Finite Group Databasebeta

← C3×#73136 #11920914

Subgroups — C3×#73136 #11920914

Order 1152.

208 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 36 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
1C3×A4×Q16C211yesmaximal, characteristic
2C3×#5398C211yesmaximal, characteristic
3C3×A4⋊C16C211yesmaximal, characteristic
4#73136C311yesmaximal, characteristic, direct product factor
5C3×#2188—31nomaximal
6C3×Q8×A4—21no—
7C3×A4⋊Q8—21no—
8C3×C8×A4C2211yescharacteristic
9C3×#829—41nomaximal
10C22×C3×Q16D311yescharacteristic
11A4×Q16—21no—
12A4×Q16C2×C311yescharacteristic
13#5398C2×C311yescharacteristic
14C2×C3×Q32—31no—
15C2×C3×Q32—31no—
16C3×#467—31no—
17A4⋊C16C2×C311yescharacteristic
18C3×#358—31no—
19C3×#358—31no—
20C3×C22⋊C16—31no—
21C3×C4×A4—41no—
22C3×C4×A4D411yescharacteristic
23C3×SL(2,ℤ/4)—41no—
24C32×Q16—41no—
25C3×Dic12—41no—
26C3×C3⋊C16—41no—
27#2188—31noSylow
28C22×C3×Q8—21no—
29Q8×A4—22no—
30Q8×A4—21no—
31A4⋊Q8—21no—
32C2×C3×Q16—31no—
33C2×C3×Q16—31no—
34C2×C3×Q16—31no—
35C2×C3×Q16—61no—
36C22×C3×C8C2×D311yescharacteristic
37C3×C22⋊Q8—61no—
38C8×A4—21no—
39C8×A4C22×C311yescharacteristic
40C3×Q32—62no—
41C3×Q32—61no—
42C3×Q32—61no—
43C2×C3×C16—31no—
44C2×C3×C16—31no—
45C3×#107—31no—
46C3×#103—61no—
47#829—41no—
48C2×C3×A4D811yescharacteristic
49C32×Q8—81no—
50C3×Dic6—81no—
51C32×C8—41no—
52C22×Q16C3×D311yescharacteristic
53C2×Q32—31no—
54C2×Q32—31no—
55#467—31no—
56#358—31no—
57#358—31no—
58C22⋊C16—31no—
59C2×C3×Q8—61no—
60C2×C3×Q8—61no—
61C2×C3×Q8—61no—
62C2×C3×Q8—121no—
63C22×C3×C4—41no—
64C22×C3×C4#6711yescharacteristic
65C4×A4—21no—
66C4×A4—42no—
67C4×A4—41no—
68C4×A4C3×D411yescharacteristic
69SL(2,ℤ/4)—41no—
70C3×Q16—32no—
71C3×Q16—31no—
72C3×Q16—41no—
73C3×Q16—61no—
74C3×Q16—61no—
75C3×Q16—61no—
76C3×Q16—81no—
77C3×Q16S411yescharacteristic
78C2×C3×C8—31no—
79C2×C3×C8—31no—
80C3×C4⋊C4—61no—
81C3×C4⋊C4—121no—
82C3×C22⋊C4—121no—
83Dic12—41no—
84C3×C16—61no—
85C3×C16—61no—
86C3⋊C16—41no—
87C3×A4Q3211yescharacteristic, complemented
88C32×C4—41no—
89C32×C4—161no—
90C3×Dic3—161no—
91C22×Q8—21no—
92C2×Q16—31no—
93C2×Q16—31no—
94C2×Q16—31no—
95C2×Q16—61no—
96C22×C8C2×C3×D311yescharacteristic
97C22⋊Q8—61no—
98Q32—62no—
99Q32—61no—
100Q32—61no—
101C2×C16—31no—
102C2×C16—31no—
103#107—31no—
104#103—61no—
105C23×C3#21311yescharacteristic
106C2×A4—21no—
107C2×A4C3×D811yescharacteristic
108C3×Q8—21no—
109C3×Q8—61no—
110C3×Q8—81no—
111C3×Q8—82no—
112C3×Q8—121no—
113C3×Q8—121no—
114C3×Q8—121no—
115C3×Q8—121no—
116C2×C3×C4—31no—
117C2×C3×C4—31no—
118C2×C3×C4—121no—
119C2×C3×C4—121no—
120C2×C3×C4—121no—
121C2×C3×C4—121no—
122Dic6—81no—
123C3×C8—31no—
124C3×C8—41no—
125C3×C8—81no—
126C3×C8C2×S411yescharacteristic
127C2×C32—41no—
128C2×Q8—61no—
129C2×Q8—61no—
130C2×Q8—61no—
131C2×Q8—121no—
132C22×C4—41no—
133C22×C4C3×#6711yescharacteristic
134Q16—32no—
135Q16—31no—
136Q16—61no—
137Q16—61no—
138Q16—61no—
139Q16C3×S411yescharacteristic
140C2×C8—31no—
141C2×C8—31no—
142C4⋊C4—61no—
143C4⋊C4—121no—
144C22⋊C4—121no—
145C16—61no—
146C16—61no—
147C22×C3—31no—
148C22×C3—31no—
149C22×C3#82911yescharacteristic, complemented
150A4—21no—
151A4C3×Q3211yescharacteristic, complemented
152C3×C4—31no—
153C3×C4—41no—
154C3×C4—41no—
155C3×C4—81no—
156C3×C4—121no—
157C3×C4—161no—
158C3×C4—162no—
159C3×C4—241no—
160C3×C4—241no—
161C3×C4GL(2,ℤ/4)11yescharacteristic
162Dic3—161no—
163C32—41noSylow
164C23C3×#21311yescharacteristic
165Q8—21no—
166Q8—61no—
167Q8—121no—
168Q8—121no—
169Q8—121no—
170Q8—121no—
171C2×C4—31no—
172C2×C4—31no—
173C2×C4—121no—
174C2×C4—121no—
175C2×C4—121no—
176C2×C4—121no—
177C8—31no—
178C8C2×C3×S411yescharacteristic
179C2×C3—31no—
180C2×C3—31no—
181C2×C3—41no—
182C2×C3—81no—
183C2×C3#541511yescharacteristic
184C22—31no—
185C22—31no—
186C22C3×#82911yescharacteristic, complemented
187C4—31no—
188C4—41no—
189C4—121no—
190C4—241no—
191C4—241no—
192C4C3×GL(2,ℤ/4)11yescharacteristic
193C3—41no—
194C3—81no—
195C3#7313611yescharacteristic, direct product factor
196C2—31no—
197C2—31no—
198C2C3×#541511yescharacteristic
subgroupG/H
centerC2×C3#5415
commutator, cosocleC8×A4C22×C3
FrattiniC8C2×C3×S4
FittingC22×C3×Q16D3
socleC23×C3#213
prime radicalC2×C3×A4D8
hypercenterC3×Q16S4
hypocenterA4C3×Q32
LCSG ▷ C8×A4 ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

Complements

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

NH ≅ G/Ntype
4. #73136C3direct (N × H)
87. C3×A4Q32semidirect
149. C22×C3#829semidirect
151. A4C3×Q32semidirect
186. C22C3×#829semidirect
195. C3#73136direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×Q162
C3×#53982
C3×A4⋊C162
#731363
C3×#21883
C3×#8294