Finite Group Databasebeta

← #11775876

Subgroups — #11775876

Order 1152.

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

normal subgroups only

This group has 566 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#10593730C211yesmaximal, characteristic, complemented
3#10593723C211yesmaximal, characteristic, complemented
4#10590216C214yesmaximal, complemented
5C2×#3832C412yes—
6C2×#3787—21no—
7C32×C4⋊Q8C411yescharacteristic
8#64156C2212yes—
9#64104—21no—
10#64104—21no—
11#64102—21no—
12#64102—21no—
13#64083C411yescharacteristic
14C42×C3⋊D3C2211yescharacteristic
15#63778—21no—
16#63777—21no—
17#63777C2212yes—
18#63777C2212yes—
19C4⋊#622—21no—
20#5725—62no—
21C2×C32×Q8C2×C412yes—
22#3832—44no—
23C2×C4⋊(C3⋊D3)—22no—
24C2×C4⋊(C3⋊D3)—21no—
25C2×C4⋊(C3⋊D3)—21no—
26C2×C4⋊(C3⋊D3)C2×C412yes—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×#622—22no—
32C2×#622—22no—
33#3787—24no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4—21no—
36C32×C42C2×C411yescharacteristic
37#3752—22no—
38#3752—22no—
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42#1530—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⋊D3C22⋊C411yescharacteristic
54C32×Q8—42no—
55C2×C32×C4—22no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C4⋊(C3⋊D3)—42no—
63C4⋊(C3⋊D3)—42no—
64C4⋊(C3⋊D3)—44no—
65C4⋊(C3⋊D3)—42no—
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3—41no—
69C4×C3⋊D3—44no—
70#622—24no—
71#622—42no—
72#532—91no—
73#432—91no—
74C2×#97—91no—
75#329—94no—
76C2×C3×Q8—24no—
77#239—1216no—
78C2×D12—64no—
79C2×D12—64no—
80C2×D12—64no—
81C2×D12—68no—
82C2×C4×D3—62no—
83C2×C4×D3—62no—
84C2×C4×D3—62no—
85C2×C4×D3—68no—
86C3×C4⋊C4—24no—
87C3×C4⋊C4—24no—
88C3×C42—22no—
89(C2×D3)⋊C4—68no—
90(C2×D3)⋊C4—68no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C22×C32C2×C22⋊C411yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—42no—
98C2×C3⋊D3—42no—
99C2×C3⋊D3—42no—
100C2×C3⋊D3#10012yes—
101C32×C4—21no—
102C32×C4—21no—
103C32×C4—42no—
104C32×C4#10412yes—
105C3⋊Dic3—21no—
106C3⋊Dic3—21no—
107C3⋊Dic3—21no—
108C2×#41—92no—
109C22×C8—181no—
110C4⋊Q8#15711yescharacteristic
111#127—91no—
112#124—92no—
113#121—181no—
114#121—181no—
115C4×D4—181no—
116C4×D4—181no—
117C2×C42—91no—
118C4⋊C8—181no—
119C22⋊C8—181no—
120#97—92no—
121#97—92no—
122#97—181no—
123C22×D3—62no—
124C22×D3—68no—
125C3×Q8—48no—
126C2×C3×C4—28no—
127C2×C3×C4—22no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133D12—128no—
134D12—128no—
135D12—128no—
136D12—1216no—
137C4×D3—68no—
138C4×D3—124no—
139C4×D3—1216no—
140C4×D3—124no—
141C2×C32C2×#10011yescharacteristic
142C2×C32C2×#10411yescharacteristic
143C2×C32#42111yescharacteristic
144C3⋊D3—22no—
145C3⋊D3—82no—
146#41—364no—
147C2×Q8C2×#15712yes—
148C2×D4—92no—
149C2×D4—182no—
150C2×D4—181no—
151C2×D4—181no—
152C22×C4—91no—
153C22×C4—91no—
154C22×C4—91no—
155C22×C4—182no—
156C2×C8—182no—
157C2×C8—184no—
158C2×C8—182no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C22⋊C4—182no—
162C22⋊C4—182no—
163C42—91no—
164C42—91no—
165C42—91no—
166C42C2×#15711yescharacteristic
167C22×C3—22no—
168C2×D3—64no—
169C2×D3—122no—
170C2×D3—122no—
171C2×D3—128no—
172C2×D3—128no—
173C2×D3—128no—
174C3×C4—24no—
175C3×C4—24no—
176C3×C4—24no—
177C3×C4—48no—
178Dic3—64no—
179Dic3—122no—
180Dic3—122no—
181C32#153011yescharacteristic, complemented, Sylow
182C23—91no—
183C23—182no—
184Q8—42no—
185D4—362no—
186D4—362no—
187D4—364no—
188D4—362no—
189C2×C4—22no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—182no—
194C2×C4—182no—
195C2×C4—361no—
196C2×C4—364no—
197C2×C4C22⋊#15711yescharacteristic
198C2×C4C22⋊#15711yescharacteristic
199C2×C4C22×#15711yescharacteristic
200C8—184no—
201C8—362no—
202C2×C3—22no—
203C2×C3—22no—
204C2×C3—22no—
205D3—124no—
206D3—248no—
207C22—92no—
208C22—181no—
209C22—181no—
210C22—362no—
211C22—362no—
212C22—362no—
213C22C2×C22⋊#15711yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—181no—
218C4—181no—
219C4—181no—
220C4#6378512yes—
221C3—22no—
222C2—182no—
223C2—722no—
224C2#1059382511yescharacteristic
225C2C2×#6378511yescharacteristic
226C2#1059383111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#10596196C2
cosocleC4×C3⋊Dic3C23
hypercenterC4⋊Q8#157
hypocenterC32#1530
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. #10593730C2semidirect
3. #10593723C2semidirect
4. #10590216C2semidirect
181. C32#1530semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105937302
#105937232
#105902162
#15309