Finite Group Databasebeta

← C2×#20298843 #28400161

Subgroups — C2×#20298843 #28400161

Order 14464.

544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14268635C211yesmaximal, characteristic, complemented
2C22×#14268630C211yesmaximal, characteristic, complemented
3C2×#16813602C211yesmaximal, characteristic, complemented
4C2×#16813593C211yesmaximal, characteristic
5#20298843C218yesmaximal, direct product factor
6C2×#16813555C211yesmaximal, characteristic, complemented
7C2×#16813547C211yesmaximal, characteristic, complemented
8C2×#102×C113C211yesmaximal, characteristic, complemented
9C22×Dic226C2211yescharacteristic
10C22×C22⋊D113—21no—
11C22×C4×D113C2211yescharacteristic
12C2×#14268635—24no—
13C2×#14268635C2214yescomplemented
14C2×#14268630—24no—
15C2×#14268630C2214yescomplemented
16C22×#11744751C2211yescharacteristic
17#16813602—22no—
18#16813602C2214yescomplemented
19#16813593—22no—
20#16813593C2214yes—
21C2×C4⋊Dic113—21no—
22C2×C4⋊Dic113C2211yescharacteristic
23C2×C22⋊Dic113—21no—
24C2×#14268624—21no—
25#16813555C2214yescomplemented
26#16813547C2214yescomplemented
27C22×D4×C113C2211yescharacteristic
28C22×C8×C113C2211yescharacteristic
29C2×C4⋊C4×C113C2211yescharacteristic
30#102×C113C2214yescomplemented
31C23×D113D411yescharacteristic
32C2×Dic226—22no—
33C2×Dic226—22no—
34C2×Dic226—21no—
35C2×Dic226C2312yes—
36C2×C22⋊D113—24no—
37C2×C22⋊D113—44no—
38C22×Dic113—21no—
39C22×Dic113—21no—
40C22×Dic113D411yescharacteristic
41C2×C4×D113—22no—
42C2×C4×D113—22no—
43C2×C4×D113D412yes—
44C2×C4×D113C2312yes—
45#14268635—28no—
46#14268630—28no—
47C2×#11744751D414yescomplemented
48C2×#11744751C2312yes—
49C4⋊Dic113—21no—
50C4⋊Dic113—24no—
51C4⋊Dic113C2312yes—
52C22⋊Dic113—24no—
53#14268624—24no—
54C24×C113—21no—
55C2×D4×C113—22no—
56C2×D4×C113—21no—
57C2×D4×C113—22no—
58C2×D4×C113C2312yes—
59C22×C4×C113—21no—
60C22×C4×C113C2311yescharacteristic
61C2×C8×C113—22no—
62C2×C8×C113C2312yes—
63C4⋊C4×C113—21no—
64C4⋊C4×C113C2312yes—
65C23×C113—22no—
66C23×C113—42no—
67C23×C113—42no—
68C23×C113—42no—
69C23×C113C2×D411yescharacteristic
70C22×D113—22no—
71C22×D113—22no—
72C22×D113—22no—
73C22×D113C2×D412yes—
74D4×C113—22no—
75D4×C113—22no—
76D4×C113—42no—
77C2×C4×C113—22no—
78C2×C4×C113—42no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D412yes—
81C2×C4×C113#4112yes—
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—48no—
84C2×Dic113—22no—
85C2×Dic113—22no—
86C2×Dic113—22no—
87C2×Dic113—42no—
88C2×Dic113—42no—
89C2×Dic113C2×D412yes—
90C4×D113—24no—
91C4×D113—22no—
92C4×D113—22no—
93Dic226—22no—
94Dic226—22no—
95Dic226—42no—
96C8×C113—22no—
97#11744751C2×D414yescomplemented
98C22×C113—42no—
99C22×C113—42no—
100C22×C113—42no—
101C22×C113—84no—
102C22×C113#12112yes—
103C22×C113AGL(1,ℤ/8)12yes—
104C22×C113#13712yes—
105C22×C113C22×D411yescharacteristic
106C2×D113—22no—
107C2×D113—22no—
108C2×D113—22no—
109C2×D113—44no—
110C4×C113—42no—
111C4×C113#12112yes—
112C4×C113C22×D411yescharacteristic
113C4×C113C2×#4111yescharacteristic
114Dic113—22no—
115Dic113—42no—
116Dic113—42no—
117C2×C113—82no—
118C2×C113#46814yescomplemented
119C2×C113C2×#12111yescharacteristic
120C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C113C2×#13711yescharacteristic
122D113—42no—
123C2×#468—1131nomaximal, Sylow
124C113C2×#46811yescharacteristic, complemented, Sylow
125C22×SD16—1131no—
126C22×M16—1131no—
127C2×C22⋊Q8—1131no—
128C2×#121—1131no—
129#468—1138no—
130C2×#107—1131no—
131C2×#103—1131no—
132C2×#102D11311yescharacteristic, complemented
133C22×Q8—1131no—
134C22×D4—2261no—
135C22×D4C2×D11311yescharacteristic
136C23×C4—1131no—
137C2×SD16—1134no—
138C2×SD16—2264no—
139C2×M16—1134no—
140C2×M16—2264no—
141C22×C8—1131no—
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#107—1134no—
153#103—1134no—
154#102C2×D11314yescomplemented
155C24—21no—
156C24—1131no—
157C2×Q8—1132no—
158C2×Q8—2262no—
159C2×Q8—2262no—
160C2×Q8—2261no—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—4524no—
165C2×D4—2264no—
166C2×D4C22×D11312yes—
167C22×C4—21no—
168C22×C4—1131no—
169C22×C4—1132no—
170C22×C4—1132no—
171C22×C4—2261no—
172C22×C4—2261no—
173C22×C4—2262no—
174C22×C4—2262no—
175C22×C4C22×D11311yescharacteristic
176SD16—2268no—
177M16—2268no—
178C2×C8—22no—
179C2×C8—1134no—
180C2×C8—1132no—
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—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—1132no—
194C23—2262no—
195C23—2262no—
196C23—2262no—
197C23D4×D11311yescharacteristic
198Q8—4522no—
199Q8—2262no—
200Q8—2262no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—4528no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—1132no—
208C2×C4—4522no—
209C2×C4—4522no—
210C2×C4—2262no—
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—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—4524no—
227C22—2262no—
228C22—2262no—
229C22—2262no—
230C22#1681359512yes—
231C22#1681364612yes—
232C22#1681365112yes—
233C22C2×D4×D11311yescharacteristic
234C4—42no—
235C4—4522no—
236C4—4522no—
237C4—2262no—
238C4#1681359512yes—
239C4C2×D4×D11311yescharacteristic
240C4C2×#1426864711yescharacteristic
241C2—82no—
242C2—4522no—
243C2#2029884314yesdirect product factor
244C2C2×#1681359511yescharacteristic
245C2C2×#1681364611yescharacteristic
246C2C2×#1681365111yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#102×C113C2
socleC23×C113C2×D4
prime radicalC2×#16813593C2
hypercenterC2×#102D113
hypocenterC113C2×#468
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#14268635C2semidirect
2. C22×#14268630C2semidirect
3. C2×#16813602C2semidirect
5. #20298843C2direct (N × H)
6. C2×#16813555C2semidirect
7. C2×#16813547C2semidirect
8. C2×#102×C113C2semidirect
13. C2×#14268635C22semidirect
15. C2×#14268630C22semidirect
18. #16813602C22semidirect
25. #16813555C22semidirect
26. #16813547C22semidirect
30. #102×C113C22semidirect
47. C2×#11744751D4semidirect
97. #11744751C2×D4semidirect
118. C2×C113#468semidirect
124. C113C2×#468semidirect
132. C2×#102D113semidirect
154. #102C2×D113semidirect
243. C2#20298843direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142686352
C22×#142686302
C2×#168136022
C2×#168135932
#202988432
C2×#168135552
C2×#168135472
C2×#102×C1132
C2×#468113