Finite Group Databasebeta

← #29835590

Subgroups — #29835590

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456400C211yesmaximal, characteristic, complemented
2#21456390C211yesmaximal, characteristic
3#21448104C211yesmaximal, characteristic, complemented
4#21448087C211yesmaximal, characteristic, complemented
5#21448063C211yesmaximal, characteristic, complemented
6#21448057C211yesmaximal, characteristic, complemented
7#21447934C211yesmaximal, characteristic
8#21447932C211yesmaximal, characteristic
9#21447925C211yesmaximal, characteristic, complemented
10Q32×Dic61C211yesmaximal, characteristic, complemented
11#21447675C211yesmaximal, characteristic, complemented
12#21447670C211yesmaximal, characteristic, complemented
13#21447668C211yesmaximal, characteristic, complemented
14M32×Dic61C211yesmaximal, characteristic, complemented
15C61×#2219C211yesmaximal, characteristic, complemented
16#16840314—21no—
17#16840298—21no—
18C2×#14519723C2211yescharacteristic
19C2×#14519722C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21C2×#14519717C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840147C2211yescharacteristic
25#16840140C2211yescharacteristic
26#16840118—21no—
27#16840111—21no—
28#16840003C2211yescharacteristic
29#16840001—21no—
30#16839998C2211yescharacteristic
31#16839993—21no—
32Q16×Dic61C2211yescharacteristic
33Q16×Dic61C2211yescharacteristic
34#16839856C2211yescharacteristic
35#16839854—21no—
36#16839847—21no—
37#16839844C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839537C2211yescharacteristic
49#16839537C2211yescharacteristic
50C16×Dic61C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C2×M32×C61C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C61×#467C2211yescharacteristic
56C61×#367C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758202—21no—
61C2×#11758201—21no—
62C2×D488C2311yescharacteristic
63C22×#92418D411yescharacteristic
64#14519776—21no—
65#14519775—21no—
66#14519772—41no—
67#14519768—21no—
68#14519767—41no—
69#14519766—21no—
70#14519761—41no—
71#14519756—21no—
72#14519754—41no—
73#14519751—21no—
74Q8×Dic61—21no—
75Q8×Dic61—21no—
76#14519742—21no—
77#14519742—41no—
78#14519739—21no—
79#14519737—41no—
80#14519735—41no—
81#14519733—41no—
82C2×C4×Dic61D411yescharacteristic
83#14519723—22no—
84#14519722—22no—
85#14519720—22no—
86#14519717—22no—
87C2×#11758185C2311yescharacteristic
88C2×#11758185C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519708—21no—
93#14519702—21no—
94#14519701—21no—
95#14519701—21no—
96#14519700—21no—
97#14519699—21no—
98#14519697—21no—
99C8×Dic61D411yescharacteristic
100C8×Dic61D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61C2311yescharacteristic
104C2×Q16×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22⋊Q8×C61—21no—
107C22⋊Q8×C61—21no—
108Q32×C61—22no—
109M32×C61—22no—
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#103×C61—21no—
115#103×C61—21no—
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61—41no—
120C22×Dic61D811yescharacteristic
121C22×Dic61D811yescharacteristic
122C2×D244—21no—
123C2×C4×D61—41no—
124C2×Dic122—21no—
125C2×Dic122—41no—
126Q16×C61—21no—
127Q16×C61—21no—
128Q16×C61—21no—
129Q16×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2411yescharacteristic
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊Dic61—41no—
141#11758202—42no—
142#11758201—42no—
143#11758198—41no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151C4⋊Dic61—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61D811yescharacteristic
162C4×Dic61D811yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165C2×#92418—22no—
166C2×#92418C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168Dic244—21no—
169Dic244—21no—
170D488—21no—
171D488—21no—
172C16×C61—21no—
173C16×C61#4112yes—
174#11758185—21no—
175#11758185#4112yes—
176C23×C61C2×D811yescharacteristic
177C22×D61—41no—
178Q8×C61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C22⋊D61—82no—
191C2×Dic61—22no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200D244—41no—
201D244—41no—
202C4×D61—82no—
203Dic122—41no—
204Dic122—41no—
205Dic122—82no—
206C8×C61—21no—
207C8×C61C2×#4111yescharacteristic
208C8×C61C2×#4111yescharacteristic
209#92418—21no—
210#92418#13512yes—
211#33738—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61C22×D811yescharacteristic
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—81no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61#53211yescharacteristic
225C4×C61C2×#13511yescharacteristic
226Dic61—21no—
227Dic61—21no—
228Dic61—21no—
229Dic61—81no—
230Dic61—81no—
231Dic61—81no—
232Dic61#51012yes—
233#3170—611no—
234#3168—611no—
235#2255—611no—
236#2251—611no—
237#2245—611no—
238#2243—611no—
239#2220—611no—
240#2220—611no—
241#2219—611no—
242#2219D6111yescharacteristic, complemented
243C4×Q32—611no—
244C4×Q32—611no—
245C4×SD32—611no—
246C4×SD32—611no—
247C4×M32—611no—
248C2×C61—41no—
249C2×C61#316911yescharacteristic
250C2×C61C2×#51011yescharacteristic
251C2×C61#341411yescharacteristic
252D61—161no—
253#533—1221no—
254#529—1221no—
255C2×Q32—611no—
256C2×Q32C2×D6111yescharacteristic
257C2×SD32—611no—
258C2×SD32—611no—
259C2×M32—611no—
260C2×M32C2×D6111yescharacteristic
261#500—611no—
262#499—611no—
263#495—611no—
264#494—611no—
265#488—1221no—
266#487—1221no—
267#467—611no—
268#467—1221no—
269#467C2×D6111yescharacteristic
270#467C2×D6111yescharacteristic
271#466—611no—
272#465—1221no—
273C4×Q16—611no—
274C4×Q16—611no—
275C4×Q16—611no—
276C4×Q16—1221no—
277C4×SD16—1221no—
278C4×D8—611no—
279C2×C4×C8—611no—
280#367—611no—
281#367C2×D6111yescharacteristic
282#366—611no—
283#366—611no—
284#358—611no—
285#358—611no—
286#358—611no—
287#358—611no—
288#358C2×D6111yescharacteristic
289#358C2×D6111yescharacteristic
290#357—611no—
291#357—611no—
292#346—611no—
293#346—611no—
294C4×C16—611no—
295C4×C16—611no—
296C61#3373811yescharacteristic, complemented, Sylow
297C2×Q16—611no—
298C2×Q16—1221no—
299C2×Q16C22×D6111yescharacteristic
300C2×Q16C22×D6111yescharacteristic
301C2×SD16—1221no—
302C2×D8—611no—
303C22×C8—611no—
304C22×C8C22×D6111yescharacteristic
305C4⋊Q8—1221no—
306C4⋊Q8—1221no—
307#126—2441no—
308#125—1221no—
309#125—2441no—
310#124—1221no—
311#123—2441no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—1221no—
315C22⋊Q8—2441no—
316#121—1221no—
317C4×Q8—1221no—
318C4×Q8—1221no—
319C4×Q8—1221no—
320C4×Q8—2441no—
321C4×D4—1221no—
322C4×D4—2441no—
323#117—2441no—
324#117—2441no—
325C2×C42—611no—
326Q32—22no—
327Q32—1222no—
328SD32—1222no—
329SD32—1222no—
330M32—22no—
331M32—1222no—
332C2×C16—611no—
333C2×C16—611no—
334C2×C16C22×D6111yescharacteristic
335C2×C16C22×D6111yescharacteristic
336#107—611no—
337#107—611no—
338#107—1221no—
339#107C22×D6111yescharacteristic
340#107C22×D6111yescharacteristic
341#106—1221no—
342#103—21no—
343#103—21no—
344#103—1221no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#102—1221no—
349#102—1221no—
350C4×C8—611no—
351C4×C8—611no—
352C4×C8—611no—
353C4×C8—611no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—1221no—
357C2×Q8—2441no—
358C2×D4—1221no—
359C2×D4—2441no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—2441no—
363C22×C4D4×D6111yescharacteristic
364Q16—21no—
365Q16—21no—
366Q16—21no—
367Q16—21no—
368Q16—1221no—
369Q16—1221no—
370Q16—2442no—
371SD16—2442no—
372D8—1221no—
373D8—1221no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—611no—
377C2×C8—611no—
378C2×C8—1222no—
379C2×C8D4×D6111yescharacteristic
380C2×C8C23×D6111yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—1221no—
386C4⋊C4—1221no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C42—611no—
404C42—611no—
405C42—611no—
406C42—611no—
407C42—2441no—
408C42—2441no—
409C42—2441no—
410C16—21no—
411C16—612no—
412C16—1221no—
413C16#1175822412yes—
414C23—2441no—
415C23D8×D6111yescharacteristic
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—4882no—
421Q8—2441no—
422Q8—2441no—
423D4—4882no—
424D4—2441no—
425D4—2441no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—611no—
433C2×C4—611no—
434C2×C4—611no—
435C2×C4—611no—
436C2×C4—1222no—
437C2×C4—4882no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4D8×D6111yescharacteristic
443C2×C4C2×D4×D6111yescharacteristic
444C8—21no—
445C8—612no—
446C8—1221no—
447C8#41×D6111yescharacteristic
448C8C2×#1175822411yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22C2×D8×D6111yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—612no—
462C4—1221no—
463C4—1221no—
464C4—1221no—
465C4—4881no—
466C4—4881no—
467C4—4881no—
468C4#1684030711yescharacteristic
469C4#135×D6111yescharacteristic
470C2—41no—
471C2—9761no—
472C2#2145639311yescharacteristic
473C2#510×D6111yescharacteristic
474C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2219C2
socleC22×C61C22×D8
prime radical#16839998C22
hypercenter#2219D61
hypocenterC61#33738
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. #21456400C2semidirect
3. #21448104C2semidirect
4. #21448087C2semidirect
5. #21448063C2semidirect
6. #21448057C2semidirect
9. #21447925C2semidirect
10. Q32×Dic61C2semidirect
11. #21447675C2semidirect
12. #21447670C2semidirect
13. #21447668C2semidirect
14. M32×Dic61C2semidirect
15. C61×#2219C2semidirect
242. #2219D61semidirect
296. C61#33738semidirect

Maximal subgroups

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

subgroupindex
#214564002
#214563902
#214481042
#214480872
#214480632
#214480572
#214479342
#214479322
#214479252
Q32×Dic612
#214476752
#214476702
#214476682
M32×Dic612
C61×#22192
#3373861