Finite Group Databasebeta

← #11798048

Subgroups — #11798048

Order 1152.

798 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#3745C211yesmaximal, characteristic, complemented
2C32×#466C211yesmaximal, characteristic, complemented
3C2×#63653C212yesmaximal, complemented
4#10589415C211yesmaximal, characteristic, complemented
5#10589357C212yesmaximal, complemented
6#71075—34nomaximal
7C22×C4⋊(C3⋊D3)—21no—
8C2×C32×D8C2211yescharacteristic, complemented
9C22×C32×C8C2211yescharacteristic
10C32×#121—21no—
11C2×#3745—21no—
12C2×#3745—24no—
13C2×#3745C2212yes—
14C32×#107C2211yescharacteristic, complemented
15C32×#102—21no—
16#63653—24no—
17C2×C3⋊(C3⋊C16)C2212yescomplemented
18C22×D24—34no—
19C3×#466D314yescomplemented
20C2×#826—38no—
21#4549—34no—
22#4491—38no—
23C23×C3⋊D3—41no—
24C2×C32×D4—21no—
25C2×C32×D4—41no—
26C22×C32×C4D411yescharacteristic
27C2×C4⋊(C3⋊D3)—24no—
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—42no—
30C2×C4⋊(C3⋊D3)—41no—
31C32×D8—22no—
32C2×C32×C8—22no—
33C2×C32×C8D411yescharacteristic
34C2×C32×C8C2311yescharacteristic
35C32×C4⋊C4—21no—
36C32×C22⋊C4—41no—
37#3745—24no—
38#3745—22no—
39#3745D414yescomplemented
40C3⋊(C3⋊C16)—22no—
41#2184—91noSylow
42C22×D12—64no—
43C2×C3×D8C2×D314yescomplemented
44C22×C3×C8C2×D314yes—
45C3×#121—24no—
46C2×D24—38no—
47C2×D24—616no—
48C2×D24—64no—
49C3×#107C2×D314yescomplemented
50C3×#102—24no—
51#826—616no—
52C2×C3⋊C16—38no—
53C23×C32—41no—
54C23×C32D811yescharacteristic
55C22×C3⋊D3—44no—
56C22×C3⋊D3—42no—
57C22×C3⋊D3—82no—
58C22×C3⋊D3—82no—
59C32×D4—41no—
60C32×D4—41no—
61C32×D4—82no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4D811yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C4⋊(C3⋊D3)—24no—
68C4⋊(C3⋊D3)—44no—
69C4⋊(C3⋊D3)—42no—
70C32×C8—21no—
71C32×C8C2×D412yes—
72C22×D8—91no—
73C2×D16—92no—
74#466C3⋊D311yescharacteristic, complemented
75#357—92no—
76C22⋊C16—91no—
77C23×D3—124no—
78C2×C3×D4—24no—
79C2×C3×D4—44no—
80C22×C3×C4#6714yes—
81C2×D12—616no—
82C2×D12—68no—
83C2×D12—128no—
84C2×D12—124no—
85C3×D8—28no—
86C2×C3×C8—28no—
87C2×C3×C8#6714yes—
88C2×C3×C8C22×D314yes—
89C3×C4⋊C4—24no—
90C3×C22⋊C4—44no—
91D24—316no—
92D24—616no—
93D24—68no—
94C3⋊C16—68no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—81no—
98C22×C32—81no—
99C22×C32—81no—
100C22×C32D1612yescomplemented
101C22×C32C2×D811yescharacteristic
102C2×C3⋊D3—44no—
103C2×C3⋊D3—88no—
104C2×C3⋊D3—82no—
105C2×C3⋊D3—82no—
106C32×C4—21no—
107C32×C4—81no—
108C32×C4#12011yescharacteristic
109C32×C4AGL(1,ℤ/8)11yescharacteristic
110C22×D4—181no—
111C2×D8—92no—
112C2×D8—184no—
113C2×D8—181no—
114C2×D8C2×C3⋊D311yescharacteristic, complemented
115C22×C8C2×C3⋊D311yescharacteristic
116#121—21no—
117D16—184no—
118C2×C16—92no—
119#107C2×C3⋊D311yescharacteristic, complemented
120#102—21no—
121C23×C3—44no—
122C23×C3#21314yes—
123C22×D3—1216no—
124C22×D3—128no—
125C22×D3—248no—
126C22×D3—248no—
127C3×D4—44no—
128C3×D4—44no—
129C3×D4—88no—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—44no—
133C2×C3×C4#21314yes—
134C2×C3×C4C2×#6714yes—
135D12—616no—
136D12—1216no—
137D12—128no—
138C3×C8—24no—
139C3×C8D3×D418yes—
140C2×C32—22no—
141C2×C32—161no—
142C2×C32#44711yescharacteristic
143C2×C32C2×D1611yescharacteristic
144C2×C32#50911yescharacteristic
145C3⋊D3—84no—
146C24—361no—
147C2×D4—21no—
148C2×D4—41no—
149C2×D4—184no—
150C2×D4—182no—
151C2×D4—362no—
152C2×D4—361no—
153C22×C4#63811yescharacteristic
154D8—22no—
155D8—94no—
156D8—184no—
157D8—182no—
158C2×C8—22no—
159C2×C8#63811yescharacteristic
160C2×C8C22×C3⋊D311yescharacteristic
161C4⋊C4—21no—
162C22⋊C4—41no—
163C16—182no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3—84no—
167C22×C3—84no—
168C22×C3—84no—
169C22×C3#82618yescomplemented
170C22×C3C2×#21314yes—
171C2×D3—1216no—
172C2×D3—2432no—
173C2×D3—248no—
174C2×D3—248no—
175C3×C4—24no—
176C3×C4—84no—
177C3×C4#93714yes—
178C3×C4#94914yes—
179C32#218411yescharacteristic, complemented, Sylow
180C23—41no—
181C23—364no—
182C23—362no—
183C23—722no—
184C23—722no—
185C23#375311yescharacteristic
186D4—41no—
187D4—41no—
188D4—82no—
189D4—184no—
190D4—364no—
191D4—362no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4#375311yescharacteristic
196C2×C4C2×#63811yescharacteristic
197C8—21no—
198C8D4×C3⋊D312yes—
199C2×C3—28no—
200C2×C3—164no—
201C2×C3#503614yes—
202C2×C3C2×#82614yes—
203C2×C3#519314yes—
204D3—2416no—
205C22—21no—
206C22—21no—
207C22—81no—
208C22—81no—
209C22—81no—
210C22—364no—
211C22—728no—
212C22—722no—
213C22—722no—
214C22#6365312yescomplemented
215C22C2×#375311yescharacteristic
216C4—21no—
217C4—81no—
218C4#6414611yescharacteristic
219C4#6415811yescharacteristic
220C3#7107514yescomplemented
221C2—22no—
222C2—161no—
223C2—724no—
224C2#1059273511yescharacteristic
225C2C2×#6365311yescharacteristic
226C2#1059289211yescharacteristic
subgroupG/H
centerC22C2×#3753
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#466C2
socleC22×C32C2×D8
hypercenter#466C3⋊D3
hypocenterC32#2184
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22×#3745C2semidirect
2. C32×#466C2semidirect
3. C2×#63653C2semidirect
4. #10589415C2semidirect
5. #10589357C2semidirect
8. C2×C32×D8C22semidirect
14. C32×#107C22semidirect
17. C2×C3⋊(C3⋊C16)C22semidirect
19. C3×#466D3semidirect
39. #3745D4semidirect
43. C2×C3×D8C2×D3semidirect
49. C3×#107C2×D3semidirect
74. #466C3⋊D3semidirect
100. C22×C32D16semidirect
114. C2×D8C2×C3⋊D3semidirect
119. #107C2×C3⋊D3semidirect
169. C22×C3#826semidirect
179. C32#2184semidirect
214. C22#63653semidirect
220. C3#71075semidirect

Maximal subgroups

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

subgroupindex
C22×#37452
C32×#4662
C2×#636532
#105894152
#105893572
#710753