Finite Group Databasebeta

← #11775426

Subgroups — #11775426

Order 1152.

562 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 56 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#10596196C211yesmaximal, characteristic
2#10593737C211yesmaximal, characteristic, complemented
3#10593731C211yesmaximal, characteristic, complemented
4#10590157C214yesmaximal, complemented
5C2×#3832—21no—
6C32×C4⋊Q8C411yescharacteristic, complemented
7#64156—21no—
8#64104—21no—
9#64104C2212yes—
10#64102—21no—
11#64102C412yescomplemented
12#64083C411yescharacteristic, complemented
13C42×C3⋊D3C2211yescharacteristic
14#63781—21no—
15#63781—21no—
16#63781C2212yes—
17#63779—21no—
18#63778C2212yes—
19#63777—21no—
20#5725—62no—
21C22×#157—22no—
22C2×C32×Q8—21no—
23#3832—44no—
24C2×C4⋊(C3⋊D3)—22no—
25C2×C4⋊(C3⋊D3)—21no—
26C2×C4⋊(C3⋊D3)—21no—
27C2×C4⋊(C3⋊D3)C2×C412yes—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×#622—22no—
33C32×C4⋊C4—21no—
34C32×C4⋊C4C2×C412yes—
35C32×C42C2×C411yescharacteristic
36#3752—22no—
37#3752—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41#1514—91nomaximal, Sylow
42C2×#239—64no—
43C3×C4⋊Q8—22no—
44#947—64no—
45#895—64no—
46#895—64no—
47#893—64no—
48#893—64no—
49#874—62no—
50C42×D3—62no—
51C22×C3⋊D3—22no—
52C22×C3⋊D3C2×D411yescharacteristic
53C2×#157—42no—
54C2×#157—42no—
55C2×#157—42no—
56C32×Q8—42no—
57C2×C32×C4—22no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C22×C411yescharacteristic
61C2×C3⋊Dic3C22⋊C411yescharacteristic
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C2×D411yescharacteristic
64C4⋊(C3⋊D3)—42no—
65C4⋊(C3⋊D3)—42no—
66C4⋊(C3⋊D3)—42no—
67C4⋊(C3⋊D3)—44no—
68C4×C3⋊D3—22no—
69C4×C3⋊D3—41no—
70C4×C3⋊D3—41no—
71C4×C3⋊D3—44no—
72#622—42no—
73#532—91no—
74#432—91no—
75#383—91no—
76#327—94no—
77C2×C3×Q8—24no—
78#239—1216no—
79C2×D12—64no—
80C2×D12—64no—
81C2×D12—64no—
82C2×D12—68no—
83C2×C4×D3—62no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—68no—
87C3×C4⋊C4—24no—
88C3×C4⋊C4—24no—
89C3×C42—22no—
90(C2×D3)⋊C4—68no—
91(C2×D3)⋊C4—68no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C22×C32C2×C22⋊C411yescharacteristic
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—42no—
99C2×C3⋊D3—42no—
100C2×C3⋊D3—42no—
101C2×C3⋊D3AGL(1,ℤ/8)12yes—
102#157—82no—
103C32×C4—21no—
104C32×C4—21no—
105C32×C4—21no—
106C32×C4—42no—
107C3⋊Dic3—21no—
108C3⋊Dic3—21no—
109C3⋊Dic3—21no—
110C2×#41—181no—
111C4⋊Q8#15711yescharacteristic, complemented
112#127—91no—
113#124—181no—
114#121—92no—
115#121—181no—
116C4×D4—92no—
117C4×D4—181no—
118C2×C42—91no—
119C4⋊C8—181no—
120C22⋊C8—92no—
121#97—181no—
122#95—92no—
123#95—181no—
124#95—181no—
125C22×D3—62no—
126C22×D3—68no—
127C3×Q8—48no—
128C2×C3×C4—28no—
129C2×C3×C4—22no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×Dic3—62no—
133C2×Dic3—62no—
134C2×Dic3—62no—
135D12—128no—
136D12—128no—
137D12—128no—
138D12—1216no—
139C4×D3—68no—
140C4×D3—1216no—
141C4×D3—124no—
142C4×D3—124no—
143C2×C32#41011yescharacteristic
144C2×C32#41811yescharacteristic
145C2×C32#42111yescharacteristic
146C3⋊D3—22no—
147C3⋊D3—82no—
148#41—364no—
149C2×Q8—21no—
150C2×D4—92no—
151C2×D4—182no—
152C2×D4—181no—
153C2×D4—181no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—182no—
158C22×C4—182no—
159C2×C8—182no—
160C4⋊C4—21no—
161C4⋊C4C2×#15712yes—
162C22⋊C4—182no—
163C22⋊C4—182no—
164C42—91no—
165C42—91no—
166C42—91no—
167C42C2×#15711yescharacteristic
168C22×C3—22no—
169C2×D3—64no—
170C2×D3—122no—
171C2×D3—122no—
172C2×D3—128no—
173C2×D3—128no—
174C2×D3—128no—
175C3×C4—24no—
176C3×C4—24no—
177C3×C4—24no—
178C3×C4—48no—
179Dic3—64no—
180Dic3—122no—
181Dic3—122no—
182C32#151411yescharacteristic, complemented, Sylow
183C23—91no—
184C23—182no—
185Q8—42no—
186D4—362no—
187D4—362no—
188D4—362no—
189D4—364no—
190C2×C4—22no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—182no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—364no—
198C2×C4—362no—
199C2×C4—362no—
200C2×C4—362no—
201C2×C4C22⋊#15711yescharacteristic
202C2×C4C22⋊#15711yescharacteristic
203C2×C4C22×#15711yescharacteristic
204C8—362no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—22no—
208D3—124no—
209D3—248no—
210C22—92no—
211C22—181no—
212C22—181no—
213C22—362no—
214C22—362no—
215C22—362no—
216C22C2×C22⋊#15711yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—42no—
221C4—181no—
222C4—181no—
223C4—181no—
224C4—722no—
225C3—22no—
226C2—182no—
227C2—722no—
228C2#1059381411yescharacteristic
229C2#1059383111yescharacteristic
230C2#1059383211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#10596196C2
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593737C2semidirect
3. #10593731C2semidirect
4. #10590157C2semidirect
6. C32×C4⋊Q8C4semidirect
11. #64102C4semidirect
12. #64083C4semidirect
111. C4⋊Q8#157semidirect
182. C32#1514semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105937372
#105937312
#105901572
#15149