Finite Group Databasebeta

← C3×#67688 #11771105

Subgroups — C3×#67688 #11771105

Order 1152.

475 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 475 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C32×#407C211yesmaximal, characteristic
2C2×C3×#830C212yesmaximal
3C3×#1298—31nomaximal
4#67688C311yesmaximal, characteristic, direct product factor
5C23×C32×C4C2211yescharacteristic
6C2×C32×M16C412yes—
7C22×C3×C3⋊C8—22no—
8C32×C22⋊C8—22no—
9C3×#830—22no—
10C3×#830C414yes—
11C3×#407—21no—
12C3×#407D311yescharacteristic
13C3×#407C2×C311yescharacteristic
14C2×C3×C22⋊C8—32no—
15C2×#830C2×C312yes—
16C24×C32Q811yescharacteristic
17C22×C32×C4—42no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C32×C4C2×C412yes—
20C22×C32×C4D412yes—
21C22×C32×C4D411yescharacteristic
22C32×M16—42no—
23C2×C32×C8—22no—
24C2×C3×C3⋊C8—24no—
25C2×C3×C3⋊C8—44no—
26#1298—31noSylow
27C23×C3×C4—21no—
28C23×C3×C4C2×D311yescharacteristic
29C23×C3×C4C22×C311yescharacteristic
30C2×C3×M16—22no—
31C2×C3×M16Dic312yes—
32C2×C3×M16C3×C412yes—
33C22×C3×C8—62no—
34C22×C3⋊C8—22no—
35C3×C22⋊C8—24no—
36C3×C22⋊C8—22no—
37C3×C22⋊C8—22no—
38C3×C22⋊C8—34no—
39C3×C22⋊C8—62no—
40#830—22no—
41#830C3×C414yes—
42C23×C32—24no—
43C23×C32—41no—
44C23×C32C4⋊C412yes—
45C23×C32C4⋊C411yescharacteristic
46C2×C32×C4—22no—
47C2×C32×C4—24no—
48C2×C32×C4—42no—
49C2×C32×C4—41no—
50C2×C32×C4C4211yescharacteristic
51C2×C32×C4C22⋊C412yes—
52C2×C32×C4C22⋊C411yescharacteristic
53C32×C8—42no—
54C3×C3⋊C8—44no—
55#407C3×D311yescharacteristic
56C2×C22⋊C8—32no—
57C24×C3—21no—
58C24×C3Dic611yescharacteristic
59C24×C3C3×Q811yescharacteristic
60C22×C3×C4—22no—
61C22×C3×C4—21no—
62C22×C3×C4—21no—
63C22×C3×C4—22no—
64C22×C3×C4—42no—
65C22×C3×C4—42no—
66C22×C3×C4—44no—
67C22×C3×C4C4×D312yes—
68C22×C3×C4D1211yescharacteristic
69C22×C3×C4C2×Dic311yescharacteristic
70C22×C3×C4#6712yes—
71C22×C3×C4C2×C3×C412yes—
72C22×C3×C4C2×C3×C411yescharacteristic
73C22×C3×C4C3×D411yescharacteristic
74C22×C3×C4C3×D412yes—
75C3×M16—44no—
76C3×M16—42no—
77C3×M16—42no—
78C2×C3×C8—24no—
79C2×C3×C8—22no—
80C2×C3×C8—22no—
81C2×C3×C8—64no—
82C2×C3×C8—124no—
83C2×C3⋊C8—24no—
84C2×C3⋊C8—44no—
85C22×C32—21no—
86C22×C32—22no—
87C22×C32—22no—
88C22×C32—22no—
89C22×C32—44no—
90C22×C32#9511yescharacteristic
91C22×C32#10814yes—
92C32×C4—21no—
93C32×C4—22no—
94C32×C4#9912yes—
95C23×C4C2×C3×D311yescharacteristic
96C2×M16C3×Dic312yes—
97C22×C8—62no—
98C22⋊C8—22no—
99C22⋊C8—34no—
100C22⋊C8—62no—
101C23×C3—24no—
102C23×C3—24no—
103C23×C3—22no—
104C23×C3—21no—
105C23×C3—44no—
106C23×C3—41no—
107C23×C3—41no—
108C23×C3—42no—
109C23×C3Dic3⋊C412yes—
110C23×C3C4⋊Dic311yescharacteristic
111C23×C3C3×C4⋊C412yes—
112C23×C3C3×C4⋊C411yescharacteristic
113C2×C3×C4—24no—
114C2×C3×C4—24no—
115C2×C3×C4—22no—
116C2×C3×C4—24no—
117C2×C3×C4—22no—
118C2×C3×C4—21no—
119C2×C3×C4—22no—
120C2×C3×C4—21no—
121C2×C3×C4—44no—
122C2×C3×C4—42no—
123C2×C3×C4—41no—
124C2×C3×C4—42no—
125C2×C3×C4—41no—
126C2×C3×C4—44no—
127C2×C3×C4—42no—
128C2×C3×C4C4×Dic311yescharacteristic
129C2×C3×C4(C2×D3)⋊C412yes—
130C2×C3×C4#21711yescharacteristic
131C2×C3×C4C3×C4211yescharacteristic
132C2×C3×C4C3×C22⋊C412yes—
133C2×C3×C4C3×C22⋊C411yescharacteristic
134C3×C8—44no—
135C3×C8—42no—
136C3×C8—42no—
137C3×C8—124no—
138C3⋊C8—44no—
139C2×C32—24no—
140C2×C32—41no—
141C2×C32#34112yes—
142C2×C32#34211yescharacteristic
143C24C3×Dic611yescharacteristic
144C22×C4—42no—
145C22×C4C3×C4×D312yes—
146C22×C4C3×D1211yescharacteristic
147C22×C4C2×C3×Dic311yescharacteristic
148C22×C4C3×#6712yes—
149M16—42no—
150C2×C8—22no—
151C2×C8—64no—
152C2×C8—124no—
153C22×C3—22no—
154C22×C3—22no—
155C22×C3—22no—
156C22×C3—22no—
157C22×C3—22no—
158C22×C3—21no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—21no—
162C22×C3—24no—
163C22×C3—21no—
164C22×C3—42no—
165C22×C3—42no—
166C22×C3—42no—
167C22×C3—44no—
168C22×C3—44no—
169C22×C3—48no—
170C22×C3#82214yes—
171C22×C3C3⋊#9511yescharacteristic
172C22×C3C3×#9511yescharacteristic
173C22×C3C3×#10814yes—
174C3×C4—22no—
175C3×C4—22no—
176C3×C4—21no—
177C3×C4—22no—
178C3×C4—21no—
179C3×C4—22no—
180C3×C4—42no—
181C3×C4#83412yes—
182C3×C4C3×#9912yes—
183C32#129811yescharacteristic, complemented, Sylow
184C23—24no—
185C23—41no—
186C23C3×Dic3⋊C412yes—
187C23C3×C4⋊Dic311yescharacteristic
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4C3×C4×Dic311yescharacteristic
193C2×C4C3×(C2×D3)⋊C412yes—
194C2×C4C3×#21711yescharacteristic
195C8—42no—
196C8—124no—
197C2×C3—24no—
198C2×C3—24no—
199C2×C3—21no—
200C2×C3—22no—
201C2×C3—44no—
202C2×C3—42no—
203C2×C3—41no—
204C2×C3—41no—
205C2×C3#452611yescharacteristic
206C2×C3#455812yes—
207C2×C3C3×#34112yes—
208C2×C3C3×#34211yescharacteristic
209C22—22no—
210C22—22no—
211C22—21no—
212C22—22no—
213C22—44no—
214C22C3×#82214yes—
215C22C3×C3⋊#9511yescharacteristic
216C4—22no—
217C4—21no—
218C4C3×#83412yes—
219C3—21no—
220C3#6768811yescharacteristic, direct product factor
221C3C3×#129811yescharacteristic, complemented
222C2—24no—
223C2—41no—
224C2C3×#452611yescharacteristic
225C2C3×#455812yes—
subgroupG/H
centerC2×C3×C4#217
commutatorC2×C3×C4C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×#407C2
socleC22×C32#95
prime radicalC24×C32Q8
cosocleC23×C3×C4C22×C3
hypercenterC3×#407D3
hypocenterC3C3×#1298
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
4. #67688C3direct (N × H)
183. C32#1298semidirect
220. C3#67688direct (N × H)
221. C3C3×#1298semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
C2×C3×#8302
C3×#12983
#676883