Finite Group Databasebeta

← #11781185

Subgroups — #11781185

Order 1152.

387 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 96 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
1D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×#5008C212yesmaximal
3#10590312C211yesmaximal, characteristic, complemented
4#10589100C211yesmaximal, characteristic, complemented
5#10589095C212yesmaximal, complemented
6#71133—32nomaximal
7C32×C4×D4C2211yescharacteristic
8C22×C3⋊(C3⋊C8)—21no—
9C3×#869C2212yes—
10#63657—21no—
11C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#832—22no—
14C3×#808—22no—
15C3×C4⋊(C3⋊C8)C2212yes—
16#63576—21no—
17#63576—21no—
18C3×#476—32no—
19#5078—32no—
20D4×C3⋊C8—32no—
21D4×C3⋊C8—61no—
22#5008D312yes—
23#4546—32no—
24#4481—32no—
25#4479—32no—
26C2×C32×D4D411yescharacteristic
27C22×C32×C4—21no—
28C2×C3×Dic6—22no—
29C32×C4⋊C4D411yescharacteristic
30C32×C22⋊C4—21no—
31C32×C42C2311yescharacteristic
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)—42no—
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#1675—91noSylow
40C3×C4⋊Q8—32no—
41C3×C4×D4—21no—
42C3×C4×D4C2×D312yes—
43C22×C3⋊C8—62no—
44C22×C3⋊C8—62no—
45#869C2×D312yes—
46C3×#106—62no—
47C3×C4⋊C8—32no—
48C3×#102—62no—
49#832—22no—
50#830—62no—
51#830—62no—
52#808—22no—
53#807—62no—
54#807—62no—
55C4⋊(C3⋊C8)—32no—
56C4⋊(C3⋊C8)—61no—
57C4⋊(C3⋊C8)C2×D312yes—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C23×C32—21no—
61C32×D4—21no—
62C32×D4Q1612yes—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4#4111yescharacteristic
69C2×C3×Dic3—42no—
70C3×Dic6—82no—
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)—41no—
73C3⋊(C3⋊C8)SD1612yes—
74C3×C3⋊C8—42no—
75#500—91no—
76#476—32no—
77C8×D4—91no—
78#335—91no—
79#333—92no—
80C2×C3×Q8—62no—
81C2×C3×D4—21no—
82C2×C3×D4#6712yes—
83C22×C3×C4—22no—
84C22×C3×C4—22no—
85C2×Dic6—22no—
86C2×C3×C8—62no—
87C3×C4⋊C4—21no—
88C3×C4⋊C4—62no—
89C3×C4⋊C4—62no—
90C3×C4⋊C4#6712yes—
91C3×C22⋊C4—22no—
92C3×C22⋊C4—22no—
93C3×C42—21no—
94C3×C42C22×D312yes—
95C4⋊Dic3—22no—
96C4⋊Dic3—22no—
97C2×C3⋊C8—22no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—124no—
105C2×C3⋊C8—124no—
106C22×C32—22no—
107C22×C32—41no—
108C22×C32—41no—
109C22×C32#12111yescharacteristic
110C32×C4—21no—
111C32×C4—41no—
112C32×C4C2×SD1611yescharacteristic
113C32×C4C2×Q1611yescharacteristic
114C32×C4#13511yescharacteristic
115C32×C4#13711yescharacteristic
116C3×Dic3—82no—
117C22×C8—181no—
118C4⋊Q8—32no—
119C4×D4D3211yescharacteristic
120#107—181no—
121#107—181no—
122#106—62no—
123C4⋊C8—32no—
124C4⋊C8—91no—
125#102—62no—
126C22⋊C8—181no—
127C4×C8—91no—
128C23×C3—22no—
129C23×C3—22no—
130C3×Q8—242no—
131C3×D4—22no—
132C3×D4—22no—
133C3×D4—22no—
134C3×D4#21614yes—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—42no—
141C2×C3×C4—42no—
142C2×C3×C4—42no—
143C2×C3×C4—42no—
144C2×C3×C4—122no—
145C2×C3×C4D3×D412yes—
146C2×C3×C4#23712yes—
147C2×C3×C4C2×#6712yes—
148C2×Dic3—42no—
149Dic6—82no—
150C3×C8—122no—
151C3⋊C8—34no—
152C3⋊C8—42no—
153C3⋊C8—62no—
154C3⋊C8—62no—
155C3⋊C8—121no—
156C3⋊C8—122no—
157C3⋊C8—122no—
158C2×C32—42no—
159C2×C32#46111yescharacteristic
160C2×C32#46711yescharacteristic
161C2×C32#47211yescharacteristic
162C2×Q8—62no—
163C2×D4#62511yescharacteristic
164C22×C4—21no—
165C2×C8—62no—
166C2×C8—91no—
167C2×C8—91no—
168C2×C8—181no—
169C2×C8—362no—
170C4⋊C4—62no—
171C4⋊C4—62no—
172C4⋊C4#62511yescharacteristic
173C22⋊C4—21no—
174C42C2×D3211yescharacteristic
175C22×C3—24no—
176C22×C3—24no—
177C22×C3—21no—
178C22×C3—42no—
179C22×C3—42no—
180C22×C3—42no—
181C22×C3—42no—
182C22×C3#93912yes—
183C3×C4—22no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—41no—
189C3×C4—42no—
190C3×C4—42no—
191C3×C4—242no—
192C3×C4D3×SD1612yes—
193C3×C4#91512yes—
194C3×C4C2×#21612yes—
195C3×C4#95012yes—
196Dic3—82no—
197C32#167511yescharacteristic, complemented, Sylow
198C23—21no—
199Q8—242no—
200D4—21no—
201D4#371812yes—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—122no—
206C2×C4#380511yescharacteristic
207C2×C4C2×#62511yescharacteristic
208C2×C4#381111yescharacteristic
209C8—92no—
210C8—122no—
211C8—181no—
212C8—361no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—44no—
217C2×C3—44no—
218C2×C3#505112yes—
219C2×C3#516212yes—
220C2×C3#519912yes—
221C22—22no—
222C22—41no—
223C22—41no—
224C22#6398011yescharacteristic
225C4—21no—
226C4—41no—
227C4—242no—
228C4#6382211yescharacteristic
229C4C2×#371811yescharacteristic
230C4#6393011yescharacteristic
231C4#6393111yescharacteristic
232C3—21no—
233C3#7113312yescomplemented
234C2—42no—
235C2#1059118811yescharacteristic
236C2#1059149711yescharacteristic
237C2#1059167811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1675
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590312C2semidirect
4. #10589100C2semidirect
5. #10589095C2semidirect
197. C32#1675semidirect
233. C3#71133semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊(C3⋊C8)2
C3×#50082
#105903122
#105891002
#105890952
#711333