Finite Group Databasebeta

← C3×#10588749 #13142945

Subgroups — C3×#10588749 #13142945

Order 1728.

344 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 106 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×C9×#125C211yesmaximal, characteristic, complemented
2C3×#63437C211yesmaximal, characteristic
3C3×#63369C212yesmaximal
4C3×#63368C212yesmaximal, complemented
5C3×C4×C9⋊C8C211yesmaximal, characteristic, complemented
6C3×#5068—31nomaximal
7#10588749C311yesmaximal, characteristic, direct product factor
8C2×C3×D36C2211yescharacteristic
9C2×C3×Dic18C2211yescharacteristic
10C3×C9×C4⋊C4—22no—
11C3×C9×C4⋊C4C2212yes—
12C3×C42×C9C2211yescharacteristic
13C3×(C2×D9)⋊C4—22no—
14C2×C3×C9⋊C8C2212yes—
15C32×#125D311yescharacteristic
16C3×#875—31no—
17C3×#810—32no—
18C3×#809—32no—
19C3×C4×C3⋊C8—31no—
20C9×#125—21no—
21C9×#125C2×C311yescharacteristic, complemented
22#63437C2×C311yescharacteristic
23#63369C2×C312yes—
24#63368C2×C312yescomplemented
25C4×C9⋊C8C2×C311yescharacteristic, complemented
26C22×C3×D9—21no—
27C2×C3×C4×C9—22no—
28C2×C3×C4×C9D412yes—
29C2×C3×C4×C9C2311yescharacteristic
30C2×C3×Dic9—21no—
31C3×D36—22no—
32C3×Dic18—22no—
33C3×C9⋊C8—22no—
34C3×#488—91no—
35#5068—31no—
36C2×C3×D12—31no—
37C2×C3×Dic6—31no—
38C32×C4⋊C4—22no—
39C32×C4⋊C4C2×D312yes—
40C32×C42C2×D311yescharacteristic
41C3×(C2×D3)⋊C4—62no—
42C2×C3×C3⋊C8—32no—
43C2×D36C22×C311yescharacteristic
44C2×Dic18C22×C311yescharacteristic
45C9×C4⋊C4—24no—
46C9×C4⋊C4—22no—
47C9×C4⋊C4—22no—
48C9×C4⋊C4C22×C312yes—
49C42×C9—21no—
50C42×C9C22×C311yescharacteristic
51(C2×D9)⋊C4—22no—
52C2×C9⋊C8C22×C312yes—
53C22×C3×C9C2×D411yescharacteristic
54C2×C3×D9—41no—
55C2×C3×D9—42no—
56C3×C4×C9—22no—
57C3×C4×C9—42no—
58C3×C4×C9#4112yes—
59C3×Dic9—41no—
60C3×#125—21no—
61C3×#125D911yescharacteristic, complemented
62C3×#125C3×D311yescharacteristic
63C3×#124—91no—
64#875—31no—
65C3×#103—92no—
66C3×#102—92no—
67C3×C4×C8—91no—
68#810—32no—
69#809—32no—
70C4×C3⋊C8—31no—
71C22×C3×D3—61no—
72C2×C32×C4—22no—
73C2×C32×C4#6712yes—
74C2×C32×C4C22×D311yescharacteristic
75C2×C3×Dic3—61no—
76C3×D12—62no—
77C3×Dic6—62no—
78C22×D9—21no—
79C3×C3⋊C8—62no—
80C2×C4×C9—24no—
81C2×C4×C9—22no—
82C2×C4×C9—22no—
83C2×C4×C9—21no—
84C2×C4×C9C3×D412yes—
85C2×C4×C9C23×C311yescharacteristic
86C2×Dic9—21no—
87D36—22no—
88Dic18—22no—
89C9⋊C8—22no—
90#488—91noSylow
91C2×C3×C9#12411yescharacteristic
92C2×C3×C9#13512yes—
93C3×D9—81no—
94C2×C3×Q8—91no—
95C2×C3×D4—91no—
96C2×D12—31no—
97C2×Dic6—31no—
98C2×C3×C8—92no—
99C3×C4⋊C4—24no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4C2×D912yes—
104C3×C4⋊C4C2×C3×D312yes—
105C3×C22⋊C4—182no—
106C3×C42—21no—
107C3×C42C2×D911yescharacteristic
108C3×C42C2×C3×D311yescharacteristic
109(C2×D3)⋊C4—62no—
110C2×C3⋊C8—32no—
111C22×C32C2×#6711yescharacteristic
112C2×C3×D3—121no—
113C2×C3×D3—122no—
114C32×C4—22no—
115C32×C4—42no—
116C32×C4#23912yes—
117C3×Dic3—121no—
118C22×C9—21no—
119C22×C9C2×C3×D411yescharacteristic
120C2×D9—41no—
121C2×D9—42no—
122C4×C9—22no—
123C4×C9—22no—
124C4×C9—42no—
125C4×C9—44no—
126C4×C9—42no—
127C4×C9C3×#4112yes—
128Dic9—41no—
129#125C3×D911yescharacteristic, complemented
130#124—91no—
131#103—92no—
132#102—92no—
133C4×C8—91no—
134C3×C9#48811yescharacteristic, complemented, Sylow
135C23×C3—181no—
136C22×D3—61no—
137C3×Q8—182no—
138C3×D4—182no—
139C2×C3×C4—24no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—21no—
144C2×C3×C4—181no—
145C2×C3×C4#61112yes—
146C2×C3×C4C22×D911yescharacteristic
147C2×C3×C4C3×#6712yes—
148C2×C3×C4C22×C3×D311yescharacteristic
149C2×Dic3—61no—
150D12—62no—
151Dic6—62no—
152C3×C8—182no—
153C3⋊C8—62no—
154C2×C32#94711yescharacteristic
155C2×C32#95012yes—
156C3×D3—241no—
157C2×C9—21no—
158C2×C9—22no—
159C2×C9C3×#12411yescharacteristic
160C2×C9C3×#13512yes—
161D9—81no—
162C2×Q8—91no—
163C2×D4—91no—
164C2×C8—92no—
165C4⋊C4—22no—
166C4⋊C4C2×C3×D912yes—
167C22⋊C4—182no—
168C42C2×C3×D911yescharacteristic
169C22×C3—21no—
170C22×C3—361no—
171C22×C3—362no—
172C22×C3C2×#61111yescharacteristic
173C22×C3C2×C3×#6711yescharacteristic
174C2×D3—121no—
175C2×D3—122no—
176C3×C4—22no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—42no—
180C3×C4—44no—
181C3×C4—42no—
182C3×C4—42no—
183C3×C4—361no—
184C3×C4#370112yes—
185C3×C4C3×#23912yes—
186Dic3—121no—
187C32#506811yescharacteristic
188C9—21no—
189C9C3×#48811yescharacteristic, complemented
190C23—181no—
191Q8—182no—
192D4—182no—
193C2×C4—22no—
194C2×C4—181no—
195C2×C4C3×#61112yes—
196C2×C4C22×C3×D911yescharacteristic
197C8—182no—
198C2×C3—21no—
199C2×C3—22no—
200C2×C3—721no—
201C2×C3#6350911yescharacteristic
202C2×C3#6351312yes—
203C2×C3C3×#94711yescharacteristic
204C2×C3C3×#95012yes—
205D3—241no—
206C22—361no—
207C22—362no—
208C22C2×C3×#61111yescharacteristic
209C4—22no—
210C4—42no—
211C4—361no—
212C4C3×#370112yes—
213C3—21no—
214C3#1058874911yescharacteristic, direct product factor
215C3C3×#506811yescharacteristic
216C2—721no—
217C2C3×#6350911yescharacteristic
218C2C3×#6351312yes—
subgroupG/H
centerC22×C3C2×#611
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#125C2
socleC22×C32C2×#67
prime radicalC2×C3×D36C22
hypercenterC3×#125D9
hypocenterC9C3×#488
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
1. C3×C9×#125C2semidirect
4. C3×#63368C2semidirect
5. C3×C4×C9⋊C8C2semidirect
7. #10588749C3direct (N × H)
21. C9×#125C2×C3semidirect
24. #63368C2×C3semidirect
25. C4×C9⋊C8C2×C3semidirect
61. C3×#125D9semidirect
129. #125C3×D9semidirect
134. C3×C9#488semidirect
189. C9C3×#488semidirect
214. C3#10588749direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1252
C3×#634372
C3×#633692
C3×#633682
C3×C4×C9⋊C82
C3×#50683
#105887493