Finite Group Databasebeta

← C3⋊D3×#124 #10596144

Subgroups — C3⋊D3×#124 #10596144

Order 576.

990 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 199 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
1C2×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×D4×C3⋊D3C211yesmaximal, characteristic
3C32×#124C211yesmaximal, characteristic, complemented
4#64156C211yesmaximal, characteristic, complemented
5#64145C211yesmaximal, characteristic, complemented
6#64094C214yesmaximal, complemented
7C22⋊C4×C3⋊D3C214yesmaximal, complemented
8#64084C211yesmaximal, characteristic, complemented
9C42×C3⋊D3C211yesmaximal, characteristic, complemented
10D3×#124—34nomaximal
11C23×C3⋊D3C2212yes—
12C2×C32×Q8C2211yescharacteristic, complemented
13C2×C32×D4C2211yescharacteristic
14C2×#638C2212yes—
15Q8×C3⋊D3—24no—
16D4×C3⋊D3—24no—
17C2×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C4×C3⋊D3C2212yes—
19C2×C4×C3⋊D3C2212yes—
20C2×C4×C3⋊D3C2211yescharacteristic
21C2×#634C2211yescharacteristic, complemented
22C2×#634C2212yescomplemented
23C32×C22⋊C4C2214yescomplemented
24C32×C42C2211yescharacteristic, complemented
25#3757C2214yescomplemented
26#3752C2214yescomplemented
27#3752C2214yescomplemented
28C4×C3⋊Dic3C2212yescomplemented
29C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×D3×Q8—34no—
31C2×D3×D4—34no—
32C3×#124D314yescomplemented
33#947—34no—
34#936—34no—
35#885—316no—
36D3×C22⋊C4—316no—
37#875—34no—
38C42×D3—34no—
39C23×C32C2312yes—
40C22×C3⋊D3—24no—
41C22×C3⋊D3—28no—
42C22×C3⋊D3C2312yes—
43C22×C3⋊D3C2311yescharacteristic
44C32×Q8—22no—
45C32×D4—22no—
46C2×C32×C4C2312yes—
47C2×C32×C4C2312yes—
48C2×C32×C4C2311yescharacteristic
49#638—24no—
50C2×C3⋊Dic3C2312yes—
51C2×C3⋊Dic3C2312yes—
52C2×C3⋊Dic3C2311yescharacteristic
53C4⋊(C3⋊D3)—22no—
54C4×C3⋊D3—24no—
55C4×C3⋊D3—24no—
56C4×C3⋊D3D414yes—
57#634—22no—
58#634—24no—
59C2×#124—91noSylow
60C23×D3—38no—
61C2×C3×Q8C2×D314yescomplemented
62C2×C3×D4C2×D314yes—
63C2×#67—38no—
64D3×Q8—616no—
65D3×D4—616no—
66C2×D12—34no—
67C2×C4×D3—34no—
68C2×C4×D3—38no—
69C2×C4×D3—38no—
70C2×Dic6—34no—
71C2×Dic6—38no—
72C3×C22⋊C4C2×D3116yescomplemented
73C3×C42C2×D314yescomplemented
74#217—316no—
75(C2×D3)⋊C4—316no—
76(C2×D3)⋊C4—316no—
77C4×Dic3—38no—
78C4×Dic3—34no—
79C22×C32—22no—
80C22×C32—24no—
81C22×C32C2411yescharacteristic
82C2×C3⋊D3—22no—
83C2×C3⋊D3—24no—
84C2×C3⋊D3—48no—
85C2×C3⋊D3C2×D412yes—
86C2×C3⋊D3#4114yes—
87C32×C4—22no—
88C32×C4—22no—
89C32×C4C2×D412yes—
90C3⋊Dic3—22no—
91C3⋊Dic3—22no—
92C3⋊Dic3C2×D412yes—
93C22×Q8—91no—
94C22×D4—91no—
95#124—91no—
96#124—91no—
97#124—94no—
98#124—91no—
99#124C3⋊D311yescharacteristic, direct product factor
100C2×C22⋊C4—94no—
101C2×C42—91no—
102C23×C3C22×D318yes—
103C22×D3—34no—
104C22×D3—38no—
105C22×D3—616no—
106C22×D3—632no—
107C3×Q8—28no—
108C3×D4—28no—
109C2×C3×C4C22×D318yes—
110C2×C3×C4C22×D318yes—
111C2×C3×C4C22×D314yes—
112#67—616no—
113C2×Dic3—34no—
114C2×Dic3—38no—
115C2×Dic3—38no—
116D12—68no—
117C4×D3—316no—
118C4×D3—616no—
119C4×D3—616no—
120Dic6—616no—
121Dic6—68no—
122C2×C32—42no—
123C2×C32C22×D411yescharacteristic
124C2×C32C2×#4112yes—
125C3⋊D3—42no—
126C3⋊D3#12414yesdirect product factor
127C24—92no—
128C2×Q8—92no—
129C2×Q8—91no—
130C2×Q8—184no—
131C2×Q8C2×C3⋊D311yescharacteristic, complemented
132C2×D4—92no—
133C2×D4—91no—
134C2×D4—184no—
135C2×D4C2×C3⋊D311yescharacteristic
136C22×C4—91no—
137C22×C4—92no—
138C22×C4—92no—
139C22⋊C4—94no—
140C22⋊C4—94no—
141C22⋊C4—94no—
142C22⋊C4C2×C3⋊D314yescomplemented
143C42—92no—
144C42—91no—
145C42C2×C3⋊D311yescharacteristic, complemented
146C22×C3—28no—
147C22×C3—216no—
148C22×C3C23×D314yes—
149C2×D3—38no—
150C2×D3—316no—
151C2×D3—68no—
152C2×D3—616no—
153C2×D3—1232no—
154C3×C4—28no—
155C3×C4—28no—
156C3×C4D3×D418yes—
157Dic3—38no—
158Dic3—68no—
159Dic3—68no—
160C32C2×#12411yescharacteristic, complemented, Sylow
161C23—91no—
162C23—92no—
163C23—184no—
164C23—188no—
165C23C22×C3⋊D312yes—
166Q8—22no—
167Q8—184no—
168Q8—182no—
169D4—22no—
170D4—184no—
171D4—182no—
172C2×C4—91no—
173C2×C4—94no—
174C2×C4—92no—
175C2×C4—92no—
176C2×C4—184no—
177C2×C4—184no—
178C2×C4C22×C3⋊D312yes—
179C2×C4C22×C3⋊D312yes—
180C2×C4C22×C3⋊D311yescharacteristic
181C2×C3—48no—
182C2×C3C2×D3×D414yes—
183C2×C3D3×#4118yes—
184D3—316no—
185D3—128no—
186C22—22no—
187C22—24no—
188C22—92no—
189C22—94no—
190C22—182no—
191C22—184no—
192C22—368no—
193C22C23×C3⋊D311yescharacteristic
194C4—22no—
195C4—22no—
196C4—92no—
197C4—182no—
198C4—182no—
199C4D4×C3⋊D312yes—
200C3D3×#12414yescomplemented
201C2—42no—
202C2—94no—
203C2—362no—
204C2C2×D4×C3⋊D311yescharacteristic
205C2#41×C3⋊D312yes—
subgroupG/H
center, FrattiniC22C23×C3⋊D3
commutator, socle, cosocleC22×C32C24
FittingC32×#124C2
prime radicalC2×D4×C3⋊D3C2
hypercenter#124C3⋊D3
hypocenterC32C2×#124
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊D3C2semidirect
3. C32×#124C2semidirect
4. #64156C2semidirect
5. #64145C2semidirect
6. #64094C2semidirect
7. C22⋊C4×C3⋊D3C2semidirect
8. #64084C2semidirect
9. C42×C3⋊D3C2semidirect
12. C2×C32×Q8C22semidirect
21. C2×#634C22semidirect
22. C2×#634C22semidirect
23. C32×C22⋊C4C22semidirect
24. C32×C42C22semidirect
25. #3757C22semidirect
26. #3752C22semidirect
27. #3752C22semidirect
28. C4×C3⋊Dic3C22semidirect
29. C4×C3⋊Dic3C22semidirect
32. C3×#124D3semidirect
61. C2×C3×Q8C2×D3semidirect
72. C3×C22⋊C4C2×D3semidirect
73. C3×C42C2×D3semidirect
99. #124C3⋊D3direct (N × H)
126. C3⋊D3#124direct (N × H)
131. C2×Q8C2×C3⋊D3semidirect
142. C22⋊C4C2×C3⋊D3semidirect
145. C42C2×C3⋊D3semidirect
160. C32C2×#124semidirect
200. C3D3×#124semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊D32
C2×D4×C3⋊D32
C32×#1242
#641562
#641452
#640942
C22⋊C4×C3⋊D32
#640842
C42×C3⋊D32
D3×#1243