Finite Group Databasebeta

← #11781720

Subgroups — #11781720

Order 1152.

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

normal subgroups only

This group has 457 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#10592537C211yesmaximal, characteristic, complemented
2#10590355C212yesmaximal, complemented
3#10590352C211yesmaximal, characteristic, complemented
4C3×#4485C212yesmaximal, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#68399—32nomaximal
7C2×#3743—21no—
8C4×C4⋊(C3⋊D3)C2211yescharacteristic
9C3×#874C2212yes—
10C2×#3714—22no—
11C2×#3713—21no—
12C2×#3713—21no—
13C32×C4⋊C8C2211yescharacteristic
14#63647—21no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2212yes—
17#63563—22no—
18#5073—32no—
19#5072—32no—
20#4843—32no—
21#4838—32no—
22#4838—61no—
23C3×#331—32no—
24#4485D312yescomplemented
25#4480—32no—
26C2×C4⋊(C3⋊D3)D411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C3×D12—22no—
29C2×C3×D12—22no—
30C2×C3×D12—22no—
31C2×C32×C8—21no—
32C32×C42C2311yescharacteristic
33#3752—21no—
34C4⋊(C3⋊Dic3)D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37#3743—42no—
38C2×C3×C3⋊C8—22no—
39#3714—44no—
40#3713—42no—
41#3713—42no—
42#1687—91noSylow
43C3×#127—32no—
44C2×#213—62no—
45C2×#213—62no—
46C2×#213—62no—
47C2×D24—62no—
48C2×ΓL(1,𝔽25)—62no—
49C2×ΓL(1,𝔽25)—62no—
50#874C2×D312yes—
51C4×D12—32no—
52C4×D12—61no—
53C3×C4⋊C8—21no—
54C3×C4⋊C8—32no—
55C3×C4⋊C8C2×D312yes—
56#832—62no—
57#821—62no—
58(C2×D3)⋊C8—62no—
59(C2×D3)⋊C8—62no—
60C4⋊(C3⋊C8)C2×D312yes—
61C4×C3⋊C8—32no—
62C4×C3⋊C8—61no—
63C22×C3⋊D3—21no—
64C22×C3×D3—42no—
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4#4111yescharacteristic
68C2×C3⋊Dic3—21no—
69C4⋊(C3⋊D3)—22no—
70C4×C3⋊D3—41no—
71C4×C3⋊D3—41no—
72C3×D12—42no—
73C3×D12—42no—
74C3×D12—42no—
75C3×D12—42no—
76C3×D12—82no—
77C32×C8—41no—
78C3⋊(C3⋊C8)—21no—
79C3⋊(C3⋊C8)D812yescomplemented
80C3×C3⋊C8—42no—
81#493—91no—
82#459—92no—
83#436—91no—
84#334—91no—
85#331—32no—
86C2×C3×D4—62no—
87C2×C3×D4—62no—
88C2×C3×D4—62no—
89C2×D12—22no—
90C2×D12—22no—
91C2×D12—22no—
92C2×D12—32no—
93C2×D12—61no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C3×C8—22no—
97C2×C3×C8—22no—
98C2×C3×C8—62no—
99C3×C42—21no—
100C3×C42C22×D312yes—
101#213—124no—
102#213—124no—
103#213—124no—
104(C2×D3)⋊C4—62no—
105(C2×D3)⋊C4—62no—
106C4⋊Dic3—32no—
107C4⋊Dic3—61no—
108C2×C3⋊C8—22no—
109C2×C3⋊C8—32no—
110C2×C3⋊C8—32no—
111C2×C3⋊C8—61no—
112C2×C3⋊C8—61no—
113D24—124no—
114ΓL(1,𝔽25)—124no—
115ΓL(1,𝔽25)—124no—
116C22×C32#12111yescharacteristic
117C2×C3⋊D3—41no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3—41no—
120C2×C3×D3—82no—
121C2×C3×D3—82no—
122C2×C3×D3—82no—
123C32×C4—21no—
124C32×C4C2×D811yescharacteristic
125C32×C4AGL(1,ℤ/8)12yes—
126C32×C4AGL(1,ℤ/8)11yescharacteristic
127C3⋊Dic3—41no—
128C2×D8—182no—
129C2×D8—181no—
130C2×D8—181no—
131C2×M16—181no—
132#127—32no—
133C4×D4—91no—
134C4⋊C8—32no—
135C4⋊C8D3211yescharacteristic
136#102—182no—
137C22⋊C8—181no—
138C4×C8—91no—
139C23×C3—122no—
140C22×D3—42no—
141C22×D3—62no—
142C22×D3—62no—
143C3×D4—122no—
144C3×D4—122no—
145C3×D4—122no—
146C3×D4—122no—
147C3×D4—242no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4#23512yes—
152C2×C3×C4D3×D412yes—
153C2×C3×C4D3×D412yes—
154C2×Dic3—62no—
155C2×Dic3—62no—
156D12—42no—
157D12—42no—
158D12—42no—
159D12—42no—
160D12—62no—
161D12—62no—
162D12—82no—
163D12—122no—
164C4×D3—122no—
165C4×D3—122no—
166C4×D3—122no—
167C4×D3—122no—
168C3×C8—42no—
169C3×C8—42no—
170C3×C8—122no—
171C3⋊C8—34no—
172C3⋊C8—42no—
173C3⋊C8—62no—
174C3⋊C8—62no—
175C3⋊C8—121no—
176C2×C32#45911yescharacteristic
177C2×C32#46911yescharacteristic
178C2×C32#47211yescharacteristic
179C3⋊D3—81no—
180C3×D3—162no—
181C2×D4—62no—
182C2×D4—62no—
183C2×D4—62no—
184C2×D4—91no—
185C22×C4—181no—
186D8—362no—
187D8—364no—
188D8—362no—
189M16—362no—
190C2×C8—21no—
191C2×C8—62no—
192C2×C8—91no—
193C2×C8—91no—
194C4⋊C4—91no—
195C22⋊C4—181no—
196C42C2×D3211yescharacteristic
197C22×C3—21no—
198C22×C3—242no—
199C22×C3—242no—
200C22×C3—242no—
201C22×C3#88412yes—
202C2×D3—82no—
203C2×D3—82no—
204C2×D3—82no—
205C2×D3—122no—
206C2×D3—122no—
207C2×D3—122no—
208C2×D3—122no—
209C2×D3—122no—
210C2×D3—122no—
211C3×C4—22no—
212C3×C4—22no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—41no—
216C3×C4D3×D812yes—
217C3×C4#91112yes—
218C3×C4#91412yes—
219C3×C4#91412yes—
220Dic3—122no—
221Dic3—122no—
222C32#168711yescharacteristic, complemented, Sylow
223C23—122no—
224C23—181no—
225D4—122no—
226D4—122no—
227D4—122no—
228D4—122no—
229D4—182no—
230D4—242no—
231C2×C4—181no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4#379811yescharacteristic
235C2×C4#380211yescharacteristic
236C2×C4#381111yescharacteristic
237C8—41no—
238C8—92no—
239C8—122no—
240C8—181no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—482no—
245C2×C3#474912yes—
246C2×C3#478212yes—
247C2×C3#478612yes—
248D3—162no—
249D3—242no—
250D3—242no—
251C22—242no—
252C22—242no—
253C22—242no—
254C22—361no—
255C22—361no—
256C22—361no—
257C22#6391211yescharacteristic
258C4—21no—
259C4—361no—
260C4#6379812yes—
261C4#6392611yescharacteristic
262C4#6394111yescharacteristic
263C3—21no—
264C3#6839912yescomplemented
265C2—482no—
266C2—721no—
267C2#1059055111yescharacteristic
268C2#1059084011yescharacteristic
269C2#1059098811yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1687
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. #10592537C2semidirect
2. #10590355C2semidirect
3. #10590352C2semidirect
4. C3×#4485C2semidirect
5. #10589098C2semidirect
24. #4485D3semidirect
79. C3⋊(C3⋊C8)D8semidirect
222. C32#1687semidirect
264. C3#68399semidirect

Maximal subgroups

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

subgroupindex
#105925372
#105903552
#105903522
C3×#44852
#105890982
#683993