Finite Group Databasebeta

← #11920950

Subgroups — #11920950

Order 1152.

346 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 31 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⋊#857C212yesmaximal, complemented
2C3×#384⋊C3C211yesmaximal, characteristic, complemented
3#72994—33nomaximal
4#69593—31nomaximal
5C4⋊(C3⋊S4)—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3⋊#857—22no—
8#5510—31no—
9C2×#857—36no—
10C3×#384D311yescharacteristic, complemented
11#4966—32no—
12C2×#805—32no—
13#384⋊C3D313yescomplemented
14#4530—31no—
15C2×C3⋊S4—42no—
16C3×C4×A4—41no—
17C3×C42⋊C3D411yescharacteristic, complemented
18#2039—91noSylow
19C2×#235—32no—
20C4⋊S4—123no—
21C2×C3×C4⋊C4—31no—
22C2×C3×C4⋊C4—31no—
23C2×C3×C42C2×D311yescharacteristic
24#930—61no—
25#930—61no—
26C2×#208—32no—
27#897—62no—
28#895—62no—
29C2×C42⋊C3C2×D313yes—
30#857—66no—
31#810—62no—
32#809—62no—
33#805—62no—
34#805—62no—
35C2×C3×A4—41no—
36C3⋊S4—82no—
37C4⋊(C3⋊D3)—161no—
38#537—91no—
39C2×#104—92no—
40#417—92no—
41#384C3⋊D311yescharacteristic, complemented
42#343—91no—
43C2×S4—126no—
44C22×C3×C4—31no—
45C22×C3×C4—31no—
46C22×C3×C4S411yescharacteristic
47C2×#67—62no—
48#235—62no—
49#235—62no—
50#235—62no—
51#235—62no—
52C2×D12—32no—
53C2×D12—61no—
54C2×D12—61no—
55C2×C4×D3—62no—
56C2×Dic6—32no—
57C4×A4—43no—
58C3×C4⋊C4—62no—
59C3×C4⋊C4—62no—
60C3×C42—31no—
61C3×C42D1211yescharacteristic, complemented
62(C2×D3)⋊C4—62no—
63(C2×D3)⋊C4—62no—
64C4⋊Dic3—61no—
65C4⋊Dic3—61no—
66#208—62no—
67#208—62no—
68C2×C3⋊C8—62no—
69C42⋊C3D1213yescomplemented
70C2×C3⋊D3—162no—
71C3×A4—41no—
72C32×C4—161no—
73C2×#41—92no—
74C2×M16—92no—
75C22⋊Q8—182no—
76#121—182no—
77#121—181no—
78#121—181no—
79C2×C4⋊C4—31no—
80C2×C4⋊C4—31no—
81C2×C42C2×C3⋊D311yescharacteristic
82#104—182no—
83#104—182no—
84#103—182no—
85#102—182no—
86C23×C3C2×S411yescharacteristic
87C22×D3—62no—
88C2×A4—43no—
89S4—246no—
90C2×C3×C4—32no—
91C2×C3×C4—32no—
92C2×C3×C4—31no—
93C2×C3×C4—31no—
94C2×C3×C4—61no—
95C2×C3×C4—61no—
96C2×C3×C4—121no—
97#67—122no—
98#67—122no—
99C2×Dic3—62no—
100D12—62no—
101D12—62no—
102D12—241no—
103D12—241no—
104D12—483no—
105C4×D3—122no—
106C4×D3—122no—
107Dic6—62no—
108Dic6—62no—
109C3⋊C8—122no—
110C2×C32—161no—
111C3⋊D3—322no—
112#41—182no—
113#41—182no—
114#41—182no—
115#41—182no—
116C2×Q8—92no—
117C2×D4—92no—
118C2×D4—181no—
119C2×D4—181no—
120C2×D4—182no—
121C22×C4—31no—
122C22×C4—31no—
123C22×C4—182no—
124C22×C4C3⋊S411yescharacteristic
125M16—182no—
126M16—182no—
127C2×C8—182no—
128C4⋊C4—62no—
129C4⋊C4—62no—
130C4⋊C4—181no—
131C4⋊C4—181no—
132C22⋊C4—182no—
133C22⋊C4—182no—
134C42—31no—
135C42C4⋊(C3⋊D3)11yescharacteristic, complemented
136C22×C3—31no—
137C22×C3—31no—
138C22×C3C4⋊S411yescharacteristic
139C2×D3—122no—
140C2×D3—122no—
141C2×D3—122no—
142C2×D3—486no—
143A4—43no—
144C3×C4—32no—
145C3×C4—32no—
146C3×C4—41no—
147C3×C4—121no—
148C3×C4—163no—
149Dic3—122no—
150C32—161noSylow
151C23—182no—
152C23C2×C3⋊S411yescharacteristic
153Q8—182no—
154Q8—182no—
155D4—182no—
156D4—182no—
157D4—362no—
158D4—362no—
159D4—721no—
160D4—721no—
161C2×C4—32no—
162C2×C4—32no—
163C2×C4—31no—
164C2×C4—31no—
165C2×C4—61no—
166C2×C4—61no—
167C2×C4—121no—
168C2×C4—182no—
169C2×C4—362no—
170C2×C4—362no—
171C8—362no—
172C2×C3—31no—
173C2×C3—31no—
174C2×C3—163no—
175C2×C3#857⋊C211yescharacteristic
176D3—242no—
177D3—966no—
178C22—31no—
179C22—31no—
180C22—362no—
181C22—362no—
182C22—362no—
183C22C4⋊(C3⋊S4)11yescharacteristic
184C4—32no—
185C4—32no—
186C4—41no—
187C4—121no—
188C4—362no—
189C3—163no—
190C3#7299411yescharacteristic, complemented
191C2—31no—
192C2—31no—
193C2—722no—
194C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, cosocleC2×C3×C42⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#384D3
socleC23×C3C2×S4
hypocenterC3×C42⋊C3D4
LCSG ▷ C2×C3×C42⋊C3 ▷ C3×C42⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#857C2semidirect
2. C3×#384⋊C3C2semidirect
10. C3×#384D3semidirect
13. #384⋊C3D3semidirect
17. C3×C42⋊C3D4semidirect
41. #384C3⋊D3semidirect
61. C3×C42D12semidirect
69. C42⋊C3D12semidirect
135. C42C4⋊(C3⋊D3)semidirect
190. C3#72994semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#8572
C3×#384⋊C32
#729943
#695933
C4⋊(C3⋊S4)4