Finite Group Databasebeta

← #11798419

Subgroups — #11798419

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
2C32×#510C211yesmaximal, characteristic, complemented
3#10592891C211yesmaximal, characteristic, complemented
4C2×#63655C211yesmaximal, characteristic, complemented
5#10589433C211yesmaximal, characteristic, complemented
6#10589382C211yesmaximal, characteristic, complemented
7#10589381C211yesmaximal, characteristic, complemented
8#71523—34nomaximal
9#64366—21no—
10C32×#135C2211yescharacteristic
11C2×C32×Q16C2211yescharacteristic, complemented
12#64158—21no—
13#64151—21no—
14#64128—21no—
15#64123—22no—
16D8×C3⋊D3—21no—
17C2×#3745C2211yescharacteristic
18#64110C2211yescharacteristic
19C32×Q32—21no—
20C32×SD32—21no—
21C32×M32C2211yescharacteristic, complemented
22#63663—21no—
23#63655—22no—
24#63646C2211yescharacteristic, complemented
25C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
26#5769—34no—
27C3×#510D314yescomplemented
28#5192—34no—
29C2×#828—34no—
30#4567—34no—
31#4516—34no—
32#4515—34no—
33C32×#41—21no—
34C2×C32×Q8—21no—
35#3832—22no—
36D4×C3⋊D3—22no—
37D4×C3⋊D3—42no—
38#3828—41no—
39#3828D411yescharacteristic
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—41no—
42C32×Q16—21no—
43C32×Q16—21no—
44C32×Q16D411yescharacteristic
45C32×SD16—21no—
46C32×D8D411yescharacteristic
47C2×C32×C8C2311yescharacteristic
48#3756—41no—
49#3755—22no—
50#3755—41no—
51#3753—22no—
52#3748—21no—
53#3748D411yescharacteristic
54#3745—21no—
55#3745D412yes—
56#3743—21no—
57C8×C3⋊D3—21no—
58C32×C16—21no—
59C3⋊(C3⋊C16)—21no—
60#2194—91noSylow
61#1009—64no—
62C3×#135C2×D314yes—
63C2×C3×Q16C2×D314yescomplemented
64#949—64no—
65#942—64no—
66#919—64no—
67#914—68no—
68D3×D8—64no—
69C2×D24—34no—
70#901—34no—
71C3×Q32—24no—
72C3×SD32—24no—
73C3×M32C2×D314yescomplemented
74#836—64no—
75#828—68no—
76#819—34no—
77C2×C3⋊C16—34no—
78C22×C3⋊D3—42no—
79C22×C3⋊D3—41no—
80C32×Q8—21no—
81C32×Q8—41no—
82C32×Q8—41no—
83C32×D4—21no—
84C32×D4—41no—
85C2×C32×C4—41no—
86C2×C32×C4—41no—
87C2×C32×C4C2×D411yescharacteristic
88#638—21no—
89#638—42no—
90C4⋊(C3⋊D3)—22no—
91C4⋊(C3⋊D3)—42no—
92C4⋊(C3⋊D3)—41no—
93C4⋊(C3⋊D3)D811yescharacteristic
94C4×C3⋊D3—21no—
95C4×C3⋊D3—42no—
96#634D811yescharacteristic
97C32×C8C2×D411yescharacteristic
98C32×C8C2×D411yescharacteristic
99C3⋊(C3⋊C8)—21no—
100C3⋊(C3⋊C8)—41no—
101#576—91no—
102#510C3⋊D311yescharacteristic, complemented
103C2×SD32—91no—
104#473—91no—
105#361—91no—
106#359—91no—
107#350—91no—
108C3×#41—24no—
109C2×C3×Q8—24no—
110#239—68no—
111D3×D4—68no—
112D3×D4—128no—
113#235—34no—
114#235—124no—
115C2×D12—64no—
116C2×D12—124no—
117C3×Q16—24no—
118C3×Q16—24no—
119C3×Q16#6714yes—
120C3×SD16—24no—
121C3×D8#6714yes—
122C2×C3×C8C22×D314yes—
123#216—124no—
124#215—68no—
125#215—124no—
126#213—68no—
127#208—34no—
128#208—64no—
129D24—38no—
130D24—64no—
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—81no—
143C32×C4#12011yescharacteristic
144C32×C4C2×D811yescharacteristic
145C3⋊Dic3—21no—
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×Q16C2×C3⋊D311yescharacteristic, complemented
153C2×D8—91no—
154C2×D8—181no—
155#131—91no—
156Q32—21no—
157SD32—21no—
158SD32—182no—
159M32C2×C3⋊D311yescharacteristic, complemented
160C2×C16—91no—
161#108—91no—
162#101—181no—
163C22×D3—128no—
164C22×D3—124no—
165C3×Q8—24no—
166C3×Q8—44no—
167C3×Q8—44no—
168C3×D4—24no—
169C3×D4—44no—
170C2×C3×C4—44no—
171C2×C3×C4—44no—
172C2×C3×C4D3×D414yes—
173#67—64no—
174#67—128no—
175D12—34no—
176D12—68no—
177D12—128no—
178D12—124no—
179C4×D3—64no—
180C4×D3—128no—
181Dic6—34no—
182C3×C8D3×D414yes—
183C3×C8C2×#6714yes—
184C3⋊C8—64no—
185C3⋊C8—124no—
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—21no—
196C2×D4—182no—
197C2×D4—181no—
198C2×D4—361no—
199C2×D4—362no—
200Q16—21no—
201Q16—21no—
202Q16—361no—
203Q16#63811yescharacteristic
204SD16—21no—
205SD16—182no—
206SD16—361no—
207D8—92no—
208D8—182no—
209D8—181no—
210D8#63811yescharacteristic
211M16—91no—
212M16—181no—
213M16—181no—
214C2×C8—181no—
215C2×C8C22×C3⋊D311yescharacteristic
216C16—21no—
217C16—181no—
218C22×C3—44no—
219C22×C3#91114yes—
220C2×D3—64no—
221C2×D3—128no—
222C2×D3—488no—
223C2×D3—484no—
224C3×C4—44no—
225C3×C4—84no—
226C3×C4D3×D814yes—
227C3×C4#93714yes—
228Dic3—64no—
229C32#219411yescharacteristic, complemented, Sylow
230C23—362no—
231C23—361no—
232Q8—21no—
233Q8—41no—
234Q8—41no—
235Q8—91no—
236D4—21no—
237D4—41no—
238D4—91no—
239D4—181no—
240D4—182no—
241D4—362no—
242D4—362no—
243D4—361no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—181no—
247C2×C4—362no—
248C2×C4D4×C3⋊D311yescharacteristic
249C8—181no—
250C8—361no—
251C8D4×C3⋊D311yescharacteristic
252C8C2×#63811yescharacteristic
253C2×C3—24no—
254C2×C3—84no—
255C2×C3#515614yes—
256D3—124no—
257D3—248no—
258C22—41no—
259C22—181no—
260C22—362no—
261C22—1441no—
262C22—1442no—
263C22#6412011yescharacteristic
264C4—41no—
265C4—81no—
266C4—181no—
267C4D8×C3⋊D311yescharacteristic
268C4#6414611yescharacteristic
269C3#7152314yescomplemented
270C2—21no—
271C2—81no—
272C2—361no—
273C2—722no—
274C2#1059285511yescharacteristic
subgroupG/H
centerC2#10592855
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#510C2
socleC2×C32#447
prime radical#10596240C2
hypercenter#510C3⋊D3
hypocenterC32#2194
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C32×#510C2semidirect
3. #10592891C2semidirect
4. C2×#63655C2semidirect
5. #10589433C2semidirect
6. #10589382C2semidirect
7. #10589381C2semidirect
11. C2×C32×Q16C22semidirect
21. C32×M32C22semidirect
24. #63646C22semidirect
25. C2×C3⋊(C3⋊C16)C22semidirect
27. C3×#510D3semidirect
63. C2×C3×Q16C2×D3semidirect
73. C3×M32C2×D3semidirect
102. #510C3⋊D3semidirect
152. C2×Q16C2×C3⋊D3semidirect
159. M32C2×C3⋊D3semidirect
229. C32#2194semidirect
269. C3#71523semidirect

Maximal subgroups

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

subgroupindex
#105962402
C32×#5102
#105928912
C2×#636552
#105894332
#105893822
#105893812
#715233