Finite Group Databasebeta

← C3×#2868⋊C3 #11919514

Subgroups — C3×#2868⋊C3 #11919514

Order 1152.

312 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 54 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×#384⋊C3C212yesmaximal
2C3×C4×C42⋊C3C211yesmaximal, characteristic
3C3×#2868C311yesmaximal, characteristic, complemented
4#2868⋊C3C313yesmaximal, direct product factor
5C3×Q8×A4—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C2×C3×C4⋊Q8—31no—
8C2×C3×C4⋊Q8—31no—
9C3×#384—32no—
10C3×#384C2×C312yes—
11C3×C43C2×C311yescharacteristic
12#384⋊C3C2×C316yes—
13C4×C42⋊C3C2×C313yes—
14C3×C4×A4—41no—
15C3×C4×A4—42no—
16C3×C42⋊C3Q811yescharacteristic, complemented
17#2868C3211yescharacteristic, complemented, Sylow
18C22×C3×Q8—31no—
19C22×C3×Q8A411yescharacteristic
20Q8×A4—43no—
21C3×C4⋊Q8—62no—
22C3×C4⋊Q8—62no—
23C3×C4⋊Q8—62no—
24C3×C4⋊Q8—62no—
25C2×C3×C4⋊C4—32no—
26C2×C3×C4⋊C4—32no—
27C2×C3×C4⋊C4—32no—
28C2×C3×C4⋊C4—32no—
29C2×C3×C42—31no—
30C2×C3×C42—31no—
31C2×C3×C42C22×C311yescharacteristic
32C2×C42⋊C3C22×C313yes—
33C2×C3×A4—41no—
34C32×Q8—161no—
35C2×C4⋊Q8—31no—
36C2×C4⋊Q8—31no—
37#384—32no—
38#384C2×C3212yes—
39C43C2×C3211yescharacteristic
40C2×C3×Q8—61no—
41C2×C3×Q8—61no—
42C2×C3×Q8—61no—
43C2×C3×Q8—62no—
44C2×C3×Q8—61no—
45C2×C3×Q8—62no—
46C22×C3×C4—31no—
47C22×C3×C4—31no—
48C22×C3×C4—32no—
49C22×C3×C4C2×A411yescharacteristic
50C22×C3×C4C2×A412yes—
51C4×A4—43no—
52C4×A4—46no—
53C3×C4⋊C4—64no—
54C3×C4⋊C4—64no—
55C3×C4⋊C4—64no—
56C3×C4⋊C4—64no—
57C3×C42—31no—
58C3×C42—34no—
59C3×C42—32no—
60C3×C42—32no—
61C3×C42C3×Q811yescharacteristic, complemented
62C42⋊C3C3×Q813yescomplemented
63C3×A4—41no—
64C32×C4—162no—
65C32×C4—161no—
66C22×Q8—31no—
67C22×Q8C3×A411yescharacteristic
68C4⋊Q8—62no—
69C4⋊Q8—62no—
70C4⋊Q8—62no—
71C4⋊Q8—62no—
72C2×C4⋊C4—32no—
73C2×C4⋊C4—32no—
74C2×C4⋊C4—32no—
75C2×C4⋊C4—32no—
76C2×C42—31no—
77C2×C42—31no—
78C2×C42C22×C3211yescharacteristic
79C23×C3C22×A411yescharacteristic
80C2×A4—43no—
81C3×Q8—41no—
82C3×Q8—121no—
83C3×Q8—121no—
84C3×Q8—122no—
85C3×Q8—121no—
86C3×Q8—163no—
87C2×C3×C4—32no—
88C2×C3×C4—32no—
89C2×C3×C4—32no—
90C2×C3×C4—34no—
91C2×C3×C4—31no—
92C2×C3×C4—31no—
93C2×C3×C4—31no—
94C2×C3×C4—31no—
95C2×C3×C4—62no—
96C2×C3×C4—62no—
97C2×C3×C4—64no—
98C2×C32—161no—
99C2×Q8—61no—
100C2×Q8—61no—
101C2×Q8—61no—
102C2×Q8—62no—
103C2×Q8—61no—
104C2×Q8—62no—
105C22×C4—31no—
106C22×C4—31no—
107C22×C4—32no—
108C22×C4C2×C3×A411yescharacteristic
109C22×C4C2×C3×A412yes—
110C4⋊C4—64no—
111C4⋊C4—64no—
112C4⋊C4—64no—
113C4⋊C4—64no—
114C42—31no—
115C42—32no—
116C42—32no—
117C42—34no—
118C42C32×Q811yescharacteristic, complemented
119C22×C3—31no—
120C22×C3—31no—
121C22×C3Q8×A411yescharacteristic
122A4—43no—
123C3×C4—34no—
124C3×C4—32no—
125C3×C4—32no—
126C3×C4—31no—
127C3×C4—42no—
128C3×C4—122no—
129C3×C4—166no—
130C3×C4—163no—
131C3×C4#127⋊C311yescharacteristic
132C32—161noSylow
133C23C22×C3×A411yescharacteristic
134Q8—41no—
135Q8—121no—
136Q8—121no—
137Q8—122no—
138Q8—121no—
139C2×C4—32no—
140C2×C4—32no—
141C2×C4—32no—
142C2×C4—34no—
143C2×C4—31no—
144C2×C4—31no—
145C2×C4—31no—
146C2×C4—31no—
147C2×C4—62no—
148C2×C4—62no—
149C2×C4—64no—
150C2×C3—31no—
151C2×C3—31no—
152C2×C3—163no—
153C2×C3C2×#127⋊C311yescharacteristic
154C22—31no—
155C22—31no—
156C22C3×Q8×A411yescharacteristic
157C4—32no—
158C4—32no—
159C4—34no—
160C4—31no—
161C4—42no—
162C4—122no—
163C4C3×#127⋊C311yescharacteristic
164C3—163no—
165C3#2868⋊C311yescharacteristic, direct product factor
166C2—31no—
167C2—31no—
168C2C2×C3×#127⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×#127⋊C3
commutator, cosocleC2×C42C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2868C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypercenterC3×C4#127⋊C3
hypocenterC42C32×Q8
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
3. C3×#2868C3semidirect
4. #2868⋊C3C3direct (N × H)
16. C3×C42⋊C3Q8semidirect
17. #2868C32semidirect
61. C3×C42C3×Q8semidirect
62. C42⋊C3C3×Q8semidirect
118. C42C32×Q8semidirect
165. C3#2868⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#384⋊C32
C3×C4×C42⋊C32
C3×#28683
#2868⋊C33
C3×Q8×A44