Finite Group Databasebeta

← C3×A4×#97 #11919518

Subgroups — C3×A4×#97 #11919518

Order 1152.

440 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 144 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×A4C212yesmaximal
2C3×C42×A4C211yesmaximal, characteristic
3C22×C3×#97C311yesmaximal, characteristic, complemented
4A4×#97C313yesmaximal, direct product factor
5C2×C3×C4×A4C412yes—
6C2×C3×C4×A4C2211yescharacteristic
7C3×C8×A4C414yescomplemented
8C32×#97—41nomaximal
9C23×C3×C8C2×C312yes—
10C22×C3×C42C2×C311yescharacteristic
11C2×C8×A4C2×C316yes—
12C42×A4C2×C313yes—
13C2×C3×#97—31no—
14C2×C3×#97—32no—
15C2×C3×#97—31no—
16C22×C3×A4C2×C411yescharacteristic
17C3×C4×A4—22no—
18C3×C4×A4C2×C412yes—
19C2×C32×C8—42no—
20C32×C42—41no—
21C22×#97C3211yescharacteristic, complemented, Sylow
22C23×C3×C4C3×C412yes—
23C23×C3×C4C22×C311yescharacteristic
24C2×C4×A4C3×C416yes—
25C2×C4×A4C22×C313yes—
26C22×C3×C8—32no—
27C22×C3×C8—34no—
28C22×C3×C8—32no—
29C22×C3×C8C3×C414yescomplemented
30C2×C3×C42—31no—
31C2×C3×C42—31no—
32C2×C3×C42—32no—
33C8×A4C3×C4112yescomplemented
34C3×#97—32no—
35C3×#97—32no—
36C3×#97—31no—
37C3×#97—43no—
38C3×#97A411yescharacteristic, direct product factor
39C2×C3×A4C4211yescharacteristic
40C2×C3×A4M1612yes—
41C2×C32×C4—42no—
42C2×C32×C4—41no—
43C32×C8—44no—
44C23×C8C2×C3212yes—
45C22×C42C2×C3211yescharacteristic
46C2×#97—31no—
47C2×#97—32no—
48C2×#97—31no—
49C24×C3C2×C3×C411yescharacteristic
50C22×A4C2×C3×C413yes—
51C22×C3×C4—22no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—32no—
55C22×C3×C4—32no—
56C22×C3×C4—32no—
57C22×C3×C4—62no—
58C22×C3×C4C2×C3×C412yes—
59C4×A4—26no—
60C4×A4C2×C3×C416yes—
61C2×C3×C8—34no—
62C2×C3×C8—32no—
63C2×C3×C8—34no—
64C2×C3×C8—34no—
65C2×C3×C8—34no—
66C2×C3×C8—46no—
67C2×C3×C8C2×A412yes—
68C3×C42—32no—
69C3×C42—32no—
70C3×C42—31no—
71C3×C42—43no—
72C3×C42C2×A411yescharacteristic
73C22×C32—41no—
74C3×A4#9711yescharacteristic, direct product factor
75C32×C4—42no—
76C32×C4—82no—
77C23×C4C32×C412yes—
78C23×C4C22×C3211yescharacteristic
79C22×C8—32no—
80C22×C8—32no—
81C22×C8—34no—
82C22×C8C32×C414yescomplemented
83C2×C42—31no—
84C2×C42—31no—
85C2×C42—32no—
86#97—32no—
87#97—32no—
88#97—31no—
89#97C3×A411yescharacteristic, direct product factor
90C23×C3—31no—
91C23×C3—32no—
92C23×C3—31no—
93C23×C3C3×C4211yescharacteristic
94C23×C3C3×M1612yes—
95C2×A4C3×C4213yes—
96C2×A4C3×M1616yes—
97C2×C3×C4—32no—
98C2×C3×C4—31no—
99C2×C3×C4—32no—
100C2×C3×C4—32no—
101C2×C3×C4—32no—
102C2×C3×C4—32no—
103C2×C3×C4—43no—
104C2×C3×C4—46no—
105C2×C3×C4—62no—
106C2×C3×C4—62no—
107C2×C3×C4—62no—
108C2×C3×C4—62no—
109C2×C3×C4C4×A412yes—
110C2×C3×C4C22×A411yescharacteristic
111C3×C8—34no—
112C3×C8—412no—
113C3×C8C4×A414yescomplemented
114C2×C32—41no—
115C2×C32—42no—
116C24C2×C32×C411yescharacteristic
117C22×C4—22no—
118C22×C4—31no—
119C22×C4—31no—
120C22×C4—32no—
121C22×C4—32no—
122C22×C4—32no—
123C22×C4—62no—
124C22×C4C2×C32×C412yes—
125C2×C8—34no—
126C2×C8—32no—
127C2×C8—34no—
128C2×C8—34no—
129C2×C8—34no—
130C2×C8C2×C3×A412yes—
131C42—32no—
132C42—31no—
133C42—32no—
134C42C2×C3×A411yescharacteristic
135C22×C3—31no—
136C22×C3—32no—
137C22×C3—32no—
138C22×C3—31no—
139C22×C3—31no—
140C22×C3—32no—
141C22×C3—32no—
142C22×C3—43no—
143C22×C3C3×#9711yescharacteristic, complemented
144C22×C3C2×C4×A411yescharacteristic
145A4C3×#9713yesdirect product factor
146C3×C4—22no—
147C3×C4—32no—
148C3×C4—46no—
149C3×C4—62no—
150C3×C4—86no—
151C3×C4C2×C4×A412yes—
152C32—41noSylow
153C23—31no—
154C23—32no—
155C23—31no—
156C23C32×C4211yescharacteristic
157C23C32×M1612yes—
158C2×C4—32no—
159C2×C4—31no—
160C2×C4—32no—
161C2×C4—32no—
162C2×C4—32no—
163C2×C4—32no—
164C2×C4—62no—
165C2×C4—62no—
166C2×C4—62no—
167C2×C4—62no—
168C2×C4C3×C4×A412yes—
169C2×C4C22×C3×A411yescharacteristic
170C8—34no—
171C8C3×C4×A414yescomplemented
172C2×C3—31no—
173C2×C3—32no—
174C2×C3—31no—
175C2×C3—43no—
176C2×C3—46no—
177C2×C3C42×A411yescharacteristic
178C2×C3A4×M1612yes—
179C22—31no—
180C22—32no—
181C22—32no—
182C22—31no—
183C22—31no—
184C22—32no—
185C22—32no—
186C22C32×#9711yescharacteristic, complemented
187C22C2×C3×C4×A411yescharacteristic
188C4—22no—
189C4—32no—
190C4—62no—
191C4C2×C3×C4×A412yes—
192C3—43no—
193C3A4×#9711yescharacteristic, direct product factor
194C2—31no—
195C2—31no—
196C2—32no—
197C2C3×C42×A411yescharacteristic
198C2C3×A4×M1612yes—
subgroupG/H
centerC2×C3×C4C22×A4
commutatorC23C32×C42
FrattiniC2×C4C22×C3×A4
FittingC22×C3×#97C3
socleC24×C3C2×C3×C4
prime radicalC22×C3×A4C2×C4
cosocleC23×C4C22×C32
hypercenterC3×#97A4
hypocenterC22C32×#97
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3×C4 ◁ C3×#97

Complements

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

NH ≅ G/Ntype
3. C22×C3×#97C3semidirect
4. A4×#97C3direct (N × H)
7. C3×C8×A4C4semidirect
21. C22×#97C32semidirect
29. C22×C3×C8C3×C4semidirect
33. C8×A4C3×C4semidirect
38. C3×#97A4direct (N × H)
74. C3×A4#97direct (N × H)
82. C22×C8C32×C4semidirect
89. #97C3×A4direct (N × H)
113. C3×C8C4×A4semidirect
143. C22×C3C3×#97semidirect
145. A4C3×#97direct (N × H)
171. C8C3×C4×A4semidirect
186. C22C32×#97semidirect
193. C3A4×#97direct (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×C42×A42
C22×C3×#973
A4×#973
C32×#974