Finite Group Databasebeta

← #11794016

Subgroups — #11794016

Order 1152.

1080 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 217 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
2C2×#63641C211yesmaximal, characteristic, complemented
3#10592687C212yesmaximal, complemented
4C2×#63636C212yesmaximal, complemented
5C32×#340C211yesmaximal, characteristic, complemented
6#68862—34nomaximal
7C22×C4⋊(C3⋊D3)C2212yes—
8C22×C32×C8C2211yescharacteristic
9C2×C32×C4⋊C4C2212yes—
10C2×#3752—22no—
11C2×#3752—22no—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×#3745—24no—
15C2×#3745—22no—
16#63641—22no—
17#63636—24no—
18C22×D24—34no—
19C2×Dic3⋊C8—34no—
20#4988—38no—
21C2×#809—38no—
22C3×#340D314yescomplemented
23C23×C3⋊D3—22no—
24C22×C32×C4—22no—
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—22no—
30C2×C4⋊(C3⋊D3)—22no—
31C2×C4⋊(C3⋊D3)—22no—
32C2×C4⋊(C3⋊D3)—22no—
33C2×C4⋊(C3⋊D3)D414yes—
34C2×C32×C8—22no—
35C2×C32×C8D412yes—
36C32×C4⋊C4—22no—
37C32×C4⋊C4—22no—
38#3752—44no—
39#3752—44no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3—21no—
42C2×C3⋊(C3⋊C8)—22no—
43C2×C3⋊(C3⋊C8)—21no—
44#3745—28no—
45#2054—91noSylow
46C22×D12—38no—
47C22×C3×C8C2×D314yes—
48C2×C3×C4⋊C4C2×D318yes—
49C2×(C2×D3)⋊C4—68no—
50C2×(C2×D3)⋊C4—68no—
51C2×C4×Dic3—34no—
52C22×C3⋊C8—34no—
53C2×D24—616no—
54C2×D24—68no—
55Dic3⋊C8—68no—
56#809—616no—
57C23×C32C2×D411yescharacteristic
58C22×C3⋊D3—24no—
59C22×C3⋊D3—42no—
60C22×C3⋊D3—42no—
61C22×C3⋊D3—42no—
62C22×C3⋊D3—42no—
63C22×C3⋊D3—42no—
64C22×C3⋊D3—42no—
65C2×C32×C4—42no—
66C2×C32×C4—42no—
67C2×C32×C4—42no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×D412yes—
70C2×C32×C4#4112yes—
71C2×C32×C4#4111yescharacteristic
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3D812yescomplemented
77C4⋊(C3⋊D3)—24no—
78C4⋊(C3⋊D3)—24no—
79C4⋊(C3⋊D3)—42no—
80C4⋊(C3⋊D3)—42no—
81C32×C8—22no—
82C3⋊(C3⋊C8)—41no—
83C22×D8—91no—
84C2×C4⋊C8—91no—
85C2×#102—92no—
86#390—92no—
87#340C3⋊D311yescharacteristic, complemented
88C23×D3—68no—
89C22×C3×C4—28no—
90C22×C3×C4C22×D314yes—
91C22×Dic3—34no—
92C22×Dic3—34no—
93C2×D12—316no—
94C2×D12—68no—
95C2×D12—68no—
96C2×D12—68no—
97C2×D12—68no—
98C2×D12—68no—
99C2×C3×C8—28no—
100C2×C3×C8D1218yes—
101C3×C4⋊C4—28no—
102C3×C4⋊C4—28no—
103(C2×D3)⋊C4—1216no—
104(C2×D3)⋊C4—1216no—
105C4×Dic3—64no—
106C4×Dic3—64no—
107C2×C3⋊C8—64no—
108C2×C3⋊C8—68no—
109D24—632no—
110C22×C32#12112yes—
111C22×C32#12111yescharacteristic
112C22×C32C2×D811yescharacteristic
113C22×C32#13511yescharacteristic
114C22×C32AGL(1,ℤ/8)12yes—
115C2×C3⋊D3—44no—
116C2×C3⋊D3—44no—
117C2×C3⋊D3—44no—
118C2×C3⋊D3—82no—
119C2×C3⋊D3—82no—
120C2×C3⋊D3—82no—
121C2×C3⋊D3—82no—
122C32×C4—82no—
123C32×C4#12011yescharacteristic
124C32×C4#12312yes—
125C32×C4#12411yescharacteristic
126C3⋊Dic3—22no—
127C3⋊Dic3—41no—
128C22×D4—92no—
129C2×D8—184no—
130C2×D8—182no—
131C22×C8—91no—
132C22×C8C2×C3⋊D311yescharacteristic
133C2×C4⋊C4C2×C3⋊D312yes—
134C2×C22⋊C4—182no—
135C2×C22⋊C4—182no—
136C2×C42—91no—
137C4⋊C8—182no—
138#102—184no—
139C23×C3D3×D414yes—
140C22×D3—616no—
141C22×D3—128no—
142C22×D3—128no—
143C22×D3—128no—
144C22×D3—128no—
145C22×D3—128no—
146C22×D3—128no—
147C2×C3×C4—48no—
148C2×C3×C4—48no—
149C2×C3×C4—48no—
150C2×C3×C4C2×D1214yes—
151C2×C3×C4#23518yes—
152C2×C3×C4D3×D418yes—
153C2×C3×C4#23914yes—
154C2×Dic3—38no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C2×Dic3—68no—
159D12—616no—
160D12—616no—
161D12—128no—
162D12—128no—
163C3×C8—28no—
164C3⋊C8—124no—
165C2×C32#39411yescharacteristic
166C2×C32#45912yes—
167C2×C32#46312yes—
168C2×C32#46611yescharacteristic
169C2×C32#46911yescharacteristic
170C3⋊D3—84no—
171C24—182no—
172C2×D4—94no—
173C2×D4—182no—
174C2×D4—182no—
175C2×D4—182no—
176C2×D4—182no—
177C2×D4—182no—
178C22×C4—22no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4C22×C3⋊D311yescharacteristic
182D8—188no—
183C2×C8—22no—
184C2×C8—181no—
185C2×C8—182no—
186C2×C8C4⋊(C3⋊D3)12yes—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C22⋊C4—364no—
190C22⋊C4—364no—
191C42—181no—
192C42—181no—
193C22×C3#88418yes—
194C22×C3#89514yes—
195C22×C3D3×D814yes—
196C22×C3#91418yes—
197C22×C3#91914yes—
198C2×D3—1216no—
199C2×D3—1216no—
200C2×D3—1216no—
201C2×D3—248no—
202C2×D3—248no—
203C2×D3—248no—
204C2×D3—248no—
205C3×C4—88no—
206C3×C4#87514yes—
207C3×C4#88214yes—
208C3×C4#89418yes—
209Dic3—68no—
210Dic3—124no—
211C32#205411yescharacteristic, complemented, Sylow
212C23—184no—
213C23—362no—
214C23—362no—
215C23—362no—
216C23—362no—
217C23—362no—
218C23—362no—
219C23D4×C3⋊D311yescharacteristic
220D4—184no—
221D4—184no—
222D4—362no—
223D4—362no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—92no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—182no—
232C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
233C2×C4#382812yes—
234C2×C4D4×C3⋊D312yes—
235C2×C4#383211yescharacteristic
236C8—22no—
237C8—361no—
238C2×C3#467214yes—
239C2×C3#478618yes—
240C2×C3#481918yes—
241C2×C3#486514yes—
242C2×C3#488314yes—
243D3—2416no—
244C22—364no—
245C22—364no—
246C22—364no—
247C22—722no—
248C22—722no—
249C22—722no—
250C22—722no—
251C22#6409312yes—
252C22#6410411yescharacteristic
253C22D8×C3⋊D311yescharacteristic
254C22#6412312yes—
255C22#6412811yescharacteristic
256C4—82no—
257C4—182no—
258C4—361no—
259C4#6408411yescharacteristic
260C4#6409111yescharacteristic
261C4#6410312yes—
262C3#6886214yescomplemented
263C2—724no—
264C2#1059237111yescharacteristic
265C2#1059248512yes—
266C2#1059251812yes—
267C2#1059256411yescharacteristic
268C2#1059258211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×#3745C2
hypercenter#340C3⋊D3
hypocenterC32#2054
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#63641C2semidirect
3. #10592687C2semidirect
4. C2×#63636C2semidirect
5. C32×#340C2semidirect
22. C3×#340D3semidirect
76. C2×C3⋊Dic3D8semidirect
87. #340C3⋊D3semidirect
211. C32#2054semidirect
262. C3#68862semidirect

Maximal subgroups

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

subgroupindex
C22×#37452
C2×#636412
#105926872
C2×#636362
C32×#3402
#688623