Finite Group Databasebeta

← D3×#392 #76752

Subgroups — D3×#392 #76752

Order 384.

1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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×D4C213yesmaximal, complemented
2C2×D3×C22⋊C4C213yesmaximal, complemented
3C3×#392C211yesmaximal, characteristic, complemented
4#5223C213yesmaximal, complemented
5#4960C213yesmaximal, complemented
6#4671C211yesmaximal, characteristic, complemented
7D3×#95C211yesmaximal, characteristic, complemented
8C2×#392—31nomaximal, Sylow
9C24×D3C2213yes—
10C22×C3×D4C2213yescomplemented
11C22×#67C2216yescomplemented
12C2×D3×D4—224no—
13C2×D3×D4—212no—
14C22×D12C2213yescomplemented
15C22×C4×D3C2211yescharacteristic
16C22×C4×D3C2213yes—
17C2×C3×C22⋊C4C2213yescomplemented
18C2×#217C2213yescomplemented
19C2×(C2×D3)⋊C4C2213yescomplemented
20C2×(C2×D3)⋊C4C2213yescomplemented
21D3×C22⋊C4—212no—
22C3×#95C2211yescharacteristic, complemented
23C3⋊#95C2213yescomplemented
24C23×D4—33no—
25C22×C22⋊C4—33no—
26#392—33no—
27#392—33no—
28#392—31no—
29#392D311yescharacteristic, direct product factor
30C2×#95—31no—
31C24×C3C2313yes—
32C23×D3—26no—
33C23×D3—212no—
34C23×D3—212no—
35C23×D3—26no—
36C23×D3D4112yescomplemented
37C23×D3C2313yes—
38C23×D3C2311yescharacteristic
39C2×C3×D4—212no—
40C2×C3×D4—26no—
41C22×C3×C4C2311yescharacteristic
42C22×C3×C4C2313yes—
43C2×#67—212no—
44C2×#67—212no—
45C2×#67—212no—
46C22×Dic3C2311yescharacteristic
47C22×Dic3C2313yes—
48D3×D4—296no—
49C2×D12—212no—
50C2×D12—26no—
51C2×C4×D3—212no—
52C2×C4×D3—26no—
53C2×C4×D3D4112yescomplemented
54C3×C22⋊C4—26no—
55#217—26no—
56(C2×D3)⋊C4—26no—
57(C2×D3)⋊C4—26no—
58C25—33no—
59C22×D4—36no—
60C22×D4—33no—
61C22×D4—612no—
62C22×D4—624no—
63C22×D4C2×D313yescomplemented
64C23×C4—33no—
65C23×C4—31no—
66C2×C22⋊C4—33no—
67C2×C22⋊C4—33no—
68C2×C22⋊C4—33no—
69C2×C22⋊C4—612no—
70C2×C22⋊C4C2×D313yescomplemented
71#95—33no—
72#95C2×D311yescharacteristic, complemented
73C23×C3—23no—
74C23×C3—26no—
75C23×C3—26no—
76C23×C3—23no—
77C23×C3C2×D416yescomplemented
78C23×C3C2411yescharacteristic
79C22×D3—23no—
80C22×D3—26no—
81C22×D3—26no—
82C22×D3—23no—
83C22×D3—248no—
84C22×D3—224no—
85C22×D3—412no—
86C22×D3—424no—
87C22×D3—412no—
88C22×D3C2×D416yes—
89C22×D3C2×D416yes—
90C22×D3C2×D416yescomplemented
91C22×D3#4112yes—
92C3×D4—224no—
93C2×C3×C4—26no—
94C2×C3×C4—23no—
95C2×C3×C4C2×D416yescomplemented
96#67—248no—
97C2×Dic3—26no—
98C2×Dic3—23no—
99C2×Dic3C2×D416yescomplemented
100D12—224no—
101C4×D3—224no—
102C4×D3—44no—
103C24—31no—
104C24—312no—
105C24—33no—
106C24—66no—
107C24—612no—
108C24—612no—
109C24—66no—
110C24C22×D313yes—
111C2×D4—212no—
112C2×D4—26no—
113C2×D4—612no—
114C2×D4—612no—
115C2×D4—696no—
116C2×D4—612no—
117C2×D4—612no—
118C2×D4—66no—
119C22×C4—33no—
120C22×C4—312no—
121C22×C4—31no—
122C22×C4—612no—
123C22×C4—66no—
124C22×C4C22×D311yescharacteristic
125C22×C4C22×D313yes—
126C22⋊C4—26no—
127C22⋊C4—66no—
128C22⋊C4—66no—
129C22⋊C4—66no—
130C22×C3—212no—
131C22×C3—26no—
132C22×C3—43no—
133C22×C3—46no—
134C22×C3—43no—
135C22×C3C22×D413yes—
136C22×C3C22×D413yes—
137C22×C3C2×#4111yescharacteristic
138C2×D3—212no—
139C2×D3—26no—
140C2×D3—43no—
141C2×D3—46no—
142C2×D3—43no—
143C2×D3—448no—
144C2×D3#120112yes—
145C2×D3#121112yes—
146C2×D3#12714yes—
147C3×C4—26no—
148C3×C4—41no—
149Dic3—26no—
150Dic3—41no—
151C23—23no—
152C23—26no—
153C23—26no—
154C23—23no—
155C23—36no—
156C23—36no—
157C23—32no—
158C23—36no—
159C23—648no—
160C23—624no—
161C23—63no—
162C23—66no—
163C23—66no—
164C23—63no—
165C23—1212no—
166C23—1212no—
167C23—1224no—
168C23D3×D416yescomplemented
169C23C23×D311yescharacteristic
170D4—224no—
171D4—624no—
172D4—648no—
173C2×C4—26no—
174C2×C4—23no—
175C2×C4—36no—
176C2×C4—624no—
177C2×C4—66no—
178C2×C4—63no—
179C2×C4—124no—
180C2×C4D3×D416yescomplemented
181C2×C3—46no—
182C2×C3C2×#12013yes—
183C2×C3C2×#12113yes—
184C2×C3C2×#12711yescharacteristic
185D3—46no—
186D3#39218yesdirect product factor
187C22—212no—
188C22—26no—
189C22—34no—
190C22—312no—
191C22—312no—
192C22—43no—
193C22—43no—
194C22—46no—
195C22—612no—
196C22—66no—
197C22—1248no—
198C22—123no—
199C22—123no—
200C22—126no—
201C22C2×D3×D413yes—
202C22C2×D3×D413yes—
203C22D3×#4111yescharacteristic
204C4—26no—
205C4—41no—
206C4—66no—
207C4—121no—
208C3C2×#39211yescharacteristic, complemented, Sylow
209C2—38no—
210C2—46no—
211C2—126no—
212C2D3×#12013yes—
213C2D3×#12113yes—
214C2D3×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#392C2
hypercenter#392D3
hypocenterC3C2×#392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D3×D4C2semidirect
2. C2×D3×C22⋊C4C2semidirect
3. C3×#392C2semidirect
4. #5223C2semidirect
5. #4960C2semidirect
6. #4671C2semidirect
7. D3×#95C2semidirect
10. C22×C3×D4C22semidirect
11. C22×#67C22semidirect
14. C22×D12C22semidirect
17. C2×C3×C22⋊C4C22semidirect
18. C2×#217C22semidirect
19. C2×(C2×D3)⋊C4C22semidirect
20. C2×(C2×D3)⋊C4C22semidirect
22. C3×#95C22semidirect
23. C3⋊#95C22semidirect
29. #392D3direct (N × H)
36. C23×D3D4semidirect
53. C2×C4×D3D4semidirect
63. C22×D4C2×D3semidirect
70. C2×C22⋊C4C2×D3semidirect
72. #95C2×D3semidirect
77. C23×C3C2×D4semidirect
90. C22×D3C2×D4semidirect
95. C2×C3×C4C2×D4semidirect
99. C2×Dic3C2×D4semidirect
168. C23D3×D4semidirect
180. C2×C4D3×D4semidirect
186. D3#392direct (N × H)
208. C3C2×#392semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D42
C2×D3×C22⋊C42
C3×#3922
#52232
#49602
#46712
D3×#952
C2×#3923