Finite Group Databasebeta

← C3⋊D3×#543 #11901857

Subgroups — C3⋊D3×#543 #11901857

Order 1152.

3888 conjugacy classes of subgroups; only the 841 normal subgroups are shown.

normal subgroups only

This group has 3888 conjugacy classes of subgroups — too many to draw. Only its 841 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
1C32×#543C211yesmaximal, characteristic, complemented
2#10596105C2112yesmaximal, complemented
3C3⋊D3×C22⋊Q8C2112yesmaximal, complemented
4C2×C22⋊C4×C3⋊D3C213yesmaximal
5#10595954C213yesmaximal, complemented
6D3×#543—34nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C2×Q8×C3⋊D3C2214yescomplemented
9C22×C4×C3⋊D3C2216yes—
10C32×C22⋊Q8C22112yescomplemented
11C2×C32×C22⋊C4C2213yes—
12C2×#3757C2213yes—
13#64155C22112yescomplemented
14C2×#3752C2216yes—
15#64133C22112yescomplemented
16#64106C22112yescomplemented
17#64105C22124yescomplemented
18C4⋊C4×C3⋊D3C22112yescomplemented
19C22⋊C4×C3⋊D3C22112yes—
20C22⋊C4×C3⋊D3C22112yes—
21#64087C22124yescomplemented
22C3×#543D314yescomplemented
23#5634—348no—
24D3×C22⋊Q8—348no—
25C2×D3×C22⋊C4—312no—
26#5483—312no—
27C24×C32C2311yescharacteristic
28C23×C3⋊D3—44no—
29C23×C3⋊D3Q818yescomplemented
30C23×C3⋊D3C2313yes—
31C23×C3⋊D3C2313yes—
32C2×C32×Q8C2314yescomplemented
33C22×C32×C4C2316yes—
34C22×C3⋊Dic3C2316yes—
35Q8×C3⋊D3—48no—
36C2×C4×C3⋊D3—412no—
37C2×C4×C3⋊D3C23112yes—
38C2×C4×C3⋊D3C23112yes—
39C2×#634C23112yescomplemented
40C32×C4⋊C4C23112yescomplemented
41C32×C22⋊C4C23112yes—
42#3757C23112yes—
43#3752C23124yes—
44C4⋊(C3⋊Dic3)C23112yescomplemented
45#3750C23124yescomplemented
46C2×#543—91noSylow
47C24×D3—34no—
48C2×D3×Q8—316no—
49C22×C4×D3—324no—
50C3×C22⋊Q8C2×D3148yescomplemented
51C2×C3×C22⋊C4C2×D3112yes—
52C2×#217—312no—
53#946—348no—
54C2×(C2×D3)⋊C4—324no—
55#924—348no—
56#897—348no—
57#896—396no—
58D3×C4⋊C4—348no—
59D3×C22⋊C4—348no—
60D3×C22⋊C4—348no—
61#878—396no—
62C23×C32—42no—
63C23×C32C2×Q814yescomplemented
64C23×C32C2413yes—
65C22×C3⋊D3—212no—
66C22×C3⋊D3—416no—
67C22×C3⋊D3—46no—
68C22×C3⋊D3C2×Q8112yes—
69C22×C3⋊D3C2×Q8112yescomplemented
70C22×C3⋊D3C2413yes—
71C22×C3⋊D3C2411yescharacteristic
72C32×Q8—44no—
73C2×C32×C4—46no—
74C2×C32×C4C24112yes—
75C2×C3⋊Dic3—46no—
76C2×C3⋊Dic3C24112yes—
77C4×C3⋊D3—224no—
78C4×C3⋊D3—412no—
79#634—412no—
80#543—912no—
81#543—93no—
82#543C3⋊D311yescharacteristic, direct product factor
83C2×C22⋊Q8—912no—
84C22×C22⋊C4—93no—
85C24×C3C22×D314yes—
86C23×D3—312no—
87C23×D3—332no—
88C23×D3—312no—
89C23×D3—1216no—
90C2×C3×Q8C22×D3116yescomplemented
91C22×C3×C4C22×D3124yes—
92C22×Dic3—324no—
93D3×Q8—1232no—
94C2×C4×D3—348no—
95C2×C4×D3—348no—
96C2×C4×D3—1248no—
97C2×Dic6—348no—
98C3×C4⋊C4C22×D3148yescomplemented
99C3×C22⋊C4C22×D3148yes—
100#217—348no—
101(C2×D3)⋊C4—396no—
102C4⋊Dic3—348no—
103Dic3⋊C4—396no—
104C22×C32—26no—
105C22×C32—44no—
106C22×C32C22×Q816yes—
107C22×C32C2511yescharacteristic
108C2×C3⋊D3—26no—
109C2×C3⋊D3—224no—
110C2×C3⋊D3—412no—
111C2×C3⋊D3C22×Q816yes—
112C2×C3⋊D3C22×Q812yes—
113C2×C3⋊D3H(5,𝔽2)14yes—
114C32×C4—212no—
115C3⋊Dic3—212no—
116C25—91no—
117C22×Q8—94no—
118C23×C4—96no—
119C22⋊Q8—912no—
120C22⋊Q8—912no—
121C22⋊Q8—924no—
122C22⋊Q8—912no—
123C22⋊Q8—924no—
124C22⋊Q8C2×C3⋊D3112yescomplemented
125C2×C4⋊C4—912no—
126C2×C22⋊C4—93no—
127C2×C22⋊C4—96no—
128C2×C22⋊C4—912no—
129C2×C22⋊C4—912no—
130C2×C22⋊C4C2×C3⋊D313yes—
131C23×C3—48no—
132C23×C3D3×Q8116yescomplemented
133C23×C3C23×D3112yes—
134C22×D3—34no—
135C22×D3—348no—
136C22×D3—312no—
137C22×D3—348no—
138C22×D3—648no—
139C22×D3—1264no—
140C22×D3—1224no—
141C3×Q8—416no—
142C2×C3×C4—424no—
143C2×C3×C4C23×D3148yes—
144C2×Dic3—348no—
145C2×Dic3—1224no—
146C4×D3—696no—
147C4×D3—1248no—
148Dic6—1248no—
149C2×C32—26no—
150C2×C32C23×Q811yescharacteristic
151C2×C32C2×H(5,𝔽2)12yes—
152C3⋊D3—26no—
153C3⋊D3#54314yesdirect product factor
154C24—93no—
155C24—93no—
156C24—98no—
157C24—364no—
158C24C22×C3⋊D311yescharacteristic
159C2×Q8—912no—
160C2×Q8—368no—
161C2×Q8C22×C3⋊D314yescomplemented
162C22×C4—96no—
163C22×C4—912no—
164C22×C4—912no—
165C22×C4—3612no—
166C22×C4C22×C3⋊D316yes—
167C4⋊C4—924no—
168C4⋊C4—912no—
169C4⋊C4C22×C3⋊D3112yescomplemented
170C22⋊C4—912no—
171C22⋊C4—924no—
172C22⋊C4C22×C3⋊D3112yes—
173C22×C3—224no—
174C22×C3—416no—
175C22×C3C2×D3×Q8124yes—
176C22×C3C24×D314yes—
177C2×D3—38no—
178C2×D3—316no—
179C2×D3—324no—
180C2×D3—696no—
181C2×D3—624no—
182C2×D3—1248no—
183C3×C4—248no—
184Dic3—648no—
185C32C2×#54311yescharacteristic, complemented, Sylow
186C23—42no—
187C23—91no—
188C23—912no—
189C23—93no—
190C23—912no—
191C23—1812no—
192C23—366no—
193C23—3616no—
194C23Q8×C3⋊D314yescomplemented
195C23C23×C3⋊D313yes—
196Q8—44no—
197Q8—3612no—
198C2×C4—46no—
199C2×C4—912no—
200C2×C4—1824no—
201C2×C4—3612no—
202C2×C4—366no—
203C2×C4C23×C3⋊D3112yes—
204C2×C3—224no—
205C2×C3C22×D3×Q814yes—
206C2×C3D3×H(5,𝔽2)18yes—
207D3—316no—
208D3—624no—
209C22—26no—
210C22—44no—
211C22—92no—
212C22—94no—
213C22—96no—
214C22—1824no—
215C22—186no—
216C22—3612no—
217C22C2×Q8×C3⋊D316yes—
218C22C24×C3⋊D311yescharacteristic
219C4—212no—
220C4—1812no—
221C3D3×#54314yescomplemented
222C2—26no—
223C2—94no—
224C2—186no—
225C2C22×Q8×C3⋊D311yescharacteristic
226C2C3⋊D3×H(5,𝔽2)12yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#543C2
prime radicalC24×C3⋊D3C22
hypercenter#543C3⋊D3
hypocenterC32C2×#543
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. C32×#543C2semidirect
2. #10596105C2semidirect
3. C3⋊D3×C22⋊Q8C2semidirect
5. #10595954C2semidirect
8. C2×Q8×C3⋊D3C22semidirect
10. C32×C22⋊Q8C22semidirect
13. #64155C22semidirect
15. #64133C22semidirect
16. #64106C22semidirect
17. #64105C22semidirect
18. C4⋊C4×C3⋊D3C22semidirect
21. #64087C22semidirect
22. C3×#543D3semidirect
29. C23×C3⋊D3Q8semidirect
32. C2×C32×Q8C23semidirect
39. C2×#634C23semidirect
40. C32×C4⋊C4C23semidirect
44. C4⋊(C3⋊Dic3)C23semidirect
45. #3750C23semidirect
50. C3×C22⋊Q8C2×D3semidirect
63. C23×C32C2×Q8semidirect
69. C22×C3⋊D3C2×Q8semidirect
82. #543C3⋊D3direct (N × H)
90. C2×C3×Q8C22×D3semidirect
98. C3×C4⋊C4C22×D3semidirect
124. C22⋊Q8C2×C3⋊D3semidirect
132. C23×C3D3×Q8semidirect
153. C3⋊D3#543direct (N × H)
161. C2×Q8C22×C3⋊D3semidirect
169. C4⋊C4C22×C3⋊D3semidirect
185. C32C2×#543semidirect
194. C23Q8×C3⋊D3semidirect
221. C3D3×#543semidirect

Maximal subgroups

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

subgroupindex
C32×#5432
#105961052
C3⋊D3×C22⋊Q82
C2×C22⋊C4×C3⋊D32
#105959542
D3×#5433