Finite Group Databasebeta

← C2×#20268017 #27204701

Subgroups — C2×#20268017 #27204701

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×C8×D103C211yesmaximal, characteristic, complemented
2C2×#15692997C211yesmaximal, characteristic, complemented
3C2×#15692992C211yesmaximal, characteristic
4#20268017C218yesmaximal, direct product factor
5C2×#15692953C211yesmaximal, characteristic, complemented
6C2×#15692945C211yesmaximal, characteristic, complemented
7C2×#15692942C211yesmaximal, characteristic, complemented
8C22×SD16×C103C211yesmaximal, characteristic, complemented
9C22×C22⋊D103—21no—
10C22×C4×D103C2211yescharacteristic
11C22×C103⋊C8C2211yescharacteristic
12C2×C8×D103—24no—
13C2×C8×D103C2214yescomplemented
14#15692997—22no—
15#15692997C2214yescomplemented
16#15692992—22no—
17#15692992C2214yes—
18C2×C4⋊Dic103C2211yescharacteristic
19C2×C4⋊Dic103C2211yescharacteristic
20C2×Dic103⋊C4—21no—
21C2×C22⋊Dic103—21no—
22C2×(C2×D103)⋊C4—21no—
23#15692953C2214yescomplemented
24#15692945C2214yescomplemented
25#15692942C2214yescomplemented
26C22×Q8×C103C2211yescharacteristic
27C22×D4×C103C2211yescharacteristic
28C2×SD16×C103—24no—
29C2×SD16×C103C2214yescomplemented
30C22×C8×C103C2211yescharacteristic
31C23×D103D411yescharacteristic
32C2×C22⋊D103—24no—
33C2×C22⋊D103—44no—
34C22×Dic103—21no—
35C22×Dic103—21no—
36C22×Dic103D411yescharacteristic
37C2×C4×D103—22no—
38C2×C4×D103—22no—
39C2×C4×D103D412yes—
40C2×C4×D103C2312yes—
41C2×C103⋊C8—22no—
42C2×C103⋊C8C2312yes—
43C8×D103—28no—
44C4⋊Dic103—21no—
45C4⋊Dic103—21no—
46C4⋊Dic103C2312yes—
47C4⋊Dic103C2312yes—
48Dic103⋊C4—24no—
49C22⋊Dic103—24no—
50(C2×D103)⋊C4—24no—
51C24×C103—21no—
52C2×Q8×C103—21no—
53C2×Q8×C103—22no—
54C2×Q8×C103—22no—
55C2×Q8×C103C2312yes—
56C2×D4×C103—22no—
57C2×D4×C103—21no—
58C2×D4×C103—22no—
59C2×D4×C103C2312yes—
60C22×C4×C103—21no—
61C22×C4×C103C2311yescharacteristic
62SD16×C103—28no—
63C2×C8×C103D414yescomplemented
64C2×C8×C103C2312yes—
65C23×C103—22no—
66C23×C103—42no—
67C23×C103—42no—
68C23×C103—42no—
69C23×C103C2×D411yescharacteristic
70C22×D103—22no—
71C22×D103—22no—
72C22×D103SD1614yescomplemented
73C22×D103C2×D412yes—
74Q8×C103—22no—
75Q8×C103—22no—
76Q8×C103—42no—
77D4×C103—22no—
78D4×C103—22no—
79D4×C103—42no—
80C2×C4×C103—22no—
81C2×C4×C103—42no—
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103C2×D412yes—
84C2×C4×C103#4112yes—
85C2×C4×C103C2411yescharacteristic
86C22⋊D103—48no—
87C2×Dic103—22no—
88C2×Dic103—22no—
89C2×Dic103—22no—
90C2×Dic103—42no—
91C2×Dic103—42no—
92C2×Dic103C2×D412yes—
93C4×D103—24no—
94C4×D103—22no—
95C4×D103—22no—
96C8×C103C2×D414yescomplemented
97C103⋊C8—22no—
98C22×C103—42no—
99C22×C103—42no—
100C22×C103—42no—
101C22×C103—84no—
102C22×C103#12112yes—
103C22×C103C2×SD1612yes—
104C22×C103#13512yes—
105C22×C103C22×D411yescharacteristic
106C2×D103—22no—
107C2×D103—22no—
108C2×D103—28no—
109C2×D103C2×SD1614yescomplemented
110C4×C103—42no—
111C4×C103#12112yes—
112C4×C103C22×D411yescharacteristic
113C4×C103C2×#4111yescharacteristic
114Dic103—22no—
115Dic103—42no—
116Dic103—42no—
117C2×C103—82no—
118C2×C103#46514yescomplemented
119C2×C103C2×#12111yescharacteristic
120C2×C103C22×SD1611yescharacteristic
121C2×C103C2×#13511yescharacteristic
122D103—24no—
123C2×#465—1031nomaximal, Sylow
124C103C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16D10311yescharacteristic, complemented
126C23×C8—1031no—
127C2×C22⋊Q8—1031no—
128C2×#121—1031no—
129#465—1038no—
130C2×#106—1031no—
131C2×#103—1031no—
132C2×#102—1031no—
133C22×Q8C2×D10311yescharacteristic
134C22×D4—2061no—
135C22×D4C2×D10311yescharacteristic
136C23×C4—1031no—
137C2×SD16—24no—
138C2×SD16C2×D10314yescomplemented
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—1031no—
149C2×C4⋊C4—2061no—
150C2×C22⋊C4—2061no—
151C2×C22⋊C4—2061no—
152#106—1034no—
153#103—1034no—
154#102—1034no—
155C24—21no—
156C24—1031no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D10312yes—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—4124no—
165C2×D4—2064no—
166C2×D4C22×D10312yes—
167C22×C4—21no—
168C22×C4—1031no—
169C22×C4—1032no—
170C22×C4—1032no—
171C22×C4—2061no—
172C22×C4—2061no—
173C22×C4—2062no—
174C22×C4—2062no—
175C22×C4C22×D10311yescharacteristic
176SD16—28no—
177C2×C8—1032no—
178C2×C8—2062no—
179C2×C8—2068no—
180C2×C8C22⋊D10314yescomplemented
181C2×C8C22×D10312yes—
182C4⋊C4—1032no—
183C4⋊C4—1032no—
184C4⋊C4—2064no—
185C4⋊C4—2061no—
186C4⋊C4—2061no—
187C22⋊C4—2064no—
188C22⋊C4—2064no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—1032no—
194C23—1034no—
195C23—2062no—
196C23—2062no—
197C23D4×D10311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—4128no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—1032no—
208C2×C4—4122no—
209C2×C4—4122no—
210C2×C4—2062no—
211C2×C4—2062no—
212C2×C4—2062no—
213C2×C4—2062no—
214C2×C4—2062no—
215C2×C4—2064no—
216C2×C4D4×D10311yescharacteristic
217C2×C4C2×C22⋊D10312yes—
218C2×C4#1311010412yes—
219C2×C4C23×D10311yescharacteristic
220C8—2062no—
221C8C2×C22⋊D10314yescomplemented
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—1034no—
227C22—2062no—
228C22—2068no—
229C22—2062no—
230C22#1569299212yes—
231C22SD16×D10312yes—
232C22#1569304212yes—
233C22C2×D4×D10311yescharacteristic
234C4—42no—
235C4—4122no—
236C4—4122no—
237C4—2062no—
238C4#1569299212yes—
239C4C22×C22⋊D10311yescharacteristic
240C4C2×#1311010411yescharacteristic
241C2—82no—
242C2—2064no—
243C2#2026801714yesdirect product factor
244C2C2×#1569299211yescharacteristic
245C2C2×SD16×D10311yescharacteristic
246C2C2×#1569304211yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×SD16×C103C2
socleC23×C103C2×D4
prime radicalC2×#15692992C2
hypercenterC22×SD16D103
hypocenterC103C2×#465
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C8×D103C2semidirect
2. C2×#15692997C2semidirect
4. #20268017C2direct (N × H)
5. C2×#15692953C2semidirect
6. C2×#15692945C2semidirect
7. C2×#15692942C2semidirect
8. C22×SD16×C103C2semidirect
13. C2×C8×D103C22semidirect
15. #15692997C22semidirect
23. #15692953C22semidirect
24. #15692945C22semidirect
25. #15692942C22semidirect
29. C2×SD16×C103C22semidirect
63. C2×C8×C103D4semidirect
72. C22×D103SD16semidirect
96. C8×C103C2×D4semidirect
109. C2×D103C2×SD16semidirect
118. C2×C103#465semidirect
124. C103C2×#465semidirect
125. C22×SD16D103semidirect
138. C2×SD16C2×D103semidirect
180. C2×C8C22⋊D103semidirect
221. C8C2×C22⋊D103semidirect
243. C2#20268017direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×D1032
C2×#156929972
C2×#156929922
#202680172
C2×#156929532
C2×#156929452
C2×#156929422
C22×SD16×C1032
C2×#465103