Finite Group Databasebeta

← C3×#67629 #11771243

Subgroups — C3×#67629 #11771243

Order 1152.

493 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 493 conjugacy classes of subgroups — too many to draw. Only its 114 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×#381C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3C3×#1306—31nomaximal
4#67629C311yesmaximal, characteristic, direct product factor
5C23×C32×C4C2211yescharacteristic
6C2×C32×C22⋊C4C412yes—
7C2×C3×#208—22no—
8C32×#95—22no—
9C3×#830—22no—
10C3×#830C414yescomplemented
11C3×#407—32no—
12C3×#381—21no—
13C3×#381D311yescharacteristic
14C3×#381C2×C311yescharacteristic
15#5207C2×C312yes—
16C24×C32C2×C411yescharacteristic
17C22×C32×C4—22no—
18C22×C32×C4—42no—
19C22×C32×C4C2×C412yes—
20C22×C32×C4D412yes—
21C22×C32×C4D411yescharacteristic
22C22×C32×C4Q811yescharacteristic
23C32×C22⋊C4—42no—
24C3×#208—44no—
25C2×C3×C3⋊C8—24no—
26#1306—31noSylow
27C23×C3×C4—21no—
28C23×C3×C4C2×D311yescharacteristic
29C23×C3×C4C22×C311yescharacteristic
30C2×C3×M16—62no—
31C2×C3×C22⋊C4—22no—
32C2×C3×C22⋊C4Dic312yes—
33C2×C3×C22⋊C4C3×C412yes—
34C2×#208—22no—
35C3×C22⋊C8—34no—
36C3×C22⋊C8—62no—
37C3×#95—24no—
38C3×#95—22no—
39C3×#95—22no—
40#830—22no—
41#830C3×C414yescomplemented
42C23×C32—22no—
43C23×C32—42no—
44C23×C32C4211yescharacteristic
45C23×C32C22⋊C411yescharacteristic
46C23×C32C4⋊C411yescharacteristic
47C2×C32×C4—24no—
48C2×C32×C4—42no—
49C2×C32×C4—41no—
50C2×C32×C4—41no—
51C2×C32×C4—44no—
52C2×C32×C4—42no—
53C2×C32×C4C22⋊C412yes—
54C2×C32×C4C4⋊C412yes—
55C3×C3⋊C8—44no—
56#407—32no—
57#381C3×D311yescharacteristic
58C24×C3—21no—
59C24×C3C2×Dic311yescharacteristic
60C24×C3C2×C3×C411yescharacteristic
61C22×C3×C4—24no—
62C22×C3×C4—22no—
63C22×C3×C4—22no—
64C22×C3×C4—21no—
65C22×C3×C4—22no—
66C22×C3×C4—21no—
67C22×C3×C4—22no—
68C22×C3×C4—42no—
69C22×C3×C4—42no—
70C22×C3×C4—44no—
71C22×C3×C4Dic611yescharacteristic
72C22×C3×C4C4×D312yes—
73C22×C3×C4D1211yescharacteristic
74C22×C3×C4#6712yes—
75C22×C3×C4C2×C3×C412yes—
76C22×C3×C4C3×D411yescharacteristic
77C22×C3×C4C3×D412yes—
78C22×C3×C4C3×Q811yescharacteristic
79C3×M16—124no—
80C2×C3×C8—64no—
81C3×C22⋊C4—44no—
82C3×C22⋊C4—42no—
83C3×C22⋊C4—42no—
84#208—44no—
85C2×C3⋊C8—24no—
86C22×C32—22no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—22no—
90C22×C32—22no—
91C22×C32—44no—
92C22×C32#9511yescharacteristic
93C22×C32#9912yes—
94C32×C4—22no—
95C32×C4—22no—
96C32×C4—82no—
97C23×C4C2×C3×D311yescharacteristic
98C2×M16—62no—
99C2×C22⋊C4C3×Dic312yes—
100C22⋊C8—34no—
101C22⋊C8—62no—
102#95—22no—
103C23×C3—24no—
104C23×C3—22no—
105C23×C3—22no—
106C23×C3—21no—
107C23×C3—21no—
108C23×C3—21no—
109C23×C3—42no—
110C23×C3—42no—
111C23×C3—44no—
112C23×C3C4×Dic311yescharacteristic
113C23×C3C4⋊Dic311yescharacteristic
114C23×C3#21711yescharacteristic
115C23×C3C3×C4211yescharacteristic
116C23×C3C3×C22⋊C411yescharacteristic
117C23×C3C3×C4⋊C411yescharacteristic
118C2×C3×C4—24no—
119C2×C3×C4—24no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—44no—
123C2×C3×C4—41no—
124C2×C3×C4—42no—
125C2×C3×C4—41no—
126C2×C3×C4—42no—
127C2×C3×C4—41no—
128C2×C3×C4—41no—
129C2×C3×C4—42no—
130C2×C3×C4—44no—
131C2×C3×C4—42no—
132C2×C3×C4—44no—
133C2×C3×C4—48no—
134C2×C3×C4—44no—
135C2×C3×C4—44no—
136C2×C3×C4—42no—
137C2×C3×C4—42no—
138C2×C3×C4Dic3⋊C412yes—
139C2×C3×C4(C2×D3)⋊C412yes—
140C2×C3×C4C3×C22⋊C412yes—
141C2×C3×C4C3×C4⋊C412yes—
142C3×C8—124no—
143C3⋊C8—44no—
144C2×C32—22no—
145C2×C32—41no—
146C2×C32—41no—
147C2×C32#34211yescharacteristic
148C2×C32#34412yes—
149C24C2×C3×Dic311yescharacteristic
150C22×C4—22no—
151C22×C4—42no—
152C22×C4C3×Dic611yescharacteristic
153C22×C4C3×C4×D312yes—
154C22×C4C3×D1211yescharacteristic
155C22×C4C3×#6712yes—
156M16—124no—
157C2×C8—64no—
158C22⋊C4—42no—
159C22×C3—24no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—22no—
167C22×C3—22no—
168C22×C3—21no—
169C22×C3—21no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—21no—
173C22×C3—22no—
174C22×C3—42no—
175C22×C3—42no—
176C22×C3—48no—
177C22×C3—44no—
178C22×C3—44no—
179C22×C3C3⋊#9511yescharacteristic
180C22×C3#83412yes—
181C22×C3C3×#9511yescharacteristic
182C22×C3C3×#9912yes—
183C3×C4—22no—
184C3×C4—22no—
185C3×C4—22no—
186C3×C4—22no—
187C3×C4—42no—
188C3×C4—42no—
189C3×C4—84no—
190C3×C4—82no—
191C3×C4—82no—
192C32#130611yescharacteristic, complemented, Sylow
193C23—22no—
194C23—42no—
195C23C3×C4×Dic311yescharacteristic
196C23C3×C4⋊Dic311yescharacteristic
197C23C3×#21711yescharacteristic
198C2×C4—24no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4C3×Dic3⋊C412yes—
205C2×C4C3×(C2×D3)⋊C412yes—
206C8—124no—
207C2×C3—24no—
208C2×C3—22no—
209C2×C3—22no—
210C2×C3—21no—
211C2×C3—22no—
212C2×C3—42no—
213C2×C3—42no—
214C2×C3—41no—
215C2×C3—41no—
216C2×C3—41no—
217C2×C3—41no—
218C2×C3#452611yescharacteristic
219C2×C3#453312yes—
220C2×C3C3×#34211yescharacteristic
221C2×C3C3×#34412yes—
222C22—22no—
223C22—21no—
224C22—21no—
225C22—22no—
226C22—22no—
227C22—44no—
228C22C3×C3⋊#9511yescharacteristic
229C22C3×#83412yes—
230C4—22no—
231C4—22no—
232C4—82no—
233C3—21no—
234C3#6762911yescharacteristic, direct product factor
235C3C3×#130611yescharacteristic, complemented
236C2—22no—
237C2—41no—
238C2—41no—
239C2C3×#452611yescharacteristic
240C2C3×#453312yes—
subgroupG/H
centerC22×C3C3⋊#95
commutatorC23×C3C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×#381C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC3×#381D3
hypocenterC3C3×#1306
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
4. #67629C3direct (N × H)
10. C3×#830C4semidirect
41. #830C3×C4semidirect
192. C32#1306semidirect
234. C3#67629direct (N × H)
235. C3C3×#1306semidirect

Maximal subgroups

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

subgroupindex
C32×#3812
C3×#52072
C3×#13063
#676293