Finite Group Databasebeta

← #11799116

Subgroups — #11799116

Order 1152.

393 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 72 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#10592895C211yesmaximal, characteristic, complemented
2C3×#5193C212yesmaximal, complemented
3#10590886C211yesmaximal, characteristic, complemented
4#10589135C211yesmaximal, characteristic, complemented
5#10589127C212yesmaximal, complemented
6#71514—32nomaximal
7C32×#135C2211yescharacteristic
8#64157—21no—
9C2×C3×D24C2212yes—
10#63914—21no—
11C2×#3713—21no—
12#63664—21no—
13#63646C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15C3×#828—22no—
16C3×#826—22no—
17C3×#812C2212yes—
18C3×#509—32no—
19#5196—32no—
20#5196—61no—
21#5193D312yescomplemented
22#5151—32no—
23#4563—32no—
24#4516—32no—
25#4511—32no—
26C32×#41—21no—
27C2×C3×D12—22no—
28C2×#625—42no—
29C32×Q16D411yescharacteristic, complemented
30C32×SD16—21no—
31C32×D8D411yescharacteristic, complemented
32C2×C32×C8C2311yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34#3748—21no—
35#3748—41no—
36C2×C3⋊(C3⋊C8)—41no—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C3×D24—22no—
39C3×D24—22no—
40#3713—41no—
41#3713—41no—
42C3×C3⋊C16—22no—
43#2213—91noSylow
44C3×#135—21no—
45C3×#135C2×D312yes—
46C2×C3×D8—32no—
47#948—62no—
48#948—62no—
49#940—62no—
50C2×#213—62no—
51C2×D24C2×D312yes—
52C3×SD32—62no—
53C3×D16—62no—
54C3×M32—32no—
55#837—62no—
56#837—62no—
57#828—22no—
58#826—22no—
59#819—32no—
60#819—61no—
61C8×Dic3—32no—
62C8×Dic3—61no—
63#812C2×D312yes—
64C22×C3×D3—42no—
65C32×Q8—21no—
66C32×D4—21no—
67C32×D4—41no—
68C2×C32×C4—41no—
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3—21no—
71C3×D12—42no—
72C3×D12—42no—
73#625—84no—
74C32×C8C2×D411yescharacteristic
75C32×C8#4111yescharacteristic
76C3⋊(C3⋊C8)—41no—
77C3⋊(C3⋊C8)D811yescharacteristic
78C3⋊(C3⋊C8)D811yescharacteristic
79#509—32no—
80#493—91no—
81#443—91no—
82#364—91no—
83#361—92no—
84C3×#41—22no—
85C3×#41—22no—
86C2×C3×D4—62no—
87C2×#67—124no—
88C2×D12—22no—
89C3×Q16—21no—
90C3×Q16#6712yescomplemented
91C3×SD16—22no—
92C3×SD16—22no—
93C3×D8—21no—
94C3×D8—62no—
95C3×D8—62no—
96C3×D8#6712yescomplemented
97C2×C3×C8—21no—
98C2×C3×C8C22×D312yes—
99#213—122no—
100#213—122no—
101C4×Dic3—32no—
102C4×Dic3—61no—
103#208—62no—
104#208—62no—
105#208—122no—
106#208—122no—
107C2×C3⋊C8—32no—
108C2×C3⋊C8—61no—
109C2×C3⋊C8—122no—
110C2×C3⋊C8—122no—
111D24—22no—
112D24—22no—
113C3×C16—62no—
114C3⋊C16—22no—
115C22×C32—41no—
116C22×C32AGL(1,ℤ/8)11yescharacteristic
117C2×C3×D3—84no—
118C2×C3×D3—82no—
119C32×C4—41no—
120C32×C4#12111yescharacteristic
121C32×C4C2×D811yescharacteristic
122C3⋊Dic3—22no—
123#135D3211yescharacteristic
124C2×D8—32no—
125C2×D8—181no—
126#131—181no—
127#127—181no—
128SD32—62no—
129D16—62no—
130M32—32no—
131#108—91no—
132#104—181no—
133C4×C8—91no—
134C23×C3—122no—
135C22×D3—42no—
136C3×Q8—22no—
137C3×Q8—22no—
138C3×D4—22no—
139C3×D4—22no—
140C3×D4—42no—
141C3×D4—42no—
142C3×D4—122no—
143C3×D4—122no—
144C2×C3×C4—21no—
145C2×C3×C4—42no—
146C2×C3×C4—42no—
147C2×C3×C4D3×D412yes—
148#67—248no—
149C2×Dic3—62no—
150C2×Dic3—121no—
151D12—42no—
152D12—42no—
153C3×C8—21no—
154C3×C8—21no—
155C3×C8#23712yes—
156C3×C8C2×#6712yes—
157C3⋊C8—32no—
158C3⋊C8—32no—
159C3⋊C8—61no—
160C3⋊C8—61no—
161C3⋊C8—122no—
162C3⋊C8—122no—
163C2×C32—21no—
164C2×C32—81no—
165C2×C32#45911yescharacteristic
166C3×D3—162no—
167#41—21no—
168C2×D4—62no—
169C2×D4—362no—
170Q16#62511yescharacteristic, complemented
171SD16—21no—
172D8—62no—
173D8—62no—
174D8—361no—
175D8—361no—
176D8#62511yescharacteristic, complemented
177M16—181no—
178M16—361no—
179C2×C8—91no—
180C2×C8—361no—
181C2×C8C2×D3211yescharacteristic
182C42—91no—
183C16—62no—
184C22×C3—21no—
185C22×C3—42no—
186C22×C3—42no—
187C22×C3—244no—
188C22×C3—242no—
189C22×C3#91112yes—
190C2×D3—84no—
191C2×D3—82no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—42no—
195C3×C4—42no—
196C3×C4D3×D812yes—
197C3×C4#93912yes—
198Dic3—64no—
199Dic3—122no—
200C32#221311yescharacteristic, complemented, Sylow
201C23—122no—
202Q8—21no—
203D4—21no—
204D4—41no—
205D4—122no—
206D4—122no—
207D4—724no—
208C2×C4—41no—
209C2×C4—181no—
210C2×C4#381111yescharacteristic
211C8—91no—
212C8—91no—
213C8—361no—
214C8#380511yescharacteristic
215C8C2×#62511yescharacteristic
216C2×C3—22no—
217C2×C3—21no—
218C2×C3—41no—
219C2×C3—82no—
220C2×C3—82no—
221C2×C3—482no—
222C2×C3#515012yes—
223D3—162no—
224C22—41no—
225C22—244no—
226C22—242no—
227C22#6392711yescharacteristic
228C4—41no—
229C4—182no—
230C4#6392611yescharacteristic
231C4#6398011yescharacteristic
232C3—21no—
233C3#7151412yescomplemented
234C2—21no—
235C2—81no—
236C2—482no—
237C2#1059148611yescharacteristic
subgroupG/H
centerC2#10591486
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#135C22
socleC2×C32#459
hypercenter#135D32
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #10592895C2semidirect
2. C3×#5193C2semidirect
3. #10590886C2semidirect
4. #10589135C2semidirect
5. #10589127C2semidirect
21. #5193D3semidirect
29. C32×Q16D4semidirect
31. C32×D8D4semidirect
90. C3×Q16#67semidirect
96. C3×D8#67semidirect
170. Q16#625semidirect
176. D8#625semidirect
200. C32#2213semidirect
233. C3#71514semidirect

Maximal subgroups

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

subgroupindex
#105928952
C3×#51932
#105908862
#105891352
#105891272
#715143