Finite Group Databasebeta

← D3×#6296 #13049535

Subgroups — D3×#6296 #13049535

Order 1296.

555 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 555 conjugacy classes of subgroups — too many to draw. Only its 86 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⋊#6296C213yesmaximal, complemented
2C3×#6296C211yesmaximal, characteristic, complemented
3C3×D3×C3⋊Dic3C213yesmaximal
4C2×#6296—31nomaximal
5D3×#627—33nomaximal
6C2×C33×D3C2211yescharacteristic
7C3×C3⋊(C3⋊Dic3)C2213yes—
8C32×C3⋊Dic3C2213yes—
9C2×C3×C3⋊Dic3—33no—
10#6296—33no—
11#6296—33no—
12#6296—63no—
13#6296D311yescharacteristic, direct product factor
14#6293—36no—
15D3×C3⋊Dic3D313yes—
16C3×#627—33no—
17C3×D3×Dic3—36no—
18C3×D3×Dic3—63no—
19C2×C34C2311yescharacteristic
20C33×D3Q812yescomplemented
21C2×#627—93no—
22D3×Dic6—93no—
23C22×C33—31no—
24C2×C32×D3—23no—
25C2×C32×D3—41no—
26C2×C32×D3C2×D313yes—
27C3⋊(C3⋊Dic3)C2×D313yes—
28C3×C3⋊Dic3—23no—
29C3×C3⋊Dic3—36no—
30C3×C3⋊Dic3—33no—
31C3×C3⋊Dic3—63no—
32C3×C3⋊Dic3—66no—
33C3×C3⋊Dic3—123no—
34C3×C3⋊Dic3C2×D313yes—
35C3×C3⋊Dic3C2×D313yes—
36C32×Dic3—36no—
37C32×Dic3—63no—
38C34C2×Q811yescharacteristic, complemented, Sylow
39C2×C3⋊Dic3—33no—
40#634—93no—
41C2×C3×Dic3—96no—
42C2×C3×Dic3—183no—
43C3×C4×D3—93no—
44C3×Dic6—93no—
45#627—33no—
46#627—96no—
47#627—96no—
48#627—93no—
49#627—186no—
50D3×Dic3—36no—
51D3×Dic3—63no—
52C2×C33—23no—
53C2×C33—23no—
54C2×C33—32no—
55C2×C33—43no—
56C2×C33—41no—
57C2×C33—81no—
58C2×C33C22×D313yes—
59C2×C33C22×D311yescharacteristic
60C32×D3—26no—
61C32×D3—42no—
62C32×D3Dic616yescomplemented
63D3×Q8—271no—
64C2×Dic6—273no—
65C22×C32—33no—
66C22×C32—63no—
67C22×C32—121no—
68C2×C3×D3—23no—
69C2×C3×D3—41no—
70C2×C3×D3D3213yes—
71C32×C4—93no—
72C3⋊Dic3—36no—
73C3⋊Dic3—33no—
74C3⋊Dic3—63no—
75C3⋊Dic3—66no—
76C3⋊Dic3—123no—
77C3⋊Dic3D3213yes—
78C3×Dic3—36no—
79C3×Dic3—36no—
80C3×Dic3—66no—
81C3×Dic3—63no—
82C3×Dic3—63no—
83C3×Dic3—93no—
84C3×Dic3—96no—
85C3×Dic3—123no—
86C3×Dic3—186no—
87C3×Dic3—183no—
88C3×Dic3—363no—
89C33—23no—
90C33—23no—
91C33—41no—
92C33—43no—
93C33—81no—
94C33C2×Dic613yescomplemented
95C33D3×Q811yescharacteristic, complemented
96C3×Q8—271no—
97C2×C3×C4—273no—
98C2×Dic3—96no—
99C2×Dic3—183no—
100C4×D3—93no—
101Dic6—93no—
102Dic6—276no—
103Dic6—273no—
104Dic6—273no—
105Dic6—543no—
106C2×C32—26no—
107C2×C32—23no—
108C2×C32—23no—
109C2×C32—36no—
110C2×C32—43no—
111C2×C32—41no—
112C2×C32—43no—
113C2×C32—43no—
114C2×C32—41no—
115C2×C32—66no—
116C2×C32—83no—
117C2×C32—83no—
118C2×C32—81no—
119C2×C32—122no—
120C2×C32C2×D3213yes—
121C2×C32C2×D3213yes—
122C3×D3—26no—
123C3×D3—42no—
124C3×D3#62716yescomplemented
125C2×Q8—811noSylow
126C22×C3—33no—
127C22×C3—63no—
128C22×C3—121no—
129C2×D3#111311yescharacteristic
130C3×C4—93no—
131C3×C4—93no—
132C3×C4—183no—
133C3×C4—273no—
134Dic3—36no—
135Dic3—63no—
136Dic3—96no—
137Dic3—93no—
138Dic3—186no—
139Dic3—183no—
140Dic3—363no—
141C32—23no—
142C32—26no—
143C32—23no—
144C32—41no—
145C32—43no—
146C32—43no—
147C32—43no—
148C32—41no—
149C32—83no—
150C32—83no—
151C32—81no—
152C32D3×Dic613yescomplemented
153C32C2×#62713yescomplemented
154Q8—271no—
155Q8—813no—
156C2×C4—273no—
157C2×C3—23no—
158C2×C3—23no—
159C2×C3—36no—
160C2×C3—43no—
161C2×C3—41no—
162C2×C3—66no—
163C2×C3—81no—
164C2×C3—122no—
165C2×C3D3313yes—
166C2×C3C2×#111311yescharacteristic
167D3#629612yesdirect product factor
168C22—31no—
169C4—93no—
170C4—273no—
171C3—23no—
172C3—23no—
173C3—41no—
174C3—43no—
175C3—81no—
176C3D3×#62713yescomplemented
177C3C2×#629611yescharacteristic, complemented
178C2—32no—
179C2D3×#111311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×#1113
commutator, Fitting, socle, cosocleC2×C34C23
prime radicalC2×C33×D3C22
hypocenterC34C2×Q8
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊#6296C2semidirect
2. C3×#6296C2semidirect
13. #6296D3direct (N × H)
20. C33×D3Q8semidirect
38. C34C2×Q8semidirect
62. C32×D3Dic6semidirect
94. C33C2×Dic6semidirect
95. C33D3×Q8semidirect
124. C3×D3#627semidirect
152. C32D3×Dic6semidirect
153. C32C2×#627semidirect
167. D3#6296direct (N × H)
176. C3D3×#627semidirect
177. C3C2×#6296semidirect

Maximal subgroups

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

subgroupindex
C3⋊#62962
C3×#62962
C3×D3×C3⋊Dic32
C2×#62963
D3×#6273