Finite Group Databasebeta

← D3×#508 #82029

Subgroups — D3×#508 #82029

Order 384.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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
1D3×#135C212yesmaximal, complemented
2C3×#508C211yesmaximal, characteristic, complemented
3#5194C212yesmaximal, complemented
4#4919C211yesmaximal, characteristic, complemented
5D3×Q32C211yesmaximal, characteristic, complemented
6#4916C212yesmaximal, complemented
7D3×SD32C212yesmaximal, complemented
8#4912C211yesmaximal, characteristic, complemented
9D3×D16C211yesmaximal, characteristic, complemented
10#4904C211yesmaximal, characteristic, complemented
11C2×D3×C16C211yesmaximal, characteristic, complemented
12C2×#508—31nomaximal, Sylow
13D3×#41—22no—
14C3×#135C2212yescomplemented
15#950—22no—
16#919C2212yescomplemented
17D3×Q16C2212yes—
18#916—22no—
19D3×SD16—22no—
20#912C2212yescomplemented
21D3×D8C2212yes—
22#904C2212yescomplemented
23C2×D3×C8C2211yescharacteristic
24C3×Q32C2211yescharacteristic, complemented
25C3×SD32C2212yescomplemented
26C3×D16C2211yescharacteristic, complemented
27C2×C3×C16C2211yescharacteristic, complemented
28#829C2212yescomplemented
29#828C2212yescomplemented
30#827C2212yescomplemented
31#826C2212yescomplemented
32C2×C3⋊C16C2211yescharacteristic, complemented
33Dic24C2211yescharacteristic, complemented
34#800C2212yescomplemented
35D48C2211yescharacteristic, complemented
36D3×C16C2211yescharacteristic
37D3×C16C2211yescharacteristic
38D3×C16C2211yescharacteristic, complemented
39D3×C16C2211yescharacteristic, complemented
40C2×#135—32no—
41#508—32no—
42#508—31no—
43#508—32no—
44#508—31no—
45#508—31no—
46#508D311yescharacteristic, direct product factor
47C2×Q32—31no—
48C2×SD32—32no—
49C2×D16—31no—
50C22×C16—31no—
51C3×#41—22no—
52#239—22no—
53D3×Q8—22no—
54#237—22no—
55#237—42no—
56D3×D4—22no—
57D3×D4—42no—
58#235—22no—
59#235—42no—
60C2×C4×D3—42no—
61C2×C4×D3D411yescharacteristic
62C3×Q16C2312yes—
63C3×SD16—22no—
64C3×D8C2312yes—
65C2×C3×C8C2311yescharacteristic
66#216—22no—
67#215—22no—
68#214—22no—
69#213—22no—
70C2×C3⋊C8D411yescharacteristic
71Dic12C2312yes—
72D24C2312yes—
73#204—22no—
74D3×C8D411yescharacteristic
75D3×C8D411yescharacteristic
76D3×C8C2311yescharacteristic
77D3×C8C2311yescharacteristic
78C3×C16C2311yescharacteristic
79C3×C16C2311yescharacteristic
80C3⋊C16C2311yescharacteristic
81C3⋊C16C2311yescharacteristic
82C2×#41—62no—
83#135—32no—
84#135—32no—
85#135—32no—
86#135—62no—
87#135—62no—
88#135C2×D312yescomplemented
89C2×Q16—32no—
90C2×SD16—62no—
91C2×D8—32no—
92C22×C8—31no—
93Q32—32no—
94Q32—31no—
95Q32C2×D311yescharacteristic, complemented
96SD32—32no—
97SD32—32no—
98SD32—32no—
99SD32C2×D312yescomplemented
100D16—32no—
101D16—31no—
102D16C2×D311yescharacteristic, complemented
103C2×C16—31no—
104C2×C16—31no—
105C2×C16—31no—
106C2×C16—31no—
107C2×C16—31no—
108C2×C16C2×D311yescharacteristic, complemented
109C22×D3—42no—
110C22×D3D811yescharacteristic
111C3×Q8—22no—
112C3×D4—22no—
113C3×D4—42no—
114C2×C3×C4—42no—
115C2×C3×C4C2×D411yescharacteristic
116#67—42no—
117#67—42no—
118#67—42no—
119C2×Dic3—42no—
120C2×Dic3D811yescharacteristic
121D12—22no—
122D12—42no—
123C4×D3—42no—
124C4×D3—42no—
125C4×D3—42no—
126C4×D3D811yescharacteristic
127C4×D3D811yescharacteristic
128C4×D3C2×D411yescharacteristic
129C4×D3C2×D411yescharacteristic
130Dic6—22no—
131Dic6—42no—
132C3×C8C2×D411yescharacteristic
133C3×C8C2411yescharacteristic
134C3⋊C8C2×D411yescharacteristic
135C3⋊C8C2×D411yescharacteristic
136#41—22no—
137#41—62no—
138#41—62no—
139#41—62no—
140#41—122no—
141#41—122no—
142C2×Q8—62no—
143C2×D4—62no—
144C2×D4—122no—
145C22×C4—31no—
146C22×C4—122no—
147Q16—32no—
148Q16—62no—
149Q16C22×D312yes—
150SD16—22no—
151SD16—62no—
152SD16—62no—
153SD16—62no—
154D8—32no—
155D8—62no—
156D8C22×D312yes—
157C2×C8—31no—
158C2×C8—31no—
159C2×C8—31no—
160C2×C8—31no—
161C2×C8—31no—
162C2×C8C22×D311yescharacteristic
163C16—31no—
164C16—31no—
165C16C22×D311yescharacteristic
166C16C22×D311yescharacteristic
167C22×C3—42no—
168C22×C3C2×D811yescharacteristic
169C2×D3—22no—
170C2×D3—42no—
171C2×D3—84no—
172C2×D3C2×D811yescharacteristic
173C2×D3C2×D811yescharacteristic
174C3×C4—42no—
175C3×C4C2×D811yescharacteristic
176C3×C4C22×D411yescharacteristic
177Dic3—42no—
178Dic3C2×D811yescharacteristic
179Dic3C2×D811yescharacteristic
180C23—31no—
181C23—122no—
182Q8—22no—
183Q8—62no—
184Q8—122no—
185D4—22no—
186D4—42no—
187D4—62no—
188D4—122no—
189D4—122no—
190D4—122no—
191D4—122no—
192C2×C4—31no—
193C2×C4—31no—
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—42no—
198C2×C4—122no—
199C2×C4—122no—
200C2×C4—122no—
201C2×C4—122no—
202C2×C4D3×D411yescharacteristic
203C8—31no—
204C8—31no—
205C8D3×D411yescharacteristic
206C8C23×D311yescharacteristic
207C2×C3—21no—
208C2×C3—82no—
209C2×C3C22×D811yescharacteristic
210D3—21no—
211D3—82no—
212D3#50812yesdirect product factor
213C22—31no—
214C22—31no—
215C22—42no—
216C22—62no—
217C22—122no—
218C22—244no—
219C22D3×D811yescharacteristic
220C4—31no—
221C4—31no—
222C4—42no—
223C4—122no—
224C4D3×D811yescharacteristic
225C4C2×D3×D411yescharacteristic
226C3C2×#50811yescharacteristic, complemented, Sylow
227C2—21no—
228C2—32no—
229C2—61no—
230C2—82no—
231C2—242no—
232C2C2×D3×D811yescharacteristic
subgroupG/H
centerC4D3×D8
commutator, cosocleC3×C8C24
FrattiniC8C23×D3
FittingC3×#508C2
socleC2×C3C22×D8
hypercenter#508D3
hypocenterC3C2×#508
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. D3×#135C2semidirect
2. C3×#508C2semidirect
3. #5194C2semidirect
4. #4919C2semidirect
5. D3×Q32C2semidirect
6. #4916C2semidirect
7. D3×SD32C2semidirect
8. #4912C2semidirect
9. D3×D16C2semidirect
10. #4904C2semidirect
11. C2×D3×C16C2semidirect
14. C3×#135C22semidirect
16. #919C22semidirect
20. #912C22semidirect
22. #904C22semidirect
24. C3×Q32C22semidirect
25. C3×SD32C22semidirect
26. C3×D16C22semidirect
27. C2×C3×C16C22semidirect
28. #829C22semidirect
29. #828C22semidirect
30. #827C22semidirect
31. #826C22semidirect
32. C2×C3⋊C16C22semidirect
33. Dic24C22semidirect
34. #800C22semidirect
35. D48C22semidirect
38. D3×C16C22semidirect
39. D3×C16C22semidirect
46. #508D3direct (N × H)
88. #135C2×D3semidirect
95. Q32C2×D3semidirect
99. SD32C2×D3semidirect
102. D16C2×D3semidirect
108. C2×C16C2×D3semidirect
212. D3#508direct (N × H)
226. C3C2×#508semidirect

Maximal subgroups

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

subgroupindex
D3×#1352
C3×#5082
#51942
#49192
D3×Q322
#49162
D3×SD322
#49122
D3×D162
#49042
C2×D3×C162
C2×#5083