Finite Group Databasebeta

← C3×#73104 #11920882

Subgroups — C3×#73104 #11920882

Order 1152.

236 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C2×C3×C8×A4C211yesmaximal, characteristic
2C3×A4⋊C16C212yesmaximal, complemented
3#73104C311yesmaximal, characteristic, direct product factor
4C3×#2112—31nomaximal
5C2×C3×C4×A4C411yescharacteristic
6C3×C8×A4C411yescharacteristic
7C3×C8×A4C2211yescharacteristic
8C3×#812—41nomaximal
9C23×C3×C8D311yescharacteristic
10C2×C8×A4—21no—
11C2×C8×A4C2×C311yescharacteristic
12C2×C3×M32—31no—
13C2×C3×M32—31no—
14A4⋊C16C2×C312yescomplemented
15C3×C22⋊C16—32no—
16C3×C22⋊C16—32no—
17C22×C3×A4C811yescharacteristic
18C3×C4×A4C811yescharacteristic
19C3×C4×A4C2×C411yescharacteristic
20C2×C32×C8—41no—
21C3×C3⋊C16—42no—
22#2112—31noSylow
23C23×C3×C4Dic311yescharacteristic
24C2×C4×A4—21no—
25C2×C4×A4C3×C411yescharacteristic
26C22×C3×C8—31no—
27C22×C3×C8—31no—
28C22×C3×C8—31no—
29C22×C3×C8—31no—
30C22×C3×C8Dic311yescharacteristic
31C22×C3×C8C2×D311yescharacteristic
32C8×A4—21no—
33C8×A4—21no—
34C8×A4C3×C411yescharacteristic
35C8×A4C22×C311yescharacteristic
36C3×M32—61no—
37C3×M32—61no—
38C3×M32—61no—
39C3×M32—61no—
40C2×C3×C16—32no—
41C2×C3×C16—32no—
42#812—41no—
43C2×C3×A4—21no—
44C2×C3×A4C2×C811yescharacteristic
45C2×C32×C4—41no—
46C32×C8—41no—
47C32×C8—41no—
48C23×C8C3×D311yescharacteristic
49C2×M32—31no—
50C2×M32—31no—
51C22⋊C16—32no—
52C22⋊C16—32no—
53C24×C3C3⋊C811yescharacteristic
54C22×A4—21no—
55C22×A4C3×C811yescharacteristic
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4C3⋊C811yescharacteristic
61C22×C3×C4C2×Dic311yescharacteristic
62C4×A4—21no—
63C4×A4—21no—
64C4×A4C3×C811yescharacteristic
65C4×A4C2×C3×C411yescharacteristic
66C2×C3×C8—31no—
67C2×C3×C8—31no—
68C2×C3×C8—31no—
69C2×C3×C8—31no—
70C2×C3×C8—31no—
71C2×C3×C8—31no—
72C2×C3×C8—31no—
73C2×C3×C8—41no—
74C2×C3×C8—61no—
75C2×C3×C8—81no—
76C2×C3×C8S411yescharacteristic
77C3×C16—62no—
78C3×C16—62no—
79C3⋊C16—42no—
80C22×C32—41no—
81C3×A4M3211yescharacteristic, complemented
82C32×C4—41no—
83C32×C4—41no—
84C23×C4C3×Dic311yescharacteristic
85C22×C8—31no—
86C22×C8—31no—
87C22×C8—31no—
88C22×C8—31no—
89C22×C8C3×Dic311yescharacteristic
90C22×C8C2×C3×D311yescharacteristic
91M32—61no—
92M32—61no—
93M32—61no—
94M32—61no—
95C2×C16—32no—
96C2×C16—32no—
97C23×C3—21no—
98C23×C3—31no—
99C23×C3—31no—
100C23×C3—61no—
101C23×C3C2×C3⋊C811yescharacteristic
102C2×A4—22no—
103C2×A4—21no—
104C2×A4—21no—
105C2×A4C2×C3×C811yescharacteristic
106C2×C3×C4—31no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—31no—
112C2×C3×C4—31no—
113C2×C3×C4—41no—
114C2×C3×C4—61no—
115C2×C3×C4—81no—
116C2×C3×C4SL(2,ℤ/4)11yescharacteristic
117C3×C8—31no—
118C3×C8—31no—
119C3×C8—41no—
120C3×C8—41no—
121C3×C8—81no—
122C3×C8—81no—
123C3×C8SL(2,ℤ/4)11yescharacteristic
124C3×C8C2×S411yescharacteristic
125C2×C32—41no—
126C2×C32—81no—
127C24C3×C3⋊C811yescharacteristic
128C22×C4—31no—
129C22×C4—31no—
130C22×C4—31no—
131C22×C4—31no—
132C22×C4C3×C3⋊C811yescharacteristic
133C22×C4C2×C3×Dic311yescharacteristic
134C2×C8—31no—
135C2×C8—31no—
136C2×C8—31no—
137C2×C8—31no—
138C2×C8—31no—
139C2×C8—31no—
140C2×C8—31no—
141C2×C8—61no—
142C2×C8C3×S411yescharacteristic
143C16—62no—
144C16—62no—
145C22×C3—31no—
146C22×C3—31no—
147C22×C3—32no—
148C22×C3—31no—
149C22×C3—41no—
150C22×C3—61no—
151C22×C3—61no—
152C22×C3—61no—
153C22×C3—81no—
154C22×C3#81211yescharacteristic, complemented
155C22×C3A4⋊C811yescharacteristic
156A4—21no—
157A4C3×M3211yescharacteristic, complemented
158C3×C4—31no—
159C3×C4—31no—
160C3×C4—41no—
161C3×C4—41no—
162C3×C4—81no—
163C3×C4—81no—
164C3×C4A4⋊C811yescharacteristic
165C3×C4C2×SL(2,ℤ/4)11yescharacteristic
166C32—41noSylow
167C23—21no—
168C23—31no—
169C23—31no—
170C23—61no—
171C23C2×C3×C3⋊C811yescharacteristic
172C2×C4—31no—
173C2×C4—31no—
174C2×C4—31no—
175C2×C4—31no—
176C2×C4—31no—
177C2×C4—31no—
178C2×C4—31no—
179C2×C4—61no—
180C2×C4C3×SL(2,ℤ/4)11yescharacteristic
181C8—31no—
182C8—31no—
183C8C3×SL(2,ℤ/4)11yescharacteristic
184C8C2×C3×S411yescharacteristic
185C2×C3—21no—
186C2×C3—31no—
187C2×C3—31no—
188C2×C3—41no—
189C2×C3—61no—
190C2×C3—81no—
191C2×C3—82no—
192C2×C3—81no—
193C2×C3C2×A4⋊C811yescharacteristic
194C22—31no—
195C22—31no—
196C22—32no—
197C22—31no—
198C22—61no—
199C22—61no—
200C22—61no—
201C22C3×#81211yescharacteristic, complemented
202C22C3×A4⋊C811yescharacteristic
203C4—31no—
204C4—31no—
205C4C3×A4⋊C811yescharacteristic
206C4C2×C3×SL(2,ℤ/4)11yescharacteristic
207C3—41no—
208C3—81no—
209C3#7310411yescharacteristic, direct product factor
210C2—21no—
211C2—31no—
212C2—31no—
213C2—61no—
214C2C2×C3×A4⋊C811yescharacteristic
subgroupG/H
centerC3×C8C2×S4
commutatorC2×A4C2×C3×C8
FrattiniC8C2×C3×S4
FittingC23×C3×C8D3
socleC23×C3C2×C3⋊C8
prime radicalC22×C3×A4C8
cosocleC8×A4C22×C3
hypercenterC2×C3×C8S4
hypocenterA4C3×M32
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C3×C8 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
2. C3×A4⋊C16C2semidirect
3. #73104C3direct (N × H)
14. A4⋊C16C2×C3semidirect
81. C3×A4M32semidirect
154. C22×C3#812semidirect
157. A4C3×M32semidirect
201. C22C3×#812semidirect
209. C3#73104direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C3×A4⋊C162
#731043
C3×#21123
C3×#8124