Finite Group Databasebeta

← #30594502

Subgroups — #30594502

Order 15616.

286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461699C211yesmaximal, characteristic
2#21461696C211yesmaximal, characteristic
3#21447429C211yesmaximal, characteristic
4C2×#14519848—21no—
5C2×#14519846—21no—
6#16840733—21no—
7#16840704—21no—
8#16840638C412yescomplemented
9#16840636C412yes—
10C22×C8×D61C2211yescharacteristic
11C2×#14519717C411yescharacteristic, complemented
12#16839541—21no—
13#16839541—21no—
14C2×M32×C61C411yescharacteristic, complemented
15C2×#11758213—22no—
16C2×C4⋊#6923—22no—
17C2×C22⋊#6923—41no—
18#14519848—41no—
19#14519848—41no—
20#14519846—41no—
21#14519846—41no—
22#14519834—41no—
23C22⋊#92420—41no—
24(C2×#6923)⋊C4—41no—
25C22×C4×D61D411yescharacteristic
26C22×#92418Q811yescharacteristic
27C2×C8×D61—41no—
28C2×C8×D61—41no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519717—41no—
34C2×#11758185—21no—
35C22×C8×C61C2×C411yescharacteristic
36M32×C61—41no—
37C2×C16×C61—21no—
38C23×D61SD1611yescharacteristic
39C22×#6923—42no—
40C22×C4×C61C4⋊C411yescharacteristic
41C22×Dic61SD1611yescharacteristic
42C2×C4×D61—41no—
43C2×C4×D61—41no—
44C2×C4×D61C22⋊C411yescharacteristic
45C2×C4×D61C22⋊C411yescharacteristic
46C2×C4×D61D811yescharacteristic
47C2×C4×D61Q1611yescharacteristic
48C22⋊#6923—82no—
49C2×#92420—42no—
50C4⋊#6923—42no—
51C4⋊#6923—42no—
52#11758213—42no—
53#11758213—42no—
54C2×C8×C61—21no—
55C2×C8×C61—21no—
56C2×C8×C61C4211yescharacteristic
57C2×C8×C61C22⋊C411yescharacteristic
58C2×#92418—41no—
59C2×#92418C4⋊C411yescharacteristic
60C2×#92418C4⋊C411yescharacteristic
61C8×D61—21no—
62C8×D61—21no—
63C8×D61—21no—
64C8×D61—21no—
65C8×D61—41no—
66C8×D61—41no—
67C16×C61—41no—
68#11758185—41no—
69C23×C61#10611yescharacteristic
70C22×D61—21no—
71C22×D61—21no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61#10211yescharacteristic
75C22×D61#10311yescharacteristic
76C2×#6923—82no—
77C2×#6923—82no—
78C2×#6923—82no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61#9511yescharacteristic
82C2×C4×C61#10711yescharacteristic
83C2×Dic61—41no—
84C2×Dic61#10211yescharacteristic
85C2×Dic61#10311yescharacteristic
86C4×D61—21no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—41no—
91C4×D61—41no—
92#92420—82no—
93C8×C61—21no—
94C8×C61#9911yescharacteristic
95C8×C61#9911yescharacteristic
96#92418—21no—
97#92418—21no—
98#7235—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#34011yescharacteristic
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61#36111yescharacteristic
111C2×D61#36211yescharacteristic
112#6923—162no—
113C4×C61—21no—
114C4×C61H(3,ℤ/4)11yescharacteristic
115C4×C61#34211yescharacteristic
116Dic61—21no—
117Dic61—21no—
118#2112—611no—
119#1810—611no—
120#1808—611no—
121C2×C61—41no—
122C2×C61#128911yescharacteristic
123C2×C61#138711yescharacteristic
124C2×C61#138911yescharacteristic
125D61—21no—
126D61—21no—
127D61—41no—
128C23×C8—611no—
129C2×M32—611no—
130C2×M32#692311yescharacteristic, complemented
131C2×#108—1221no—
132C2×#107—1221no—
133#407—1221no—
134#380—1221no—
135C22⋊C16—1221no—
136C22⋊C16—1221no—
137#341—612no—
138#340—612no—
139C61#723511yescharacteristic, complemented, Sylow
140C23×C4—611no—
141C2×M16—1222no—
142C22×C8—611no—
143C22×C8—611no—
144C22×C8—611no—
145C22×C8—611no—
146C22×C8—611no—
147C22×C8—2441no—
148C22×C8—2441no—
149C22×C8C2×#692311yescharacteristic
150C2×C4⋊C4—1222no—
151C2×C22⋊C4—2441no—
152M32—41no—
153M32—2441no—
154C2×C16—21no—
155C2×C16—1221no—
156#108—2441no—
157#108—2441no—
158#107—2441no—
159#107—2441no—
160C22⋊C8—2441no—
161C22⋊C8—2441no—
162#95—2441no—
163C24—611no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—2441no—
170C22×C4—2441no—
171C22×C4—2442no—
172C22×C4C4⋊#692311yescharacteristic
173M16—2442no—
174M16—2442no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—611no—
178C2×C8—611no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8—1221no—
182C2×C8—1221no—
183C2×C8—2441no—
184C2×C8—2441no—
185C2×C8—2441no—
186C2×C8—2442no—
187C2×C8C4×#692311yescharacteristic
188C2×C8C22⋊#692311yescharacteristic
189C4⋊C4—2442no—
190C4⋊C4—2442no—
191C22⋊C4—4882no—
192C16—41no—
193C16—2441no—
194C23—611no—
195C23—611no—
196C23—1221no—
197C23—1221no—
198C23—2441no—
199C23—2441no—
200C23#1451984511yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—611no—
204C2×C4—611no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—4882no—
210C2×C4—4882no—
211C2×C4—4882no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4(C2×#6923)⋊C411yescharacteristic
216C2×C4#1451984611yescharacteristic
217C8—21no—
218C8—1221no—
219C8—1221no—
220C8—4882no—
221C8#1451983511yescharacteristic
222C8#1451983611yescharacteristic
223C22—21no—
224C22—21no—
225C22—21no—
226C22—611no—
227C22—611no—
228C22—1221no—
229C22—1221no—
230C22—1221no—
231C22—1221no—
232C22—1221no—
233C22—2442no—
234C22—2442no—
235C22#1684063611yescharacteristic
236C4—21no—
237C4—1221no—
238C4—1221no—
239C4—9762no—
240C4#1684063011yescharacteristic
241C4#1684064011yescharacteristic
242C2—41no—
243C2—1221no—
244C2—1221no—
245C2—2441no—
246C2#2146068211yescharacteristic
247C2#2146089411yescharacteristic
248C2#2146090011yescharacteristic
subgroupG/H
centerC22#16840636
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC2×M32×C61C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenterC2×M32#6923
hypocenterC61#7235
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
8. #16840638C4semidirect
11. C2×#14519717C4semidirect
14. C2×M32×C61C4semidirect
130. C2×M32#6923semidirect
139. C61#7235semidirect

Maximal subgroups

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

subgroupindex
#214616992
#214616962
#214474292
#723561