Finite Group Databasebeta

← #11799843

Subgroups — #11799843

Order 1152.

426 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 105 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#10592582C211yesmaximal, characteristic
2#10592579C211yesmaximal, characteristic, complemented
3C32×#366C211yesmaximal, characteristic, complemented
4#10589375C211yesmaximal, characteristic, complemented
5#10589373C211yesmaximal, characteristic, complemented
6#10589357C211yesmaximal, characteristic, complemented
7#10589356C211yesmaximal, characteristic, complemented
8#69323—34nomaximal
9C2×#3745C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11#64104—21no—
12#64101—21no—
13C2×C32×C16C2211yescharacteristic
14C32×#107C2211yescharacteristic
15C32×#107C2211yescharacteristic
16#63645C2211yescharacteristic
17C2×C3⋊(C3⋊C16)C2211yescharacteristic
18#63636—21no—
19#63635—21no—
20#4883—34no—
21#4880—34no—
22C3×#366D314yescomplemented
23#4509—34no—
24(C2×D3)⋊C16—34no—
25#4491—34no—
26#4490—34no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4⋊(C3⋊D3)—41no—
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C32×C8C2311yescharacteristic
31C32×C4⋊C4—21no—
32C32×C4⋊C4—21no—
33#3752—41no—
34#3752—41no—
35C4⋊(C3⋊Dic3)—21no—
36C4×C3⋊Dic3—41no—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3745—21no—
39#3745—21no—
40C8×C3⋊D3—21no—
41C8×C3⋊D3—21no—
42C32×C16—21no—
43C3⋊(C3⋊C16)—21no—
44#2234—91noSylow
45C2×D24—34no—
46C2×D3×C8—34no—
47#895—64no—
48#892—64no—
49C2×C3×C16C2×D314yes—
50C3×#107C2×D314yes—
51C3×#107C2×D314yes—
52#818—34no—
53C2×C3⋊C16—34no—
54#809—64no—
55#808—64no—
56C22×C3⋊D3—41no—
57C22×C3⋊D3D811yescharacteristic
58C2×C32×C4—41no—
59C2×C32×C4—41no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3—41no—
62C2×C3⋊Dic3D811yescharacteristic
63C4⋊(C3⋊D3)—41no—
64C4⋊(C3⋊D3)—41no—
65C4⋊(C3⋊D3)—82no—
66C4×C3⋊D3—21no—
67C4×C3⋊D3—21no—
68C32×C8#4111yescharacteristic
69C32×C8#4111yescharacteristic
70C3⋊(C3⋊C8)—21no—
71#466—91no—
72#427—91no—
73#367—91no—
74#366C3⋊D311yescharacteristic, complemented
75#357—91no—
76#357—91no—
77C22⋊C16—91no—
78C2×D12—64no—
79C2×D12—124no—
80C2×C4×D3—34no—
81C2×C3×C8C22×D314yes—
82C3×C4⋊C4—24no—
83C3×C4⋊C4—24no—
84(C2×D3)⋊C4—124no—
85(C2×D3)⋊C4—124no—
86C4⋊Dic3—64no—
87C4×Dic3—124no—
88C2×C3⋊C8—34no—
89D24—64no—
90D24—64no—
91D3×C8—64no—
92D3×C8—64no—
93C3×C16—24no—
94C3⋊C16—64no—
95C22×C32C2×D811yescharacteristic
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—81no—
100C2×C3⋊D3—81no—
101C2×C3⋊D3—81no—
102C32×C4—81no—
103C32×C4—81no—
104C32×C4#12311yescharacteristic
105C32×C4#13711yescharacteristic
106C3⋊Dic3—21no—
107C3⋊Dic3—81no—
108C2×D8—91no—
109C22×C8—91no—
110#121—181no—
111#117—181no—
112C2×C16—91no—
113C2×C16C2×C3⋊D311yescharacteristic
114#107—91no—
115#107C2×C3⋊D311yescharacteristic
116#107C2×C3⋊D311yescharacteristic
117#106—181no—
118#102—181no—
119C22×D3—34no—
120C22×D3—124no—
121C2×C3×C4—44no—
122C2×C3×C4—44no—
123C2×C3×C4D3×D414yes—
124C2×Dic3—34no—
125C2×Dic3—124no—
126D12—124no—
127D12—124no—
128D12—248no—
129C4×D3—64no—
130C4×D3—64no—
131C3×C8#23514yes—
132C3×C8#23914yes—
133C3⋊C8—64no—
134C2×C32#48011yescharacteristic
135C2×C32#50811yescharacteristic
136C2×C32#50911yescharacteristic
137C3⋊D3—41no—
138C3⋊D3—161no—
139C2×D4—181no—
140C2×D4—361no—
141C22×C4—91no—
142D8—181no—
143D8—181no—
144C2×C8—91no—
145C2×C8—181no—
146C2×C8—181no—
147C2×C8C22×C3⋊D311yescharacteristic
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—181no—
151C22⋊C4—361no—
152C22⋊C4—361no—
153C42—361no—
154C16—21no—
155C16—181no—
156C22×C3D3×D814yes—
157C2×D3—64no—
158C2×D3—64no—
159C2×D3—64no—
160C2×D3—244no—
161C2×D3—244no—
162C2×D3—244no—
163C3×C4—84no—
164C3×C4—84no—
165C3×C4#89414yes—
166C3×C4#91814yes—
167Dic3—64no—
168Dic3—244no—
169C32#223411yescharacteristic, complemented, Sylow
170C23—91no—
171C23—361no—
172D4—361no—
173D4—361no—
174D4—722no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—91no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—361no—
181C2×C4D4×C3⋊D311yescharacteristic
182C8—181no—
183C8#382811yescharacteristic
184C8#383211yescharacteristic
185C2×C3#488214yes—
186C2×C3#491114yes—
187C2×C3#491914yes—
188D3—124no—
189D3—484no—
190C22—181no—
191C22—181no—
192C22—181no—
193C22—721no—
194C22—721no—
195C22—721no—
196C22D8×C3⋊D311yescharacteristic
197C4—81no—
198C4—81no—
199C4—181no—
200C4—721no—
201C4#6410311yescharacteristic
202C4#6412711yescharacteristic
203C3#6932314yescomplemented
204C2—361no—
205C2—1441no—
206C2#1059258111yescharacteristic
207C2#1059261011yescharacteristic
208C2#1059261811yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#366C2
socleC22×C32C2×D8
prime radical#10592582C2
hypercenter#366C3⋊D3
hypocenterC32#2234
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
2. #10592579C2semidirect
3. C32×#366C2semidirect
4. #10589375C2semidirect
5. #10589373C2semidirect
6. #10589357C2semidirect
7. #10589356C2semidirect
22. C3×#366D3semidirect
74. #366C3⋊D3semidirect
169. C32#2234semidirect
203. C3#69323semidirect

Maximal subgroups

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

subgroupindex
#105925822
#105925792
C32×#3662
#105893752
#105893732
#105893572
#105893562
#693233