Finite Group Databasebeta

← #29593550

Subgroups — #29593550

Order 15616.

362 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458792C211yesmaximal, characteristic
2#21448074C211yesmaximal, characteristic, complemented
3#21447865C211yesmaximal, characteristic, complemented
4#21445190C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8#16840432—21no—
9C2×#14519722—21no—
10C2×#14519721—22no—
11#16840142C2211yescharacteristic
12#16840137—21no—
13#16840048—21no—
14#16839955—22no—
15#16839954—21no—
16C8×Dic122C2211yescharacteristic
17C4×D488C2211yescharacteristic
18D8×Dic61—21no—
19#16839567—21no—
20C4×#11758185C2211yescharacteristic
21#16839507—21no—
22C61×#493C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758224—41no—
26C2×Dic244—21no—
27C2×Dic244—21no—
28C2×D488D411yescharacteristic
29C2×#11758199—22no—
30#14519777—21no—
31#14519773—22no—
32#14519749—42no—
33#14519748—41no—
34C4×Dic122D411yescharacteristic
35C4×D244—21no—
36D4×Dic61—22no—
37#14519722—42no—
38#14519721—44no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519709—41no—
42C4⋊#92418D411yescharacteristic
43#14519706—21no—
44#14519702—41no—
45#14519699—21no—
46#14519698—22no—
47C8×Dic61—21no—
48C2×D8×C61—21no—
49C2×D8×C61D412yes—
50#127×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61—22no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×C22⋊D61—42no—
58C2×C22⋊D61—42no—
59C22×Dic61—42no—
60#11758224—82no—
61#11758224—82no—
62C2×D244—21no—
63C2×C4×D61—41no—
64C2×Dic122—41no—
65C2×Dic122D811yescharacteristic
66D8×C61—42no—
67D8×C61—41no—
68D8×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C42×C61C2×D411yescharacteristic
73C22⋊Dic61—42no—
74#11758199—82no—
75#11758198—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61D811yescharacteristic
80#11758196—21no—
81C4×Dic61—21no—
82C2×#92418—21no—
83Dic244—42no—
84Dic244—41no—
85Dic244—41no—
86D488—21no—
87D488—21no—
88C16×C61—41no—
89#11758185—22no—
90C23×C61—42no—
91C22×D61—41no—
92D4×C61—42no—
93D4×C61—42no—
94D4×C61—81no—
95D4×C61—81no—
96D4×C61—161no—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C2×D811yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C22⋊D61—84no—
101C22⋊D61—162no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—41no—
105C2×Dic61—84no—
106C2×Dic61—81no—
107D244—41no—
108D244—41no—
109C4×D61—81no—
110C4×D61—81no—
111Dic122—21no—
112Dic122—81no—
113Dic122—81no—
114Dic122SD3212yescomplemented
115C8×C61—21no—
116C8×C61—81no—
117C8×C61#13511yescharacteristic
118C8×C61AGL(1,ℤ/8)11yescharacteristic
119#92418—41no—
120#12332—611nomaximal, Sylow
121C22×C61—82no—
122C22×C61—82no—
123C22×C61—82no—
124C22×C61#44711yescharacteristic
125C2×D61—81no—
126C2×D61—81no—
127C2×D61—81no—
128C4×C61—21no—
129C4×C61#44911yescharacteristic
130C4×C61#45311yescharacteristic
131C4×C61C2×SD3211yescharacteristic
132C4×C61#50911yescharacteristic
133Dic61—22no—
134Dic61—41no—
135Dic61—81no—
136Dic61—161no—
137#3391—611no—
138#2248—611no—
139#2208—611no—
140#1670—611no—
141#1361D6111yescharacteristic, complemented
142Q8⋊C16—611no—
143#1331—611no—
144C2×C61—162no—
145C2×C61#162111yescharacteristic
146C2×C61#218711yescharacteristic
147C2×C61#219411yescharacteristic
148D61—161no—
149#550—1221no—
150C2×SD32—1221no—
151C2×SD32—1222no—
152#494—611no—
153#493—1221no—
154#493C2×D6111yescharacteristic
155#475—1221no—
156#459—1221no—
157#459—1222no—
158C8×Q8—611no—
159C4×D8—611no—
160C4×D8—1221no—
161C4⋊C16C2×D6111yescharacteristic
162#358—1221no—
163C4×C16—611no—
164#335C2×D6111yescharacteristic
165#332—1221no—
166C61#1233211yescharacteristic, complemented, Sylow
167C2×#41—2441no—
168C2×Q16—1221no—
169C2×Q16—1221no—
170C2×D8—21no—
171C2×D8—611no—
172C2×D8—1222no—
173C2×D8D24412yes—
174C4⋊Q8—1221no—
175#127—21no—
176#127—1222no—
177#121—2441no—
178#121—2442no—
179C4×Q8—611no—
180C4×D4—1222no—
181C4×D4—1221no—
182SD32—2442no—
183SD32—2444no—
184C2×C16—21no—
185C2×C16—1221no—
186#107—611no—
187#106—2441no—
188C4⋊C8—21no—
189C4⋊C8—611no—
190C4⋊C8—1221no—
191#103—2441no—
192#102—1222no—
193#102—1221no—
194C4×C8—1221no—
195C4×C8C22×D6111yescharacteristic
196#41—4882no—
197#41—4882no—
198C2×Q8—611no—
199C2×Q8—2441no—
200C2×D4—22no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—1221no—
204C2×D4—2442no—
205C2×D4—2442no—
206C22×C4—2442no—
207C22×C4—2441no—
208Q16—2442no—
209Q16—2441no—
210Q16—2441no—
211D8—42no—
212D8—41no—
213D8—41no—
214D8—1221no—
215D8—1221no—
216D8—4882no—
217C2×C8—41no—
218C2×C8—1221no—
219C2×C8C2×D24411yescharacteristic
220C2×C8D4×D6111yescharacteristic
221C4⋊C4—611no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C22⋊C4—2442no—
227C22⋊C4—2441no—
228C42—1221no—
229C42D4×D6111yescharacteristic
230C16—41no—
231C16—1222no—
232C23—42no—
233C23—2441no—
234Q8—612no—
235Q8—1221no—
236Q8—4881no—
237Q8—4881no—
238D4—42no—
239D4—42no—
240D4—81no—
241D4—81no—
242D4—161no—
243D4—9762no—
244D4—4884no—
245D4—2441no—
246D4—2441no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—4884no—
250C2×C4—4881no—
251C2×C4—4881no—
252C2×C4—4881no—
253C2×C4—2441no—
254C2×C4#1451974711yescharacteristic
255C2×C4D8×D6111yescharacteristic
256C2×C4#1451980411yescharacteristic
257C8—21no—
258C8—81no—
259C8—2441no—
260C8#1451979811yescharacteristic
261C8#1451980111yescharacteristic
262C22—82no—
263C22—82no—
264C22—82no—
265C22—4881no—
266C22—4881no—
267C22—4881no—
268C22#1683989711yescharacteristic
269C4—21no—
270C4—1222no—
271C4—9761no—
272C4—4881no—
273C4—2441no—
274C4#1683990811yescharacteristic
275C4#1683993211yescharacteristic
276C4SD32×D6111yescharacteristic
277C4#1684019611yescharacteristic
278C2—162no—
279C2—9761no—
280C2#2144488511yescharacteristic
281C2#2144774911yescharacteristic
282C2#2144779311yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#447
prime radical#21458792C2
hypercenter#1361D61
hypocenterC61#12332
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #21448074C2semidirect
3. #21447865C2semidirect
4. #21445190C2semidirect
5. #21443797C2semidirect
6. #21443779C2semidirect
7. C61×#1361C2semidirect
114. Dic122SD32semidirect
141. #1361D61semidirect
166. C61#12332semidirect

Maximal subgroups

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

subgroupindex
#214587922
#214480742
#214478652
#214451902
#214437972
#214437792
C61×#13612
#1233261