Finite Group Databasebeta

← #11775149

Subgroups — #11775149

Order 1152.

582 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 60 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#10593733C211yesmaximal, characteristic, complemented
3#10593730C211yesmaximal, characteristic, complemented
4#10590157C214yesmaximal, complemented
5C2×#3832—21no—
6C2×C4×#157—21no—
7C32×C4⋊Q8C411yescharacteristic, complemented
8#64156—21no—
9#64104—21no—
10#64104C2212yes—
11#64102—21no—
12#64102C412yescomplemented
13#64083C411yescharacteristic, complemented
14C42×C3⋊D3C2211yescharacteristic
15#63781—21no—
16#63781C2212yes—
17#63778C2212yes—
18#63777—21no—
19C4⋊#622—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—
33C4×#157—24no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4C2×C412yes—
36C32×C42C2×C411yescharacteristic
37#3752—22no—
38#3752—22no—
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42#1505—91nomaximal, Sylow
43C2×#239—64no—
44C3×C4⋊Q8—22no—
45#947—64no—
46#895—64no—
47#895—64no—
48#893—64no—
49#893—64no—
50#874—62no—
51C42×D3—62no—
52C22×C3⋊D3—22no—
53C22×C3⋊D3C2×D411yescharacteristic
54C2×#157—24no—
55C2×#157—42no—
56C2×#157—42no—
57C32×Q8—42no—
58C2×C32×C4—22no—
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C4⋊(C3⋊D3)—42no—
66C4⋊(C3⋊D3)—42no—
67C4⋊(C3⋊D3)—44no—
68C4⋊(C3⋊D3)—42no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3—22no—
71C4×C3⋊D3—41no—
72C4×C3⋊D3—44no—
73#622—42no—
74#532—91no—
75#432—91no—
76#376—91no—
77#327—94no—
78C2×C3×Q8—24no—
79#239—1216no—
80C2×D12—64no—
81C2×D12—64no—
82C2×D12—64no—
83C2×D12—68no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—68no—
88C3×C4⋊C4—24no—
89C3×C4⋊C4—24no—
90C3×C42—22no—
91(C2×D3)⋊C4—68no—
92(C2×D3)⋊C4—68no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C4×Dic3—62no—
96C22×C32C2×C22⋊C411yescharacteristic
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—42no—
100C2×C3⋊D3—42no—
101C2×C3⋊D3—42no—
102C2×C3⋊D3AGL(1,ℤ/8)12yes—
103#157—44no—
104C32×C4—21no—
105C32×C4—21no—
106C32×C4—42no—
107C32×C4#10412yes—
108C3⋊Dic3—21no—
109C3⋊Dic3—21no—
110C3⋊Dic3—21no—
111C2×#41—181no—
112C4⋊Q8#15711yescharacteristic, complemented
113#127—91no—
114#124—181no—
115#121—92no—
116#121—181no—
117C4×D4—92no—
118C4×D4—181no—
119C2×C42—91no—
120C2×C42—181no—
121C4⋊C8—181no—
122C22⋊C8—92no—
123#97—181no—
124#95—92no—
125#95—181no—
126C22×D3—62no—
127C22×D3—68no—
128C3×Q8—48no—
129C2×C3×C4—28no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×Dic3—62no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136D12—128no—
137D12—128no—
138D12—128no—
139D12—1216no—
140C4×D3—68no—
141C4×D3—124no—
142C4×D3—1216no—
143C4×D3—124no—
144C2×C32#41011yescharacteristic
145C2×C32#41811yescharacteristic
146C2×C32C2×#10411yescharacteristic
147C3⋊D3—22no—
148C3⋊D3—82no—
149#41—364no—
150C2×Q8—21no—
151C2×D4—92no—
152C2×D4—182no—
153C2×D4—181no—
154C2×D4—181no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—182no—
159C22×C4—182no—
160C2×C8—182no—
161C4⋊C4—21no—
162C4⋊C4C2×#15712yes—
163C22⋊C4—182no—
164C22⋊C4—182no—
165C42—91no—
166C42—91no—
167C42—91no—
168C42—184no—
169C42C2×#15711yescharacteristic
170C22×C3—22no—
171C2×D3—64no—
172C2×D3—122no—
173C2×D3—122no—
174C2×D3—128no—
175C2×D3—128no—
176C2×D3—128no—
177C3×C4—24no—
178C3×C4—24no—
179C3×C4—24no—
180C3×C4—48no—
181Dic3—64no—
182Dic3—122no—
183Dic3—122no—
184C32#150511yescharacteristic, complemented, Sylow
185C23—91no—
186C23—182no—
187Q8—42no—
188D4—362no—
189D4—362no—
190D4—364no—
191D4—362no—
192C2×C4—22no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4—184no—
199C2×C4—361no—
200C2×C4—364no—
201C2×C4—362no—
202C2×C4—362no—
203C2×C4C22⋊#15711yescharacteristic
204C2×C4C22⋊#15711yescharacteristic
205C2×C4C22×#15711yescharacteristic
206C8—362no—
207C2×C3—22no—
208C2×C3—22no—
209C2×C3—22no—
210D3—124no—
211D3—248no—
212C22—92no—
213C22—181no—
214C22—181no—
215C22—362no—
216C22—362no—
217C22—362no—
218C22C2×C22⋊#15711yescharacteristic
219C4—21no—
220C4—21no—
221C4—42no—
222C4—181no—
223C4—181no—
224C4—181no—
225C4—364no—
226C4#6378512yes—
227C3—22no—
228C2—182no—
229C2—722no—
230C2#1059381411yescharacteristic
231C2C2×#6378511yescharacteristic
232C2#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#1505
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. #10593733C2semidirect
3. #10593730C2semidirect
4. #10590157C2semidirect
7. C32×C4⋊Q8C4semidirect
12. #64102C4semidirect
13. #64083C4semidirect
112. C4⋊Q8#157semidirect
184. C32#1505semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105937332
#105937302
#105901572
#15059