Finite Group Databasebeta

← #11783084

Subgroups — #11783084

Order 1152.

978 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C22×#3792C212yesmaximal
2C22×C4×C3⋊Dic3C211yesmaximal, characteristic
3#10590207C214yesmaximal, complemented
4C23×C32×C4C411yescharacteristic
5C23×C3⋊Dic3C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C2×#3792—24no—
8C2×#3792—24no—
9C2×#3792C418yescomplemented
10C22×#622C2214yes—
11C2×C4×C3⋊Dic3—24no—
12C2×C4×C3⋊Dic3C412yes—
13C2×C4×C3⋊Dic3C2212yes—
14C22×C4×Dic3—62no—
15C24×C32C2×C411yescharacteristic
16C22×C32×C4—22no—
17C22×C32×C4—24no—
18C22×C32×C4C2×C412yes—
19C22×C3⋊Dic3—22no—
20C22×C3⋊Dic3—24no—
21C22×C3⋊Dic3C2×C412yes—
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3C2×C414yes—
24C22×C3⋊Dic3D412yes—
25C22×C3⋊Dic3D414yes—
26C22×C3⋊Dic3Q812yes—
27C22×C3⋊Dic3C2311yescharacteristic
28#3792—216no—
29C2×#622—24no—
30C2×#622—24no—
31C2×#622C2×C418yescomplemented
32C4×C3⋊Dic3—24no—
33C4×C3⋊Dic3—24no—
34#1728—91nomaximal, Sylow
35C23×C3×C4—22no—
36C23×Dic3—62no—
37C23×Dic3—62no—
38C2×C4×Dic3—64no—
39C2×C4×Dic3—64no—
40C2×C4×Dic3—616no—
41C23×C32—22no—
42C23×C32—22no—
43C23×C32C4212yes—
44C23×C32C22⋊C412yes—
45C23×C32C4⋊C412yes—
46C23×C32C22×C411yescharacteristic
47C2×C32×C4—28no—
48C2×C32×C4—22no—
49C2×C32×C4—22no—
50C2×C32×C4M1614yescomplemented
51C2×C3⋊Dic3—28no—
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3C4212yes—
55C2×C3⋊Dic3C22⋊C412yes—
56C2×C3⋊Dic3C22⋊C418yes—
57C2×C3⋊Dic3C4⋊C412yes—
58C2×C3⋊Dic3C4⋊C418yes—
59C2×C3⋊Dic3M1614yescomplemented
60C2×C3⋊Dic3C22×C412yes—
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D412yes—
63C2×C3⋊Dic3C2×Q811yescharacteristic
64#622—28no—
65C22×M16—92no—
66C22×C42—91no—
67#336—94no—
68C24×C3—22no—
69C22×C3×C4—28no—
70C22×C3×C4—216no—
71C22×C3×C4—24no—
72C22×Dic3—62no—
73C22×Dic3—64no—
74C22×Dic3—68no—
75C22×Dic3—62no—
76C22×Dic3—68no—
77C22×Dic3—64no—
78C22×Dic3—64no—
79C22×Dic3—68no—
80C22×Dic3—616no—
81C4×Dic3—616no—
82C4×Dic3—616no—
83C22×C32—24no—
84C22×C32—22no—
85C22×C32—22no—
86C22×C32—24no—
87C22×C32#9514yes—
88C22×C32C2×C4211yescharacteristic
89C22×C32C2×C22⋊C411yescharacteristic
90C22×C32C2×C4⋊C411yescharacteristic
91C22×C32C2×M1612yes—
92C22×C32C2×M1612yes—
93C32×C4—24no—
94C3⋊Dic3—24no—
95C3⋊Dic3#9514yes—
96C3⋊Dic3C2×C22⋊C412yes—
97C3⋊Dic3C2×C4⋊C412yes—
98C23×C4—91no—
99C23×C4—91no—
100C23×C4#15711yescharacteristic
101C2×M16—98no—
102C2×M16—184no—
103C2×M16—184no—
104C22×C8—94no—
105C2×C42—92no—
106C2×C42—92no—
107C2×C42—184no—
108C23×C3—28no—
109C23×C3—28no—
110C23×C3—22no—
111C23×C3—24no—
112C23×C3—24no—
113C23×C3—24no—
114C2×C3×C4—28no—
115C2×C3×C4—232no—
116C2×C3×C4—28no—
117C2×C3×C4—28no—
118C2×Dic3—64no—
119C2×Dic3—64no—
120C2×Dic3—616no—
121C2×Dic3—64no—
122C2×Dic3—616no—
123C2×Dic3—68no—
124C2×Dic3—64no—
125C2×Dic3—64no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—68no—
129C2×Dic3—632no—
130C2×Dic3—68no—
131C2×C32—24no—
132C2×C32C2×#9511yescharacteristic
133C2×C32C4×M1612yes—
134C2×C32#40711yescharacteristic
135C2×C32#40711yescharacteristic
136C2×C32#42312yes—
137C24C2×#15711yescharacteristic
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—91no—
141C22×C4—91no—
142C22×C4—94no—
143C22×C4—92no—
144C22×C4—92no—
145C22×C4—94no—
146C22×C4—92no—
147C22×C4—184no—
148C22×C4—182no—
149C22×C4C2×#15712yes—
150M16—1816no—
151C2×C8—98no—
152C2×C8—184no—
153C2×C8—184no—
154C42—184no—
155C42—184no—
156C22×C3—28no—
157C22×C3—28no—
158C22×C3—216no—
159C22×C3—216no—
160C22×C3—24no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—24no—
164C22×C3—28no—
165C22×C3—22no—
166C3×C4—216no—
167Dic3—68no—
168Dic3—64no—
169Dic3—64no—
170Dic3—616no—
171C32#172811yescharacteristic, complemented, Sylow
172C23—22no—
173C23—22no—
174C23C4×#15712yes—
175C23C4⋊#15712yes—
176C23C22⋊#15712yes—
177C23C22×#15711yescharacteristic
178C2×C4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—92no—
182C2×C4—92no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—92no—
186C2×C4—98no—
187C2×C4—98no—
188C2×C4—92no—
189C2×C4—92no—
190C2×C4—94no—
191C2×C4—188no—
192C2×C4—182no—
193C2×C4—182no—
194C2×C4#379214yescomplemented
195C8—188no—
196C2×C3—216no—
197C2×C3—24no—
198C2×C3—22no—
199C2×C3—24no—
200C2×C3—22no—
201C2×C3—22no—
202C22—24no—
203C22—22no—
204C22—24no—
205C22—22no—
206C22#6378114yes—
207C22#6428312yes—
208C22C2×C4×#15711yescharacteristic
209C22C2×C4⋊#15711yescharacteristic
210C22C2×#379212yes—
211C22C2×C22⋊#15711yescharacteristic
212C4—24no—
213C4—92no—
214C4—92no—
215C4—94no—
216C4—184no—
217C3—22no—
218C2—24no—
219C2C4×#379212yes—
220C2#1059380211yescharacteristic
221C2#1059380512yes—
222C2C2×#6378111yescharacteristic
223C2#1059384511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC23×C32×C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32#1728
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10590207C2semidirect
9. C2×#3792C4semidirect
31. C2×#622C2×C4semidirect
50. C2×C32×C4M16semidirect
59. C2×C3⋊Dic3M16semidirect
171. C32#1728semidirect
194. C2×C4#3792semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C22×C4×C3⋊Dic32
#105902072
#17289