Finite Group Databasebeta

← #11781120

Subgroups — #11781120

Order 1152.

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

normal subgroups only

This group has 411 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×#5019C212yesmaximal
3#10590312C211yesmaximal, characteristic, complemented
4#10589100C211yesmaximal, characteristic, complemented
5#10589093C212yesmaximal, complemented
6#71037—32nomaximal
7C32×C4×D4C2211yescharacteristic
8C22×C3⋊(C3⋊C8)—21no—
9C2×C3×#214—22no—
10C3×#869C2212yes—
11#63657—21no—
12C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#810—22no—
15C3×C4⋊(C3⋊C8)C2212yes—
16#63576—21no—
17#63576—21no—
18C3×#461—32no—
19#5078—32no—
20#5019D312yes—
21D4×C3⋊C8—32no—
22D4×C3⋊C8—61no—
23#4547—32no—
24#4482—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×#214—44no—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C2×C3×C3⋊C8—22no—
40#1673—91noSylow
41C2×C3×SD16—62no—
42C3×C4⋊Q8—32no—
43C3×C4×D4—21no—
44C3×C4×D4C2×D312yes—
45C2×#214—22no—
46C22×C3⋊C8—62no—
47C22×C3⋊C8—62no—
48#869C2×D312yes—
49C3×C4⋊C8—32no—
50C3×#103—62no—
51#830—62no—
52#830—62no—
53#810—22no—
54#807—62no—
55#807—62no—
56C4⋊(C3⋊C8)—32no—
57C4⋊(C3⋊C8)—61no—
58C4⋊(C3⋊C8)C2×D312yes—
59C4×C3⋊C8—32no—
60C4×C3⋊C8—61no—
61C23×C32—21no—
62C32×D4—21no—
63C32×D4D812yes—
64C2×C32×C4—21no—
65C2×C32×C4—41no—
66C2×C32×C4—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4#4111yescharacteristic
70C2×C3×Dic3—42no—
71C3×Dic6—42no—
72C3×Dic6—42no—
73C3⋊(C3⋊C8)—21no—
74C3⋊(C3⋊C8)—41no—
75C3⋊(C3⋊C8)SD1612yescomplemented
76C3×C3⋊C8—42no—
77#500—91no—
78#461—32no—
79C8×D4—91no—
80#335—91no—
81#332—92no—
82C2×C3×Q8—62no—
83C2×C3×D4—21no—
84C2×C3×D4#6712yes—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C2×Dic6—22no—
88C3×SD16—124no—
89C2×C3×C8—62no—
90C3×C4⋊C4—21no—
91C3×C4⋊C4—62no—
92C3×C4⋊C4—62no—
93C3×C4⋊C4#6712yes—
94C3×C22⋊C4—22no—
95C3×C22⋊C4—22no—
96C3×C42—21no—
97C3×C42C22×D312yes—
98#214—44no—
99C4⋊Dic3—22no—
100C4⋊Dic3—22no—
101C2×C3⋊C8—22no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—62no—
107C2×C3⋊C8—62no—
108C2×C3⋊C8—124no—
109C2×C3⋊C8—124no—
110C22×C32—22no—
111C22×C32—41no—
112C22×C32—41no—
113C22×C32#12111yescharacteristic
114C32×C4—21no—
115C32×C4—41no—
116C32×C4C2×D811yescharacteristic
117C32×C4C2×SD1611yescharacteristic
118C32×C4#13511yescharacteristic
119C32×C4#13711yescharacteristic
120C3×Dic3—82no—
121C2×SD16—62no—
122C22×C8—181no—
123C4⋊Q8—32no—
124C4×D4D3211yescharacteristic
125#107—181no—
126#107—181no—
127C4⋊C8—32no—
128C4⋊C8—91no—
129#103—62no—
130C22⋊C8—181no—
131C4×C8—91no—
132C23×C3—22no—
133C23×C3—22no—
134C3×Q8—122no—
135C3×Q8—122no—
136C3×D4—22no—
137C3×D4—22no—
138C3×D4—22no—
139C3×D4#21314yes—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—42no—
146C2×C3×C4—42no—
147C2×C3×C4—42no—
148C2×C3×C4—42no—
149C2×C3×C4—122no—
150C2×C3×C4D3×D412yes—
151C2×C3×C4#23712yes—
152C2×C3×C4C2×#6712yes—
153C2×Dic3—42no—
154Dic6—42no—
155Dic6—42no—
156C3×C8—122no—
157C3⋊C8—34no—
158C3⋊C8—42no—
159C3⋊C8—62no—
160C3⋊C8—62no—
161C3⋊C8—121no—
162C3⋊C8—122no—
163C3⋊C8—122no—
164C2×C32—42no—
165C2×C32#46111yescharacteristic
166C2×C32#46611yescharacteristic
167C2×C32#47311yescharacteristic
168C2×Q8—62no—
169C2×D4#62511yescharacteristic
170C22×C4—21no—
171SD16—124no—
172C2×C8—62no—
173C2×C8—91no—
174C2×C8—91no—
175C2×C8—181no—
176C2×C8—362no—
177C4⋊C4—62no—
178C4⋊C4—62no—
179C4⋊C4#62511yescharacteristic
180C22⋊C4—21no—
181C42C2×D3211yescharacteristic
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—21no—
185C22×C3—42no—
186C22×C3—42no—
187C22×C3—42no—
188C22×C3—42no—
189C22×C3#93912yes—
190C3×C4—22no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—21no—
195C3×C4—41no—
196C3×C4—42no—
197C3×C4—42no—
198C3×C4—242no—
199C3×C4D3×SD1612yes—
200C3×C4#91512yes—
201C3×C4C2×#21312yes—
202C3×C4#95012yes—
203Dic3—82no—
204C32#167311yescharacteristic, complemented, Sylow
205C23—21no—
206Q8—122no—
207Q8—122no—
208D4—21no—
209D4#371312yes—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—122no—
214C2×C4#380511yescharacteristic
215C2×C4C2×#62511yescharacteristic
216C2×C4#381111yescharacteristic
217C8—92no—
218C8—122no—
219C8—181no—
220C8—361no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—44no—
225C2×C3—44no—
226C2×C3#503812yes—
227C2×C3#516212yes—
228C2×C3#520412yes—
229C22—22no—
230C22—41no—
231C22—41no—
232C22#6398011yescharacteristic
233C4—21no—
234C4—41no—
235C4—242no—
236C4C2×#371311yescharacteristic
237C4#6382211yescharacteristic
238C4#6393011yescharacteristic
239C4#6393111yescharacteristic
240C3—21no—
241C3#7103712yescomplemented
242C2—42no—
243C2#1059116611yescharacteristic
244C2#1059149711yescharacteristic
245C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1673
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. #10589093C2semidirect
75. C3⋊(C3⋊C8)SD16semidirect
204. C32#1673semidirect
241. C3#71037semidirect

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×#50192
#105903122
#105891002
#105890932
#710373