Finite Group Databasebeta

← #11781752

Subgroups — #11781752

Order 1152.

415 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592530C211yesmaximal, characteristic, complemented
2#10590377C212yesmaximal, complemented
3#10590352C211yesmaximal, characteristic
4C3×#4485C212yesmaximal, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#68413—32nomaximal
7C4×#634C2211yescharacteristic
8C3×#874C2212yes—
9C2×#3716—22no—
10C2×#3713—21no—
11C2×#3713—21no—
12C32×C4⋊C8C2211yescharacteristic
13#63642—21no—
14#63641—21no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2212yes—
17#63563—22no—
18#5075—32no—
19#5073—32no—
20#4848—32no—
21#4831—32no—
22#4831—61no—
23C3×#331—32no—
24#4485D312yescomplemented
25#4480—32no—
26C2×#634D411yescharacteristic
27C2×C3×D12—22no—
28C2×C3×D12—22no—
29C2×C3×D12—22no—
30C2×C32×C8—21no—
31C32×C42C2311yescharacteristic
32C4⋊(C3⋊Dic3)D411yescharacteristic
33#3750—21no—
34C4×C3⋊Dic3—21no—
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C2×C3×C3⋊C8—22no—
38#3716—44no—
39#3713—42no—
40#3713—42no—
41#1688—91noSylow
42C3×#127—32no—
43C2×#214—62no—
44C2×#213—62no—
45C2×#213—62no—
46C2×#204—62no—
47#874C2×D312yes—
48C4×Dic6—32no—
49C4×Dic6—61no—
50C3×C4⋊C8—21no—
51C3×C4⋊C8—32no—
52C3×C4⋊C8C2×D312yes—
53#832—62no—
54#821—62no—
55#815—62no—
56#815—62no—
57Dic3⋊C8—62no—
58Dic3⋊C8—62no—
59C4⋊(C3⋊C8)C2×D312yes—
60C4×C3⋊C8—32no—
61C4×C3⋊C8—61no—
62C22×C3×D3—42no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4#4111yescharacteristic
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68#634—22no—
69C3×D12—42no—
70C3×D12—42no—
71C3×D12—42no—
72C3×D12—42no—
73C3×D12—82no—
74C32×C8—41no—
75C3⋊(C3⋊C8)—21no—
76C3⋊(C3⋊C8)SD1612yescomplemented
77C3×C3⋊C8—42no—
78#493—91no—
79#460—92no—
80#446—91no—
81#334—91no—
82#331—32no—
83C2×C3×D4—62no—
84C2×C3×D4—62no—
85C2×C3×D4—62no—
86C2×D12—22no—
87C2×D12—22no—
88C2×D12—22no—
89C2×Dic6—32no—
90C2×Dic6—61no—
91C2×C3×C8—22no—
92C2×C3×C8—22no—
93C2×C3×C8—62no—
94C3×C42—21no—
95C3×C42C22×D312yes—
96#214—124no—
97#213—124no—
98#213—124no—
99C4⋊Dic3—32no—
100C4⋊Dic3—61no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103C4×Dic3—62no—
104C4×Dic3—62no—
105C2×C3⋊C8—22no—
106C2×C3⋊C8—32no—
107C2×C3⋊C8—32no—
108C2×C3⋊C8—61no—
109C2×C3⋊C8—61no—
110#204—124no—
111C22×C32#12111yescharacteristic
112C2×C3×D3—82no—
113C2×C3×D3—82no—
114C2×C3×D3—82no—
115C32×C4—21no—
116C32×C4C2×SD1611yescharacteristic
117C32×C4AGL(1,ℤ/8)11yescharacteristic
118C32×C4AGL(1,ℤ/8)12yes—
119C3⋊Dic3—41no—
120C3⋊Dic3—41no—
121C2×SD16—182no—
122C2×D8—181no—
123C2×D8—181no—
124#127—32no—
125C4×Q8—91no—
126C4⋊C8—32no—
127C4⋊C8—181no—
128C4⋊C8D3211yescharacteristic
129#102—182no—
130#97—181no—
131C4×C8—91no—
132C23×C3—122no—
133C22×D3—42no—
134C3×D4—122no—
135C3×D4—122no—
136C3×D4—122no—
137C3×D4—122no—
138C3×D4—242no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4#23512yes—
143C2×C3×C4D3×D412yes—
144C2×C3×C4D3×D412yes—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149D12—42no—
150D12—42no—
151D12—42no—
152D12—42no—
153D12—82no—
154Dic6—62no—
155Dic6—62no—
156Dic6—122no—
157C3×C8—42no—
158C3×C8—42no—
159C3×C8—122no—
160C3⋊C8—34no—
161C3⋊C8—42no—
162C3⋊C8—62no—
163C3⋊C8—62no—
164C3⋊C8—121no—
165C2×C32#46011yescharacteristic
166C2×C32#46911yescharacteristic
167C2×C32#47211yescharacteristic
168C3×D3—162no—
169C2×Q8—91no—
170C2×D4—62no—
171C2×D4—62no—
172C2×D4—62no—
173SD16—364no—
174D8—362no—
175D8—362no—
176C2×C8—21no—
177C2×C8—62no—
178C2×C8—91no—
179C2×C8—91no—
180C4⋊C4—91no—
181C4⋊C4—181no—
182C42—181no—
183C42C2×D3211yescharacteristic
184C22×C3—21no—
185C22×C3—242no—
186C22×C3—242no—
187C22×C3—242no—
188C22×C3#88412yes—
189C2×D3—82no—
190C2×D3—82no—
191C2×D3—82no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—41no—
197C3×C4#91112yes—
198C3×C4#91112yes—
199C3×C4D3×SD1612yes—
200C3×C4#91412yes—
201Dic3—122no—
202Dic3—122no—
203Dic3—122no—
204Dic3—122no—
205C32#168811yescharacteristic, complemented, Sylow
206C23—122no—
207Q8—182no—
208D4—122no—
209D4—122no—
210D4—122no—
211D4—122no—
212D4—242no—
213C2×C4—181no—
214C2×C4—181no—
215C2×C4#379811yescharacteristic
216C2×C4#380211yescharacteristic
217C2×C4#381111yescharacteristic
218C8—41no—
219C8—92no—
220C8—122no—
221C8—181no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—482no—
226C2×C3#474912yes—
227C2×C3#476212yes—
228C2×C3#478212yes—
229D3—162no—
230C22—242no—
231C22—242no—
232C22—242no—
233C22#6391211yescharacteristic
234C4—21no—
235C4—361no—
236C4—361no—
237C4#6379812yes—
238C4#6392711yescharacteristic
239C4#6394011yescharacteristic
240C3—21no—
241C3#6841312yescomplemented
242C2—482no—
243C2#1059055311yescharacteristic
244C2#1059084011yescharacteristic
245C2#1059098811yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590352C2
hypercenterC4⋊C8D32
hypocenterC32#1688
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
1. #10592530C2semidirect
2. #10590377C2semidirect
4. C3×#4485C2semidirect
5. #10589098C2semidirect
24. #4485D3semidirect
76. C3⋊(C3⋊C8)SD16semidirect
205. C32#1688semidirect
241. C3#68413semidirect

Maximal subgroups

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

subgroupindex
#105925302
#105903772
#105903522
C3×#44852
#105890982
#684133