Finite Group Databasebeta

← #11799101

Subgroups — #11799101

Order 1152.

510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#10592850C211yesmaximal, characteristic, complemented
2#10592846C211yesmaximal, characteristic, complemented
3#10592607C211yesmaximal, characteristic, complemented
4#10592594C211yesmaximal, characteristic, complemented
5C32×#361C211yesmaximal, characteristic, complemented
6#10589377C211yesmaximal, characteristic, complemented
7#10589361C211yesmaximal, characteristic, complemented
8#69263—34nomaximal
9C2×C32×D8C2211yescharacteristic
10#64149—21no—
11C2×#3753—21no—
12#64116—21no—
13#64113C2211yescharacteristic
14C2×#3745C2211yescharacteristic
15C32×M32C2211yescharacteristic
16C32×#108C2211yescharacteristic
17#63654—21no—
18#63653—21no—
19#63652—21no—
20C8×C3⋊Dic3C2211yescharacteristic
21#63639C2211yescharacteristic
22#63627—21no—
23#63626—21no—
24#5151—34no—
25#5147—34no—
26#4908—34no—
27#4895—34no—
28C3×#361D314yescomplemented
29#4511—34no—
30#4495—34no—
31C2×C32×D4—21no—
32C2×#638—42no—
33#3828—21no—
34C2×C4⋊(C3⋊D3)—21no—
35C32×D8—21no—
36C32×D8—21no—
37C32×M16—21no—
38C2×C32×C8C2311yescharacteristic
39#3753—41no—
40#3753—41no—
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)D411yescharacteristic
43#3746D411yescharacteristic, complemented
44#3745—21no—
45#3745—21no—
46#3745D411yescharacteristic, complemented
47#3744—21no—
48#3743—41no—
49C8×C3⋊D3—41no—
50C32×C16—21no—
51C3⋊(C3⋊C16)—21no—
52#2213—91noSylow
53C2×C3×D8C2×D314yes—
54#940—64no—
55C2×#213—64no—
56#907—64no—
57#904—34no—
58C2×D24—34no—
59C3×M32C2×D314yes—
60C3×#108C2×D314yes—
61#827—64no—
62#826—64no—
63#825—64no—
64C8×Dic3—34no—
65#812—34no—
66#800—64no—
67D48—64no—
68C23×C32—41no—
69C22×C3⋊D3—41no—
70C32×D4—41no—
71C32×D4—41no—
72C2×C32×C4C2×D411yescharacteristic
73#638—41no—
74#638—84no—
75C2×C3⋊Dic3—21no—
76C4⋊(C3⋊D3)—21no—
77C4⋊(C3⋊D3)—41no—
78C4⋊(C3⋊D3)—41no—
79C4×C3⋊D3—41no—
80#634—21no—
81C32×C8—41no—
82C32×C8C2×D411yescharacteristic
83C32×C8#4111yescharacteristic
84C3⋊(C3⋊C8)D811yescharacteristic
85C3⋊(C3⋊C8)D811yescharacteristic
86#509—91no—
87#509—91no—
88#493—91no—
89#443—91no—
90#364—91no—
91#361—91no—
92#361C3⋊D311yescharacteristic, complemented
93C2×C3×D4—24no—
94C2×#67—128no—
95#235—64no—
96C2×D12—64no—
97C3×D8—24no—
98C3×D8—24no—
99C3×M16—24no—
100C2×C3×C8C22×D314yes—
101#213—124no—
102#213—124no—
103C4×Dic3—34no—
104C2×C3⋊C8—34no—
105Dic12—34no—
106D24—34no—
107D24—64no—
108D24—64no—
109#204—64no—
110ΓL(1,𝔽25)—124no—
111D3×C8—124no—
112C3×C16—24no—
113C3⋊C16—64no—
114C22×C32—82no—
115C22×C32—81no—
116C22×C32AGL(1,ℤ/8)11yescharacteristic
117C2×C3⋊D3—41no—
118C2×C3⋊D3—82no—
119C2×C3⋊D3—81no—
120C32×C4#12111yescharacteristic
121C32×C4C2×D811yescharacteristic
122C3⋊Dic3—22no—
123C3⋊Dic3—41no—
124#135—91no—
125C2×D8—91no—
126C2×D8—181no—
127C2×D8C2×C3⋊D311yescharacteristic
128#131—181no—
129#127—181no—
130SD32—181no—
131SD32—181no—
132D16—181no—
133D16—181no—
134M32—91no—
135M32C2×C3⋊D311yescharacteristic
136#108C2×C3⋊D311yescharacteristic
137#104—181no—
138C4×C8—91no—
139C23×C3—44no—
140C22×D3—124no—
141C3×D4—44no—
142C3×D4—44no—
143C2×C3×C4D3×D414yes—
144#67—124no—
145#67—2416no—
146C2×Dic3—64no—
147D12—64no—
148D12—124no—
149D12—124no—
150C4×D3—124no—
151Dic6—64no—
152C3×C8—44no—
153C3×C8#23514yes—
154C3×C8D3×D414yes—
155C3⋊C8—34no—
156C3⋊C8—34no—
157C2×C32—21no—
158C2×C32—161no—
159C2×C32#45911yescharacteristic
160C3⋊D3—81no—
161C3⋊D3—161no—
162#41—181no—
163C2×D4—21no—
164C2×D4—181no—
165C2×D4—362no—
166Q16—91no—
167SD16—181no—
168D8—21no—
169D8—21no—
170D8—91no—
171D8—181no—
172D8—181no—
173D8—361no—
174D8—361no—
175M16—21no—
176M16—361no—
177C2×C8—91no—
178C2×C8—361no—
179C2×C8C22×C3⋊D311yescharacteristic
180C42—91no—
181C16—21no—
182C16—181no—
183C22×C3—88no—
184C22×C3—84no—
185C22×C3#91414yes—
186C2×D3—124no—
187C2×D3—248no—
188C2×D3—244no—
189C3×C4#88414yes—
190C3×C4D3×D814yes—
191Dic3—68no—
192Dic3—124no—
193C32#221311yescharacteristic, complemented, Sylow
194C23—41no—
195C23—361no—
196Q8—181no—
197D4—41no—
198D4—41no—
199D4—181no—
200D4—361no—
201D4—361no—
202D4—361no—
203D4—724no—
204C2×C4—181no—
205C2×C4—361no—
206C2×C4D4×C3⋊D311yescharacteristic
207C8—41no—
208C8—91no—
209C8—91no—
210C8#382811yescharacteristic
211C8D4×C3⋊D311yescharacteristic
212C2×C3—24no—
213C2×C3—164no—
214C2×C3#478614yes—
215D3—244no—
216D3—484no—
217C22—82no—
218C22—81no—
219C22—361no—
220C22—722no—
221C22—721no—
222C22#6412311yescharacteristic
223C4—182no—
224C4—361no—
225C4#6409311yescharacteristic
226C4D8×C3⋊D311yescharacteristic
227C3#6926314yescomplemented
228C2—21no—
229C2—161no—
230C2—721no—
231C2—1441no—
232C2#1059248511yescharacteristic
subgroupG/H
centerC2#10592485
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#361C2
socleC2×C32#459
hypercenter#361C3⋊D3
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #10592850C2semidirect
2. #10592846C2semidirect
3. #10592607C2semidirect
4. #10592594C2semidirect
5. C32×#361C2semidirect
6. #10589377C2semidirect
7. #10589361C2semidirect
28. C3×#361D3semidirect
43. #3746D4semidirect
46. #3745D4semidirect
92. #361C3⋊D3semidirect
193. C32#2213semidirect
227. C3#69263semidirect

Maximal subgroups

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

subgroupindex
#105928502
#105928462
#105926072
#105925942
C32×#3612
#105893772
#105893612
#692633