Finite Group Databasebeta

← C3×#64226 #11724281

Subgroups — C3×#64226 #11724281

Order 864.

226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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×#3798C211yesmaximal, characteristic
2C3×#3797C211yesmaximal, characteristic, complemented
3C3×#3788C211yesmaximal, characteristic, complemented
4C3×#3776C212yesmaximal, complemented
5C3×#3775C212yesmaximal, complemented
6#64226C311yesmaximal, characteristic, direct product factor
7C3×C4×C3⋊D3C2211yescharacteristic
8C32×C4×D3—21no—
9C32×Dic6—21no—
10C3×#627C2212yes—
11C3×#627C2211yescharacteristic
12C3×#626—21no—
13C3×#625C2211yescharacteristic
14C3×#624—21no—
15C3×#622C2212yes—
16C3×D3×Q8—61no—
17C3×#235—61no—
18#3798C2×C311yescharacteristic
19#3797C2×C311yescharacteristic, complemented
20#3788C2×C311yescharacteristic, complemented
21#3776C2×C312yescomplemented
22#3775C2×C312yescomplemented
23C2×C3×C3⋊D3D411yescharacteristic
24C2×C32×D3—21no—
25C33×C4D411yescharacteristic
26C3×C3⋊Dic3C2311yescharacteristic
27C32×Dic3—22no—
28C32×Dic3—21no—
29C3×#137—91nomaximal
30C32×Q8—61no—
31C2×C32×C4—61no—
32C4×C3⋊D3C22×C311yescharacteristic
33C3×#67—61no—
34C3×#67—61no—
35C3×D12—61no—
36C3×C4×D3—21no—
37C3×C4×D3—21no—
38C3×C4×D3—41no—
39C3×C4×D3—61no—
40C3×C4×D3—61no—
41C3×C4×D3—62no—
42C3×Dic6—21no—
43C3×Dic6—21no—
44C3×Dic6—41no—
45C3×Dic6—61no—
46C3×Dic6—62no—
47#627C22×C312yes—
48#627C22×C311yescharacteristic
49#626—21no—
50#625C22×C311yescharacteristic
51#624—21no—
52#622C22×C312yes—
53C2×C33C2×D411yescharacteristic
54C3×C3⋊D3—21no—
55C32×D3—41no—
56C3×#41—91no—
57C2×C3×Q8—91no—
58D3×Q8—61no—
59#235—61no—
60C3×Q16—92no—
61C3×SD16—92no—
62C3×M16—91no—
63C22×C32—61no—
64C2×C3⋊D3C3×D411yescharacteristic
65C2×C3×D3—21no—
66C2×C3×D3—21no—
67C2×C3×D3—41no—
68C2×C3×D3—61no—
69C2×C3×D3—61no—
70C32×C4—21no—
71C32×C4—21no—
72C32×C4—41no—
73C32×C4—41no—
74C32×C4—62no—
75C32×C4—61no—
76C32×C4C3×D411yescharacteristic
77C3⋊Dic3C23×C311yescharacteristic
78C3×Dic3—22no—
79C3×Dic3—21no—
80C3×Dic3—22no—
81C3×Dic3—21no—
82C3×Dic3—42no—
83C3×Dic3—41no—
84C3×Dic3—61no—
85C3×Dic3—61no—
86#137—91noSylow
87C33#13711yescharacteristic, complemented, Sylow
88C3×Q8—61no—
89C3×Q8—61no—
90C3×Q8—92no—
91C3×Q8—91no—
92C3×Q8—121no—
93C3×D4—91no—
94C3×D4—181no—
95C2×C3×C4—61no—
96C2×C3×C4—61no—
97C2×C3×C4—91no—
98C2×C3×C4—121no—
99C2×C3×C4—181no—
100#67—61no—
101#67—61no—
102D12—61no—
103C4×D3—21no—
104C4×D3—61no—
105C4×D3—61no—
106C4×D3—62no—
107Dic6—21no—
108Dic6—61no—
109Dic6—62no—
110C3×C8—92no—
111C2×C32—21no—
112C2×C32—21no—
113C2×C32—41no—
114C2×C32—41no—
115C2×C32—121no—
116C2×C32C2×C3×D411yescharacteristic
117C3⋊D3—21no—
118C3×D3—41no—
119C3×D3—42no—
120C3×D3—41no—
121C3×D3—62no—
122C3×D3—121no—
123#41—91no—
124C2×Q8—91no—
125Q16—92no—
126SD16—92no—
127M16—91no—
128C22×C3—61no—
129C22×C3—61no—
130C22×C3—91no—
131C22×C3—121no—
132C2×D3—21no—
133C2×D3—61no—
134C2×D3—61no—
135C3×C4—21no—
136C3×C4—21no—
137C3×C4—41no—
138C3×C4—41no—
139C3×C4—62no—
140C3×C4—61no—
141C3×C4—61no—
142C3×C4—62no—
143C3×C4—91no—
144C3×C4—121no—
145C3×C4—122no—
146C3×C4GO+(4,𝔽2)11yescharacteristic
147Dic3—22no—
148Dic3—21no—
149Dic3—61no—
150Dic3—61no—
151C32—21no—
152C32—21no—
153C32—41no—
154C32—41no—
155C32C3×#13711yescharacteristic, complemented
156Q8—61no—
157Q8—92no—
158Q8—91no—
159D4—91no—
160D4—181no—
161C2×C4—61no—
162C2×C4—91no—
163C2×C4—181no—
164C8—92no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3—41no—
168C2×C3—41no—
169C2×C3—121no—
170C2×C3—122no—
171C2×C3—121no—
172C2×C3—181no—
173C2×C3C2×GO+(4,𝔽2)11yescharacteristic
174D3—41no—
175D3—62no—
176D3—121no—
177C22—61no—
178C22—91no—
179C4—61no—
180C4—62no—
181C4—91no—
182C4C3×GO+(4,𝔽2)11yescharacteristic
183C3—21no—
184C3—21no—
185C3—41no—
186C3—41no—
187C3#6422611yescharacteristic, direct product factor
188C2—121no—
189C2—181no—
190C2C2×C3×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C3C2×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C23×C3
FrattiniC2C2×C3×GO+(4,𝔽2)
FittingC33×C4D4
socleC2×C33C2×D4
prime radicalC3×#3798C2
hypercenterC3×C4GO+(4,𝔽2)
hypocenterC32C3×#137
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×#3797C2semidirect
3. C3×#3788C2semidirect
4. C3×#3776C2semidirect
5. C3×#3775C2semidirect
6. #64226C3direct (N × H)
19. #3797C2×C3semidirect
20. #3788C2×C3semidirect
21. #3776C2×C3semidirect
22. #3775C2×C3semidirect
87. C33#137semidirect
155. C32C3×#137semidirect
187. C3#64226direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#37982
C3×#37972
C3×#37882
C3×#37762
C3×#37752
#642263
C3×#1379