Finite Group Databasebeta

← C2×D3×SD32 #82020

Subgroups — C2×D3×SD32 #82020

Order 384.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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×D3×Q16C211yesmaximal, characteristic, complemented
2C2×D3×D8C211yesmaximal, characteristic
3C2×C3×SD32C211yesmaximal, characteristic, complemented
4C2×#828C211yesmaximal, characteristic, complemented
5C2×#827C211yesmaximal, characteristic, complemented
6D3×SD32C218yesmaximal, direct product factor
7C2×#800C211yesmaximal, characteristic, complemented
8C2×D3×C16C211yesmaximal, characteristic, complemented
9C22×SD32—31nomaximal, Sylow
10C2×D3×Q8—21no—
11C2×D3×D4—21no—
12C2×C3×Q16C2211yescharacteristic, complemented
13C2×C3×D8C2211yescharacteristic
14C2×#216—21no—
15C2×#213—21no—
16D3×Q16—22no—
17D3×Q16C2214yescomplemented
18D3×D8—22no—
19D3×D8C2214yes—
20C2×Dic12C2211yescharacteristic, complemented
21C2×D24C2211yescharacteristic
22C2×D3×C8C2211yescharacteristic
23C3×SD32C2214yescomplemented
24C2×C3×C16C2211yescharacteristic, complemented
25#828C2214yescomplemented
26#827C2214yescomplemented
27C2×C3⋊C16C2211yescharacteristic, complemented
28#800C2214yescomplemented
29D3×C16C2214yescomplemented
30C22×Q16—31no—
31C22×D8—31no—
32C2×SD32—31no—
33C2×SD32—31no—
34C2×SD32—38no—
35C2×SD32—31no—
36C2×SD32D311yescharacteristic, direct product factor
37C22×C16—31no—
38C23×D3—41no—
39C2×C3×Q8—21no—
40C2×C3×D4—21no—
41C2×#67—41no—
42D3×Q8—24no—
43D3×Q8—42no—
44D3×D4—24no—
45D3×D4—42no—
46C2×D12—21no—
47C2×C4×D3—41no—
48C2×C4×D3D411yescharacteristic
49C2×Dic6—21no—
50C2×Dic6—41no—
51C3×Q16—21no—
52C3×Q16C2312yescomplemented
53C3×D8—21no—
54C3×D8C2312yes—
55C2×C3×C8C2311yescharacteristic
56#216—24no—
57#213—24no—
58C2×C3⋊C8D411yescharacteristic
59Dic12—21no—
60Dic12C2312yescomplemented
61D24—21no—
62D24C2312yes—
63D3×C8D412yes—
64D3×C8C2312yes—
65C3×C16C2312yescomplemented
66C3⋊C16C2312yescomplemented
67C22×Q8—61no—
68C22×D4—61no—
69C2×Q16—34no—
70C2×Q16—31no—
71C2×Q16—62no—
72C2×Q16—61no—
73C2×Q16C2×D311yescharacteristic, complemented
74C2×D8—34no—
75C2×D8—31no—
76C2×D8—62no—
77C2×D8—61no—
78C2×D8C2×D311yescharacteristic
79C22×C8—31no—
80SD32—34no—
81SD32—34no—
82SD32—34no—
83SD32C2×D314yesdirect product factor
84C2×C16—31no—
85C2×C16—34no—
86C2×C16C2×D311yescharacteristic, complemented
87C23×C3—41no—
88C22×D3—41no—
89C22×D3—44no—
90C22×D3—84no—
91C22×D3D811yescharacteristic
92C3×Q8—22no—
93C3×Q8—41no—
94C3×D4—22no—
95C3×D4—41no—
96C2×C3×C4—41no—
97C2×C3×C4C2×D411yescharacteristic
98#67—44no—
99C2×Dic3—41no—
100C2×Dic3D811yescharacteristic
101D12—22no—
102D12—41no—
103C4×D3—44no—
104C4×D3D812yes—
105C4×D3C2×D412yes—
106Dic6—22no—
107Dic6—41no—
108Dic6—44no—
109C3×C8C2×D411yescharacteristic
110C3×C8C2411yescharacteristic
111C3⋊C8C2×D412yes—
112C24—121no—
113C2×Q8—21no—
114C2×Q8—64no—
115C2×Q8—61no—
116C2×Q8—121no—
117C2×Q8—122no—
118C2×D4—21no—
119C2×D4—64no—
120C2×D4—61no—
121C2×D4—122no—
122C2×D4—121no—
123C22×C4—31no—
124C22×C4—121no—
125Q16—21no—
126Q16—32no—
127Q16—64no—
128Q16—61no—
129Q16C22×D312yescomplemented
130D8—21no—
131D8—32no—
132D8—64no—
133D8—61no—
134D8C22×D312yes—
135C2×C8—31no—
136C2×C8—32no—
137C2×C8—32no—
138C2×C8C22×D311yescharacteristic
139C16—32no—
140C16C22×D312yescomplemented
141C22×C3—42no—
142C22×C3—82no—
143C22×C3C2×D811yescharacteristic
144C2×D3—42no—
145C2×D3—82no—
146C2×D3—88no—
147C2×D3SD3214yesdirect product factor
148C2×D3C2×D812yes—
149C3×C4—42no—
150C3×C4C2×D811yescharacteristic
151C3×C4C22×D411yescharacteristic
152Dic3—42no—
153Dic3C2×D812yes—
154C23—31no—
155C23—41no—
156C23—124no—
157C23—121no—
158C23—244no—
159Q8—22no—
160Q8—41no—
161Q8—62no—
162Q8—124no—
163Q8—121no—
164D4—22no—
165D4—41no—
166D4—62no—
167D4—124no—
168D4—121no—
169C2×C4—31no—
170C2×C4—32no—
171C2×C4—32no—
172C2×C4—41no—
173C2×C4—124no—
174C2×C4—121no—
175C2×C4D3×D411yescharacteristic
176C8—32no—
177C8D3×D411yescharacteristic
178C8C23×D311yescharacteristic
179C2×C3—82no—
180C2×C3C2×SD3212yescomplemented
181C2×C3C22×D811yescharacteristic
182D3—82no—
183D3C2×SD3214yesdirect product factor
184C22—34no—
185C22—32no—
186C22—42no—
187C22—82no—
188C22—122no—
189C22—248no—
190C22—242no—
191C22D3×D811yescharacteristic
192C4—32no—
193C4—42no—
194C4—122no—
195C4D3×D811yescharacteristic
196C4C2×D3×D411yescharacteristic
197C3C22×SD3211yescharacteristic, complemented, Sylow
198C2—34no—
199C2—82no—
200C2—242no—
201C2D3×SD3212yesdirect product factor
202C2C2×D3×D811yescharacteristic
subgroupG/H
centerC22D3×D8
commutator, cosocleC3×C8C24
FrattiniC8C23×D3
FittingC2×C3×SD32C2
socleC22×C3C2×D8
prime radicalC2×D3×D8C2
hypercenterC2×SD32D3
hypocenterC3C22×SD32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×D3×Q16C2semidirect
3. C2×C3×SD32C2semidirect
4. C2×#828C2semidirect
5. C2×#827C2semidirect
6. D3×SD32C2direct (N × H)
7. C2×#800C2semidirect
8. C2×D3×C16C2semidirect
12. C2×C3×Q16C22semidirect
17. D3×Q16C22semidirect
20. C2×Dic12C22semidirect
23. C3×SD32C22semidirect
24. C2×C3×C16C22semidirect
25. #828C22semidirect
26. #827C22semidirect
27. C2×C3⋊C16C22semidirect
28. #800C22semidirect
29. D3×C16C22semidirect
36. C2×SD32D3direct (N × H)
52. C3×Q16C23semidirect
60. Dic12C23semidirect
65. C3×C16C23semidirect
66. C3⋊C16C23semidirect
73. C2×Q16C2×D3semidirect
83. SD32C2×D3direct (N × H)
86. C2×C16C2×D3semidirect
129. Q16C22×D3semidirect
140. C16C22×D3semidirect
147. C2×D3SD32direct (N × H)
180. C2×C3C2×SD32semidirect
183. D3C2×SD32direct (N × H)
197. C3C22×SD32semidirect
201. C2D3×SD32direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×Q162
C2×D3×D82
C2×C3×SD322
C2×#8282
C2×#8272
D3×SD322
C2×#8002
C2×D3×C162
C22×SD323