Finite Group Databasebeta

← #14516161

Subgroups — #14516161

Order 1944.

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

normal subgroups only

This group has 288 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×#6859C211yesmaximal, characteristic, complemented
2C2×#92201C211yesmaximal, characteristic, complemented
3#11757324C211yesmaximal, characteristic, complemented
4#10619977—31nomaximal
5#10619630—31nomaximal
6#10619630—32nomaximal
7C2×#6859—21no—
8C2×#6859C2211yescharacteristic
9#92201—21no—
10C22×C3×H(3,𝔽3)D311yescharacteristic
11C2×C3⋊((C3⋊D3)⋊C3)—31no—
12C3⋊((C3⋊Dic3)⋊C3)—31no—
13C22×C32⋊C9D311yescharacteristic, complemented
14C22×C32⋊C9D312yescomplemented
15C2×#4169—31no—
16C2×#4169—32no—
17#66316—31no—
18#66316—32no—
19#6859D411yescharacteristic, complemented, Sylow
20#6312—31no—
21C3×#638—91no—
22#6233—31no—
23#6233—32no—
24#638⋊C3—93no—
25C2×C3×H(3,𝔽3)—21no—
26C2×C3×H(3,𝔽3)C2×D311yescharacteristic
27C3⋊((C3⋊D3)⋊C3)—61no—
28C2×C32⋊C9—21no—
29C2×C32⋊C9—22no—
30C2×C32⋊C9C2×D311yescharacteristic
31C2×C32⋊C9C2×D312yes—
32#4169—61no—
33#4169—62no—
34C22×C33—31no—
35C22×C33C3⋊D311yescharacteristic
36C2×C3⋊(C3⋊D3)—31no—
37C2×C3×C3⋊D3—91no—
38C3⋊(C3⋊Dic3)—31no—
39C3×C3⋊Dic3—91no—
40C22×H(3,𝔽3)—33no—
41C22×C3×C9—31no—
42C22×C3×C9—32no—
43C2×C3⋊D9—31no—
44C2×C3⋊D9—32no—
45C2×(C3⋊D3)⋊C3—93no—
46C3⋊Dic9—31no—
47C3⋊Dic9—32no—
48(C3⋊Dic3)⋊C3—93no—
49C3×H(3,𝔽3)#6711yescharacteristic
50C32⋊C9#6711yescharacteristic, complemented
51C32⋊C9#6712yescomplemented
52#638—91no—
53#638—93no—
54#638—272no—
55#638—271no—
56C3×#67—271no—
57C3×#67—272no—
58C3×#67—271no—
59#611—271no—
60#611—272no—
61C2×C33—21no—
62C2×C33—31no—
63C2×C33—61no—
64C2×C33C2×C3⋊D311yescharacteristic
65C3⋊(C3⋊D3)—61no—
66C3×C3⋊D3—181no—
67C2×H(3,𝔽3)—33no—
68C2×H(3,𝔽3)—63no—
69C2×C3×C9—31no—
70C2×C3×C9—32no—
71C2×C3×C9—61no—
72C2×C3×C9—62no—
73C3⋊D9—61no—
74C3⋊D9—62no—
75(C3⋊D3)⋊C3—183no—
76C22×C32—31no—
77C22×C32—33no—
78C22×C32—32no—
79C22×C32—31no—
80C22×C32—92no—
81C22×C32—91no—
82C22×C32#27211yescharacteristic
83C2×C3⋊D3—91no—
84C2×C3⋊D3—93no—
85C2×C3⋊D3—272no—
86C2×C3⋊D3—271no—
87C2×C3×D3—271no—
88C2×C3×D3—272no—
89C2×C3×D3—271no—
90C3⋊Dic3—91no—
91C3⋊Dic3—93no—
92C3⋊Dic3—272no—
93C3⋊Dic3—271no—
94C3×Dic3—271no—
95C3×Dic3—272no—
96C3×Dic3—271no—
97C22×C9—91no—
98C22×C9—92no—
99C2×D9—271no—
100C2×D9—272no—
101Dic9—271no—
102Dic9—272no—
103C33—31no—
104C33#63811yescharacteristic
105H(3,𝔽3)—33no—
106C3×C9—31no—
107C3×C9—32no—
108C3×D4—811no—
109#67—271no—
110#67—272no—
111#67—271no—
112#67—813no—
113C2×C32—21no—
114C2×C32—31no—
115C2×C32—33no—
116C2×C32—32no—
117C2×C32—31no—
118C2×C32—61no—
119C2×C32—63no—
120C2×C32—62no—
121C2×C32—61no—
122C2×C32—92no—
123C2×C32—91no—
124C2×C32—182no—
125C2×C32—181no—
126C2×C32C2×#27211yescharacteristic
127C3⋊D3—181no—
128C3⋊D3—183no—
129C3⋊D3—542no—
130C3⋊D3—541no—
131C3×D3—541no—
132C3×D3—542no—
133C3×D3—541no—
134C2×C9—91no—
135C2×C9—92no—
136C2×C9—181no—
137C2×C9—182no—
138D9—541no—
139D9—542no—
140C22×C3—93no—
141C22×C3—91no—
142C22×C3—811no—
143C22×C3#418311yescharacteristic
144C22×C3#418412yes—
145C22×C3#418511yescharacteristic
146C2×D3—271no—
147C2×D3—272no—
148C2×D3—271no—
149C2×D3—813no—
150C3×C4—811no—
151Dic3—271no—
152Dic3—272no—
153Dic3—271no—
154Dic3—813no—
155C32—31no—
156C32—33no—
157C32—32no—
158C32—31no—
159C32—92no—
160C32—91no—
161C32#623511yescharacteristic
162C9—91no—
163C9—92no—
164D4—811noSylow
165C2×C3—21no—
166C2×C3—22no—
167C2×C3—21no—
168C2×C3—93no—
169C2×C3—91no—
170C2×C3—181no—
171C2×C3—183no—
172C2×C3—1621no—
173C2×C3C2×#418311yescharacteristic
174C2×C3C2×#418412yes—
175C2×C3C2×#418511yescharacteristic
176D3—541no—
177D3—542no—
178D3—541no—
179D3—1623no—
180C22—811no—
181C22#9220111yescharacteristic, complemented
182C4—811no—
183C3—93no—
184C3—91no—
185C3#1061967911yescharacteristic
186C3#1061968112yes—
187C3#1061968311yescharacteristic
188C2—21no—
189C2—1621no—
190C2C2×#9220111yescharacteristic
subgroupG/H
centerC2C2×#92201
commutator, cosocleC2×#6859C22
FrattiniC2×C33C2×C3⋊D3
FittingC22×#6859C2
socleC2×C32C2×#272
hypercenterC22#92201
hypocenter#6859D4
LCSG ▷ C2×#6859 ▷ #6859
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6859C2semidirect
2. C2×#92201C2semidirect
3. #11757324C2semidirect
13. C22×C32⋊C9D3semidirect
14. C22×C32⋊C9D3semidirect
19. #6859D4semidirect
50. C32⋊C9#67semidirect
51. C32⋊C9#67semidirect
181. C22#92201semidirect

Maximal subgroups

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

subgroupindex
C22×#68592
C2×#922012
#117573242
#106199773
#106196303