Finite Group Databasebeta

← #11788809

Subgroups — #11788809

Order 1152.

942 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 229 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×#519C211yesmaximal, characteristic, complemented
2#10596287C211yesmaximal, characteristic
3C2×#63663C211yesmaximal, characteristic, complemented
4#10592704C212yesmaximal
5#10589397C212yesmaximal, complemented
6#71663—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9C32×C4×Q8—24no—
10C32×#117—22no—
11C32×#117C2212yes—
12#64156C412yescomplemented
13#64155—22no—
14#64153C412yescomplemented
15#64138—22no—
16#64135C2211yescharacteristic
17C2×#3748C2212yes—
18#63663—22no—
19#63632—24no—
20C3×#519D314yescomplemented
21#5816—34no—
22C2×#836—34no—
23#5005—38no—
24#4531—38no—
25C2×C32×Q8—22no—
26C2×C32×Q8—22no—
27C2×C32×Q8C2×C412yes—
28C2×C32×Q8D412yes—
29C22×C32×C4D412yes—
30C22×C32×C4C2311yescharacteristic
31C2×#638—21no—
32#3828—22no—
33#3828—22no—
34C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×#634C2×C411yescharacteristic
37C32×C4⋊C4—24no—
38C32×C4⋊C4—22no—
39C32×C22⋊C4—22no—
40C32×C42—24no—
41C32×C42D414yes—
42#3757—21no—
43#3752—24no—
44C4⋊(C3⋊Dic3)—21no—
45#3750—24no—
46C4×C3⋊Dic3C2×C412yes—
47#3748—22no—
48#3748—22no—
49C2×C3⋊(C3⋊C8)—22no—
50#1912—91noSylow
51C22×C3×Q8C2×D314yes—
52C2×#235—34no—
53C3×C4×Q8—216no—
54C3×#117—28no—
55C3×#117C2×D318yes—
56#947—38no—
57#946—68no—
58#944—38no—
59#929—68no—
60#926—34no—
61C2×#208—38no—
62#836—68no—
63#805—616no—
64C23×C32C2×D411yescharacteristic
65C22×C3⋊D3—21no—
66C32×Q8—24no—
67C32×Q8—24no—
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—24no—
71C2×C32×C4C22⋊C414yes—
72C2×C32×C4C22×C411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D412yes—
75C2×C32×C4#4112yes—
76#638—41no—
77#638—41no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—21no—
80C4⋊(C3⋊D3)—22no—
81C4×C3⋊D3—42no—
82#634—22no—
83C3⋊(C3⋊C8)—42no—
84#536—91no—
85#519C3⋊D311yescharacteristic, complemented
86#421—92no—
87C2×#101—91no—
88H(3,ℤ/4)—92no—
89C2×C3×Q8—28no—
90C2×C3×Q8—28no—
91C2×C3×Q8C4×D318yes—
92C2×C3×Q8D1218yes—
93C22×C3×C4#6718yes—
94C22×C3×C4C22×D314yes—
95C2×#67—64no—
96#235—68no—
97#235—68no—
98C2×D12—34no—
99C2×C4×D3—64no—
100C2×Dic6—34no—
101C3×C4⋊C4—216no—
102C3×C4⋊C4—28no—
103C3×C22⋊C4—28no—
104C3×C42—216no—
105C3×C42#67116yes—
106#217—64no—
107(C2×D3)⋊C4—616no—
108C4⋊Dic3—64no—
109Dic3⋊C4—616no—
110C4×Dic3—38no—
111#208—68no—
112#208—68no—
113C2×C3⋊C8—68no—
114C22×C32—41no—
115C22×C32C2×C22⋊C411yescharacteristic
116C22×C32#12011yescharacteristic
117C22×C32#12311yescharacteristic
118C2×C3⋊D3—42no—
119C2×C3⋊D3—41no—
120C32×C4—24no—
121C32×C4—44no—
122C32×C4C4×D412yes—
123C32×C4#12112yes—
124C3⋊Dic3—42no—
125C3⋊Dic3—41no—
126C2×#41—91no—
127C22×Q8C2×C3⋊D311yescharacteristic
128C2×M16—92no—
129C4⋊Q8—92no—
130#124—92no—
131#123—182no—
132C22⋊Q8—182no—
133C4×Q8—24no—
134#117—22no—
135#117—91no—
136#117C2×C3⋊D312yes—
137#104—184no—
138#101—182no—
139C23×C3C2×#6714yes—
140C22×D3—64no—
141C3×Q8—216no—
142C3×Q8—216no—
143C2×C3×C4—28no—
144C2×C3×C4—28no—
145C2×C3×C4—216no—
146C2×C3×C4(C2×D3)⋊C4116yes—
147C2×C3×C4C2×C4×D314yes—
148C2×C3×C4C2×D1214yes—
149C2×C3×C4#23518yes—
150C2×C3×C4C2×#6718yes—
151#67—124no—
152#67—124no—
153C2×Dic3—68no—
154C2×Dic3—64no—
155D12—68no—
156C4×D3—128no—
157Dic6—68no—
158C3⋊C8—128no—
159C2×C32—21no—
160C2×C32—21no—
161C2×C32—21no—
162C2×C32#38611yescharacteristic
163C3⋊D3—81no—
164#41—182no—
165#41—182no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—91no—
169C2×Q8C4×C3⋊D312yes—
170C2×Q8C4⋊(C3⋊D3)12yes—
171C2×D4—91no—
172C2×D4—181no—
173C22×C4—181no—
174C22×C4#63812yes—
175C22×C4C22×C3⋊D311yescharacteristic
176M16—182no—
177M16—182no—
178C2×C8—182no—
179C4⋊C4—24no—
180C4⋊C4—22no—
181C4⋊C4—184no—
182C4⋊C4—181no—
183C22⋊C4—22no—
184C22⋊C4—181no—
185C22⋊C4—184no—
186C42—24no—
187C42—92no—
188C42#63814yes—
189C22×C3—44no—
190C22×C3C2×(C2×D3)⋊C414yes—
191C22×C3#92914yes—
192C22×C3#95314yes—
193C2×D3—128no—
194C2×D3—124no—
195C3×C4—216no—
196C3×C4—416no—
197C3×C4C4×#6718yes—
198C3×C4#93018yes—
199Dic3—128no—
200Dic3—124no—
201C32#191211yescharacteristic, complemented, Sylow
202C23—181no—
203C23C2×#63811yescharacteristic
204Q8—24no—
205Q8—24no—
206Q8—182no—
207D4—182no—
208D4—361no—
209D4—361no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—24no—
213C2×C4—182no—
214C2×C4—181no—
215C2×C4—362no—
216C2×C4#375214yes—
217C2×C4C2×C4×C3⋊D311yescharacteristic
218C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
219C2×C4#382812yes—
220C2×C4C2×#63812yes—
221C8—362no—
222C2×C3—24no—
223C2×C3—24no—
224C2×C3—24no—
225C2×C3#521314yes—
226D3—244no—
227C22—41no—
228C22—362no—
229C22—361no—
230C22C2×#375211yescharacteristic
231C22#6413811yescharacteristic
232C22#6416211yescharacteristic
233C4—24no—
234C4—44no—
235C4—362no—
236C4—361no—
237C4C4×#63812yes—
238C4#6413912yes—
239C3#7166314yescomplemented
240C2—21no—
241C2—21no—
242C2—21no—
243C2—721no—
244C2#1059291211yescharacteristic
subgroupG/H
centerC2#10592912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#519C2
socleC2×C32#386
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#519C3⋊D3
hypocenterC32#1912
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
3. C2×#63663C2semidirect
5. #10589397C2semidirect
12. #64156C4semidirect
14. #64153C4semidirect
20. C3×#519D3semidirect
85. #519C3⋊D3semidirect
201. C32#1912semidirect
239. C3#71663semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
#105962872
C2×#636632
#105927042
#105893972
#716633