Finite Group Databasebeta

← #14516157

Subgroups — #14516157

Order 1944.

368 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 39 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
1C22×#6857C211yesmaximal, characteristic, complemented
2C2×#92199C211yesmaximal, characteristic, complemented
3#11757322C211yesmaximal, characteristic, complemented
4#10619980—32nomaximal
5#10619977—31nomaximal
6#10619630—31nomaximal
7C2×#6857—21no—
8C2×#6857C2211yescharacteristic
9#92199—21no—
10C22×C3×3−1+2D312yescomplemented
11C22×C3×H(3,𝔽3)D311yescharacteristic
12C2×C3⋊AGL(1,ℤ/9)—32no—
13C2×C3⋊((C3⋊D3)⋊C3)—31no—
14C3⋊(3−1+2⋊C4)—32no—
15C3⋊((C3⋊Dic3)⋊C3)—31no—
16C22×C32⋊C9D311yescharacteristic, complemented
17C2×#4169—31no—
18#66316—31no—
19#6857D411yescharacteristic, complemented, Sylow
20#6312—31no—
21C3×#638—91no—
22#6233—32no—
23#6233—31no—
24#611⋊C3—96no—
25#638⋊C3—93no—
26C2×C3×3−1+2—22no—
27C2×C3×3−1+2C2×D312yes—
28C2×C3×H(3,𝔽3)—21no—
29C2×C3×H(3,𝔽3)C2×D311yescharacteristic
30C3⋊AGL(1,ℤ/9)—62no—
31C3⋊((C3⋊D3)⋊C3)—61no—
32C2×C32⋊C9—21no—
33C2×C32⋊C9C2×D311yescharacteristic
34#4169—61no—
35C22×C33—31no—
36C22×C33C3⋊D311yescharacteristic
37C2×C3⋊(C3⋊D3)—31no—
38C2×C3×C3⋊D3—91no—
39C3⋊(C3⋊Dic3)—31no—
40C3×C3⋊Dic3—91no—
41C22×3−1+2—36no—
42C22×H(3,𝔽3)—33no—
43C22×C3×C9—32no—
44C22×C3×C9—31no—
45C2×C3⋊D9—32no—
46C2×C3⋊D9—31no—
47C2×AGL(1,ℤ/9)—96no—
48C2×(C3⋊D3)⋊C3—93no—
49C3⋊Dic9—32no—
50C3⋊Dic9—31no—
513−1+2⋊C4—96no—
52(C3⋊Dic3)⋊C3—93no—
53C3×3−1+2#6712yescomplemented
54C3×H(3,𝔽3)#6711yescharacteristic
55C32⋊C9#6711yescharacteristic, complemented
56#638—91no—
57#638—93no—
58#638—272no—
59#638—271no—
60C3×#67—271no—
61C3×#67—272no—
62C3×#67—271no—
63#611—96no—
64#611—271no—
65C2×C33—21no—
66C2×C33—31no—
67C2×C33—61no—
68C2×C33C2×C3⋊D311yescharacteristic
69C3⋊(C3⋊D3)—61no—
70C3×C3⋊D3—181no—
71C2×3−1+2—36no—
72C2×3−1+2—66no—
73C2×H(3,𝔽3)—33no—
74C2×H(3,𝔽3)—63no—
75C2×C3×C9—32no—
76C2×C3×C9—31no—
77C2×C3×C9—62no—
78C2×C3×C9—61no—
79C3⋊D9—62no—
80C3⋊D9—61no—
81AGL(1,ℤ/9)—186no—
82(C3⋊D3)⋊C3—183no—
83C22×C32—31no—
84C22×C32—33no—
85C22×C32—32no—
86C22×C32—31no—
87C22×C32—92no—
88C22×C32—91no—
89C22×C32#27211yescharacteristic
90C2×C3⋊D3—91no—
91C2×C3⋊D3—93no—
92C2×C3⋊D3—272no—
93C2×C3⋊D3—271no—
94C2×C3×D3—271no—
95C2×C3×D3—272no—
96C2×C3×D3—271no—
97C3⋊Dic3—91no—
98C3⋊Dic3—93no—
99C3⋊Dic3—272no—
100C3⋊Dic3—271no—
101C3×Dic3—271no—
102C3×Dic3—272no—
103C3×Dic3—271no—
104C22×C9—36no—
105C22×C9—91no—
106C2×D9—96no—
107C2×D9—271no—
108Dic9—96no—
109Dic9—271no—
110C33—31no—
111C33#63811yescharacteristic
1123−1+2—36no—
113H(3,𝔽3)—33no—
114C3×C9—32no—
115C3×C9—31no—
116C3×D4—811no—
117#67—272no—
118#67—271no—
119#67—271no—
120#67—813no—
121C2×C32—21no—
122C2×C32—31no—
123C2×C32—33no—
124C2×C32—32no—
125C2×C32—31no—
126C2×C32—61no—
127C2×C32—63no—
128C2×C32—62no—
129C2×C32—61no—
130C2×C32—92no—
131C2×C32—91no—
132C2×C32—182no—
133C2×C32—181no—
134C2×C32C2×#27211yescharacteristic
135C3⋊D3—181no—
136C3⋊D3—183no—
137C3⋊D3—542no—
138C3⋊D3—541no—
139C3×D3—541no—
140C3×D3—542no—
141C3×D3—541no—
142C2×C9—36no—
143C2×C9—66no—
144C2×C9—91no—
145C2×C9—181no—
146D9—186no—
147D9—541no—
148C22×C3—93no—
149C22×C3—91no—
150C22×C3—811no—
151C22×C3#418312yes—
152C22×C3#418311yescharacteristic
153C22×C3#418411yescharacteristic
154C2×D3—272no—
155C2×D3—271no—
156C2×D3—271no—
157C2×D3—813no—
158C3×C4—811no—
159Dic3—272no—
160Dic3—271no—
161Dic3—271no—
162Dic3—813no—
163C32—31no—
164C32—32no—
165C32—33no—
166C32—31no—
167C32—92no—
168C32—91no—
169C32#623511yescharacteristic
170C9—36no—
171C9—91no—
172D4—811noSylow
173C2×C3—22no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—93no—
177C2×C3—91no—
178C2×C3—181no—
179C2×C3—183no—
180C2×C3—1621no—
181C2×C3C2×#418312yes—
182C2×C3C2×#418311yescharacteristic
183C2×C3C2×#418411yescharacteristic
184D3—542no—
185D3—541no—
186D3—541no—
187D3—1623no—
188C22—811no—
189C22#9219911yescharacteristic, complemented
190C4—811no—
191C3—93no—
192C3—91no—
193C3#1061967912yes—
194C3#1061967911yescharacteristic
195C3#1061968111yescharacteristic
196C2—21no—
197C2—1621no—
198C2C2×#9219911yescharacteristic
subgroupG/H
centerC2C2×#92199
commutator, cosocleC2×#6857C22
FrattiniC2×C33C2×C3⋊D3
FittingC22×#6857C2
socleC2×C32C2×#272
hypercenterC22#92199
hypocenter#6857D4
LCSG ▷ C2×#6857 ▷ #6857
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6857C2semidirect
2. C2×#92199C2semidirect
3. #11757322C2semidirect
10. C22×C3×3−1+2D3semidirect
16. C22×C32⋊C9D3semidirect
19. #6857D4semidirect
53. C3×3−1+2#67semidirect
55. C32⋊C9#67semidirect
189. C22#92199semidirect

Maximal subgroups

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

subgroupindex
C22×#68572
C2×#921992
#117573222
#106199803
#106199773
#106196303