Finite Group Databasebeta

← #11799121

Subgroups — #11799121

Order 1152.

393 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 66 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#10592594C211yesmaximal, characteristic, complemented
2#10590886C211yesmaximal, characteristic, complemented
3#10590633C212yesmaximal, complemented
4C3×#4495C212yesmaximal, complemented
5#10589135C211yesmaximal, characteristic, complemented
6#69263—32nomaximal
7#64116—21no—
8#64113C2211yescharacteristic
9C2×C3×D24C2212yes—
10#63914—21no—
11C2×#3713—21no—
12C32×#108C2211yescharacteristic
13#63652—21no—
14C8×C3⋊Dic3C2211yescharacteristic
15C3×#812C2212yes—
16#63548—22no—
17#63546—22no—
18#5151—32no—
19#5147—32no—
20#4908—32no—
21#4895—32no—
22#4895—61no—
23C3×#361—32no—
24#4511—32no—
25#4495D312yescomplemented
26#3828—21no—
27C2×C3×D12—22no—
28C2×#625—42no—
29C32×M16—21no—
30C2×C32×C8C2311yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33#3746D411yescharacteristic, complemented
34#3745D411yescharacteristic, complemented
35#3744—21no—
36#3743—41no—
37C8×C3⋊D3—41no—
38C3×D24—22no—
39C3×D24—22no—
40#3713—41no—
41#3713—41no—
42C3×C3⋊C16—22no—
43#2213—91noSylow
44C2×C3×D8—32no—
45#940—62no—
46C2×#213—62no—
47#907—62no—
48#907—62no—
49#904—32no—
50#904—61no—
51C2×D24C2×D312yes—
52C3×M32—32no—
53C3×#108—21no—
54C3×#108C2×D312yes—
55#827—62no—
56#826—62no—
57#825—62no—
58#825—62no—
59C8×Dic3—32no—
60C8×Dic3—61no—
61#812C2×D312yes—
62#800—62no—
63D48—62no—
64C22×C3×D3—42no—
65C2×C32×C4C2×D411yescharacteristic
66#638—41no—
67C2×C3⋊Dic3—21no—
68C4⋊(C3⋊D3)—21no—
69C4×C3⋊D3—41no—
70#634—21no—
71C3×D12—42no—
72C3×D12—42no—
73#625—84no—
74C32×C8—41no—
75C32×C8C2×D411yescharacteristic
76C32×C8#4111yescharacteristic
77C3⋊(C3⋊C8)D811yescharacteristic
78C3⋊(C3⋊C8)D811yescharacteristic
79#509—92no—
80#493—91no—
81#443—91no—
82#364—91no—
83#361—32no—
84C2×C3×D4—62no—
85C2×#67—124no—
86#235—62no—
87#235—62no—
88C2×D12—22no—
89C3×D8—62no—
90C3×D8—62no—
91C3×M16—22no—
92C3×M16—22no—
93C2×C3×C8—21no—
94C2×C3×C8C22×D312yes—
95#213—122no—
96#213—122no—
97C4×Dic3—32no—
98C4×Dic3—61no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—61no—
101Dic12—32no—
102Dic12—61no—
103D24—22no—
104D24—22no—
105D24—32no—
106D24—61no—
107#204—62no—
108#204—62no—
109ΓL(1,𝔽25)—122no—
110ΓL(1,𝔽25)—122no—
111D3×C8—122no—
112D3×C8—122no—
113C3×C16—62no—
114C3⋊C16—22no—
115C22×C32AGL(1,ℤ/8)11yescharacteristic
116C2×C3⋊D3—41no—
117C2×C3×D3—84no—
118C2×C3×D3—82no—
119C32×C4#12111yescharacteristic
120C32×C4C2×D811yescharacteristic
121C3⋊Dic3—22no—
122C3⋊Dic3—41no—
123#135—91no—
124C2×D8—32no—
125C2×D8—181no—
126#131—181no—
127#127—181no—
128SD32—182no—
129D16—182no—
130M32—32no—
131#108D3211yescharacteristic
132#104—181no—
133C4×C8—91no—
134C23×C3—122no—
135C22×D3—42no—
136C3×D4—122no—
137C3×D4—122no—
138C2×C3×C4—21no—
139C2×C3×C4D3×D412yes—
140#67—122no—
141#67—122no—
142#67—248no—
143C2×Dic3—62no—
144C2×Dic3—121no—
145D12—42no—
146D12—42no—
147D12—62no—
148D12—62no—
149C4×D3—122no—
150C4×D3—122no—
151Dic6—62no—
152Dic6—62no—
153C3×C8—21no—
154C3×C8—21no—
155C3×C8—42no—
156C3×C8—42no—
157C3×C8#23512yes—
158C3×C8D3×D412yes—
159C3⋊C8—32no—
160C3⋊C8—32no—
161C3⋊C8—61no—
162C3⋊C8—61no—
163C2×C32—21no—
164C2×C32#45911yescharacteristic
165C3⋊D3—81no—
166C3×D3—162no—
167#41—181no—
168C2×D4—62no—
169C2×D4—362no—
170Q16—91no—
171SD16—181no—
172D8—62no—
173D8—62no—
174D8—91no—
175D8—361no—
176D8—361no—
177M16—21no—
178M16—361no—
179C2×C8—91no—
180C2×C8—361no—
181C2×C8C2×D3211yescharacteristic
182C42—91no—
183C16—62no—
184C22×C3—21no—
185C22×C3—244no—
186C22×C3—242no—
187C22×C3#91412yes—
188C2×D3—84no—
189C2×D3—82no—
190C2×D3—122no—
191C2×D3—122no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4#88412yes—
195C3×C4D3×D812yes—
196Dic3—64no—
197Dic3—122no—
198Dic3—122no—
199Dic3—122no—
200C32#221311yescharacteristic, complemented, Sylow
201C23—122no—
202Q8—181no—
203D4—122no—
204D4—122no—
205D4—181no—
206D4—361no—
207D4—724no—
208C2×C4—181no—
209C2×C4—361no—
210C2×C4#381111yescharacteristic
211C8—41no—
212C8—91no—
213C8—91no—
214C8#379811yescharacteristic
215C8#380211yescharacteristic
216C2×C3—22no—
217C2×C3—21no—
218C2×C3—41no—
219C2×C3—482no—
220C2×C3#478612yes—
221D3—162no—
222D3—242no—
223D3—242no—
224C22—244no—
225C22—242no—
226C22—361no—
227C22#6394111yescharacteristic
228C4—182no—
229C4—361no—
230C4#6391211yescharacteristic
231C4#6392611yescharacteristic
232C3—21no—
233C3#6926312yescomplemented
234C2—21no—
235C2—482no—
236C2—721no—
237C2#1059055111yescharacteristic
subgroupG/H
centerC2#10590551
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32#459
hypercenter#108D32
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10592594C2semidirect
2. #10590886C2semidirect
3. #10590633C2semidirect
4. C3×#4495C2semidirect
5. #10589135C2semidirect
25. #4495D3semidirect
33. #3746D4semidirect
34. #3745D4semidirect
200. C32#2213semidirect
233. C3#69263semidirect

Maximal subgroups

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

subgroupindex
#105925942
#105908862
#105906332
C3×#44952
#105891352
#692633