Finite Group Databasebeta

← #11781190

Subgroups — #11781190

Order 1152.

387 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592533C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic, complemented
3#10590300C212yesmaximal
4C3×#4481C212yesmaximal, complemented
5#10589100C211yesmaximal, characteristic, complemented
6#68497—32nomaximal
7C2×C8×C3⋊D3—21no—
8C4×C4⋊(C3⋊D3)C2211yescharacteristic
9C3×#869C2212yes—
10C32×C4⋊C8C2211yescharacteristic
11#63647—21no—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×C4⋊(C3⋊C8)C2212yes—
14#63576—21no—
15#63576—21no—
16#63573—22no—
17#63564—22no—
18#5084—32no—
19#5078—32no—
20#4842—32no—
21#4834—32no—
22#4834—61no—
23C3×#333—32no—
24#4481D312yescomplemented
25#4479—32no—
26C2×C4⋊(C3⋊D3)D411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C3×Dic6—22no—
29C2×C32×C8—21no—
30C32×C42C2311yescharacteristic
31#3752—21no—
32C4⋊(C3⋊Dic3)D411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C8×C3⋊D3—42no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#1675—91noSylow
40C3×C4⋊Q8—32no—
41C2×D3×C8—62no—
42C2×D3×C8—62no—
43C4×D12—32no—
44C4×D12—61no—
45#869C2×D312yes—
46C3×C4⋊C8—21no—
47C3×C4⋊C8—32no—
48C3×C4⋊C8C2×D312yes—
49#821—62no—
50(C2×D3)⋊C8—62no—
51(C2×D3)⋊C8—62no—
52#817—62no—
53#809—62no—
54#808—62no—
55#807—62no—
56#807—62no—
57C4⋊(C3⋊C8)C2×D312yes—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C22×C3⋊D3—21no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4#4111yescharacteristic
64C2×C3⋊Dic3—21no—
65C4⋊(C3⋊D3)—21no—
66C4⋊(C3⋊D3)Q1612yes—
67C4×C3⋊D3—41no—
68C4×C3⋊D3—41no—
69C2×C3×Dic3—42no—
70C3×Dic6—82no—
71C32×C8—41no—
72C3⋊(C3⋊C8)—21no—
73C3⋊(C3⋊C8)SD1612yes—
74C3×C3⋊C8—42no—
75#500—91no—
76#476—92no—
77C8×D4—91no—
78#335—91no—
79#333—32no—
80C2×C3×Q8—62no—
81C2×D12—32no—
82C2×D12—61no—
83C2×C4×D3—62no—
84C2×C4×D3—62no—
85C2×Dic6—22no—
86C2×C3×C8—22no—
87C2×C3×C8—22no—
88C2×C3×C8—62no—
89C3×C4⋊C4—62no—
90C3×C4⋊C4—62no—
91C3×C42—21no—
92C3×C42C22×D312yes—
93(C2×D3)⋊C4—62no—
94(C2×D3)⋊C4—62no—
95C4⋊Dic3—22no—
96C4⋊Dic3—22no—
97C4⋊Dic3—32no—
98C4⋊Dic3—61no—
99C2×C3⋊C8—22no—
100C2×C3⋊C8—32no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—61no—
104D3×C8—124no—
105D3×C8—124no—
106C22×C32#12111yescharacteristic
107C2×C3⋊D3—22no—
108C2×C3⋊D3—41no—
109C2×C3⋊D3—41no—
110C32×C4—21no—
111C32×C4C2×SD1611yescharacteristic
112C32×C4C2×Q1611yescharacteristic
113C32×C4#13511yescharacteristic
114C32×C4#13711yescharacteristic
115C3⋊Dic3—41no—
116C3×Dic3—82no—
117C22×C8—181no—
118C4⋊Q8—32no—
119C4×D4—91no—
120#107—181no—
121#107—181no—
122#106—182no—
123C4⋊C8—32no—
124C4⋊C8D3211yescharacteristic
125#102—182no—
126C22⋊C8—181no—
127C4×C8—91no—
128C22×D3—62no—
129C22×D3—62no—
130C3×Q8—242no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—122no—
135C2×C3×C4#23512yes—
136C2×C3×C4D3×D412yes—
137C2×C3×C4D3×D412yes—
138C2×Dic3—42no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141D12—34no—
142D12—62no—
143D12—62no—
144D12—62no—
145C4×D3—122no—
146C4×D3—122no—
147C4×D3—122no—
148C4×D3—122no—
149Dic6—82no—
150C3×C8—42no—
151C3×C8—42no—
152C3×C8—122no—
153C3⋊C8—34no—
154C3⋊C8—42no—
155C3⋊C8—62no—
156C3⋊C8—62no—
157C3⋊C8—121no—
158C2×C32#46111yescharacteristic
159C2×C32#46711yescharacteristic
160C2×C32#47211yescharacteristic
161C3⋊D3—42no—
162C2×Q8—62no—
163C2×D4—91no—
164C22×C4—181no—
165C2×C8—21no—
166C2×C8—62no—
167C2×C8—91no—
168C2×C8—91no—
169C2×C8—362no—
170C4⋊C4—62no—
171C4⋊C4—62no—
172C4⋊C4—91no—
173C22⋊C4—181no—
174C42C2×D3211yescharacteristic
175C22×C3—21no—
176C22×C3#88412yes—
177C2×D3—64no—
178C2×D3—64no—
179C2×D3—122no—
180C2×D3—122no—
181C2×D3—122no—
182C2×D3—122no—
183C3×C4—22no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—41no—
189C3×C4—242no—
190C3×C4D3×SD1612yes—
191C3×C4#91612yes—
192C3×C4D3×Q1612yes—
193C3×C4#91812yes—
194Dic3—82no—
195Dic3—122no—
196Dic3—122no—
197C32#167511yescharacteristic, complemented, Sylow
198C23—181no—
199Q8—242no—
200D4—92no—
201D4—181no—
202C2×C4—122no—
203C2×C4—181no—
204C2×C4—361no—
205C2×C4—361no—
206C2×C4#379811yescharacteristic
207C2×C4#380211yescharacteristic
208C2×C4#381111yescharacteristic
209C8—41no—
210C8—92no—
211C8—122no—
212C8—181no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3#474912yes—
217C2×C3#481312yes—
218C2×C3#481812yes—
219D3—124no—
220D3—124no—
221C22—182no—
222C22—361no—
223C22—361no—
224C22#6391211yescharacteristic
225C4—21no—
226C4—242no—
227C4—361no—
228C4#6380211yescharacteristic
229C4#6380911yescharacteristic
230C4#6393011yescharacteristic
231C4#6394511yescharacteristic
232C3—21no—
233C3#6849712yescomplemented
234C2—362no—
235C2#1059056511yescharacteristic
236C2#1059085511yescharacteristic
237C2#1059098811yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1675
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10590312C2semidirect
4. C3×#4481C2semidirect
5. #10589100C2semidirect
24. #4481D3semidirect
197. C32#1675semidirect
233. C3#68497semidirect

Maximal subgroups

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

subgroupindex
#105925332
#105903122
#105903002
C3×#44812
#105891002
#684973