Finite Group Databasebeta

← Dic6×C42⋊C3 #11921114

Subgroups — Dic6×C42⋊C3 #11921114

Order 1152.

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

normal subgroups only

This group has 297 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×C4×C42⋊C3C211yesmaximal, characteristic
2Dic3×C42⋊C3C212yesmaximal
3C42×Dic6C311yesmaximal, characteristic, complemented
4Q8×C42⋊C3—31nomaximal
5A4×Dic6—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C2×C4×Dic6—31no—
8C3×C43C2×C311yescharacteristic
9C4×C4⋊Dic3—31no—
10C4×Dic3⋊C4—32no—
11C42×Dic3C2×C312yes—
12C4×C42⋊C3—21no—
13C4×C42⋊C3—32no—
14C4×C42⋊C3D311yescharacteristic
15C3×C4×A4—41no—
16Dic3×A4—42no—
17C3×C42⋊C3Q811yescharacteristic, complemented
18C42×Q8—31noSylow
19C22×Dic6A411yescharacteristic
20Q8×A4—121no—
21C2×C3×C42—31no—
22C2×C3×C42—31no—
23C2×C3×C42C22×C311yescharacteristic
24C2×C4⋊Dic3—31no—
25C2×Dic3⋊C4—32no—
26C2×C4×Dic3—32no—
27C2×C4×Dic3—32no—
28C4×Dic6—32no—
29C4×Dic6—34no—
30C4×Dic6—32no—
31C2×C42⋊C3—21no—
32C2×C42⋊C3C2×D311yescharacteristic
33C3⋊#95—32no—
34C2×C3×A4—41no—
35C3×Dic6—161no—
36C2×C4×Q8—91no—
37C4×C4⋊C4—92no—
38C4×C4⋊C4—91no—
39C43—32no—
40C43C3×D311yescharacteristic
41C22×C3×C4—31no—
42C22×C3×C4—31no—
43C22×C3×C4C2×A411yescharacteristic
44C22×Dic3—32no—
45C22×Dic3C2×A412yes—
46C2×Dic6—31no—
47C2×Dic6—31no—
48C2×Dic6—32no—
49C4×A4—41no—
50C4×A4—81no—
51C4×A4—122no—
52C3×C42—31no—
53C3×C42—32no—
54C3×C42—32no—
55C3×C42—62no—
56C3×C42C3×Q811yescharacteristic, complemented
57C4⋊Dic3—32no—
58C4⋊Dic3—32no—
59Dic3⋊C4—34no—
60Dic3⋊C4—34no—
61C4×Dic3—34no—
62C4×Dic3—34no—
63C4×Dic3—64no—
64C42⋊C3—21no—
65C42⋊C3Dic611yescharacteristic, direct product factor
66C3×A4—41no—
67C32×C4—161no—
68C3×Dic3—162no—
69C22×Q8—31no—
70C4×Q8—92no—
71C4×Q8—92no—
72C4×Q8—94no—
73C2×C4⋊C4—92no—
74C2×C4⋊C4—91no—
75C2×C42—31no—
76C2×C42—31no—
77C2×C42—92no—
78C2×C42—92no—
79C2×C42C2×C3×D311yescharacteristic
80#95—92no—
81C23×C3C22×A411yescharacteristic
82C2×A4—41no—
83C2×A4—81no—
84C3×Q8—481no—
85C2×C3×C4—32no—
86C2×C3×C4—32no—
87C2×C3×C4—31no—
88C2×C3×C4—31no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4—32no—
92C2×C3×C4—62no—
93C2×Dic3—32no—
94C2×Dic3—32no—
95C2×Dic3—34no—
96C2×Dic3—64no—
97Dic6—32no—
98Dic6—31no—
99Dic6—32no—
100Dic6C42⋊C311yescharacteristic, direct product factor
101C2×C32—161no—
102C2×Q8—91no—
103C2×Q8—91no—
104C2×Q8—92no—
105C22×C4—31no—
106C22×C4—31no—
107C22×C4—32no—
108C22×C4—92no—
109C22×C4D3×A411yescharacteristic
110C4⋊C4—94no—
111C4⋊C4—94no—
112C4⋊C4—92no—
113C4⋊C4—92no—
114C42—31no—
115C42—32no—
116C42—32no—
117C42—62no—
118C42—94no—
119C42—94no—
120C42—184no—
121C42C3×Dic611yescharacteristic, complemented
122C22×C3—31no—
123C22×C3—31no—
124C22×C3Q8×A411yescharacteristic
125A4—41no—
126A4—81no—
127C3×C4—32no—
128C3×C4—32no—
129C3×C4—31no—
130C3×C4—62no—
131C3×C4—161no—
132C3×C4—321no—
133C3×C4—482no—
134C3×C4C2×C42⋊C311yescharacteristic
135Dic3—32no—
136Dic3—64no—
137Dic3C2×C42⋊C312yes—
138C32—161noSylow
139C23C2×D3×A411yescharacteristic
140Q8—31no—
141Q8—92no—
142Q8—92no—
143Q8—91no—
144C2×C4—32no—
145C2×C4—32no—
146C2×C4—31no—
147C2×C4—31no—
148C2×C4—31no—
149C2×C4—31no—
150C2×C4—32no—
151C2×C4—62no—
152C2×C4—92no—
153C2×C4—92no—
154C2×C4—94no—
155C2×C4—184no—
156C2×C3—31no—
157C2×C3—31no—
158C2×C3—161no—
159C2×C3—321no—
160C2×C3C22×C42⋊C311yescharacteristic
161C22—31no—
162C22—31no—
163C22A4×Dic611yescharacteristic
164C4—32no—
165C4—32no—
166C4—31no—
167C4—32no—
168C4—62no—
169C4—92no—
170C4—184no—
171C4D3×C42⋊C311yescharacteristic
172C3—161no—
173C3—321no—
174C3Q8×C42⋊C311yescharacteristic, complemented
175C2—31no—
176C2—31no—
177C2C2×D3×C42⋊C311yescharacteristic
subgroupG/H
centerC2C2×D3×C42⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×C43C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypercenterC4D3×C42⋊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. C42×Dic6C3semidirect
17. C3×C42⋊C3Q8semidirect
56. C3×C42C3×Q8semidirect
65. C42⋊C3Dic6direct (N × H)
100. Dic6C42⋊C3direct (N × H)
121. C42C3×Dic6semidirect
174. C3Q8×C42⋊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
Dic3×C42⋊C32
C42×Dic63
Q8×C42⋊C33
A4×Dic64