Finite Group Databasebeta

← C2×#64239 #10596534

Subgroups — C2×#64239 #10596534

Order 576.

418 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 89 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×#627C211yesmaximal, characteristic, complemented
2C2×#3805C211yesmaximal, characteristic
3C2×#3792C211yesmaximal, characteristic, complemented
4C2×#3776C212yesmaximal, complemented
5#64239C218yesmaximal, direct product factor
6C2×#3775C212yesmaximal, complemented
7C22×C3⋊Dic3C2211yescharacteristic
8C2×C3×#67—21no—
9C22×C3×Dic3—21no—
10C2×#627—22no—
11C2×#627—21no—
12C2×#627C2211yescharacteristic
13C2×#627C2212yes—
14C2×#627C2214yescomplemented
15C2×#625C2211yescharacteristic
16#3805—22no—
17#3805C2214yes—
18C2×D3×Dic3—21no—
19#3792C2214yescomplemented
20C2×#622C2212yes—
21#3776C2218yescomplemented
22#3775C2218yescomplemented
23C2×#237—61no—
24C22×Dic6—61no—
25C23×C32D411yescharacteristic
26C22×C3×D3—21no—
27C2×C3⋊Dic3D411yescharacteristic
28C2×C3⋊Dic3D412yes—
29C2×C3⋊Dic3C2311yescharacteristic
30C2×C3⋊Dic3C2312yes—
31C3×#67—24no—
32C2×C3×Dic3—21no—
33C2×C3×Dic3—22no—
34C2×C3×Dic3—24no—
35#627—21no—
36#627—22no—
37#627—24no—
38#627C2314yes—
39#627C2312yes—
40#625—21no—
41#625C2312yes—
42D3×Dic3—24no—
43#622C2314yes—
44C2×#137—91nomaximal, Sylow
45C2×C3×D4—61no—
46C22×C3×C4—61no—
47C2×#67—21no—
48C2×#67—61no—
49C22×Dic3—21no—
50C22×Dic3—61no—
51C22×Dic3—61no—
52C22×Dic3—61no—
53#237—64no—
54#237—64no—
55C2×C4×D3—61no—
56C2×Dic6—62no—
57C2×Dic6—61no—
58C2×Dic6—64no—
59C2×Dic6—64no—
60C2×Dic6—62no—
61C22×C32—22no—
62C22×C32C2×D412yes—
63C22×C32C2×D411yescharacteristic
64C2×C3×D3—22no—
65C2×C3×D3—42no—
66C3⋊Dic3C2×D412yes—
67C3⋊Dic3C2×D411yescharacteristic
68C3⋊Dic3C2411yescharacteristic
69C3×Dic3—22no—
70C3×Dic3—24no—
71C2×#41—91no—
72C22×Q8—91no—
73#137—98no—
74C2×Q16—92no—
75C2×SD16—92no—
76C2×M16—91no—
77C23×C3—21no—
78C23×C3—21no—
79C23×C3—61no—
80C22×D3—21no—
81C3×D4—64no—
82C2×C3×C4—64no—
83C2×C3×C4—62no—
84C2×C3×C4—61no—
85#67—24no—
86#67—62no—
87#67—62no—
88C2×Dic3—24no—
89C2×Dic3—22no—
90C2×Dic3—21no—
91C2×Dic3—62no—
92C2×Dic3—61no—
93C2×Dic3—61no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C2×Dic3—61no—
97C2×Dic3—61no—
98C2×Dic3—62no—
99C2×Dic3—64no—
100C4×D3—64no—
101Dic6—64no—
102Dic6—62no—
103Dic6—64no—
104Dic6—68no—
105Dic6—62no—
106C2×C32—22no—
107C2×C32#13712yescomplemented
108C2×C32C22×D411yescharacteristic
109C3×D3—42no—
110#41—94no—
111#41—182no—
112C2×Q8—92no—
113C2×Q8—91no—
114C2×Q8—94no—
115C2×Q8—182no—
116C2×Q8—181no—
117C2×D4—61no—
118C2×D4—91no—
119C22×C4—61no—
120C22×C4—91no—
121C22×C4—181no—
122Q16—98no—
123SD16—98no—
124M16—94no—
125C2×C8—92no—
126C22×C3—24no—
127C22×C3—22no—
128C22×C3—22no—
129C22×C3—21no—
130C22×C3—21no—
131C22×C3—42no—
132C22×C3—62no—
133C22×C3—122no—
134C2×D3—22no—
135C2×D3—42no—
136C3×C4—64no—
137C3×C4—62no—
138Dic3—24no—
139Dic3—22no—
140Dic3—62no—
141Dic3—61no—
142Dic3—61no—
143Dic3—61no—
144Dic3—61no—
145Dic3—62no—
146C32C2×#13711yescharacteristic, complemented, Sylow
147C23—61no—
148C23GO+(4,𝔽2)11yescharacteristic
149Q8—94no—
150Q8—92no—
151Q8—184no—
152Q8—182no—
153Q8—181no—
154D4—64no—
155D4—92no—
156D4—181no—
157C2×C4—64no—
158C2×C4—62no—
159C2×C4—61no—
160C2×C4—92no—
161C2×C4—92no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—184no—
165C8—94no—
166C2×C3—24no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—22no—
170C2×C3—22no—
171C2×C3—42no—
172C2×C3—122no—
173D3—42no—
174C22—22no—
175C22—62no—
176C22—122no—
177C22C2×GO+(4,𝔽2)12yes—
178C22C2×GO+(4,𝔽2)11yescharacteristic
179C4—64no—
180C4—62no—
181C4—91no—
182C4—92no—
183C4—91no—
184C3—21no—
185C3—21no—
186C2—22no—
187C2—122no—
188C2#6423912yesdirect product factor
189C2C22×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC22C2×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C24
FrattiniC2C22×GO+(4,𝔽2)
FittingC23×C32D4
socleC22×C32C2×D4
prime radicalC2×#3805C2
hypercenterC23GO+(4,𝔽2)
hypocenterC32C2×#137
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#627C2semidirect
3. C2×#3792C2semidirect
4. C2×#3776C2semidirect
5. #64239C2direct (N × H)
6. C2×#3775C2semidirect
14. C2×#627C22semidirect
19. #3792C22semidirect
21. #3776C22semidirect
22. #3775C22semidirect
107. C2×C32#137semidirect
146. C32C2×#137semidirect
188. C2#64239direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#6272
C2×#38052
C2×#37922
C2×#37762
#642392
C2×#37752
C2×#1379