Finite Group Databasebeta

← Dic6×C32⋊C9 #14517282

Subgroups — Dic6×C32⋊C9 #14517282

Order 1944.

423 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 423 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C3×C4×C32⋊C9C211yesmaximal, characteristic
2Dic3×C32⋊C9C212yesmaximal
3C33×Dic6C311yesmaximal, characteristic
4C3×C9×Dic6C313yesmaximal, complemented
5Q8×C32⋊C9—31nomaximal
6C2×C3×C32⋊C9C2211yescharacteristic
7C34×C4C2×C311yescharacteristic
8C33×Dic3C2×C312yes—
9C32×C4×C9C2×C313yes—
10C3×C9×Dic3C2×C316yes—
11C4×C32⋊C9—21no—
12C4×C32⋊C9—23no—
13C4×C32⋊C9—32no—
14C4×C32⋊C9D311yescharacteristic
15C3×C32⋊C9Q811yescharacteristic, complemented, Sylow
16C33×Q8—31no—
17C32×Dic6—31no—
18C32×Dic6—32no—
19C32×Dic6C913yescomplemented
20C32×Dic6C3211yescharacteristic
21C3×Q8×C9—33no—
22C9×Dic6—33no—
23C2×C34C22×C311yescharacteristic
24C2×C32×C9C22×C313yes—
25C2×C32⋊C9—21no—
26C2×C32⋊C9—23no—
27C2×C32⋊C9C2×D311yescharacteristic
28C33×C4—23no—
29C33×C4—21no—
30C33×C4—31no—
31C33×C4—32no—
32C33×C4—32no—
33C33×C4—61no—
34C33×C4—62no—
35C33×C4C2×C913yes—
36C33×C4C3×D311yescharacteristic
37C33×C4C2×C3211yescharacteristic
38C32×Dic3—32no—
39C32×Dic3—34no—
40C32×Dic3C2×C916yes—
41C32×Dic3C2×C3212yes—
42C3×C4×C9—23no—
43C3×C4×C9—33no—
44C3×C4×C9—36no—
45C3×C4×C9—63no—
46C3×C4×C9C3×D313yes—
47C9×Dic3—36no—
48C34C3×Q811yescharacteristic
49C32×C9C3×Q813yescomplemented
50C32⋊C9—21no—
51C32⋊C9—23no—
52C32⋊C9Dic611yescharacteristic, direct product factor
53C32×Q8—31no—
54C32×Q8—33no—
55C32×Q8—91no—
56C32×Q8—92no—
57C3×Dic6—33no—
58C3×Dic6C3×C911yescharacteristic
59C3×Dic6H(3,𝔽3)11yescharacteristic
60C3×Dic63−1+212yes—
61Q8×C9—93no—
62C2×C33—23no—
63C2×C33—21no—
64C2×C33—31no—
65C2×C33—32no—
66C2×C33—61no—
67C2×C33—62no—
68C2×C33C22×C913yes—
69C2×C33C2×C3×D311yescharacteristic
70C2×C33C22×C3211yescharacteristic
71C2×C3×C9—23no—
72C2×C3×C9—33no—
73C2×C3×C9—63no—
74C2×C3×C9C2×C3×D313yes—
75C32×C4—21no—
76C32×C4—21no—
77C32×C4—22no—
78C32×C4—23no—
79C32×C4—32no—
80C32×C4—31no—
81C32×C4—32no—
82C32×C4—33no—
83C32×C4—36no—
84C32×C4—63no—
85C32×C4—66no—
86C32×C4—63no—
87C32×C4—61no—
88C32×C4—62no—
89C32×C4—92no—
90C32×C4—94no—
91C32×C4D3×C913yes—
92C32×C4C2×C3×C911yescharacteristic
93C32×C4C2×H(3,𝔽3)11yescharacteristic
94C32×C4C2×3−1+212yes—
95C32×C4C32×D311yescharacteristic
96C3×Dic3—36no—
97C3×Dic3C2×C3×C912yes—
98C3×Dic3C2×H(3,𝔽3)12yes—
99C3×Dic3C2×3−1+214yes—
100C4×C9—33no—
101C4×C9—63no—
102C4×C9—96no—
103C33—23no—
104C33—21no—
105C33—31no—
106C33—32no—
107C33—61no—
108C33—62no—
109C33Q8×C913yescomplemented
110C33C3×Dic611yescharacteristic
111C33C32×Q811yescharacteristic
112C3×C9—23no—
113C3×C9—33no—
114C3×C9—63no—
115C3×C9C3×Dic613yescomplemented
116C3×Q8—31no—
117C3×Q8—31no—
118C3×Q8—32no—
119C3×Q8—93no—
120Dic6C32⋊C911yescharacteristic, direct product factor
121C2×C32—21no—
122C2×C32—21no—
123C2×C32—22no—
124C2×C32—23no—
125C2×C32—31no—
126C2×C32—32no—
127C2×C32—33no—
128C2×C32—63no—
129C2×C32—66no—
130C2×C32—63no—
131C2×C32—61no—
132C2×C32—62no—
133C2×C32C2×D3×C913yes—
134C2×C32C22×C3×C911yescharacteristic
135C2×C32C22×H(3,𝔽3)11yescharacteristic
136C2×C32C22×3−1+212yes—
137C2×C32C2×C32×D311yescharacteristic
138C2×C9—33no—
139C2×C9—63no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—22no—
143C3×C4—32no—
144C3×C4—32no—
145C3×C4—34no—
146C3×C4—33no—
147C3×C4—63no—
148C3×C4—96no—
149C3×C4C2×C32⋊C911yescharacteristic
150C3×C4C3×D3×C911yescharacteristic
151C3×C4D3×H(3,𝔽3)11yescharacteristic
152C3×C4D3×3−1+212yes—
153Dic3C2×C32⋊C912yes—
154C32—21no—
155C32—21no—
156C32—22no—
157C32—23no—
158C32—31no—
159C32—32no—
160C32—33no—
161C32—63no—
162C32—63no—
163C32—66no—
164C32—61no—
165C32—62no—
166C32C9×Dic613yescomplemented
167C32C3×Q8×C911yescharacteristic
168C32Q8×H(3,𝔽3)11yescharacteristic
169C32Q8×3−1+212yes—
170C32C32×Dic611yescharacteristic
171C9—33no—
172C9—63no—
173Q8—31noSylow
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—22no—
177C2×C3—33no—
178C2×C3—63no—
179C2×C3C22×C32⋊C911yescharacteristic
180C2×C3C2×C3×D3×C911yescharacteristic
181C2×C3C2×D3×H(3,𝔽3)11yescharacteristic
182C2×C3C2×D3×3−1+212yes—
183C4—32no—
184C4D3×C32⋊C911yescharacteristic
185C3—21no—
186C3—21no—
187C3—22no—
188C3—33no—
189C3—63no—
190C3Q8×C32⋊C911yescharacteristic, complemented
191C3C3×C9×Dic611yescharacteristic
192C3Dic6×H(3,𝔽3)11yescharacteristic
193C3Dic6×3−1+212yes—
194C2C2×D3×C32⋊C911yescharacteristic
subgroupG/H
center, FrattiniC2×C32C2×C32×D3
commutatorC2×C32C22×C3×C9
FittingC3×C4×C32⋊C9C2
socle, cosocleC2×C33C22×C32
prime radicalC2×C34C22×C3
hypercenterC4×C32⋊C9D3
hypocenterC3Q8×C32⋊C9
LCSG ▷ C2×C32 ▷ C3
UCSC1 ◁ C2×C32 ◁ C4×C32⋊C9

Complements

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

NH ≅ G/Ntype
4. C3×C9×Dic6C3semidirect
15. C3×C32⋊C9Q8semidirect
19. C32×Dic6C9semidirect
49. C32×C9C3×Q8semidirect
52. C32⋊C9Dic6direct (N × H)
109. C33Q8×C9semidirect
115. C3×C9C3×Dic6semidirect
120. Dic6C32⋊C9direct (N × H)
166. C32C9×Dic6semidirect
190. C3Q8×C32⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C32⋊C92
Dic3×C32⋊C92
C33×Dic63
C3×C9×Dic63
Q8×C32⋊C93