Finite Group Databasebeta

← #29591517

Subgroups — #29591517

Order 15616.

300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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#21456403C211yesmaximal, characteristic
2#21447573C211yesmaximal, characteristic
3#21444581C211yesmaximal, characteristic
4#21443878C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, characteristic, complemented
6#21443868C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8#16840317—21no—
9C2×#14519716—21no—
10#16840167C2211yescharacteristic
11#16840112—21no—
12#16840000—21no—
13#16840000C412yes—
14Q16×Dic61—21no—
15Q16×Dic61C412yes—
16#16839818—21no—
17C4×C8×D61C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839580—21no—
20#16839515C2211yescharacteristic
21#16839512—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61D411yescharacteristic
27#14519777—21no—
28#14519768—41no—
29#14519757—41no—
30#14519753—22no—
31Q8×Dic61—22no—
32#14519742—41no—
33#14519735—41no—
34C42×D61D411yescharacteristic
35#14519716—42no—
36C2×#11758185—21no—
37#14519711—21no—
38#14519711C2×C412yes—
39C4⋊#92418—21no—
40#14519701—22no—
41#14519701—22no—
42#14519689—41no—
43#14519687—41no—
44C4×#92418D411yescharacteristic
45C8×Dic61C2×C411yescharacteristic
46C8×Dic61D411yescharacteristic
47C2×Q16×C61—21no—
48C2×Q16×C61C2×C412yes—
49C4⋊Q8×C61—21no—
50C2×C16×C61—21no—
51C4⋊C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—22no—
54C2×C4×D61C22⋊C411yescharacteristic
55C2×C4×D61D811yescharacteristic
56C2×C4×D61SD1611yescharacteristic
57C2×Dic122—41no—
58Q16×C61—42no—
59Q16×C61—41no—
60Q16×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61C22×C411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67#11758198—42no—
68C4⋊Dic61—22no—
69C4⋊Dic61—41no—
70C4⋊Dic61—42no—
71#11758196—42no—
72C4×Dic61—42no—
73C4×Dic61C22⋊C411yescharacteristic
74C4×Dic61D811yescharacteristic
75C4×Dic61SD1611yescharacteristic
76C2×#92418—41no—
77C2×#92418C22⋊C411yescharacteristic
78C2×#92418C22⋊C411yescharacteristic
79C8×D61—21no—
80C8×D61—21no—
81C8×D61—41no—
82C16×C61—41no—
83#11758185—41no—
84C22×D61#10211yescharacteristic
85Q8×C61—42no—
86Q8×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61C2×SD1611yescharacteristic
91C2×Dic61—42no—
92C2×Dic61#10211yescharacteristic
93C2×Dic61#10211yescharacteristic
94C2×Dic61#10211yescharacteristic
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—41no—
100Dic122—82no—
101C8×C61—21no—
102C8×C61—81no—
103C8×C61AGL(1,ℤ/8)11yescharacteristic
104C8×C61#13711yescharacteristic
105#92418—21no—
106#92418—21no—
107#92418—81no—
108#11987—611nomaximal, Sylow
109C22×C61C2×#10211yescharacteristic
110C2×D61—21no—
111C2×D61—21no—
112C2×D61—21no—
113C4×C61—21no—
114C4×C61—82no—
115C4×C61#41311yescharacteristic
116C4×C61#41711yescharacteristic
117C4×C61#51011yescharacteristic
118C4×C61#51011yescharacteristic
119Dic61—21no—
120Dic61—21no—
121Dic61—21no—
122Dic61—82no—
123#3170—611no—
124#2150—611no—
125#1568—611no—
126#1365—611no—
127#1365—611no—
128#1362—611no—
129#1362D6111yescharacteristic, complemented
130C2×C61#154711yescharacteristic
131C2×C61#214111yescharacteristic
132C2×C61#214811yescharacteristic
133D61—41no—
134#533—1221no—
135C2×M32—1221no—
136#500—611no—
137#494C2×D6111yescharacteristic
138#487—1221no—
139#467—612no—
140#467—1221no—
141C4×Q16—612no—
142C4×Q16—1221no—
143#432—1221no—
144C2×C4×C8—611no—
145C4⋊C16—611no—
146C4⋊C16—1221no—
147C4⋊C16C2×D6111yescharacteristic
148#335—611no—
149#335C2×D6111yescharacteristic
150#334—1221no—
151C61#1198711yescharacteristic, complemented, Sylow
152C2×Q16—21no—
153C2×Q16C4×D6112yes—
154C22×C8—611no—
155C22×C8—611no—
156C4⋊Q8—21no—
157C4⋊Q8—1221no—
158#125—2441no—
159C22⋊Q8—1222no—
160C22⋊Q8—2441no—
161C4×Q8—1222no—
162C4×Q8—2441no—
163#117—2441no—
164C2×C42—611no—
165M32—2442no—
166C2×C16—21no—
167C2×C16—1221no—
168#107—612no—
169#107—1221no—
170C4⋊C8—21no—
171C4⋊C8—1221no—
172#103—1222no—
173#103—1222no—
174C22⋊C8—2441no—
175#97—2441no—
176C4×C8—611no—
177C4×C8—611no—
178C4×C8—611no—
179C4×C8C22×D6111yescharacteristic
180C2×Q8—22no—
181C2×Q8—2441no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188C2×C8—41no—
189C2×C8—611no—
190C2×C8—611no—
191C2×C8—1221no—
192C2×C8—1221no—
193C2×C8—2441no—
194C2×C8—2441no—
195C2×C8C2×C4×D6111yescharacteristic
196C2×C8D4×D6111yescharacteristic
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—1222no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2441no—
203C22⋊C4—2442no—
204C42—611no—
205C42—611no—
206C42—611no—
207C42—2442no—
208C42D4×D6111yescharacteristic
209C16—41no—
210C16—2441no—
211C23—611no—
212Q8—42no—
213Q8—42no—
214Q8—4882no—
215C2×C4—42no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—611no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—2441no—
224C2×C4—2442no—
225C2×C4C22⋊C4×D6111yescharacteristic
226C2×C4D8×D6111yescharacteristic
227C2×C4SD16×D6111yescharacteristic
228C8—21no—
229C8—81no—
230C8—1221no—
231C8—1221no—
232C8—4881no—
233C8#1451980111yescharacteristic
234C8#1451980611yescharacteristic
235C22—1221no—
236C22—1221no—
237C22—1221no—
238C22#102×D6111yescharacteristic
239C4—21no—
240C4—82no—
241C4—1221no—
242C4—1221no—
243C4—1221no—
244C4—4882no—
245C4#1683974311yescharacteristic
246C4#1683976011yescharacteristic
247C4#1684020111yescharacteristic
248C4#1684020411yescharacteristic
249C2—2441no—
250C2#2144449311yescharacteristic
251C2#2144753711yescharacteristic
252C2#2144756711yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC4×C8×C61C23
hypercenter#1362D61
hypocenterC61#11987
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
4. #21443878C2semidirect
5. #21443876C2semidirect
6. #21443868C2semidirect
7. C61×#1362C2semidirect
129. #1362D61semidirect
151. C61#11987semidirect

Maximal subgroups

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

subgroupindex
#214564032
#214475732
#214445812
#214438782
#214438762
#214438682
C61×#13622
#1198761