Finite Group Databasebeta

← #11799801

Subgroups — #11799801

Order 1152.

450 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 137 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×C32×#107C211yesmaximal, characteristic, complemented
2#10592814C211yesmaximal, characteristic
3#10589415C211yesmaximal, characteristic, complemented
4#10589357C212yesmaximal, complemented
5#10589356C212yesmaximal, complemented
6#70600—34nomaximal
7C22×C32×C8C2211yescharacteristic
8C2×C32×C4⋊C4—21no—
9#64139—21no—
10C2×#3745C2211yescharacteristic
11C32×#107—21no—
12C32×#107C2212yes—
13#63648—21no—
14#63645C2211yescharacteristic
15C2×C3⋊(C3⋊C16)C2212yes—
16C2×C3×#107D314yescomplemented
17#5115—34no—
18#4549—34no—
19#4491—38no—
20#4490—38no—
21C22×C32×C4—41no—
22C22×C32×C4D411yescharacteristic
23C2×#638—41no—
24C2×C4⋊(C3⋊D3)—21no—
25C2×C32×C8—22no—
26C2×C32×C8D411yescharacteristic
27C2×C32×C8C2311yescharacteristic
28C32×C4⋊C4—22no—
29C32×C4⋊C4—41no—
30#3752—41no—
31C4⋊(C3⋊Dic3)—21no—
32#3745—22no—
33C3⋊(C3⋊C16)—22no—
34#2233—91noSylow
35C22×C3×C8C2×D314yes—
36C2×C3×C4⋊C4—24no—
37#930—64no—
38C2×D24—34no—
39C3×#107—24no—
40C3×#107C2×D318yes—
41#821—64no—
42#818—34no—
43C2×C3⋊C16—38no—
44C23×C32D811yescharacteristic
45C22×C3⋊D3—41no—
46C2×C32×C4—21no—
47C2×C32×C4—21no—
48C2×C32×C4—42no—
49C2×C32×C4—82no—
50C2×C32×C4D811yescharacteristic
51C2×C32×C4C2×D411yescharacteristic
52#638—82no—
53C2×C3⋊Dic3—41no—
54C4⋊(C3⋊D3)—41no—
55C4⋊(C3⋊D3)—41no—
56C32×C8—21no—
57C32×C8#4112yes—
58#466—91no—
59C2×#107C3⋊D311yescharacteristic, complemented
60#367—92no—
61#357—92no—
62C22⋊C16—91no—
63C22×C3×C4—44no—
64C22×C3×C4#6714yes—
65C2×#67—124no—
66C2×D12—64no—
67C2×C3×C8—28no—
68C2×C3×C8#6714yes—
69C2×C3×C8C22×D314yes—
70C3×C4⋊C4—28no—
71C3×C4⋊C4—44no—
72(C2×D3)⋊C4—124no—
73C4⋊Dic3—64no—
74D24—68no—
75C3⋊C16—68no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32SD3212yes—
79C22×C32C2×D811yescharacteristic
80C2×C3⋊D3—81no—
81C2×C3⋊D3—81no—
82C2×C3⋊D3—81no—
83C32×C4—21no—
84C32×C4—82no—
85C32×C4#12311yescharacteristic
86C32×C4#13711yescharacteristic
87C3⋊Dic3—81no—
88C2×D8—91no—
89C22×C8C2×C3⋊D311yescharacteristic
90#121—181no—
91C2×C4⋊C4—21no—
92C2×C16—92no—
93#107—21no—
94#107—91no—
95#107C2×C3⋊D312yes—
96#102—181no—
97C23×C3#21314yes—
98C22×D3—124no—
99C2×C3×C4—24no—
100C2×C3×C4—24no—
101C2×C3×C4—48no—
102C2×C3×C4—88no—
103C2×C3×C4#21314yes—
104C2×C3×C4C2×#6714yes—
105#67—248no—
106C2×Dic3—124no—
107D12—124no—
108D12—124no—
109C3×C8—24no—
110C3×C8#23518yes—
111C2×C32—22no—
112C2×C32#48011yescharacteristic
113C2×C32C2×SD3211yescharacteristic
114C2×C32#50911yescharacteristic
115C3⋊D3—161no—
116C2×D4—181no—
117C2×D4—361no—
118C22×C4—41no—
119C22×C4#63811yescharacteristic
120D8—182no—
121C2×C8—22no—
122C2×C8#63811yescharacteristic
123C2×C8C22×C3⋊D311yescharacteristic
124C4⋊C4—22no—
125C4⋊C4—41no—
126C4⋊C4—181no—
127C22⋊C4—361no—
128C16—182no—
129C22×C3—24no—
130C22×C3—24no—
131C22×C3#82818yes—
132C22×C3C2×#21314yes—
133C2×D3—244no—
134C2×D3—244no—
135C2×D3—244no—
136C3×C4—24no—
137C3×C4—88no—
138C3×C4#92914yes—
139C3×C4#94214yes—
140Dic3—244no—
141C32#223311yescharacteristic, complemented, Sylow
142C23—361no—
143C23#375311yescharacteristic
144D4—361no—
145D4—361no—
146D4—722no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—42no—
150C2×C4—82no—
151C2×C4—361no—
152C2×C4#375311yescharacteristic
153C2×C4C2×#63811yescharacteristic
154C8—21no—
155C8#382812yes—
156C2×C3—28no—
157C2×C3#496714yes—
158C2×C3#514714yes—
159C2×C3C2×#82814yes—
160D3—484no—
161C22—21no—
162C22—21no—
163C22—721no—
164C22—721no—
165C22—721no—
166C22#6365512yes—
167C22C2×#375311yescharacteristic
168C4—21no—
169C4—82no—
170C4—721no—
171C4#6413811yescharacteristic
172C4#6415111yescharacteristic
173C3#7060014yescomplemented
174C2—22no—
175C2—1441no—
176C2#1059266611yescharacteristic
177C2#1059284611yescharacteristic
178C2C2×#6365511yescharacteristic
subgroupG/H
centerC22C2×#3753
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC2×C32×#107C2
socleC22×C32C2×D8
prime radical#10592814C2
hypercenterC2×#107C3⋊D3
hypocenterC32#2233
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×C32×#107C2semidirect
3. #10589415C2semidirect
4. #10589357C2semidirect
5. #10589356C2semidirect
16. C2×C3×#107D3semidirect
59. C2×#107C3⋊D3semidirect
141. C32#2233semidirect
173. C3#70600semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1072
#105928142
#105894152
#105893572
#105893562
#706003