Finite Group Databasebeta

← C3×C3⋊D3×#95 #13162705

Subgroups — C3×C3⋊D3×#95 #13162705

Order 1728.

2284 conjugacy classes of subgroups; only the 470 normal subgroups are shown.

normal subgroups only

This group has 2284 conjugacy classes of subgroups — too many to draw. Only its 470 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
1C22×C3×C4×C3⋊D3C213yesmaximal
2C33×#95C211yesmaximal, characteristic, complemented
3C3×#63658C213yesmaximal, complemented
4C3⋊D3×#95C311yesmaximal, characteristic, direct product factor
5C3×D3×#95—34nomaximal
6C23×C3×C3⋊D3C2211yescharacteristic
7C22×C33×C4C2213yes—
8C22×C3×C3⋊Dic3C2213yes—
9C2×C3×C4×C3⋊D3—212no—
10C2×C3×C4×C3⋊D3C4112yescomplemented
11C22×C4×C3⋊D3C2×C313yes—
12C22×C3×C4×D3—312no—
13C32×#95—24no—
14C32×#95D314yescomplemented
15C32×#95C2×C311yescharacteristic, complemented
16#63658C2×C313yescomplemented
17C3×C3⋊#95—312no—
18C23×C33C2311yescharacteristic
19C22×C3×C3⋊D3C2×C416yes—
20C22×C3×C3⋊D3D416yes—
21C22×C3×C3⋊D3Q812yes—
22C2×C33×C4—26no—
23C2×C33×C4C2×C416yescomplemented
24C2×C3×C3⋊Dic3—26no—
25C2×C3×C3⋊Dic3C2×C416yescomplemented
26C3×C4×C3⋊D3—224no—
27C2×C3×#95—91no—
28D3×#95—34no—
29C23×C3⋊D3C22×C311yescharacteristic
30C23×C3×D3—34no—
31C22×C32×C4—212no—
32C22×C32×C4C2×D3112yes—
33C22×C32×C4C22×C313yes—
34C22×C3⋊Dic3C22×C313yes—
35C2×C4×C3⋊D3—212no—
36C2×C4×C3⋊D3C3×C4112yescomplemented
37C22×C3×Dic3—312no—
38C2×C3×C4×D3—348no—
39C2×C3×C4×D3—648no—
40C22×C33C22×C413yes—
41C22×C33C2×D413yes—
42C22×C33C2×Q811yescharacteristic
43C2×C3×C3⋊D3C4214yes—
44C2×C3×C3⋊D3C22⋊C4112yes—
45C2×C3×C3⋊D3C4⋊C4112yes—
46C33×C4—26no—
47C3×C3⋊Dic3—26no—
48C23×C3×C4—93no—
49C22×C4×D3—312no—
50C3×#95—24no—
51C3×#95—93no—
52C3×#95C3×D314yescomplemented
53C3×#95C3⋊D311yescharacteristic, direct product factor
54C3⋊#95—312no—
55C23×C32—24no—
56C23×C32C22×D314yes—
57C23×C32C23×C311yescharacteristic
58C22×C3⋊D3C2×C3×C416yes—
59C22×C3⋊D3C3×D416yes—
60C22×C3⋊D3C3×Q812yes—
61C22×C3×D3—324no—
62C22×C3×D3—324no—
63C22×C3×D3—38no—
64C2×C32×C4—26no—
65C2×C32×C4—224no—
66C2×C32×C4—224no—
67C2×C32×C4—424no—
68C2×C32×C4C4×D3124yescomplemented
69C2×C32×C4C2×C3×C416yescomplemented
70C2×C3⋊Dic3—26no—
71C2×C3⋊Dic3C2×C3×C416yescomplemented
72C4×C3⋊D3—224no—
73C2×C3×Dic3—324no—
74C2×C3×Dic3—624no—
75C3×C4×D3—696no—
76C2×#95—91noSylow
77C2×C33C2×C4211yescharacteristic
78C2×C33C2×C22⋊C413yes—
79C2×C33C2×C4⋊C413yes—
80C3×C3⋊D3#9518yesdirect product factor
81C24×C3—91no—
82C23×D3—34no—
83C22×C3×C4—212no—
84C22×C3×C4—93no—
85C22×C3×C4—912no—
86C22×C3×C4—1812no—
87C22×C3×C4C2×C3×D3112yes—
88C22×C3×C4C2×C3⋊D313yes—
89C22×Dic3—312no—
90C2×C4×D3—348no—
91C2×C4×D3—648no—
92C22×C32—212no—
93C22×C32—212no—
94C22×C32—24no—
95C22×C32C2×C4×D3112yes—
96C22×C32D3×D4112yes—
97C22×C32D3×Q814yes—
98C22×C32C22×C3×C413yes—
99C22×C32C2×C3×D413yes—
100C22×C32C2×C3×Q811yescharacteristic
101C2×C3⋊D3C3×C4214yes—
102C2×C3⋊D3C3×C22⋊C4112yes—
103C2×C3⋊D3C3×C4⋊C4112yes—
104C2×C3×D3—316no—
105C2×C3×D3—348no—
106C2×C3×D3—348no—
107C32×C4—26no—
108C32×C4—224no—
109C32×C4—424no—
110C3⋊Dic3—26no—
111C3×Dic3—624no—
112C23×C4—93no—
113#95—93no—
114#95C3×C3⋊D311yescharacteristic, direct product factor
115C33C2×#9511yescharacteristic, complemented, Sylow
116C23×C3—24no—
117C23×C3—96no—
118C23×C3—96no—
119C23×C3—92no—
120C23×C3C22×C3×D314yes—
121C23×C3C22×C3⋊D311yescharacteristic
122C22×D3—324no—
123C22×D3—324no—
124C22×D3—38no—
125C2×C3×C4—224no—
126C2×C3×C4—26no—
127C2×C3×C4—224no—
128C2×C3×C4—424no—
129C2×C3×C4—96no—
130C2×C3×C4—1824no—
131C2×C3×C4—186no—
132C2×C3×C4C3×C4×D3124yescomplemented
133C2×C3×C4C4×C3⋊D316yescomplemented
134C2×Dic3—324no—
135C2×Dic3—624no—
136C4×D3—696no—
137C2×C32—212no—
138C2×C32—212no—
139C2×C32—24no—
140C2×C32C42×D314yes—
141C2×C32D3×C22⋊C4112yes—
142C2×C32D3×C4⋊C4112yes—
143C2×C32C2×C3×C4211yescharacteristic
144C2×C32C2×C3×C22⋊C413yes—
145C2×C32C2×C3×C4⋊C413yes—
146C3⋊D3C3×#9518yesdirect product factor
147C3×D3—332no—
148C24—91no—
149C22×C4—93no—
150C22×C4—912no—
151C22×C4—1812no—
152C22×C4C2×C3×C3⋊D313yes—
153C22×C3—212no—
154C22×C3—212no—
155C22×C3—24no—
156C22×C3—94no—
157C22×C3—912no—
158C22×C3—912no—
159C22×C3C2×C3×C4×D3112yes—
160C22×C3C3×D3×D4112yes—
161C22×C3C3×D3×Q814yes—
162C22×C3C2×C4×C3⋊D313yes—
163C22×C3D4×C3⋊D313yes—
164C22×C3Q8×C3⋊D311yescharacteristic
165C2×D3—348no—
166C2×D3—348no—
167C2×D3—316no—
168C3×C4—224no—
169C3×C4—26no—
170C3×C4—424no—
171C3×C4—186no—
172Dic3—624no—
173C32—24no—
174C32D3×#9514yescomplemented
175C32C2×C3×#9511yescharacteristic, complemented
176C23—96no—
177C23—96no—
178C23—92no—
179C23C22×C3×C3⋊D311yescharacteristic
180C2×C4—26no—
181C2×C4—96no—
182C2×C4—1824no—
183C2×C4—186no—
184C2×C4C3×C4×C3⋊D316yescomplemented
185C2×C3—24no—
186C2×C3—212no—
187C2×C3—212no—
188C2×C3—98no—
189C2×C3C3×C42×D314yes—
190C2×C3C3×D3×C22⋊C4112yes—
191C2×C3C3×D3×C4⋊C4112yes—
192C2×C3C42×C3⋊D311yescharacteristic
193C2×C3C22⋊C4×C3⋊D313yes—
194C2×C3C4⋊C4×C3⋊D313yes—
195D3—332no—
196C22—94no—
197C22—912no—
198C22—912no—
199C22C2×C3×C4×C3⋊D313yes—
200C22C3×D4×C3⋊D313yes—
201C22C3×Q8×C3⋊D311yescharacteristic
202C4—26no—
203C4—186no—
204C3—24no—
205C3C3×D3×#9514yescomplemented
206C3C3⋊D3×#9511yescharacteristic, direct product factor
207C2—98no—
208C2C3×C42×C3⋊D311yescharacteristic
209C2C3×C22⋊C4×C3⋊D313yes—
210C2C3×C4⋊C4×C3⋊D313yes—
subgroupG/H
centerC23×C3C22×C3⋊D3
commutatorC2×C32C2×C3×C42
FrattiniC23C22×C3×C3⋊D3
FittingC33×#95C2
socleC23×C33C23
prime radicalC23×C3×C3⋊D3C22
cosocleC23×C32C23×C3
hypercenterC3×#95C3⋊D3
hypocenterC32C2×C3×#95
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
2. C33×#95C2semidirect
3. C3×#63658C2semidirect
4. C3⋊D3×#95C3direct (N × H)
10. C2×C3×C4×C3⋊D3C4semidirect
14. C32×#95D3semidirect
15. C32×#95C2×C3semidirect
16. #63658C2×C3semidirect
23. C2×C33×C4C2×C4semidirect
25. C2×C3×C3⋊Dic3C2×C4semidirect
36. C2×C4×C3⋊D3C3×C4semidirect
52. C3×#95C3×D3semidirect
53. C3×#95C3⋊D3direct (N × H)
68. C2×C32×C4C4×D3semidirect
69. C2×C32×C4C2×C3×C4semidirect
71. C2×C3⋊Dic3C2×C3×C4semidirect
80. C3×C3⋊D3#95direct (N × H)
114. #95C3×C3⋊D3direct (N × H)
115. C33C2×#95semidirect
132. C2×C3×C4C3×C4×D3semidirect
133. C2×C3×C4C4×C3⋊D3semidirect
146. C3⋊D3C3×#95direct (N × H)
174. C32D3×#95semidirect
175. C32C2×C3×#95semidirect
184. C2×C4C3×C4×C3⋊D3semidirect
205. C3C3×D3×#95semidirect
206. C3C3⋊D3×#95direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C33×#952
C3×#636582
C3⋊D3×#953
C3×D3×#953