Finite Group Databasebeta

← #11771848

Subgroups — #11771848

Order 1152.

378 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#10592814C211yesmaximal, characteristic
2C32×#340C211yesmaximal, characteristic, complemented
3#10589415C211yesmaximal, characteristic, complemented
4#67485—34nomaximal
5C22×C32×C8C2211yescharacteristic
6C2×C32×C4⋊C4—21no—
7#64139—21no—
8C2×#3745C411yescharacteristic, complemented
9#63648—21no—
10#63645C411yescharacteristic, complemented
11C2×C3⋊(C3⋊C16)—21no—
12#5115—34no—
13C3×#340D314yescomplemented
14#4549—34no—
15C22×C32×C4—41no—
16C22×C32×C4D411yescharacteristic
17C2×#638—41no—
18C2×C4⋊(C3⋊D3)—21no—
19C2×C32×C8—41no—
20C2×C32×C8C2×C411yescharacteristic
21C2×C32×C8D411yescharacteristic
22C32×C4⋊C4—22no—
23C32×C4⋊C4—41no—
24#3752—41no—
25C4⋊(C3⋊Dic3)—21no—
26#3745—41no—
27C3⋊(C3⋊C16)—41no—
28#1347—91noSylow
29C22×C3×C8C2×D314yes—
30C2×C3×C4⋊C4—24no—
31#930—64no—
32C2×D24—34no—
33#821—64no—
34#818—34no—
35C2×C3⋊C16—64no—
36C23×C32D811yescharacteristic
37C22×C3⋊D3—41no—
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4—42no—
41C2×C32×C4—81no—
42C2×C32×C4—81no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4SD1611yescharacteristic
45#638—81no—
46#638—81no—
47C2×C3⋊Dic3—41no—
48C4⋊(C3⋊D3)—41no—
49C4⋊(C3⋊D3)—41no—
50C32×C8—21no—
51C32×C8—21no—
52#466—91no—
53C22⋊C16—91no—
54#340C3⋊D311yescharacteristic, complemented
55C22×C3×C4—44no—
56C22×C3×C4#6714yes—
57C2×#67—124no—
58C2×D12—64no—
59C2×C3×C8—44no—
60C2×C3×C8C4×D314yes—
61C2×C3×C8D1214yes—
62C3×C4⋊C4—28no—
63C3×C4⋊C4—44no—
64(C2×D3)⋊C4—124no—
65C4⋊Dic3—64no—
66D24—124no—
67C3⋊C16—124no—
68C22×C32—21no—
69C22×C32—21no—
70C22×C32#10211yescharacteristic
71C22×C32D1611yescharacteristic
72C22×C32SD3211yescharacteristic
73C2×C3⋊D3—81no—
74C2×C3⋊D3—81no—
75C2×C3⋊D3—81no—
76C32×C4—21no—
77C32×C4—82no—
78C32×C4#9911yescharacteristic
79C32×C4#10411yescharacteristic
80C3⋊Dic3—81no—
81C2×D8—91no—
82C22×C8C2×C3⋊D311yescharacteristic
83#121—181no—
84C2×C4⋊C4—21no—
85C2×C16—181no—
86#107—91no—
87#102—181no—
88C23×C3#21314yes—
89C22×D3—124no—
90C2×C3×C4—24no—
91C2×C3×C4—24no—
92C2×C3×C4—48no—
93C2×C3×C4—84no—
94C2×C3×C4—84no—
95C2×C3×C4(C2×D3)⋊C414yes—
96C2×C3×C4#21514yes—
97#67—244no—
98#67—244no—
99C2×Dic3—124no—
100D12—124no—
101D12—124no—
102C3×C8—24no—
103C3×C8—24no—
104C2×C32—21no—
105C2×C32—21no—
106C2×C32#32711yescharacteristic
107C2×C32#35711yescharacteristic
108C2×C32#36011yescharacteristic
109C3⋊D3—161no—
110C2×D4—181no—
111C2×D4—361no—
112C22×C4—41no—
113C22×C4#63811yescharacteristic
114D8—361no—
115C2×C8—41no—
116C2×C8C4×C3⋊D311yescharacteristic
117C2×C8C4⋊(C3⋊D3)11yescharacteristic
118C4⋊C4—22no—
119C4⋊C4—41no—
120C4⋊C4—181no—
121C22⋊C4—361no—
122C16—361no—
123C22×C3—24no—
124C22×C3—24no—
125C22×C3#80914yes—
126C22×C3#82614yes—
127C22×C3#82814yes—
128C2×D3—244no—
129C2×D3—244no—
130C2×D3—244no—
131C3×C4—24no—
132C3×C4—88no—
133C3×C4#80514yes—
134C3×C4#80614yes—
135Dic3—244no—
136C32#134711yescharacteristic, complemented, Sylow
137C23—361no—
138C23#375311yescharacteristic
139D4—361no—
140D4—361no—
141D4—721no—
142D4—721no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—42no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—361no—
149C2×C4#375211yescharacteristic
150C2×C4#375511yescharacteristic
151C8—21no—
152C8—21no—
153C2×C3—24no—
154C2×C3—24no—
155C2×C3#445114yes—
156C2×C3#448814yes—
157C2×C3#449114yes—
158D3—484no—
159C22—21no—
160C22—21no—
161C22—721no—
162C22—721no—
163C22—721no—
164C22#6363611yescharacteristic
165C22#6365311yescharacteristic
166C22#6365511yescharacteristic
167C4—21no—
168C4—82no—
169C4—721no—
170C4#6363211yescharacteristic
171C4#6363311yescharacteristic
172C3#6748514yescomplemented
173C2—21no—
174C2—21no—
175C2—1441no—
176C2#1058931711yescharacteristic
177C2#1058935411yescharacteristic
178C2#1058935711yescharacteristic
subgroupG/H
centerC22#63636
commutatorC2×C32×C8C2×C4
FrattiniC22×C8C2×C3⋊D3
FittingC32×#340C2
socleC22×C32#102
prime radical#10592814C2
cosocleC22×C32×C8C22
hypercenter#340C3⋊D3
hypocenterC32#1347
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C32×#340C2semidirect
3. #10589415C2semidirect
8. C2×#3745C4semidirect
10. #63645C4semidirect
13. C3×#340D3semidirect
54. #340C3⋊D3semidirect
136. C32#1347semidirect
172. C3#67485semidirect

Maximal subgroups

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

subgroupindex
#105928142
C32×#3402
#105894152
#674853