Finite Group Databasebeta

← #11787802

Subgroups — #11787802

Order 1152.

1080 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 241 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×#518C211yesmaximal, characteristic
2C2×#64145C211yesmaximal, characteristic
3C2×#63660C211yesmaximal, characteristic
4#10592703C212yesmaximal, complemented
5#10589398C212yesmaximal, complemented
6#71649—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#634C2211yescharacteristic
9C32×C4×D4—24no—
10C32×#117C2212yes—
11C2×C32×C22⋊C4—22no—
12C2×#3757—22no—
13#64145—22no—
14#64145C414yescomplemented
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2212yes—
17#63660—22no—
18#63637—24no—
19C3×#518D314yes—
20C2×#936—34no—
21C2×#833—34no—
22#5004—38no—
23#4532—38no—
24C24×C32D412yes—
25C2×C32×D4—22no—
26C2×C32×D4—22no—
27C2×C32×D4C2×C412yes—
28C2×C32×D4D412yes—
29C22×C32×C4—24no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—21no—
33C2×#634—22no—
34C2×#634—22no—
35C2×#634—21no—
36C2×#634C2×C412yescomplemented
37C32×C4⋊C4D414yes—
38C32×C22⋊C4—24no—
39C32×C22⋊C4—22no—
40C32×C42—22no—
41#3757—28no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3C2×C412yescomplemented
44#3748—22no—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—22no—
47#1885—91noSylow
48C22×C3×D4C2×D314yes—
49C22×Dic6—34no—
50C3×C4×D4—216no—
51C3×#117C2×D318yes—
52C2×C3×C22⋊C4—28no—
53C2×#217—68no—
54#936—316no—
55#936—68no—
56C2×C4×Dic3—34no—
57C2×#208—38no—
58#833—68no—
59#810—616no—
60C23×C32—22no—
61C23×C32—22no—
62C23×C32—44no—
63C23×C32C22⋊C414yes—
64C23×C32C2×D411yescharacteristic
65C32×D4—24no—
66C32×D4—24no—
67C2×C32×C4—24no—
68C2×C32×C4—84no—
69C2×C32×C4C22×C411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×D412yes—
72C2×C32×C4#4112yes—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—42no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—41no—
78#634—24no—
79#634—42no—
80C3⋊(C3⋊C8)—42no—
81C2×#124—91no—
82#518C3⋊D311yescharacteristic
83#419—92no—
84C2×#100—91no—
85#339—92no—
86C24×C3#6718yes—
87C2×C3×D4—28no—
88C2×C3×D4—28no—
89C2×C3×D4C4×D318yes—
90C2×C3×D4D1218yes—
91C22×C3×C4—216no—
92C22×C3×C4C22×D314yes—
93C22×Dic3—64no—
94C22×Dic3—64no—
95C2×Dic6—38no—
96C2×Dic6—68no—
97C2×Dic6—68no—
98C2×Dic6—64no—
99C3×C4⋊C4#67116yes—
100C3×C22⋊C4—216no—
101C3×C22⋊C4—28no—
102C3×C42—28no—
103#217—632no—
104C4×Dic3—38no—
105C4×Dic3—64no—
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—44no—
118C32×C4C4×D412yes—
119C32×C4#12112yes—
120C3⋊Dic3—42no—
121C3⋊Dic3—42no—
122C22×Q8—91no—
123C22×D4C2×C3⋊D311yescharacteristic
124C2×M16—92no—
125#124—94no—
126#124—182no—
127C4×D4—24no—
128#117C2×C3⋊D312yes—
129C2×C22⋊C4—22no—
130C2×C22⋊C4—182no—
131C2×C42—91no—
132#103—184no—
133#100—182no—
134C23×C3—28no—
135C23×C3—28no—
136C23×C3—416no—
137C23×C3(C2×D3)⋊C4116yes—
138C23×C3C2×#6714yes—
139C3×D4—216no—
140C3×D4—216no—
141C2×C3×C4—216no—
142C2×C3×C4—816no—
143C2×C3×C4C2×C4×D314yes—
144C2×C3×C4C2×D1214yes—
145C2×C3×C4#23518yes—
146C2×C3×C4C2×#6718yes—
147C2×Dic3—68no—
148C2×Dic3—68no—
149C2×Dic3—128no—
150C2×Dic3—124no—
151C2×Dic3—124no—
152Dic6—616no—
153Dic6—128no—
154C3⋊C8—128no—
155C2×C32—21no—
156C2×C32—21no—
157C2×C32—44no—
158C2×C32#38611yescharacteristic
159C2×C32#45512yes—
160C24#63812yes—
161C2×Q8—92no—
162C2×Q8—181no—
163C2×Q8—182no—
164C2×Q8—182no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4C4×C3⋊D312yes—
168C2×D4C4⋊(C3⋊D3)12yes—
169C22×C4—24no—
170C22×C4—181no—
171C22×C4—181no—
172C22×C4C22×C3⋊D311yescharacteristic
173M16—182no—
174M16—182no—
175C2×C8—182no—
176C4⋊C4#63814yes—
177C22⋊C4—24no—
178C22⋊C4—22no—
179C22⋊C4—188no—
180C42—22no—
181C42—92no—
182C42—181no—
183C22×C3—28no—
184C22×C3—216no—
185C22×C3—416no—
186C22×C3—416no—
187C22×C3—88no—
188C22×C3C2×(C2×D3)⋊C414yes—
189C22×C3#92914yes—
190C22×C3#95314yes—
191C3×C4—416no—
192C3×C4C4×#6718yes—
193C3×C4#93018yes—
194Dic3—128no—
195Dic3—128no—
196C32#188511yescharacteristic, complemented, Sylow
197C23—22no—
198C23—22no—
199C23—44no—
200C23#375214yes—
201C23C2×#63811yescharacteristic
202Q8—184no—
203Q8—362no—
204D4—24no—
205D4—24no—
206C2×C4—24no—
207C2×C4—84no—
208C2×C4—182no—
209C2×C4—182no—
210C2×C4—362no—
211C2×C4—361no—
212C2×C4—361no—
213C2×C4C2×C4×C3⋊D311yescharacteristic
214C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
215C2×C4#382812yes—
216C2×C4C2×#63812yes—
217C8—362no—
218C2×C3—24no—
219C2×C3—24no—
220C2×C3—416no—
221C2×C3#521314yes—
222C2×C3#524218yes—
223C22—22no—
224C22—24no—
225C22—44no—
226C22—44no—
227C22—82no—
228C22C2×#375211yescharacteristic
229C22#6413811yescharacteristic
230C22#6416211yescharacteristic
231C4—44no—
232C4—362no—
233C4—362no—
234C4C4×#63812yes—
235C4#6413912yes—
236C3#7164914yescomplemented
237C2—21no—
238C2—21no—
239C2—44no—
240C2#1059291211yescharacteristic
241C2#1059294112yes—
subgroupG/H
centerC22#64162
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#518C2
socleC22×C32#120
prime radicalC22×C32×D4C22
cosocleC22×C32×C4C23
hypercenter#518C3⋊D3
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
4. #10592703C2semidirect
5. #10589398C2semidirect
14. #64145C4semidirect
36. C2×#634C2×C4semidirect
43. C4×C3⋊Dic3C2×C4semidirect
196. C32#1885semidirect
236. C3#71649semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C2×#641452
C2×#636602
#105927032
#105893982
#716493