Finite Group Databasebeta

← C2×#21447605 #29833045

Subgroups — C2×#21447605 #29833045

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519717C211yesmaximal, characteristic
2C2×#16839800C211yesmaximal, characteristic
3#21447605C218yesmaximal, direct product factor
4C2×#16839589C212yesmaximal, complemented
5C2×#16839587C212yesmaximal, complemented
6C22×#107×C61C211yesmaximal, characteristic
7C2×#14519736—21no—
8C2×#14519717C418yescomplemented
9C2×#14519717C2214yes—
10C22×#11758185C2212yes—
11#16839800—22no—
12#16839800C2214yes—
13C2×#14519711C2211yescharacteristic
14C2×#14519711C2211yescharacteristic
15C2×#14519709—21no—
16#16839589C2218yescomplemented
17#16839587C2218yescomplemented
18C23×C8×C61C2211yescharacteristic
19C22×C4⋊C4×C61—21no—
20C2×#107×C61—21no—
21C2×#107×C61—22no—
22C2×#107×C61C2212yes—
23C2×#107×C61C2214yes—
24#14519736—24no—
25#14519736—42no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C22⋊Dic61—41no—
29C2×C4×Dic61—41no—
30#14519717C2×C4116yescomplemented
31C2×#11758185C2×C418yescomplemented
32C2×#11758185C2314yes—
33#14519711—21no—
34#14519711—21no—
35#14519711C2312yes—
36#14519711C2312yes—
37#14519709—24no—
38C23×C4×C61—41no—
39C23×C4×C61D411yescharacteristic
40C22×C8×C61C2×C414yes—
41C22×C8×C61D411yescharacteristic
42C22×C8×C61D412yes—
43C22×C8×C61Q814yes—
44C22×C8×C61C2311yescharacteristic
45C22×C8×C61C2312yes—
46C2×C4⋊C4×C61—22no—
47C2×C4⋊C4×C61—24no—
48C2×C4⋊C4×C61—41no—
49C2×C4⋊C4×C61—42no—
50#107×C61—24no—
51#107×C61—22no—
52#107×C61C2314yes—
53C24×C61D811yescharacteristic
54C22×C4×C61—44no—
55C22×C4×C61—42no—
56C22×C4×C61—84no—
57C22×C4×C61C4⋊C414yes—
58C22×C4×C61D811yescharacteristic
59C22×C4×C61D812yes—
60C22×C4×C61Q1614yes—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D412yes—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C2×C8×C61C4⋊C414yes—
66C2×C8×C61C4⋊C418yes—
67C2×C8×C61C22×C412yes—
68C2×C8×C61C22×C414yes—
69C2×C8×C61C2×D412yes—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×Q812yes—
72C2×C8×C61C2×Q814yes—
73C2×C8×C61C2411yescharacteristic
74C4⋊C4×C61—24no—
75C4⋊C4×C61—44no—
76C4⋊C4×C61—42no—
77C22⋊Dic61—44no—
78C4⋊Dic61—22no—
79C4⋊Dic61—22no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4×Dic61—44no—
83#11758185C22×C418yescomplemented
84C23×C61—22no—
85C23×C61—22no—
86C23×C61#10714yes—
87C23×C61C2×D812yes—
88C23×C61C2×D811yescharacteristic
89C2×C4×C61—44no—
90C2×C4×C61—88no—
91C2×C4×C61—84no—
92C2×C4×C61#10718yes—
93C2×C4×C61#10714yes—
94C2×C4×C61C2×C4⋊C414yes—
95C2×C4×C61C2×C4⋊C412yes—
96C2×C4×C61C2×D812yes—
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61C2×Q1614yes—
99C2×C4×C61C2×Q1612yes—
100C2×C4×C61C22×D411yescharacteristic
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—82no—
104C2×Dic61—82no—
105C8×C61C2×C4⋊C412yes—
106C8×C61C2×C4⋊C414yes—
107C8×C61C23×C411yescharacteristic
108C8×C61C22×Q811yescharacteristic
109C2×#2159—611nomaximal, Sylow
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—28no—
113C22×C61C2×#10714yes—
114C22×C61C2×#10712yes—
115C22×C61#50912yes—
116C22×C61#51012yes—
117C22×C61C22×D811yescharacteristic
118C4×C61—84no—
119C4×C61C2×#10714yes—
120C4×C61C2×#10712yes—
121C4×C61C22×C4⋊C411yescharacteristic
122C4×C61C22×Q1611yescharacteristic
123Dic61—82no—
124Dic61—82no—
125C22×M32—611no—
126C2×#427—611no—
127C22×#107D6111yescharacteristic
128#2159—618no—
129C2×#367—612no—
130C2×#366—612no—
131C2×C61—24no—
132C2×C61#215914yescomplemented
133C2×C61C22×#10711yescharacteristic
134C2×C61C2×#50911yescharacteristic
135C2×C61C2×#51011yescharacteristic
136C23×C8C2×D6111yescharacteristic
137C2×#117—1221no—
138C22×C4⋊C4—21no—
139C2×M32—618no—
140C2×M32—614no—
141C22×C16—612no—
142#427—614no—
143#427—1222no—
144C2×#107—21no—
145C2×#107—22no—
146C2×#107—611no—
147C2×#107—611no—
148C2×#107C2×D6112yes—
149C2×#107C2×D6114yes—
150C2×#106—1221no—
151#367—618no—
152#366—618no—
153C61C2×#215911yescharacteristic, complemented, Sylow
154C23×C4—41no—
155C23×C4C22⋊D6111yescharacteristic
156C22×C8Dic12214yes—
157C22×C8C4×D6114yes—
158C22×C8C22⋊D6111yescharacteristic
159C22×C8C22⋊D6112yes—
160C22×C8C22×D6111yescharacteristic
161C22×C8C22×D6112yes—
162#117—1224no—
163#117—2442no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4—1221no—
170C2×C22⋊C4—2441no—
171C2×C42—2441no—
172M32—6116no—
173C2×C16—618no—
174C2×C16—614no—
175#107—24no—
176#107—22no—
177#107—612no—
178#107—612no—
179#107—1221no—
180#107—1221no—
181#107C22×D6114yes—
182#106—1224no—
183C24#1175819911yescharacteristic
184C22×C4—44no—
185C22×C4—42no—
186C22×C4—84no—
187C22×C4—2441no—
188C22×C4—2441no—
189C22×C4#1175819614yes—
190C22×C4#1175819912yes—
191C22×C4#1175819911yescharacteristic
192C22×C4#1175820214yes—
193C22×C4C2×C22⋊D6112yes—
194C22×C4C2×C22⋊D6111yescharacteristic
195C2×C8#1175819614yes—
196C2×C8#1175819618yes—
197C2×C8C2×Dic12212yes—
198C2×C8C2×Dic12214yes—
199C2×C8C2×C4×D6112yes—
200C2×C8C2×C4×D6114yes—
201C2×C8C2×C22⋊D6112yes—
202C2×C8C2×C22⋊D6111yescharacteristic
203C2×C8C23×D6111yescharacteristic
204C4⋊C4—24no—
205C4⋊C4—44no—
206C4⋊C4—42no—
207C4⋊C4—1222no—
208C4⋊C4—1222no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C22⋊C4—2444no—
212C42—2444no—
213C16—618no—
214C23—22no—
215C23—22no—
216C23#1451971014yes—
217C23C2×#1175819912yes—
218C23C2×#1175819911yescharacteristic
219C2×C4—44no—
220C2×C4—88no—
221C2×C4—84no—
222C2×C4—4882no—
223C2×C4—4882no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4#1451971018yes—
227C2×C4#1451971014yes—
228C2×C4C2×#1175819614yes—
229C2×C4C2×#1175819612yes—
230C2×C4C2×#1175819912yes—
231C2×C4C2×#1175819911yescharacteristic
232C2×C4C2×#1175820214yes—
233C2×C4C2×#1175820212yes—
234C2×C4C22×C22⋊D6111yescharacteristic
235C8C2×#1175819612yes—
236C8C2×#1175819614yes—
237C8C22×C4×D6111yescharacteristic
238C8C22×Dic12211yescharacteristic
239C22—22no—
240C22—28no—
241C22—22no—
242C22C2×#1451971014yes—
243C22C2×#1451971012yes—
244C22#1684019812yes—
245C22#1684020312yes—
246C22C22×#1175819911yescharacteristic
247C4—84no—
248C4—4882no—
249C4—4882no—
250C4C2×#1451971014yes—
251C4C2×#1451971012yes—
252C4C22×#1175819611yescharacteristic
253C4C22×#1175820211yescharacteristic
254C2—24no—
255C2#2144760514yesdirect product factor
256C2C22×#1451971011yescharacteristic
257C2C2×#1684019811yescharacteristic
258C2C2×#1684020311yescharacteristic
subgroupG/H
centerC23C2×#11758199
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC22×#107×C61C2
socleC23×C61C2×D8
prime radicalC24×C61D8
cosocleC2×C8×C61C24
hypercenterC22×#107D61
hypocenterC61C2×#2159
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
3. #21447605C2direct (N × H)
4. C2×#16839589C2semidirect
5. C2×#16839587C2semidirect
8. C2×#14519717C4semidirect
16. #16839589C22semidirect
17. #16839587C22semidirect
30. #14519717C2×C4semidirect
31. C2×#11758185C2×C4semidirect
83. #11758185C22×C4semidirect
132. C2×C61#2159semidirect
153. C61C2×#2159semidirect
255. C2#21447605direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197172
C2×#168398002
#214476052
C2×#168395892
C2×#168395872
C22×#107×C612
C2×#215961