Finite Group Databasebeta

← #11778328

Subgroups — #11778328

Order 1152.

846 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 129 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#10595981C211yesmaximal, characteristic
2#10592678C211yesmaximal, characteristic, complemented
3#10592437C212yesmaximal, complemented
4C32×#324C211yesmaximal, characteristic, complemented
5#10589336C212yesmaximal, complemented
6#68133—34nomaximal
7C2×#3828—21no—
8C22×#634C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10#64139—21no—
11#64139C2212yes—
12C2×#3750—21no—
13C2×#3744—22no—
14#64106—22no—
15#64104—22no—
16C32×C22⋊C8C2212yes—
17#63658—21no—
18#63658C2211yescharacteristic
19#63643—22no—
20#5510—34no—
21#4979—34no—
22#4738—38no—
23C3×#324D314yescomplemented
24#4470—38no—
25C22×C32×C4D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C2×#638—22no—
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31#3828—42no—
32#3828—42no—
33C2×C4⋊(C3⋊D3)—21no—
34C2×C4⋊(C3⋊D3)—21no—
35C2×C4⋊(C3⋊D3)D412yes—
36C2×C4×C3⋊D3—22no—
37C2×#634—22no—
38C2×#634—21no—
39C2×#634—42no—
40C2×C32×C8—22no—
41C32×C4⋊C4—22no—
42#3752—22no—
43#3752—22no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)D412yes—
46#3750—42no—
47#3744—44no—
48#1604—91noSylow
49C2×#235—64no—
50C22×Dic6—34no—
51C2×C3×C4⋊C4C2×D314yes—
52#930—38no—
53#930—64no—
54C2×Dic3⋊C4—64no—
55C2×#204—68no—
56#897—68no—
57#895—68no—
58C3×C22⋊C8C2×D318yes—
59C3⋊#95—34no—
60C3⋊#95—64no—
61#816—68no—
62C23×C32C2×D411yescharacteristic
63C22×C3⋊D3—22no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4—41no—
68C2×C32×C4—41no—
69C2×C32×C4SD1612yescomplemented
70C2×C32×C4C2×D412yes—
71#638—42no—
72#638—42no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3—41no—
80C4⋊(C3⋊D3)—42no—
81C4⋊(C3⋊D3)—42no—
82C4⋊(C3⋊D3)—81no—
83C4×C3⋊D3—44no—
84#634—24no—
85#634—42no—
86#634—42no—
87C32×C8—42no—
88#537—91no—
89#448—92no—
90#395—91no—
91#327—92no—
92#324C3⋊D311yescharacteristic, complemented
93C22×C3×C4D1214yes—
94C22×C3×C4D1214yes—
95C22×C3×C4C22×D314yes—
96C2×#67—68no—
97C22×Dic3—64no—
98C22×Dic3—64no—
99#235—128no—
100#235—128no—
101C2×D12—38no—
102C2×D12—64no—
103C2×D12—64no—
104C2×C4×D3—68no—
105C2×Dic6—68no—
106C2×Dic6—64no—
107C2×Dic6—128no—
108C2×C3×C8—28no—
109C3×C4⋊C4—28no—
110(C2×D3)⋊C4—68no—
111(C2×D3)⋊C4—68no—
112C4⋊Dic3—38no—
113C4⋊Dic3—64no—
114Dic3⋊C4—128no—
115#204—1216no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32#12011yescharacteristic
119C22×C32C2×SD1611yescharacteristic
120C22×C32AGL(1,ℤ/8)11yescharacteristic
121C2×C3⋊D3—42no—
122C2×C3⋊D3—42no—
123C2×C3⋊D3—42no—
124C32×C4—22no—
125C32×C4—22no—
126C32×C4—41no—
127C3⋊Dic3—42no—
128C3⋊Dic3—42no—
129C3⋊Dic3—42no—
130C2×#41—181no—
131C22×Q8—91no—
132C2×SD16—182no—
133C22⋊Q8—182no—
134#121—92no—
135#121—182no—
136#121—181no—
137C2×C4⋊C4—181no—
138C2×C4⋊C4C2×C3⋊D311yescharacteristic
139#103—182no—
140C22⋊C8C2×C3⋊D312yes—
141#95—91no—
142#95—181no—
143C23×C3C2×D1214yes—
144C22×D3—68no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—44no—
149C2×C3×C4—44no—
150C2×C3×C4#20418yescomplemented
151C2×C3×C4D3×D418yes—
152#67—128no—
153#67—128no—
154C2×Dic3—68no—
155C2×Dic3—68no—
156C2×Dic3—68no—
157C2×Dic3—124no—
158C2×Dic3—124no—
159C2×Dic3—124no—
160C2×Dic3—124no—
161D12—128no—
162D12—128no—
163D12—244no—
164C4×D3—1216no—
165Dic6—616no—
166Dic6—128no—
167Dic6—128no—
168C3×C8—48no—
169C2×C32—21no—
170C2×C32—21no—
171C2×C32#45011yescharacteristic
172C2×C32#45611yescharacteristic
173C2×C32B(4,𝔽2)11yescharacteristic
174C3⋊D3—82no—
175#41—362no—
176#41—362no—
177C2×Q8—181no—
178C2×Q8—182no—
179C2×Q8—362no—
180C2×D4—92no—
181C2×D4—181no—
182C2×D4—181no—
183C2×D4—182no—
184C22×C4—182no—
185C22×C4—181no—
186C22×C4—181no—
187C22×C4C4⋊(C3⋊D3)11yescharacteristic
188C22×C4C4⋊(C3⋊D3)11yescharacteristic
189C22×C4C22×C3⋊D311yescharacteristic
190SD16—364no—
191C2×C8—22no—
192C4⋊C4—22no—
193C4⋊C4—92no—
194C4⋊C4—181no—
195C4⋊C4—362no—
196C22⋊C4—182no—
197C22⋊C4—182no—
198C22×C3—24no—
199C22×C3—24no—
200C22×C3#88214yes—
201C22×C3C2×#20414yes—
202C22×C3#90814yes—
203C2×D3—128no—
204C2×D3—128no—
205C2×D3—128no—
206C3×C4—28no—
207C3×C4—28no—
208C3×C4—44no—
209Dic3—128no—
210Dic3—128no—
211Dic3—128no—
212C32#160411yescharacteristic, complemented, Sylow
213C23—182no—
214C23C2×C4⋊(C3⋊D3)11yescharacteristic
215Q8—184no—
216Q8—362no—
217Q8—362no—
218D4—362no—
219D4—362no—
220D4—362no—
221D4—362no—
222D4—721no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—182no—
229C2×C4—182no—
230C2×C4—182no—
231C2×C4—364no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4#374412yescomplemented
237C2×C4D4×C3⋊D312yes—
238C8—42no—
239C2×C3—24no—
240C2×C3—24no—
241C2×C3#473114yes—
242C2×C3#474114yes—
243C2×C3#475214yes—
244D3—248no—
245C22—21no—
246C22—21no—
247C22—362no—
248C22—362no—
249C22—362no—
250C22#6409111yescharacteristic
251C22C2×#374411yescharacteristic
252C22#6411711yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—362no—
257C4—362no—
258C4—362no—
259C3#6813314yescomplemented
260C2—21no—
261C2—21no—
262C2—722no—
263C2#1059243011yescharacteristic
264C2#1059244011yescharacteristic
265C2#1059245111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32#120
prime radical#10595981C2
hypercenter#324C3⋊D3
hypocenterC32#1604
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #10592678C2semidirect
3. #10592437C2semidirect
4. C32×#324C2semidirect
5. #10589336C2semidirect
23. C3×#324D3semidirect
69. C2×C32×C4SD16semidirect
92. #324C3⋊D3semidirect
150. C2×C3×C4#204semidirect
212. C32#1604semidirect
236. C2×C4#3744semidirect
259. C3#68133semidirect

Maximal subgroups

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

subgroupindex
#105959812
#105926782
#105924372
C32×#3242
#105893362
#681333