Finite Group Databasebeta

← #11800111

Subgroups — #11800111

Order 1152.

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

normal subgroups only

This group has 341 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#10592890C211yesmaximal, characteristic
2#10590875C211yesmaximal, characteristic, complemented
3C3×#4564C212yesmaximal, complemented
4#10589116C212yesmaximal
5#10589102C211yesmaximal, characteristic, complemented
6#69216—32nomaximal
7C2×C32×Q16C2211yescharacteristic
8#64156—21no—
9C2×#3755—21no—
10C2×#3745C2211yescharacteristic
11#63872—21no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63574—21no—
16#5191—32no—
17#5191—61no—
18#4878—32no—
19C3×#358—32no—
20#4564D312yescomplemented
21#4509—32no—
22Dic3×C16—32no—
23#4491—32no—
24C2×C32×Q8—21no—
25C2×C4⋊(C3⋊D3)—21no—
26C32×Q16—22no—
27C2×C32×C8C2311yescharacteristic
28#3755—42no—
29#3752—42no—
30C4×C3⋊Dic3D411yescharacteristic
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32#3745—22no—
33C3×C4⋊Dic3—22no—
34Dic3⋊Dic3—42no—
35C3×C3⋊C16—22no—
36#2242—91noSylow
37C2×C3×Q16—21no—
38C2×C3×Q16C2×D312yes—
39#947—62no—
40#947—62no—
41C2×#215—62no—
42C2×#215—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—
53C22×C3⋊D3—41no—
54C32×Q8—41no—
55C32×Q8—41no—
56C2×C32×C4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3D812yes—
59C4⋊(C3⋊D3)—41no—
60C4⋊(C3⋊D3)—41no—
61C2×C3×Dic3—42no—
62C32×C8#4112yes—
63C3⋊(C3⋊C8)SD1612yes—
64#499—91no—
65#495—91no—
66#358—32no—
67#357—92no—
68C4×C16—91no—
69C2×C3×Q8—22no—
70C2×C3×Q8—22no—
71C2×D12—62no—
72C2×D12—62no—
73C3×Q16—22no—
74C3×Q16—22no—
75C3×Q16—42no—
76C2×C3×C8—21no—
77C2×C3×C8C22×D312yes—
78C3×C4⋊C4—62no—
79#215—124no—
80#215—124no—
81(C2×D3)⋊C4—122no—
82(C2×D3)⋊C4—122no—
83(C2×D3)⋊C4—124no—
84C4⋊Dic3—22no—
85C4⋊Dic3—122no—
86Dic3⋊C4—122no—
87C4×Dic3—32no—
88C4×Dic3—61no—
89C2×C3⋊C8—32no—
90C2×C3⋊C8—61no—
91D24—62no—
92D24—62no—
93D24—122no—
94C3×C16—62no—
95C3⋊C16—22no—
96C22×C32C2×D811yescharacteristic
97C2×C3⋊D3—81no—
98C2×C3⋊D3—82no—
99C32×C4—81no—
100C32×C4#12411yescharacteristic
101C32×C4C2×SD1611yescharacteristic
102C3⋊Dic3—22no—
103C3×Dic3—82no—
104C2×Q16D3211yescharacteristic
105C2×SD16—181no—
106C2×D8—91no—
107#125—181no—
108#124—181no—
109C2×C16—32no—
110#107—32no—
111#106—181no—
112C4×C8—91no—
113C22×D3—122no—
114C22×D3—122no—
115C3×Q8—42no—
116C3×Q8—42no—
117C3×Q8—42no—
118C3×Q8—42no—
119C2×C3×C4—21no—
120C2×C3×C4—42no—
121C2×C3×C4—42no—
122C2×C3×C4—122no—
123C2×C3×C4D3×D412yes—
124C2×Dic3—32no—
125C2×Dic3—32no—
126C2×Dic3—42no—
127C2×Dic3—62no—
128D12—122no—
129D12—122no—
130D12—122no—
131D12—122no—
132C3×C8—22no—
133C3×C8#23512yes—
134C3×C8#23712yes—
135C3⋊C8—34no—
136C3⋊C8—62no—
137C2×C32#48611yescharacteristic
138C2×C32#50812yes—
139C3⋊D3—161no—
140C2×Q8—21no—
141C2×D4—181no—
142Q16—22no—
143SD16—362no—
144D8—182no—
145C2×C8—91no—
146C2×C8C2×D3211yescharacteristic
147C4⋊C4—62no—
148C4⋊C4—362no—
149C22⋊C4—362no—
150C42—91no—
151C16—62no—
152C22×C3—21no—
153C22×C3D3×D812yes—
154C2×D3—242no—
155C2×D3—244no—
156C2×D3—242no—
157C2×D3—242no—
158C2×D3—242no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—82no—
162C3×C4—82no—
163C3×C4—242no—
164C3×C4#88512yes—
165C3×C4D3×SD1612yes—
166Dic3—62no—
167Dic3—62no—
168Dic3—82no—
169Dic3—122no—
170C32#224211yescharacteristic, complemented, Sylow
171C23—361no—
172Q8—41no—
173Q8—41no—
174D4—361no—
175D4—361no—
176C2×C4—41no—
177C2×C4—92no—
178C2×C4—122no—
179C2×C4#381111yescharacteristic
180C8—92no—
181C8#380412yes—
182C2×C3—22no—
183C2×C3—21no—
184C2×C3#476012yes—
185C2×C3#491612yes—
186C2×C3#491912yes—
187D3—482no—
188D3—482no—
189C22—722no—
190C22—721no—
191C22#6392611yescharacteristic
192C4—81no—
193C4—182no—
194C4—242no—
195C4#6393011yescharacteristic
196C4#6395311yescharacteristic
197C3—21no—
198C3#6921612yescomplemented
199C2—1441no—
200C2#1059104912yes—
201C2#1059140211yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenterC2×Q16D32
hypocenterC32#2242
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10590875C2semidirect
3. C3×#4564C2semidirect
5. #10589102C2semidirect
20. #4564D3semidirect
170. C32#2242semidirect
198. C3#69216semidirect

Maximal subgroups

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

subgroupindex
#105928902
#105908752
C3×#45642
#105891162
#105891022
#692163