Finite Group Databasebeta

← #11787869

Subgroups — #11787869

Order 1152.

1332 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 1332 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×#127C211yesmaximal, characteristic
2#10596269C211yesmaximal, characteristic, complemented
3C2×#63660C211yesmaximal, characteristic, complemented
4#10592914C212yesmaximal, complemented
5#10589389C212yesmaximal, complemented
6#71763—34nomaximal
7C22×C32×D4—22no—
8C22×C32×D4C2211yescharacteristic
9C22×C32×D4C2211yescharacteristic
10C32×#127—22no—
11C32×#127C414yescomplemented
12C2×C32×C42C2211yescharacteristic
13C2×#3757—22no—
14D4×C3⋊Dic3—24no—
15#64135C2212yes—
16C2×#3748C2212yes—
17#63660—22no—
18#63659—24no—
19C2×C3×#127D314yes—
20#5798—34no—
21C2×#833—34no—
22#5215—38no—
23#4523—38no—
24C24×C32—21no—
25C24×C32D412yes—
26C2×C32×D4—28no—
27C2×C32×D4—22no—
28C2×C32×D4—22no—
29C2×C32×D4—21no—
30C2×C32×D4—22no—
31C2×C32×D4—22no—
32C2×C32×D4—48no—
33C2×C32×D4C2×C412yes—
34C2×C32×D4C2×C412yescomplemented
35C2×C32×D4D412yes—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—24no—
39C32×C42—21no—
40C32×C42C2×C412yescomplemented
41#3757—24no—
42#3757—22no—
43C4⋊(C3⋊Dic3)D414yescomplemented
44C4×C3⋊Dic3—22no—
45#3748—22no—
46#3748—22no—
47C2×C3⋊(C3⋊C8)—22no—
48#1887—91noSylow
49C22×C3×D4—28no—
50C22×C3×D4C2×D314yes—
51C22×C3×D4C2×D314yes—
52C3×#127—28no—
53C3×#127Dic3116yescomplemented
54C2×C3×C42C2×D314yes—
55C2×#217—68no—
56D4×Dic3—616no—
57#926—38no—
58C2×#208—38no—
59#833—68no—
60#832—616no—
61C23×C32—22no—
62C23×C32—22no—
63C23×C32—22no—
64C23×C32—44no—
65C23×C32—44no—
66C23×C32—41no—
67C23×C32—41no—
68C23×C32C22⋊C414yes—
69C23×C32C2×D411yescharacteristic
70C32×D4—24no—
71C32×D4—24no—
72C32×D4—24no—
73C32×D4—416no—
74C32×D4—42no—
75C2×C32×C4—24no—
76C2×C32×C4—22no—
77C2×C32×C4C22×C411yescharacteristic
78C2×C32×C4C2×D412yes—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4#4112yes—
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3—84no—
83C3⋊(C3⋊C8)—42no—
84C2×#127C3⋊D311yescharacteristic
85#518—91no—
86#418—92no—
87C2×#100—91no—
88#339—92no—
89C24×C3—24no—
90C24×C3#6718yes—
91C2×C3×D4—232no—
92C2×C3×D4—28no—
93C2×C3×D4—28no—
94C2×C3×D4—28no—
95C2×C3×D4—28no—
96C2×C3×D4—24no—
97C2×C3×D4—432no—
98C2×C3×D4C2×Dic318yes—
99C2×C3×D4C2×Dic318yescomplemented
100C2×C3×D4#6718yes—
101C22×C3×C4—24no—
102C22×C3×C4C22×D314yes—
103C22×Dic3—616no—
104C3×C42—24no—
105C3×C42C2×Dic318yescomplemented
106#217—616no—
107#217—68no—
108C4⋊Dic3—316no—
109C4×Dic3—68no—
110#208—68no—
111#208—68no—
112C2×C3⋊C8—68no—
113C22×C32—22no—
114C22×C32—24no—
115C22×C32—44no—
116C22×C32—44no—
117C22×C32—44no—
118C22×C32—42no—
119C22×C32—82no—
120C22×C32—82no—
121C22×C32—82no—
122C22×C32C2×C22⋊C411yescharacteristic
123C22×C32#12011yescharacteristic
124C22×C32#12311yescharacteristic
125C32×C4—24no—
126C32×C4C4×D412yes—
127C32×C4#12112yes—
128C3⋊Dic3—44no—
129C22×D4—22no—
130C22×D4C2×C3⋊D311yescharacteristic
131C22×D4C2×C3⋊D311yescharacteristic
132C2×M16—92no—
133#127—22no—
134#127C3⋊Dic314yescomplemented
135C4×D4—184no—
136#117—92no—
137C2×C22⋊C4—182no—
138C2×C42C2×C3⋊D311yescharacteristic
139#102—184no—
140#100—182no—
141C23×C3—28no—
142C23×C3—28no—
143C23×C3—28no—
144C23×C3—416no—
145C23×C3—416no—
146C23×C3—44no—
147C23×C3—44no—
148C23×C3#217116yes—
149C23×C3C2×#6714yes—
150C3×D4—216no—
151C3×D4—216no—
152C3×D4—216no—
153C3×D4—464no—
154C3×D4—48no—
155C2×C3×C4—216no—
156C2×C3×C4—28no—
157C2×C3×C4D3×D418yes—
158C2×C3×C4#23718yes—
159C2×C3×C4C22×Dic314yes—
160C2×C3×C4C2×#6714yes—
161C2×Dic3—616no—
162C2×Dic3—2416no—
163C3⋊C8—128no—
164C2×C32—21no—
165C2×C32—21no—
166C2×C32—44no—
167C2×C32—82no—
168C2×C32#38611yescharacteristic
169C2×C32#45312yes—
170C24—21no—
171C24#63812yes—
172C2×D4—28no—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—22no—
177C2×D4—21no—
178C2×D4—48no—
179C2×D4C2×C3⋊Dic312yes—
180C2×D4C2×C3⋊Dic312yescomplemented
181C2×D4#63812yes—
182C22×C4—21no—
183C22×C4—184no—
184C22×C4C22×C3⋊D311yescharacteristic
185M16—182no—
186M16—182no—
187C2×C8—182no—
188C4⋊C4—94no—
189C22⋊C4—184no—
190C22⋊C4—182no—
191C42—21no—
192C42—182no—
193C42C2×C3⋊Dic312yescomplemented
194C22×C3—28no—
195C22×C3—216no—
196C22×C3—416no—
197C22×C3—416no—
198C22×C3—416no—
199C22×C3—48no—
200C22×C3—88no—
201C22×C3—88no—
202C22×C3—88no—
203C22×C3#93514yes—
204C22×C3#93714yes—
205C22×C3C2×#21714yes—
206C3×C4—216no—
207C3×C4D4×Dic318yes—
208C3×C4#93918yes—
209Dic3—1216no—
210C32#188711yescharacteristic, complemented, Sylow
211C23—22no—
212C23—22no—
213C23—22no—
214C23—44no—
215C23—44no—
216C23—41no—
217C23—41no—
218C23#375714yes—
219C23C2×#63811yescharacteristic
220D4—24no—
221D4—24no—
222D4—24no—
223D4—416no—
224D4—42no—
225C2×C4—24no—
226C2×C4—22no—
227C2×C4—184no—
228C2×C4—724no—
229C2×C4D4×C3⋊D312yes—
230C2×C4#383012yes—
231C2×C4C22×C3⋊Dic311yescharacteristic
232C2×C4C2×#63811yescharacteristic
233C8—362no—
234C2×C3—24no—
235C2×C3—24no—
236C2×C3—416no—
237C2×C3—88no—
238C2×C3#507718yes—
239C2×C3#522014yes—
240C22—22no—
241C22—24no—
242C22—44no—
243C22—44no—
244C22—44no—
245C22—42no—
246C22—82no—
247C22—82no—
248C22—82no—
249C22#6414411yescharacteristic
250C22#6414611yescharacteristic
251C22C2×#375711yescharacteristic
252C4—24no—
253C4—364no—
254C4D4×C3⋊Dic312yes—
255C4#6414812yes—
256C3#7176314yescomplemented
257C2—21no—
258C2—21no—
259C2—44no—
260C2—82no—
261C2#1059277612yes—
262C2#1059291911yescharacteristic
subgroupG/H
centerC22#64146
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
Fitting, prime radicalC2×C32×#127C2
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC2×#127C3⋊D3
hypocenterC32#1887
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
2. #10596269C2semidirect
3. C2×#63660C2semidirect
4. #10592914C2semidirect
5. #10589389C2semidirect
11. C32×#127C4semidirect
34. C2×C32×D4C2×C4semidirect
40. C32×C42C2×C4semidirect
43. C4⋊(C3⋊Dic3)D4semidirect
53. C3×#127Dic3semidirect
99. C2×C3×D4C2×Dic3semidirect
105. C3×C42C2×Dic3semidirect
134. #127C3⋊Dic3semidirect
180. C2×D4C2×C3⋊Dic3semidirect
193. C42C2×C3⋊Dic3semidirect
210. C32#1887semidirect
256. C3#71763semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1272
#105962692
C2×#636602
#105929142
#105893892
#717633