Finite Group Databasebeta

← #73311⋊C3 #11921115

Subgroups — #73311⋊C3 #11921115

Order 1152.

285 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 33 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×C4×C42⋊C3C211yesmaximal, characteristic
2C3⋊(#384⋊C3)C212yesmaximal
3#73311C311yesmaximal, characteristic, complemented
4#2868⋊C3—31nomaximal
5A4×Dic6—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C2×#869—31no—
8C2×#869—31no—
9C3×C43C2×C311yescharacteristic
10#4935—32no—
11#4935C2×C312yes—
12#384⋊C3—32no—
13C4×C42⋊C3—21no—
14C4×C42⋊C3D311yescharacteristic
15C3×C4×A4—41no—
16Dic3×A4—42no—
17C3×C42⋊C3Q811yescharacteristic, complemented
18#2868—31noSylow
19C22×Dic6—31no—
20C22×Dic6A411yescharacteristic
21Q8×A4—121no—
22C2×C3×C42—31no—
23C2×C3×C42—31no—
24C2×C3×C42C22×C311yescharacteristic
25C2×C4⋊Dic3—32no—
26C2×C4⋊Dic3—32no—
27C2×C4⋊Dic3—32no—
28C2×C4⋊Dic3—32no—
29#869—62no—
30#869—62no—
31#869—62no—
32#869—62no—
33C2×C42⋊C3—21no—
34C2×C42⋊C3C2×D311yescharacteristic
35C2×C3×A4—41no—
36C3×Dic6—161no—
37C2×C4⋊Q8—91no—
38C2×C4⋊Q8—91no—
39#384—32no—
40#384—92no—
41C43C3×D311yescharacteristic
42C22×C3×C4—31no—
43C22×C3×C4—31no—
44C22×C3×C4C2×A411yescharacteristic
45C22×Dic3—32no—
46C22×Dic3C2×A412yes—
47C2×Dic6—61no—
48C2×Dic6—62no—
49C2×Dic6—61no—
50C2×Dic6—61no—
51C2×Dic6—62no—
52C2×Dic6—61no—
53C4×A4—41no—
54C4×A4—81no—
55C4×A4—122no—
56C3×C42—31no—
57C3×C42—32no—
58C3×C42—32no—
59C3×C42—34no—
60C3×C42C3×Q811yescharacteristic, complemented
61C4⋊Dic3—64no—
62C4⋊Dic3—64no—
63C4⋊Dic3—64no—
64C4⋊Dic3—64no—
65C42⋊C3—21no—
66C42⋊C3Dic611yescharacteristic, complemented
67C3×A4—41no—
68C32×C4—161no—
69C3×Dic3—162no—
70C22×Q8—31no—
71C22×Q8—91no—
72C4⋊Q8—182no—
73C4⋊Q8—182no—
74C4⋊Q8—182no—
75C4⋊Q8—182no—
76C2×C4⋊C4—92no—
77C2×C4⋊C4—92no—
78C2×C4⋊C4—92no—
79C2×C4⋊C4—92no—
80C2×C42—31no—
81C2×C42—31no—
82C2×C42C2×C3×D311yescharacteristic
83C23×C3C22×A411yescharacteristic
84C2×A4—41no—
85C2×A4—81no—
86C3×Q8—481no—
87C2×C3×C4—32no—
88C2×C3×C4—32no—
89C2×C3×C4—34no—
90C2×C3×C4—32no—
91C2×C3×C4—31no—
92C2×C3×C4—31no—
93C2×C3×C4—31no—
94C2×C3×C4—31no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—64no—
98Dic6—41no—
99Dic6—121no—
100Dic6—121no—
101Dic6—122no—
102Dic6—121no—
103C2×C32—161no—
104C2×Q8—181no—
105C2×Q8—181no—
106C2×Q8—181no—
107C2×Q8—182no—
108C2×Q8—181no—
109C2×Q8—182no—
110C22×C4—31no—
111C22×C4—31no—
112C22×C4—32no—
113C22×C4—92no—
114C22×C4D3×A411yescharacteristic
115C4⋊C4—184no—
116C4⋊C4—184no—
117C4⋊C4—184no—
118C4⋊C4—184no—
119C42—31no—
120C42—32no—
121C42—32no—
122C42—34no—
123C42C3×Dic611yescharacteristic, complemented
124C22×C3—31no—
125C22×C3—31no—
126C22×C3Q8×A411yescharacteristic
127A4—41no—
128A4—81no—
129C3×C4—34no—
130C3×C4—32no—
131C3×C4—32no—
132C3×C4—31no—
133C3×C4—161no—
134C3×C4—321no—
135C3×C4—482no—
136C3×C4#127⋊C311yescharacteristic
137Dic3—42no—
138Dic3—122no—
139C32—161noSylow
140C23C2×D3×A411yescharacteristic
141Q8—121no—
142Q8—361no—
143Q8—361no—
144Q8—362no—
145Q8—361no—
146C2×C4—32no—
147C2×C4—32no—
148C2×C4—32no—
149C2×C4—34no—
150C2×C4—31no—
151C2×C4—31no—
152C2×C4—31no—
153C2×C4—31no—
154C2×C4—182no—
155C2×C4—182no—
156C2×C4—184no—
157C2×C3—31no—
158C2×C3—31no—
159C2×C3—161no—
160C2×C3—321no—
161C2×C3C2×#127⋊C311yescharacteristic
162C22—31no—
163C22—31no—
164C22A4×Dic611yescharacteristic
165C4—32no—
166C4—32no—
167C4—34no—
168C4—31no—
169C4—122no—
170C4—362no—
171C4C3⋊(#127⋊C3)11yescharacteristic
172C3—161no—
173C3—321no—
174C3#2868⋊C311yescharacteristic, complemented
175C2—31no—
176C2—31no—
177C2C2×C3⋊(#127⋊C3)11yescharacteristic
subgroupG/H
centerC2C2×C3⋊(#127⋊C3)
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×C43C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypercenterC4C3⋊(#127⋊C3)
hypocenterC3×C42C3×Q8
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
3. #73311C3semidirect
17. C3×C42⋊C3Q8semidirect
60. C3×C42C3×Q8semidirect
66. C42⋊C3Dic6semidirect
123. C42C3×Dic6semidirect
174. C3#2868⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C42⋊C32
C3⋊(#384⋊C3)2
#733113
#2868⋊C33
A4×Dic64