Finite Group Databasebeta

← C2×C3×#4621 #11920761

Subgroups — C2×C3×#4621 #11920761

Order 1152.

288 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 34 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×#95⋊C3C211yesmaximal, characteristic
2C3×#4621C212yesmaximal, direct product factor
3C2×#4621C311yesmaximal, characteristic, direct product factor
4C2×C3×#328—31nomaximal
5C2×C3×SL(2,ℤ/4)—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7C2×C3×C22⋊Q8—31no—
8C2×C3×C22⋊C8—31no—
9C2×C3×#95D311yescharacteristic
10C2×#95⋊C3—21no—
11C2×#95⋊C3C2×C311yescharacteristic
12#4621C2×C312yesdirect product factor
13C3×#328—32no—
14C3×#328—32no—
15C22×C3×A4—41no—
16C3×SL(2,ℤ/4)—42no—
17C2×#328—31noSylow
18C22×C3×Q8—31no—
19C23×C3×C4—31no—
20C2×SL(2,ℤ/4)—41no—
21C22×C3×C8—61no—
22C3×C22⋊Q8—32no—
23C3×C22⋊Q8—32no—
24C3×C22⋊Q8—61no—
25C3×C22⋊Q8—61no—
26C2×C3×C4⋊C4—31no—
27C2×C3×C4⋊C4—61no—
28C2×C3×C22⋊C4—61no—
29C3×C22⋊C8—32no—
30C3×C22⋊C8—61no—
31C3×#95—31no—
32C3×#95C2×D311yescharacteristic
33#95⋊C3—21no—
34#95⋊C3C22×C311yescharacteristic
35C2×C3×A4—42no—
36C2×C3×A4—41no—
37C2×C3×Dic3—161no—
38C2×C22⋊Q8—31no—
39C2×C22⋊C8—31no—
40C2×#95C3×D311yescharacteristic
41#328—32no—
42#328—32no—
43C24×C3S411yescharacteristic
44C22×A4—41no—
45C22×A4—81no—
46C2×C3×Q8—32no—
47C2×C3×Q8—61no—
48C2×C3×Q8—122no—
49C22×C3×C4—31no—
50C22×C3×C4—31no—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C22×C3×C4—61no—
56C22×C3×C4—61no—
57C22×C3×C4—122no—
58SL(2,ℤ/4)—42no—
59C2×C3×C8—62no—
60C2×C3×C8—122no—
61C3×C4⋊C4—32no—
62C3×C4⋊C4—61no—
63C3×C4⋊C4—62no—
64C3×C4⋊C4—62no—
65C3×C22⋊C4—62no—
66C3×C22⋊C4—62no—
67C22×C32—161no—
68C3×A4—41no—
69C3×Dic3—162no—
70C22×Q8—31no—
71C23×C4—31no—
72C22×C8—61no—
73C22⋊Q8—32no—
74C22⋊Q8—32no—
75C22⋊Q8—61no—
76C22⋊Q8—61no—
77C2×C4⋊C4—31no—
78C2×C4⋊C4—61no—
79C2×C22⋊C4—61no—
80C22⋊C8—32no—
81C22⋊C8—61no—
82#95—31no—
83#95C2×C3×D311yescharacteristic
84C23×C3—31no—
85C23×C3—31no—
86C23×C3—32no—
87C23×C3#22612yes—
88C23×C3C2×S411yescharacteristic
89C2×A4—41no—
90C2×A4—42no—
91C2×A4—81no—
92C2×A4—82no—
93C3×Q8—122no—
94C3×Q8—122no—
95C2×C3×C4—31no—
96C2×C3×C4—31no—
97C2×C3×C4—31no—
98C2×C3×C4—31no—
99C2×C3×C4—62no—
100C2×C3×C4—62no—
101C2×C3×C4—62no—
102C2×C3×C4—62no—
103C2×C3×C4—121no—
104C2×C3×C4—121no—
105C2×C3×C4—121no—
106C2×C3×C4—121no—
107C2×C3×C4—121no—
108C2×C3×C4—122no—
109C2×C3×C4—121no—
110C2×Dic3—161no—
111C3×C8—122no—
112C2×C32—161no—
113C2×C32—162no—
114C24C3×S411yescharacteristic
115C2×Q8—32no—
116C2×Q8—61no—
117C2×Q8—122no—
118C22×C4—31no—
119C22×C4—31no—
120C22×C4—31no—
121C22×C4—31no—
122C22×C4—31no—
123C22×C4—31no—
124C22×C4—61no—
125C22×C4—61no—
126C22×C4—122no—
127C2×C8—62no—
128C2×C8—122no—
129C4⋊C4—32no—
130C4⋊C4—61no—
131C4⋊C4—62no—
132C4⋊C4—62no—
133C22⋊C4—62no—
134C22⋊C4—62no—
135C22×C3—31no—
136C22×C3—32no—
137C22×C3—31no—
138C22×C3—31no—
139C22×C3—32no—
140C22×C3—32no—
141C22×C3—61no—
142C22×C3—161no—
143C22×C3—321no—
144C22×C3#85711yescharacteristic
145C22×C3C2×#22611yescharacteristic
146A4—41no—
147A4—81no—
148C3×C4—61no—
149C3×C4—61no—
150C3×C4—61no—
151C3×C4—61no—
152C3×C4—122no—
153C3×C4—122no—
154Dic3—162no—
155C32—161noSylow
156C23—31no—
157C23—31no—
158C23—32no—
159C23C3×#22612yes—
160C23C2×C3×S411yescharacteristic
161Q8—122no—
162Q8—122no—
163C2×C4—31no—
164C2×C4—31no—
165C2×C4—31no—
166C2×C4—31no—
167C2×C4—62no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—121no—
172C2×C4—121no—
173C2×C4—121no—
174C2×C4—121no—
175C2×C4—122no—
176C2×C4—121no—
177C2×C4—121no—
178C8—122no—
179C2×C3—31no—
180C2×C3—31no—
181C2×C3—32no—
182C2×C3—161no—
183C2×C3—162no—
184C2×C3—321no—
185C2×C3—322no—
186C2×C3#462112yesdirect product factor
187C2×C3C2×#85711yescharacteristic
188C22—31no—
189C22—32no—
190C22—31no—
191C22—31no—
192C22—32no—
193C22—32no—
194C22—61no—
195C22C3×#85711yescharacteristic
196C22C2×C3×#22611yescharacteristic
197C4—61no—
198C4—61no—
199C4—61no—
200C4—61no—
201C4—122no—
202C4—122no—
203C3—161no—
204C3—321no—
205C3C2×#462111yescharacteristic, direct product factor
206C2—31no—
207C2—31no—
208C2—32no—
209C2C3×#462112yesdirect product factor
210C2C2×C3×#85711yescharacteristic
subgroupG/H
center, hypercenterC22×C3#857
commutator, cosocle, hypocenter#95⋊C3C22×C3
FrattiniC23C2×C3×S4
FittingC2×C3×#95D3
socleC24×C3S4
prime radicalC2×C3×#95⋊C3C2
LCSG ▷ #95⋊C3
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
2. C3×#4621C2direct (N × H)
3. C2×#4621C3direct (N × H)
12. #4621C2×C3direct (N × H)
186. C2×C3#4621direct (N × H)
205. C3C2×#4621direct (N × H)
209. C2C3×#4621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#95⋊C32
C3×#46212
C2×#46213
C2×C3×#3283
C2×C3×SL(2,ℤ/4)4