Finite Group Databasebeta

← #11777621

Subgroups — #11777621

Order 1152.

546 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C4×#3745C211yesmaximal, characteristic
2#10592387C211yesmaximal, characteristic, complemented
3C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C32×#322C211yesmaximal, characteristic, complemented
5#10589325C211yesmaximal, characteristic, complemented
6#10589325C211yesmaximal, characteristic, complemented
7#10589323C211yesmaximal, characteristic, complemented
8#68081—34nomaximal
9C2×#3745C411yescharacteristic
10C2×#3743—21no—
11C2×C8×C3⋊D3—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14C32×C4×C8C2211yescharacteristic
15C32×C4×C8C2211yescharacteristic
16C32×C4×C8C2211yescharacteristic
17#63648C411yescharacteristic
18#63648C411yescharacteristic
19#63647—21no—
20#63647—21no—
21#63645C411yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C4×D24—34no—
25#4688—34no—
26C8×D12—34no—
27C3×#322D314yescomplemented
28#4459—34no—
29#4459—34no—
30#4457—34no—
31C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
32C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C2×C32×C8—21no—
36C2×C32×C8C2×C411yescharacteristic
37C2×C32×C8C2×C411yescharacteristic
38C2×C32×C8D411yescharacteristic
39C2×C32×C8D411yescharacteristic
40C32×C42C2311yescharacteristic
41#3752—21no—
42#3752—21no—
43C4⋊(C3⋊Dic3)C2×C411yescharacteristic
44C4⋊(C3⋊Dic3)C2×C411yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)—21no—
47#3745—22no—
48#3743—42no—
49C8×C3⋊D3—42no—
50#1586—91noSylow
51C2×D24—34no—
52C2×ΓL(1,𝔽25)—64no—
53C2×D3×C8—64no—
54C4×D12—34no—
55C4×D12—34no—
56C3×C4×C8C2×D314yes—
57C3×C4×C8C2×D314yes—
58C3×C4×C8C2×D314yes—
59#821—34no—
60#821—34no—
61(C2×D3)⋊C8—64no—
62(C2×D3)⋊C8—64no—
63#818—34no—
64C4⋊(C3⋊C8)—34no—
65C4⋊(C3⋊C8)—34no—
66C22×C3⋊D3—21no—
67C22×C3⋊D3—21no—
68C2×C32×C4C22×C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C4⋊(C3⋊D3)—21no—
74C4⋊(C3⋊D3)—21no—
75C4⋊(C3⋊D3)—21no—
76C4⋊(C3⋊D3)M1612yescomplemented
77C4×C3⋊D3—41no—
78C4×C3⋊D3—41no—
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81C32×C8—22no—
82C32×C8—21no—
83C32×C8—21no—
84C32×C8—21no—
85C32×C8—21no—
86C3⋊(C3⋊C8)—41no—
87C3⋊(C3⋊C8)—41no—
88C4×D8—91no—
89#436—91no—
90C8×D4—91no—
91#334—91no—
92D4⋊C8—91no—
93D4⋊C8—91no—
94#322C3⋊D311yescharacteristic, complemented
95C2×D12—34no—
96C2×D12—34no—
97C2×C4×D3—64no—
98C2×C4×D3—64no—
99C2×C3×C8—24no—
100C2×C3×C8C4×D314yes—
101C2×C3×C8C4×D314yes—
102C2×C3×C8D1214yes—
103C2×C3×C8D1214yes—
104C3×C42C22×D314yes—
105(C2×D3)⋊C4—64no—
106(C2×D3)⋊C4—64no—
107C4⋊Dic3—34no—
108C4⋊Dic3—34no—
109C2×C3⋊C8—64no—
110C2×C3⋊C8—64no—
111D24—68no—
112ΓL(1,𝔽25)—128no—
113D3×C8—128no—
114C22×C32C4×D411yescharacteristic
115C2×C3⋊D3—22no—
116C2×C3⋊D3—41no—
117C2×C3⋊D3—41no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3—41no—
120C2×C3⋊D3—41no—
121C32×C4—21no—
122C32×C4C2×M1611yescharacteristic
123C32×C4#13111yescharacteristic
124C32×C4AGL(1,ℤ/8)11yescharacteristic
125C32×C4AGL(1,ℤ/8)11yescharacteristic
126C3⋊Dic3—41no—
127C3⋊Dic3—41no—
128C2×D8—91no—
129C2×M16—181no—
130C22×C8—181no—
131C4×D4—91no—
132C4×D4—91no—
133#107—91no—
134C4⋊C8—91no—
135C4⋊C8—91no—
136#102—91no—
137#102—91no—
138C22⋊C8—181no—
139C22⋊C8—181no—
140C4×C8C2×C3⋊D311yescharacteristic
141C4×C8C2×C3⋊D311yescharacteristic
142C4×C8C2×C3⋊D311yescharacteristic
143C22×D3—64no—
144C22×D3—64no—
145C2×C3×C4C2×C4×D314yes—
146C2×C3×C4C2×D1214yes—
147C2×C3×C4#23514yes—
148C2×Dic3—64no—
149C2×Dic3—64no—
150D12—38no—
151D12—64no—
152D12—64no—
153D12—64no—
154C4×D3—124no—
155C4×D3—124no—
156C4×D3—124no—
157C4×D3—124no—
158C3×C8—28no—
159C3×C8—24no—
160C3×C8—24no—
161C3×C8—24no—
162C3×C8—24no—
163C3⋊C8—124no—
164C3⋊C8—124no—
165C2×C32#43511yescharacteristic
166C2×C32#44211yescharacteristic
167C2×C32#44311yescharacteristic
168C3⋊D3—42no—
169C3⋊D3—81no—
170C2×D4—91no—
171C2×D4—91no—
172C22×C4—181no—
173C22×C4—181no—
174D8—182no—
175M16—362no—
176C2×C8—21no—
177C2×C8—181no—
178C2×C8—181no—
179C2×C8—362no—
180C2×C8C4×C3⋊D311yescharacteristic
181C2×C8C4×C3⋊D311yescharacteristic
182C2×C8C4⋊(C3⋊D3)11yescharacteristic
183C2×C8C4⋊(C3⋊D3)11yescharacteristic
184C4⋊C4—91no—
185C4⋊C4—91no—
186C22⋊C4—181no—
187C22⋊C4—181no—
188C42C22×C3⋊D311yescharacteristic
189C22×C3C4×D1214yes—
190C2×D3—68no—
191C2×D3—124no—
192C2×D3—124no—
193C2×D3—124no—
194C2×D3—124no—
195C2×D3—124no—
196C3×C4—24no—
197C3×C4D3×M1614yes—
198C3×C4#90714yes—
199C3×C4#90814yes—
200C3×C4#90814yes—
201Dic3—124no—
202Dic3—124no—
203C32#158611yescharacteristic, complemented, Sylow
204C23—181no—
205C23—181no—
206D4—92no—
207D4—181no—
208D4—181no—
209D4—181no—
210C2×C4—181no—
211C2×C4—181no—
212C2×C4—361no—
213C2×C4—361no—
214C2×C4—361no—
215C2×C4—361no—
216C2×C4C2×C4×C3⋊D311yescharacteristic
217C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
218C2×C4#382811yescharacteristic
219C8—22no—
220C8—21no—
221C8—21no—
222C8—21no—
223C8—21no—
224C8—361no—
225C8—361no—
226C2×C3#470014yes—
227C2×C3#470614yes—
228C2×C3#471114yes—
229D3—128no—
230D3—244no—
231C22—182no—
232C22—361no—
233C22—361no—
234C22—361no—
235C22—361no—
236C22—361no—
237C22C4×C4⋊(C3⋊D3)11yescharacteristic
238C4—21no—
239C4—361no—
240C4—361no—
241C4M16×C3⋊D311yescharacteristic
242C4#6411611yescharacteristic
243C4#6411711yescharacteristic
244C4#6411711yescharacteristic
245C3#6808114yescomplemented
246C2—362no—
247C2—721no—
248C2#1059239911yescharacteristic
249C2#1059240511yescharacteristic
250C2#1059241011yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#322C2
socleC22×C32C4×D4
prime radicalC2×#3745C4
cosocleC32×C42C23
hypercenter#322C3⋊D3
hypocenterC32#1586
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
2. #10592387C2semidirect
3. C8×C4⋊(C3⋊D3)C2semidirect
4. C32×#322C2semidirect
5. #10589325C2semidirect
6. #10589325C2semidirect
7. #10589323C2semidirect
27. C3×#322D3semidirect
76. C4⋊(C3⋊D3)M16semidirect
94. #322C3⋊D3semidirect
203. C32#1586semidirect
245. C3#68081semidirect

Maximal subgroups

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

subgroupindex
C4×#37452
#105923872
C8×C4⋊(C3⋊D3)2
C32×#3222
#105893252
#105893232
#680813