Finite Group Databasebeta

← C3×C4⋊C4×D9 #11721445

Subgroups — C3×C4⋊C4×D9 #11721445

Order 864.

302 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 120 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×C4×D9C212yesmaximal
2C2×C3×C4×D9C211yesmaximal, characteristic
3C3×C9×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×C4⋊Dic9C211yesmaximal, characteristic, complemented
5C3×Dic9⋊C4C212yesmaximal, complemented
6C3×D3×C4⋊C4—31nomaximal
7C4⋊C4×D9C311yesmaximal, characteristic, direct product factor
8C22×C3×D9C2211yescharacteristic
9C2×C3×C4×C9C2212yes—
10C2×C3×C4×C9C2211yescharacteristic
11C2×C3×Dic9C2212yes—
12C2×C3×Dic9C2211yescharacteristic
13C3×C4×D9—24no—
14C3×C4×D9C414yescomplemented
15C2×C3×C4×D3—31no—
16C2×C3×C4×D3—32no—
17C32×C4⋊C4D311yescharacteristic
18C3×C4⋊Dic3—31no—
19C3×Dic3⋊C4—32no—
20C2×C4×D9C2×C312yes—
21C2×C4×D9C2×C311yescharacteristic
22C9×C4⋊C4—21no—
23C9×C4⋊C4C2×C311yescharacteristic, complemented
24C4⋊Dic9C2×C311yescharacteristic, complemented
25Dic9⋊C4C2×C312yescomplemented
26C22×C3×C9C2311yescharacteristic
27C2×C3×D9C2×C412yes—
28C2×C3×D9D412yes—
29C2×C3×D9Q812yes—
30C3×C4×C9—22no—
31C3×C4×C9C2×C412yescomplemented
32C3×Dic9—22no—
33C3×Dic9C2×C412yescomplemented
34C2×C3×C4⋊C4—91no—
35D3×C4⋊C4—31no—
36C22×C3×D3—31no—
37C2×C32×C4C2×D312yes—
38C2×C32×C4C2×D311yescharacteristic
39C2×C3×Dic3—31no—
40C2×C3×Dic3—32no—
41C3×C4×D3—34no—
42C3×C4×D3—64no—
43C22×D9C22×C311yescharacteristic
44C2×C4×C9—21no—
45C2×C4×C9—22no—
46C2×C4×C9C22×C312yes—
47C2×C4×C9C22×C311yescharacteristic
48C2×Dic9C22×C312yes—
49C2×Dic9C22×C311yescharacteristic
50C4×D9—24no—
51C4×D9C3×C414yescomplemented
52C2×C3×C9C22×C411yescharacteristic
53C2×C3×C9C2×D411yescharacteristic
54C2×C3×C9C2×Q811yescharacteristic
55C3×D9C4⋊C414yesdirect product factor
56C22×C3×C4—91no—
57C22×C3×C4—92no—
58C2×C4×D3—31no—
59C2×C4×D3—32no—
60C3×C4⋊C4—21no—
61C3×C4⋊C4—92no—
62C3×C4⋊C4—91no—
63C3×C4⋊C4D911yescharacteristic, direct product factor
64C3×C4⋊C4C3×D311yescharacteristic
65C4⋊Dic3—31no—
66Dic3⋊C4—32no—
67C22×C32C22×D311yescharacteristic
68C2×C3×D3—32no—
69C2×C3×D3—32no—
70C2×C3×D3—32no—
71C32×C4—22no—
72C32×C4C4×D312yes—
73C3×Dic3—32no—
74C3×Dic3—62no—
75C22×C9—21no—
76C22×C9C23×C311yescharacteristic
77C2×D9C2×C3×C412yes—
78C2×D9C3×D412yes—
79C2×D9C3×Q812yes—
80C4×C9—22no—
81C4×C9—22no—
82C4×C9—42no—
83C4×C9C2×C3×C412yescomplemented
84Dic9—22no—
85Dic9C2×C3×C412yescomplemented
86C2×C4⋊C4—91noSylow
87C3×C9C2×C4⋊C411yescharacteristic, complemented, Sylow
88C23×C3—91no—
89C22×D3—31no—
90C2×C3×C4—21no—
91C2×C3×C4—22no—
92C2×C3×C4—91no—
93C2×C3×C4—94no—
94C2×C3×C4—92no—
95C2×C3×C4—184no—
96C2×C3×C4C2×D912yes—
97C2×C3×C4C2×D911yescharacteristic
98C2×C3×C4C2×C3×D312yes—
99C2×C3×C4C2×C3×D311yescharacteristic
100C2×Dic3—31no—
101C2×Dic3—32no—
102C4×D3—34no—
103C4×D3—64no—
104C2×C32C2×C4×D311yescharacteristic
105C2×C32D3×D411yescharacteristic
106C2×C32D3×Q811yescharacteristic
107C3×D3—34no—
108C2×C9—21no—
109C2×C9—21no—
110C2×C9—21no—
111C2×C9C22×C3×C411yescharacteristic
112C2×C9C2×C3×D411yescharacteristic
113C2×C9C2×C3×Q811yescharacteristic
114D9C3×C4⋊C414yesdirect product factor
115C22×C4—91no—
116C22×C4—92no—
117C4⋊C4—92no—
118C4⋊C4—91no—
119C4⋊C4C3×D911yescharacteristic, direct product factor
120C22×C3—21no—
121C22×C3—92no—
122C22×C3—92no—
123C22×C3—92no—
124C22×C3C22×D911yescharacteristic
125C22×C3C22×C3×D311yescharacteristic
126C2×D3—32no—
127C2×D3—32no—
128C2×D3—32no—
129C3×C4—22no—
130C3×C4—22no—
131C3×C4—22no—
132C3×C4—42no—
133C3×C4—92no—
134C3×C4—182no—
135C3×C4C4×D912yescomplemented
136C3×C4C3×C4×D312yes—
137Dic3—32no—
138Dic3—62no—
139C32D3×C4⋊C411yescharacteristic
140C9—21no—
141C9C2×C3×C4⋊C411yescharacteristic, complemented
142C23—91no—
143C2×C4—91no—
144C2×C4—94no—
145C2×C4—92no—
146C2×C4—184no—
147C2×C4C2×C3×D912yes—
148C2×C4C2×C3×D911yescharacteristic
149C2×C3—21no—
150C2×C3—21no—
151C2×C3—21no—
152C2×C3—94no—
153C2×C3C2×C4×D911yescharacteristic
154C2×C3D4×D911yescharacteristic
155C2×C3Q8×D911yescharacteristic
156C2×C3C2×C3×C4×D311yescharacteristic
157C2×C3C3×D3×D411yescharacteristic
158C2×C3C3×D3×Q811yescharacteristic
159D3—34no—
160C22—92no—
161C22—92no—
162C22—92no—
163C22C22×C3×D911yescharacteristic
164C4—22no—
165C4—92no—
166C4—182no—
167C4C3×C4×D912yescomplemented
168C3—21no—
169C3C4⋊C4×D911yescharacteristic, direct product factor
170C3C3×D3×C4⋊C411yescharacteristic
171C2—94no—
172C2C2×C3×C4×D911yescharacteristic
173C2C3×D4×D911yescharacteristic
174C2C3×Q8×D911yescharacteristic
subgroupG/H
centerC22×C3C22×D9
commutatorC2×C9C22×C3×C4
FrattiniC22×C3C22×C3×D3
FittingC3×C9×C4⋊C4C2
socleC22×C32C22×D3
prime radicalC22×C3×D9C22
cosocleC22×C9C23×C3
hypercenterC3×C4⋊C4D9
hypocenterC9C2×C3×C4⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×C9×C4⋊C4C2semidirect
4. C3×C4⋊Dic9C2semidirect
5. C3×Dic9⋊C4C2semidirect
7. C4⋊C4×D9C3direct (N × H)
14. C3×C4×D9C4semidirect
23. C9×C4⋊C4C2×C3semidirect
24. C4⋊Dic9C2×C3semidirect
25. Dic9⋊C4C2×C3semidirect
31. C3×C4×C9C2×C4semidirect
33. C3×Dic9C2×C4semidirect
51. C4×D9C3×C4semidirect
55. C3×D9C4⋊C4direct (N × H)
63. C3×C4⋊C4D9direct (N × H)
83. C4×C9C2×C3×C4semidirect
85. Dic9C2×C3×C4semidirect
87. C3×C9C2×C4⋊C4semidirect
114. D9C3×C4⋊C4direct (N × H)
119. C4⋊C4C3×D9direct (N × H)
135. C3×C4C4×D9semidirect
141. C9C2×C3×C4⋊C4semidirect
167. C4C3×C4×D9semidirect
169. C3C4⋊C4×D9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D92
C3×C9×C4⋊C42
C3×C4⋊Dic92
C3×Dic9⋊C42
C3×D3×C4⋊C43
C4⋊C4×D93