Finite Group Databasebeta

← #14517023

Subgroups — #14517023

Order 1944.

353 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 353 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C3⋊#66330C211yesmaximal, characteristic
2C3⋊#66321C211yesmaximal, characteristic
3C3×#66322C211yesmaximal, characteristic
4C3⋊#6296—31nomaximal
5#10619881—31nomaximal
6#10619552—33nomaximal
7C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
8C3×C3⋊(C3⋊Dic3)—31no—
9C3×C3⋊(C3⋊Dic3)D311yescharacteristic
10C32×C3⋊Dic3—31no—
11C3⋊#1084D311yescharacteristic
12C3⋊(3−1+2⋊C4)—61no—
13C3⋊((C3⋊Dic3)⋊C3)—31no—
14C3×(C3⋊Dic3)⋊C3—31no—
15#66330—33no—
16#66330—63no—
17#66322D313yes—
18#66321—33no—
19C3×AΣL(1,𝔽27)Q811yescharacteristic, complemented, Sylow
20#6296—91no—
21#6296—93no—
22#6293—91no—
23#6293—91no—
24#6293—91no—
25#6196—93no—
26C2×C34C2×D311yescharacteristic
27C2×C3×3−1+2—21no—
28C2×C3×H(3,𝔽3)C2×D311yescharacteristic
29C2×AΣL(1,𝔽27)—23no—
30C2×AΣL(1,𝔽27)C2×D313yes—
31C3⋊(C3⋊Dic3)—31no—
32C3⋊(C3⋊Dic3)—31no—
33C3⋊(C3⋊Dic3)C3⋊D311yescharacteristic
34C3×C3⋊Dic3—33no—
35C3×C3⋊Dic3—31no—
36C3×C3⋊Dic3—31no—
37C3×C3⋊Dic3—91no—
38C3×C3⋊Dic3—91no—
39C3×C3⋊Dic3—93no—
40C3×C3⋊Dic3—93no—
41C3×C3⋊Dic3—91no—
42C3×C3⋊Dic3—91no—
43C3×C3⋊Dic3—181no—
44C3×C3⋊Dic3—183no—
45C32×Dic3—91no—
46C32×Dic3—91no—
47C32×Dic3—91no—
48C32×Dic3—181no—
49#1084—33no—
50#1084—181no—
51C3⋊Dic9—61no—
523−1+2⋊C4—183no—
53(C3⋊Dic3)⋊C3—33no—
54(C3⋊Dic3)⋊C3—93no—
55C34Dic611yescharacteristic, complemented
56C3×3−1+2—21no—
57C3×H(3,𝔽3)Dic611yescharacteristic, complemented
58AΣL(1,𝔽27)—23no—
59AΣL(1,𝔽27)Dic613yescomplemented
60#634—271no—
61#634—271no—
62#627—271no—
63#627—271no—
64#627—273no—
65#627—273no—
66#627—273no—
67#627—271no—
68C2×C33—21no—
69C2×C33—31no—
70C2×C33—33no—
71C2×C33—31no—
72C2×C33—61no—
73C2×C33—63no—
74C2×C33D3211yescharacteristic
75C2×C33C2×C3⋊D311yescharacteristic
76C2×3−1+2—23no—
77C2×3−1+2—121no—
78C2×H(3,𝔽3)—61no—
79C2×H(3,𝔽3)D3213yes—
80C2×C3×C9—61no—
81C32×C4—271no—
82C32×C4—271no—
83C3⋊Dic3—31no—
84C3⋊Dic3—31no—
85C3⋊Dic3—91no—
86C3⋊Dic3—91no—
87C3⋊Dic3—91no—
88C3⋊Dic3—93no—
89C3⋊Dic3—93no—
90C3⋊Dic3—91no—
91C3⋊Dic3—93no—
92C3⋊Dic3—183no—
93C3⋊Dic3—181no—
94C3⋊Dic3—271no—
95C3⋊Dic3—541no—
96C3×Dic3—93no—
97C3×Dic3—93no—
98C3×Dic3—93no—
99C3×Dic3—91no—
100C3×Dic3—91no—
101C3×Dic3—91no—
102C3×Dic3—181no—
103C3×Dic3—183no—
104C3×Dic3—273no—
105C3×Dic3—271no—
106C3×Dic3—273no—
107C3×Dic3—271no—
108C3×Dic3—273no—
109C3×Dic3—271no—
110C3×Dic3—541no—
111C3×Dic3—543no—
112Dic9—183no—
113C33—21no—
114C33—31no—
115C33—33no—
116C33—31no—
117C33—61no—
118C33—63no—
119C33#62711yescharacteristic
120C33#63411yescharacteristic, complemented
1213−1+2—23no—
1223−1+2—121no—
123H(3,𝔽3)—61no—
124H(3,𝔽3)#62713yescomplemented
125C3×C9—61no—
126Dic6—811no—
127Dic6—811no—
128Dic6—811no—
129Dic6—813no—
130Dic6—813no—
131C2×C32—21no—
132C2×C32—31no—
133C2×C32—33no—
134C2×C32—31no—
135C2×C32—33no—
136C2×C32—33no—
137C2×C32—63no—
138C2×C32—61no—
139C2×C32—63no—
140C2×C32—63no—
141C2×C32—61no—
142C2×C32—91no—
143C2×C32—123no—
144C2×C32—181no—
145C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
146C2×C32D3×C3⋊D311yescharacteristic
147C2×C9—63no—
148C3×C4—273no—
149C3×C4—273no—
150C3×C4—271no—
151C3×C4—271no—
152C3×C4—811no—
153Dic3—91no—
154Dic3—91no—
155Dic3—91no—
156Dic3—181no—
157Dic3—271no—
158Dic3—273no—
159Dic3—273no—
160Dic3—273no—
161Dic3—271no—
162Dic3—271no—
163Dic3—541no—
164Dic3—543no—
165Dic3—813no—
166C32—21no—
167C32—33no—
168C32—31no—
169C32—33no—
170C32—31no—
171C32—33no—
172C32—61no—
173C32—63no—
174C32—63no—
175C32—63no—
176C32—61no—
177C32—91no—
178C32—123no—
179C32—181no—
180C32#619611yescharacteristic
181C32#629311yescharacteristic
182C9—63no—
183Q8—2431noSylow
184C2×C3—21no—
185C2×C3—31no—
186C2×C3—33no—
187C2×C3—61no—
188C2×C3—63no—
189C2×C3—93no—
190C2×C3#4174⋊C211yescharacteristic
191C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
192C4—271no—
193C4—271no—
194C4—811no—
195C3—21no—
196C3—31no—
197C3—33no—
198C3—61no—
199C3—63no—
200C3—93no—
201C3#1061955211yescharacteristic, complemented
202C3#1061988111yescharacteristic
203C2#4175⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2#4175⋊D3
commutator, Fitting, prime radical, cosocleC2×C3×AΣL(1,𝔽27)C22
FrattiniC2×C32D3×C3⋊D3
socleC2×C32((C3⋊D3)⋊C3)⋊C2
hypocenterC3×AΣL(1,𝔽27)Q8
LCSG ▷ C2×C3×AΣL(1,𝔽27) ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
19. C3×AΣL(1,𝔽27)Q8semidirect
55. C34Dic6semidirect
57. C3×H(3,𝔽3)Dic6semidirect
59. AΣL(1,𝔽27)Dic6semidirect
120. C33#634semidirect
124. H(3,𝔽3)#627semidirect
201. C3#10619552semidirect

Maximal subgroups

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

subgroupindex
C3⋊#663302
C3⋊#663212
C3×#663222
C3⋊#62963
#106198813
#106195523