Finite Group Databasebeta

← #11796726

Subgroups — #11796726

Order 1152.

660 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 137 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×Q16×C3⋊D3C211yesmaximal, characteristic
2C2×#63625C211yesmaximal, characteristic
3#10592579C211yesmaximal, characteristic
4C32×#358C211yesmaximal, characteristic, complemented
5#10589430C211yesmaximal, characteristic, complemented
6#10589369C211yesmaximal, characteristic, complemented
7#10589358C211yesmaximal, characteristic, complemented
8#69222—34nomaximal
9C2×Q8×C3⋊D3—21no—
10C2×C32×Q16C2211yescharacteristic
11C2×#3756—21no—
12Q16×C3⋊D3—22no—
13Q16×C3⋊D3C414yescomplemented
14C2×#3746C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16#64101—21no—
17C2×C32×C16C2211yescharacteristic
18C32×#107C2211yescharacteristic
19#63645C2211yescharacteristic
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21#63635—21no—
22#63625—22no—
23C2×D3×Q16—34no—
24C2×#798—34no—
25#4880—34no—
26C3×#358D314yescomplemented
27#4564—34no—
28#4503—34no—
29#4492—34no—
30C2×C32×Q8—21no—
31Q8×C3⋊D3—24no—
32Q8×C3⋊D3—42no—
33C2×C4×C3⋊D3—41no—
34C2×C4×C3⋊D3D411yescharacteristic
35C2×#634—21no—
36C2×#634—41no—
37C32×Q16—21no—
38C32×Q16C2×C412yes—
39C2×C32×C8C2311yescharacteristic
40C32×C4⋊C4—21no—
41#3756—24no—
42#3752—41no—
43C4⋊(C3⋊Dic3)—21no—
44C4×C3⋊Dic3—41no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46#3746—21no—
47#3746C2×C412yes—
48C8×C3⋊D3C2×C412yes—
49C8×C3⋊D3D412yes—
50C32×C16—21no—
51C3⋊(C3⋊C16)—21no—
52#2141—91noSylow
53C2×D3×Q8—64no—
54C2×C3×Q16C2×D314yes—
55C2×#216—64no—
56D3×Q16—316no—
57D3×Q16—68no—
58C2×Dic12—34no—
59C2×D3×C8—34no—
60#892—64no—
61C2×C3×C16C2×D314yes—
62C3×#107C2×D314yes—
63#818—34no—
64C2×C3⋊C16—34no—
65#808—64no—
66#798—68no—
67C22×C3⋊D3D811yescharacteristic
68C32×Q8—22no—
69C32×Q8—41no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3D811yescharacteristic
76C4×C3⋊D3—44no—
77C4×C3⋊D3C22⋊C412yes—
78C4×C3⋊D3SD1612yes—
79#634—22no—
80#634—41no—
81#634—44no—
82C32×C8C22×C411yescharacteristic
83C32×C8C2×D411yescharacteristic
84C3⋊(C3⋊C8)C22⋊C412yes—
85C22×Q16—91no—
86C2×M32—91no—
87#427—91no—
88#358—91no—
89#358—91no—
90#358—91no—
91#358C3⋊D311yescharacteristic, complemented
92C2×C3×Q8—24no—
93D3×Q8—616no—
94D3×Q8—128no—
95C2×C4×D3—34no—
96C2×C4×D3—124no—
97C2×Dic6—64no—
98C2×Dic6—124no—
99C3×Q16—24no—
100C3×Q16C4×D318yes—
101C2×C3×C8C22×D314yes—
102C3×C4⋊C4—24no—
103#216—616no—
104(C2×D3)⋊C4—124no—
105C4⋊Dic3—64no—
106C4×Dic3—124no—
107C2×C3⋊C8—34no—
108Dic12—38no—
109Dic12—64no—
110D3×C8—38no—
111D3×C8—38no—
112C3×C16—24no—
113C3⋊C16—64no—
114C22×C32C2×D811yescharacteristic
115C2×C3⋊D3—21no—
116C2×C3⋊D3—21no—
117C2×C3⋊D3#10212yes—
118C32×C4—42no—
119C32×C4—81no—
120C32×C4C2×C22⋊C411yescharacteristic
121C32×C4C2×SD1611yescharacteristic
122C3⋊Dic3—42no—
123C3⋊Dic3—81no—
124C3⋊Dic3#10212yes—
125C22×Q8—181no—
126C2×Q16—94no—
127C2×Q16—91no—
128C2×Q16—182no—
129C2×Q16—181no—
130C2×Q16C2×C3⋊D311yescharacteristic
131C22×C8—91no—
132#117—181no—
133M32—182no—
134C2×C16—91no—
135C2×C16C2×C3⋊D311yescharacteristic
136#107—91no—
137#107C2×C3⋊D311yescharacteristic
138#106—181no—
139C22×D3—34no—
140C3×Q8—28no—
141C3×Q8—44no—
142C2×C3×C4—44no—
143C2×C3×C4—44no—
144C2×C3×C4D3×D414yes—
145C2×Dic3—34no—
146C2×Dic3—124no—
147C2×Dic3—124no—
148C4×D3—38no—
149C4×D3—38no—
150C4×D3—1216no—
151Dic6—68no—
152Dic6—1216no—
153Dic6—124no—
154C3×C8C2×C4×D314yes—
155C3×C8D3×D414yes—
156C3⋊C8—38no—
157C2×C32C2×#10211yescharacteristic
158C2×C32#51011yescharacteristic
159C2×C32#51011yescharacteristic
160C3⋊D3—22no—
161C2×Q8—21no—
162C2×Q8—184no—
163C2×Q8—181no—
164C2×Q8—361no—
165C2×Q8—362no—
166C22×C4—91no—
167C22×C4—361no—
168Q16—21no—
169Q16—92no—
170Q16—184no—
171Q16—181no—
172Q16C4×C3⋊D312yes—
173C2×C8—91no—
174C2×C8—92no—
175C2×C8—92no—
176C2×C8C22×C3⋊D311yescharacteristic
177C4⋊C4—21no—
178C4⋊C4—181no—
179C22⋊C4—361no—
180C42—361no—
181C16—21no—
182C16—181no—
183C22×C3D3×D814yes—
184C2×D3—38no—
185C2×D3—64no—
186C2×D3—64no—
187C3×C4—48no—
188C3×C4—84no—
189C3×C4D3×C22⋊C414yes—
190C3×C4D3×SD1614yes—
191Dic3—38no—
192Dic3—128no—
193Dic3—244no—
194C32#214111yescharacteristic, complemented, Sylow
195C23—91no—
196Q8—22no—
197Q8—41no—
198Q8—182no—
199Q8—364no—
200Q8—361no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—91no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—364no—
207C2×C4—361no—
208C2×C4—361no—
209C2×C4D4×C3⋊D311yescharacteristic
210C8—92no—
211C8C2×C4×C3⋊D311yescharacteristic
212C8D4×C3⋊D311yescharacteristic
213C2×C3D3×#10214yes—
214C2×C3#491514yes—
215C2×C3#491814yes—
216D3—68no—
217C22—92no—
218C22—181no—
219C22—181no—
220C22D8×C3⋊D311yescharacteristic
221C4—42no—
222C4—81no—
223C4—92no—
224C4—362no—
225C4—721no—
226C4C22⋊C4×C3⋊D311yescharacteristic
227C4SD16×C3⋊D311yescharacteristic
228C3#6922214yescomplemented
229C2—182no—
230C2C3⋊D3×#10211yescharacteristic
231C2#1059261411yescharacteristic
232C2#1059261711yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#358C2
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
cosocleC2×C32×C8C23
hypercenter#358C3⋊D3
hypocenterC32#2141
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
4. C32×#358C2semidirect
5. #10589430C2semidirect
6. #10589369C2semidirect
7. #10589358C2semidirect
13. Q16×C3⋊D3C4semidirect
26. C3×#358D3semidirect
91. #358C3⋊D3semidirect
194. C32#2141semidirect
228. C3#69222semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
C2×#636252
#105925792
C32×#3582
#105894302
#105893692
#105893582
#692223