Finite Group Databasebeta

← C2×#20268021 #27204705

Subgroups — C2×#20268021 #27204705

Order 13184.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#13110094C211yesmaximal, characteristic, complemented
2C22×C8×D103C211yesmaximal, characteristic, complemented
3C2×#15693001C211yesmaximal, characteristic, complemented
4C2×#15692996C211yesmaximal, characteristic
5#20268021C218yesmaximal, direct product factor
6C2×#15692944C211yesmaximal, characteristic, complemented
7C2×#15692941C211yesmaximal, characteristic, complemented
8C2×#106×C103C211yesmaximal, characteristic, complemented
9C22×Dic206C2211yescharacteristic
10C22×D412—21no—
11C22×D412C2211yescharacteristic
12C22×C4×D103C2211yescharacteristic
13C2×#13110094—24no—
14C2×#13110094C2214yescomplemented
15C22×C103⋊C8C2211yescharacteristic
16C2×C8×D103—24no—
17C2×C8×D103C2214yescomplemented
18#15693001—22no—
19#15693001C2214yescomplemented
20#15692996—22no—
21#15692996C2214yes—
22C2×C4⋊Dic103—21no—
23C2×(C2×D103)⋊C4—21no—
24C2×(C2×D103)⋊C4—21no—
25#15692944C2214yescomplemented
26#15692941C2214yescomplemented
27C22×C8×C103C2211yescharacteristic
28C2×C4⋊C4×C103C2211yescharacteristic
29C2×C4⋊C4×C103C2211yescharacteristic
30#106×C103C2214yescomplemented
31C23×D103—21no—
32C23×D103D411yescharacteristic
33C2×Dic206—22no—
34C2×Dic206—22no—
35C2×Dic206—21no—
36C2×Dic206C2312yes—
37C2×D412—22no—
38C2×D412—22no—
39C2×D412—24no—
40C2×D412—21no—
41C2×D412—44no—
42C2×D412C2312yes—
43C22×Dic103—21no—
44C22×Dic103D411yescharacteristic
45C2×C4×D103—22no—
46C2×C4×D103—22no—
47C2×C4×D103D412yes—
48C2×C4×D103C2312yes—
49#13110094—28no—
50C2×C103⋊C8—22no—
51C2×C103⋊C8C2312yes—
52C8×D103—28no—
53C4⋊Dic103—24no—
54(C2×D103)⋊C4—24no—
55(C2×D103)⋊C4—24no—
56C22×C4×C103—21no—
57C22×C4×C103—21no—
58C22×C4×C103C2311yescharacteristic
59C2×C8×C103D414yescomplemented
60C2×C8×C103C2312yes—
61C4⋊C4×C103—21no—
62C4⋊C4×C103—21no—
63C4⋊C4×C103C2312yes—
64C4⋊C4×C103C2312yes—
65C23×C103C2×D411yescharacteristic
66C22×D103—22no—
67C22×D103—22no—
68C22×D103—22no—
69C22×D103—42no—
70C22×D103—42no—
71C22×D103—42no—
72C22×D103SD1614yescomplemented
73C22×D103C2×D412yes—
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103—42no—
77C2×C4×C103—42no—
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2×D412yes—
80C2×C4×C103#4112yes—
81C2×C4×C103C2411yescharacteristic
82C2×Dic103—22no—
83C2×Dic103—22no—
84C2×Dic103—42no—
85C2×Dic103C2×D412yes—
86D412—22no—
87D412—22no—
88D412—48no—
89D412—42no—
90C4×D103—24no—
91C4×D103—22no—
92C4×D103—22no—
93Dic206—22no—
94Dic206—22no—
95Dic206—42no—
96C8×C103C2×D414yescomplemented
97C103⋊C8—22no—
98C22×C103#12112yes—
99C22×C103C2×SD1612yes—
100C22×C103#13512yes—
101C22×C103C22×D411yescharacteristic
102C2×D103—22no—
103C2×D103—22no—
104C2×D103—28no—
105C2×D103—42no—
106C2×D103—42no—
107C2×D103—42no—
108C2×D103—84no—
109C2×D103C2×SD1614yescomplemented
110C4×C103—42no—
111C4×C103—42no—
112C4×C103#12112yes—
113C4×C103C22×D411yescharacteristic
114C4×C103C2×#4111yescharacteristic
115Dic103—22no—
116Dic103—42no—
117C2×C103#46514yescomplemented
118C2×C103C2×#12111yescharacteristic
119C2×C103C22×SD1611yescharacteristic
120C2×C103C2×#13511yescharacteristic
121D103—24no—
122D103—82no—
123C2×#465—1031nomaximal, Sylow
124C103C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—1031no—
126C23×C8—1031no—
127C2×C22⋊Q8—1031no—
128C2×#121—1031no—
129#465—1038no—
130C2×#106D10311yescharacteristic, complemented
131C2×#103—1031no—
132C2×#102—1031no—
133C22×Q8—1031no—
134C22×D4—1031no—
135C22×D4—2061no—
136C23×C4—1031no—
137C2×SD16—1034no—
138C2×SD16—2064no—
139C22×C8—1031no—
140C22×C8—1034no—
141C22×C8—2064no—
142C22×C8C2×D10311yescharacteristic
143C22⋊Q8—1034no—
144C22⋊Q8—2062no—
145#121—1034no—
146#121—2062no—
147C2×C4⋊C4—2061no—
148C2×C4⋊C4C2×D10311yescharacteristic
149C2×C4⋊C4C2×D10311yescharacteristic
150C2×C22⋊C4—2061no—
151C2×C22⋊C4—2061no—
152#106C2×D10314yescomplemented
153#103—1034no—
154#102—1034no—
155C24—1031no—
156C24—2061no—
157C2×Q8—1032no—
158C2×Q8—2062no—
159C2×Q8—2062no—
160C2×Q8—2061no—
161C2×D4—1032no—
162C2×D4—4124no—
163C2×D4—2064no—
164C2×D4—2061no—
165C2×D4—2062no—
166C2×D4—2062no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—1031no—
170C22×C4—1032no—
171C22×C4—1032no—
172C22×C4—2061no—
173C22×C4—2062no—
174C22×C4—2062no—
175C22×C4C22×D10311yescharacteristic
176SD16—2068no—
177C2×C8—1032no—
178C2×C8—2062no—
179C2×C8—2068no—
180C2×C8D41214yescomplemented
181C2×C8C22×D10312yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—2064no—
185C4⋊C4C22×D10312yes—
186C4⋊C4C22×D10312yes—
187C22⋊C4—2064no—
188C22⋊C4—2064no—
189C23—1032no—
190C23—1034no—
191C23—4122no—
192C23—4122no—
193C23—4122no—
194C23—2062no—
195C23—2062no—
196C23—2062no—
197C23D4×D10311yescharacteristic
198Q8—4122no—
199Q8—2062no—
200Q8—2062no—
201D4—4128no—
202D4—4122no—
203D4—2062no—
204D4—2062no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—1032no—
210C2×C4—4122no—
211C2×C4—2062no—
212C2×C4—2062no—
213C2×C4—2062no—
214C2×C4—2062no—
215C2×C4—2064no—
216C2×C4D4×D10311yescharacteristic
217C2×C4C2×D41212yes—
218C2×C4#1311010612yes—
219C2×C4C23×D10311yescharacteristic
220C8—2062no—
221C8C2×D41214yescomplemented
222C22—8244no—
223C22—1034no—
224C22—4122no—
225C22—4122no—
226C22—4122no—
227C22—2062no—
228C22—2068no—
229C22—2062no—
230C22#1569299612yes—
231C22SD16×D10312yes—
232C22#1569304212yes—
233C22C2×D4×D10311yescharacteristic
234C4—42no—
235C4—42no—
236C4—4122no—
237C4—2062no—
238C4#1569299612yes—
239C4C22×D41211yescharacteristic
240C4C2×#1311010611yescharacteristic
241C2—8242no—
242C2—2064no—
243C2#2026802114yesdirect product factor
244C2C2×#1569299611yescharacteristic
245C2C2×SD16×D10311yescharacteristic
246C2C2×#1569304211yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#106×C103C2
socleC23×C103C2×D4
prime radicalC2×#15692996C2
hypercenterC2×#106D103
hypocenterC103C2×#465
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C22×#13110094C2semidirect
2. C22×C8×D103C2semidirect
3. C2×#15693001C2semidirect
5. #20268021C2direct (N × H)
6. C2×#15692944C2semidirect
7. C2×#15692941C2semidirect
8. C2×#106×C103C2semidirect
14. C2×#13110094C22semidirect
17. C2×C8×D103C22semidirect
19. #15693001C22semidirect
25. #15692944C22semidirect
26. #15692941C22semidirect
30. #106×C103C22semidirect
59. C2×C8×C103D4semidirect
72. C22×D103SD16semidirect
96. C8×C103C2×D4semidirect
109. C2×D103C2×SD16semidirect
117. C2×C103#465semidirect
124. C103C2×#465semidirect
130. C2×#106D103semidirect
152. #106C2×D103semidirect
180. C2×C8D412semidirect
221. C8C2×D412semidirect
243. C2#20268021direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100942
C22×C8×D1032
C2×#156930012
C2×#156929962
#202680212
C2×#156929442
C2×#156929412
C2×#106×C1032
C2×#465103