Finite Group Databasebeta

← #13069887

Subgroups — #13069887

Order 1408.

274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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×#66985C211yesmaximal, characteristic
2C11×#418C211yesmaximal, characteristic, complemented
3C2×#66897C211yesmaximal, characteristic, complemented
4#10622745C211yesmaximal, characteristic, complemented
5#10622737C211yesmaximal, characteristic, complemented
6#10622618C211yesmaximal, characteristic, complemented
7#10622171C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C11×#117C2211yescharacteristic
12C2×#4324—21no—
13#66985—22no—
14#66985—22no—
15C2×#4323—21no—
16C2×#4318C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19C11×#102—22no—
20#66897—22no—
21#66888—21no—
22#66887—21no—
23#66886—22no—
24#66869—22no—
25C24×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11D412yes—
32C22×C4×C11C2311yescharacteristic
33C2×C22⋊D11—21no—
34#4339—21no—
35#4339—21no—
36#4339—21no—
37#4339—21no—
38C2×D44D411yescharacteristic
39C2×C4×D11—21no—
40C2×Dic22D411yescharacteristic
41C11×M16—21no—
42C11×M16—21no—
43C2×C8×C11—21no—
44C11×C4⋊C4—21no—
45C11×C22⋊C4—21no—
46C42×C11—21no—
47#4324—24no—
48#4323—24no—
49#4318—21no—
50#4318—21no—
51#4318—21no—
52#4318—21no—
53#4318D412yes—
54#4318D412yes—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58#2048—111nomaximal, Sylow
59C23×C11—22no—
60C23×C11—41no—
61C23×C11—41no—
62C23×C11—82no—
63C23×C11#4111yescharacteristic
64C22×D11—21no—
65D4×C11—22no—
66D4×C11—22no—
67D4×C11—41no—
68D4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C2×C4×C11#4111yescharacteristic
76C22⋊D11—41no—
77C22⋊D11—41no—
78C2×Dic11—21no—
79D44—21no—
80D44—21no—
81C4×D11—41no—
82C4×D11—41no—
83Dic22—21no—
84Dic22—21no—
85C8×C11—41no—
86C11⋊C8—22no—
87C11⋊C8—22no—
88C11⋊C8—41no—
89C2×AGL(1,ℤ/8)—111no—
90#430—111no—
91#421—111no—
92#418D1111yescharacteristic, complemented
93#413—111no—
94C2×#100—111no—
95#344—111no—
96C22×C11—41no—
97C22×C11—42no—
98C22×C11—82no—
99C22×C11—82no—
100C22×C11—82no—
101C22×C11#12111yescharacteristic
102C22×C11#12311yescharacteristic
103C22×C11#12411yescharacteristic
104C2×D11—41no—
105C2×D11—81no—
106C4×C11—81no—
107C4×C11#12011yescharacteristic
108C4×C11#12111yescharacteristic
109C4×C11#12111yescharacteristic
110C4×C11#12311yescharacteristic
111Dic11—41no—
112C2×#41—111no—
113C22×D4C2×D1111yescharacteristic
114AGL(1,ℤ/8)—222no—
115AGL(1,ℤ/8)—222no—
116C2×SD16—221no—
117C2×D8—221no—
118C2×M16—111no—
119C2×M16—111no—
120C2×M16—111no—
121C2×M16C2×D1111yescharacteristic
122#117C2×D1111yescharacteristic
123#108—222no—
124#104—222no—
125#102—22no—
126#101—221no—
127#100—221no—
128#100—222no—
129C2×C11—21no—
130C2×C11—21no—
131C2×C11—21no—
132C2×C11—82no—
133C2×C11#39411yescharacteristic
134D11—81no—
135C24—21no—
136#41—221no—
137#41—221no—
138#41—221no—
139#41—221no—
140C2×Q8—111no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—111no—
147C2×D4—221no—
148C2×D4C22⋊D1112yes—
149C22×C4—221no—
150C22×C4C22×D1111yescharacteristic
151SD16—224no—
152D8—224no—
153M16—21no—
154M16—21no—
155M16—112no—
156M16—112no—
157M16—221no—
158M16—221no—
159M16—221no—
160M16—221no—
161C2×C8—21no—
162C2×C8—221no—
163C2×C8—221no—
164C2×C8—221no—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C11#204811yescharacteristic, complemented, Sylow
169C23—22no—
170C23—41no—
171C23—41no—
172C23—82no—
173C23—221no—
174C23#434111yescharacteristic
175Q8—221no—
176Q8—221no—
177D4—22no—
178D4—22no—
179D4—41no—
180D4—41no—
181D4—221no—
182D4—221no—
183D4—441no—
184D4—441no—
185C2×C4—41no—
186C2×C4—221no—
187C2×C4—441no—
188C2×C4—441no—
189C2×C4#433911yescharacteristic
190C2×C4#433911yescharacteristic
191C2×C4D4×D1111yescharacteristic
192C2×C4D4×D1111yescharacteristic
193C2×C4D4×D1111yescharacteristic
194C2×C4C2×C22⋊D1111yescharacteristic
195C8—41no—
196C8—222no—
197C8—222no—
198C8—441no—
199C22—41no—
200C22—42no—
201C22—82no—
202C22—82no—
203C22—82no—
204C22—441no—
205C22—881no—
206C22#6693611yescharacteristic
207C22#6693811yescharacteristic
208C22#6699211yescharacteristic
209C4—81no—
210C4—441no—
211C4#6693711yescharacteristic
212C4#6693711yescharacteristic
213C4#6698211yescharacteristic
214C4#6699011yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—82no—
219C2—881no—
220C2#1062257211yescharacteristic
subgroupG/H
centerC2#10622572
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#418C2
socleC2×C11#394
prime radicalC2×#66985C2
hypercenter#418D11
hypocenterC11#2048
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C11×#418C2semidirect
3. C2×#66897C2semidirect
4. #10622745C2semidirect
5. #10622737C2semidirect
6. #10622618C2semidirect
7. #10622171C2semidirect
92. #418D11semidirect
168. C11#2048semidirect

Maximal subgroups

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

subgroupindex
C2×#669852
C11×#4182
C2×#668972
#106227452
#106227372
#106226182
#106221712
#204811