Finite Group Databasebeta

← #10619559⋊C3 #14516926

Subgroups — #10619559⋊C3 #14516926

Order 1944.

180 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 34 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
1#66331⋊C3C211yesmaximal, characteristic
2#66324⋊C3C211yesmaximal, characteristic
3#11757587C211yesmaximal, characteristic
4#6189⋊C3—31nomaximal
5C3×#6196—31nomaximal
6#10619559C311yesmaximal, characteristic, complemented
7C2×#6910C2211yescharacteristic
8C3⋊(3−1+2⋊C4)D311yescharacteristic
9C3×#1084D311yescharacteristic
10Dic3×3−1+2—31no—
11C3×3−1+2⋊C4—31no—
12C3×3−1+2⋊C4—61no—
13C3×(C3⋊Dic3)⋊C3—31no—
14C3×(C3⋊Dic3)⋊C3—31no—
15#66331C2×C311yescharacteristic
16#66324—21no—
17#66324C2×C311yescharacteristic
18#66323—21no—
19#66323C2×C311yescharacteristic
20#6910Q811yescharacteristic, complemented, Sylow
21C3×#627—91no—
22C3×#627—91no—
233−1+2⋊Q8—91no—
24#6196—31no—
25#6189—31no—
26C2×C3×3−1+2—21no—
27C2×C3×3−1+2C2×D311yescharacteristic
28C2×C3×H(3,𝔽3)C2×D311yescharacteristic
29C2×#731—21no—
30C2×#731—21no—
31C2×#731—41no—
32C2×#731C22×C311yescharacteristic
33C3×C3⋊Dic3—31no—
34C3×C3⋊Dic3—31no—
35C32×Dic3—31no—
36C32×Dic3—91no—
37C32×Dic3—91no—
38C32×Dic3—91no—
39C4×3−1+2—91no—
40#1084C3×D311yescharacteristic
41C3⋊Dic9C3×D311yescharacteristic
423−1+2⋊C4—31no—
433−1+2⋊C4—61no—
443−1+2⋊C4—61no—
453−1+2⋊C4—61no—
463−1+2⋊C4—61no—
473−1+2⋊C4—91no—
48(C3⋊Dic3)⋊C3—31no—
49(C3⋊Dic3)⋊C3—31no—
50(C3⋊Dic3)⋊C3—61no—
51(C3⋊Dic3)⋊C3—61no—
52C9×Dic3—31no—
53C9×Dic3—61no—
54C3×Dic9—31no—
55C3×Dic9—61no—
56C3×3−1+2—21no—
57C3×3−1+2Dic611yescharacteristic, complemented
58C3×H(3,𝔽3)Dic611yescharacteristic
59#731—21no—
60#731—21no—
61#731—41no—
62#731C3×Q811yescharacteristic, complemented
63C3×Dic6—271no—
64C3×Dic6—271no—
65C3×Dic6—271no—
66#627—91no—
67#627—91no—
68Dic18—91no—
69C2×C33—31no—
70C2×C33D3211yescharacteristic
71C2×3−1+2—21no—
72C2×3−1+2—31no—
73C2×3−1+2—41no—
74C2×3−1+2—61no—
75C2×3−1+2—61no—
76C2×3−1+2—61no—
77C2×H(3,𝔽3)—21no—
78C2×H(3,𝔽3)—61no—
79C2×H(3,𝔽3)C2×C3×D311yescharacteristic
80C2×C3×C9—21no—
81C2×C3×C9—61no—
82C2×C3×C9C2×C3×D311yescharacteristic
83C32×C4—91no—
84C32×C4—271no—
85C32×C4—271no—
86C3⋊Dic3—31no—
87C3⋊Dic3—31no—
88C3×Dic3—31no—
89C3×Dic3—91no—
90C3×Dic3—91no—
91C3×Dic3—91no—
92C3×Dic3—91no—
93C3×Dic3—91no—
94C3×Dic3—91no—
95C3×Dic3—91no—
96C3×Dic3—181no—
97C3×Dic3—181no—
98C3×Dic3—181no—
99C3×Dic3—271no—
100C3×Dic3—271no—
101C4×C9—91no—
102C4×C9—181no—
103Dic9—31no—
104Dic9—61no—
105Dic9—91no—
106C33—31no—
107C33#62711yescharacteristic
1083−1+2—21no—
1093−1+2—31no—
1103−1+2—41no—
1113−1+2—61no—
1123−1+2—61no—
1133−1+2—61no—
114H(3,𝔽3)—21no—
115H(3,𝔽3)—61no—
116H(3,𝔽3)C3×Dic611yescharacteristic
117C3×C9—21no—
118C3×C9—61no—
119C3×C9C3×Dic611yescharacteristic, complemented
120C3×Q8—811no—
121Dic6—271no—
122Dic6—271no—
123Dic6—271no—
124C2×C32—21no—
125C2×C32—31no—
126C2×C32—61no—
127C2×C32—91no—
128C2×C32—91no—
129C2×C32—181no—
130C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
131C2×C32C3×D3211yescharacteristic
132C2×C9—31no—
133C2×C9—61no—
134C2×C9—61no—
135C2×C9—121no—
136C3×C4—91no—
137C3×C4—271no—
138C3×C4—271no—
139C3×C4—271no—
140C3×C4—271no—
141C3×C4—271no—
142C3×C4—541no—
143C3×C4—541no—
144Dic3—31no—
145Dic3—91no—
146Dic3—91no—
147Dic3—91no—
148Dic3—271no—
149Dic3—271no—
150C32—21no—
151C32—31no—
152C32—61no—
153C32—91no—
154C32—91no—
155C32—181no—
156C32#619611yescharacteristic
157C32C3×#62711yescharacteristic
158C9—31no—
159C9—61no—
160C9—61no—
161C9—121no—
162Q8—811noSylow
163C2×C3—31no—
164C2×C3—31no—
165C2×C3—61no—
166C2×C3—91no—
167C2×C3—181no—
168C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
169C4—91no—
170C4—271no—
171C4—271no—
172C3—31no—
173C3—31no—
174C3—61no—
175C3—91no—
176C3—181no—
177C3C3×#619611yescharacteristic
178C2(#4176⋊C2)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2(#4176⋊C2)⋊C3
commutator, cosocleC2×#731C22×C3
FrattiniC2×C32C3×D32
FittingC2×#6910C22
socleC2×C3C3×((C3⋊D3)⋊C3)⋊C2
prime radicalC2×C3×H(3,𝔽3)C2×D3
hypocenter#731C3×Q8
LCSG ▷ C2×#731 ▷ #731
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
6. #10619559C3semidirect
20. #6910Q8semidirect
57. C3×3−1+2Dic6semidirect
62. #731C3×Q8semidirect
119. C3×C9C3×Dic6semidirect

Maximal subgroups

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

subgroupindex
#66331⋊C32
#66324⋊C32
#117575872
#6189⋊C33
C3×#61963
#106195593