Finite Group Databasebeta

← C3×#10590874 #13157836

Subgroups — C3×#10590874 #13157836

Order 1728.

482 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 136 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×#63872C212yesmaximal
2C3×C8×C3⋊Dic3C211yesmaximal, characteristic
3C32×#817C212yesmaximal
4C3×#63576C212yesmaximal
5C3×#4858—32nomaximal
6#10590874C311yesmaximal, characteristic, direct product factor
7C2×C33×C8C2211yescharacteristic
8C3×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
10C32×C4⋊Dic3C2214yes—
11C3×Dic3⋊Dic3—24no—
12C3×#890—34no—
13#63872C2×C312yes—
14C32×#106—32no—
15C8×C3⋊Dic3C2×C311yescharacteristic
16C3×#817—22no—
17C3×#817D312yes—
18C3×#817C2×C312yes—
19C3×C8×Dic3—32no—
20C3×C8×Dic3—61no—
21C3×#807—34no—
22#63576C2×C312yes—
23C2×C33×C4C2311yescharacteristic
24C2×C3×C3⋊Dic3D412yes—
25C2×C32×Dic3—24no—
26C33×C8Q812yes—
27C3×C3⋊(C3⋊C8)Q812yes—
28C3×#499—91no—
29#4858—32no—
30C2×C32×C8—21no—
31C2×C32×C8—22no—
32C2×C32×C8—41no—
33C2×C32×C8C2×D312yes—
34C2×C32×C8C22×C311yescharacteristic
35C32×C4⋊C4—34no—
36C4×C3⋊Dic3C22×C311yescharacteristic
37C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
38C3×C4⋊Dic3—24no—
39C3×C4⋊Dic3—64no—
40C3×C4⋊Dic3C2×D314yes—
41C3×C4⋊Dic3C22×C314yes—
42C3×Dic3⋊C4—64no—
43C3×C4×Dic3—32no—
44C3×C4×Dic3—61no—
45C2×C3×C3⋊C8—32no—
46C2×C3×C3⋊C8—61no—
47Dic3⋊Dic3—24no—
48C22×C33C2×D411yescharacteristic
49C33×C4C2×Q811yescharacteristic
50C33×C4C2×Q811yescharacteristic
51C3×C3⋊Dic3—22no—
52C32×Dic3—44no—
53C3×#125—92no—
54#890—34no—
55C3×#107—92no—
56C3×#106—32no—
57C3×#106—32no—
58C3×#106—62no—
59C3×C4×C8—91no—
60#817C3×D312yes—
61C8×Dic3—32no—
62C8×Dic3—61no—
63#807—34no—
64C2×C32×C4—21no—
65C2×C32×C4—22no—
66C2×C32×C4—41no—
67C2×C32×C4—64no—
68C2×C32×C4C22×D312yes—
69C2×C32×C4C23×C311yescharacteristic
70C2×C3⋊Dic3C3×D412yes—
71C2×C3×Dic3—24no—
72C2×C3×Dic3—24no—
73C2×C3×Dic3—34no—
74C2×C3×Dic3—44no—
75C2×C3×Dic3—62no—
76C32×C8—22no—
77C32×C8—24no—
78C32×C8—42no—
79C32×C8Dic614yes—
80C32×C8C3×Q812yes—
81C3⋊(C3⋊C8)C3×Q812yes—
82C3×C3⋊C8—34no—
83C3×C3⋊C8—62no—
84#499—91noSylow
85C2×C33C4⋊Q811yescharacteristic
86C2×C33#13512yes—
87C2×C3×C8—21no—
88C2×C3×C8—22no—
89C2×C3×C8—41no—
90C2×C3×C8—91no—
91C2×C3×C8D3211yescharacteristic
92C2×C3×C8C2×C3×D312yes—
93C3×C4⋊C4—34no—
94C3×C4⋊C4—34no—
95C3×C4⋊C4—64no—
96C3×C4⋊C4—184no—
97C3×C42—91no—
98C4⋊Dic3—64no—
99C4⋊Dic3C2×C3×D314yes—
100Dic3⋊C4—64no—
101C4×Dic3—32no—
102C4×Dic3—61no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—61no—
105C22×C32—21no—
106C22×C32—22no—
107C22×C32—41no—
108C22×C32D3×D412yes—
109C22×C32C2×C3×D411yescharacteristic
110C32×C4—21no—
111C32×C4—21no—
112C32×C4—22no—
113C32×C4—22no—
114C32×C4—41no—
115C32×C4—41no—
116C32×C4—124no—
117C32×C4C2×Dic612yes—
118C32×C4D3×Q812yes—
119C32×C4C2×C3×Q811yescharacteristic
120C32×C4C2×C3×Q811yescharacteristic
121C3⋊Dic3—22no—
122C3×Dic3—44no—
123C3×Dic3—44no—
124C3×Dic3—64no—
125C3×Dic3—64no—
126C3×Dic3—84no—
127#125—92no—
128#107—92no—
129#106—32no—
130C4×C8—91no—
131C33#49911yescharacteristic, complemented, Sylow
132C2×C3×C4—22no—
133C2×C3×C4—21no—
134C2×C3×C4—41no—
135C2×C3×C4—64no—
136C2×C3×C4—64no—
137C2×C3×C4—92no—
138C2×C3×C4—124no—
139C2×C3×C4C2×D3211yescharacteristic
140C2×C3×C4C22×C3×D312yes—
141C2×Dic3—24no—
142C2×Dic3—34no—
143C2×Dic3—62no—
144C3×C8—24no—
145C3×C8—22no—
146C3×C8—42no—
147C3×C8—92no—
148C3×C8#62712yes—
149C3×C8C3×Dic614yes—
150C3⋊C8—34no—
151C3⋊C8—62no—
152C2×C32—22no—
153C2×C32—24no—
154C2×C32—22no—
155C2×C32—21no—
156C2×C32—41no—
157C2×C32—42no—
158C2×C32#88812yes—
159C2×C32#91614yes—
160C2×C32C3×C4⋊Q811yescharacteristic
161C2×C32C3×#13512yes—
162C2×C8—91no—
163C2×C8C3×D3211yescharacteristic
164C4⋊C4—34no—
165C4⋊C4—184no—
166C42—91no—
167C22×C3—21no—
168C22×C3—22no—
169C22×C3—41no—
170C22×C3#380211yescharacteristic
171C22×C3C3×D3×D412yes—
172C3×C4—21no—
173C3×C4—22no—
174C3×C4—22no—
175C3×C4—21no—
176C3×C4—41no—
177C3×C4—41no—
178C3×C4—124no—
179C3×C4—124no—
180C3×C4—182no—
181C3×C4—244no—
182C3×C4#379711yescharacteristic
183C3×C4C2×#62711yescharacteristic
184C3×C4C2×C3×Dic612yes—
185C3×C4C3×D3×Q812yes—
186Dic3—44no—
187Dic3—64no—
188Dic3—64no—
189C32—21no—
190C32—22no—
191C32—41no—
192C32#485812yescomplemented
193C32C3×#49911yescharacteristic, complemented
194C2×C4—64no—
195C2×C4—92no—
196C2×C4C2×C3×D3211yescharacteristic
197C8—92no—
198C8C3×#62712yes—
199C2×C3—22no—
200C2×C3—24no—
201C2×C3—22no—
202C2×C3—21no—
203C2×C3—42no—
204C2×C3—41no—
205C2×C3#6380912yes—
206C2×C3#6391911yescharacteristic
207C2×C3C3×#88812yes—
208C2×C3C3×#91614yes—
209C22C3×#380211yescharacteristic
210C4—124no—
211C4—182no—
212C4C3×#379711yescharacteristic
213C4C2×C3×#62711yescharacteristic
214C3—22no—
215C3—21no—
216C3—41no—
217C3#1059087411yescharacteristic, direct product factor
218C3C3×#485812yescomplemented
219C2C3×#6380912yes—
220C2C3×#6391911yescharacteristic
subgroupG/H
centerC22×C3#3802
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socle, prime radicalC22×C33C2×D4
hypercenterC2×C3×C8D32
hypocenterC32C3×#499
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
6. #10590874C3direct (N × H)
131. C33#499semidirect
192. C32#4858semidirect
193. C32C3×#499semidirect
217. C3#10590874direct (N × H)
218. C3C3×#4858semidirect

Maximal subgroups

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

subgroupindex
C3×#638722
C3×C8×C3⋊Dic32
C32×#8172
C3×#635762
C3×#48583
#105908743