Finite Group Databasebeta

← #29663539

Subgroups — #29663539

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#21457136C211yesmaximal, characteristic, complemented
2#21456737C211yesmaximal, characteristic
3#21456193C211yesmaximal, characteristic, complemented
4#21454562C211yesmaximal, characteristic, complemented
5#21445379C212yesmaximal, complemented
6#21445351C212yesmaximal, complemented
7#21445255C212yesmaximal, complemented
8#21445227C212yesmaximal, complemented
9#21444569C211yesmaximal, characteristic, complemented
10#21444477C211yesmaximal, characteristic, complemented
11C2×C61×#331C211yesmaximal, characteristic, complemented
12C2×#14519783—21no—
13#16840319C2211yescharacteristic
14#16840312C2211yescharacteristic
15#16840138—21no—
16#16840126—22no—
17#16840108—21no—
18#16840108C2212yes—
19#16840108C2212yes—
20#16840053C2212yescomplemented
21#16840048—21no—
22#16839991—22no—
23#16839968C2212yescomplemented
24#16839963—21no—
25#16839954C2212yes—
26#16839954C2212yes—
27#16839896—22no—
28#16839839C2212yescomplemented
29#16839832—22no—
30#16839827C2212yescomplemented
31#16839815C2211yescharacteristic
32#16839767—21no—
33#16839767—21no—
34#16839728—21no—
35C4×#11758194C2211yescharacteristic
36#16839514C2212yescomplemented
37#16839512C2212yescomplemented
38#16839510C2211yescharacteristic, complemented
39#16839510C2211yescharacteristic, complemented
40#16839507C2211yescharacteristic, complemented
41#16839507C2211yescharacteristic, complemented
42C2×#127×C61C2211yescharacteristic
43C2×C4⋊C8×C61C2211yescharacteristic
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#331C2212yes—
46C61×#331C2212yes—
47C2×#11758222—21no—
48C2×#11758190—22no—
49C2×#11758199—22no—
50C2×#11758199—22no—
51#14519783—44no—
52C2×#11758194D411yescharacteristic
53C2×#11758194D411yescharacteristic
54C2×#11758189—22no—
55C2×C8×D61—22no—
56#14519777D411yescharacteristic
57#14519777C2311yescharacteristic
58#14519777C2311yescharacteristic
59#14519774D411yescharacteristic
60#14519769—21no—
61#14519765—21no—
62#14519756—21no—
63#14519756—21no—
64#14519751—21no—
65#14519751D412yes—
66C4×Dic122—21no—
67C4×Dic122—21no—
68C4×D244—21no—
69C4×D244C2312yes—
70#14519736—21no—
71#14519709—22no—
72C4⋊#92418C2311yescharacteristic
73C4⋊#92418C2311yescharacteristic
74#14519702—22no—
75#14519699—22no—
76#14519698—22no—
77#14519698—22no—
78#14519698—22no—
79#14519698—22no—
80#14519698—22no—
81#14519698—22no—
82C22⋊#92418—21no—
83#14519689—22no—
84#14519689—22no—
85#14519688D412yes—
86C4×#92418—21no—
87C4×#92418C2312yes—
88C22×D4×C61—21no—
89C22×D4×C61—21no—
90C22×D4×C61—21no—
91C22×C8×C61—21no—
92C22×C8×C61—21no—
93#127×C61—21no—
94#127×C61—21no—
95#127×C61—21no—
96#127×C61C2312yes—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61—21no—
100C4⋊C8×C61C2312yes—
101C4⋊C8×C61C2311yescharacteristic
102C4⋊C8×C61C2311yescharacteristic
103C24×C61—41no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61—41no—
110C2×D4×C61—42no—
111C2×D4×C61—42no—
112C2×D4×C61—81no—
113C2×D4×C61—81no—
114C2×D4×C61—82no—
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C2×C22⋊D61—22no—
119#11758222—42no—
120#11758222—42no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244C2×D412yes—
124C2×C4×D61—22no—
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×Dic122—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61—22no—
131C2×C8×C61—42no—
132C2×C8×C61—81no—
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C42×C61C2411yescharacteristic
137C22⋊Dic61—41no—
138#11758199—82no—
139#11758199—82no—
140#11758198—22no—
141#11758198—22no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61C2×D412yes—
148#11758196—41no—
149#11758196—41no—
150C4×Dic61—41no—
151#11758194—22no—
152#11758194—22no—
153C2×#92418—21no—
154C2×#92418—21no—
155C2×#92418C2×D412yes—
156C2×#92418C2×D412yes—
157#11758190—82no—
158#11758189—44no—
159C8×D61—44no—
160C23×C61—42no—
161C23×C61—82no—
162C23×C61—82no—
163C23×C61—82no—
164C23×C61#12111yescharacteristic
165C22×D61—22no—
166D4×C61—42no—
167D4×C61—42no—
168D4×C61—42no—
169D4×C61—42no—
170D4×C61—82no—
171D4×C61—82no—
172D4×C61—82no—
173D4×C61—82no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#13512yes—
181C2×C4×C61AGL(1,ℤ/8)12yes—
182C2×C4×C61C22×D411yescharacteristic
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C2×#4111yescharacteristic
185C22⋊D61—44no—
186C2×Dic61—22no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189D244—22no—
190D244—22no—
191D244—42no—
192D244—81no—
193C4×D61—42no—
194C4×D61—42no—
195Dic122—42no—
196Dic122—41no—
197Dic122—41no—
198Dic122—81no—
199C8×C61—41no—
200C8×C61—41no—
201C8×C61—42no—
202#92418—22no—
203#92418—22no—
204#92418—41no—
205#92418—41no—
206#19234—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—82no—
210C22×C61—82no—
211C22×C61—82no—
212C22×C61—164no—
213C22×C61#46312yes—
214C22×C61C2×#12111yescharacteristic
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—42no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61#46312yes—
222C4×C61C2×#13511yescharacteristic
223C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
224C4×C61#57611yescharacteristic
225C4×C61#57711yescharacteristic
226Dic61—42no—
227Dic61—81no—
228Dic61—81no—
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#1542—611no—
239C2×#331D6111yescharacteristic, complemented
240C2×C61—22no—
241C2×C61—162no—
242C2×C61C2×#46311yescharacteristic
243C2×C61#306211yescharacteristic
244C2×C61#306811yescharacteristic
245D61—82no—
246C2×#131—1221no—
247#533—611no—
248#532—611no—
249C2×#127C2×D6111yescharacteristic
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#431—611no—
267C2×C4⋊C8C2×D6111yescharacteristic
268C2×C4⋊C8C2×D6111yescharacteristic
269#418—1221no—
270#418—1221no—
271#408—1221no—
272C4×M16—611no—
273#335—612no—
274#334—612no—
275#333—611no—
276#333—611no—
277#332—611no—
278#332—611no—
279#331C2×D6112yes—
280#331C2×D6112yes—
281C61#1923411yescharacteristic, complemented, Sylow
282C2×#41—1221no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
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—21no—
295C22×C8—1222no—
296C4⋊Q8—611no—
297C4⋊Q8—611no—
298C4⋊Q8—611no—
299#127—21no—
300#127—21no—
301#127—21no—
302#127—611no—
303#127C22×D6112yes—
304#125—1221no—
305#124—1221no—
306C22⋊Q8—1221no—
307C22⋊Q8—1221no—
308#121—612no—
309#121—1221no—
310C4×Q8—1221no—
311C4×Q8—1221no—
312C4×D4—612no—
313C4×D4—1221no—
314#117—1221no—
315C2×C42C22×D6111yescharacteristic
316#106—1222no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8—611no—
320C4⋊C8—611no—
321C4⋊C8C22×D6111yescharacteristic
322C4⋊C8C22×D6111yescharacteristic
323C4⋊C8C22×D6112yes—
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—1222no—
333C22⋊C8—1222no—
334C22⋊C8—1221no—
335#97—612no—
336C4×C8—612no—
337C4×C8—1221no—
338C24—41no—
339#41—2442no—
340#41—2442no—
341C2×Q8—1221no—
342C2×Q8—1221no—
343C2×Q8—1221no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—81no—
353C2×D4—81no—
354C2×D4—82no—
355C2×D4—612no—
356C2×D4—1222no—
357C2×D4—1221no—
358C2×D4—1221no—
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—22no—
372C2×C8—42no—
373C2×C8—81no—
374C2×C8—612no—
375C2×C8—612no—
376C2×C8—1221no—
377C2×C8—1221no—
378C2×C8—2444no—
379C4⋊C4—612no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C22⋊C4—1222no—
388C22⋊C4—1222no—
389C22⋊C4—2441no—
390C42—2441no—
391C42#1175822211yescharacteristic
392C42D4×D6111yescharacteristic
393C42D4×D6111yescharacteristic
394C42C23×D6111yescharacteristic
395C23—42no—
396C23—82no—
397C23—82no—
398C23—82no—
399C23—1222no—
400C23#1451975011yescharacteristic
401Q8—4881no—
402Q8—2441no—
403Q8—2441no—
404Q8—2442no—
405D4—42no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—82no—
410D4—82no—
411D4—82no—
412D4—82no—
413D4—1222no—
414D4—1222no—
415D4—4881no—
416D4—2444no—
417D4—2442no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—1222no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4#1451975011yescharacteristic
427C2×C4#1451975011yescharacteristic
428C2×C4#1451975011yescharacteristic
429C2×C4#1451979812yes—
430C2×C4#1451980112yes—
431C2×C4C2×D4×D6111yescharacteristic
432C2×C4C2×D4×D6111yescharacteristic
433C2×C4C2×#1175822211yescharacteristic
434C8—41no—
435C8—41no—
436C8—42no—
437C8—1222no—
438C8—1222no—
439C8—2441no—
440C8—2441no—
441C22—21no—
442C22—21no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—164no—
447C22—2442no—
448C22—2442no—
449C22—2442no—
450C22#1683997612yes—
451C22C2×#1451975011yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—4881no—
456C4—4881no—
457C4—2442no—
458C4#1683997612yes—
459C4C2×#1451979811yescharacteristic
460C4C2×#1451980111yescharacteristic
461C4#1684056311yescharacteristic
462C4#1684056811yescharacteristic
463C2—22no—
464C2—162no—
465C2—4882no—
466C2C2×#1683997611yescharacteristic
467C2#2145549711yescharacteristic
468C2#2145554611yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#331C2
socleC22×C61C2×#121
prime radical#21456737C2
hypercenterC2×#331D61
hypocenterC61#19234
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. #21457136C2semidirect
3. #21456193C2semidirect
4. #21454562C2semidirect
5. #21445379C2semidirect
6. #21445351C2semidirect
7. #21445255C2semidirect
8. #21445227C2semidirect
9. #21444569C2semidirect
10. #21444477C2semidirect
11. C2×C61×#331C2semidirect
20. #16840053C22semidirect
23. #16839968C22semidirect
28. #16839839C22semidirect
30. #16839827C22semidirect
36. #16839514C22semidirect
37. #16839512C22semidirect
38. #16839510C22semidirect
39. #16839510C22semidirect
40. #16839507C22semidirect
41. #16839507C22semidirect
239. C2×#331D61semidirect
281. C61#19234semidirect

Maximal subgroups

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

subgroupindex
#214571362
#214567372
#214561932
#214545622
#214453792
#214453512
#214452552
#214452272
#214445692
#214444772
C2×C61×#3312
#1923461