Finite Group Databasebeta

← #14518793

Subgroups — #14518793

Order 1944.

1320 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 138 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⋊(C3⋊(C3⋊D9))C211yesmaximal, characteristic, complemented
2C2×C3×C9×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C3⋊Dic9C211yesmaximal, characteristic, complemented
4#10620152—31nomaximal
5#10619880—34nomaximal
6#10619878—33nomaximal
7C2×C33×C9C2211yescharacteristic
8C3⋊(C3⋊(C3⋊D9))—21no—
9C3×C9×C3⋊D3—21no—
10C2×C3⋊(C3⋊(C3⋊D3))—31no—
11C2×C32×C3⋊D3D311yescharacteristic
12C32×C3⋊Dic3—31no—
13C2×C3⋊(C3⋊D9)—33no—
14C2×C3⋊(C3⋊D9)—34no—
15C2×C3⋊(C3⋊D9)—612no—
16C2×C3⋊(C3⋊D9)—64no—
17C2×C9×C3⋊D3D313yescomplemented
18C2×C3×D3×C9—34no—
19C3×C3⋊Dic9D314yescomplemented
20C32×Dic9—33no—
21C33×C9D411yescharacteristic, complemented, Sylow
22#6292—93no—
23#6292—91no—
24#6291—94no—
25#6233—91no—
26#6195—912no—
27C2×C34C2×D311yescharacteristic
28C3⋊(C3⋊(C3⋊D3))—61no—
29C32×C3⋊D3—21no—
30C2×C32×C9—24no—
31C2×C32×C9—212no—
32C2×C32×C9C2×D313yes—
33C2×C32×C9C2×D314yes—
34C3⋊(C3⋊D9)—68no—
35C3⋊(C3⋊D9)—624no—
36C3⋊(C3⋊D9)—64no—
37C3⋊(C3⋊D9)—63no—
38C9×C3⋊D3—23no—
39C3×D3×C9—64no—
40C2×C3⋊(C3⋊D3)—93no—
41C2×C3⋊(C3⋊D3)—94no—
42C2×C3⋊(C3⋊D3)—91no—
43C2×C3⋊(C3⋊D3)—184no—
44C2×C3⋊(C3⋊D3)—1812no—
45C2×C3×C3⋊D3D913yescomplemented
46C2×C3×C3⋊D3C3⋊D311yescharacteristic
47C2×C32×D3—34no—
48C3×C3⋊Dic3—34no—
49C32×Dic3—93no—
50C32×Dic3—91no—
51C22×C3×C9—91no—
52C2×C3⋊D9—912no—
53C2×C3⋊D9—91no—
54C2×C3⋊D9—1812no—
55C2×C3⋊D9—184no—
56C2×C3⋊D9—1812no—
57C2×C3⋊D9—1824no—
58C2×D3×C9—312no—
59C3⋊Dic9C3⋊D311yescharacteristic, complemented
60C3×Dic9—312no—
61C34#6711yescharacteristic
62C32×C9—24no—
63C32×C9—212no—
64C32×C9D1214yescomplemented
65C32×C9#6713yescomplemented
66#638—271no—
67C4⋊(C3⋊D3)—271no—
68#626—274no—
69#626—2712no—
70#611—273no—
71C2×C33—212no—
72C2×C33—24no—
73C2×C33C2×D913yes—
74C2×C33D3214yes—
75C2×C33C2×C3⋊D311yescharacteristic
76C3⋊(C3⋊D3)—188no—
77C3⋊(C3⋊D3)—1824no—
78C3⋊(C3⋊D3)—183no—
79C3⋊(C3⋊D3)—184no—
80C3⋊(C3⋊D3)—181no—
81C3×C3⋊D3—23no—
82C3×C3⋊D3—21no—
83C32×D3—64no—
84C2×C3×C9—224no—
85C2×C3×C9—212no—
86C2×C3×C9—24no—
87C2×C3×C9—212no—
88C2×C3×C9—181no—
89C2×C3×C9D32112yes—
90C2×C3×C9C2×C3⋊D311yescharacteristic
91C3⋊D9—1848no—
92C3⋊D9—1824no—
93C3⋊D9—188no—
94C3⋊D9—1824no—
95C3⋊D9—1812no—
96C3⋊D9—181no—
97D3×C9—612no—
98C22×C32—91no—
99C2×C3⋊D3—271no—
100C2×C3⋊D3—271no—
101C2×C3⋊D3—2712no—
102C2×C3⋊D3—274no—
103C2×C3⋊D3—544no—
104C2×C3⋊D3—5412no—
105C2×C3⋊D3—5412no—
106C2×C3⋊D3—544no—
107C2×C3⋊D3—5424no—
108C2×C3⋊D3C3⋊D911yescharacteristic, complemented
109C2×C3×D3—312no—
110C2×C3×D3—34no—
111C32×C4—271no—
112C3⋊Dic3—31no—
113C3×Dic3—912no—
114C3×Dic3—94no—
115C22×C9—93no—
116C2×D9—273no—
117C2×D9—5412no—
118Dic9—33no—
119C33—212no—
120C33—24no—
121C33#61113yescomplemented
122C33#62614yes—
123C33#63811yescharacteristic
124C3×C9—224no—
125C3×C9—212no—
126C3×C9—24no—
127C3×C9—212no—
128C3×C9#626112yescomplemented
129C3×C9C4⋊(C3⋊D3)11yescharacteristic, complemented
130#67—811no—
131#67—813no—
132D12—814no—
133C2×C32—224no—
134C2×C32—212no—
135C2×C32—212no—
136C2×C32—24no—
137C2×C32—24no—
138C2×C32—181no—
139C2×C32D3×D9112yes—
140C2×C32C2×C3⋊D911yescharacteristic
141C2×C32D3×C3⋊D314yes—
142C2×C32D3×C3⋊D311yescharacteristic
143C3⋊D3—21no—
144C3⋊D3—548no—
145C3⋊D3—5448no—
146C3⋊D3—5424no—
147C3⋊D3—5424no—
148C3⋊D3—548no—
149C3⋊D3—5412no—
150C3⋊D3—541no—
151C3⋊D3—544no—
152C3⋊D3—541no—
153C3×D3—612no—
154C3×D3—64no—
155C2×C9—212no—
156C2×C9—183no—
157C2×C9D3×C3⋊D313yes—
158D9—5424no—
159D9—543no—
160C22×C3—93no—
161C22×C3—91no—
162C2×D3—34no—
163C2×D3—813no—
164C2×D3—814no—
165C2×D3—811no—
166C2×D3—16212no—
167C2×D3—1624no—
168C3×C4—274no—
169Dic3—93no—
170Dic3—91no—
171C32—224no—
172C32—212no—
173C32—212no—
174C32—24no—
175C32—24no—
176C32#6195112yescomplemented
177C32#623311yescharacteristic, complemented
178C32#629114yes—
179C32#629211yescharacteristic
180C9—212no—
181C9#629213yescomplemented
182D4—2431noSylow
183C2×C3—212no—
184C2×C3—24no—
185C2×C3—183no—
186C2×C3—181no—
187C2×C3D9×C3⋊D313yes—
188C2×C3D3×C3⋊D914yes—
189C2×C3C3⋊D3211yescharacteristic
190D3—64no—
191D3—16224no—
192D3—1628no—
193D3—1623no—
194D3—1624no—
195D3—1621no—
196C22—91no—
197C22—2431no—
198C4—271no—
199C3—212no—
200C3—24no—
201C3#1061987813yescomplemented
202C3#1061988014yescomplemented
203C3#1062015211yescharacteristic
204C2—181no—
205C2—4861no—
206C2C3⋊D3×C3⋊D911yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊D3×C3⋊D9
commutator, Fitting, cosocleC2×C33×C9C22
FrattiniC2×C3C3⋊D32
socleC2×C34C2×D3
hypocenterC33×C9D4
LCSG ▷ C2×C33×C9 ▷ C33×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(C3⋊(C3⋊D9))C2semidirect
2. C2×C3×C9×C3⋊D3C2semidirect
3. C32×C3⋊Dic9C2semidirect
17. C2×C9×C3⋊D3D3semidirect
19. C3×C3⋊Dic9D3semidirect
21. C33×C9D4semidirect
45. C2×C3×C3⋊D3D9semidirect
59. C3⋊Dic9C3⋊D3semidirect
64. C32×C9D12semidirect
65. C32×C9#67semidirect
108. C2×C3⋊D3C3⋊D9semidirect
121. C33#611semidirect
128. C3×C9#626semidirect
129. C3×C9C4⋊(C3⋊D3)semidirect
176. C32#6195semidirect
177. C32#6233semidirect
181. C9#6292semidirect
201. C3#10619878semidirect
202. C3#10619880semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊(C3⋊D9))2
C2×C3×C9×C3⋊D32
C32×C3⋊Dic92
#106201523
#106198803
#106198783