Finite Group Databasebeta

← #11798162

Subgroups — #11798162

Order 1152.

768 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×D8×C3⋊D3C211yesmaximal, characteristic
2C2×#63654C211yesmaximal, characteristic, complemented
3C2×#63627C211yesmaximal, characteristic, complemented
4#10592586C211yesmaximal, characteristic, complemented
5C32×#357C211yesmaximal, characteristic, complemented
6#10589373C211yesmaximal, characteristic, complemented
7#10589357C211yesmaximal, characteristic, complemented
8#69193—34nomaximal
9C2×D4×C3⋊D3—21no—
10C2×C32×D8C2211yescharacteristic
11C2×#3753—21no—
12D8×C3⋊D3—22no—
13D8×C3⋊D3—22no—
14C2×#3746C2211yescharacteristic, complemented
15C2×#3745C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17#64106—21no—
18C2×C32×C16C2211yescharacteristic, complemented
19C32×#107C2211yescharacteristic, complemented
20#63654—22no—
21C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
22#63637—21no—
23#63627—22no—
24C2×D3×D8—34no—
25C2×#827—34no—
26C2×#800—34no—
27#4887—34no—
28C3×#357D314yescomplemented
29(C2×D3)⋊C16—34no—
30#4491—34no—
31C23×C3⋊D3—41no—
32C2×C32×D4—21no—
33C2×#638—41no—
34D4×C3⋊D3—24no—
35D4×C3⋊D3—42no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×#634—21no—
39C32×D8—21no—
40C32×D8D412yes—
41C2×C32×C8C2311yescharacteristic
42C32×C4⋊C4—21no—
43#3753—24no—
44#3752—41no—
45C4⋊(C3⋊Dic3)—41no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#3746—21no—
48#3746—21no—
49#3745—21no—
50#3745D412yes—
51C8×C3⋊D3—21no—
52C8×C3⋊D3—21no—
53C32×C16—21no—
54C3⋊(C3⋊C16)—21no—
55#2187—91noSylow
56C2×D3×D4—64no—
57C2×C3×D8C2×D314yes—
58C2×#213—64no—
59D3×D8—68no—
60D3×D8—68no—
61C2×Dic12—34no—
62C2×D24—34no—
63C2×D3×C8—34no—
64#897—64no—
65C2×C3×C16C2×D314yescomplemented
66C3×#107C2×D314yescomplemented
67#827—68no—
68C2×C3⋊C16—34no—
69#810—64no—
70#800—68no—
71C23×C32—41no—
72C22×C3⋊D3—44no—
73C22×C3⋊D3—41no—
74C22×C3⋊D3—82no—
75C22×C3⋊D3—82no—
76C22×C3⋊D3D811yescharacteristic
77C32×D4—22no—
78C32×D4—41no—
79C2×C32×C4—41no—
80C2×C32×C4C2×D411yescharacteristic
81#638—44no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3D811yescharacteristic
84C4⋊(C3⋊D3)—22no—
85C4⋊(C3⋊D3)—41no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—21no—
88#634—41no—
89#634—41no—
90C32×C8C2×D411yescharacteristic
91C32×C8C2×D411yescharacteristic
92C3⋊(C3⋊C8)—21no—
93C22×D8—91no—
94C2×SD32—91no—
95C2×SD32—91no—
96#467—91no—
97#357—91no—
98#357C3⋊D311yescharacteristic, complemented
99C22⋊C16—91no—
100C23×D3—124no—
101C2×C3×D4—24no—
102C2×#67—124no—
103D3×D4—616no—
104D3×D4—128no—
105C2×D12—64no—
106C2×C4×D3—34no—
107C2×Dic6—64no—
108C3×D8—24no—
109C3×D8D1218yes—
110C2×C3×C8C22×D314yes—
111C3×C4⋊C4—24no—
112#213—616no—
113(C2×D3)⋊C4—124no—
114C4⋊Dic3—124no—
115C2×C3⋊C8—34no—
116Dic12—64no—
117Dic12—64no—
118D24—38no—
119D24—64no—
120D3×C8—64no—
121D3×C8—64no—
122C3×C16—24no—
123C3⋊C16—64no—
124C22×C32—42no—
125C22×C32—81no—
126C22×C32—81no—
127C22×C32C2×D811yescharacteristic
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—42no—
131C2×C3⋊D3—88no—
132C2×C3⋊D3—81no—
133C2×C3⋊D3—81no—
134C2×C3⋊D3SD3212yescomplemented
135C32×C4—81no—
136C32×C4#12011yescharacteristic
137C32×C4AGL(1,ℤ/8)11yescharacteristic
138C3⋊Dic3—21no—
139C3⋊Dic3—81no—
140C22×D4—181no—
141C2×Q16—91no—
142C2×D8—91no—
143C2×D8—181no—
144C2×D8—182no—
145C2×D8—182no—
146C2×D8C2×C3⋊D311yescharacteristic
147C22×C8—91no—
148C22⋊Q8—181no—
149SD32—182no—
150SD32—182no—
151C2×C16—91no—
152C2×C16C2×C3⋊D311yescharacteristic, complemented
153#107C2×C3⋊D311yescharacteristic, complemented
154#103—181no—
155C23×C3—44no—
156C22×D3—34no—
157C22×D3—1216no—
158C22×D3—124no—
159C22×D3—248no—
160C22×D3—248no—
161C3×D4—28no—
162C3×D4—44no—
163C2×C3×C4—44no—
164C2×C3×C4D3×D414yes—
165#67—1216no—
166C2×Dic3—34no—
167C2×Dic3—124no—
168D12—68no—
169D12—124no—
170C4×D3—64no—
171C4×D3—64no—
172Dic6—124no—
173Dic6—124no—
174C3×C8C2×D1214yes—
175C3×C8D3×D414yes—
176C3⋊C8—64no—
177C2×C32—82no—
178C2×C32#44711yescharacteristic
179C2×C32C2×SD3211yescharacteristic
180C2×C32#50911yescharacteristic
181C3⋊D3—22no—
182C3⋊D3—82no—
183C24—361no—
184C2×Q8—181no—
185C2×D4—21no—
186C2×D4—184no—
187C2×D4—181no—
188C2×D4—361no—
189C2×D4—362no—
190C22×C4—91no—
191Q16—181no—
192Q16—181no—
193D8—21no—
194D8—92no—
195D8—184no—
196D8—181no—
197D8C4⋊(C3⋊D3)12yes—
198C2×C8—91no—
199C2×C8—181no—
200C2×C8—181no—
201C2×C8C22×C3⋊D311yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—361no—
204C22⋊C4—361no—
205C16—21no—
206C16—181no—
207C22×C3—48no—
208C22×C3—84no—
209C22×C3—84no—
210C22×C3D3×D814yes—
211C2×D3—38no—
212C2×D3—64no—
213C2×D3—64no—
214C2×D3—128no—
215C2×D3—2432no—
216C2×D3—244no—
217C2×D3—244no—
218C3×C4—84no—
219C3×C4#88214yes—
220C3×C4#91414yes—
221Dic3—64no—
222Dic3—244no—
223C32#218711yescharacteristic, complemented, Sylow
224C23—41no—
225C23—91no—
226C23—364no—
227C23—361no—
228C23—722no—
229C23—722no—
230Q8—361no—
231Q8—361no—
232D4—22no—
233D4—41no—
234D4—182no—
235D4—364no—
236D4—361no—
237C2×C4—41no—
238C2×C4—91no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—361no—
242C2×C4D4×C3⋊D311yescharacteristic
243C8—181no—
244C8C2×C4⋊(C3⋊D3)11yescharacteristic
245C8D4×C3⋊D311yescharacteristic
246C2×C3—88no—
247C2×C3#477314yes—
248C2×C3#491114yes—
249C2×C3D3×SD3214yes—
250D3—68no—
251D3—248no—
252C22—42no—
253C22—81no—
254C22—81no—
255C22—92no—
256C22—181no—
257C22—181no—
258C22—362no—
259C22—728no—
260C22—721no—
261C22—721no—
262C22D8×C3⋊D311yescharacteristic
263C4—81no—
264C4—181no—
265C4—721no—
266C4#6409111yescharacteristic
267C4#6412311yescharacteristic
268C3#6919314yescomplemented
269C2—82no—
270C2—182no—
271C2—722no—
272C2#1059247211yescharacteristic
273C2#1059261011yescharacteristic
274C2C3⋊D3×SD3211yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#357C2
socleC22×C32C2×D8
prime radicalC2×D8×C3⋊D3C2
hypercenter#357C3⋊D3
hypocenterC32#2187
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#63654C2semidirect
3. C2×#63627C2semidirect
4. #10592586C2semidirect
5. C32×#357C2semidirect
6. #10589373C2semidirect
7. #10589357C2semidirect
14. C2×#3746C22semidirect
18. C2×C32×C16C22semidirect
19. C32×#107C22semidirect
21. C2×C3⋊(C3⋊C16)C22semidirect
28. C3×#357D3semidirect
65. C2×C3×C16C2×D3semidirect
66. C3×#107C2×D3semidirect
98. #357C3⋊D3semidirect
134. C2×C3⋊D3SD32semidirect
152. C2×C16C2×C3⋊D3semidirect
153. #107C2×C3⋊D3semidirect
223. C32#2187semidirect
268. C3#69193semidirect

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
C2×#636542
C2×#636272
#105925862
C32×#3572
#105893732
#105893572
#691933