Finite Group Databasebeta

← #11787805

Subgroups — #11787805

Order 1152.

1080 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 261 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×C32×#124C211yesmaximal, characteristic
2#10596269C211yesmaximal, characteristic
3#10592924C212yesmaximal, complemented
4C2×#63660C211yesmaximal, characteristic
5#10589389C212yesmaximal, complemented
6#71723—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C22×C32×D4C2211yescharacteristic
9C32×#124—22no—
10C32×#124C414yescomplemented
11C2×C32×C22⋊C4—22no—
12C2×C32×C42C2211yescharacteristic
13C2×#3757—22no—
14D4×C3⋊Dic3—24no—
15#64135C2212yes—
16C2×#3748C2212yes—
17#63662—24no—
18#63660—22no—
19C2×C3×#124D314yes—
20#5798—34no—
21#5225—38no—
22C2×#833—34no—
23#4523—38no—
24C24×C32D412yes—
25C2×C32×Q8—21no—
26C2×C32×Q8—22no—
27C2×C32×Q8—22no—
28C2×C32×Q8C2×C412yescomplemented
29C2×C32×D4—22no—
30C2×C32×D4—22no—
31C2×C32×D4C2×C412yes—
32C2×C32×D4D412yes—
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—24no—
37C32×C22⋊C4—28no—
38C32×C42—21no—
39C32×C42C2×C412yescomplemented
40#3757—24no—
41#3757—22no—
42C4⋊(C3⋊Dic3)D414yes—
43C4×C3⋊Dic3—22no—
44#3748—22no—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—22no—
47#1885—91noSylow
48C22×C3×Q8C2×D314yes—
49C22×C3×D4C2×D314yes—
50C3×#124—28no—
51C3×#124Dic3116yescomplemented
52C2×C3×C22⋊C4—28no—
53C2×C3×C42C2×D314yes—
54C2×#217—68no—
55D4×Dic3—616no—
56#926—38no—
57C2×#208—38no—
58#835—616no—
59#833—68no—
60C23×C32—22no—
61C23×C32—22no—
62C23×C32—44no—
63C23×C32C22⋊C414yes—
64C23×C32C2×D411yescharacteristic
65C32×Q8—24no—
66C32×Q8—42no—
67C32×D4—24no—
68C32×D4—24no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—42no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4C22×C411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4#4112yes—
78C2×C3⋊Dic3—24no—
79C2×C3⋊Dic3—84no—
80C3⋊(C3⋊C8)—42no—
81C2×#124C3⋊D311yescharacteristic
82#518—91no—
83#419—92no—
84C2×#100—91no—
85#339—92no—
86C24×C3#6718yes—
87C2×C3×Q8—24no—
88C2×C3×Q8—28no—
89C2×C3×Q8—28no—
90C2×C3×Q8C2×Dic318yescomplemented
91C2×C3×D4—28no—
92C2×C3×D4—28no—
93C2×C3×D4C2×Dic318yes—
94C2×C3×D4#6718yes—
95C22×C3×C4—24no—
96C22×C3×C4—24no—
97C22×C3×C4C22×D314yes—
98C22×Dic3—616no—
99C3×C22⋊C4—232no—
100C3×C42—24no—
101C3×C42C2×Dic318yescomplemented
102#217—616no—
103#217—68no—
104C4⋊Dic3—316no—
105C4×Dic3—68no—
106#208—68no—
107#208—68no—
108C2×C3⋊C8—68no—
109C22×C32—22no—
110C22×C32—24no—
111C22×C32—44no—
112C22×C32—44no—
113C22×C32—82no—
114C22×C32C2×C22⋊C411yescharacteristic
115C22×C32#12011yescharacteristic
116C22×C32#12311yescharacteristic
117C32×C4—42no—
118C32×C4—42no—
119C32×C4C4×D412yes—
120C32×C4#12112yes—
121C3⋊Dic3—44no—
122C22×Q8C2×C3⋊D311yescharacteristic
123C22×D4C2×C3⋊D311yescharacteristic
124C2×M16—92no—
125#124—22no—
126#124C3⋊Dic314yescomplemented
127C4×D4—184no—
128#117—92no—
129C2×C22⋊C4—22no—
130C2×C22⋊C4—182no—
131C2×C42C2×C3⋊D311yescharacteristic
132#103—184no—
133#100—182no—
134C23×C3—28no—
135C23×C3—28no—
136C23×C3—416no—
137C23×C3#217116yes—
138C23×C3C2×#6714yes—
139C3×Q8—216no—
140C3×Q8—48no—
141C3×D4—216no—
142C3×D4—216no—
143C2×C3×C4—28no—
144C2×C3×C4—28no—
145C2×C3×C4—48no—
146C2×C3×C4—44no—
147C2×C3×C4—44no—
148C2×C3×C4D3×D418yes—
149C2×C3×C4#23718yes—
150C2×C3×C4C22×Dic314yes—
151C2×C3×C4C2×#6714yes—
152C2×Dic3—616no—
153C2×Dic3—2416no—
154C3⋊C8—128no—
155C2×C32—21no—
156C2×C32—21no—
157C2×C32—44no—
158C2×C32#38611yescharacteristic
159C2×C32#45512yes—
160C24#63812yes—
161C2×Q8—21no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8C2×C3⋊Dic312yescomplemented
165C2×D4—22no—
166C2×D4—22no—
167C2×D4C2×C3⋊Dic312yes—
168C2×D4#63812yes—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—184no—
172C22×C4C22×C3⋊D311yescharacteristic
173M16—182no—
174M16—182no—
175C2×C8—182no—
176C4⋊C4—94no—
177C22⋊C4—28no—
178C22⋊C4—184no—
179C22⋊C4—182no—
180C42—21no—
181C42—182no—
182C42C2×C3⋊Dic312yescomplemented
183C22×C3—28no—
184C22×C3—216no—
185C22×C3—416no—
186C22×C3—416no—
187C22×C3—88no—
188C22×C3#93514yes—
189C22×C3#93714yes—
190C22×C3C2×#21714yes—
191C3×C4—48no—
192C3×C4—48no—
193C3×C4D4×Dic318yes—
194C3×C4#93918yes—
195Dic3—1216no—
196C32#188511yescharacteristic, complemented, Sylow
197C23—22no—
198C23—22no—
199C23—44no—
200C23#375714yes—
201C23C2×#63811yescharacteristic
202Q8—24no—
203Q8—42no—
204D4—24no—
205D4—24no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—184no—
212C2×C4—724no—
213C2×C4D4×C3⋊D312yes—
214C2×C4#383012yes—
215C2×C4C22×C3⋊Dic311yescharacteristic
216C2×C4C2×#63811yescharacteristic
217C8—362no—
218C2×C3—24no—
219C2×C3—24no—
220C2×C3—416no—
221C2×C3#506118yes—
222C2×C3#522014yes—
223C22—22no—
224C22—24no—
225C22—44no—
226C22—44no—
227C22—82no—
228C22#6414411yescharacteristic
229C22#6414611yescharacteristic
230C22C2×#375711yescharacteristic
231C4—42no—
232C4—42no—
233C4—364no—
234C4D4×C3⋊Dic312yes—
235C4#6414812yes—
236C3#7172314yescomplemented
237C2—21no—
238C2—21no—
239C2—44no—
240C2#1059276012yes—
241C2#1059291911yescharacteristic
subgroupG/H
centerC22#64146
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#124C2
socleC22×C32#120
prime radicalC22×C32×D4C22
cosocleC22×C32×C4C23
hypercenterC2×#124C3⋊D3
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
3. #10592924C2semidirect
5. #10589389C2semidirect
10. C32×#124C4semidirect
28. C2×C32×Q8C2×C4semidirect
39. C32×C42C2×C4semidirect
51. C3×#124Dic3semidirect
90. C2×C3×Q8C2×Dic3semidirect
101. C3×C42C2×Dic3semidirect
126. #124C3⋊Dic3semidirect
164. C2×Q8C2×C3⋊Dic3semidirect
182. C42C2×C3⋊Dic3semidirect
196. C32#1885semidirect
236. C3#71723semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1242
#105962692
#105929242
C2×#636602
#105893892
#717233