Finite Group Databasebeta

← C22×#95⋊C9 #11919389

Subgroups — C22×#95⋊C9 #11919389

Order 1152.

713 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 713 conjugacy classes of subgroups — too many to draw. Only its 79 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×#95⋊C9C213yesmaximal, direct product factor
2C22×C3×#95C311yesmaximal, characteristic
3C23×C22⋊C9—41nomaximal
4#95⋊C9C2211yescharacteristic, direct product factor
5C24×C3×C4—31no—
6C2×C3×#95—33no—
7C2×C3×#95C2×C313yes—
8C22×C22⋊C9—44no—
9C22×C22⋊C9—43no—
10C22×#95C911yescharacteristic, complemented, Sylow
11C25×C3A411yescharacteristic
12C23×C3×C4—36no—
13C23×C3×C4—32no—
14C23×C3×C4—33no—
15C23×C3×C4—33no—
16C23×C3×C4—68no—
17C3×#95—33no—
18C3×#95—32no—
19C3×#95C22×C311yescharacteristic
20C23×C9—161no—
21C2×C22⋊C9—46no—
22C2×C22⋊C9—41no—
23C24×C4—31no—
24C2×#95—33no—
25C2×#95C2×C913yescomplemented
26C24×C3—33no—
27C24×C3—34no—
28C24×C3—31no—
29C24×C3SL(2,𝔽3)14yes—
30C24×C3C2×A413yes—
31C22×C3×C4—36no—
32C22×C3×C4—36no—
33C22×C3×C4—36no—
34C22×C3×C4—36no—
35C22×C3×C4—31no—
36C22×C3×C4—33no—
37C22×C3×C4—612no—
38C22×C3×C4—612no—
39C22×C3×C4—624no—
40C22×C3×C4—68no—
41C22×C9—164no—
42C22×C9—163no—
43C22⋊C9—41no—
44C25C22⋊C911yescharacteristic
45C23×C4—36no—
46C23×C4—32no—
47C23×C4—33no—
48C23×C4—33no—
49C23×C4—68no—
50#95—33no—
51#95—32no—
52#95C22×C911yescharacteristic, complemented
53C23×C3—33no—
54C23×C3—36no—
55C23×C3—312no—
56C23×C3—312no—
57C23×C3—32no—
58C23×C3—34no—
59C23×C3—34no—
60C23×C3—33no—
61C23×C3—33no—
62C23×C3C42⋊C311yescharacteristic
63C23×C3C2×SL(2,𝔽3)16yes—
64C23×C3C22×A411yescharacteristic
65C2×C3×C4—32no—
66C2×C3×C4—36no—
67C2×C3×C4—62no—
68C2×C3×C4—66no—
69C2×C3×C4—612no—
70C2×C3×C4—612no—
71C2×C3×C4—612no—
72C2×C3×C4—612no—
73C2×C9—166no—
74C2×C9—161no—
75C24—33no—
76C24—34no—
77C24—31no—
78C24Q8⋊C914yes—
79C24C2×C22⋊C913yes—
80C22×C4—36no—
81C22×C4—36no—
82C22×C4—36no—
83C22×C4—36no—
84C22×C4—31no—
85C22×C4—33no—
86C22×C4—612no—
87C22×C4—612no—
88C22×C4—624no—
89C22×C4—68no—
90C22×C3—31no—
91C22×C3—36no—
92C22×C3—36no—
93C22×C3—38no—
94C22×C3—36no—
95C22×C3—312no—
96C22×C3—36no—
97C22×C3—31no—
98C22×C3—33no—
99C22×C3#95⋊C314yes—
100C22×C3C2×C42⋊C313yes—
101C22×C3C22×SL(2,𝔽3)11yescharacteristic
102C3×C4—62no—
103C3×C4—66no—
104C9—161noSylow
105C23—33no—
106C23—36no—
107C23—312no—
108C23—312no—
109C23—32no—
110C23—34no—
111C23—34no—
112C23—33no—
113C23—33no—
114C23C42⋊C911yescharacteristic
115C23C2×Q8⋊C916yes—
116C23C22×C22⋊C911yescharacteristic
117C2×C4—32no—
118C2×C4—36no—
119C2×C4—62no—
120C2×C4—66no—
121C2×C4—612no—
122C2×C4—612no—
123C2×C4—612no—
124C2×C4—612no—
125C2×C3—31no—
126C2×C3—36no—
127C2×C3—31no—
128C2×C3C2×#95⋊C316yes—
129C2×C3C22×C42⋊C311yescharacteristic
130C22—31no—
131C22—36no—
132C22—36no—
133C22—38no—
134C22—31no—
135C22—33no—
136C22—36no—
137C22—36no—
138C22—312no—
139C22#95⋊C914yesdirect product factor
140C22C2×C42⋊C913yes—
141C22C22×Q8⋊C911yescharacteristic
142C4—62no—
143C4—66no—
144C3C22×#95⋊C311yescharacteristic
145C2—31no—
146C2—31no—
147C2—36no—
148C2C2×#95⋊C916yesdirect product factor
149C2C22×C42⋊C911yescharacteristic
subgroupG/H
center, hypercenterC23×C3C42⋊C3
commutator, hypocenter#95C22×C9
FrattiniC23×C3C22×A4
FittingC22×C3×#95C3
socle, prime radicalC25×C3A4
cosocleC3×#95C22×C3
LCSG ▷ #95
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C2×#95⋊C9C2direct (N × H)
4. #95⋊C9C22direct (N × H)
10. C22×#95C9semidirect
25. C2×#95C2×C9semidirect
52. #95C22×C9semidirect
139. C22#95⋊C9direct (N × H)
148. C2C2×#95⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#95⋊C92
C22×C3×#953
C23×C22⋊C94