Finite Group Databasebeta

← C3×#73146 #11920924

Subgroups — C3×#73146 #11920924

Order 1152.

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

normal subgroups only

This group has 420 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×Q8×A4C211yesmaximal, characteristic
2C3×#5409C212yesmaximal
3#73146C311yesmaximal, characteristic, direct product factor
4C3×#1784—31nomaximal
5C3×Q8×A4—22no—
6C2×C3×C4×A4C412yes—
7C2×C3×C4×A4C2211yescharacteristic
8C3×A4⋊C8—22no—
9C3×#836—41nomaximal
10C23×C3×Q8D311yescharacteristic
11C2×Q8×A4—21no—
12C2×Q8×A4C2×C311yescharacteristic
13#5409C2×C312yes—
14C2×C3×#101—32no—
15C2×C3×#101—31no—
16C2×C3×#101—31no—
17C3×#407—32no—
18C22×C3×A4C2×C411yescharacteristic
19C2×C32×Q8—41no—
20C3×C4×A4—22no—
21C3×C4×A4D412yes—
22C3×#208—42no—
23#1784—31noSylow
24C22×C3×Q8—22no—
25C22×C3×Q8—31no—
26C22×C3×Q8—31no—
27C22×C3×Q8—32no—
28C22×C3×Q8—62no—
29C23×C3×C4Dic312yes—
30C23×C3×C4C2×D311yescharacteristic
31Q8×A4—24no—
32Q8×A4—22no—
33C2×C4×A4—22no—
34C2×C4×A4—21no—
35C2×C4×A4C3×C412yes—
36C2×C4×A4C22×C311yescharacteristic
37C2×C3×M16—32no—
38C2×C3×M16—32no—
39A4⋊C8—22no—
40C3×#101—64no—
41C3×#101—62no—
42C3×#101—61no—
43C3×#101—61no—
44C3×C22⋊C8—62no—
45C3×C22⋊C8—62no—
46#836—41no—
47C2×C3×A4—21no—
48C2×C3×A4C22⋊C411yescharacteristic
49C32×Q8—82no—
50C2×C32×C4—42no—
51C2×C32×C4—41no—
52C3×C3⋊C8—82no—
53C23×Q8C3×D311yescharacteristic
54C2×#101—32no—
55C2×#101—31no—
56C2×#101—31no—
57#407—32no—
58C24×C3C2×Dic311yescharacteristic
59C22×A4—21no—
60C22×A4C2×C3×C411yescharacteristic
61C2×C3×Q8—34no—
62C2×C3×Q8—32no—
63C2×C3×Q8—31no—
64C2×C3×Q8—41no—
65C2×C3×Q8—61no—
66C2×C3×Q8—62no—
67C2×C3×Q8—62no—
68C2×C3×Q8—62no—
69C2×C3×Q8—64no—
70C2×C3×Q8—64no—
71C2×C3×Q8—81no—
72C2×C3×Q8S411yescharacteristic
73C22×C3×C4—22no—
74C22×C3×C4—31no—
75C22×C3×C4—32no—
76C22×C3×C4—32no—
77C22×C3×C4—31no—
78C22×C3×C4—32no—
79C22×C3×C4—62no—
80C22×C3×C4#6712yes—
81C4×A4—24no—
82C4×A4—22no—
83C4×A4—22no—
84C4×A4C3×D412yes—
85C3×M16—62no—
86C3×M16—62no—
87C3×M16—62no—
88C3×M16—62no—
89C2×C3×C8—62no—
90C2×C3×C8—62no—
91#208—42no—
92C22×C32—41no—
93C3×A4#10111yescharacteristic, complemented
94C32×C4—42no—
95C32×C4—82no—
96C22×Q8—22no—
97C22×Q8—31no—
98C22×Q8—31no—
99C22×Q8—32no—
100C22×Q8—62no—
101C23×C4C3×Dic312yes—
102C23×C4C2×C3×D311yescharacteristic
103C2×M16—32no—
104C2×M16—32no—
105#101—64no—
106#101—62no—
107#101—61no—
108#101—61no—
109C22⋊C8—62no—
110C22⋊C8—62no—
111C23×C3—21no—
112C23×C3—31no—
113C23×C3—31no—
114C23×C3—61no—
115C23×C3#21711yescharacteristic
116C2×A4—22no—
117C2×A4—21no—
118C2×A4—21no—
119C2×A4C3×C22⋊C411yescharacteristic
120C3×Q8—22no—
121C3×Q8—64no—
122C3×Q8—64no—
123C3×Q8—62no—
124C3×Q8—82no—
125C3×Q8—84no—
126C2×C3×C4—31no—
127C2×C3×C4—32no—
128C2×C3×C4—32no—
129C2×C3×C4—32no—
130C2×C3×C4—34no—
131C2×C3×C4—32no—
132C2×C3×C4—41no—
133C2×C3×C4—42no—
134C2×C3×C4—62no—
135C2×C3×C4—62no—
136C2×C3×C4—61no—
137C2×C3×C4—62no—
138C2×C3×C4—81no—
139C2×C3×C4—82no—
140C2×C3×C4SL(2,ℤ/4)12yes—
141C2×C3×C4C2×S411yescharacteristic
142C3×C8—122no—
143C3×C8—122no—
144C3⋊C8—82no—
145C2×C32—41no—
146C2×C32—81no—
147C24C2×C3×Dic311yescharacteristic
148C2×Q8—34no—
149C2×Q8—31no—
150C2×Q8—32no—
151C2×Q8—61no—
152C2×Q8—62no—
153C2×Q8—62no—
154C2×Q8—62no—
155C2×Q8—64no—
156C2×Q8—64no—
157C2×Q8C3×S411yescharacteristic
158C22×C4—22no—
159C22×C4—31no—
160C22×C4—32no—
161C22×C4—32no—
162C22×C4—31no—
163C22×C4—32no—
164C22×C4—62no—
165C22×C4C3×#6712yes—
166M16—62no—
167M16—62no—
168M16—62no—
169M16—62no—
170C2×C8—62no—
171C2×C8—62no—
172C22×C3—31no—
173C22×C3—31no—
174C22×C3—32no—
175C22×C3—31no—
176C22×C3—41no—
177C22×C3—61no—
178C22×C3—61no—
179C22×C3—61no—
180C22×C3—81no—
181C22×C3#83611yescharacteristic, complemented
182C22×C3C2×SL(2,ℤ/4)11yescharacteristic
183A4—21no—
184A4C3×#10111yescharacteristic, complemented
185C3×C4—22no—
186C3×C4—32no—
187C3×C4—42no—
188C3×C4—62no—
189C3×C4—82no—
190C3×C4—84no—
191C3×C4—82no—
192C3×C4GL(2,ℤ/4)12yes—
193C32—41noSylow
194C23—21no—
195C23—31no—
196C23—31no—
197C23—61no—
198C23C3×#21711yescharacteristic
199Q8—22no—
200Q8—64no—
201Q8—64no—
202Q8—62no—
203C2×C4—31no—
204C2×C4—32no—
205C2×C4—32no—
206C2×C4—32no—
207C2×C4—34no—
208C2×C4—32no—
209C2×C4—62no—
210C2×C4—62no—
211C2×C4—61no—
212C2×C4—62no—
213C2×C4C3×SL(2,ℤ/4)12yes—
214C2×C4C2×C3×S411yescharacteristic
215C8—122no—
216C8—122no—
217C2×C3—21no—
218C2×C3—31no—
219C2×C3—31no—
220C2×C3—41no—
221C2×C3—61no—
222C2×C3—81no—
223C2×C3—82no—
224C2×C3—81no—
225C2×C3#543211yescharacteristic
226C22—31no—
227C22—31no—
228C22—32no—
229C22—31no—
230C22—61no—
231C22—61no—
232C22—61no—
233C22C3×#83611yescharacteristic, complemented
234C22C2×C3×SL(2,ℤ/4)11yescharacteristic
235C4—22no—
236C4—32no—
237C4—62no—
238C4C3×GL(2,ℤ/4)12yes—
239C3—41no—
240C3—81no—
241C3#7314611yescharacteristic, direct product factor
242C2—21no—
243C2—31no—
244C2—31no—
245C2—61no—
246C2C3×#543211yescharacteristic
subgroupG/H
centerC2×C3#5432
commutatorC22×A4C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC23×C3×Q8D3
socleC23×C3#217
prime radicalC22×C3×A4C2×C4
cosocleC2×C4×A4C22×C3
hypercenterC2×C3×Q8S4
hypocenterA4C3×#101
LCSG ▷ C22×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×Q8

Complements

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

NH ≅ G/Ntype
3. #73146C3direct (N × H)
93. C3×A4#101semidirect
181. C22×C3#836semidirect
184. A4C3×#101semidirect
233. C22C3×#836semidirect
241. C3#73146direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C3×#54092
#731463
C3×#17843
C3×#8364