Finite Group Databasebeta

← C3×#67690 #11771426

Subgroups — C3×#67690 #11771426

Order 1152.

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

normal subgroups only

This group has 303 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×#408C211yesmaximal, characteristic
2C3×#4553C212yesmaximal, complemented
3C3×#1321—31nomaximal
4#67690C311yesmaximal, characteristic, direct product factor
5C2×C32×#41C411yescharacteristic
6C2×C32×M16C2211yescharacteristic
7C22×C32×C8C411yescharacteristic
8C32×C22⋊C8—22no—
9C3×#812—22no—
10C3×#408—21no—
11C3×#408D311yescharacteristic
12C3×#408C2×C311yescharacteristic
13C3×#349—32no—
14#4553C2×C312yescomplemented
15C32×#41—41no—
16C32×#41—41no—
17C2×C32×Q8C811yescharacteristic
18C2×C32×D4—21no—
19C2×C32×D4C811yescharacteristic
20C22×C32×C4—21no—
21C22×C32×C4C2×C411yescharacteristic
22C32×M16—41no—
23C2×C32×C8—21no—
24C2×C32×C8—41no—
25C2×C32×C8D412yes—
26C3×C3⋊C16—42no—
27#1321—31noSylow
28C2×C3×#41—21no—
29C2×C3×#41Dic311yescharacteristic
30C2×C3×#41C3×C411yescharacteristic
31C2×C3×M16—21no—
32C2×C3×M16C2×D311yescharacteristic
33C2×C3×M16C22×C311yescharacteristic
34C22×C3×C8—21no—
35C22×C3×C8Dic311yescharacteristic
36C22×C3×C8C3×C411yescharacteristic
37C3×M32—62no—
38C3×C22⋊C8—24no—
39C3×C22⋊C8—22no—
40C3×C22⋊C8—22no—
41#812—22no—
42C23×C32—21no—
43C23×C32M1611yescharacteristic
44C32×Q8—41no—
45C32×D4—41no—
46C32×D4—42no—
47C2×C32×C4—21no—
48C2×C32×C4—21no—
49C2×C32×C4—21no—
50C2×C32×C4—41no—
51C2×C32×C4—41no—
52C2×C32×C4C22⋊C411yescharacteristic
53C2×C32×C4C2×C811yescharacteristic
54C32×C8—22no—
55C32×C8—41no—
56#408C3×D311yescharacteristic
57#349—32no—
58C3×#41—42no—
59C3×#41—42no—
60C3×#41—41no—
61C3×#41—41no—
62C3×#41—41no—
63C3×#41—41no—
64C2×C3×Q8—21no—
65C2×C3×Q8C3⋊C811yescharacteristic
66C2×C3×Q8C3×C811yescharacteristic
67C2×C3×D4—22no—
68C2×C3×D4—21no—
69C2×C3×D4—21no—
70C2×C3×D4—21no—
71C2×C3×D4C3⋊C811yescharacteristic
72C2×C3×D4C3×C811yescharacteristic
73C22×C3×C4—22no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4C2×Dic311yescharacteristic
78C22×C3×C4C2×C3×C411yescharacteristic
79C3×M16—41no—
80C3×M16—41no—
81C3×M16—42no—
82C2×C3×C8—22no—
83C2×C3×C8—21no—
84C2×C3×C8—21no—
85C2×C3×C8—22no—
86C2×C3×C8—42no—
87C2×C3×C8—41no—
88C2×C3×C8—41no—
89C2×C3×C8#6712yes—
90C2×C3×C8C3×D412yes—
91C3×C16—122no—
92C3⋊C16—42no—
93C22×C32—21no—
94C22×C32—41no—
95C22×C32—42no—
96C22×C32—41no—
97C22×C32C22⋊C811yescharacteristic
98C32×C4—21no—
99C32×C4—41no—
100C32×C4#9911yescharacteristic
101C32×C4#10011yescharacteristic
102C2×#41C3×Dic311yescharacteristic
103C2×M16C2×C3×D311yescharacteristic
104C22×C8C3×Dic311yescharacteristic
105M32—62no—
106C22⋊C8—22no—
107C23×C3—22no—
108C23×C3—21no—
109C23×C3—21no—
110C23×C3—21no—
111C23×C3#20811yescharacteristic
112C23×C3C3×M1611yescharacteristic
113C3×Q8—41no—
114C3×Q8—41no—
115C3×Q8—42no—
116C3×D4—41no—
117C3×D4—41no—
118C3×D4—42no—
119C3×D4—44no—
120C3×D4—42no—
121C3×D4—42no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—22no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—42no—
134C2×C3×C4—42no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4C2×C3⋊C811yescharacteristic
140C2×C3×C4#21711yescharacteristic
141C2×C3×C4C3×C22⋊C411yescharacteristic
142C2×C3×C4C2×C3×C811yescharacteristic
143C3×C8—22no—
144C3×C8—22no—
145C3×C8—42no—
146C3×C8—42no—
147C3×C8—41no—
148C3×C8—41no—
149C2×C32—21no—
150C2×C32—41no—
151C2×C32—81no—
152C2×C32#32311yescharacteristic
153#41—41no—
154#41—41no—
155C2×Q8C3×C3⋊C811yescharacteristic
156C2×D4—21no—
157C2×D4C3×C3⋊C811yescharacteristic
158C22×C4—21no—
159C22×C4C2×C3×Dic311yescharacteristic
160M16—41no—
161C2×C8—21no—
162C2×C8—41no—
163C2×C8C3×#6712yes—
164C16—122no—
165C22×C3—22no—
166C22×C3—21no—
167C22×C3—21no—
168C22×C3—21no—
169C22×C3—41no—
170C22×C3—41no—
171C22×C3—42no—
172C22×C3—42no—
173C22×C3—44no—
174C22×C3—42no—
175C22×C3—42no—
176C22×C3—41no—
177C22×C3—41no—
178C22×C3#83011yescharacteristic
179C22×C3C3×C22⋊C811yescharacteristic
180C3×C4—22no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—42no—
186C3×C4—41no—
187C3×C4—41no—
188C3×C4#83311yescharacteristic
189C3×C4#83411yescharacteristic
190C3×C4C3×#9911yescharacteristic
191C3×C4C3×#10011yescharacteristic
192C32#132111yescharacteristic, complemented, Sylow
193C23—21no—
194C23C3×#20811yescharacteristic
195Q8—41no—
196D4—41no—
197D4—42no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4C2×C3×C3⋊C811yescharacteristic
204C2×C4C3×#21711yescharacteristic
205C8—22no—
206C8—41no—
207C2×C3—22no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—42no—
212C2×C3—41no—
213C2×C3—41no—
214C2×C3—82no—
215C2×C3—81no—
216C2×C3—81no—
217C2×C3#452511yescharacteristic
218C2×C3C3×#32311yescharacteristic
219C22—21no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22C3×#83011yescharacteristic
224C4—21no—
225C4—41no—
226C4C3×#83311yescharacteristic
227C4C3×#83411yescharacteristic
228C3—21no—
229C3#6769011yescharacteristic, direct product factor
230C3C3×#132111yescharacteristic, complemented
231C2—21no—
232C2—41no—
233C2—81no—
234C2C3×#452511yescharacteristic
subgroupG/H
centerC3×C4#834
commutatorC2×C3×C4C2×C3×C8
FrattiniC2×M16C2×C3×D3
FittingC32×#408C2
socleC2×C32#323
prime radicalC2×C32×#41C4
cosocleC2×C3×M16C22×C3
hypercenterC3×#408D3
hypocenterC3C3×#1321
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ C3×#408

Complements

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

NH ≅ G/Ntype
2. C3×#4553C2semidirect
4. #67690C3direct (N × H)
14. #4553C2×C3semidirect
192. C32#1321semidirect
229. C3#67690direct (N × H)
230. C3C3×#1321semidirect

Maximal subgroups

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

subgroupindex
C32×#4082
C3×#45532
C3×#13213
#676903