Finite Group Databasebeta

← C3×#67681 #11771413

Subgroups — C3×#67681 #11771413

Order 1152.

351 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 74 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
2C3×#4553C212yesmaximal, complemented
3C3×#1320—31nomaximal
4#67681C311yesmaximal, characteristic, direct product factor
5C23×C32×C4C411yescharacteristic
6C2×C32×M16C411yescharacteristic
7C2×C32×M16C2211yescharacteristic
8C32×C22⋊C8—22no—
9C3×#812—22no—
10C3×#407—21no—
11C3×#407D311yescharacteristic
12C3×#407C2×C311yescharacteristic
13C3×#349—32no—
14#4553C2×C312yescomplemented
15C24×C32C811yescharacteristic
16C22×C32×C4—21no—
17C22×C32×C4—21no—
18C22×C32×C4—41no—
19C22×C32×C4—41no—
20C22×C32×C4C811yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C32×M16—41no—
23C32×M16—41no—
24C2×C32×C8—21no—
25C2×C32×C8D412yes—
26C3×C3⋊C16—42no—
27#1320—31noSylow
28C23×C3×C4—21no—
29C23×C3×C4Dic311yescharacteristic
30C23×C3×C4C3×C411yescharacteristic
31C2×C3×M16—21no—
32C2×C3×M16—21no—
33C2×C3×M16Dic311yescharacteristic
34C2×C3×M16C3×C411yescharacteristic
35C2×C3×M16C2×D311yescharacteristic
36C2×C3×M16C22×C311yescharacteristic
37C3×M32—62no—
38C3×C22⋊C8—24no—
39C3×C22⋊C8—22no—
40C3×C22⋊C8—22no—
41#812—22no—
42C23×C32—21no—
43C23×C32—42no—
44C23×C32—41no—
45C23×C32C2×C811yescharacteristic
46C2×C32×C4—21no—
47C2×C32×C4—21no—
48C2×C32×C4—21no—
49C2×C32×C4—42no—
50C2×C32×C4—41no—
51C2×C32×C4—41no—
52C2×C32×C4—41no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C32×C4M1611yescharacteristic
55C32×C8—22no—
56C32×C8—41no—
57#407C3×D311yescharacteristic
58#349—32no—
59C24×C3—21no—
60C24×C3C3⋊C811yescharacteristic
61C24×C3C3×C811yescharacteristic
62C22×C3×C4—22no—
63C22×C3×C4—22no—
64C22×C3×C4—21no—
65C22×C3×C4—21no—
66C22×C3×C4—21no—
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—21no—
70C22×C3×C4—42no—
71C22×C3×C4—42no—
72C22×C3×C4—41no—
73C22×C3×C4—41no—
74C22×C3×C4—41no—
75C22×C3×C4—41no—
76C22×C3×C4C3⋊C811yescharacteristic
77C22×C3×C4C3×C811yescharacteristic
78C22×C3×C4C2×Dic311yescharacteristic
79C22×C3×C4C2×C3×C411yescharacteristic
80C3×M16—41no—
81C3×M16—41no—
82C3×M16—42no—
83C3×M16—42no—
84C3×M16—41no—
85C3×M16—41no—
86C2×C3×C8—22no—
87C2×C3×C8—21no—
88C2×C3×C8—21no—
89C2×C3×C8—22no—
90C2×C3×C8#6712yes—
91C2×C3×C8C3×D412yes—
92C3×C16—122no—
93C3⋊C16—42no—
94C22×C32—22no—
95C22×C32—21no—
96C22×C32—41no—
97C22×C32—41no—
98C22×C32—42no—
99C22×C32—42no—
100C22×C32—41no—
101C22×C32C22⋊C811yescharacteristic
102C32×C4—21no—
103C32×C4—41no—
104C32×C4#9911yescharacteristic
105C32×C4#10011yescharacteristic
106C23×C4C3×Dic311yescharacteristic
107C2×M16C3×Dic311yescharacteristic
108C2×M16C2×C3×D311yescharacteristic
109M32—62no—
110C22⋊C8—22no—
111C23×C3—22no—
112C23×C3—21no—
113C23×C3—21no—
114C23×C3—21no—
115C23×C3—41no—
116C23×C3—41no—
117C23×C3—42no—
118C23×C3—42no—
119C23×C3—42no—
120C23×C3—44no—
121C23×C3C2×C3⋊C811yescharacteristic
122C23×C3C2×C3×C811yescharacteristic
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—44no—
135C2×C3×C4—42no—
136C2×C3×C4—42no—
137C2×C3×C4—42no—
138C2×C3×C4—42no—
139C2×C3×C4—42no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—41no—
143C2×C3×C4—41no—
144C2×C3×C4—41no—
145C2×C3×C4—41no—
146C2×C3×C4#20811yescharacteristic
147C2×C3×C4#21711yescharacteristic
148C2×C3×C4C3×C22⋊C411yescharacteristic
149C2×C3×C4C3×M1611yescharacteristic
150C3×C8—22no—
151C3×C8—22no—
152C3×C8—42no—
153C3×C8—42no—
154C3×C8—41no—
155C3×C8—41no—
156C2×C32—21no—
157C2×C32—42no—
158C2×C32—41no—
159C2×C32#32311yescharacteristic
160C24C3×C3⋊C811yescharacteristic
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4C3×C3⋊C811yescharacteristic
166C22×C4C2×C3×Dic311yescharacteristic
167M16—41no—
168M16—41no—
169C2×C8—21no—
170C2×C8C3×#6712yes—
171C16—122no—
172C22×C3—22no—
173C22×C3—24no—
174C22×C3—22no—
175C22×C3—22no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—41no—
180C22×C3—41no—
181C22×C3—42no—
182C22×C3—42no—
183C22×C3—42no—
184C22×C3—41no—
185C22×C3—41no—
186C22×C3—42no—
187C22×C3—42no—
188C22×C3—44no—
189C22×C3—44no—
190C22×C3—42no—
191C22×C3—42no—
192C22×C3—41no—
193C22×C3—41no—
194C22×C3#83011yescharacteristic
195C22×C3C3×C22⋊C811yescharacteristic
196C3×C4—22no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—21no—
201C3×C4—42no—
202C3×C4—41no—
203C3×C4—41no—
204C3×C4#83311yescharacteristic
205C3×C4#83411yescharacteristic
206C3×C4C3×#9911yescharacteristic
207C3×C4C3×#10011yescharacteristic
208C32#132011yescharacteristic, complemented, Sylow
209C23—21no—
210C23—41no—
211C23—42no—
212C23C2×C3×C3⋊C811yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4C3×#20811yescharacteristic
221C2×C4C3×#21711yescharacteristic
222C8—22no—
223C8—41no—
224C2×C3—22no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—42no—
229C2×C3—44no—
230C2×C3—42no—
231C2×C3—41no—
232C2×C3—42no—
233C2×C3—41no—
234C2×C3#452511yescharacteristic
235C2×C3C3×#32311yescharacteristic
236C22—22no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—41no—
243C22C3×#83011yescharacteristic
244C4—21no—
245C4—41no—
246C4C3×#83311yescharacteristic
247C4C3×#83411yescharacteristic
248C3—21no—
249C3#6768111yescharacteristic, direct product factor
250C3C3×#132011yescharacteristic, complemented
251C2—21no—
252C2—42no—
253C2—41no—
254C2C3×#452511yescharacteristic
subgroupG/H
centerC3×C4#834
commutatorC23×C3C2×C3×C8
FrattiniC2×M16C2×C3×D3
FittingC32×#407C2
socleC2×C32#323
prime radicalC24×C32C8
cosocleC2×C3×M16C22×C3
hypercenterC3×#407D3
hypocenterC3C3×#1320
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C3×#4553C2semidirect
4. #67681C3direct (N × H)
14. #4553C2×C3semidirect
208. C32#1320semidirect
249. C3#67681direct (N × H)
250. C3C3×#1320semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
C3×#45532
C3×#13203
#676813