Finite Group Databasebeta

← C2×#5061 #82950

Subgroups — C2×#5061 #82950

Order 384.

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×#1004C211yesmaximal, characteristic
2C2×C3×#124C211yesmaximal, characteristic, complemented
3C2×#942C212yesmaximal, complemented
4C2×#833C211yesmaximal, characteristic, complemented
5#5061C218yesmaximal, direct product factor
6C2×#805C212yesmaximal, complemented
7C2×#455—31nomaximal, Sylow
8C22×C3×Q8C2211yescharacteristic, complemented
9C22×C3×D4C2211yescharacteristic
10C22×#67—22no—
11#1004—22no—
12#1004—24no—
13#1004C2214yes—
14C2×#237—22no—
15C2×D3×D4—22no—
16C2×#235C2212yes—
17C3×#124—22no—
18C3×#124C2214yescomplemented
19C2×C3×C22⋊C4—22no—
20C2×C3×C42C2211yescharacteristic, complemented
21C2×#216—22no—
22#942—24no—
23#942C2218yescomplemented
24C2×#215—22no—
25C2×#208C2212yescomplemented
26#833C2214yescomplemented
27#805C2218yescomplemented
28C2×H(5,𝔽2)—31no—
29C2×#137—32no—
30C2×#124D311yescharacteristic, complemented
31#455—38no—
32C2×#104—32no—
33C2×#100—31no—
34C24×C3D412yes—
35C23×D3—22no—
36C2×C3×Q8—21no—
37C2×C3×Q8—22no—
38C2×C3×Q8—22no—
39C2×C3×Q8C2312yescomplemented
40C2×C3×D4—22no—
41C2×C3×D4—22no—
42C2×C3×D4D412yes—
43C2×C3×D4C2312yes—
44C22×C3×C4—21no—
45C22×C3×C4—21no—
46C22×C3×C4C2311yescharacteristic
47C2×#67—24no—
48C2×#67—28no—
49C2×#67—22no—
50C2×#67—28no—
51C22×Dic3—22no—
52#237—28no—
53#237—28no—
54D3×D4—28no—
55D3×D4—28no—
56#235—22no—
57#235—22no—
58#235D414yes—
59#235C2314yes—
60C2×D12D412yes—
61C2×C4×D3—22no—
62C2×Dic6D412yes—
63C3×C22⋊C4—28no—
64C3×C42—21no—
65C3×C42C2312yescomplemented
66#216—28no—
67#215—28no—
68#208—22no—
69#208C2314yescomplemented
70C2×C3⋊C8—22no—
71H(5,𝔽2)—34no—
72H(5,𝔽2)—64no—
73H(5,𝔽2)—62no—
74C2×#41—32no—
75C2×#41—62no—
76C22×Q8C2×D311yescharacteristic, complemented
77C22×D4—62no—
78C22×D4—62no—
79C22×D4C2×D311yescharacteristic
80#137—38no—
81#137—64no—
82C2×Q16—62no—
83C2×SD16—62no—
84C2×M16—32no—
85#124—22no—
86#124C2×D314yescomplemented
87C2×C22⋊C4—22no—
88C2×C42C2×D311yescharacteristic, complemented
89#104—38no—
90#100—34no—
91C23×C3—22no—
92C23×C3—22no—
93C23×C3—44no—
94C23×C3C2×D411yescharacteristic
95C23×C3C2×D414yes—
96C22×D3—22no—
97C22×D3—28no—
98C22×D3—84no—
99C3×Q8—24no—
100C3×Q8—42no—
101C3×D4—24no—
102C3×D4—24no—
103C2×C3×C4—22no—
104C2×C3×C4—22no—
105C2×C3×C4—42no—
106C2×C3×C4—41no—
107C2×C3×C4—41no—
108C2×C3×C4C2×D412yes—
109C2×C3×C4C2×D412yes—
110C2×C3×C4C2×D411yescharacteristic
111C2×C3×C4C2411yescharacteristic
112#67—216no—
113#67—24no—
114#67—24no—
115C2×Dic3—28no—
116C2×Dic3—22no—
117D12—22no—
118D12C2×D414yes—
119C4×D3—24no—
120C4×D3—24no—
121Dic6—22no—
122Dic6C2×D414yes—
123C3⋊C8—24no—
124C24—62no—
125C24#6712yes—
126#41—34no—
127#41—34no—
128#41—68no—
129#41—68no—
130#41—62no—
131#41—62no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—32no—
136C2×Q8C22×D312yescomplemented
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—32no—
140C2×D4—68no—
141C2×D4—68no—
142C2×D4—64no—
143C2×D4—68no—
144C2×D4—62no—
145C2×D4—68no—
146C2×D4#6712yes—
147C2×D4C22×D312yes—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—62no—
151C22×C4—62no—
152C22×C4C22×D311yescharacteristic
153Q16—68no—
154SD16—68no—
155M16—34no—
156M16—62no—
157C2×C8—62no—
158C22⋊C4—28no—
159C42—21no—
160C42C22×D312yescomplemented
161C22×C3—22no—
162C22×C3—24no—
163C22×C3—44no—
164C22×C3—44no—
165C22×C3—82no—
166C22×C3#12011yescharacteristic
167C22×C3#12011yescharacteristic
168C22×C3C22×D411yescharacteristic
169C2×D3—24no—
170C2×D3—44no—
171C2×D3—88no—
172C3×C4—42no—
173C3×C4—42no—
174C3×C4#12012yes—
175C3×C4C22×D412yes—
176Dic3—24no—
177C23—22no—
178C23—22no—
179C23—44no—
180C23—68no—
181C23—62no—
182C23—244no—
183C23C2×#6711yescharacteristic
184C23C2×#6714yes—
185Q8—24no—
186Q8—34no—
187Q8—42no—
188Q8—62no—
189D4—24no—
190D4—24no—
191D4—34no—
192D4—616no—
193D4—64no—
194D4—64no—
195D4—62no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—68no—
202C2×C4—62no—
203C2×C4—64no—
204C2×C4—64no—
205C2×C4D3×D412yes—
206C2×C4D3×D412yes—
207C2×C4C2×#6711yescharacteristic
208C2×C4C23×D311yescharacteristic
209C8—64no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—44no—
213C2×C3#45512yescomplemented
214C2×C3C2×#12011yescharacteristic
215D3—44no—
216C22—22no—
217C22—24no—
218C22—44no—
219C22—44no—
220C22—64no—
221C22—82no—
222C22—124no—
223C22—248no—
224C22#93711yescharacteristic
225C22#93711yescharacteristic
226C22C22×#6711yescharacteristic
227C4—42no—
228C4—42no—
229C4—64no—
230C4#93712yes—
231C4C2×D3×D412yes—
232C3C2×#45511yescharacteristic, complemented, Sylow
233C2—21no—
234C2—21no—
235C2—44no—
236C2—124no—
237C2#506112yesdirect product factor
238C2C2×#93711yescharacteristic
subgroupG/H
centerC22#937
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC2×C3×#124C2
socleC22×C3#120
prime radicalC2×#1004C2
hypercenterC2×#124D3
hypocenterC3C2×#455
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×C3×#124C2semidirect
3. C2×#942C2semidirect
4. C2×#833C2semidirect
5. #5061C2direct (N × H)
6. C2×#805C2semidirect
8. C22×C3×Q8C22semidirect
18. C3×#124C22semidirect
20. C2×C3×C42C22semidirect
23. #942C22semidirect
25. C2×#208C22semidirect
26. #833C22semidirect
27. #805C22semidirect
30. C2×#124D3semidirect
39. C2×C3×Q8C23semidirect
65. C3×C42C23semidirect
69. #208C23semidirect
76. C22×Q8C2×D3semidirect
86. #124C2×D3semidirect
88. C2×C42C2×D3semidirect
136. C2×Q8C22×D3semidirect
160. C42C22×D3semidirect
213. C2×C3#455semidirect
232. C3C2×#455semidirect
237. C2#5061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#10042
C2×C3×#1242
C2×#9422
C2×#8332
#50612
C2×#8052
C2×#4553