Finite Group Databasebeta

← #72277508

Subgroups — #72277508

Order 2916.

253 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 253 conjugacy classes of subgroups — too many to draw. Only its 27 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#13091301C211yesmaximal, characteristic, complemented
2#13091300C211yesmaximal, characteristic, complemented
3#13091299C211yesmaximal, characteristic, complemented
4#92294⋊C2—31nomaximal
5#4179⋊D3—31nomaximal
6#92191⋊C2—33nomaximal
7#10624839C2211yescharacteristic, complemented, Sylow
8C3⋊#4185D311yescharacteristic, complemented
9C3⋊#4178—31no—
10C3⋊#4178—61no—
11#92296D311yescharacteristic, complemented
12#92295—31no—
13#92294—31no—
14C3×#4179—31no—
15#92216—33no—
16#92216—63no—
17#92192D313yescomplemented
18#92191—33no—
19#66431—91no—
20((C3⋊D3)⋊C3)⋊D3—91no—
21#4178⋊C2—93no—
22((C3⋊D3)⋊C9)⋊C2—91no—
23D92—91no—
24C3×#732—21no—
25C3×#732C2×D311yescharacteristic
26#6887C2×D311yescharacteristic, complemented
27#6879—23no—
28#6879C2×D313yescomplemented
29C3⋊#272—31no—
30C3⋊#272—61no—
31C3⋊((C3⋊D3)⋊C3)—91no—
32C9×C3⋊D3—91no—
33C3×C3⋊D9—31no—
34C3×C3⋊D9—31no—
35C3×(C3⋊D3)⋊C3—91no—
36#4185—33no—
37#4185—181no—
38#4181—31no—
39C9⋊D9C3⋊D311yescharacteristic, complemented
40#4179—33no—
41#4178—93no—
42#4178—183no—
43D9⋊C9—181no—
44#4169—91no—
45(C3⋊D3)⋊C9—91no—
46C9×D9—91no—
47C9×D9—91no—
48C9×D9—181no—
49#1113—271no—
50D3×C3⋊D3—271no—
51((C3⋊D3)⋊C3)⋊C2—273no—
52D3×D9—271no—
53D3×D9—271no—
54D3×D9—271no—
55C3×H(3,𝔽3)—31no—
56C3×H(3,𝔽3)—61no—
57C32×C9D3211yescharacteristic
58#732—23no—
59#732—61no—
60#732—121no—
61#732D3213yes—
62C9⋊C9—61no—
63C32⋊C9—31no—
64C92—21no—
65C92C2×C3⋊D311yescharacteristic, complemented
66C3⋊(C3⋊D3)—91no—
67C3×C3⋊D3—91no—
68C3×C3⋊D3—91no—
69C3×C3⋊D3—91no—
70C3×C3⋊D3—271no—
71C3×C3⋊D3—541no—
72C32×D3—271no—
73#272—93no—
74#272—183no—
75#272—541no—
76#272—541no—
77#272—541no—
78C3⋊D9—31no—
79C3⋊D9—31no—
80C3⋊D9—91no—
81(C3⋊D3)⋊C3—93no—
82(C3⋊D3)⋊C3—273no—
83D3×C9—271no—
84D3×C9—271no—
85D3×C9—271no—
86D3×C9—541no—
87C3×D9—91no—
88C3×D9—91no—
89C3×D9—181no—
90C3×D9—181no—
91C3×D9—271no—
92C2×C3⋊D3—811no—
93D32—811no—
94D32—811no—
95D32—813no—
96D32—811no—
97C2×D9—811no—
98C2×D9—811no—
99C33—91no—
100C33—181no—
101C33((C3⋊D3)⋊C3)⋊C211yescharacteristic
102H(3,𝔽3)—33no—
103H(3,𝔽3)—63no—
104H(3,𝔽3)—181no—
105H(3,𝔽3)—181no—
106H(3,𝔽3)—181no—
107C3×C9—21no—
108C3×C9—31no—
109C3×C9—31no—
110C3×C9—61no—
111C3×C9—61no—
112C3×C9D3×C3⋊D311yescharacteristic
113C2×C32—811no—
114C3⋊D3—91no—
115C3⋊D3—91no—
116C3⋊D3—91no—
117C3⋊D3—271no—
118C3⋊D3—273no—
119C3⋊D3—541no—
120C3⋊D3—811no—
121C3⋊D3—1621no—
122C3×D3—273no—
123C3×D3—271no—
124C3×D3—271no—
125C3×D3—271no—
126C3×D3—271no—
127C3×D3—541no—
128C3×D3—813no—
129C3×D3—811no—
130C3×D3—811no—
131C3×D3—1623no—
132C2×C9—811no—
133C2×C9—811no—
134D9—91no—
135D9—91no—
136D9—181no—
137D9—181no—
138D9—271no—
139D9—811no—
140C2×D3—2431no—
141C2×D3—2431no—
142C2×D3—2431no—
143C2×D3—2433no—
144C32—21no—
145C32—91no—
146C32—93no—
147C32—183no—
148C32—271no—
149C32—541no—
150C32—541no—
151C32—1081no—
152C32#4178⋊C211yescharacteristic
153C32((C3⋊D3)⋊C3)⋊D311yescharacteristic
154C9—31no—
155C9—61no—
156C9—91no—
157C9—181no—
158C2×C3—811no—
159C2×C3—811no—
160C2×C3—813no—
161C2×C3—811no—
162D3—271no—
163D3—271no—
164D3—271no—
165D3—271no—
166D3—541no—
167D3—811no—
168D3—811no—
169D3—813no—
170D3—1623no—
171D3—2433no—
172C22—7291noSylow
173C3—31no—
174C3—31no—
175C3—61no—
176C3—273no—
177C3—543no—
178C3#4179⋊D311yescharacteristic
179C2—811no—
180C2—811no—
181C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenter#10624839C22
FrattiniC3×C9D3×C3⋊D3
socleC3#4179⋊D3
LCSG ▷ #10624839
UCSC1

Complements

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

NH ≅ G/Ntype
1. #13091301C2semidirect
2. #13091300C2semidirect
3. #13091299C2semidirect
7. #10624839C22semidirect
8. C3⋊#4185D3semidirect
11. #92296D3semidirect
17. #92192D3semidirect
26. #6887C2×D3semidirect
28. #6879C2×D3semidirect
39. C9⋊D9C3⋊D3semidirect
65. C92C2×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
#130913012
#130913002
#130912992
#92294⋊C23
#4179⋊D33
#92191⋊C23