Finite Group Databasebeta

← #11757861⋊C2 #14518211

Subgroups — #11757861⋊C2 #14518211

Order 1944.

214 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 30 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#11757861C211yesmaximal, characteristic, complemented
2C22×#4208C311yesmaximal, characteristic, complemented
3D3×C9⋊A4—31nomaximal
4#10619773C311yesmaximal, characteristic, complemented
5#10619772C311yesmaximal, characteristic, complemented
6#10619771C311yesmaximal, characteristic, complemented
7#6913⋊C2—41nomaximal
8C22×#737C2×C311yescharacteristic, complemented
9C2×#4208—31no—
10C2×#4208—31no—
11#66436—21no—
12C3×C9⋊A4D311yescharacteristic, complemented
13#66366—21no—
14#66365—21no—
15#66364—21no—
16#66363C2×C311yescharacteristic
17#66362C2×C311yescharacteristic, complemented
18#66361C2×C311yescharacteristic, complemented
19#6913—41noSylow
20C3×D3×A4—31no—
21C22×#272C3211yescharacteristic
22C22×D3×C9—31no—
23C22×D3×C9—91no—
24C2×C9⋊A4—91no—
25D3×C22⋊C9—31no—
26D3×C22⋊C9—31no—
27C2×#737—31no—
28#4208—31no—
29#4208A411yescharacteristic, complemented
30D3×3−1+2—121no—
31#4178—41no—
32#4176—41no—
33#4174—41no—
34C32×A4C3×D311yescharacteristic
35C22×3−1+2—21no—
36C22×3−1+2—61no—
37C22×H(3,𝔽3)C2×C3211yescharacteristic
38C22×C3×C9—31no—
39C22×C3×C9C3×D311yescharacteristic
40C2×#272—31no—
41C2×#272—31no—
42C2×D3×C9—91no—
43C2×D3×C9—93no—
44C2×D3×C9—93no—
45C2×D3×C9—91no—
46C22⋊H(3,𝔽3)—21no—
47#1094—21no—
48#1094—21no—
49C3×C22⋊C9C3×D311yescharacteristic
50C3×C22⋊C9C3×D311yescharacteristic
51C9⋊A4—31no—
52C9⋊A4—61no—
53C9⋊A4—61no—
54C9⋊A4—61no—
55C9×A4—61no—
56#737—81no—
57#737C2×A411yescharacteristic, complemented
58C3×3−1+2—41no—
59#733—81no—
60#732—41no—
61#731—41no—
62#731—81no—
63AΣL(1,𝔽27)—41no—
64AΣL(1,𝔽27)—81no—
65C22×C3×D3—31no—
66C22×C3×D3—91no—
67C2×C3×A4—91no—
68D3×A4—91no—
69C23×C9—91no—
70C2×C22⋊C9—91no—
71C2×C22⋊C9—91no—
72C32×D3—121no—
73C2×3−1+2—61no—
74C2×3−1+2—63no—
75C2×3−1+2—361no—
76C2×H(3,𝔽3)—31no—
77C2×C3×C9—33no—
78C2×C3×C9—31no—
79#272—31no—
80#272C3×A411yescharacteristic
81D3×C9—31no—
82D3×C9—91no—
83D3×C9—93no—
84D3×C9—91no—
85D3×C9—121no—
86D3×C9—121no—
87C22×C32—31no—
88C22×C32C32×D311yescharacteristic
89C2×C3×D3—91no—
90C2×C3×D3—93no—
91C2×C3×D3—93no—
92C2×C3×D3—91no—
93C3×A4—31no—
94C3×A4—61no—
95C3×A4—91no—
96C22×C9—21no—
97C22×C9—61no—
98C22×C9—271no—
99C22×C9—271no—
100C22×C9(C3⋊D3)⋊C311yescharacteristic
101C22⋊C9—31no—
102C22⋊C9—31no—
103C22⋊C9—61no—
104C22⋊C9—61no—
105C33—41no—
1063−1+2—21no—
1073−1+2—61no—
1083−1+2—81no—
1093−1+2—81no—
1103−1+2—121no—
1113−1+2—241no—
1123−1+2—241no—
1133−1+2—241no—
114H(3,𝔽3)—81no—
115H(3,𝔽3)C2×C3×A411yescharacteristic
116C3×C9—31no—
117C3×C9—41no—
118C3×C9—41no—
119C3×C9—241no—
120C3×C9D3×A411yescharacteristic
121C23×C3—91no—
122C22×D3—31no—
123C22×D3—91no—
124C2×A4—271no—
125C2×C32—33no—
126C2×C32—31no—
127C2×C32—361no—
128C3×D3—31no—
129C3×D3—91no—
130C3×D3—93no—
131C3×D3—91no—
132C3×D3—361no—
133C2×C9—31no—
134C2×C9—61no—
135C2×C9—63no—
136C2×C9—91no—
137C2×C9—271no—
138C2×C9—361no—
139C2×C9—361no—
140C22×C3—31no—
141C22×C3—91no—
142C22×C3—271no—
143C22×C3—271no—
144C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
145C2×D3—91no—
146C2×D3—93no—
147C2×D3—93no—
148C2×D3—91no—
149A4—91no—
150A4—181no—
151C32—31no—
152C32—121no—
153C32—241no—
154C32—361no—
155C32C3×D3×A411yescharacteristic
156C9—21no—
157C9—61no—
158C9—121no—
159C9—121no—
160C9—241no—
161C9—241no—
162C9(C3⋊D3)⋊A411yescharacteristic
163C23—91noSylow
164C2×C3—31no—
165C2×C3—91no—
166C2×C3—93no—
167C2×C3—91no—
168C2×C3—271no—
169C2×C3—1081no—
170D3—31no—
171D3—91no—
172D3—91no—
173D3—93no—
174C22—271no—
175C22—271no—
176C22#6913⋊C211yescharacteristic, complemented
177C3—31no—
178C3—91no—
179C3—361no—
180C3—721no—
181C3C3×(C3⋊D3)⋊A411yescharacteristic
182C2—31no—
183C2—91no—
184C2—271no—
subgroupG/H
centerC3C3×(C3⋊D3)⋊A4
commutator, cosocle, hypocenterC22×H(3,𝔽3)C2×C32
FrattiniC32C3×D3×A4
FittingC22×#737C2×C3
socleC22×C3C3×(C3⋊D3)⋊C3
hypercenterC9(C3⋊D3)⋊A4
LCSG ▷ C22×H(3,𝔽3)
UCSC1 ◁ C3 ◁ C9

Complements

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

NH ≅ G/Ntype
1. #11757861C2semidirect
2. C22×#4208C3semidirect
4. #10619773C3semidirect
5. #10619772C3semidirect
6. #10619771C3semidirect
8. C22×#737C2×C3semidirect
12. C3×C9⋊A4D3semidirect
17. #66362C2×C3semidirect
18. #66361C2×C3semidirect
29. #4208A4semidirect
57. #737C2×A4semidirect
176. C22#6913⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117578612
C22×#42083
D3×C9⋊A43
#106197733
#106197723
#106197713
#6913⋊C24