Finite Group Databasebeta

← C23×(C22⋊C9)⋊C4 #11921416

Subgroups — C23×(C22⋊C9)⋊C4 #11921416

Order 1152.

3074 conjugacy classes of subgroups; only the 386 normal subgroups are shown.

normal subgroups only

This group has 3074 conjugacy classes of subgroups — too many to draw. Only its 386 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
1C24×C22⋊C9C211yesmaximal, characteristic
2C22×(C22⋊C9)⋊C4C2114yesmaximal, direct product factor
3C23×#217—31nomaximal
4C23×C22⋊C9C418yescomplemented
5C23×C22⋊C9C2217yes—
6C23×Dic9—41nomaximal
7C2×(C22⋊C9)⋊C4C22128yesdirect product factor
8C26×C3D311yescharacteristic
9C24×Dic3—31no—
10C24×Dic3—31no—
11C22×#217—314no—
12C22×#217—314no—
13C24×C9—41no—
14C22×C22⋊C9C2×C4128yescomplemented
15C22×C22⋊C9C2317yes—
16C22×Dic9—414no—
17(C22⋊C9)⋊C4C2318yesdirect product factor
18C23×C22⋊C4—91noSylow
19C25×C3—31no—
20C25×C3—38no—
21C25×C3—37no—
22C25×C3Dic318yes—
23C25×C3C2×D317yes—
24C23×Dic3—314no—
25C23×Dic3—314no—
26C23×Dic3—68no—
27C23×Dic3—67no—
28C23×Dic3—61no—
29C2×#217—384no—
30C2×#217—328no—
31C23×C9—48no—
32C23×C9—47no—
33C2×C22⋊C9C22×C4114yescomplemented
34C2×C22⋊C9C2411yescharacteristic
35C2×Dic9—428no—
36C26D911yescharacteristic
37C24×C4—91no—
38C24×C4—91no—
39C22×C22⋊C4—914no—
40C22×C22⋊C4—914no—
41C24×C3—38no—
42C24×C3—38no—
43C24×C3—37no—
44C24×C3—37no—
45C24×C3—356no—
46C24×C3—328no—
47C24×C3—321no—
48C24×C3—628no—
49C24×C3—67no—
50C24×C3C2×Dic3128yes—
51C24×C3S411yescharacteristic
52C24×C3C22×D317yes—
53C22×Dic3—328no—
54C22×Dic3—328no—
55C22×Dic3—656no—
56C22×Dic3—642no—
57C22×Dic3—614no—
58#217—356no—
59#217—38no—
60C22×C9—428no—
61C22×C9—47no—
62C22⋊C9C23×C411yescharacteristic, complemented
63Dic9—48no—
64C25—31no—
65C25—37no—
66C25—38no—
67C25Dic918yescomplemented
68C25C2×D917yes—
69C23×C4—914no—
70C23×C4—914no—
71C23×C4—188no—
72C23×C4—187no—
73C23×C4—181no—
74C2×C22⋊C4—984no—
75C2×C22⋊C4—928no—
76C23×C3—328no—
77C23×C3—328no—
78C23×C3—356no—
79C23×C3—37no—
80C23×C3—321no—
81C23×C3—37no—
82C23×C3—384no—
83C23×C3—314no—
84C23×C3—642no—
85C23×C3—656no—
86C23×C3—67no—
87C23×C3SL(2,ℤ/4)18yes—
88C23×C3C22×Dic3114yes—
89C23×C3C2×S417yes—
90C23×C3C23×D311yescharacteristic
91C2×Dic3—38no—
92C2×Dic3—38no—
93C2×Dic3—656no—
94C2×Dic3—628no—
95C2×Dic3—628no—
96C2×C9—414no—
97C2×C9—41no—
98C24—38no—
99C24—38no—
100C24—37no—
101C24—37no—
102C24—321no—
103C24—356no—
104C24—328no—
105C24—67no—
106C24—628no—
107C24C2×Dic9128yescomplemented
108C24(C22⋊C9)⋊C211yescharacteristic
109C24C22×D917yes—
110C22×C4—928no—
111C22×C4—928no—
112C22×C4—1856no—
113C22×C4—1842no—
114C22×C4—1814no—
115C22⋊C4—956no—
116C22⋊C4—98no—
117C22×C3—314no—
118C22×C3—31no—
119C22×C3—314no—
120C22×C3—314no—
121C22×C3—384no—
122C22×C3—31no—
123C22×C3—37no—
124C22×C3—67no—
125C22×C3—628no—
126C22×C3C2×SL(2,ℤ/4)128yes—
127C22×C3C23×Dic311yescharacteristic
128C22×C3C22×S417yes—
129Dic3—68no—
130Dic3—68no—
131C9—41noSylow
132C23—37no—
133C23—321no—
134C23—328no—
135C23—328no—
136C23—356no—
137C23—37no—
138C23—384no—
139C23—314no—
140C23—67no—
141C23—642no—
142C23—656no—
143C23(C22⋊C9)⋊C418yesdirect product factor
144C23C22×Dic9114yescomplemented
145C23C2×(C22⋊C9)⋊C217yes—
146C23C23×D911yescharacteristic
147C2×C4—98no—
148C2×C4—98no—
149C2×C4—1856no—
150C2×C4—1828no—
151C2×C4—1828no—
152C2×C3—31no—
153C2×C3—31no—
154C2×C3—314no—
155C2×C3C22×SL(2,ℤ/4)114yes—
156C2×C3C23×S411yescharacteristic
157C22—314no—
158C22—31no—
159C22—31no—
160C22—37no—
161C22—314no—
162C22—314no—
163C22—384no—
164C22—67no—
165C22—628no—
166C22C2×(C22⋊C9)⋊C4128yesdirect product factor
167C22C23×Dic911yescharacteristic, complemented
168C22C22×(C22⋊C9)⋊C217yes—
169C4—188no—
170C4—188no—
171C3C23×SL(2,ℤ/4)11yescharacteristic
172C2—31no—
173C2—31no—
174C2—314no—
175C2C22×(C22⋊C9)⋊C4114yesdirect product factor
176C2C23×(C22⋊C9)⋊C211yescharacteristic
subgroupG/H
center, hypercenterC24(C22⋊C9)⋊C2
commutator, hypocenterC22⋊C9C23×C4
FrattiniC2×C3C23×S4
Fitting, socle, prime radicalC26×C3D3
cosocleC2×C22⋊C9C24
LCSG ▷ C22⋊C9
UCSC1 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊C9)⋊C4C2direct (N × H)
4. C23×C22⋊C9C4semidirect
7. C2×(C22⋊C9)⋊C4C22direct (N × H)
14. C22×C22⋊C9C2×C4semidirect
17. (C22⋊C9)⋊C4C23direct (N × H)
33. C2×C22⋊C9C22×C4semidirect
62. C22⋊C9C23×C4semidirect
67. C25Dic9semidirect
107. C24C2×Dic9semidirect
143. C23(C22⋊C9)⋊C4direct (N × H)
144. C23C22×Dic9semidirect
166. C22C2×(C22⋊C9)⋊C4direct (N × H)
167. C22C23×Dic9semidirect
175. C2C22×(C22⋊C9)⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊C92
C22×(C22⋊C9)⋊C42
C23×#2173
C23×Dic94