Finite Group Databasebeta

← #14517760

Subgroups — #14517760

Order 1944.

843 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 843 conjugacy classes of subgroups — too many to draw. Only its 105 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×C3×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
2C2×C3⋊#4183C211yesmaximal, characteristic, complemented
3C3⋊#66330C211yesmaximal, characteristic, complemented
4C3×#6312—31nomaximal
5#10619980—32nomaximal
6#10619977—31nomaximal
7#10619679—39nomaximal
8C2×C3×AΣL(1,𝔽27)—21no—
9C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
10C3⋊#4183—21no—
11C22×C34D311yescharacteristic, complemented
12C2×C3×C3⋊(C3⋊D3)—31no—
13C3×C3⋊(C3⋊Dic3)—31no—
14C22×C3×3−1+2D312yescomplemented
15C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
16C2×C3⋊AGL(1,ℤ/9)—32no—
17C2×C3⋊((C3⋊D3)⋊C3)—31no—
18C3⋊(3−1+2⋊C4)—32no—
19C3⋊((C3⋊Dic3)⋊C3)—31no—
20C22×AΣL(1,𝔽27)D319yescomplemented
21C2×#4183—39no—
22#66330—39no—
23C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
24#6312—31no—
25#6312—31no—
26C3×#638—99no—
27C3×#638—91no—
28C3×#638—93no—
29#6233—32no—
30#611⋊C3—96no—
31#638⋊C3—93no—
32C2×C34—21no—
33C2×C34C2×D311yescharacteristic
34C3×C3⋊(C3⋊D3)—61no—
35C2×C3×3−1+2—22no—
36C2×C3×3−1+2C2×D312yes—
37C2×C3×H(3,𝔽3)—21no—
38C2×C3×H(3,𝔽3)C2×D311yescharacteristic
39C3⋊AGL(1,ℤ/9)—62no—
40C3⋊((C3⋊D3)⋊C3)—61no—
41C2×AΣL(1,𝔽27)—29no—
42C2×AΣL(1,𝔽27)C2×D319yes—
43#4183—69no—
44C22×C33—31no—
45C22×C33—39no—
46C22×C33—31no—
47C22×C33—61no—
48C22×C33C3⋊D311yescharacteristic
49C22×C33C3⋊D313yescomplemented
50C2×C3⋊(C3⋊D3)—31no—
51C2×C3⋊(C3⋊D3)—31no—
52C2×C3×C3⋊D3—99no—
53C2×C3×C3⋊D3—93no—
54C2×C3×C3⋊D3—91no—
55C3⋊(C3⋊Dic3)—31no—
56C3⋊(C3⋊Dic3)—31no—
57C3×C3⋊Dic3—99no—
58C3×C3⋊Dic3—93no—
59C3×C3⋊Dic3—91no—
60C22×3−1+2—62no—
61C22×3−1+2C3⋊D316yescomplemented
62C22×H(3,𝔽3)—61no—
63C22×H(3,𝔽3)C3⋊D313yescomplemented
64C22×C3×C9—32no—
65C2×C3⋊D9—32no—
66C2×AGL(1,ℤ/9)—96no—
67C2×(C3⋊D3)⋊C3—93no—
68C3⋊Dic9—32no—
693−1+2⋊C4—96no—
70(C3⋊Dic3)⋊C3—93no—
71C34#6711yescharacteristic, complemented
72C3×3−1+2#6712yescomplemented
73C3×H(3,𝔽3)#6711yescharacteristic, complemented
74AΣL(1,𝔽27)#6719yescomplemented
75#638—99no—
76#638—93no—
77#638—91no—
78#638—93no—
79#638—273no—
80C3×#67—279no—
81C3×#67—273no—
82C3×#67—271no—
83#611—96no—
84C2×C33—21no—
85C2×C33—23no—
86C2×C33—31no—
87C2×C33—39no—
88C2×C33—31no—
89C2×C33—61no—
90C2×C33—61no—
91C2×C33—62no—
92C2×C33—61no—
93C2×C33—69no—
94C2×C33C2×C3⋊D311yescharacteristic
95C2×C33C2×C3⋊D313yes—
96C3⋊(C3⋊D3)—61no—
97C3⋊(C3⋊D3)—61no—
98C3×C3⋊D3—189no—
99C3×C3⋊D3—181no—
100C3×C3⋊D3—183no—
101C2×3−1+2—26no—
102C2×3−1+2—62no—
103C2×3−1+2—64no—
104C2×3−1+2C2×C3⋊D316yes—
105C2×H(3,𝔽3)—23no—
106C2×H(3,𝔽3)—61no—
107C2×H(3,𝔽3)—62no—
108C2×H(3,𝔽3)C2×C3⋊D313yes—
109C2×C3×C9—32no—
110C2×C3×C9—62no—
111C3⋊D9—62no—
112AGL(1,ℤ/9)—186no—
113(C3⋊D3)⋊C3—183no—
114C22×C32—21no—
115C22×C32—39no—
116C22×C32—33no—
117C22×C32—39no—
118C22×C32—33no—
119C22×C32—33no—
120C22×C32—69no—
121C22×C32—93no—
122C22×C32#27211yescharacteristic
123C22×C32C3⋊(C3⋊D3)11yescharacteristic
124C2×C3⋊D3—99no—
125C2×C3⋊D3—93no—
126C2×C3⋊D3—91no—
127C2×C3⋊D3—93no—
128C2×C3⋊D3—273no—
129C2×C3×D3—279no—
130C2×C3×D3—273no—
131C2×C3×D3—271no—
132C3⋊Dic3—99no—
133C3⋊Dic3—93no—
134C3⋊Dic3—91no—
135C3⋊Dic3—93no—
136C3⋊Dic3—273no—
137C3×Dic3—279no—
138C3×Dic3—273no—
139C3×Dic3—271no—
140C22×C9—36no—
141C2×D9—96no—
142Dic9—96no—
143C33—31no—
144C33—39no—
145C33—31no—
146C33—61no—
147C33#63811yescharacteristic
148C33#63813yescomplemented
1493−1+2—62no—
1503−1+2#63816yescomplemented
151H(3,𝔽3)—61no—
152H(3,𝔽3)#63813yescomplemented
153C3×C9—32no—
154C3×D4—811no—
155#67—279no—
156#67—273no—
157#67—271no—
158#67—813no—
159C2×C32—21no—
160C2×C32—22no—
161C2×C32—21no—
162C2×C32—21no—
163C2×C32—39no—
164C2×C32—33no—
165C2×C32—39no—
166C2×C32—33no—
167C2×C32—33no—
168C2×C32—63no—
169C2×C32—63no—
170C2×C32—69no—
171C2×C32—63no—
172C2×C32—69no—
173C2×C32—618no—
174C2×C32—69no—
175C2×C32—93no—
176C2×C32—183no—
177C2×C32C2×#27211yescharacteristic
178C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
179C3⋊D3—189no—
180C3⋊D3—183no—
181C3⋊D3—181no—
182C3⋊D3—183no—
183C3⋊D3—543no—
184C3×D3—549no—
185C3×D3—543no—
186C3×D3—541no—
187C2×C9—36no—
188C2×C9—66no—
189D9—186no—
190C22×C3—39no—
191C22×C3—31no—
192C22×C3—61no—
193C22×C3—93no—
194C22×C3—811no—
195C22×C3#418313yescomplemented
196C22×C3C3⋊#27211yescharacteristic
197C2×D3—279no—
198C2×D3—273no—
199C2×D3—271no—
200C2×D3—813no—
201C3×C4—811no—
202Dic3—279no—
203Dic3—273no—
204Dic3—271no—
205Dic3—813no—
206C32—21no—
207C32—39no—
208C32—39no—
209C32—33no—
210C32—33no—
211C32—33no—
212C32—69no—
213C32—93no—
214C32#623511yescharacteristic
215C32#631211yescharacteristic
216C9—36no—
217D4—811noSylow
218C2×C3—23no—
219C2×C3—21no—
220C2×C3—39no—
221C2×C3—31no—
222C2×C3—61no—
223C2×C3—69no—
224C2×C3—62no—
225C2×C3—61no—
226C2×C3—93no—
227C2×C3—183no—
228C2×C3—1621no—
229C2×C3C2×#418313yes—
230C2×C3C2×C3⋊#27211yescharacteristic
231D3—549no—
232D3—543no—
233D3—541no—
234D3—1623no—
235C22—811no—
236C22C3⋊#418311yescharacteristic, complemented
237C4—811no—
238C3—39no—
239C3—31no—
240C3—61no—
241C3—93no—
242C3#1061967913yescomplemented
243C3#1061999411yescharacteristic
244C2—21no—
245C2—1621no—
246C2C2×C3⋊#418311yescharacteristic
subgroupG/H
centerC2C2×C3⋊#4183
commutator, cosocleC2×C3×AΣL(1,𝔽27)C22
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC22×C3×AΣL(1,𝔽27)C2
socleC2×C32C2×#272
hypercenterC22C3⋊#4183
hypocenterC3×AΣL(1,𝔽27)D4
LCSG ▷ C2×C3×AΣL(1,𝔽27) ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×AΣL(1,𝔽27)C2semidirect
2. C2×C3⋊#4183C2semidirect
3. C3⋊#66330C2semidirect
11. C22×C34D3semidirect
14. C22×C3×3−1+2D3semidirect
15. C22×C3×H(3,𝔽3)D3semidirect
20. C22×AΣL(1,𝔽27)D3semidirect
23. C3×AΣL(1,𝔽27)D4semidirect
49. C22×C33C3⋊D3semidirect
61. C22×3−1+2C3⋊D3semidirect
63. C22×H(3,𝔽3)C3⋊D3semidirect
71. C34#67semidirect
72. C3×3−1+2#67semidirect
73. C3×H(3,𝔽3)#67semidirect
74. AΣL(1,𝔽27)#67semidirect
148. C33#638semidirect
150. 3−1+2#638semidirect
152. H(3,𝔽3)#638semidirect
195. C22×C3#4183semidirect
236. C22C3⋊#4183semidirect
242. C3#10619679semidirect

Maximal subgroups

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

subgroupindex
C22×C3×AΣL(1,𝔽27)2
C2×C3⋊#41832
C3⋊#663302
C3×#63123
#106199803
#106199773
#106196793