Finite Group Databasebeta

← #11781715

Subgroups — #11781715

Order 1152.

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

normal subgroups only

This group has 457 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#10592711C211yesmaximal, characteristic, complemented
2C3×#5015C212yesmaximal, complemented
3#10590352C211yesmaximal, characteristic, complemented
4#10589098C211yesmaximal, characteristic, complemented
5#10589090C212yesmaximal, complemented
6#71009—32nomaximal
7C32×C4×D4C2211yescharacteristic
8C2×#3748—21no—
9C2×C3×#213—22no—
10C3×#874C2212yes—
11C2×#3713—21no—
12C2×#3713—21no—
13#63657—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#809—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×#459—32no—
19#5073—32no—
20#5015D312yescomplemented
21#5012—32no—
22#5012—61no—
23#4544—32no—
24#4485—32no—
25#4480—32no—
26C2×C32×D4D411yescharacteristic
27C22×C32×C4—21no—
28C2×C3×D12—22no—
29C2×C3×D12—22no—
30C2×C3×D12—22no—
31C32×C4⋊C4D411yescharacteristic
32C32×C22⋊C4—21no—
33C32×C42C2311yescharacteristic
34#3748—42no—
35C2×C3⋊(C3⋊C8)—21no—
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C3×#213—44no—
39C2×C3×C3⋊C8—22no—
40#3713—42no—
41#3713—42no—
42#1687—91noSylow
43C2×C3×D8—62no—
44C3×#127—32no—
45C3×C4×D4—21no—
46C3×C4×D4C2×D312yes—
47C2×#213—22no—
48C2×#213—62no—
49C2×#213—62no—
50C2×#208—62no—
51C2×#208—62no—
52#874C2×D312yes—
53C3×C4⋊C8—32no—
54C3×#102—62no—
55#830—62no—
56#830—62no—
57#809—22no—
58C4⋊(C3⋊C8)—32no—
59C4⋊(C3⋊C8)—61no—
60C4⋊(C3⋊C8)C2×D312yes—
61C4×C3⋊C8—32no—
62C4×C3⋊C8—61no—
63C23×C32—21no—
64C22×C3×D3—42no—
65C32×D4—22no—
66C2×C32×C4—21no—
67C2×C32×C4—41no—
68C2×C32×C4—41no—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4#4111yescharacteristic
72C3×D12—42no—
73C3×D12—42no—
74C3×D12—42no—
75C3×D12—42no—
76C3×D12—82no—
77C3⋊(C3⋊C8)—21no—
78C3⋊(C3⋊C8)—41no—
79C3⋊(C3⋊C8)D812yescomplemented
80C3×C3⋊C8—42no—
81#493—91no—
82#459—32no—
83#436—91no—
84#334—91no—
85#331—92no—
86C2×C3×D4—21no—
87C2×C3×D4—62no—
88C2×C3×D4—62no—
89C2×C3×D4—62no—
90C2×C3×D4#6712yes—
91C22×C3×C4—22no—
92C22×C3×C4—22no—
93C2×D12—22no—
94C2×D12—22no—
95C2×D12—22no—
96C3×D8—124no—
97C2×C3×C8—62no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4#6712yes—
100C3×C22⋊C4—22no—
101C3×C22⋊C4—22no—
102C3×C42—21no—
103C3×C42C22×D312yes—
104#213—44no—
105#213—124no—
106#213—124no—
107#208—124no—
108#208—124no—
109C2×C3⋊C8—22no—
110C2×C3⋊C8—32no—
111C2×C3⋊C8—32no—
112C2×C3⋊C8—61no—
113C2×C3⋊C8—61no—
114C2×C3⋊C8—62no—
115C2×C3⋊C8—62no—
116C22×C32—41no—
117C22×C32—41no—
118C22×C32—41no—
119C22×C32#12111yescharacteristic
120C2×C3×D3—82no—
121C2×C3×D3—82no—
122C2×C3×D3—82no—
123C32×C4—21no—
124C32×C4—41no—
125C32×C4C2×D811yescharacteristic
126C32×C4AGL(1,ℤ/8)11yescharacteristic
127C32×C4AGL(1,ℤ/8)12yes—
128C2×D8—62no—
129C2×D8—181no—
130C2×D8—181no—
131C2×M16—181no—
132#127—32no—
133C4×D4D3211yescharacteristic
134C4⋊C8—32no—
135C4⋊C8—91no—
136#102—62no—
137C22⋊C8—181no—
138C4×C8—91no—
139C23×C3—22no—
140C23×C3—22no—
141C23×C3—122no—
142C22×D3—42no—
143C3×D4—22no—
144C3×D4—22no—
145C3×D4—42no—
146C3×D4—122no—
147C3×D4—122no—
148C3×D4—122no—
149C3×D4—122no—
150C3×D4—242no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—42no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—42no—
160C2×C3×C4D3×D412yes—
161C2×C3×C4#23712yes—
162C2×C3×C4C2×#6712yes—
163D12—42no—
164D12—42no—
165D12—42no—
166D12—42no—
167D12—82no—
168C3×C8—122no—
169C3⋊C8—34no—
170C3⋊C8—42no—
171C3⋊C8—62no—
172C3⋊C8—62no—
173C3⋊C8—121no—
174C3⋊C8—122no—
175C3⋊C8—122no—
176C2×C32—81no—
177C2×C32#45911yescharacteristic
178C2×C32#46911yescharacteristic
179C2×C32#47211yescharacteristic
180C3×D3—162no—
181C2×D4—62no—
182C2×D4—62no—
183C2×D4—62no—
184C2×D4#62511yescharacteristic
185C22×C4—21no—
186D8—124no—
187D8—362no—
188D8—362no—
189M16—362no—
190C2×C8—62no—
191C2×C8—91no—
192C2×C8—91no—
193C2×C8—181no—
194C4⋊C4#62511yescharacteristic
195C22⋊C4—21no—
196C42C2×D3211yescharacteristic
197C22×C3—21no—
198C22×C3—42no—
199C22×C3—42no—
200C22×C3—42no—
201C22×C3—42no—
202C22×C3—42no—
203C22×C3—42no—
204C22×C3—242no—
205C22×C3—242no—
206C22×C3—242no—
207C22×C3#93912yes—
208C2×D3—82no—
209C2×D3—82no—
210C2×D3—82no—
211C3×C4—22no—
212C3×C4—22no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—41no—
216C3×C4—42no—
217C3×C4—42no—
218C3×C4D3×D812yes—
219C3×C4#91112yes—
220C3×C4#93212yes—
221C3×C4#94912yes—
222C32#168711yescharacteristic, complemented, Sylow
223C23—21no—
224C23—122no—
225D4—22no—
226D4—122no—
227D4—122no—
228D4—122no—
229D4—122no—
230D4—242no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4#380511yescharacteristic
235C2×C4C2×#62511yescharacteristic
236C2×C4#381111yescharacteristic
237C8—92no—
238C8—122no—
239C8—181no—
240C8—361no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—82no—
245C2×C3—82no—
246C2×C3—482no—
247C2×C3#503912yes—
248C2×C3#515012yes—
249C2×C3#519912yes—
250D3—162no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—242no—
255C22—242no—
256C22—242no—
257C22#6398011yescharacteristic
258C4—21no—
259C4—41no—
260C4#6382312yes—
261C4#6392611yescharacteristic
262C4#6392711yescharacteristic
263C3—21no—
264C3#7100912yescomplemented
265C2—81no—
266C2—482no—
267C2#1059116711yescharacteristic
268C2#1059148611yescharacteristic
269C2#1059167811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
hypercenterC4×D4D32
hypocenterC32#1687
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
1. #10592711C2semidirect
2. C3×#5015C2semidirect
3. #10590352C2semidirect
4. #10589098C2semidirect
5. #10589090C2semidirect
20. #5015D3semidirect
79. C3⋊(C3⋊C8)D8semidirect
222. C32#1687semidirect
264. C3#71009semidirect

Maximal subgroups

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

subgroupindex
#105927112
C3×#50152
#105903522
#105890982
#105890902
#710093