Finite Group Databasebeta

← #11774683

Subgroups — #11774683

Order 1152.

742 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 68 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#10593806C211yesmaximal, characteristic, complemented
3C4×#3792C211yesmaximal, 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#63777—21no—
17#63777—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—44no—
32#3792—24no—
33C2×#622—22no—
34C2×#622—22no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4C2×C412yes—
37#3752—22no—
38#3752—22no—
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3C2311yescharacteristic
43#1490—91nomaximal, Sylow
44C22×D12—62no—
45C22×C4×D3—64no—
46C2×C3×C4⋊C4—22no—
47C2×(C2×D3)⋊C4—64no—
48C2×C4×Dic3—62no—
49#893—64no—
50#893—64no—
51#893—64no—
52#893—64no—
53C23×C32C22⋊C411yescharacteristic
54C22×C3⋊D3—24no—
55C22×C3⋊D3—22no—
56C22×C3⋊D3—42no—
57C22×C3⋊D3—42no—
58C2×C32×C4—22no—
59C2×C32×C4—22no—
60C2×C32×C4—42no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22×C411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C4⋊(C3⋊D3)—24no—
70C4⋊(C3⋊D3)—22no—
71C4⋊(C3⋊D3)M1614yescomplemented
72C4×C3⋊D3—44no—
73C4×C3⋊D3—44no—
74#622—24no—
75#622—42no—
76C2×C4×D4—91no—
77#432—91no—
78C4×M16—91no—
79D4⋊C8—94no—
80C23×D3—64no—
81C22×C3×C4—24no—
82C22×C3×C4—22no—
83C22×Dic3—62no—
84C22×Dic3—62no—
85C2×D12—64no—
86C2×D12—64no—
87C2×D12—616no—
88C2×C4×D3—68no—
89C2×C4×D3—68no—
90C2×C4×D3—1216no—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—24no—
93(C2×D3)⋊C4—68no—
94(C2×D3)⋊C4—68no—
95C4×Dic3—62no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32#10412yes—
102C22×C32C2×C22⋊C411yescharacteristic
103C2×C3⋊D3—24no—
104C2×C3⋊D3—48no—
105C2×C3⋊D3—42no—
106C2×C3⋊D3—42no—
107C32×C4—21no—
108C32×C4—42no—
109C32×C4C2×M1612yes—
110C3⋊Dic3—21no—
111C3⋊Dic3—21no—
112C3⋊Dic3—21no—
113C3⋊Dic3AGL(1,ℤ/8)12yes—
114C22×D4—91no—
115C23×C4—181no—
116C2×M16—181no—
117C4×D4—92no—
118C4×D4—92no—
119C4×D4—181no—
120C4×D4—181no—
121C2×C4⋊C4#15711yescharacteristic
122C2×C22⋊C4—181no—
123C2×C42—91no—
124C4⋊C8—92no—
125C22⋊C8—181no—
126#97—181no—
127#97—181no—
128C4×C8—92no—
129C23×C3—22no—
130C22×D3—68no—
131C22×D3—616no—
132C22×D3—128no—
133C22×D3—128no—
134C2×C3×C4—28no—
135C2×C3×C4—28no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138C2×C3×C4—48no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—68no—
144C2×Dic3—124no—
145D12—68no—
146D12—616no—
147D12—68no—
148C4×D3—1216no—
149C4×D3—1216no—
150C2×C32—22no—
151C2×C32#40711yescharacteristic
152C2×C32#41811yescharacteristic
153C2×C32C2×#10411yescharacteristic
154C3⋊D3—44no—
155C24—181no—
156C2×D4—92no—
157C2×D4—184no—
158C2×D4—181no—
159C22×C4—21no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—182no—
163C22×C4—182no—
164C22×C4—364no—
165C22×C4C2×#15711yescharacteristic
166M16—184no—
167C2×C8—182no—
168C2×C8—182no—
169C4⋊C4—21no—
170C4⋊C4C2×#15712yes—
171C22⋊C4—182no—
172C22⋊C4—182no—
173C42—91no—
174C42—91no—
175C42—91no—
176C42—91no—
177C22×C3—24no—
178C22×C3—24no—
179C22×C3—22no—
180C22×C3—24no—
181C2×D3—616no—
182C2×D3—128no—
183C2×D3—1232no—
184C2×D3—128no—
185C3×C4—24no—
186C3×C4—24no—
187C3×C4—48no—
188Dic3—64no—
189Dic3—64no—
190Dic3—122no—
191Dic3—122no—
192C32#149011yescharacteristic, complemented, Sylow
193C23—184no—
194C23—182no—
195C23—362no—
196C23—362no—
197C23C22⋊#15711yescharacteristic
198D4—94no—
199D4—184no—
200D4—182no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—182no—
209C2×C4—182no—
210C2×C4—364no—
211C2×C4—364no—
212C2×C4C22⋊#15711yescharacteristic
213C2×C4C22×#15711yescharacteristic
214C8—184no—
215C8—362no—
216C2×C3—28no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—22no—
220D3—1216no—
221C22—21no—
222C22—21no—
223C22—184no—
224C22—368no—
225C22—362no—
226C22—362no—
227C22#6378512yes—
228C22C2×C22⋊#15711yescharacteristic
229C4—21no—
230C4—42no—
231C4—92no—
232C4—181no—
233C4—181no—
234C4—181no—
235C4#6428312yes—
236C3—22no—
237C2—22no—
238C2—364no—
239C2#1059380211yescharacteristic
240C2#1059381411yescharacteristic
241C2C2×#6378511yescharacteristic
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#1490
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. #10593806C2semidirect
3. C4×#3792C2semidirect
4. #10590160C2semidirect
18. C4⋊#622C22semidirect
19. C4×#622C22semidirect
71. C4⋊(C3⋊D3)M16semidirect
192. C32#1490semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105938062
C4×#37922
#105901602
#14909