Finite Group Databasebeta

← #13069894

Subgroups — #13069894

Order 1408.

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

normal subgroups only

This group has 254 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×#66995C211yesmaximal, characteristic
2C11×#419C211yesmaximal, characteristic, complemented
3C2×#66900C211yesmaximal, characteristic, complemented
4#10622745C211yesmaximal, characteristic
5#10622737C211yesmaximal, characteristic, complemented
6#10622618C211yesmaximal, characteristic
7#10622171C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C11×#117C2211yescharacteristic
12C2×#4326—21no—
13#66995—22no—
14#66995—22no—
15C2×#4325—21no—
16C2×#4318C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19C11×#103—22no—
20#66900—22no—
21#66888—21no—
22#66887—21no—
23#66886—22no—
24#66869—22no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11—21no—
30C2×Q8×C11D412yes—
31C22×C4×C11—21no—
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#4326—24no—
48#4325—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#2049—111nomaximal, Sylow
59C23×C11#4111yescharacteristic
60C22×D11—21no—
61Q8×C11—22no—
62Q8×C11—22no—
63Q8×C11—41no—
64Q8×C11—41no—
65C2×C4×C11—22no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11#4111yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C22⋊D11—41no—
76C22⋊D11—41no—
77C2×Dic11—21no—
78D44—21no—
79D44—21no—
80C4×D11—41no—
81C4×D11—41no—
82Dic22—21no—
83Dic22—21no—
84C8×C11—41no—
85C11⋊C8—22no—
86C11⋊C8—22no—
87C11⋊C8—41no—
88C2×#137—111no—
89#430—111no—
90#421—111no—
91#419D1111yescharacteristic, complemented
92#413—111no—
93C2×#101—111no—
94#344—111no—
95C22×C11—41no—
96C22×C11#12111yescharacteristic
97C22×C11#12311yescharacteristic
98C22×C11#12411yescharacteristic
99C2×D11—41no—
100C2×D11—81no—
101C4×C11—42no—
102C4×C11—81no—
103C4×C11#12011yescharacteristic
104C4×C11#12111yescharacteristic
105C4×C11#12111yescharacteristic
106C4×C11#12311yescharacteristic
107Dic11—41no—
108C2×#41—111no—
109C22×Q8C2×D1111yescharacteristic
110#137—222no—
111#137—222no—
112C2×Q16—221no—
113C2×SD16—221no—
114C2×M16—111no—
115C2×M16—111no—
116C2×M16—111no—
117C2×M16C2×D1111yescharacteristic
118#117C2×D1111yescharacteristic
119#108—222no—
120#104—222no—
121#103—22no—
122#101—221no—
123#101—222no—
124#100—221no—
125C2×C11—21no—
126C2×C11—21no—
127C2×C11—21no—
128C2×C11#39411yescharacteristic
129D11—81no—
130#41—221no—
131#41—221no—
132#41—221no—
133#41—221no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—111no—
140C2×Q8C22⋊D1112yes—
141C2×D4—111no—
142C2×D4—221no—
143C22×C4—21no—
144C22×C4—221no—
145C22×C4C22×D1111yescharacteristic
146Q16—224no—
147SD16—224no—
148M16—21no—
149M16—21no—
150M16—112no—
151M16—112no—
152M16—221no—
153M16—221no—
154M16—221no—
155M16—221no—
156C2×C8—21no—
157C2×C8—221no—
158C2×C8—221no—
159C2×C8—221no—
160C4⋊C4—21no—
161C22⋊C4—21no—
162C42—21no—
163C11#204911yescharacteristic, complemented, Sylow
164C23—221no—
165C23#434111yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—221no—
171Q8—221no—
172D4—221no—
173D4—221no—
174D4—441no—
175D4—441no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—221no—
181C2×C4—441no—
182C2×C4—441no—
183C2×C4#433911yescharacteristic
184C2×C4#433911yescharacteristic
185C2×C4D4×D1111yescharacteristic
186C2×C4D4×D1111yescharacteristic
187C2×C4D4×D1111yescharacteristic
188C2×C4C2×C22⋊D1111yescharacteristic
189C8—41no—
190C8—222no—
191C8—222no—
192C8—441no—
193C22—41no—
194C22—441no—
195C22—881no—
196C22#6693611yescharacteristic
197C22#6693811yescharacteristic
198C22#6699211yescharacteristic
199C4—42no—
200C4—81no—
201C4—441no—
202C4#6693711yescharacteristic
203C4#6693711yescharacteristic
204C4#6698211yescharacteristic
205C4#6699011yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—881no—
210C2#1062257211yescharacteristic
subgroupG/H
centerC2#10622572
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#419C2
socleC2×C11#394
prime radicalC2×#4339C22
hypercenter#419D11
hypocenterC11#2049
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C11×#419C2semidirect
3. C2×#66900C2semidirect
5. #10622737C2semidirect
7. #10622171C2semidirect
91. #419D11semidirect
163. C11#2049semidirect

Maximal subgroups

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

subgroupindex
C2×#669952
C11×#4192
C2×#669002
#106227452
#106227372
#106226182
#106221712
#204911