Finite Group Databasebeta

← #11779337

Subgroups — #11779337

Order 1152.

507 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593963C211yesmaximal, characteristic
2#10592784C211yesmaximal, characteristic
3C3×#5091C212yesmaximal, complemented
4#10589091C211yesmaximal, characteristic
5#10589083C212yesmaximal, complemented
6#71159—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C2×#3755—22no—
9#64083C2211yescharacteristic
10C3×C4×Dic6C2212yes—
11#63897—22no—
12#63894—22no—
13#63864—22no—
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#810—22no—
16C3×#807—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18#5585—32no—
19C3×#477—32no—
20#5091D312yescomplemented
21#5085—32no—
22#5085—61no—
23#4535—32no—
24#4485—32no—
25#4484—32no—
26C2×C32×Q8—21no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)D412yes—
29C2×C3×Dic6D412yes—
30C2×#624—22no—
31C32×C4⋊C4—22no—
32C32×C42C2311yescharacteristic
33#3755—44no—
34C2×C3⋊(C3⋊C8)—21no—
35C3×C4⋊Dic3D412yes—
36C3×Dic3⋊C4—22no—
37C3×C4×Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#3722—22no—
40#3722—24no—
41#1630—91noSylow
42C3×C4⋊Q8—21no—
43C3×C4⋊Q8C2×D312yes—
44C3×C4×Q8—32no—
45#947—62no—
46C2×#215—64no—
47C2×#215—64no—
48#894—64no—
49#893—62no—
50#875—62no—
51#874—32no—
52#874—61no—
53C4×D12—62no—
54C4×Dic6C2×D312yes—
55C3×#107—62no—
56C3×C4⋊C8—32no—
57C3×#103—62no—
58#810—22no—
59#807—22no—
60C4⋊(C3⋊C8)C2×D312yes—
61C4×C3⋊C8—32no—
62C4×C3⋊C8—61no—
63C22×C3⋊D3—22no—
64C32×Q8—42no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D412yes—
68C4⋊(C3⋊D3)—42no—
69C4⋊(C3⋊D3)—42no—
70C4⋊(C3⋊D3)—42no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C3×Dic6—22no—
74C3×Dic6—22no—
75#624—82no—
76C3⋊(C3⋊C8)—22no—
77C3×C3⋊C8—42no—
78#559—91no—
79#492—91no—
80#477—32no—
81#331—91no—
82Q8⋊C8—92no—
83C2×C3×Q8—22no—
84C2×C3×Q8—22no—
85C2×C3×Q8—32no—
86C2×D12—34no—
87C2×D12—62no—
88C2×D12—62no—
89C2×D12—62no—
90C2×D12—122no—
91C2×C4×D3—64no—
92C2×Dic6#6712yes—
93C2×C3×C8—62no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—22no—
96C3×C4⋊C4—32no—
97C3×C4⋊C4—42no—
98C3×C4⋊C4—62no—
99C3×C42—21no—
100C3×C42—62no—
101C3×C42C22×D312yes—
102#215—128no—
103#215—128no—
104(C2×D3)⋊C4—64no—
105(C2×D3)⋊C4—64no—
106(C2×D3)⋊C4—64no—
107C4⋊Dic3#6712yes—
108Dic3⋊C4—22no—
109C4×Dic3—22no—
110C2×C3⋊C8—22no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—62no—
113C22×C32#12011yescharacteristic
114C2×C3⋊D3—44no—
115C2×C3⋊D3—42no—
116C32×C4—21no—
117C32×C4—81no—
118C32×C4#13512yes—
119C32×C4#13712yes—
120C3×Dic3—42no—
121C3×Dic3—42no—
122C2×SD16—182no—
123C4⋊Q8D3211yescharacteristic
124#127—91no—
125#124—182no—
126#123—182no—
127C4×Q8—32no—
128C4×D4—182no—
129#107—62no—
130C4⋊C8—32no—
131#103—62no—
132C4×C8—91no—
133C22×D3—64no—
134C22×D3—122no—
135C3×Q8—44no—
136C3×Q8—44no—
137C3×Q8—62no—
138C3×Q8—62no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—42no—
142C2×C3×C4—42no—
143C2×C3×C4—62no—
144C2×C3×C4—62no—
145C2×C3×C4D3×D412yes—
146C2×C3×C4D3×D412yes—
147C2×C3×C4C2×#6712yes—
148C2×Dic3—22no—
149C2×Dic3—22no—
150D12—124no—
151D12—124no—
152D12—122no—
153D12—122no—
154D12—122no—
155D12—122no—
156D12—242no—
157D12—242no—
158C4×D3—244no—
159Dic6—22no—
160Dic6—22no—
161C3×C8—122no—
162C3⋊C8—42no—
163C3⋊C8—64no—
164C3⋊C8—64no—
165C2×C32#45212yes—
166C2×C32#45311yescharacteristic
167C3⋊D3—82no—
168C2×Q8—21no—
169C2×Q8—32no—
170C2×D4—92no—
171C2×D4—182no—
172C22×C4—182no—
173SD16—364no—
174C2×C8—62no—
175C2×C8—181no—
176C4⋊C4—22no—
177C4⋊C4—32no—
178C4⋊C4—62no—
179C22⋊C4—184no—
180C22⋊C4—182no—
181C42—62no—
182C42C2×D3211yescharacteristic
183C22×C3—21no—
184C22×C3#93712yes—
185C2×D3—124no—
186C2×D3—124no—
187C2×D3—124no—
188C2×D3—242no—
189C2×D3—244no—
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—82no—
195C3×C4—82no—
196C3×C4—122no—
197C3×C4—122no—
198C3×C4#91812yes—
199C3×C4#91912yes—
200C3×C4#94212yes—
201C3×C4#95012yes—
202Dic3—42no—
203Dic3—42no—
204C32#163011yescharacteristic, complemented, Sylow
205C23—182no—
206Q8—42no—
207Q8—62no—
208Q8—62no—
209D4—362no—
210D4—362no—
211D4—362no—
212C2×C4—41no—
213C2×C4—62no—
214C2×C4—62no—
215C2×C4—722no—
216C2×C4D3×#6712yes—
217C2×C4#381111yescharacteristic
218C8—122no—
219C8—182no—
220C2×C3—21no—
221C2×C3—22no—
222C2×C3#504712yes—
223C2×C3#518712yes—
224C2×C3#519812yes—
225D3—244no—
226D3—482no—
227C22—362no—
228C22—364no—
229C22#6398311yescharacteristic
230C4—21no—
231C4—81no—
232C4—122no—
233C4—122no—
234C4#6394812yes—
235C4#6394912yes—
236C3—21no—
237C3#7115912yescomplemented
238C2—722no—
239C2#1059152211yescharacteristic
240C2#1059165712yes—
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4⋊Q8D32
hypocenterC32#1630
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5091C2semidirect
5. #10589083C2semidirect
20. #5091D3semidirect
204. C32#1630semidirect
237. C3#71159semidirect

Maximal subgroups

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

subgroupindex
#105939632
#105927842
C3×#50912
#105890912
#105890832
#711593