Finite Group Databasebeta

← #11782630

Subgroups — #11782630

Order 1152.

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

normal subgroups only

This group has 594 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×#498C211yesmaximal, characteristic, complemented
2#10592792C211yesmaximal, characteristic, complemented
3#10592784C211yesmaximal, characteristic
4#10592784C211yesmaximal, characteristic
5#10592777C211yesmaximal, characteristic, complemented
6#10592393C211yesmaximal, characteristic
7#10589320C211yesmaximal, characteristic, complemented
8#71335—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3755—22no—
12C2×#3755—22no—
13#64083C2211yescharacteristic
14#64078C2211yescharacteristic
15C32×#106—22no—
16C32×C4×C8C2211yescharacteristic
17#63648—22no—
18#63637—22no—
19#63634—22no—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#498D314yescomplemented
23#5093—34no—
24#5085—34no—
25#5085—34no—
26#5078—34no—
27#4694—34no—
28#4454—34no—
29C2×C32×Q8—21no—
30C2×C32×Q8—21no—
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)—21no—
34C2×#634—21no—
35C2×C32×C8D412yes—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C42C2311yescharacteristic
41#3755—44no—
42#3755—44no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C2×C3⋊(C3⋊C8)D412yes—
46C2×C3⋊(C3⋊C8)D412yes—
47#1714—91noSylow
48C3×C4⋊Q8C2×D314yes—
49C3×C4⋊Q8C2×D314yes—
50C2×#215—68no—
51C2×#215—68no—
52#874—34no—
53#869—34no—
54C3×#106—28no—
55C3×C4×C8C2×D314yes—
56#821—68no—
57#810—68no—
58#807—68no—
59C4×C3⋊C8—34no—
60C4×C3⋊C8—34no—
61C22×C3⋊D3—41no—
62C32×Q8—42no—
63C32×Q8—42no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—41no—
70C4⋊(C3⋊D3)—42no—
71C4⋊(C3⋊D3)—42no—
72C4⋊(C3⋊D3)—42no—
73#634—42no—
74C32×C8—22no—
75C3⋊(C3⋊C8)—22no—
76C3⋊(C3⋊C8)SD1614yescomplemented
77#500—91no—
78#498C3⋊D311yescharacteristic, complemented
79#492—91no—
80#492—91no—
81#487—91no—
82#486—91no—
83#322—91no—
84C2×C3×Q8—24no—
85C2×C3×Q8—24no—
86C2×D12—64no—
87C2×D12—64no—
88C2×D12—64no—
89C2×Dic6—64no—
90C2×C3×C8#6718yes—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—24no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C3×C42C22×D314yes—
96#215—1216no—
97#215—1216no—
98C4⋊Dic3—64no—
99C4⋊Dic3—64no—
100C2×C3⋊C8—38no—
101C2×C3⋊C8—38no—
102C22×C32#12711yescharacteristic
103C2×C3⋊D3—81no—
104C2×C3⋊D3—81no—
105C2×C3⋊D3—81no—
106C32×C4—81no—
107C32×C4—81no—
108C32×C4C2×SD1612yes—
109C32×C4AGL(1,ℤ/8)12yes—
110C32×C4#13712yes—
111C3⋊Dic3—81no—
112C2×SD16—182no—
113C2×SD16—182no—
114C4⋊Q8—91no—
115C4⋊Q8C2×C3⋊D311yescharacteristic
116C4⋊Q8C2×C3⋊D311yescharacteristic
117#127—91no—
118#107—182no—
119#106—22no—
120#103—182no—
121#102—182no—
122C4×C8—91no—
123C4×C8—91no—
124C4×C8C2×C3⋊D311yescharacteristic
125C22×D3—124no—
126C3×Q8—48no—
127C3×Q8—48no—
128C2×C3×C4—44no—
129C2×C3×C4—44no—
130C2×C3×C4D3×D414yes—
131C2×C3×C4D3×D414yes—
132C2×C3×C4C2×#6714yes—
133C2×Dic3—124no—
134D12—128no—
135D12—128no—
136D12—128no—
137Dic6—128no—
138C3×C8—28no—
139C3⋊C8—316no—
140C3⋊C8—68no—
141C2×C32#49211yescharacteristic
142C2×C32#49611yescharacteristic
143C2×C32#49711yescharacteristic
144C3⋊D3—161no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—181no—
148C2×D4—181no—
149C2×D4—181no—
150C2×D4—181no—
151SD16—364no—
152SD16—364no—
153C2×C8—92no—
154C2×C8—92no—
155C2×C8#63812yes—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—181no—
161C4⋊C4—181no—
162C42C22×C3⋊D311yescharacteristic
163C22×C3#94014yes—
164C2×D3—244no—
165C2×D3—244no—
166C2×D3—244no—
167C3×C4—84no—
168C3×C4—84no—
169C3×C4D3×SD1618yes—
170C3×C4#91418yes—
171C3×C4#94218yes—
172Dic3—244no—
173C32#171411yescharacteristic, complemented, Sylow
174C23—361no—
175Q8—42no—
176Q8—42no—
177Q8—362no—
178D4—362no—
179D4—362no—
180D4—362no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—361no—
184C2×C4D4×C3⋊D311yescharacteristic
185C2×C4D4×C3⋊D311yescharacteristic
186C2×C4C2×#63811yescharacteristic
187C8—22no—
188C8—94no—
189C8—182no—
190C2×C3#508614yes—
191C2×C3#517514yes—
192C2×C3#517614yes—
193D3—484no—
194C22—721no—
195C22—721no—
196C22—721no—
197C22#6414911yescharacteristic
198C4—81no—
199C4—81no—
200C4—721no—
201C4SD16×C3⋊D312yes—
202C4#6412312yes—
203C4#6415112yes—
204C3#7133514yescomplemented
205C2—1441no—
206C2#1059278511yescharacteristic
207C2#1059287411yescharacteristic
208C2#1059287511yescharacteristic
subgroupG/H
centerC22#64149
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#498C2
socleC22×C32#127
prime radical#64083C22
hypercenter#498C3⋊D3
hypocenterC32#1714
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. C32×#498C2semidirect
2. #10592792C2semidirect
5. #10592777C2semidirect
7. #10589320C2semidirect
22. C3×#498D3semidirect
76. C3⋊(C3⋊C8)SD16semidirect
78. #498C3⋊D3semidirect
173. C32#1714semidirect
204. C3#71335semidirect

Maximal subgroups

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

subgroupindex
C32×#4982
#105927922
#105927842
#105927772
#105923932
#105893202
#713353