Finite Group Databasebeta

← #11782670

Subgroups — #11782670

Order 1152.

660 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C32×#486C211yesmaximal, characteristic, complemented
2#10592784C211yesmaximal, characteristic, complemented
3#10592779C211yesmaximal, characteristic, complemented
4#10592772C211yesmaximal, characteristic
5#10592769C211yesmaximal, characteristic, complemented
6#10592392C211yesmaximal, characteristic, complemented
7#10589320C211yesmaximal, characteristic, complemented
8#71185—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×#127C2211yescharacteristic
11C2×#3755—22no—
12C2×#3753—22no—
13C2×#3744—22no—
14#64083C2211yescharacteristic
15#64078C2211yescharacteristic
16C32×#102—22no—
17C32×C4×C8C2211yescharacteristic
18#63659—22no—
19#63635—22no—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#486D314yescomplemented
23#5085—34no—
24#5080—34no—
25#5073—34no—
26#5070—34no—
27#4693—34no—
28#4454—34no—
29C2×C32×Q8—21no—
30C2×C32×D4—21no—
31C2×C32×D4—21no—
32C2×C32×D4—21no—
33C2×C4⋊(C3⋊D3)—21no—
34C2×C4⋊(C3⋊D3)—21no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×#634—21no—
37C2×C32×C8D412yes—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C42C2311yescharacteristic
41#3755—44no—
42#3753—44no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C2×C3⋊(C3⋊C8)D412yes—
46C2×C3⋊(C3⋊C8)D412yes—
47#3744—44no—
48#1715—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C3×#127C2×D314yes—
51C2×#215—68no—
52C2×#213—68no—
53C2×#204—68no—
54#874—34no—
55#869—34no—
56C3×#102—28no—
57C3×C4×C8C2×D314yes—
58#832—68no—
59#808—68no—
60C4×C3⋊C8—34no—
61C4×C3⋊C8—34no—
62C23×C32—41no—
63C22×C3⋊D3—41no—
64C32×Q8—42no—
65C32×D4—42no—
66C32×D4—42no—
67C32×D4—42no—
68C2×C32×C4—41no—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3—41no—
73C4⋊(C3⋊D3)—42no—
74C4⋊(C3⋊D3)—42no—
75C4⋊(C3⋊D3)—42no—
76#634—42no—
77C32×C8—22no—
78C3⋊(C3⋊C8)—22no—
79C3⋊(C3⋊C8)SD1614yescomplemented
80#498—91no—
81#493—91no—
82#492—91no—
83#492—91no—
84#486—91no—
85#486C3⋊D311yescharacteristic, complemented
86#322—91no—
87C2×C3×Q8—24no—
88C2×C3×D4—24no—
89C2×C3×D4—24no—
90C2×C3×D4—24no—
91C2×D12—64no—
92C2×D12—64no—
93C2×D12—64no—
94C2×Dic6—64no—
95C2×C3×C8#6718yes—
96C3×C4⋊C4—24no—
97C3×C4⋊C4—24no—
98C3×C42C22×D314yes—
99#215—1216no—
100#213—1216no—
101C4⋊Dic3—64no—
102C4⋊Dic3—64no—
103C2×C3⋊C8—38no—
104C2×C3⋊C8—38no—
105#204—1216no—
106C22×C32—81no—
107C22×C32—81no—
108C22×C32—81no—
109C22×C32#12711yescharacteristic
110C2×C3⋊D3—81no—
111C2×C3⋊D3—81no—
112C2×C3⋊D3—81no—
113C32×C4—81no—
114C32×C4C2×SD1612yes—
115C32×C4AGL(1,ℤ/8)12yes—
116C32×C4AGL(1,ℤ/8)12yes—
117C3⋊Dic3—81no—
118C2×SD16—182no—
119C2×SD16—182no—
120C2×D8—182no—
121C4⋊Q8—91no—
122C4⋊Q8C2×C3⋊D311yescharacteristic
123#127—91no—
124#127C2×C3⋊D311yescharacteristic
125#106—182no—
126#102—22no—
127#102—182no—
128C4×C8—91no—
129C4×C8—91no—
130C4×C8C2×C3⋊D311yescharacteristic
131C23×C3—44no—
132C22×D3—124no—
133C3×Q8—48no—
134C3×D4—48no—
135C3×D4—48no—
136C3×D4—48no—
137C2×C3×C4—44no—
138C2×C3×C4D3×D414yes—
139C2×C3×C4D3×D414yes—
140C2×C3×C4C2×#6714yes—
141C2×Dic3—124no—
142D12—128no—
143D12—128no—
144D12—128no—
145Dic6—128no—
146C3×C8—28no—
147C3⋊C8—316no—
148C3⋊C8—68no—
149C2×C32—161no—
150C2×C32#49211yescharacteristic
151C2×C32#49611yescharacteristic
152C2×C32#49611yescharacteristic
153C3⋊D3—161no—
154C2×Q8—21no—
155C2×Q8—181no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—181no—
160C2×D4—181no—
161C2×D4—181no—
162SD16—364no—
163SD16—364no—
164D8—364no—
165C2×C8—92no—
166C2×C8—92no—
167C2×C8#63812yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—181no—
171C4⋊C4—181no—
172C42C22×C3⋊D311yescharacteristic
173C22×C3—84no—
174C22×C3—84no—
175C22×C3—84no—
176C22×C3#94014yes—
177C2×D3—244no—
178C2×D3—244no—
179C2×D3—244no—
180C3×C4—84no—
181C3×C4#91118yes—
182C3×C4D3×SD1618yes—
183C3×C4#94918yes—
184Dic3—244no—
185C32#171511yescharacteristic, complemented, Sylow
186C23—41no—
187C23—361no—
188Q8—42no—
189Q8—362no—
190D4—42no—
191D4—42no—
192D4—42no—
193D4—362no—
194D4—362no—
195D4—362no—
196C2×C4—41no—
197C2×C4—361no—
198C2×C4D4×C3⋊D311yescharacteristic
199C2×C4D4×C3⋊D311yescharacteristic
200C2×C4C2×#63811yescharacteristic
201C8—22no—
202C8—94no—
203C8—182no—
204C2×C3—164no—
205C2×C3#505814yes—
206C2×C3#515414yes—
207C2×C3#517514yes—
208D3—484no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—721no—
213C22—721no—
214C22—721no—
215C22#6414911yescharacteristic
216C4—81no—
217C4—721no—
218C4#6412012yes—
219C4SD16×C3⋊D312yes—
220C4#6415812yes—
221C3#7118514yescomplemented
222C2—161no—
223C2—1441no—
224C2#1059275711yescharacteristic
225C2#1059285311yescharacteristic
226C2#1059287411yescharacteristic
subgroupG/H
centerC22#64149
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#486C2
socleC22×C32#127
prime radical#10592772C2
hypercenter#486C3⋊D3
hypocenterC32#1715
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. C32×#486C2semidirect
2. #10592784C2semidirect
3. #10592779C2semidirect
5. #10592769C2semidirect
6. #10592392C2semidirect
7. #10589320C2semidirect
22. C3×#486D3semidirect
79. C3⋊(C3⋊C8)SD16semidirect
85. #486C3⋊D3semidirect
185. C32#1715semidirect
221. C3#71185semidirect

Maximal subgroups

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

subgroupindex
C32×#4862
#105927842
#105927792
#105927722
#105927692
#105923922
#105893202
#711853