Finite Group Databasebeta

← C2×#20298775 #28399903

Subgroups — C2×#20298775 #28399903

Order 14464.

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

normal subgroups only

This group has 760 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
1C2×#16813667C211yesmaximal, characteristic
2C2×#16813653C212yesmaximal, complemented
3#20298775C218yesmaximal, direct product factor
4C2×#16813550C212yesmaximal, complemented
5C2×#16813539C211yesmaximal, characteristic, complemented
6C2×#124×C113C211yesmaximal, characteristic, complemented
7#16813667—24no—
8#16813667—22no—
9#16813667C2214yes—
10C2×#14268647C2212yes—
11C2×#14268646—22no—
12C22×C22⋊D113—22no—
13C2×D4×D113—22no—
14#16813653—24no—
15#16813653C2218yescomplemented
16C2×#14268637—22no—
17C2×#14268634—22no—
18C2×#14268631C2212yescomplemented
19#16813550C2218yescomplemented
20#16813539C2214yescomplemented
21C22×Q8×C113C2211yescharacteristic, complemented
22C22×D4×C113C2211yescharacteristic
23#124×C113—22no—
24#124×C113C2214yescomplemented
25C2×C22⋊C4×C113—22no—
26C2×C42×C113C2211yescharacteristic, complemented
27C23×D113—22no—
28#14268647—22no—
29#14268647—22no—
30#14268647D414yes—
31#14268647C2314yes—
32#14268646—28no—
33#14268646—28no—
34C2×Dic226D412yes—
35C2×D452D412yes—
36C2×C22⋊D113—24no—
37C2×C22⋊D113—28no—
38C2×C22⋊D113—22no—
39C2×C22⋊D113—28no—
40D4×D113—28no—
41D4×D113—28no—
42C22×Dic113—22no—
43C2×C4×D113—22no—
44#14268637—28no—
45#14268634—28no—
46#14268631—22no—
47#14268631C2314yescomplemented
48C2×#11744751—22no—
49C24×C113D412yes—
50C2×Q8×C113—21no—
51C2×Q8×C113—22no—
52C2×Q8×C113—22no—
53C2×Q8×C113C2312yescomplemented
54C2×D4×C113—22no—
55C2×D4×C113—22no—
56C2×D4×C113D412yes—
57C2×D4×C113C2312yes—
58C22×C4×C113—21no—
59C22×C4×C113—21no—
60C22×C4×C113C2311yescharacteristic
61C22⋊C4×C113—28no—
62C42×C113—21no—
63C42×C113C2312yescomplemented
64C23×C113—22no—
65C23×C113—22no—
66C23×C113—44no—
67C23×C113C2×D411yescharacteristic
68C23×C113C2×D414yes—
69C22×D113—22no—
70C22×D113—28no—
71C22×D113—84no—
72Q8×C113—24no—
73Q8×C113—42no—
74D4×C113—24no—
75D4×C113—24no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113—42no—
79C2×C4×C113—41no—
80C2×C4×C113—41no—
81C2×C4×C113C2×D412yes—
82C2×C4×C113C2×D412yes—
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2411yescharacteristic
85C22⋊D113—216no—
86C22⋊D113—24no—
87C22⋊D113—24no—
88C2×Dic113—28no—
89C2×Dic113—22no—
90D452—22no—
91D452C2×D414yes—
92C4×D113—24no—
93C4×D113—24no—
94Dic226—22no—
95Dic226C2×D414yes—
96#11744751—24no—
97C22×C113—22no—
98C22×C113—24no—
99C22×C113—44no—
100C22×C113—44no—
101C22×C113—82no—
102C22×C113#12011yescharacteristic
103C22×C113#12011yescharacteristic
104C22×C113C22×D411yescharacteristic
105C2×D113—24no—
106C2×D113—44no—
107C2×D113—88no—
108C4×C113—42no—
109C4×C113—42no—
110C4×C113#12012yes—
111C4×C113C22×D412yes—
112Dic113—24no—
113C2×C113—21no—
114C2×C113—21no—
115C2×C113—44no—
116C2×C113#45512yescomplemented
117C2×C113C2×#12011yescharacteristic
118D113—44no—
119C2×#455—1131nomaximal, Sylow
120C113C2×#45511yescharacteristic, complemented, Sylow
121C2×H(5,𝔽2)—1131no—
122C2×#137—1132no—
123C2×#124D11311yescharacteristic, complemented
124#455—1138no—
125C2×#104—1132no—
126C2×#100—1131no—
127H(5,𝔽2)—1134no—
128H(5,𝔽2)—2264no—
129H(5,𝔽2)—2262no—
130C2×#41—1132no—
131C2×#41—2262no—
132C22×Q8C2×D11311yescharacteristic, complemented
133C22×D4—2262no—
134C22×D4—2262no—
135C22×D4C2×D11311yescharacteristic
136#137—1138no—
137#137—2264no—
138C2×Q16—2262no—
139C2×SD16—2262no—
140C2×M16—1132no—
141#124—22no—
142#124C2×D11314yescomplemented
143C2×C22⋊C4—22no—
144C2×C42C2×D11311yescharacteristic, complemented
145#104—1138no—
146#100—1134no—
147C24—2262no—
148C24C22⋊D11312yes—
149#41—1134no—
150#41—1134no—
151#41—2268no—
152#41—2268no—
153#41—2262no—
154#41—2262no—
155C2×Q8—21no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8—1132no—
159C2×Q8C22×D11312yescomplemented
160C2×D4—22no—
161C2×D4—22no—
162C2×D4—1132no—
163C2×D4—2268no—
164C2×D4—2268no—
165C2×D4—2264no—
166C2×D4—2268no—
167C2×D4—2262no—
168C2×D4—2268no—
169C2×D4C22⋊D11312yes—
170C2×D4C22×D11312yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—2262no—
174C22×C4—2262no—
175C22×C4C22×D11311yescharacteristic
176Q16—2268no—
177SD16—2268no—
178M16—1134no—
179M16—2262no—
180C2×C8—2262no—
181C22⋊C4—28no—
182C42—21no—
183C42C22×D11312yescomplemented
184C23—22no—
185C23—22no—
186C23—44no—
187C23—9044no—
188C23—2268no—
189C23—2262no—
190C23C2×C22⋊D11311yescharacteristic
191C23C2×C22⋊D11314yes—
192Q8—24no—
193Q8—42no—
194Q8—1134no—
195Q8—2262no—
196D4—24no—
197D4—24no—
198D4—1134no—
199D4—22616no—
200D4—2264no—
201D4—2264no—
202D4—2262no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—2268no—
209C2×C4—2262no—
210C2×C4—2264no—
211C2×C4—2264no—
212C2×C4D4×D11312yes—
213C2×C4D4×D11312yes—
214C2×C4C2×C22⋊D11311yescharacteristic
215C2×C4C23×D11311yescharacteristic
216C8—2264no—
217C22—22no—
218C22—24no—
219C22—44no—
220C22—44no—
221C22—82no—
222C22—9048no—
223C22—4524no—
224C22—2264no—
225C22#1681359011yescharacteristic
226C22#1681359011yescharacteristic
227C22C22×C22⋊D11311yescharacteristic
228C4—42no—
229C4—42no—
230C4—2264no—
231C4#1681359012yes—
232C4C2×D4×D11312yes—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—4524no—
237C2#2029877512yesdirect product factor
238C2C2×#1681359011yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#124×C113C2
socleC22×C113#120
prime radicalC2×#16813667C2
hypercenterC2×#124D113
hypocenterC113C2×#455
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#16813653C2semidirect
3. #20298775C2direct (N × H)
4. C2×#16813550C2semidirect
5. C2×#16813539C2semidirect
6. C2×#124×C113C2semidirect
15. #16813653C22semidirect
18. C2×#14268631C22semidirect
19. #16813550C22semidirect
20. #16813539C22semidirect
21. C22×Q8×C113C22semidirect
24. #124×C113C22semidirect
26. C2×C42×C113C22semidirect
47. #14268631C23semidirect
53. C2×Q8×C113C23semidirect
63. C42×C113C23semidirect
116. C2×C113#455semidirect
120. C113C2×#455semidirect
123. C2×#124D113semidirect
132. C22×Q8C2×D113semidirect
142. #124C2×D113semidirect
144. C2×C42C2×D113semidirect
159. C2×Q8C22×D113semidirect
183. C42C22×D113semidirect
237. C2#20298775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168136672
C2×#168136532
#202987752
C2×#168135502
C2×#168135392
C2×#124×C1132
C2×#455113