Finite Group Databasebeta

← #29847358

Subgroups — #29847358

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451786C211yesmaximal, characteristic, complemented
2#21451783C213yesmaximal, complemented
3#21451781C211yesmaximal, characteristic, complemented
4#21451778C213yesmaximal, complemented
5#21451777C211yesmaximal, characteristic, complemented
6#21451776C211yesmaximal, characteristic, complemented
7#21451773C213yesmaximal, complemented
8#21451771C213yesmaximal, complemented
9#21449120C213yesmaximal, complemented
10#21449119C213yesmaximal, complemented
11#21449117C211yesmaximal, characteristic, complemented
12#21448305C213yesmaximal
13#21448299C213yesmaximal, complemented
14#376×D61C211yesmaximal, characteristic, complemented
15C61×#2401C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519734C2213yes—
18C2×C42×D61C2213yes—
19C61⋊#401C2211yescharacteristic
20C61⋊#401C2213yes—
21C61⋊#401C2213yes—
22#16839704C2213yes—
23#16839704C2213yes—
24#16839703C2213yes—
25#16839703C2213yes—
26#16839702C2213yes—
27#16839701C2213yes—
28#16839700C2213yes—
29#16839691C2213yes—
30#16839691C2213yes—
31#16839690C2213yes—
32#16839690C2213yes—
33#16839689C2213yes—
34#16839688C2213yes—
35#16839687C2213yes—
36#16839686C2211yescharacteristic
37#16839685C2213yes—
38#16839684C2213yes—
39#16839666C2213yes—
40#16839666C2213yes—
41#16839662C2213yes—
42#16839662C2213yes—
43#16839659C2213yes—
44#16839659C2213yes—
45#16839657C2213yes—
46#16839657C2213yes—
47#16839640C2213yes—
48#16839640C2213yes—
49#16839638C2213yes—
50#16839638C2213yes—
51#16839636C2213yes—
52#16839636C2213yes—
53#16839633C2213yes—
54#16839633C2213yes—
55C4×#11758196C2213yes—
56C4×#11758196C2213yes—
57C4×C4⋊Dic61C2213yes—
58C4×#11758198C2213yes—
59C4×#11758198C2213yes—
60C4×C22⋊Dic61C2213yes—
61#16839608C2213yes—
62#16839607C2213yes—
63#16839607C2211yescharacteristic
64#95×D61C2211yescharacteristic
65#95×D61C2213yes—
66C61×#401C2211yescharacteristic
67C61×#400C2213yes—
68C61×#397C2213yes—
69C61×#396C2211yescharacteristic
70C4×C4⋊C4×C61C2213yes—
71C4×C22⋊C4×C61C2213yes—
72C61×#376C2211yescharacteristic
73C2×#11758222—212no—
74C22×Dic122C2311yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61C2311yescharacteristic
77C22×C22⋊D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C22×C4×D61C2313yes—
80C22×C4×D61C2313yes—
81C22×C4×D61C2311yescharacteristic
82#14519734—212no—
83C2×C4⋊Dic61C2313yes—
84C2×C4⋊Dic61C2313yes—
85C2×#11758196C2313yes—
86C2×#11758196C2313yes—
87C2×#11758196C2313yes—
88C2×#11758196C2313yes—
89C2×#11758196C2313yes—
90C2×#11758196C2313yes—
91C2×C22⋊Dic61C2313yes—
92C2×C22⋊Dic61C2313yes—
93C2×#11758198C2313yes—
94C2×#11758198C2313yes—
95C2×#11758198C2313yes—
96C2×#11758198C2313yes—
97C2×#11758198C2313yes—
98C2×#11758198C2313yes—
99C2×C4×Dic61C2313yes—
100C2×C4×Dic61C2313yes—
101C2×C4×Dic61C2313yes—
102C2×C4×Dic61C2313yes—
103C42×D61—212no—
104#14519684C2313yes—
105#14519684C2313yes—
106#14519684C2313yes—
107#14519684C2313yes—
108#14519684C2313yes—
109#14519684C2313yes—
110#14519684C2313yes—
111#14519684C2313yes—
112#14519684C2313yes—
113#14519684C2313yes—
114#14519684C2313yes—
115#14519684C2313yes—
116#14519684C2313yes—
117#14519684C2313yes—
118#14519684C2313yes—
119#14519684C2313yes—
120C23×C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2313yes—
122C2×C4⋊C4×C61C2313yes—
123C2×C22⋊C4×C61C2313yes—
124C2×C22⋊C4×C61C2313yes—
125C2×C42×C61C2313yes—
126C2×C42×C61C2313yes—
127#95×C61C2311yescharacteristic
128#95×C61C2313yes—
129#95×C61C2313yes—
130#95×C61C2313yes—
131#95×C61C2313yes—
132#95×C61C2313yes—
133C24×C61C2411yescharacteristic
134C23×D61C2411yescharacteristic
135C23×D61C2411yescharacteristic
136C22×C4×C61—26no—
137C22×C4×C61C2413yes—
138C22×C4×C61C2413yes—
139C22×C4×C61C2411yescharacteristic
140C22×C4×C61C2413yes—
141C22×C4×C61C2413yes—
142C22×C4×C61C2411yescharacteristic
143C2×C22⋊D61—26no—
144C2×C22⋊D61—26no—
145C22×Dic61C2411yescharacteristic
146C22×Dic61C2413yes—
147C22×Dic61C2413yes—
148C22×Dic61C2413yes—
149C22×Dic61C2413yes—
150C22×Dic61C2411yescharacteristic
151#11758222—416no—
152C2×D244—26no—
153C2×C4×D61—26no—
154C2×C4×D61—26no—
155C2×C4×D61—26no—
156C2×C4×D61—43no—
157C2×C4×D61—43no—
158C2×C4×D61—43no—
159C2×C4×D61—43no—
160C2×C4×D61#41112yes—
161C2×Dic122—26no—
162C4⋊C4×C61—43no—
163C4⋊C4×C61—43no—
164C22⋊C4×C61—43no—
165C22⋊C4×C61—43no—
166C42×C61—26no—
167C42×C61—26no—
168C22⋊Dic61—43no—
169C22⋊Dic61—43no—
170#11758198—26no—
171#11758198—26no—
172#11758198—43no—
173#11758198—43no—
174#11758198—43no—
175#11758198—43no—
176C4⋊Dic61—43no—
177C4⋊Dic61—43no—
178#11758196—26no—
179#11758196—26no—
180#11758196—43no—
181#11758196—43no—
182#11758196—43no—
183#11758196—43no—
184C4×Dic61—26no—
185C4×Dic61—26no—
186C4×Dic61—26no—
187C4×Dic61—26no—
188C23×C61—23no—
189C23×C61—23no—
190C23×C61—21no—
191C23×C61C2511yescharacteristic
192C22×D61—23no—
193C22×D61—21no—
194C22×D61—23no—
195C22×D61—23no—
196C22×D61—21no—
197C22×D61C2×#4116yes—
198C2×C4×C61—23no—
199C2×C4×C61—23no—
200C2×C4×C61—23no—
201C2×C4×C61—23no—
202C2×C4×C61—23no—
203C2×C4×C61—23no—
204C2×C4×C61—23no—
205C2×C4×C61—23no—
206C2×C4×C61—23no—
207C2×C4×C61—23no—
208C2×C4×C61—23no—
209C2×C4×C61—23no—
210C2×C4×C61—23no—
211C2×C4×C61—44no—
212C2×C4×C61C2×#4116yes—
213C22⋊D61—44no—
214C22⋊D61—44no—
215C2×Dic61—23no—
216C2×Dic61—23no—
217C2×Dic61—23no—
218C2×Dic61—23no—
219C2×Dic61—23no—
220C2×Dic61—23no—
221C2×Dic61—23no—
222C2×Dic61—23no—
223C2×Dic61—23no—
224C2×Dic61—23no—
225C2×Dic61—23no—
226C2×Dic61—23no—
227C2×Dic61—23no—
228C2×Dic61C2×#4116yes—
229D244—44no—
230C4×D61—412no—
231C4×D61—412no—
232C4×D61—44no—
233C4×D61#126116yes—
234Dic122—44no—
235#34639—611nomaximal, Sylow
236C22×C61—41no—
237C22×C61—43no—
238C22×C61—43no—
239C22×C61C22×#4113yes—
240C22×C61#58513yes—
241C22×C61#58511yescharacteristic
242C2×D61—26no—
243C2×D61—26no—
244C2×D61—41no—
245C2×D61—43no—
246C2×D61—43no—
247C2×D61C2×#12614yes—
248C4×C61—41no—
249C4×C61—43no—
250C4×C61—43no—
251C4×C61—43no—
252C4×C61—43no—
253C4×C61C2×#12614yes—
254Dic61—41no—
255Dic61—43no—
256Dic61—43no—
257Dic61—43no—
258Dic61—43no—
259Dic61C2×#12614yes—
260#2645—611no—
261#2645—613no—
262#2644—613no—
263#2644—611no—
264#2643—611no—
265#2643—613no—
266#2643—613no—
267#2643—611no—
268#2401—613no—
269#2401—613no—
270#2401—611no—
271#2401D6111yescharacteristic, complemented
272#2297—613no—
273#2296—613no—
274C2×#376—611no—
275C2×C61—81no—
276C2×C61C22×#12611yescharacteristic
277C2×C61#345513yes—
278C2×C61#345513yes—
279D61—24no—
280D61—81no—
281C22×#41—611no—
282C2×#117—613no—
283C22×C42—613no—
284#401—613no—
285#401—613no—
286#401—611no—
287#401C2×D6111yescharacteristic
288#400—613no—
289#400—613no—
290#400—613no—
291#400—613no—
292#400—613no—
293#400—613no—
294#400—613no—
295#400C2×D6113yes—
296#397—613no—
297#397—613no—
298#397—613no—
299#397—613no—
300#397—613no—
301#397—613no—
302#397—613no—
303#397C2×D6113yes—
304#396—613no—
305#396—613no—
306#396—611no—
307#396C2×D6111yescharacteristic
308#391—613no—
309#391—613no—
310#390—613no—
311#390—613no—
312#389—613no—
313#389—613no—
314#389—613no—
315#389—613no—
316#386—613no—
317#386—613no—
318#386—613no—
319#386—613no—
320#385—613no—
321#385—613no—
322#385—613no—
323#385—613no—
324C4×C4⋊C4—613no—
325C4×C4⋊C4—613no—
326C4×C4⋊C4—613no—
327C4×C4⋊C4C2×D6113yes—
328C4×C22⋊C4—613no—
329C4×C22⋊C4—613no—
330C4×C22⋊C4—613no—
331C4×C22⋊C4C2×D6113yes—
332#376—613no—
333#376—613no—
334#376—611no—
335#376C2×D6111yescharacteristic
336C2×#95—613no—
337C2×#95—611no—
338C61#3463911yescharacteristic, complemented, Sylow
339C2×#41—12212no—
340C22×Q8—611no—
341C22×D4—611no—
342C22×D4—611no—
343C22×D4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—613no—
347C23×C4—613no—
348C23×C4C22×D6111yescharacteristic
349#117—12212no—
350C2×C4⋊C4—613no—
351C2×C4⋊C4—613no—
352C2×C4⋊C4—613no—
353C2×C4⋊C4—613no—
354C2×C4⋊C4—613no—
355C2×C4⋊C4—613no—
356C2×C4⋊C4—613no—
357C2×C4⋊C4—613no—
358C2×C4⋊C4C22×D6113yes—
359C2×C4⋊C4C22×D6113yes—
360C2×C22⋊C4—613no—
361C2×C22⋊C4—613no—
362C2×C22⋊C4—613no—
363C2×C22⋊C4—613no—
364C2×C22⋊C4—613no—
365C2×C22⋊C4—613no—
366C2×C22⋊C4—613no—
367C2×C22⋊C4—613no—
368C2×C22⋊C4C22×D6113yes—
369C2×C22⋊C4C22×D6113yes—
370C2×C42—613no—
371C2×C42—613no—
372C2×C42—613no—
373C2×C42—613no—
374C2×C42—12212no—
375C2×C42C22×D6113yes—
376C2×C42C22×D6113yes—
377#95—613no—
378#95—613no—
379#95—613no—
380#95—613no—
381#95—613no—
382#95—613no—
383#95—613no—
384#95—613no—
385#95—613no—
386#95—613no—
387#95—613no—
388#95—613no—
389#95—613no—
390#95—613no—
391#95—613no—
392#95—613no—
393#95C22×D6111yescharacteristic
394#95C22×D6113yes—
395#95C22×D6113yes—
396#95C22×D6113yes—
397#95C22×D6113yes—
398#95C22×D6113yes—
399C24—611no—
400C24—611no—
401C24C23×D6111yescharacteristic
402#41—24416no—
403C2×Q8—1226no—
404C2×D4—1226no—
405C2×D4—1226no—
406C2×D4—1226no—
407C22×C4—26no—
408C22×C4—611no—
409C22×C4—6112no—
410C22×C4—611no—
411C22×C4—613no—
412C22×C4—613no—
413C22×C4—613no—
414C22×C4—613no—
415C22×C4—1226no—
416C22×C4—1226no—
417C22×C4—1226no—
418C22×C4—2443no—
419C22×C4—2443no—
420C22×C4—2443no—
421C22×C4—2443no—
422C22×C4C23×D6111yescharacteristic
423C22×C4C23×D6113yes—
424C22×C4C23×D6113yes—
425C22×C4C23×D6113yes—
426C22×C4C23×D6113yes—
427C22×C4C23×D6111yescharacteristic
428C4⋊C4—43no—
429C4⋊C4—43no—
430C4⋊C4—1226no—
431C4⋊C4—1226no—
432C4⋊C4—2443no—
433C4⋊C4—2443no—
434C4⋊C4—2443no—
435C4⋊C4—2443no—
436C4⋊C4—2443no—
437C4⋊C4—2443no—
438C22⋊C4—43no—
439C22⋊C4—43no—
440C22⋊C4—1226no—
441C22⋊C4—1226no—
442C22⋊C4—2443no—
443C22⋊C4—2443no—
444C22⋊C4—2443no—
445C22⋊C4—2443no—
446C22⋊C4—2443no—
447C22⋊C4—2443no—
448C42—26no—
449C42—26no—
450C42—1226no—
451C42—1226no—
452C42—1226no—
453C42—1226no—
454C23—23no—
455C23—21no—
456C23—23no—
457C23—616no—
458C23—1221no—
459C23—1223no—
460C23—1223no—
461C23—1221no—
462C23—1223no—
463C23C24×D6111yescharacteristic
464Q8—2444no—
465D4—2444no—
466D4—2444no—
467D4—2444no—
468C2×C4—23no—
469C2×C4—23no—
470C2×C4—23no—
471C2×C4—23no—
472C2×C4—23no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—23no—
477C2×C4—23no—
478C2×C4—23no—
479C2×C4—23no—
480C2×C4—23no—
481C2×C4—44no—
482C2×C4—616no—
483C2×C4—6116no—
484C2×C4—1223no—
485C2×C4—1223no—
486C2×C4—1223no—
487C2×C4—1223no—
488C2×C4—1223no—
489C2×C4—1223no—
490C2×C4—1223no—
491C2×C4—1223no—
492C2×C4—1223no—
493C2×C4—1223no—
494C2×C4—1223no—
495C2×C4—1223no—
496C2×C4—1223no—
497C2×C4—24412no—
498C2×C4—24412no—
499C2×C4—2444no—
500C2×C4#41×D6116yes—
501C22—43no—
502C22—43no—
503C22—41no—
504C22—614no—
505C22—1226no—
506C22—1226no—
507C22—2443no—
508C22—2443no—
509C22—2441no—
510C22C2×#41×D6113yes—
511C22#1684059811yescharacteristic
512C22#1684059813yes—
513C4—43no—
514C4—43no—
515C4—43no—
516C4—43no—
517C4—41no—
518C4—614no—
519C4—2443no—
520C4—2443no—
521C4—2443no—
522C4—2443no—
523C4—2441no—
524C4#126×D6114yes—
525C2—81no—
526C2—1224no—
527C2—4881no—
528C2C2×#126×D6111yescharacteristic
529C2#2145920213yes—
530C2#2145920213yes—
subgroupG/H
centerC22×C4C23×D61
commutator, socle, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC61×#2401C2
prime radicalC22×#11758222C22
hypercenter#2401D61
hypocenterC61#34639
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #21451786C2semidirect
2. #21451783C2semidirect
3. #21451781C2semidirect
4. #21451778C2semidirect
5. #21451777C2semidirect
6. #21451776C2semidirect
7. #21451773C2semidirect
8. #21451771C2semidirect
9. #21449120C2semidirect
10. #21449119C2semidirect
11. #21449117C2semidirect
13. #21448299C2semidirect
14. #376×D61C2semidirect
15. C61×#2401C2semidirect
271. #2401D61semidirect
338. C61#34639semidirect

Maximal subgroups

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

subgroupindex
#214517862
#214517832
#214517812
#214517782
#214517772
#214517762
#214517732
#214517712
#214491202
#214491192
#214491172
#214483052
#214482992
#376×D612
C61×#24012
#3463961