Finite Group Databasebeta

← #11774553

Subgroups — #11774553

Order 1152.

738 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#64102C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic, complemented
3#10593801C211yesmaximal, characteristic, complemented
4#10590160C214yesmaximal, complemented
5C22×C4⋊(C3⋊D3)C411yescharacteristic
6C22×C4×C3⋊D3—21no—
7C2×#3792—21no—
8C2×C32×C4⋊C4C411yescharacteristic
9C2×#3752—21no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11#64102—21no—
12#64102—21no—
13#64102C412yes—
14#64102C2212yes—
15C22⋊#622—21no—
16#63779—21no—
17#63779—21no—
18C4⋊#622C2212yescomplemented
19C4×#622C2212yescomplemented
20C2×#893—62no—
21C23×C3⋊D3—21no—
22C22×C32×C4—21no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C4⋊(C3⋊D3)—21no—
27C2×C4⋊(C3⋊D3)—24no—
28C2×C4⋊(C3⋊D3)C2×C412yes—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—42no—
32C2×C4×C3⋊D3—42no—
33#3792—42no—
34C2×#622—22no—
35C2×#622—22no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C412yes—
38#3752—22no—
39#3752—22no—
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3C2311yescharacteristic
44#1486—91nomaximal, Sylow
45C22×D12—62no—
46C22×C4×D3—64no—
47C2×C3×C4⋊C4—22no—
48C2×(C2×D3)⋊C4—64no—
49C2×C4×Dic3—62no—
50#893—64no—
51#893—64no—
52#893—64no—
53#893—64no—
54C23×C32C22⋊C411yescharacteristic
55C22×C3⋊D3—24no—
56C22×C3⋊D3—22no—
57C22×C3⋊D3—42no—
58C22×C3⋊D3—42no—
59C2×C32×C4—22no—
60C2×C32×C4—22no—
61C2×C32×C4—42no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22×C411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3D812yes—
68C2×C3⋊Dic3SD1612yes—
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C4⋊(C3⋊D3)—24no—
72C4⋊(C3⋊D3)—22no—
73C4⋊(C3⋊D3)M1614yescomplemented
74C4×C3⋊D3—44no—
75C4×C3⋊D3—42no—
76C4×C3⋊D3—42no—
77#622—42no—
78#622—42no—
79C2×C4×D4—91no—
80#431—91no—
81#423—91no—
82D4⋊C8—94no—
83C23×D3—64no—
84C22×C3×C4—24no—
85C22×C3×C4—22no—
86C22×Dic3—62no—
87C22×Dic3—62no—
88C2×D12—64no—
89C2×D12—64no—
90C2×D12—616no—
91C2×C4×D3—68no—
92C2×C4×D3—68no—
93C2×C4×D3—128no—
94C2×C4×D3—128no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—24no—
97(C2×D3)⋊C4—68no—
98(C2×D3)⋊C4—68no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32#10212yes—
106C22×C32C2×C22⋊C411yescharacteristic
107C2×C3⋊D3—24no—
108C2×C3⋊D3—48no—
109C2×C3⋊D3—42no—
110C2×C3⋊D3—42no—
111C32×C4—21no—
112C32×C4—42no—
113C32×C4C2×M1612yes—
114C3⋊Dic3—21no—
115C3⋊Dic3—21no—
116C3⋊Dic3#10212yes—
117C3⋊Dic3C2×D811yescharacteristic
118C3⋊Dic3C2×SD1611yescharacteristic
119C22×D4—91no—
120C23×C4—181no—
121C2×M16—181no—
122C4×D4—92no—
123C4×D4—92no—
124C4×D4—181no—
125C4×D4—181no—
126C2×C4⋊C4#15711yescharacteristic
127C2×C22⋊C4—181no—
128C2×C42—91no—
129C4⋊C8—92no—
130C4⋊C8—181no—
131C4⋊C8—181no—
132C22⋊C8—181no—
133C4×C8—92no—
134C23×C3—22no—
135C22×D3—68no—
136C22×D3—616no—
137C22×D3—128no—
138C22×D3—128no—
139C2×C3×C4—28no—
140C2×C3×C4—28no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—48no—
144C2×Dic3—62no—
145C2×Dic3—64no—
146C2×Dic3—64no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—124no—
151D12—68no—
152D12—616no—
153D12—68no—
154C4×D3—1216no—
155C4×D3—128no—
156C4×D3—128no—
157C2×C32—22no—
158C2×C32#40711yescharacteristic
159C2×C32C2×#10211yescharacteristic
160C2×C32#42111yescharacteristic
161C3⋊D3—44no—
162C24—181no—
163C2×D4—92no—
164C2×D4—184no—
165C2×D4—181no—
166C22×C4—21no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—182no—
170C22×C4—182no—
171C22×C4—362no—
172C22×C4—362no—
173C22×C4C2×#15711yescharacteristic
174M16—362no—
175C2×C8—182no—
176C2×C8—182no—
177C4⋊C4—21no—
178C4⋊C4C2×#15712yes—
179C22⋊C4—182no—
180C22⋊C4—182no—
181C42—91no—
182C42—91no—
183C42—91no—
184C42—91no—
185C22×C3—24no—
186C22×C3—24no—
187C22×C3—22no—
188C22×C3—24no—
189C2×D3—616no—
190C2×D3—128no—
191C2×D3—1232no—
192C2×D3—128no—
193C3×C4—24no—
194C3×C4—24no—
195C3×C4—48no—
196Dic3—64no—
197Dic3—62no—
198Dic3—62no—
199Dic3—122no—
200Dic3—122no—
201C32#148611yescharacteristic, complemented, Sylow
202C23—184no—
203C23—182no—
204C23—362no—
205C23—362no—
206C23C22⋊#15711yescharacteristic
207D4—94no—
208D4—184no—
209D4—182no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—92no—
216C2×C4—92no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—362no—
220C2×C4—362no—
221C2×C4—364no—
222C2×C4—361no—
223C2×C4C22⋊#15711yescharacteristic
224C2×C4C22×#15711yescharacteristic
225C8—362no—
226C8—362no—
227C2×C3—28no—
228C2×C3—22no—
229C2×C3—22no—
230C2×C3—22no—
231D3—1216no—
232C22—21no—
233C22—21no—
234C22—184no—
235C22—368no—
236C22—362no—
237C22—362no—
238C22#6378212yes—
239C22C2×C22⋊#15711yescharacteristic
240C4—21no—
241C4—42no—
242C4—91no—
243C4—91no—
244C4—92no—
245C4—181no—
246C4—181no—
247C4#6428312yes—
248C3—22no—
249C2—22no—
250C2—364no—
251C2#1059380211yescharacteristic
252C2C2×#6378211yescharacteristic
253C2#1059383111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
3. #10593801C2semidirect
4. #10590160C2semidirect
18. C4⋊#622C22semidirect
19. C4×#622C22semidirect
73. C4⋊(C3⋊D3)M16semidirect
201. C32#1486semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105938052
#105938012
#105901602
#14869