Finite Group Databasebeta

← C3⋊D3×#498 #11874873

Subgroups — C3⋊D3×#498 #11874873

Order 1152.

1272 conjugacy classes of subgroups; only the 297 normal subgroups are shown.

normal subgroups only

This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 297 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⋊D3×C4⋊Q8C212yesmaximal
2C32×#498C211yesmaximal, characteristic, complemented
3#10592779C212yesmaximal, complemented
4C3⋊D3×#106C214yesmaximal
5#10592554C214yesmaximal, complemented
6C4×C8×C3⋊D3C211yesmaximal, characteristic
7#10592379C211yesmaximal, characteristic, complemented
8D3×#498—34nomaximal
9C2×Q8×C3⋊D3—22no—
10C32×C4⋊Q8C2212yes—
11#64153—22no—
12C2×C8×C3⋊D3C2212yes—
13C4⋊C4×C3⋊D3—22no—
14C4⋊C4×C3⋊D3C2214yes—
15#64097—22no—
16#64097C2214yes—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2212yes—
19C32×#106C2214yes—
20C32×C4×C8C2211yescharacteristic
21#63644C2214yes—
22C8×C3⋊Dic3C2212yes—
23#63635C2218yes—
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25D3×C4⋊Q8—38no—
26C3×#498D314yescomplemented
27#5080—38no—
28D3×#106—316no—
29#4855—316no—
30C4×D3×C8—34no—
31#4680—34no—
32C2×C32×Q8—22no—
33Q8×C3⋊D3—48no—
34C2×C4×C3⋊D3—24no—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#634—22no—
38C2×#634—24no—
39C2×C32×C8C2312yes—
40C32×C4⋊C4—22no—
41C32×C4⋊C4C2314yes—
42C32×C42C2311yescharacteristic
43C4⋊(C3⋊Dic3)—22no—
44C4⋊(C3⋊Dic3)C2314yes—
45#3750—24no—
46#3750—24no—
47C4×C3⋊Dic3D412yes—
48C4×C3⋊Dic3C2311yescharacteristic
49C2×C3⋊(C3⋊C8)C2312yes—
50C8×C3⋊D3Q818yescomplemented
51C2×#498—91noSylow
52C2×D3×Q8—68no—
53C3×C4⋊Q8C2×D318yes—
54#944—68no—
55C2×D3×C8—38no—
56D3×C4⋊C4—316no—
57D3×C4⋊C4—68no—
58#888—316no—
59#888—68no—
60C42×D3—34no—
61#869—38no—
62C3×#106C2×D3116yes—
63C3×C4×C8C2×D314yes—
64#817—316no—
65C8×Dic3—38no—
66#808—332no—
67C4×C3⋊C8—34no—
68C22×C3⋊D3C2×D411yescharacteristic
69C32×Q8—44no—
70C2×C32×C4—24no—
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2411yescharacteristic
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D412yes—
76C4×C3⋊D3—48no—
77C4×C3⋊D3SD1618yes—
78C4×C3⋊D3C2×Q814yes—
79#634—44no—
80#634—48no—
81C32×C8C2×Q814yescomplemented
82C3⋊(C3⋊C8)C2×Q814yescomplemented
83C2×C4⋊Q8—92no—
84#498—92no—
85#498—94no—
86#498—91no—
87#498C3⋊D311yescharacteristic, direct product factor
88C2×#106—94no—
89C2×C4×C8—91no—
90C2×C3×Q8—28no—
91D3×Q8—1232no—
92C2×C4×D3—38no—
93C2×C4×D3—34no—
94C2×C4×D3—616no—
95C2×Dic6—616no—
96C2×Dic6—68no—
97C2×C3×C8C22×D318yes—
98C3×C4⋊C4—28no—
99C3×C4⋊C4C22×D3116yes—
100C3×C42C22×D314yes—
101C4⋊Dic3—316no—
102C4⋊Dic3—68no—
103Dic3⋊C4—616no—
104Dic3⋊C4—616no—
105C4×Dic3—38no—
106C4×Dic3—34no—
107C2×C3⋊C8—38no—
108D3×C8—332no—
109C22×C32C22×D411yescharacteristic
110C2×C3⋊D3C4⋊Q812yes—
111C2×C3⋊D3C2×SD1614yes—
112C32×C4—44no—
113C32×C4C2×SD1614yes—
114C32×C4C22×Q812yes—
115C3⋊Dic3—44no—
116C3⋊Dic3C4⋊Q812yes—
117C3⋊Dic3C2×SD1614yes—
118C22×Q8—182no—
119C22×C8—92no—
120C4⋊Q8—94no—
121C4⋊Q8—92no—
122C4⋊Q8—182no—
123C4⋊Q8—182no—
124C4⋊Q8C2×C3⋊D312yes—
125C2×C4⋊C4—94no—
126C2×C4⋊C4—182no—
127C2×C42—91no—
128#106—94no—
129#106—98no—
130#106C2×C3⋊D314yes—
131C4×C8—92no—
132C4×C8—91no—
133C4×C8C2×C3⋊D311yescharacteristic
134C22×D3—34no—
135C3×Q8—416no—
136C2×C3×C4—216no—
137C2×C3×C4D3×D418yes—
138C2×C3×C4C23×D314yes—
139C2×Dic3—34no—
140C2×Dic3—38no—
141C2×Dic3—616no—
142C4×D3—332no—
143C4×D3—316no—
144C4×D3—1232no—
145Dic6—1232no—
146Dic6—1216no—
147C3×C8D3×Q8116yescomplemented
148C3⋊C8—316no—
149C2×C32C2×C4⋊Q811yescharacteristic
150C2×C32C22×SD1612yes—
151C3⋊D3#49814yesdirect product factor
152C2×Q8—22no—
153C2×Q8—184no—
154C2×Q8—182no—
155C2×Q8—368no—
156C22×C4—91no—
157C22×C4—92no—
158C22×C4—184no—
159C2×C8—92no—
160C2×C8—98no—
161C2×C8C22×C3⋊D312yes—
162C4⋊C4—22no—
163C4⋊C4—94no—
164C4⋊C4—184no—
165C4⋊C4—184no—
166C4⋊C4—182no—
167C4⋊C4C22×C3⋊D314yes—
168C42—91no—
169C42—92no—
170C42C22×C3⋊D311yescharacteristic
171C22×C3C2×D3×D414yes—
172C2×D3—38no—
173C2×D3—316no—
174C3×C4—416no—
175C3×C4D3×SD16116yes—
176C3×C4C2×D3×Q818yes—
177Dic3—38no—
178Dic3—316no—
179Dic3—1216no—
180C32C2×#49811yescharacteristic, complemented, Sylow
181C23—91no—
182Q8—44no—
183Q8—368no—
184Q8—364no—
185C2×C4—24no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—94no—
189C2×C4—98no—
190C2×C4—184no—
191C2×C4—368no—
192C2×C4D4×C3⋊D312yes—
193C2×C4C23×C3⋊D311yescharacteristic
194C8—94no—
195C8Q8×C3⋊D314yescomplemented
196C2×C3D3×C4⋊Q814yes—
197C2×C3C2×D3×SD1618yes—
198D3—316no—
199C22—92no—
200C22—94no—
201C22C2×D4×C3⋊D311yescharacteristic
202C4—44no—
203C4—92no—
204C4—94no—
205C4—364no—
206C4SD16×C3⋊D314yes—
207C4C2×Q8×C3⋊D312yes—
208C3D3×#49814yescomplemented
209C2—94no—
210C2C3⋊D3×C4⋊Q811yescharacteristic
211C2C2×SD16×C3⋊D312yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#498C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#498C3⋊D3
hypocenterC32C2×#498
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. C32×#498C2semidirect
3. #10592779C2semidirect
5. #10592554C2semidirect
7. #10592379C2semidirect
26. C3×#498D3semidirect
50. C8×C3⋊D3Q8semidirect
81. C32×C8C2×Q8semidirect
82. C3⋊(C3⋊C8)C2×Q8semidirect
87. #498C3⋊D3direct (N × H)
147. C3×C8D3×Q8semidirect
151. C3⋊D3#498direct (N × H)
180. C32C2×#498semidirect
195. C8Q8×C3⋊D3semidirect
208. C3D3×#498semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C32×#4982
#105927792
C3⋊D3×#1062
#105925542
C4×C8×C3⋊D32
#105923792
D3×#4983