Finite Group Databasebeta

← #11800159

Subgroups — #11800159

Order 1152.

385 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592850C211yesmaximal, characteristic
2#10590875C211yesmaximal, characteristic, complemented
3C3×#4562C212yesmaximal, complemented
4#10589116C212yesmaximal, complemented
5#10589104C211yesmaximal, characteristic, complemented
6#69186—32nomaximal
7C2×C32×D8C2211yescharacteristic
8#64149—21no—
9C2×#3753—21no—
10C2×#3745C2211yescharacteristic
11#63872—21no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63574—21no—
16#5151—32no—
17#5151—61no—
18#4878—32no—
19C3×#357—32no—
20#4562D312yescomplemented
21#4509—32no—
22#4502—32no—
23#4491—32no—
24C2×C32×D4—21no—
25C2×#638—42no—
26C2×C4⋊(C3⋊D3)—21no—
27C32×D8—22no—
28C2×C32×C8C2311yescharacteristic
29#3753—42no—
30C4×C3⋊Dic3D411yescharacteristic
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32#3745—22no—
33C3×C4⋊Dic3—22no—
34Dic3⋊Dic3—42no—
35C3×C3⋊C16—22no—
36#2244—91noSylow
37C2×C3×D8—21no—
38C2×C3×D8C2×D312yes—
39#940—62no—
40#940—62no—
41C2×#213—62no—
42C2×#213—62no—
43C2×D24—32no—
44C2×D24—61no—
45#890—62no—
46C2×C3×C16—32no—
47C3×#107—32no—
48#818C2×D312yes—
49C8×Dic3—32no—
50C8×Dic3—61no—
51C2×C3⋊C16C2×D312yes—
52#808—62no—
53C23×C32—41no—
54C22×C3⋊D3—41no—
55C32×D4—41no—
56C32×D4—41no—
57C2×C32×C4C2×D411yescharacteristic
58#638—84no—
59C2×C3⋊Dic3D812yes—
60C4⋊(C3⋊D3)—41no—
61C4⋊(C3⋊D3)—41no—
62C2×C3×Dic3—42no—
63C32×C8#4112yes—
64C3⋊(C3⋊C8)SD1612yes—
65#499—91no—
66#493—91no—
67#357—32no—
68#357—92no—
69#346—91no—
70C2×C3×D4—22no—
71C2×C3×D4—22no—
72C2×#67—122no—
73C2×#67—122no—
74C2×#67—124no—
75C2×D12—62no—
76C2×D12—62no—
77C3×D8—22no—
78C3×D8—22no—
79C3×D8—42no—
80C2×C3×C8—21no—
81C2×C3×C8C22×D312yes—
82C3×C4⋊C4—62no—
83#213—124no—
84#213—124no—
85C4⋊Dic3—22no—
86C4⋊Dic3—122no—
87Dic3⋊C4—122no—
88C4×Dic3—32no—
89C4×Dic3—61no—
90C2×C3⋊C8—32no—
91C2×C3⋊C8—61no—
92D24—62no—
93D24—62no—
94D24—122no—
95C3×C16—62no—
96C3⋊C16—22no—
97C22×C32—81no—
98C22×C32—82no—
99C22×C32C2×D811yescharacteristic
100C2×C3⋊D3—81no—
101C2×C3⋊D3—82no—
102C32×C4#12411yescharacteristic
103C32×C4C2×SD1611yescharacteristic
104C3⋊Dic3—22no—
105C3×Dic3—82no—
106C2×D8—91no—
107C2×D8—181no—
108C2×D8D3211yescharacteristic
109#127—181no—
110#125—181no—
111C2×C16—32no—
112#107—32no—
113#106—181no—
114C4×C8—91no—
115C23×C3—42no—
116C23×C3—42no—
117C22×D3—122no—
118C22×D3—122no—
119C3×D4—42no—
120C3×D4—42no—
121C3×D4—42no—
122C3×D4—42no—
123C2×C3×C4—21no—
124C2×C3×C4—122no—
125C2×C3×C4D3×D412yes—
126#67—248no—
127#67—244no—
128#67—244no—
129C2×Dic3—32no—
130C2×Dic3—32no—
131C2×Dic3—42no—
132C2×Dic3—62no—
133D12—122no—
134D12—122no—
135D12—122no—
136D12—122no—
137C3×C8—22no—
138C3×C8#23512yes—
139C3×C8#23712yes—
140C3⋊C8—34no—
141C3⋊C8—62no—
142C2×C32—161no—
143C2×C32#48611yescharacteristic
144C2×C32#50912yes—
145C3⋊D3—161no—
146C2×D4—21no—
147C2×D4—181no—
148C2×D4—362no—
149D8—22no—
150D8—182no—
151D8—362no—
152C2×C8—91no—
153C2×C8C2×D3211yescharacteristic
154C4⋊C4—62no—
155C4⋊C4—362no—
156C42—91no—
157C16—62no—
158C22×C3—21no—
159C22×C3—84no—
160C22×C3—82no—
161C22×C3—82no—
162C22×C3—82no—
163C22×C3—82no—
164C22×C3D3×D812yes—
165C2×D3—242no—
166C2×D3—244no—
167C2×D3—242no—
168C2×D3—242no—
169C2×D3—242no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—242no—
173C3×C4#88512yes—
174C3×C4D3×SD1612yes—
175Dic3—64no—
176Dic3—62no—
177Dic3—62no—
178Dic3—82no—
179C32#224411yescharacteristic, complemented, Sylow
180C23—41no—
181C23—361no—
182D4—41no—
183D4—41no—
184D4—361no—
185D4—361no—
186D4—724no—
187C2×C4—92no—
188C2×C4—122no—
189C2×C4#381111yescharacteristic
190C8—92no—
191C8#380412yes—
192C2×C3—22no—
193C2×C3—21no—
194C2×C3—162no—
195C2×C3—162no—
196C2×C3#476012yes—
197C2×C3#491112yes—
198C2×C3#491412yes—
199D3—482no—
200D3—482no—
201C22—82no—
202C22—81no—
203C22—722no—
204C22—721no—
205C22#6392611yescharacteristic
206C4—182no—
207C4—242no—
208C4#6393011yescharacteristic
209C4#6395311yescharacteristic
210C3—21no—
211C3#6918612yescomplemented
212C2—161no—
213C2—1441no—
214C2#1059103612yes—
215C2#1059140211yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC22×C32C2×D8
prime radical#10592850C2
hypercenterC2×D8D32
hypocenterC32#2244
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10590875C2semidirect
3. C3×#4562C2semidirect
4. #10589116C2semidirect
5. #10589104C2semidirect
20. #4562D3semidirect
179. C32#2244semidirect
211. C3#69186semidirect

Maximal subgroups

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

subgroupindex
#105928502
#105908752
C3×#45622
#105891162
#105891042
#691863