Finite Group Databasebeta

← D3×#393 #76862

Subgroups — D3×#393 #76862

Order 384.

1036 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 203 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×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊C4C213yesmaximal
3C3×#393C211yesmaximal, characteristic, complemented
4#5231C211yesmaximal, characteristic, complemented
5#4947C213yesmaximal, complemented
6#4673C213yesmaximal, complemented
7D3×#95C213yesmaximal, complemented
8C2×#393—31nomaximal, Sylow
9C24×D3C2211yescharacteristic
10C22×C3×Q8C2211yescharacteristic, complemented
11C2×D3×Q8—212no—
12C22×C4×D3C2213yes—
13C22×C4×D3C2213yes—
14C22×Dic6C2213yescomplemented
15C2×C3×C22⋊C4C2213yes—
16C2×#217C2213yes—
17C2×(C2×D3)⋊C4C2213yes—
18C2×(C2×D3)⋊C4C2213yes—
19D3×C22⋊C4—212no—
20C3×#95C2213yescomplemented
21C3⋊#95C2216yescomplemented
22C3⋊#95C2213yescomplemented
23C23×Q8—31no—
24C22×C22⋊C4—33no—
25#393—31no—
26#393—33no—
27#393—33no—
28#393D311yescharacteristic, direct product factor
29C2×#95—33no—
30C24×C3C2311yescharacteristic
31C23×D3—26no—
32C23×D3—26no—
33C23×D3Q814yescomplemented
34C23×D3C2311yescharacteristic
35C23×D3C2311yescharacteristic
36C2×C3×Q8—26no—
37C22×C3×C4C2313yes—
38C22×C3×C4C2313yes—
39C22×Dic3C2313yes—
40C22×Dic3C2313yes—
41D3×Q8—232no—
42C2×C4×D3—212no—
43C2×C4×D3—26no—
44C2×C4×D3—212no—
45C2×C4×D3D4112yes—
46C2×Dic6—26no—
47C2×Dic6—212no—
48C3×C22⋊C4—26no—
49#217—26no—
50(C2×D3)⋊C4—26no—
51(C2×D3)⋊C4—26no—
52C25—31no—
53C22×Q8—33no—
54C22×Q8—612no—
55C22×Q8C2×D311yescharacteristic, complemented
56C23×C4—33no—
57C23×C4—33no—
58C2×C22⋊C4—33no—
59C2×C22⋊C4—33no—
60C2×C22⋊C4—33no—
61C2×C22⋊C4—612no—
62C2×C22⋊C4C2×D313yes—
63#95—36no—
64#95—33no—
65#95C2×D313yescomplemented
66C23×C3—23no—
67C23×C3—23no—
68C23×C3C2×Q812yescomplemented
69C23×C3C2411yescharacteristic
70C22×D3—23no—
71C22×D3—23no—
72C22×D3—224no—
73C22×D3—44no—
74C22×D3—412no—
75C22×D3C2×D416yes—
76C22×D3C2×Q812yes—
77C22×D3C2×Q812yescomplemented
78C22×D3#4116yes—
79C3×Q8—28no—
80C2×C3×C4—26no—
81C2×C3×C4—23no—
82C2×C3×C4—26no—
83C2×C3×C4C2×D416yes—
84C2×Dic3—26no—
85C2×Dic3—23no—
86C2×Dic3—26no—
87C2×Dic3C2×D416yes—
88C4×D3—224no—
89C4×D3—412no—
90Dic6—224no—
91C24—31no—
92C24—34no—
93C24—31no—
94C24—66no—
95C24—66no—
96C24C22×D311yescharacteristic
97C2×Q8—26no—
98C2×Q8—612no—
99C2×Q8—632no—
100C2×Q8—66no—
101C22×C4—33no—
102C22×C4—312no—
103C22×C4—33no—
104C22×C4—612no—
105C22×C4—66no—
106C22×C4—612no—
107C22×C4C22×D313yes—
108C22×C4C22×D313yes—
109C22⋊C4—26no—
110C22⋊C4—66no—
111C22⋊C4—66no—
112C22⋊C4—66no—
113C22×C3—26no—
114C22×C3—41no—
115C22×C3—43no—
116C22×C3C22×D413yes—
117C22×C3C22×Q811yescharacteristic
118C22×C3C2×#4113yes—
119C2×D3—26no—
120C2×D3—41no—
121C2×D3—43no—
122C2×D3—416no—
123C2×D3#12014yes—
124C2×D3C22⋊Q8112yes—
125C2×D3#124112yes—
126C3×C4—26no—
127C3×C4—43no—
128Dic3—26no—
129Dic3—43no—
130C23—23no—
131C23—23no—
132C23—36no—
133C23—32no—
134C23—36no—
135C23—32no—
136C23—624no—
137C23—63no—
138C23—63no—
139C23—1212no—
140C23—124no—
141C23D3×Q812yescomplemented
142C23C23×D311yescharacteristic
143Q8—28no—
144Q8—624no—
145C2×C4—26no—
146C2×C4—23no—
147C2×C4—26no—
148C2×C4—36no—
149C2×C4—624no—
150C2×C4—66no—
151C2×C4—63no—
152C2×C4—66no—
153C2×C4—1212no—
154C2×C4D3×D416yes—
155C2×C3—42no—
156C2×C3C2×#12011yescharacteristic
157C2×C3C2×C22⋊Q813yes—
158C2×C3C2×#12413yes—
159D3—42no—
160D3#39318yesdirect product factor
161C22—26no—
162C22—312no—
163C22—34no—
164C22—312no—
165C22—43no—
166C22—41no—
167C22—66no—
168C22—1216no—
169C22—123no—
170C22—121no—
171C22C2×D3×D413yes—
172C22C2×D3×Q811yescharacteristic
173C22D3×#4113yes—
174C4—26no—
175C4—43no—
176C4—66no—
177C4—123no—
178C3C2×#39311yescharacteristic, complemented, Sylow
179C2—38no—
180C2—42no—
181C2—122no—
182C2D3×#12011yescharacteristic
183C2D3×C22⋊Q813yes—
184C2D3×#12413yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#393C2
prime radicalC24×D3C22
hypercenter#393D3
hypocenterC3C2×#393
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×D3×Q8C2semidirect
3. C3×#393C2semidirect
4. #5231C2semidirect
5. #4947C2semidirect
6. #4673C2semidirect
7. D3×#95C2semidirect
10. C22×C3×Q8C22semidirect
14. C22×Dic6C22semidirect
20. C3×#95C22semidirect
21. C3⋊#95C22semidirect
22. C3⋊#95C22semidirect
28. #393D3direct (N × H)
33. C23×D3Q8semidirect
55. C22×Q8C2×D3semidirect
65. #95C2×D3semidirect
68. C23×C3C2×Q8semidirect
77. C22×D3C2×Q8semidirect
141. C23D3×Q8semidirect
160. D3#393direct (N × H)
178. C3C2×#393semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Q82
C2×D3×C22⋊C42
C3×#3932
#52312
#49472
#46732
D3×#952
C2×#3933