Finite Group Databasebeta

← D3×#2840 #11001593

Subgroups — D3×#2840 #11001593

Order 768.

3550 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 579 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
1C3×#2840C211yesmaximal, characteristic, complemented
2#76888C2112yesmaximal, complemented
3D3×#393C2112yesmaximal, complemented
4D3×#379C213yesmaximal
5#73844C213yesmaximal, complemented
6C2×#2840—31nomaximal, Sylow
7C25×D3C2211yescharacteristic
8C22×D3×Q8C2214yescomplemented
9C2×D3×C22⋊C4C22118yes—
10C3×#393C22112yescomplemented
11C3×#379C2213yes—
12#5247C2213yes—
13#5231C22112yescomplemented
14#4955C22118yes—
15#4947C22136yescomplemented
16#4673C22136yescomplemented
17D3×#95C22112yescomplemented
18#2840—312no—
19#2840—33no—
20#2840D311yescharacteristic, direct product factor
21C2×#393—312no—
22C2×#379—33no—
23C25×C3C2311yescharacteristic
24C24×D3—412no—
25C24×D3Q818yescomplemented
26C24×D3C2313yes—
27C24×D3C2313yes—
28C22×C3×Q8C2314yescomplemented
29C2×D3×Q8—424no—
30C22×C4×D3C23112yes—
31C22×Dic6C23112yescomplemented
32C2×C3×C22⋊C4C23118yes—
33C2×#217C23118yes—
34C2×(C2×D3)⋊C4C23136yes—
35D3×C22⋊C4—436no—
36C3×#95C23112yescomplemented
37C3⋊#95C23136yescomplemented
38C26—31no—
39C23×Q8—34no—
40C22×C22⋊C4—318no—
41#393—312no—
42#393—336no—
43#393—336no—
44#393C2×D3112yescomplemented
45#379—33no—
46#379—318no—
47#379C2×D313yes—
48C2×#95—312no—
49C24×C3—46no—
50C24×C3C2×Q814yescomplemented
51C24×C3C2413yes—
52C23×D3—236no—
53C23×D3—448no—
54C23×D3—418no—
55C23×D3—464no—
56C23×D3C2×Q8112yes—
57C23×D3C2×Q8112yescomplemented
58C23×D3C2413yes—
59C23×D3C2411yescharacteristic
60C2×C3×Q8—412no—
61C22×C3×C4C24112yes—
62C22×Dic3C24112yes—
63D3×Q8—464no—
64C2×C4×D3—272no—
65C2×Dic6—436no—
66C3×C22⋊C4—418no—
67#217—418no—
68(C2×D3)⋊C4—436no—
69C25—33no—
70C25—38no—
71C25—33no—
72C25—1212no—
73C25C22×D311yescharacteristic
74C22×Q8—312no—
75C22×Q8—1224no—
76C22×Q8C22×D314yescomplemented
77C23×C4—312no—
78C2×C22⋊C4—318no—
79C2×C22⋊C4—336no—
80C2×C22⋊C4—1236no—
81C2×C22⋊C4C22×D3118yes—
82#95—336no—
83#95C22×D3112yescomplemented
84C23×C3—218no—
85C23×C3—412no—
86C23×C3—416no—
87C23×C3C22×Q816yes—
88C23×C3C2511yescharacteristic
89C22×D3—218no—
90C22×D3—272no—
91C22×D3—436no—
92C22×D3—448no—
93C22×D3—4128no—
94C22×D3—448no—
95C22×D3C22×Q816yes—
96C22×D3C22×Q812yes—
97C22×D3H(5,𝔽2)112yes—
98C3×Q8—416no—
99C2×C3×C4—236no—
100C2×Dic3—236no—
101C4×D3—448no—
102Dic6—448no—
103C24—31no—
104C24—312no—
105C24—33no—
106C24—312no—
107C24—46no—
108C24—636no—
109C24—1218no—
110C24—1248no—
111C24—1264no—
112C24D3×Q814yescomplemented
113C24C23×D313yes—
114C2×Q8—412no—
115C2×Q8—1236no—
116C2×Q8—1264no—
117C22×C4—312no—
118C22×C4—672no—
119C22×C4C23×D3112yes—
120C22⋊C4—418no—
121C22⋊C4—1236no—
122C22⋊C4—1218no—
123C22×C3—218no—
124C22×C3—416no—
125C22×C3—412no—
126C22×C3C23×Q811yescharacteristic
127C22×C3C2×H(5,𝔽2)16yes—
128C2×D3—218no—
129C2×D3—448no—
130C2×D3—412no—
131C2×D3—448no—
132C2×D3#543112yes—
133C2×D3H(3,𝔽4)116yes—
134C3×C4—412no—
135Dic3—412no—
136C23—218no—
137C23—32no—
138C23—312no—
139C23—36no—
140C23—412no—
141C23—416no—
142C23—672no—
143C23—618no—
144C23—1236no—
145C23—1248no—
146C23—12128no—
147C23—1248no—
148C23C2×D3×Q816yes—
149C23C24×D311yescharacteristic
150Q8—416no—
151Q8—1248no—
152C2×C4—236no—
153C2×C4—636no—
154C2×C4—1248no—
155C2×C3—46no—
156C2×C3C2×#54313yes—
157C2×C3C2×H(3,𝔽4)14yes—
158D3—46no—
159D3#284018yesdirect product factor
160C22—218no—
161C22—316no—
162C22—312no—
163C22—416no—
164C22—412no—
165C22—618no—
166C22—1248no—
167C22—1248no—
168C22—1212no—
169C22C22×D3×Q811yescharacteristic
170C22D3×H(5,𝔽2)16yes—
171C4—412no—
172C4—1212no—
173C3C2×#284011yescharacteristic, complemented, Sylow
174C2—38no—
175C2—46no—
176C2—126no—
177C2D3×#54313yes—
178C2D3×H(3,𝔽4)14yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2840C2
prime radicalC25×D3C22
hypercenter#2840D3
hypocenterC3C2×#2840
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2840

Complements

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

NH ≅ G/Ntype
1. C3×#2840C2semidirect
2. #76888C2semidirect
3. D3×#393C2semidirect
5. #73844C2semidirect
8. C22×D3×Q8C22semidirect
10. C3×#393C22semidirect
13. #5231C22semidirect
15. #4947C22semidirect
16. #4673C22semidirect
17. D3×#95C22semidirect
20. #2840D3direct (N × H)
25. C24×D3Q8semidirect
28. C22×C3×Q8C23semidirect
31. C22×Dic6C23semidirect
36. C3×#95C23semidirect
37. C3⋊#95C23semidirect
44. #393C2×D3semidirect
50. C24×C3C2×Q8semidirect
57. C23×D3C2×Q8semidirect
76. C22×Q8C22×D3semidirect
83. #95C22×D3semidirect
112. C24D3×Q8semidirect
159. D3#2840direct (N × H)
173. C3C2×#2840semidirect

Maximal subgroups

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

subgroupindex
C3×#28402
#768882
D3×#3932
D3×#3792
#738442
C2×#28403