Finite Group Databasebeta

← #29835592

Subgroups — #29835592

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#21456384C211yesmaximal, characteristic
3#21448103C211yesmaximal, characteristic, complemented
4#21448089C211yesmaximal, characteristic, complemented
5#21448063C211yesmaximal, characteristic, complemented
6#21448054C211yesmaximal, characteristic, complemented
7#21447930C211yesmaximal, characteristic
8#21447927C211yesmaximal, characteristic, complemented
9#21447925C211yesmaximal, characteristic, complemented
10#21447677C211yesmaximal, characteristic, complemented
11#21447675C211yesmaximal, characteristic, complemented
12#21447674C211yesmaximal, characteristic, complemented
13SD32×Dic61C211yesmaximal, characteristic, complemented
14M32×Dic61C211yesmaximal, characteristic, complemented
15C61×#2220C211yesmaximal, characteristic
16#16840314—21no—
17#16840293—21no—
18C2×Dic488C2211yescharacteristic
19C2×#14519723C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21C2×#14519717C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840145C2211yescharacteristic
25#16840140C2211yescharacteristic
26#16840115—21no—
27#16840111—21no—
28#16840003C2211yescharacteristic
29#16840003C2211yescharacteristic
30#16840001—21no—
31#16839989—21no—
32Q16×Dic61C2211yescharacteristic
33#16839856C2211yescharacteristic
34#16839856C2211yescharacteristic
35#16839854—21no—
36#16839853—21no—
37D8×Dic61C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839537C2211yescharacteristic
49#16839537C2211yescharacteristic
50C16×Dic61C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C2×M32×C61C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C61×#466C2211yescharacteristic
56C61×#366C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×Dic244C2311yescharacteristic
61C2×#11758202—21no—
62C2×#11758200—21no—
63C22×#92418D411yescharacteristic
64#14519776—21no—
65#14519775—21no—
66#14519770—41no—
67#14519768—21no—
68#14519767—41no—
69#14519764—21no—
70#14519758—41no—
71#14519756—21no—
72#14519756—21no—
73#14519754—41no—
74Q8×Dic61—21no—
75#14519742—21no—
76#14519742—21no—
77#14519742—41no—
78D4×Dic61—21no—
79D4×Dic61—41no—
80#14519733—41no—
81#14519733—41no—
82C2×C4×Dic61D411yescharacteristic
83Dic488—22no—
84#14519723—22no—
85#14519721—22no—
86#14519717—22no—
87C2×#11758185C2311yescharacteristic
88C2×#11758185C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519708—21no—
93#14519702—21no—
94#14519702—21no—
95#14519701—21no—
96#14519700—21no—
97#14519700—21no—
98#14519698—21no—
99C8×Dic61D411yescharacteristic
100C8×Dic61D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61C2311yescharacteristic
104C2×D8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22⋊Q8×C61—21no—
107#121×C61—21no—
108SD32×C61—22no—
109M32×C61—22no—
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#103×C61—21no—
115#102×C61—21no—
116C2×Q8×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C22×C4×C61C2×D411yescharacteristic
120C22×Dic61—41no—
121C22×Dic61D811yescharacteristic
122C22×Dic61D811yescharacteristic
123C2×Dic122—21no—
124C2×Dic122—21no—
125C2×Dic122—41no—
126Q16×C61—21no—
127Q16×C61—21no—
128D8×C61—21no—
129D8×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—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊Dic61—41no—
140C22⋊Dic61—41no—
141C22⋊Dic61—41no—
142C22⋊Dic61—41no—
143C22⋊Dic61—41no—
144#11758202—42no—
145#11758200—42no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150#11758196—41no—
151#11758196—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—
170Dic244—21no—
171Dic244—21no—
172C16×C61—21no—
173C16×C61#4112yes—
174#11758185—21no—
175#11758185#4112yes—
176C23×C61—41no—
177C23×C61C2×D811yescharacteristic
178Q8×C61—41no—
179Q8×C61—41no—
180D4×C61—41no—
181D4×C61—41no—
182D4×C61—82no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×Dic61—22no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—82no—
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200C2×Dic61C2×D811yescharacteristic
201Dic122—41no—
202Dic122—41no—
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×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61C22×D811yescharacteristic
219C4×C61—21no—
220C4×C61—81no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61#53211yescharacteristic
224C4×C61C2×#13511yescharacteristic
225Dic61—21no—
226Dic61—21no—
227Dic61—21no—
228Dic61—81no—
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#2220D6111yescharacteristic
241#2219—611no—
242#2219—611no—
243C4×Q32—611no—
244C4×Q32—611no—
245C4×SD32—611no—
246C4×SD32—611no—
247C4×M32—611no—
248C2×C61—41no—
249C2×C61—161no—
250C2×C61#316911yescharacteristic
251C2×C61C2×#51011yescharacteristic
252C2×C61#341411yescharacteristic
253#533—1221no—
254#529—1221no—
255C2×Q32—611no—
256C2×Q32—611no—
257C2×SD32—611no—
258C2×SD32C2×D6111yescharacteristic
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—611no—
269#467—1221no—
270#467C2×D6111yescharacteristic
271#466C2×D6111yescharacteristic
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#367—611no—
282#366—611no—
283#366C2×D6111yescharacteristic
284#358—611no—
285#358—611no—
286#358—611no—
287#358—611no—
288#358—611no—
289#358C2×D6111yescharacteristic
290#357—611no—
291#357C2×D6111yescharacteristic
292#346—611no—
293#346—611no—
294C4×C16—611no—
295C4×C16—611no—
296C61#3373811yescharacteristic, complemented, Sylow
297C2×Q16—611no—
298C2×Q16—611no—
299C2×Q16—1221no—
300C2×Q16C22×D6111yescharacteristic
301C2×SD16—1221no—
302C2×D8C22×D6111yescharacteristic
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—1221no—
314C22⋊Q8—1221no—
315C22⋊Q8—2441no—
316#121—21no—
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—1222no—
327Q32—1222no—
328SD32—22no—
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—1221no—
344#103—1221no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#102—21no—
349#102—1221no—
350C4×C8—611no—
351C4×C8—611no—
352C4×C8—611no—
353C4×C8—611no—
354C2×Q8—21no—
355C2×Q8—1221no—
356C2×Q8—1221no—
357C2×Q8—2441no—
358C2×D4—21no—
359C2×D4—41no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—2441no—
363C22×C4D4×D6111yescharacteristic
364Q16—21no—
365Q16—21no—
366Q16—1221no—
367Q16—1221no—
368Q16—1221no—
369Q16—1221no—
370Q16—2442no—
371SD16—2442no—
372D8—21no—
373D8—21no—
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—1221no—
385C4⋊C4—1221no—
386C4⋊C4—2441no—
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—41no—
415C23D8×D6111yescharacteristic
416Q8—41no—
417Q8—41no—
418Q8—4882no—
419Q8—2441no—
420Q8—2441no—
421Q8—2441no—
422Q8—2441no—
423D4—41no—
424D4—41no—
425D4—82no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—611no—
432C2×C4—611no—
433C2×C4—611no—
434C2×C4—611no—
435C2×C4—1222no—
436C2×C4—4882no—
437C2×C4—2441no—
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—81no—
453C22—81no—
454C22—81no—
455C22C2×D8×D6111yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—612no—
461C4—1221no—
462C4—1221no—
463C4—1221no—
464C4—4881no—
465C4—4881no—
466C4—4881no—
467C4—4881no—
468C4#1684030711yescharacteristic
469C4#135×D6111yescharacteristic
470C2—41no—
471C2—161no—
472C2#2145639311yescharacteristic
473C2#510×D6111yescharacteristic
474C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2220C2
socleC22×C61C22×D8
prime radicalC61×#466C22
hypercenter#2220D61
hypocenterC61#33738
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
1. #21456400C2semidirect
3. #21448103C2semidirect
4. #21448089C2semidirect
5. #21448063C2semidirect
6. #21448054C2semidirect
8. #21447927C2semidirect
9. #21447925C2semidirect
10. #21447677C2semidirect
11. #21447675C2semidirect
12. #21447674C2semidirect
13. SD32×Dic61C2semidirect
14. M32×Dic61C2semidirect
296. C61#33738semidirect

Maximal subgroups

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

subgroupindex
#214564002
#214563842
#214481032
#214480892
#214480632
#214480542
#214479302
#214479272
#214479252
#214476772
#214476752
#214476742
SD32×Dic612
M32×Dic612
C61×#22202
#3373861