Finite Group Databasebeta

← #11781747

Subgroups — #11781747

Order 1152.

415 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 88 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#10592723C211yesmaximal, characteristic, complemented
2C3×#5027C212yesmaximal, complemented
3#10590352C211yesmaximal, characteristic
4#10589098C211yesmaximal, characteristic, complemented
5#10589090C212yesmaximal, complemented
6#71025—32nomaximal
7C32×C4×Q8C2211yescharacteristic
8C2×C3×#215—22no—
9C3×#874C2212yes—
10C2×#3713—21no—
11C2×#3713—21no—
12C4⋊(C3⋊(C3⋊C8))—21no—
13C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
14#63630—21no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#809—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×#460—32no—
19#5073—32no—
20#5027D312yescomplemented
21#5024—32no—
22#5024—61no—
23#4544—32no—
24#4485—32no—
25#4480—32no—
26C2×C32×Q8D411yescharacteristic
27C2×C3×D12—22no—
28C2×C3×D12—22no—
29C2×C3×D12—22no—
30C32×C4⋊C4—21no—
31C32×C4⋊C4D411yescharacteristic
32C32×C42—21no—
33C32×C42C2311yescharacteristic
34C2×C3⋊(C3⋊C8)—21no—
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C3×#215—44no—
38C2×C3×C3⋊C8—22no—
39#3713—42no—
40#3713—42no—
41#1688—91noSylow
42C2×C3×SD16—62no—
43C3×#127—32no—
44C3×C4×Q8—21no—
45C3×C4×Q8C2×D312yes—
46C2×#215—22no—
47C2×#213—62no—
48C2×#213—62no—
49#874C2×D312yes—
50C3×C4⋊C8—32no—
51C3×#102—62no—
52#809—22no—
53C4⋊(C3⋊C8)—32no—
54C4⋊(C3⋊C8)—61no—
55C4⋊(C3⋊C8)—62no—
56C4⋊(C3⋊C8)—62no—
57C4⋊(C3⋊C8)C2×D312yes—
58#803—62no—
59#803—62no—
60C4×C3⋊C8—32no—
61C4×C3⋊C8—61no—
62C22×C3×D3—42no—
63C32×Q8—22no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4#4111yescharacteristic
69C3×D12—42no—
70C3×D12—42no—
71C3×D12—42no—
72C3×D12—42no—
73C3×D12—82no—
74C3⋊(C3⋊C8)—21no—
75C3⋊(C3⋊C8)—41no—
76C3⋊(C3⋊C8)SD1612yescomplemented
77C3×C3⋊C8—42no—
78#493—91no—
79#460—32no—
80#446—91no—
81#334—91no—
82#331—92no—
83C2×C3×Q8—21no—
84C2×C3×Q8#6712yes—
85C2×C3×D4—62no—
86C2×C3×D4—62no—
87C2×C3×D4—62no—
88C2×D12—22no—
89C2×D12—22no—
90C2×D12—22no—
91C3×SD16—124no—
92C2×C3×C8—62no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4#6712yes—
97C3×C42—22no—
98C3×C42—22no—
99C3×C42—21no—
100C3×C42C22×D312yes—
101#215—44no—
102#213—124no—
103#213—124no—
104C2×C3⋊C8—22no—
105C2×C3⋊C8—32no—
106C2×C3⋊C8—32no—
107C2×C3⋊C8—61no—
108C2×C3⋊C8—61no—
109C2×C3⋊C8—62no—
110C2×C3⋊C8—62no—
111C22×C32#12111yescharacteristic
112C2×C3×D3—82no—
113C2×C3×D3—82no—
114C2×C3×D3—82no—
115C32×C4—21no—
116C32×C4—41no—
117C32×C4—41no—
118C32×C4C2×SD1611yescharacteristic
119C32×C4AGL(1,ℤ/8)11yescharacteristic
120C32×C4AGL(1,ℤ/8)12yes—
121C2×SD16—62no—
122C2×D8—181no—
123C2×D8—181no—
124#127—32no—
125C4×Q8D3211yescharacteristic
126C4⋊C8—32no—
127C4⋊C8—91no—
128C4⋊C8—181no—
129#102—62no—
130#97—181no—
131C4×C8—91no—
132C23×C3—122no—
133C22×D3—42no—
134C3×Q8—22no—
135C3×Q8—22no—
136C3×Q8—42no—
137C3×D4—122no—
138C3×D4—122no—
139C3×D4—122no—
140C3×D4—122no—
141C3×D4—242no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4D3×D412yes—
150C2×C3×C4#23712yes—
151C2×C3×C4C2×#6712yes—
152D12—42no—
153D12—42no—
154D12—42no—
155D12—42no—
156D12—82no—
157C3×C8—122no—
158C3⋊C8—34no—
159C3⋊C8—42no—
160C3⋊C8—62no—
161C3⋊C8—62no—
162C3⋊C8—121no—
163C3⋊C8—122no—
164C3⋊C8—122no—
165C2×C32#46011yescharacteristic
166C2×C32#46911yescharacteristic
167C2×C32#47211yescharacteristic
168C3×D3—162no—
169C2×Q8#62511yescharacteristic
170C2×D4—62no—
171C2×D4—62no—
172C2×D4—62no—
173SD16—124no—
174D8—362no—
175D8—362no—
176C2×C8—62no—
177C2×C8—91no—
178C2×C8—91no—
179C2×C8—181no—
180C4⋊C4—21no—
181C4⋊C4#62511yescharacteristic
182C42—21no—
183C42C2×D3211yescharacteristic
184C22×C3—21no—
185C22×C3—242no—
186C22×C3—242no—
187C22×C3—242no—
188C22×C3#93912yes—
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—42no—
198C3×C4—42no—
199C3×C4—42no—
200C3×C4—42no—
201C3×C4D3×SD1612yes—
202C3×C4#91412yes—
203C3×C4#93212yes—
204C3×C4#94912yes—
205C32#168811yescharacteristic, complemented, Sylow
206C23—122no—
207Q8—22no—
208D4—122no—
209D4—122no—
210D4—122no—
211D4—122no—
212D4—242no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4#380511yescharacteristic
216C2×C4C2×#62511yescharacteristic
217C2×C4#381111yescharacteristic
218C8—92no—
219C8—122no—
220C8—181no—
221C8—361no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—482no—
226C2×C3#503912yes—
227C2×C3#516312yes—
228C2×C3#519912yes—
229D3—162no—
230C22—242no—
231C22—242no—
232C22—242no—
233C22#6398011yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4#6382312yes—
238C4#6394011yescharacteristic
239C4#6394111yescharacteristic
240C3—21no—
241C3#7102512yescomplemented
242C2—482no—
243C2#1059116711yescharacteristic
244C2#1059162211yescharacteristic
245C2#1059167811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#121
prime radical#10590352C2
hypercenterC4×Q8D32
hypocenterC32#1688
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
1. #10592723C2semidirect
2. C3×#5027C2semidirect
4. #10589098C2semidirect
5. #10589090C2semidirect
20. #5027D3semidirect
76. C3⋊(C3⋊C8)SD16semidirect
205. C32#1688semidirect
241. C3#71025semidirect

Maximal subgroups

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

subgroupindex
#105927232
C3×#50272
#105903522
#105890982
#105890902
#710253