Finite Group Databasebeta

← #11778128

Subgroups — #11778128

Order 1152.

798 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 149 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×#544C211yesmaximal, characteristic, complemented
2#10592745C212yesmaximal
3#10592690C211yesmaximal, characteristic
4#10589404C212yesmaximal, complemented
5#10589394C211yesmaximal, characteristic, complemented
6#71902—34nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C32×C4⋊Q8—22no—
9C32×#125—22no—
10C32×C22⋊Q8—21no—
11C32×C22⋊Q8C2212yes—
12C32×#117—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3755—22no—
15C2×#3752—21no—
16C2×#3752—21no—
17#63658C2211yescharacteristic
18#63657C2212yes—
19#63636—22no—
20C3×#544D314yescomplemented
21#5046—38no—
22#4991—34no—
23#4538—38no—
24#4528—34no—
25C23×C3⋊D3—21no—
26C2×C32×Q8—21no—
27C2×C32×Q8D412yes—
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C2×C4⋊(C3⋊D3)—22no—
33C2×C4⋊(C3⋊D3)—42no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—22no—
38C32×C4⋊C4—22no—
39C32×C4⋊C4—22no—
40C32×C4⋊C4D412yes—
41C32×C22⋊C4—22no—
42C32×C42—22no—
43#3755—44no—
44#3752—42no—
45#3752—42no—
46C2×C3⋊(C3⋊C8)—22no—
47#1599—91noSylow
48C22×D12—34no—
49C3×C4⋊Q8—28no—
50C3×#125—28no—
51C3×C22⋊Q8—24no—
52C3×C22⋊Q8C2×D318yes—
53C3×#117—24no—
54C2×C3×C4⋊C4C2×D314yes—
55C2×#215—68no—
56C2×(C2×D3)⋊C4—64no—
57C2×(C2×D3)⋊C4—64no—
58C3⋊#95—34no—
59#830—38no—
60#809—68no—
61C23×C32C2×D411yescharacteristic
62C22×C3⋊D3—22no—
63C22×C3⋊D3—41no—
64C22×C3⋊D3—41no—
65C22×C3⋊D3—41no—
66C22×C3⋊D3—41no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3—41no—
69C32×Q8—42no—
70C32×Q8—81no—
71C2×C32×C4—21no—
72C2×C32×C4—21no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4—21no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4SD1612yescomplemented
79C2×C32×C4C2×D412yes—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C4⋊(C3⋊D3)—24no—
84C4⋊(C3⋊D3)—42no—
85C3⋊(C3⋊C8)—42no—
86#544C3⋊D311yescharacteristic, complemented
87#450—92no—
88#394—91no—
89#328—92no—
90#324—91no—
91C23×D3—64no—
92C2×C3×Q8—24no—
93C2×C3×Q8#6718yes—
94C22×C3×C4#6714yes—
95C22×C3×C4#6714yes—
96C22×C3×C4C22×D314yes—
97C22×Dic3—64no—
98C2×D12—68no—
99C2×D12—128no—
100C3×C4⋊C4—24no—
101C3×C4⋊C4—24no—
102C3×C4⋊C4—24no—
103C3×C4⋊C4—28no—
104C3×C4⋊C4—28no—
105C3×C4⋊C4—28no—
106C3×C4⋊C4#6718yes—
107C3×C22⋊C4—28no—
108C3×C42—28no—
109#215—1216no—
110(C2×D3)⋊C4—128no—
111(C2×D3)⋊C4—128no—
112C2×C3⋊C8—68no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32#12011yescharacteristic
116C22×C32C2×SD1611yescharacteristic
117C22×C32#13711yescharacteristic
118C2×C3⋊D3—42no—
119C2×C3⋊D3—42no—
120C2×C3⋊D3—42no—
121C2×C3⋊D3—81no—
122C2×C3⋊D3—81no—
123C2×C3⋊D3—81no—
124C2×C3⋊D3—81no—
125C32×C4—22no—
126C32×C4—22no—
127C32×C4—42no—
128C32×C4—41no—
129C32×C4—42no—
130C3⋊Dic3—81no—
131C22×D4—91no—
132C2×SD16—182no—
133C4⋊Q8—22no—
134#125—22no—
135C22⋊Q8—21no—
136C22⋊Q8C2×C3⋊D312yes—
137#117—21no—
138C2×C4⋊C4C2×C3⋊D311yescharacteristic
139C2×C22⋊C4—181no—
140C2×C22⋊C4—181no—
141#102—182no—
142C22⋊C8—92no—
143#95—91no—
144C23×C3C2×#6714yes—
145C22×D3—68no—
146C22×D3—124no—
147C22×D3—124no—
148C22×D3—124no—
149C22×D3—124no—
150C22×D3—124no—
151C22×D3—124no—
152C3×Q8—48no—
153C3×Q8—84no—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4—28no—
157C2×C3×C4—28no—
158C2×C3×C4—24no—
159C2×C3×C4—44no—
160C2×C3×C4—44no—
161C2×C3×C4#21518yescomplemented
162C2×C3×C4C2×#6718yes—
163C2×Dic3—124no—
164C2×Dic3—124no—
165C2×Dic3—124no—
166D12—616no—
167D12—128no—
168C3⋊C8—128no—
169C2×C32—21no—
170C2×C32—21no—
171C2×C32#44811yescharacteristic
172C2×C32#45411yescharacteristic
173C2×C32B(4,𝔽2)11yescharacteristic
174C3⋊D3—82no—
175C24—181no—
176C2×Q8—21no—
177C2×Q8#63812yes—
178C2×D4—182no—
179C2×D4—362no—
180C22×C4—181no—
181C22×C4#63811yescharacteristic
182C22×C4#63811yescharacteristic
183C22×C4C22×C3⋊D311yescharacteristic
184SD16—364no—
185C2×C8—182no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4#63812yes—
193C22⋊C4—22no—
194C22⋊C4—362no—
195C22⋊C4—362no—
196C42—22no—
197C22×C3—24no—
198C22×C3—24no—
199C22×C3C2×#21514yes—
200C22×C3#94214yes—
201C22×C3#95314yes—
202C2×D3—128no—
203C2×D3—128no—
204C2×D3—128no—
205C2×D3—244no—
206C2×D3—244no—
207C2×D3—244no—
208C2×D3—244no—
209C3×C4—28no—
210C3×C4—28no—
211C3×C4—44no—
212C3×C4—48no—
213C3×C4—48no—
214Dic3—244no—
215C32#159911yescharacteristic, complemented, Sylow
216C23—182no—
217C23—361no—
218C23—361no—
219C23—361no—
220C23—361no—
221C23—361no—
222C23—361no—
223C23C2×#63811yescharacteristic
224Q8—42no—
225Q8—81no—
226D4—184no—
227D4—362no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4—361no—
238C2×C4#375512yescomplemented
239C2×C4C2×#63812yes—
240C8—362no—
241C2×C3—24no—
242C2×C3—24no—
243C2×C3#522714yes—
244C2×C3#524414yes—
245C2×C3#524514yes—
246D3—248no—
247C22—21no—
248C22—21no—
249C22—362no—
250C22—362no—
251C22—362no—
252C22—721no—
253C22—721no—
254C22—721no—
255C22—721no—
256C22C2×#375511yescharacteristic
257C22#6415111yescharacteristic
258C22#6416211yescharacteristic
259C4—22no—
260C4—22no—
261C4—41no—
262C4—42no—
263C4—42no—
264C4—721no—
265C3#7190214yescomplemented
266C2—21no—
267C2—21no—
268C2—722no—
269C2#1059292611yescharacteristic
270C2#1059294311yescharacteristic
271C2#1059294411yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#544C2
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#544C3⋊D3
hypocenterC32#1599
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C32×#544C2semidirect
4. #10589404C2semidirect
5. #10589394C2semidirect
20. C3×#544D3semidirect
78. C2×C32×C4SD16semidirect
86. #544C3⋊D3semidirect
161. C2×C3×C4#215semidirect
215. C32#1599semidirect
238. C2×C4#3755semidirect
265. C3#71902semidirect

Maximal subgroups

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

subgroupindex
C32×#5442
#105927452
#105926902
#105894042
#105893942
#719023