Finite Group Databasebeta

← #11800053

Subgroups — #11800053

Order 1152.

369 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 78 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#10592573C211yesmaximal, characteristic, complemented
2#10590886C211yesmaximal, characteristic
3C3×#4491C212yesmaximal, complemented
4#10589115C212yesmaximal, complemented
5#10589102C211yesmaximal, characteristic, complemented
6#69183—32nomaximal
7#64097—21no—
8C2×C3×D24C2212yes—
9#63914—21no—
10C2×#3713—21no—
11C32×#107C2211yescharacteristic
12#63645C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14#63634—21no—
15C2×C3×C3⋊C16C2212yes—
16#5151—32no—
17#4874—32no—
18#4874—61no—
19C3×#357—32no—
20#4562—32no—
21#4509—32no—
22Dic3×C16—32no—
23#4491D312yescomplemented
24C2×#634—41no—
25C2×C3×D12—22no—
26C2×#625—41no—
27C2×#625—41no—
28C2×C32×C8C2311yescharacteristic
29C32×C4⋊C4—21no—
30C4⋊(C3⋊Dic3)—21no—
31#3750—41no—
32C4×C3⋊Dic3D411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C3×D24—22no—
35C3×D24—22no—
36#3713—42no—
37C3×C3⋊C16—22no—
38#2240—91noSylow
39C2×C3×D8—32no—
40#940—62no—
41C2×#213—62no—
42C2×D24C2×D312yes—
43#888—62no—
44#888—62no—
45C2×C3×C16—32no—
46C3×#107—21no—
47C3×#107C2×D312yes—
48#818—32no—
49#818—61no—
50C8×Dic3—32no—
51C8×Dic3—61no—
52C2×C3⋊C16C2×D312yes—
53#807—62no—
54#807—62no—
55C22×C3×D3—42no—
56C2×C32×C4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3D811yescharacteristic
60C2×C3⋊Dic3D811yescharacteristic
61#634—82no—
62C3×D12—42no—
63C3×D12—42no—
64#625—82no—
65#625—82no—
66C32×C8#4112yes—
67C3⋊(C3⋊C8)SD1612yes—
68#500—91no—
69#493—91no—
70#357—32no—
71#357—92no—
72C4×C16—91no—
73C2×C3×D4—62no—
74C2×#67—122no—
75C2×#67—122no—
76C2×D12—22no—
77C2×Dic6—122no—
78C2×Dic6—122no—
79C3×D8—62no—
80C3×D8—62no—
81C2×C3×C8—21no—
82C2×C3×C8C22×D312yes—
83C3×C4⋊C4—22no—
84C3×C4⋊C4—22no—
85#213—124no—
86C4⋊Dic3—62no—
87C4⋊Dic3—62no—
88Dic3⋊C4—122no—
89Dic3⋊C4—122no—
90C4×Dic3—32no—
91C4×Dic3—61no—
92C2×C3⋊C8—32no—
93C2×C3⋊C8—61no—
94D24—22no—
95D24—22no—
96C3×C16—62no—
97C3⋊C16—22no—
98C22×C32C2×D811yescharacteristic
99C2×C3×D3—82no—
100C2×C3×D3—82no—
101C2×C3×D3—82no—
102C32×C4—81no—
103C32×C4#12411yescharacteristic
104C32×C4C2×SD1611yescharacteristic
105C3⋊Dic3—81no—
106C3⋊Dic3D1612yes—
107C3⋊Dic3SD3212yes—
108C2×D8—32no—
109C2×D8—181no—
110C4⋊Q8—181no—
111#127—181no—
112C2×C16—32no—
113#107—91no—
114#107—181no—
115#107D3211yescharacteristic
116C4×C8—91no—
117C23×C3—122no—
118C22×D3—42no—
119C3×D4—122no—
120C3×D4—122no—
121C2×C3×C4—21no—
122C2×C3×C4—42no—
123C2×C3×C4—42no—
124C2×C3×C4D3×D412yes—
125#67—244no—
126#67—244no—
127C2×Dic3—32no—
128C2×Dic3—32no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C2×Dic3—122no—
132C2×Dic3—122no—
133D12—42no—
134D12—42no—
135Dic6—244no—
136Dic6—244no—
137C3×C8—22no—
138C3×C8#23512yes—
139C3×C8#23712yes—
140C3⋊C8—34no—
141C3⋊C8—62no—
142C2×C32#48611yescharacteristic
143C2×C32C2×D1611yescharacteristic
144C2×C32C2×SD3211yescharacteristic
145C3×D3—162no—
146C2×Q8—361no—
147C2×D4—62no—
148C2×D4—361no—
149C2×D4—361no—
150D8—62no—
151D8—62no—
152D8—362no—
153C2×C8—91no—
154C2×C8C2×D3211yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—181no—
157C4⋊C4—361no—
158C42—91no—
159C16—62no—
160C22×C3—21no—
161C22×C3—242no—
162C22×C3—242no—
163C22×C3—242no—
164C22×C3D3×D812yes—
165C2×D3—82no—
166C2×D3—82no—
167C2×D3—82no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—82no—
171C3×C4—82no—
172C3×C4#88512yes—
173C3×C4D3×SD1612yes—
174Dic3—34no—
175Dic3—34no—
176Dic3—62no—
177Dic3—62no—
178Dic3—242no—
179Dic3—242no—
180C32#224011yescharacteristic, complemented, Sylow
181C23—122no—
182Q8—722no—
183D4—122no—
184D4—122no—
185D4—722no—
186D4—722no—
187C2×C4—41no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—361no—
191C2×C4#381111yescharacteristic
192C8—92no—
193C8#379512yes—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—482no—
198C2×C3#476012yes—
199C2×C3D3×D1612yes—
200C2×C3D3×SD3212yes—
201D3—162no—
202C22—242no—
203C22—242no—
204C22—242no—
205C22#6392611yescharacteristic
206C4—81no—
207C4—92no—
208C4—92no—
209C4—721no—
210C4#6391311yescharacteristic
211C4#6394011yescharacteristic
212C3—21no—
213C3#6918312yescomplemented
214C2—482no—
215C2#1059055211yescharacteristic
216C2#1059102511yescharacteristic
217C2#1059103911yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radical#10590886C2
hypercenter#107D32
hypocenterC32#2240
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10592573C2semidirect
3. C3×#4491C2semidirect
4. #10589115C2semidirect
5. #10589102C2semidirect
23. #4491D3semidirect
180. C32#2240semidirect
213. C3#69183semidirect

Maximal subgroups

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

subgroupindex
#105925732
#105908862
C3×#44912
#105891152
#105891022
#691833