Finite Group Databasebeta

← C2×#20268023 #27204707

Subgroups — C2×#20268023 #27204707

Order 13184.

564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13110092C211yesmaximal, characteristic, complemented
2C22×C8×D103C211yesmaximal, characteristic, complemented
3C2×#15692997C211yesmaximal, characteristic, complemented
4C2×#15692996C211yesmaximal, characteristic
5#20268023C218yesmaximal, direct product factor
6C2×#15692952C211yesmaximal, characteristic, complemented
7C2×#15692943C211yesmaximal, characteristic, complemented
8C2×#103×C103C211yesmaximal, characteristic, complemented
9C22×D412—21no—
10C22×D412C2211yescharacteristic
11C22×C4×D103C2211yescharacteristic
12C2×#13110092—24no—
13C2×#13110092C2214yescomplemented
14C22×C103⋊C8C2211yescharacteristic
15C2×C8×D103—24no—
16C2×C8×D103C2214yescomplemented
17#15692997—22no—
18#15692997C2214yescomplemented
19#15692996—22no—
20#15692996C2214yes—
21C2×C4⋊Dic103C2211yescharacteristic
22C2×Dic103⋊C4—21no—
23C2×(C2×D103)⋊C4—21no—
24C2×(C2×D103)⋊C4—21no—
25#15692952C2214yescomplemented
26#15692943C2214yescomplemented
27C22×Q8×C103C2211yescharacteristic
28C22×C8×C103C2211yescharacteristic
29C2×C4⋊C4×C103C2211yescharacteristic
30#103×C103C2214yescomplemented
31C23×D103—21no—
32C23×D103D411yescharacteristic
33C2×D412—22no—
34C2×D412—22no—
35C2×D412—24no—
36C2×D412—21no—
37C2×D412—44no—
38C2×D412C2312yes—
39C22×Dic103—21no—
40C22×Dic103D411yescharacteristic
41C2×C4×D103—22no—
42C2×C4×D103—22no—
43C2×C4×D103D412yes—
44C2×C4×D103C2312yes—
45#13110092—28no—
46C2×C103⋊C8D414yescomplemented
47C2×C103⋊C8C2312yes—
48C8×D103—28no—
49C4⋊Dic103—21no—
50C4⋊Dic103C2312yes—
51Dic103⋊C4—24no—
52(C2×D103)⋊C4—24no—
53(C2×D103)⋊C4—24no—
54C2×Q8×C103—21no—
55C2×Q8×C103—22no—
56C2×Q8×C103—22no—
57C2×Q8×C103C2312yes—
58C22×C4×C103—21no—
59C22×C4×C103—21no—
60C22×C4×C103C2311yescharacteristic
61C2×C8×C103—22no—
62C2×C8×C103C2312yes—
63C4⋊C4×C103—21no—
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—
74Q8×C103—22no—
75Q8×C103—22no—
76Q8×C103—42no—
77C2×C4×C103—22no—
78C2×C4×C103—22no—
79C2×C4×C103—42no—
80C2×C4×C103—42no—
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2×D412yes—
83C2×C4×C103#4112yes—
84C2×C4×C103C2411yescharacteristic
85C2×Dic103—22no—
86C2×Dic103—22no—
87C2×Dic103—42no—
88C2×Dic103C2×D412yes—
89D412—22no—
90D412—22no—
91D412—48no—
92D412—42no—
93C4×D103—24no—
94C4×D103—22no—
95C4×D103—22no—
96C8×C103—22no—
97C103⋊C8C2×D414yescomplemented
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×#106—1031no—
131C2×#103D10311yescharacteristic, complemented
132C2×#102—1031no—
133C22×Q8C2×D10311yescharacteristic
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—1031no—
148C2×C4⋊C4—2061no—
149C2×C4⋊C4C2×D10311yescharacteristic
150C2×C22⋊C4—2061no—
151C2×C22⋊C4—2061no—
152#106—1034no—
153#103C2×D10314yescomplemented
154#102—1034no—
155C24—1031no—
156C24—2061no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D10312yes—
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—22no—
178C2×C8—1034no—
179C2×C8—1032no—
180C2×C8—2068no—
181C2×C8C22×D10312yes—
182C4⋊C4—21no—
183C4⋊C4—1032no—
184C4⋊C4—2064no—
185C4⋊C4—2061no—
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—22no—
199Q8—22no—
200Q8—42no—
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×D10312yes—
217C2×C4D4×D10311yescharacteristic
218C2×C4#1311010512yes—
219C2×C4C23×D10311yescharacteristic
220C8—22no—
221C8—1034no—
222C22—8244no—
223C22—1034no—
224C22—4122no—
225C22—4122no—
226C22—4122no—
227C22—2062no—
228C22—2068no—
229C22—2062no—
230C22#1569299412yes—
231C22SD16×D10312yes—
232C22#1569304412yes—
233C22C2×D4×D10311yescharacteristic
234C4—42no—
235C4—42no—
236C4—4122no—
237C4—2062no—
238C4#1569299412yes—
239C4C2×D4×D10311yescharacteristic
240C4C2×#1311010511yescharacteristic
241C2—8242no—
242C2—2064no—
243C2#2026802314yesdirect product factor
244C2C2×#1569299411yescharacteristic
245C2C2×SD16×D10311yescharacteristic
246C2C2×#1569304411yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#103×C103C2
socleC23×C103C2×D4
prime radicalC2×#15692996C2
hypercenterC2×#103D103
hypocenterC103C2×#465
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#13110092C2semidirect
2. C22×C8×D103C2semidirect
3. C2×#15692997C2semidirect
5. #20268023C2direct (N × H)
6. C2×#15692952C2semidirect
7. C2×#15692943C2semidirect
8. C2×#103×C103C2semidirect
13. C2×#13110092C22semidirect
16. C2×C8×D103C22semidirect
18. #15692997C22semidirect
25. #15692952C22semidirect
26. #15692943C22semidirect
30. #103×C103C22semidirect
46. C2×C103⋊C8D4semidirect
72. C22×D103SD16semidirect
97. C103⋊C8C2×D4semidirect
109. C2×D103C2×SD16semidirect
117. C2×C103#465semidirect
124. C103C2×#465semidirect
131. C2×#103D103semidirect
153. #103C2×D103semidirect
243. C2#20268023direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100922
C22×C8×D1032
C2×#156929972
C2×#156929962
#202680232
C2×#156929522
C2×#156929432
C2×#103×C1032
C2×#465103