no—
396#102—1222no—
397#102—1222no—
398#102—2441no—
399#102—2441no—
400#97—1222no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—1221no—
409#95—1221no—
410#95C22⋊D6111yescharacteristic
411#95C22⋊D6111yescharacteristic
412C24—1221no—
413C2×D4—612no—
414C2×D4—1221no—
415C2×D4—1221no—
416C2×D4—1221no—
417C2×D4—1221no—
418C2×D4—1221no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—1221no—
424C22×C4—1224no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4C2×C22⋊D6111yescharacteristic
430C22×C4C2×C22⋊D6111yescharacteristic
431C22×C4C2×C22⋊D6111yescharacteristic
432C22×C4C2×C22⋊D6111yescharacteristic
433C22×C4C2×C22⋊D6111yescharacteristic
434C22×C4C2×C22⋊D6111yescharacteristic
435C22×C4C23×D6111yescharacteristic
436C2×C8—612no—
437C2×C8—612no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—612no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—4881no—
469C4⋊C4—2442no—
470C22⋊C4—1224no—
471C22⋊C4—4881no—
472C22⋊C4—4881no—
473C22⋊C4—2442no—
474C22⋊C4—2442no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—2442no—
481C42—2442no—
482C42Q8×D6112yes—
483C42#1175822612yes—
484C23—1222no—
485C23—2441no—
486C23—2441no—
487C23—2441no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23C22×C22⋊D6111yescharacteristic
492D4—1222no—
493D4—1222no—
494D4—2441no—
495D4—2441no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—1222no—
524C2×C4—2448no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4#1451975312yes—
534C2×C4#1451975312yes—
535C2×C4#1451980212yes—
536C2×C4C2×Q8×D6111yescharacteristic
537C2×C4#41×D6111yescharacteristic
538C2×C4#41×D6111yescharacteristic
539C2×C4C2×#1175822611yescharacteristic
540C2×C4#1451982311yescharacteristic
541C2×C4#1451982411yescharacteristic
542C8—1222no—
543C8—1222no—
544C8—2441no—
545C8—2441no—
546C22—4881no—
547C22—4881no—
548C22—4881no—
549C22—4881no—
550C22—2442no—
551C22—2442no—
552C22—2442no—
553C22C2×#1451975311yescharacteristic
554C22#1684041111yescharacteristic
555C22#1684043111yescharacteristic
556C22C2×#1451980211yescharacteristic
557C22#1684056011yescharacteristic
558C22#1684056511yescharacteristic
559C22#1684057711yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—4881no—
571C4—4881no—
572C4—2442no—
573C4#1684031811yescharacteristic
574C4#1684039211yescharacteristic
575C4#1684045011yescharacteristic
576C4#1684046511yescharacteristic
577C2—4882no—
578C2#2144952811yescharacteristic
579C2#2145561211yescharacteristic
580C2#2145566611yescharacteristic
581C2#2145825911yescharacteristic
582C2#2145831311yescharacteristic
583C2#2145885711yescharacteristic
584C2#2145889411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2570C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2570D61
hypocenterC61#26098
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2570

Complements

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

NH ≅ G/Ntype
6. #21446585C2semidirect
7. #21446577C2semidirect
8. #21446575C2semidirect
9. #21446543C2semidirect
10. #21446408C2semidirect
11. #21446401C2semidirect
12. #21445988C2semidirect
15. C61×#2570C2semidirect
285. #2570D61semidirect
351. C61#26098semidirect

Maximal subgroups

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

subgroupindex
#214487662
#214473482
#214473432
#214472042
#214471902
#214465852
#214465772
#214465752
#214465432
#214464082
#214464012
#214459882
#214458262
#214456472
C61×#25702
#2609861