Finite Group Databasebeta

← C22×C3×#95⋊C3 #11919388

Subgroups — C22×C3×#95⋊C3 #11919388

Order 1152.

824 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×C3×#95⋊C3C213yesmaximal, direct product factor
2C22×C3×#95C311yesmaximal, characteristic, complemented
3C22×#95⋊C3C313yesmaximal, direct product factor
4C23×C3×A4—41nomaximal
5C3×#95⋊C3C2211yescharacteristic, direct product factor
6C24×C3×C4—31no—
7C2×C3×#95—33no—
8C2×C3×#95C2×C313yescomplemented
9C2×#95⋊C3C2×C319yesdirect product factor
10C22×C3×A4—44no—
11C22×C3×A4—43no—
12C22×#95C3211yescharacteristic, complemented, Sylow
13C25×C3A411yescharacteristic
14C23×A4—43no—
15C23×C3×C4—36no—
16C23×C3×C4—32no—
17C23×C3×C4—33no—
18C23×C3×C4—33no—
19C23×C3×C4—68no—
20C3×#95—33no—
21C3×#95—32no—
22C3×#95C22×C311yescharacteristic, complemented
23#95⋊C3C22×C313yesdirect product factor
24C23×C32—161no—
25C2×C3×A4—46no—
26C2×C3×A4—41no—
27C24×C4—31no—
28C2×#95—33no—
29C2×#95C2×C3213yescomplemented
30C24×C3—33no—
31C24×C3—34no—
32C24×C3—31no—
33C24×C3SL(2,𝔽3)14yes—
34C24×C3C2×A413yes—
35C22×A4—412no—
36C22×A4—49no—
37C22×C3×C4—36no—
38C22×C3×C4—36no—
39C22×C3×C4—36no—
40C22×C3×C4—36no—
41C22×C3×C4—31no—
42C22×C3×C4—33no—
43C22×C3×C4—612no—
44C22×C3×C4—612no—
45C22×C3×C4—624no—
46C22×C3×C4—68no—
47C22×C32—164no—
48C22×C32—163no—
49C3×A4—41no—
50C25C3×A411yescharacteristic
51C23×C4—36no—
52C23×C4—32no—
53C23×C4—33no—
54C23×C4—33no—
55C23×C4—68no—
56#95—33no—
57#95—32no—
58#95C22×C3211yescharacteristic, complemented
59C23×C3—33no—
60C23×C3—36no—
61C23×C3—312no—
62C23×C3—312no—
63C23×C3—32no—
64C23×C3—34no—
65C23×C3—34no—
66C23×C3—33no—
67C23×C3—33no—
68C23×C3—163no—
69C23×C3C42⋊C311yescharacteristic
70C23×C3C2×SL(2,𝔽3)16yes—
71C23×C3C22×A411yescharacteristic
72C2×A4—43no—
73C2×A4—418no—
74C2×C3×C4—32no—
75C2×C3×C4—36no—
76C2×C3×C4—62no—
77C2×C3×C4—66no—
78C2×C3×C4—612no—
79C2×C3×C4—612no—
80C2×C3×C4—612no—
81C2×C3×C4—612no—
82C2×C32—166no—
83C2×C32—161no—
84C24—33no—
85C24—34no—
86C24—31no—
87C24C3×SL(2,𝔽3)14yes—
88C24C2×C3×A413yes—
89C22×C4—36no—
90C22×C4—36no—
91C22×C4—36no—
92C22×C4—36no—
93C22×C4—31no—
94C22×C4—33no—
95C22×C4—612no—
96C22×C4—612no—
97C22×C4—624no—
98C22×C4—68no—
99C22×C3—31no—
100C22×C3—36no—
101C22×C3—36no—
102C22×C3—38no—
103C22×C3—36no—
104C22×C3—312no—
105C22×C3—36no—
106C22×C3—31no—
107C22×C3—33no—
108C22×C3—1612no—
109C22×C3—169no—
110C22×C3#95⋊C314yesdirect product factor
111C22×C3C2×C42⋊C313yes—
112C22×C3C22×SL(2,𝔽3)11yescharacteristic
113A4—43no—
114C3×C4—62no—
115C3×C4—66no—
116C32—161noSylow
117C23—33no—
118C23—36no—
119C23—312no—
120C23—312no—
121C23—32no—
122C23—34no—
123C23—34no—
124C23—33no—
125C23—33no—
126C23C3×C42⋊C311yescharacteristic
127C23C2×C3×SL(2,𝔽3)16yes—
128C23C22×C3×A411yescharacteristic
129C2×C4—32no—
130C2×C4—36no—
131C2×C4—62no—
132C2×C4—66no—
133C2×C4—612no—
134C2×C4—612no—
135C2×C4—612no—
136C2×C4—612no—
137C2×C3—31no—
138C2×C3—36no—
139C2×C3—31no—
140C2×C3—163no—
141C2×C3—1618no—
142C2×C3C2×#95⋊C316yesdirect product factor
143C2×C3C22×C42⋊C311yescharacteristic
144C22—31no—
145C22—36no—
146C22—36no—
147C22—38no—
148C22—31no—
149C22—33no—
150C22—36no—
151C22—36no—
152C22—312no—
153C22C3×#95⋊C314yesdirect product factor
154C22C2×C3×C42⋊C313yes—
155C22C22×C3×SL(2,𝔽3)11yescharacteristic
156C4—62no—
157C4—66no—
158C3—163no—
159C3C22×#95⋊C311yescharacteristic, direct product factor
160C2—31no—
161C2—31no—
162C2—36no—
163C2C2×C3×#95⋊C316yesdirect product factor
164C2C22×C3×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC23×C3C42⋊C3
commutator, cosocle, hypocenter#95C22×C32
FrattiniC23C22×C3×A4
FittingC22×C3×#95C3
socleC25×C3A4
LCSG ▷ #95
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#95⋊C3C2direct (N × H)
2. C22×C3×#95C3semidirect
3. C22×#95⋊C3C3direct (N × H)
5. C3×#95⋊C3C22direct (N × H)
8. C2×C3×#95C2×C3semidirect
9. C2×#95⋊C3C2×C3direct (N × H)
12. C22×#95C32semidirect
22. C3×#95C22×C3semidirect
23. #95⋊C3C22×C3direct (N × H)
29. C2×#95C2×C32semidirect
58. #95C22×C32semidirect
110. C22×C3#95⋊C3direct (N × H)
142. C2×C3C2×#95⋊C3direct (N × H)
153. C22C3×#95⋊C3direct (N × H)
159. C3C22×#95⋊C3direct (N × H)
163. C2C2×C3×#95⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#95⋊C32
C22×C3×#953
C22×#95⋊C33
C23×C3×A44