Finite Group Databasebeta

← #11788713

Subgroups — #11788713

Order 1152.

936 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 249 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
1C32×#536C211yesmaximal, characteristic
2#10596290C211yesmaximal, characteristic
3#10592939C211yesmaximal, characteristic
4#10592924C212yesmaximal, complemented
5#10589397C212yesmaximal, complemented
6#71865—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C22×C32×Q8C2211yescharacteristic
9C32×C4⋊Q8C412yescomplemented
10C32×#124C412yescomplemented
11C32×#123—22no—
12C32×C22⋊Q8—22no—
13C32×#117C2211yescharacteristic
14#64157—24no—
15#64135C2212yes—
16C2×#3748—22no—
17C2×#3748C2212yes—
18#63662—24no—
19#63661—22no—
20C3×#536D314yes—
21#5819—34no—
22#5240—34no—
23#5225—38no—
24#4531—38no—
25C32×#41—22no—
26C32×#41—22no—
27C2×C32×Q8—21no—
28C2×C32×Q8—22no—
29C2×C32×Q8—22no—
30C2×C32×Q8C2×C412yes—
31C2×C32×Q8C2×C411yescharacteristic
32C2×C32×D4C2×C411yescharacteristic
33C2×C32×D4D412yes—
34C22×C32×C4—21no—
35C22×C32×C4D412yes—
36C22×C32×C4C2311yescharacteristic
37C32×C4⋊C4—24no—
38C32×C4⋊C4—21no—
39C32×C22⋊C4—24no—
40C32×C22⋊C4—21no—
41C32×C42C2×C412yes—
42#3757—22no—
43C4⋊(C3⋊Dic3)—22no—
44C4×C3⋊Dic3—22no—
45#3748—24no—
46#3748—22no—
47#3748—22no—
48C2×C3⋊(C3⋊C8)—24no—
49C2×C3⋊(C3⋊C8)D414yes—
50#1909—91noSylow
51C2×C3×#41C2×D314yes—
52C22×C3×Q8C2×D314yes—
53C3×C4⋊Q8Dic318yescomplemented
54C3×#124Dic318yescomplemented
55C3×#123—28no—
56C3×C22⋊Q8—28no—
57C3×#117C2×D314yes—
58#948—616no—
59#926—38no—
60C2×#208—38no—
61C2×#208—68no—
62#835—616no—
63#834—68no—
64C23×C32C22⋊C412yes—
65C23×C32C2×D411yescharacteristic
66C32×Q8—22no—
67C32×Q8—24no—
68C32×Q8—41no—
69C32×Q8—41no—
70C32×D4—24no—
71C32×D4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4—22no—
76C2×C32×C4—42no—
77C2×C32×C4C22⋊C412yes—
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D412yes—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4#4112yes—
82C2×C3⋊Dic3—42no—
83C3⋊(C3⋊C8)—24no—
84#568—91no—
85#536C3⋊D311yescharacteristic
86#419—92no—
87#410—91no—
88H(3,ℤ/4)—92no—
89C3×#41—28no—
90C3×#41—28no—
91C2×C3×Q8—24no—
92C2×C3×Q8—28no—
93C2×C3×Q8—28no—
94C2×C3×Q8C2×Dic318yes—
95C2×C3×Q8C2×Dic314yes—
96C2×C3×D4C2×Dic314yes—
97C2×C3×D4#6718yes—
98C22×C3×C4—24no—
99C22×C3×C4#6718yes—
100C22×C3×C4C22×D314yes—
101C3×C4⋊C4—216no—
102C3×C4⋊C4—24no—
103C3×C22⋊C4—216no—
104C3×C22⋊C4—24no—
105C3×C42C2×Dic318yes—
106#217—68no—
107C4⋊Dic3—68no—
108C4×Dic3—68no—
109#208—616no—
110#208—68no—
111#208—68no—
112C2×C3⋊C8—316no—
113C2×C3⋊C8—616no—
114C22×C32—22no—
115C22×C32—41no—
116C22×C32—42no—
117C22×C32C2×C22⋊C411yescharacteristic
118C22×C32#12112yes—
119C32×C4—22no—
120C32×C4—42no—
121C32×C4—42no—
122C32×C4C4×D412yes—
123C32×C4#12011yescharacteristic
124C32×C4#12311yescharacteristic
125C3⋊Dic3—82no—
126C2×#41C2×C3⋊D311yescharacteristic
127C22×Q8C2×C3⋊D311yescharacteristic
128#131—184no—
129C2×M16—92no—
130C2×M16—182no—
131C4⋊Q8C3⋊Dic312yescomplemented
132#124C3⋊Dic312yescomplemented
133#123—22no—
134C22⋊Q8—22no—
135#117—92no—
136#117C2×C3⋊D311yescharacteristic
137#103—184no—
138#99—182no—
139C23×C3#21718yes—
140C23×C3C2×#6714yes—
141C3×Q8—28no—
142C3×Q8—216no—
143C3×Q8—44no—
144C3×Q8—44no—
145C3×D4—216no—
146C3×D4—28no—
147C2×C3×C4—28no—
148C2×C3×C4—28no—
149C2×C3×C4—28no—
150C2×C3×C4—28no—
151C2×C3×C4—48no—
152C2×C3×C4#21718yes—
153C2×C3×C4D3×D418yes—
154C2×C3×C4#23718yes—
155C2×C3×C4C22×Dic314yes—
156C2×C3×C4C2×#6714yes—
157C2×Dic3—128no—
158C3⋊C8—616no—
159C2×C32—22no—
160C2×C32—21no—
161C2×C32—42no—
162C2×C32#38611yescharacteristic
163#41—22no—
164#41—22no—
165C2×Q8—21no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8C2×C3⋊Dic312yes—
169C2×Q8C2×C3⋊Dic311yescharacteristic
170C2×D4C2×C3⋊Dic311yescharacteristic
171C2×D4#63812yes—
172C22×C4—21no—
173C22×C4#63812yes—
174C22×C4C22×C3⋊D311yescharacteristic
175M16—184no—
176M16—182no—
177M16—182no—
178C2×C8—94no—
179C2×C8—184no—
180C4⋊C4—24no—
181C4⋊C4—21no—
182C4⋊C4—182no—
183C22⋊C4—24no—
184C22⋊C4—21no—
185C22⋊C4—182no—
186C42—182no—
187C42C2×C3⋊Dic312yes—
188C22×C3—28no—
189C22×C3—44no—
190C22×C3—48no—
191C22×C3#93918yes—
192C22×C3C2×#21714yes—
193C3×C4—28no—
194C3×C4—48no—
195C3×C4—48no—
196C3×C4D4×Dic318yes—
197C3×C4#93514yes—
198C3×C4#93714yes—
199Dic3—248no—
200C32#190911yescharacteristic, complemented, Sylow
201C23#375712yes—
202C23C2×#63811yescharacteristic
203Q8—22no—
204Q8—24no—
205Q8—41no—
206Q8—41no—
207D4—24no—
208D4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—362no—
215C2×C4#375712yes—
216C2×C4D4×C3⋊D312yes—
217C2×C4#383012yes—
218C2×C4C22×C3⋊Dic311yescharacteristic
219C2×C4C2×#63811yescharacteristic
220C8—184no—
221C2×C3—28no—
222C2×C3—24no—
223C2×C3—48no—
224C2×C3#522014yes—
225C22—22no—
226C22—41no—
227C22—42no—
228C22#6414812yes—
229C22C2×#375711yescharacteristic
230C4—22no—
231C4—42no—
232C4—42no—
233C4—722no—
234C4D4×C3⋊Dic312yes—
235C4#6414411yescharacteristic
236C4#6414611yescharacteristic
237C3#7186514yescomplemented
238C2—21no—
239C2—22no—
240C2—42no—
241C2#1059291911yescharacteristic
subgroupG/H
centerC2#10592919
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#536C2
socleC2×C32#386
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenter#536C3⋊D3
hypocenterC32#1909
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
4. #10592924C2semidirect
5. #10589397C2semidirect
9. C32×C4⋊Q8C4semidirect
10. C32×#124C4semidirect
53. C3×C4⋊Q8Dic3semidirect
54. C3×#124Dic3semidirect
131. C4⋊Q8C3⋊Dic3semidirect
132. #124C3⋊Dic3semidirect
200. C32#1909semidirect
237. C3#71865semidirect

Maximal subgroups

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

subgroupindex
C32×#5362
#105962902
#105929392
#105929242
#105893972
#718653