Finite Group Databasebeta

← #11781417

Subgroups — #11781417

Order 1152.

546 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 129 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×#486C211yesmaximal, characteristic, complemented
2#10592782C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic
4C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5#10589413C211yesmaximal, characteristic, complemented
6#10589410C211yesmaximal, characteristic, complemented
7#10589324C211yesmaximal, characteristic, complemented
8#71201—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×#127C2211yescharacteristic
11C2×#3755—21no—
12C2×#3753—21no—
13C2×C8×C3⋊D3—21no—
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15C32×#102—21no—
16C32×#102—21no—
17C32×C4×C8C2211yescharacteristic
18#63662—21no—
19#63659—21no—
20#63647—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#486D314yescomplemented
25#5083—34no—
26#5072—34no—
27C8×D12—34no—
28#4547—34no—
29#4544—34no—
30#4458—34no—
31C2×C32×Q8—21no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×C4⋊(C3⋊D3)D411yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×C32×C8D411yescharacteristic
38C2×C32×C8D411yescharacteristic
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C42C2311yescharacteristic
42#3755—42no—
43#3753—42no—
44#3752—21no—
45C4⋊(C3⋊Dic3)D411yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C8×C3⋊D3—42no—
50#1681—91noSylow
51C3×C4⋊Q8C2×D314yes—
52C3×#127C2×D314yes—
53C2×#215—64no—
54C2×#213—64no—
55C2×D3×C8—64no—
56C4×D12—34no—
57C3×#102—24no—
58C3×#102—24no—
59C3×C4×C8C2×D314yes—
60#835—64no—
61#832—64no—
62(C2×D3)⋊C8—64no—
63C4⋊(C3⋊C8)—34no—
64C4⋊(C3⋊C8)—34no—
65C4⋊(C3⋊C8)—34no—
66C23×C32—41no—
67C22×C3⋊D3—21no—
68C32×Q8—41no—
69C32×Q8—41no—
70C32×D4—41no—
71C32×D4—41no—
72C32×D4—41no—
73C32×D4—41no—
74C32×D4—81no—
75C2×C32×C4—41no—
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4#4111yescharacteristic
79C2×C3⋊Dic3—21no—
80C4⋊(C3⋊D3)—21no—
81C4⋊(C3⋊D3)D812yes—
82C4×C3⋊D3—41no—
83C4×C3⋊D3—41no—
84C32×C8—21no—
85C32×C8—21no—
86C3⋊(C3⋊C8)—41no—
87C3⋊(C3⋊C8)—41no—
88C3⋊(C3⋊C8)—41no—
89#486C3⋊D311yescharacteristic, complemented
90#461—91no—
91#459—91no—
92C8×D4—91no—
93#335—91no—
94#332—91no—
95#331—91no—
96C2×C3×Q8—24no—
97C2×C3×D4—24no—
98C2×C3×D4—24no—
99C2×C3×D4—24no—
100C2×D12—34no—
101C2×C4×D3—64no—
102C2×C3×C8#6714yes—
103C2×C3×C8#6714yes—
104C3×C4⋊C4—24no—
105C3×C4⋊C4—24no—
106C3×C42C22×D314yes—
107#215—128no—
108#213—128no—
109(C2×D3)⋊C4—64no—
110C4⋊Dic3—34no—
111C2×C3⋊C8—64no—
112C2×C3⋊C8—64no—
113C2×C3⋊C8—64no—
114D3×C8—128no—
115C22×C32—81no—
116C22×C32—81no—
117C22×C32—81no—
118C22×C32#12111yescharacteristic
119C2×C3⋊D3—22no—
120C2×C3⋊D3—41no—
121C2×C3⋊D3—41no—
122C32×C4—21no—
123C32×C4—81no—
124C32×C4C2×D811yescharacteristic
125C32×C4#13511yescharacteristic
126C32×C4#13511yescharacteristic
127C32×C4AGL(1,ℤ/8)11yescharacteristic
128C3⋊Dic3—41no—
129C2×SD16—181no—
130C2×D8—181no—
131C22×C8—181no—
132C4⋊Q8C2×C3⋊D311yescharacteristic
133#127C2×C3⋊D311yescharacteristic
134C4×D4—91no—
135C4⋊C8—91no—
136C4⋊C8—91no—
137C4⋊C8—91no—
138#103—181no—
139#102—21no—
140#102—21no—
141#102—181no—
142C22⋊C8—181no—
143C4×C8C2×C3⋊D311yescharacteristic
144C23×C3—44no—
145C22×D3—64no—
146C3×Q8—44no—
147C3×Q8—44no—
148C3×D4—44no—
149C3×D4—44no—
150C3×D4—44no—
151C3×D4—44no—
152C3×D4—84no—
153C2×C3×C4—44no—
154C2×C3×C4D3×D414yes—
155C2×C3×C4#23714yes—
156C2×C3×C4C2×#6714yes—
157C2×Dic3—64no—
158D12—38no—
159D12—64no—
160C4×D3—124no—
161C4×D3—124no—
162C3×C8—24no—
163C3×C8—24no—
164C3⋊C8—124no—
165C3⋊C8—124no—
166C3⋊C8—124no—
167C2×C32—161no—
168C2×C32#46311yescharacteristic
169C2×C32#46611yescharacteristic
170C2×C32#47111yescharacteristic
171C3⋊D3—42no—
172C2×Q8—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—91no—
177C22×C4—181no—
178SD16—362no—
179D8—362no—
180C2×C8—181no—
181C2×C8—181no—
182C2×C8—181no—
183C2×C8—362no—
184C2×C8#63811yescharacteristic
185C2×C8#63811yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—91no—
189C22⋊C4—181no—
190C42C22×C3⋊D311yescharacteristic
191C22×C3—84no—
192C22×C3—84no—
193C22×C3—84no—
194C22×C3#93814yes—
195C2×D3—68no—
196C2×D3—124no—
197C2×D3—124no—
198C3×C4—24no—
199C3×C4—84no—
200C3×C4D3×D814yes—
201C3×C4#91214yes—
202C3×C4#94914yes—
203C3×C4#95014yes—
204Dic3—124no—
205C32#168111yescharacteristic, complemented, Sylow
206C23—41no—
207C23—181no—
208Q8—41no—
209Q8—41no—
210D4—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—81no—
215D4—92no—
216D4—181no—
217C2×C4—41no—
218C2×C4—181no—
219C2×C4—361no—
220C2×C4—361no—
221C2×C4D4×C3⋊D311yescharacteristic
222C2×C4#383011yescharacteristic
223C2×C4C2×#63811yescharacteristic
224C8—21no—
225C8—21no—
226C8—361no—
227C8—361no—
228C8—361no—
229C2×C3—164no—
230C2×C3#505714yes—
231C2×C3#515714yes—
232C2×C3#517714yes—
233D3—128no—
234C22—81no—
235C22—81no—
236C22—81no—
237C22—182no—
238C22—361no—
239C22—361no—
240C22#6414711yescharacteristic
241C4—21no—
242C4—81no—
243C4—361no—
244C4D8×C3⋊D311yescharacteristic
245C4#6412111yescharacteristic
246C4#6415811yescharacteristic
247C4#6415911yescharacteristic
248C3#7120114yescomplemented
249C2—161no—
250C2—362no—
251C2#1059275611yescharacteristic
252C2#1059285611yescharacteristic
253C2#1059287611yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#486C2
socleC22×C32#121
prime radical#10592771C2
hypercenter#486C3⋊D3
hypocenterC32#1681
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. C32×#486C2semidirect
2. #10592782C2semidirect
4. C8×C4⋊(C3⋊D3)C2semidirect
5. #10589413C2semidirect
6. #10589410C2semidirect
7. #10589324C2semidirect
24. C3×#486D3semidirect
89. #486C3⋊D3semidirect
205. C32#1681semidirect
248. C3#71201semidirect

Maximal subgroups

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

subgroupindex
C32×#4862
#105927822
#105927712
C8×C4⋊(C3⋊D3)2
#105894132
#105894102
#105893242
#712013