Finite Group Databasebeta

← C2×#20298830 #28400137

Subgroups — C2×#20298830 #28400137

Order 14464.

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×#14268634C211yesmaximal, characteristic, complemented
2C22×C8×D113C211yesmaximal, characteristic, complemented
3C2×#16813598C211yesmaximal, characteristic, complemented
4C2×#16813597C211yesmaximal, characteristic
5#20298830C218yesmaximal, direct product factor
6C2×#16813553C211yesmaximal, characteristic, complemented
7C2×#16813544C211yesmaximal, characteristic, complemented
8C2×#103×C113C211yesmaximal, characteristic, complemented
9C22×D452—21no—
10C22×D452C2211yescharacteristic
11C22×C4×D113C2211yescharacteristic
12C2×#14268634—24no—
13C2×#14268634C2214yescomplemented
14C22×#11744751C2211yescharacteristic
15C2×C8×D113—24no—
16C2×C8×D113C2214yescomplemented
17#16813598—22no—
18#16813598C2214yescomplemented
19#16813597—22no—
20#16813597C2214yes—
21C2×C4⋊Dic113C2211yescharacteristic
22C2×#14268626—21no—
23C2×#14268624—21no—
24C2×#14268624—21no—
25#16813553C2214yescomplemented
26#16813544C2214yescomplemented
27C22×Q8×C113C2211yescharacteristic
28C22×C8×C113C2211yescharacteristic
29C2×C4⋊C4×C113C2211yescharacteristic
30#103×C113C2214yescomplemented
31C23×D113—21no—
32C23×D113D411yescharacteristic
33C2×D452—22no—
34C2×D452—22no—
35C2×D452—24no—
36C2×D452—21no—
37C2×D452—44no—
38C2×D452C2312yes—
39C22×Dic113—21no—
40C22×Dic113D411yescharacteristic
41C2×C4×D113—22no—
42C2×C4×D113—22no—
43C2×C4×D113D412yes—
44C2×C4×D113C2312yes—
45#14268634—28no—
46C2×#11744751D414yescomplemented
47C2×#11744751C2312yes—
48C8×D113—28no—
49C4⋊Dic113—21no—
50C4⋊Dic113C2312yes—
51#14268626—24no—
52#14268624—24no—
53#14268624—24no—
54C2×Q8×C113—21no—
55C2×Q8×C113—22no—
56C2×Q8×C113—22no—
57C2×Q8×C113C2312yes—
58C22×C4×C113—21no—
59C22×C4×C113—21no—
60C22×C4×C113C2311yescharacteristic
61C2×C8×C113—22no—
62C2×C8×C113C2312yes—
63C4⋊C4×C113—21no—
64C4⋊C4×C113C2312yes—
65C23×C113C2×D411yescharacteristic
66C22×D113—22no—
67C22×D113—22no—
68C22×D113—22no—
69C22×D113—42no—
70C22×D113—42no—
71C22×D113—42no—
72C22×D113SD1614yescomplemented
73C22×D113C2×D412yes—
74Q8×C113—22no—
75Q8×C113—22no—
76Q8×C113—42no—
77C2×C4×C113—22no—
78C2×C4×C113—22no—
79C2×C4×C113—42no—
80C2×C4×C113—42no—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D412yes—
83C2×C4×C113#4112yes—
84C2×C4×C113C2411yescharacteristic
85C2×Dic113—22no—
86C2×Dic113—22no—
87C2×Dic113—42no—
88C2×Dic113C2×D412yes—
89D452—22no—
90D452—22no—
91D452—48no—
92D452—42no—
93C4×D113—24no—
94C4×D113—22no—
95C4×D113—22no—
96C8×C113—22no—
97#11744751C2×D414yescomplemented
98C22×C113#12112yes—
99C22×C113C2×SD1612yes—
100C22×C113#13512yes—
101C22×C113C22×D411yescharacteristic
102C2×D113—22no—
103C2×D113—22no—
104C2×D113—28no—
105C2×D113—42no—
106C2×D113—42no—
107C2×D113—42no—
108C2×D113—84no—
109C2×D113C2×SD1614yescomplemented
110C4×C113—42no—
111C4×C113—42no—
112C4×C113#12112yes—
113C4×C113C22×D411yescharacteristic
114C4×C113C2×#4111yescharacteristic
115Dic113—22no—
116Dic113—42no—
117C2×C113#46514yescomplemented
118C2×C113C2×#12111yescharacteristic
119C2×C113C22×SD1611yescharacteristic
120C2×C113C2×#13511yescharacteristic
121D113—24no—
122D113—82no—
123C2×#465—1131nomaximal, Sylow
124C113C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—1131no—
126C23×C8—1131no—
127C2×C22⋊Q8—1131no—
128C2×#121—1131no—
129#465—1138no—
130C2×#106—1131no—
131C2×#103D11311yescharacteristic, complemented
132C2×#102—1131no—
133C22×Q8C2×D11311yescharacteristic
134C22×D4—1131no—
135C22×D4—2261no—
136C23×C4—1131no—
137C2×SD16—1134no—
138C2×SD16—2264no—
139C22×C8—1131no—
140C22×C8—1134no—
141C22×C8—2264no—
142C22×C8C2×D11311yescharacteristic
143C22⋊Q8—1134no—
144C22⋊Q8—2262no—
145#121—1134no—
146#121—2262no—
147C2×C4⋊C4—1131no—
148C2×C4⋊C4—2261no—
149C2×C4⋊C4C2×D11311yescharacteristic
150C2×C22⋊C4—2261no—
151C2×C22⋊C4—2261no—
152#106—1134no—
153#103C2×D11314yescomplemented
154#102—1134no—
155C24—1131no—
156C24—2261no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D11312yes—
161C2×D4—1132no—
162C2×D4—4524no—
163C2×D4—2264no—
164C2×D4—2261no—
165C2×D4—2262no—
166C2×D4—2262no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—1131no—
170C22×C4—1132no—
171C22×C4—1132no—
172C22×C4—2261no—
173C22×C4—2262no—
174C22×C4—2262no—
175C22×C4C22×D11311yescharacteristic
176SD16—2268no—
177C2×C8—22no—
178C2×C8—1134no—
179C2×C8—1132no—
180C2×C8—2268no—
181C2×C8C22×D11312yes—
182C4⋊C4—21no—
183C4⋊C4—1132no—
184C4⋊C4—2264no—
185C4⋊C4—2261no—
186C4⋊C4C22×D11312yes—
187C22⋊C4—2264no—
188C22⋊C4—2264no—
189C23—1134no—
190C23—1132no—
191C23—4522no—
192C23—4522no—
193C23—4522no—
194C23—2262no—
195C23—2262no—
196C23—2262no—
197C23D4×D11311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—4528no—
202D4—4522no—
203D4—2262no—
204D4—2262no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—1132no—
210C2×C4—4522no—
211C2×C4—2262no—
212C2×C4—2262no—
213C2×C4—2264no—
214C2×C4—2262no—
215C2×C4—2262no—
216C2×C4D4×D11311yescharacteristic
217C2×C4D4×D11312yes—
218C2×C4#1426864712yes—
219C2×C4C23×D11311yescharacteristic
220C8—22no—
221C8—1134no—
222C22—1134no—
223C22—9044no—
224C22—4522no—
225C22—4522no—
226C22—4522no—
227C22—2268no—
228C22—2262no—
229C22—2262no—
230C22#1681359512yes—
231C22SD16×D11312yes—
232C22#1681364512yes—
233C22C2×D4×D11311yescharacteristic
234C4—42no—
235C4—42no—
236C4—4522no—
237C4—2262no—
238C4#1681359512yes—
239C4C2×D4×D11311yescharacteristic
240C4C2×#1426864711yescharacteristic
241C2—9042no—
242C2—2264no—
243C2#2029883014yesdirect product factor
244C2C2×#1681359511yescharacteristic
245C2C2×SD16×D11311yescharacteristic
246C2C2×#1681364511yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#103×C113C2
socleC23×C113C2×D4
prime radicalC2×#16813597C2
hypercenterC2×#103D113
hypocenterC113C2×#465
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#14268634C2semidirect
2. C22×C8×D113C2semidirect
3. C2×#16813598C2semidirect
5. #20298830C2direct (N × H)
6. C2×#16813553C2semidirect
7. C2×#16813544C2semidirect
8. C2×#103×C113C2semidirect
13. C2×#14268634C22semidirect
16. C2×C8×D113C22semidirect
18. #16813598C22semidirect
25. #16813553C22semidirect
26. #16813544C22semidirect
30. #103×C113C22semidirect
46. C2×#11744751D4semidirect
72. C22×D113SD16semidirect
97. #11744751C2×D4semidirect
109. C2×D113C2×SD16semidirect
117. C2×C113#465semidirect
124. C113C2×#465semidirect
131. C2×#103D113semidirect
153. #103C2×D113semidirect
243. C2#20298830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142686342
C22×C8×D1132
C2×#168135982
C2×#168135972
#202988302
C2×#168135532
C2×#168135442
C2×#103×C1132
C2×#465113