Finite Group Databasebeta

← #29663544

Subgroups — #29663544

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457131C211yesmaximal, characteristic, complemented
2#21456739C211yesmaximal, characteristic
3#21456195C211yesmaximal, characteristic, complemented
4#21454562C211yesmaximal, characteristic, complemented
5#21445383C212yesmaximal, complemented
6#21445355C212yesmaximal, complemented
7#21445259C212yesmaximal, complemented
8#21445231C212yesmaximal, complemented
9#21444572C211yesmaximal, characteristic, complemented
10C2×#16839505C211yesmaximal, characteristic, complemented
11C61×#1542C211yesmaximal, characteristic, complemented
12C2×#14519783—21no—
13#16840312C2211yescharacteristic
14C2×#14519774C2211yescharacteristic
15#16840139—21no—
16#16840128—22no—
17#16840110C2212yes—
18#16840110C2212yes—
19#16840109—21no—
20#16840049C2212yescomplemented
21#16840047—21no—
22#16839993—22no—
23#16839964C2212yescomplemented
24#16839962—21no—
25#16839958C2212yes—
26#16839958C2212yes—
27#16839898—22no—
28#16839839C2212yescomplemented
29#16839832—22no—
30#16839827C2212yescomplemented
31C2×C4⋊#92418C2211yescharacteristic
32#16839766—21no—
33#16839766—21no—
34#16839728—21no—
35C4×#11758194C2211yescharacteristic
36#16839514C2212yescomplemented
37#16839512C2212yescomplemented
38#16839505C2212yes—
39#16839505C2212yes—
40C61×#533C2211yescharacteristic
41C61×#431C2211yescharacteristic
42C2×C4⋊C8×C61C2211yescharacteristic
43C61×#333C2211yescharacteristic, complemented
44C61×#333C2211yescharacteristic, complemented
45C61×#332C2211yescharacteristic, complemented
46C61×#332C2211yescharacteristic, complemented
47C2×#11758222—21no—
48C22×D244—21no—
49C22×D244—21no—
50C22×D244—21no—
51C2×#11758201—22no—
52C2×D488—22no—
53C2×D488—22no—
54#14519783—44no—
55C2×#11758194D411yescharacteristic
56C2×#11758194D411yescharacteristic
57C2×#11758189—22no—
58C22×#92418—21no—
59C2×C8×D61—22no—
60#14519777D411yescharacteristic
61#14519774—21no—
62#14519774—21no—
63#14519774—21no—
64#14519774D411yescharacteristic
65#14519774C2312yes—
66#14519765—21no—
67#14519751—21no—
68#14519751D412yes—
69C4×D244—21no—
70C4×D244C2312yes—
71#14519708—22no—
72C4⋊#92418—21no—
73C4⋊#92418C2312yes—
74#14519701—22no—
75#14519699—22no—
76#14519699—22no—
77#14519697—22no—
78#14519697—22no—
79#14519697—22no—
80#14519697—22no—
81#14519697—22no—
82#14519689—22no—
83#14519689—22no—
84#14519688D412yes—
85C4×#92418C2312yes—
86C22×C8×C61—21no—
87C4⋊Q8×C61C2311yescharacteristic
88C4⋊Q8×C61C2311yescharacteristic
89#125×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94#117×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99C4⋊C8×C61C2311yescharacteristic
100C4⋊C8×C61C2311yescharacteristic
101C22⋊C8×C61—21no—
102C4×C8×C61—21no—
103C23×D61—41no—
104C2×Q8×C61—21no—
105C2×Q8×C61—21no—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C2×C22⋊D61—22no—
110#11758222—42no—
111#11758222—42no—
112C2×D244—21no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—21no—
116C2×D244—22no—
117C2×D244—42no—
118C2×D244—42no—
119C2×D244—41no—
120C2×D244—41no—
121C2×D244—41no—
122C2×D244—81no—
123C2×D244—81no—
124C2×D244—82no—
125C2×D244C2×D412yes—
126C2×C4×D61—22no—
127C2×Dic122—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61—42no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C42×C61—41no—
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61#4111yescharacteristic
144C42×C61C2411yescharacteristic
145#11758201—82no—
146#11758198—22no—
147#11758198—22no—
148C4⋊Dic61—21no—
149C4⋊Dic61C2×D412yes—
150#11758194—22no—
151#11758194—22no—
152C2×#92418—22no—
153C2×#92418—81no—
154C2×#92418C2×D412yes—
155C2×#92418C2×D412yes—
156D488—82no—
157D488—82no—
158#11758189—44no—
159C8×D61—44no—
160C23×C61#12111yescharacteristic
161C22×D61—22no—
162C22×D61—42no—
163C22×D61—82no—
164C22×D61—82no—
165C22×D61—82no—
166Q8×C61—41no—
167Q8×C61—41no—
168Q8×C61—81no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#13512yes—
178C2×C4×C61AGL(1,ℤ/8)12yes—
179C2×C4×C61C22×D411yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C2×C4×C61C2×#4111yescharacteristic
182C22⋊D61—44no—
183C2×Dic61—22no—
184D244—22no—
185D244—22no—
186D244—42no—
187D244—42no—
188D244—42no—
189D244—42no—
190D244—42no—
191D244—81no—
192D244—82no—
193D244—82no—
194D244—82no—
195D244—82no—
196C4×D61—42no—
197C4×D61—42no—
198Dic122—42no—
199C8×C61—41no—
200C8×C61—41no—
201C8×C61—41no—
202C8×C61—41no—
203#92418—22no—
204#92418—22no—
205#92418—42no—
206#19234—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61#46312yes—
210C22×C61C2×#12111yescharacteristic
211C2×D61—42no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—82no—
215C2×D61—82no—
216C2×D61—82no—
217C2×D61—164no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61#46312yes—
224C4×C61C2×#13511yescharacteristic
225C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
226C4×C61#57611yescharacteristic
227C4×C61#57711yescharacteristic
228Dic61—42no—
229#3246—611no—
230#3205—611no—
231#3138—611no—
232#2935—611no—
233#1701—612no—
234#1697—612no—
235#1681—612no—
236#1677—612no—
237#1565—611no—
238#1542D6111yescharacteristic, complemented
239C2×#331—611no—
240C2×C61—22no—
241C2×C61C2×#46311yescharacteristic
242C2×C61#306211yescharacteristic
243C2×C61#306811yescharacteristic
244D61—82no—
245D61—162no—
246C2×#131—1221no—
247#533C2×D6111yescharacteristic
248#532—611no—
249C2×#127—611no—
250#493—1221no—
251#490—1222no—
252#486—612no—
253#486—612no—
254#486—1221no—
255#476—612no—
256#475—1221no—
257#465—1222no—
258#461—612no—
259#460—1221no—
260#459—612no—
261#459—612no—
262#447—1222no—
263#436—612no—
264#435—1222no—
265C8×D4—612no—
266#431C2×D6111yescharacteristic
267C2×C4⋊C8—611no—
268C2×C4⋊C8C2×D6111yescharacteristic
269#418—1221no—
270#418—1221no—
271#408—1221no—
272C4×M16—611no—
273#335—612no—
274#334—612no—
275#333C2×D6111yescharacteristic, complemented
276#333C2×D6111yescharacteristic, complemented
277#332C2×D6111yescharacteristic, complemented
278#332C2×D6111yescharacteristic, complemented
279#331—612no—
280#331—612no—
281C61#1923411yescharacteristic, complemented, Sylow
282C2×#41—1221no—
283C22×D4—1221no—
284C22×D4—1221no—
285C22×D4—1221no—
286C2×SD16—1222no—
287C2×D8—1222no—
288C2×D8—1222no—
289#131—2444no—
290C2×M16—611no—
291C2×M16—611no—
292C2×M16—1222no—
293C22×C8—21no—
294C22×C8—1222no—
295C22×C8—1221no—
296C4⋊Q8—611no—
297C4⋊Q8C22×D6111yescharacteristic
298C4⋊Q8C22×D6111yescharacteristic
299#127—611no—
300#127—612no—
301#127—1221no—
302#127—1221no—
303#127—1221no—
304#125—21no—
305#124—1221no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308#121—612no—
309#121—1221no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×D4—612no—
313C4×D4—1221no—
314#117—21no—
315C2×C42C22×D6111yescharacteristic
316#106—1222no—
317C4⋊C8—21no—
318C4⋊C8—612no—
319C4⋊C8—1221no—
320C4⋊C8C22×D6111yescharacteristic
321C4⋊C8C22×D6111yescharacteristic
322C4⋊C8C22×D6111yescharacteristic
323C4⋊C8C22×D6111yescharacteristic
324#103—1222no—
325#102—1222no—
326#102—1222no—
327#102—1222no—
328#102—1222no—
329#102—1222no—
330#102—1222no—
331#102—1222no—
332C22⋊C8—21no—
333C22⋊C8—1222no—
334C22⋊C8—1222no—
335#97—612no—
336C4×C8—21no—
337C4×C8—612no—
338C24—2441no—
339#41—2442no—
340#41—2442no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—1221no—
344C2×D4—612no—
345C2×D4—1222no—
346C2×D4—1222no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—1221no—
350C2×D4—1221no—
351C2×D4—4881no—
352C2×D4—4881no—
353C2×D4—4882no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2442no—
358C2×D4—2442no—
359C22×C4—1222no—
360C22×C4#1175822211yescharacteristic
361C22×C4D4×D6111yescharacteristic
362C22×C4D4×D6111yescharacteristic
363SD16—4882no—
364D8—4882no—
365D8—4882no—
366M16—1222no—
367M16—1222no—
368M16—2444no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—42no—
374C2×C8—612no—
375C2×C8—612no—
376C2×C8—1222no—
377C2×C8—4881no—
378C2×C8—2444no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—612no—
386C4⋊C4—1221no—
387C22⋊C4—41no—
388C22⋊C4—1222no—
389C22⋊C4—1222no—
390C42—41no—
391C42#1175822211yescharacteristic
392C42D4×D6111yescharacteristic
393C42D4×D6111yescharacteristic
394C42C23×D6111yescharacteristic
395C23—1222no—
396C23—4882no—
397C23—4882no—
398C23—4882no—
399C23—2442no—
400C23#1451975011yescharacteristic
401Q8—41no—
402Q8—41no—
403Q8—81no—
404Q8—2442no—
405D4—1222no—
406D4—1222no—
407D4—4882no—
408D4—4882no—
409D4—4882no—
410D4—4881no—
411D4—4882no—
412D4—2444no—
413D4—2442no—
414D4—2442no—
415D4—2442no—
416D4—2442no—
417D4—2442no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—1222no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4#1451975011yescharacteristic
427C2×C4#1451975011yescharacteristic
428C2×C4#1451975011yescharacteristic
429C2×C4#1451980012yes—
430C2×C4#1451980412yes—
431C2×C4C2×D4×D6111yescharacteristic
432C2×C4C2×D4×D6111yescharacteristic
433C2×C4C2×#1175822211yescharacteristic
434C8—41no—
435C8—41no—
436C8—41no—
437C8—41no—
438C8—1222no—
439C8—1222no—
440C8—2442no—
441C22—21no—
442C22—21no—
443C22—9764no—
444C22—4882no—
445C22—4882no—
446C22—4882no—
447C22—2442no—
448C22—2442no—
449C22—2442no—
450C22#1683998012yes—
451C22C2×#1451975011yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—81no—
456C4—81no—
457C4—2442no—
458C4#1683998012yes—
459C4C2×#1451980011yescharacteristic
460C4C2×#1451980411yescharacteristic
461C4#1684056411yescharacteristic
462C4#1684056911yescharacteristic
463C2—22no—
464C2—9762no—
465C2—4882no—
466C2C2×#1683998011yescharacteristic
467C2#2145550211yescharacteristic
468C2#2145555011yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1542C2
socleC22×C61C2×#121
prime radical#21456739C2
hypercenter#1542D61
hypocenterC61#19234
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #21457131C2semidirect
3. #21456195C2semidirect
4. #21454562C2semidirect
5. #21445383C2semidirect
6. #21445355C2semidirect
7. #21445259C2semidirect
8. #21445231C2semidirect
9. #21444572C2semidirect
10. C2×#16839505C2semidirect
11. C61×#1542C2semidirect
20. #16840049C22semidirect
23. #16839964C22semidirect
28. #16839839C22semidirect
30. #16839827C22semidirect
36. #16839514C22semidirect
37. #16839512C22semidirect
43. C61×#333C22semidirect
44. C61×#333C22semidirect
45. C61×#332C22semidirect
46. C61×#332C22semidirect
238. #1542D61semidirect
275. #333C2×D61semidirect
276. #333C2×D61semidirect
277. #332C2×D61semidirect
278. #332C2×D61semidirect
281. C61#19234semidirect

Maximal subgroups

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

subgroupindex
#214571312
#214567392
#214561952
#214545622
#214453832
#214453552
#214452592
#214452312
#214445722
C2×#168395052
C61×#15422
#1923461