Finite Group Databasebeta

← #11773871

Subgroups — #11773871

Order 1152.

936 conjugacy classes of subgroups; only the 257 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 257 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×C32×C4⋊C4C211yesmaximal, characteristic
2#10592906C212yesmaximal
3#10589394C214yesmaximal, complemented
4#71552—34nomaximal
5C23×C32×C4C411yescharacteristic
6C23×C32×C4C411yescharacteristic
7C23×C32×C4C2211yescharacteristic
8C2×C32×C4⋊C4—22no—
9C2×C32×C4⋊C4—22no—
10C2×C32×C4⋊C4C412yes—
11C2×C32×C4⋊C4C2212yes—
12C2×#3748—22no—
13#63657—22no—
14#63657C2214yes—
15C22×C3×C4⋊C4D314yes—
16#5207—38no—
17#4528—316no—
18C24×C32C2×C411yescharacteristic
19C22×C32×C4—21no—
20C22×C32×C4—21no—
21C22×C32×C4—24no—
22C22×C32×C4—21no—
23C22×C32×C4—21no—
24C22×C32×C4—42no—
25C22×C32×C4—42no—
26C22×C32×C4C2×C412yes—
27C22×C32×C4C2×C412yes—
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D412yes—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C32×C4⋊C4—24no—
33C32×C4⋊C4—24no—
34#3748—44no—
35C2×C3⋊(C3⋊C8)—24no—
36#1463—91noSylow
37C23×C3×C4Dic314yes—
38C23×C3×C4Dic314yes—
39C23×C3×C4C2×D314yes—
40C2×C3×C4⋊C4—28no—
41C2×C3×C4⋊C4—28no—
42C2×C3×C4⋊C4Dic318yes—
43C2×C3×C4⋊C4C2×D318yes—
44C2×#208—68no—
45#830—316no—
46#830—68no—
47C23×C32—22no—
48C23×C32—22no—
49C23×C32—22no—
50C23×C32C22⋊C411yescharacteristic
51C23×C32C22⋊C411yescharacteristic
52C23×C32C22×C411yescharacteristic
53C2×C32×C4—24no—
54C2×C32×C4—24no—
55C2×C32×C4—24no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—41no—
60C2×C32×C4—42no—
61C2×C32×C4—41no—
62C2×C32×C4—42no—
63C2×C32×C4—42no—
64C2×C32×C4—42no—
65C2×C32×C4C22⋊C412yes—
66C2×C32×C4M1614yescomplemented
67C2×C32×C4C2×D412yes—
68C3⋊(C3⋊C8)—44no—
69C22×C4⋊C4C3⋊D311yescharacteristic
70#407—92no—
71#324—94no—
72C24×C3C2×Dic314yes—
73C22×C3×C4—24no—
74C22×C3×C4—24no—
75C22×C3×C4—216no—
76C22×C3×C4—24no—
77C22×C3×C4—24no—
78C22×C3×C4—48no—
79C22×C3×C4—48no—
80C22×C3×C4C2×Dic318yes—
81C22×C3×C4C2×Dic318yes—
82C22×C3×C4C2×Dic314yes—
83C22×C3×C4#6718yes—
84C22×C3×C4#6718yes—
85C22×C3×C4C22×D314yes—
86C3×C4⋊C4—216no—
87C3×C4⋊C4—216no—
88#208—1216no—
89C2×C3⋊C8—616no—
90C22×C32—28no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32#9912yes—
98C22×C32#10112yes—
99C22×C32C2×C22⋊C411yescharacteristic
100C22×C32C2×M1612yes—
101C32×C4—24no—
102C32×C4—22no—
103C32×C4—22no—
104C32×C4—42no—
105C23×C4C3⋊Dic311yescharacteristic
106C23×C4C3⋊Dic311yescharacteristic
107C23×C4C2×C3⋊D311yescharacteristic
108C2×M16—182no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4C3⋊Dic312yes—
112C2×C4⋊C4C2×C3⋊D312yes—
113C22⋊C8—94no—
114C22⋊C8—182no—
115C23×C3—28no—
116C23×C3—28no—
117C23×C3—28no—
118C23×C3#21714yes—
119C23×C3#21714yes—
120C23×C3C22×Dic314yes—
121C2×C3×C4—216no—
122C2×C3×C4—216no—
123C2×C3×C4—216no—
124C2×C3×C4—28no—
125C2×C3×C4—28no—
126C2×C3×C4—28no—
127C2×C3×C4—44no—
128C2×C3×C4—48no—
129C2×C3×C4—44no—
130C2×C3×C4—48no—
131C2×C3×C4—48no—
132C2×C3×C4—48no—
133C2×C3×C4#208116yescomplemented
134C2×C3×C4#21718yes—
135C2×C3×C4C2×#6718yes—
136C3⋊C8—1216no—
137C2×C32—22no—
138C2×C32—22no—
139C2×C32—22no—
140C2×C32#40711yescharacteristic
141C2×C32C2×#9911yescharacteristic
142C2×C32C2×#10111yescharacteristic
143C24C2×C3⋊Dic311yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—24no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4C2×C3⋊Dic312yes—
152C22×C4C2×C3⋊Dic312yes—
153C22×C4C2×C3⋊Dic311yescharacteristic
154C22×C4#63812yes—
155C22×C4#63812yes—
156C22×C4C22×C3⋊D311yescharacteristic
157M16—364no—
158C2×C8—184no—
159C4⋊C4—24no—
160C4⋊C4—24no—
161C22×C3—232no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3—24no—
167C22×C3—24no—
168C22×C3#83418yes—
169C22×C3#83618yes—
170C22×C3C2×#20818yes—
171C22×C3C2×#21714yes—
172C3×C4—216no—
173C3×C4—28no—
174C3×C4—28no—
175C3×C4—48no—
176C32#146311yescharacteristic, complemented, Sylow
177C23—22no—
178C23—22no—
179C23—22no—
180C23#375711yescharacteristic
181C23#375711yescharacteristic
182C23C22×C3⋊Dic311yescharacteristic
183C2×C4—24no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4#374814yescomplemented
196C2×C4#375712yes—
197C2×C4C2×#63812yes—
198C8—364no—
199C2×C3—28no—
200C2×C3—28no—
201C2×C3—28no—
202C2×C3#520714yes—
203C2×C3C2×#83414yes—
204C2×C3C2×#83614yes—
205C22—28no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22#6366112yes—
213C22#6366312yes—
214C22C2×#374812yes—
215C22C2×#375711yescharacteristic
216C4—24no—
217C4—22no—
218C4—22no—
219C4—42no—
220C3#7155214yescomplemented
221C2—22no—
222C2—22no—
223C2—22no—
224C2#1059290611yescharacteristic
225C2C2×#6366111yescharacteristic
226C2C2×#6366311yescharacteristic
subgroupG/H
centerC22C2×#3757
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC22×C32×C4⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C4⋊C4C3⋊D3
hypocenterC32#1463
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10589394C2semidirect
66. C2×C32×C4M16semidirect
133. C2×C3×C4#208semidirect
176. C32#1463semidirect
195. C2×C4#3748semidirect
220. C3#71552semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
#105929062
#105893942
#715523