Finite Group Databasebeta

← C3×#63874 #11723199

Subgroups — C3×#63874 #11723199

Order 864.

434 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 120 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×C4×C3⋊D3C211yesmaximal, characteristic
2C32×C4×Dic3C212yesmaximal, complemented
3C3×#3724C212yesmaximal, complemented
4C3×#3722C212yesmaximal
5C3×#872—32nomaximal
6#63874C311yesmaximal, characteristic, direct product factor
7C22×C3×C3⋊D3C2211yescharacteristic
8C2×C33×C4C2211yescharacteristic
9C2×C3×C3⋊Dic3C2211yescharacteristic
10C3×C4×C3⋊D3C414yescomplemented
11C2×C32×Dic3C2214yes—
12C2×C4×C3⋊D3C2×C311yescharacteristic
13C2×C3×C4×D3—32no—
14C2×C3×C4×D3—61no—
15C32×C42—32no—
16C3×(C2×D3)⋊C4—34no—
17C3×Dic3⋊C4—34no—
18C3×C4×Dic3—22no—
19C3×C4×Dic3D312yescomplemented
20C3×C4×Dic3C2×C312yescomplemented
21#3724C2×C312yescomplemented
22#3722C2×C312yes—
23C22×C33C2311yescharacteristic
24C2×C3×C3⋊D3—22no—
25C2×C3×C3⋊D3C2×C412yes—
26C33×C4C2×C412yes—
27C3×C3⋊Dic3C2×C412yes—
28C32×Dic3—24no—
29C3×#117—91no—
30#872—32no—
31C22×C3⋊D3C22×C311yescharacteristic
32C22×C3×D3—32no—
33C22×C3×D3—61no—
34C2×C32×C4—21no—
35C2×C32×C4—22no—
36C2×C32×C4—34no—
37C2×C32×C4—41no—
38C2×C32×C4C2×D312yes—
39C2×C32×C4C22×C311yescharacteristic
40C2×C3⋊Dic3C22×C311yescharacteristic
41C4×C3⋊D3C3×C414yescomplemented
42C2×C3×Dic3—24no—
43C2×C3×Dic3—32no—
44C2×C3×Dic3—61no—
45C2×C3×Dic3C2×D314yes—
46C2×C3×Dic3C22×C314yes—
47C3×C4×D3—38no—
48C3×C4×D3—64no—
49C2×C33C22×C411yescharacteristic
50C2×C33#4112yes—
51C3×C3⋊D3—22no—
52C22×C3×C4—91no—
53C2×C4×D3—32no—
54C2×C4×D3—61no—
55C3×C4⋊C4—92no—
56C3×C22⋊C4—92no—
57C3×C42—32no—
58C3×C42—32no—
59C3×C42—62no—
60(C2×D3)⋊C4—34no—
61Dic3⋊C4—34no—
62C4×Dic3C3×D312yescomplemented
63C22×C32—21no—
64C22×C32—22no—
65C22×C32—41no—
66C22×C32C22×D312yes—
67C22×C32C23×C311yescharacteristic
68C2×C3⋊D3—22no—
69C2×C3⋊D3C2×C3×C412yes—
70C2×C3×D3—34no—
71C2×C3×D3—62no—
72C2×C3×D3—64no—
73C2×C3×D3—64no—
74C32×C4—22no—
75C32×C4—24no—
76C32×C4—42no—
77C32×C4—64no—
78C32×C4C4×D314yes—
79C32×C4C2×C3×C412yes—
80C3⋊Dic3C2×C3×C412yes—
81C3×Dic3—28no—
82C3×Dic3—24no—
83C3×Dic3—24no—
84C3×Dic3—34no—
85C3×Dic3—62no—
86#117—91noSylow
87C33#11711yescharacteristic, complemented, Sylow
88C23×C3—91no—
89C22×D3—32no—
90C22×D3—61no—
91C2×C3×C4—22no—
92C2×C3×C4—21no—
93C2×C3×C4—34no—
94C2×C3×C4—34no—
95C2×C3×C4—41no—
96C2×C3×C4—64no—
97C2×C3×C4—91no—
98C2×C3×C4—94no—
99C2×C3×C4D3211yescharacteristic
100C2×C3×C4C2×C3×D312yes—
101C2×Dic3—32no—
102C2×Dic3—61no—
103C2×Dic3C2×C3×D314yes—
104C4×D3—38no—
105C4×D3—64no—
106C2×C32—22no—
107C2×C32—21no—
108C2×C32—22no—
109C2×C32—24no—
110C2×C32—41no—
111C2×C32—42no—
112C2×C32C2×C4×D312yes—
113C2×C32#23514yes—
114C2×C32C22×C3×C411yescharacteristic
115C2×C32C3×#4112yes—
116C3⋊D3—22no—
117C3×D3—64no—
118C3×D3—64no—
119C22×C4—91no—
120C4⋊C4—92no—
121C22⋊C4—92no—
122C42—32no—
123C22×C3—21no—
124C22×C3—22no—
125C22×C3—41no—
126C22×C3—92no—
127C22×C3—182no—
128C22×C3C2×D3211yescharacteristic
129C22×C3C22×C3×D312yes—
130C2×D3—34no—
131C2×D3—62no—
132C2×D3—64no—
133C2×D3—64no—
134C3×C4—22no—
135C3×C4—24no—
136C3×C4—42no—
137C3×C4—68no—
138C3×C4—64no—
139C3×C4—64no—
140C3×C4—92no—
141C3×C4#62412yes—
142C3×C4C3×C4×D314yes—
143Dic3—24no—
144Dic3—34no—
145Dic3—62no—
146C32—21no—
147C32—22no—
148C32—41no—
149C32#87212yescomplemented
150C32C3×#11711yescharacteristic, complemented
151C23—91no—
152C2×C4—34no—
153C2×C4—91no—
154C2×C4—94no—
155C2×C4C3×D3211yescharacteristic
156C2×C3—24no—
157C2×C3—22no—
158C2×C3—21no—
159C2×C3—22no—
160C2×C3—42no—
161C2×C3—41no—
162C2×C3—182no—
163C2×C3#379812yes—
164C2×C3C2×#62411yescharacteristic
165C2×C3C2×C3×C4×D312yes—
166C2×C3C3×#23514yes—
167D3—64no—
168D3—64no—
169C22—92no—
170C22—182no—
171C22C2×C3×D3211yescharacteristic
172C4—64no—
173C4—92no—
174C4C3×#62412yes—
175C3—21no—
176C3—22no—
177C3—41no—
178C3#6387411yescharacteristic, direct product factor
179C3C3×#87212yescomplemented
180C2—182no—
181C2C3×#379812yes—
182C2C2×C3×#62411yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C4D32
commutatorC2×C32C22×C3×C4
FrattiniC22C2×C3×D32
FittingC2×C33×C4C22
socleC22×C33C23
prime radicalC22×C3×C3⋊D3C22
cosocleC22×C32C23×C3
hypocenterC32C3×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×Dic3C2semidirect
3. C3×#3724C2semidirect
6. #63874C3direct (N × H)
10. C3×C4×C3⋊D3C4semidirect
19. C3×C4×Dic3D3semidirect
20. C3×C4×Dic3C2×C3semidirect
21. #3724C2×C3semidirect
41. C4×C3⋊D3C3×C4semidirect
62. C4×Dic3C3×D3semidirect
87. C33#117semidirect
149. C32#872semidirect
150. C32C3×#117semidirect
178. C3#63874direct (N × H)
179. C3C3×#872semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C3⋊D32
C32×C4×Dic32
C3×#37242
C3×#37222
C3×#8723
#638743