Finite Group Databasebeta

← #11798431

Subgroups — #11798431

Order 1152.

648 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 107 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#10596240C211yesmaximal, characteristic
2#10592894C211yesmaximal, characteristic, complemented
3C2×#63627C211yesmaximal, characteristic, complemented
4#10592595C211yesmaximal, characteristic, complemented
5C32×#359C211yesmaximal, characteristic, complemented
6#10589374C211yesmaximal, characteristic, complemented
7#10589361C211yesmaximal, characteristic, complemented
8#69244—34nomaximal
9#64366—21no—
10C32×#135C2211yescharacteristic
11#64158—21no—
12#64128—21no—
13#64123—22no—
14D8×C3⋊D3—21no—
15#64118—21no—
16C2×#3746C2211yescharacteristic, complemented
17C2×#3745C2211yescharacteristic
18#64110C2211yescharacteristic
19C2×C32×C16C2211yescharacteristic, complemented
20C32×#108C2211yescharacteristic, complemented
21#63656—21no—
22#63654—21no—
23#63651—21no—
24#63639C2211yescharacteristic, complemented
25#63627—22no—
26#5769—34no—
27#5195—34no—
28C2×#800—34no—
29#4896—34no—
30C3×#359D314yescomplemented
31#4508—34no—
32#4495—34no—
33C32×#41—21no—
34#3832—22no—
35D4×C3⋊D3—22no—
36D4×C3⋊D3—42no—
37#3828—41no—
38#3828D411yescharacteristic
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—41no—
41C2×#634—21no—
42C32×Q16D411yescharacteristic
43C32×SD16—21no—
44C32×D8D411yescharacteristic
45C32×M16—21no—
46C2×C32×C8C2311yescharacteristic
47#3755—22no—
48#3753—22no—
49#3748D411yescharacteristic
50#3746—21no—
51#3746—21no—
52#3746—41no—
53#3745—21no—
54#3745D412yes—
55#3744—41no—
56#3743—21no—
57C8×C3⋊D3—21no—
58C32×C16—21no—
59C3⋊(C3⋊C16)—21no—
60#2194—91noSylow
61#1009—64no—
62C3×#135C2×D314yes—
63#949—64no—
64#919—64no—
65#914—68no—
66D3×D8—64no—
67#909—64no—
68C2×Dic12—34no—
69C2×D24—34no—
70#901—34no—
71C2×C3×C16C2×D314yescomplemented
72C3×#108C2×D314yescomplemented
73#829—64no—
74#827—64no—
75#824—64no—
76#812—34no—
77#800—68no—
78C22×C3⋊D3—42no—
79C22×C3⋊D3—41no—
80C32×Q8—21no—
81C32×D4—21no—
82C32×D4—41no—
83C2×C32×C4—41no—
84C2×C32×C4C2×D411yescharacteristic
85#638—21no—
86#638—42no—
87C2×C3⋊Dic3—41no—
88C4⋊(C3⋊D3)—22no—
89C4⋊(C3⋊D3)—42no—
90C4⋊(C3⋊D3)—41no—
91C4⋊(C3⋊D3)D811yescharacteristic
92C4×C3⋊D3—21no—
93C4×C3⋊D3—42no—
94#634—41no—
95#634—41no—
96#634D811yescharacteristic
97C32×C8—41no—
98C32×C8C2×D411yescharacteristic
99C32×C8C2×D411yescharacteristic
100C3⋊(C3⋊C8)—21no—
101#576—91no—
102#510—91no—
103C2×SD32—91no—
104#473—91no—
105#361—91no—
106#359C3⋊D311yescharacteristic, complemented
107#350—91no—
108C3×#41—24no—
109#239—68no—
110D3×D4—68no—
111D3×D4—128no—
112#235—34no—
113#235—124no—
114C2×D12—64no—
115C2×D12—124no—
116C2×Dic6—64no—
117C3×Q16D1214yes—
118C3×SD16—24no—
119C3×D8D1214yes—
120C3×M16—24no—
121C2×C3×C8C22×D314yes—
122#215—68no—
123#213—68no—
124#208—34no—
125Dic12—64no—
126Dic12—64no—
127Dic12—124no—
128D24—38no—
129D24—64no—
130#204—124no—
131ΓL(1,𝔽25)—64no—
132D3×C8—64no—
133C3×C16—24no—
134C3⋊C16—64no—
135C22×C32—41no—
136C22×C32AGL(1,ℤ/8)11yescharacteristic
137C2×C3⋊D3—21no—
138C2×C3⋊D3—42no—
139C2×C3⋊D3—162no—
140C2×C3⋊D3—161no—
141C32×C4—41no—
142C32×C4#12011yescharacteristic
143C32×C4C2×D811yescharacteristic
144C3⋊Dic3—21no—
145C3⋊Dic3—81no—
146H(5,𝔽2)—181no—
147#137—181no—
148AGL(1,ℤ/8)—181no—
149AGL(1,ℤ/8)—182no—
150#135—181no—
151#135C2×C3⋊D311yescharacteristic
152C2×Q16—91no—
153C2×D8—91no—
154C2×D8—181no—
155#131—91no—
156Q32—181no—
157SD32—182no—
158SD32—181no—
159M32—91no—
160C2×C16C2×C3⋊D311yescharacteristic, complemented
161#108C2×C3⋊D311yescharacteristic, complemented
162#101—181no—
163C22×D3—128no—
164C22×D3—124no—
165C3×Q8—24no—
166C3×D4—24no—
167C3×D4—44no—
168C2×C3×C4—44no—
169C2×C3×C4D3×D414yes—
170#67—64no—
171#67—128no—
172C2×Dic3—124no—
173D12—34no—
174D12—68no—
175D12—128no—
176D12—124no—
177C4×D3—64no—
178C4×D3—128no—
179Dic6—34no—
180Dic6—124no—
181Dic6—124no—
182C3×C8—44no—
183C3×C8C2×D1214yes—
184C3×C8D3×D414yes—
185C3⋊C8—64no—
186C2×C32—21no—
187C2×C32—81no—
188C2×C32#44711yescharacteristic
189C3⋊D3—41no—
190C3⋊D3—82no—
191#41—21no—
192#41—91no—
193#41—182no—
194#41—361no—
195C2×Q8—181no—
196C2×D4—182no—
197C2×D4—181no—
198C2×D4—361no—
199C2×D4—362no—
200Q16—181no—
201Q16—181no—
202Q16—361no—
203Q16C4⋊(C3⋊D3)11yescharacteristic
204SD16—21no—
205SD16—182no—
206SD16—361no—
207D8—92no—
208D8—182no—
209D8—181no—
210D8C4⋊(C3⋊D3)11yescharacteristic
211M16—21no—
212M16—91no—
213M16—181no—
214C2×C8—181no—
215C2×C8C22×C3⋊D311yescharacteristic
216C16—21no—
217C16—181no—
218C22×C3—44no—
219C22×C3#91414yes—
220C2×D3—64no—
221C2×D3—128no—
222C2×D3—488no—
223C2×D3—484no—
224C3×C4—44no—
225C3×C4#88214yes—
226C3×C4D3×D814yes—
227Dic3—64no—
228Dic3—244no—
229C32#219411yescharacteristic, complemented, Sylow
230C23—362no—
231C23—361no—
232Q8—21no—
233Q8—91no—
234Q8—361no—
235Q8—361no—
236D4—21no—
237D4—41no—
238D4—91no—
239D4—181no—
240D4—182no—
241D4—362no—
242D4—362no—
243D4—361no—
244C2×C4—41no—
245C2×C4—181no—
246C2×C4—362no—
247C2×C4—361no—
248C2×C4D4×C3⋊D311yescharacteristic
249C8—41no—
250C8—181no—
251C8C2×C4⋊(C3⋊D3)11yescharacteristic
252C8D4×C3⋊D311yescharacteristic
253C2×C3—24no—
254C2×C3—84no—
255C2×C3#477314yes—
256D3—124no—
257D3—248no—
258C22—41no—
259C22—181no—
260C22—362no—
261C22—1441no—
262C22—1442no—
263C22#6412311yescharacteristic
264C4—41no—
265C4—181no—
266C4—721no—
267C4#6409111yescharacteristic
268C4D8×C3⋊D311yescharacteristic
269C3#6924414yescomplemented
270C2—21no—
271C2—81no—
272C2—361no—
273C2—722no—
274C2#1059247211yescharacteristic
subgroupG/H
centerC2#10592472
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#359C2
socleC2×C32#447
prime radical#10596240C2
hypercenter#359C3⋊D3
hypocenterC32#2194
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
2. #10592894C2semidirect
3. C2×#63627C2semidirect
4. #10592595C2semidirect
5. C32×#359C2semidirect
6. #10589374C2semidirect
7. #10589361C2semidirect
16. C2×#3746C22semidirect
19. C2×C32×C16C22semidirect
20. C32×#108C22semidirect
24. #63639C22semidirect
30. C3×#359D3semidirect
71. C2×C3×C16C2×D3semidirect
72. C3×#108C2×D3semidirect
106. #359C3⋊D3semidirect
160. C2×C16C2×C3⋊D3semidirect
161. #108C2×C3⋊D3semidirect
229. C32#2194semidirect
269. C3#69244semidirect

Maximal subgroups

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

subgroupindex
#105962402
#105928942
C2×#636272
#105925952
C32×#3592
#105893742
#105893612
#692443