Finite Group Databasebeta

← #13069896

Subgroups — #13069896

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×#67004C211yesmaximal, characteristic
2C11×#413C211yesmaximal, characteristic
3#10622849C211yesmaximal, characteristic
4C2×#66888C211yesmaximal, characteristic, complemented
5#10622737C211yesmaximal, characteristic, complemented
6#10622733C211yesmaximal, characteristic, complemented
7#10622194C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12#67004—22no—
13#67004—22no—
14C2×#4326—21no—
15C2×#4324—21no—
16#66979C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19C11×#101—21no—
20C11×#100—21no—
21#66901—22no—
22#66888—22no—
23#66886—22no—
24#66880—22no—
25C11×#41—21no—
26C11×#41—21no—
27C11×#41—21no—
28C11×#41—21no—
29C2×Q8×C11D411yescharacteristic
30C2×D4×C11—21no—
31C2×D4×C11D411yescharacteristic
32C22×C4×C11—21no—
33C22×C4×C11C2311yescharacteristic
34C22×Dic11—21no—
35C2×Dic22—21no—
36C2×Dic22—21no—
37C2×Dic22—21no—
38C2×Dic22—21no—
39C2×Dic22—21no—
40C2×Dic22D412yes—
41C11×M16—21no—
42C11×M16—21no—
43C11×M16—21no—
44C11×M16—21no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C22⋊Dic11—21no—
48#4326—24no—
49#4324—24no—
50C4⋊Dic11—21no—
51C4×Dic11—21no—
52#4318—21no—
53#4318—21no—
54#4318D412yes—
55#4318D412yes—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58#2049—111nomaximal, Sylow
59C23×C11—21no—
60C23×C11#4111yescharacteristic
61Q8×C11—21no—
62Q8×C11—21no—
63D4×C11—21no—
64D4×C11—21no—
65D4×C11—41no—
66D4×C11—41no—
67C2×C4×C11—21no—
68C2×C4×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
76C2×Dic11—22no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80Dic22—22no—
81Dic22—22no—
82Dic22—41no—
83Dic22—41no—
84C8×C11—41no—
85C8×C11—41no—
86C11⋊C8—22no—
87C11⋊C8—22no—
88C2×#137—111no—
89#430—111no—
90#421—111no—
91#419—111no—
92#413D1111yescharacteristic
93C2×#101—111no—
94#344—111no—
95C22×C11—41no—
96C22×C11—41no—
97C22×C11—81no—
98C22×C11#12111yescharacteristic
99C22×C11#12311yescharacteristic
100C22×C11#12411yescharacteristic
101C4×C11—41no—
102C4×C11#12011yescharacteristic
103C4×C11#12111yescharacteristic
104C4×C11#12111yescharacteristic
105C4×C11#12311yescharacteristic
106Dic11—42no—
107Dic11—81no—
108C2×#41C2×D1111yescharacteristic
109C22×Q8—111no—
110#137—222no—
111#137—222no—
112C2×Q16—221no—
113C2×SD16—221no—
114C2×M16—111no—
115C2×M16—111no—
116C2×M16C2×D1111yescharacteristic
117C2×M16C2×D1111yescharacteristic
118#117—111no—
119#108—222no—
120#104—222no—
121#103—222no—
122#101—21no—
123#101—222no—
124#100—21no—
125C2×C11—21no—
126C2×C11—21no—
127C2×C11—21no—
128C2×C11—81no—
129C2×C11#39411yescharacteristic
130#41—21no—
131#41—21no—
132#41—21no—
133#41—21no—
134C2×Q8—112no—
135C2×Q8—221no—
136C2×Q8—221no—
137C2×Q8—221no—
138C2×Q8—221no—
139C2×Q8—221no—
140C2×Q8C22⋊D1111yescharacteristic
141C2×D4—21no—
142C2×D4C22⋊D1111yescharacteristic
143C22×C4—21no—
144C22×C4—221no—
145C22×C4C22×D1111yescharacteristic
146Q16—224no—
147SD16—224no—
148M16—21no—
149M16—21no—
150M16—21no—
151M16—21no—
152M16—112no—
153M16—112no—
154M16—221no—
155M16—221no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—221no—
159C2×C8—221no—
160C4⋊C4—221no—
161C22⋊C4—221no—
162C42—221no—
163C11#204911yescharacteristic, complemented, Sylow
164C23—21no—
165C23#433911yescharacteristic
166Q8—21no—
167Q8—21no—
168Q8—222no—
169Q8—222no—
170Q8—441no—
171Q8—441no—
172D4—21no—
173D4—21no—
174D4—41no—
175D4—41no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—222no—
180C2×C4—441no—
181C2×C4—441no—
182C2×C4—441no—
183C2×C4#433911yescharacteristic
184C2×C4D4×D1111yescharacteristic
185C2×C4D4×D1111yescharacteristic
186C2×C4D4×D1111yescharacteristic
187C2×C4#434111yescharacteristic
188C2×C4C2×C22⋊D1111yescharacteristic
189C8—41no—
190C8—41no—
191C8—222no—
192C8—222no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22#6693711yescharacteristic
197C22#6693811yescharacteristic
198C22#6698211yescharacteristic
199C4—41no—
200C4—442no—
201C4—881no—
202C4#6693611yescharacteristic
203C4#6693711yescharacteristic
204C4#6699011yescharacteristic
205C4#6699211yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—81no—
210C2#1062257211yescharacteristic
subgroupG/H
centerC2#10622572
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#413C2
socleC2×C11#394
prime radicalC2×C11×#41C22
hypercenter#413D11
hypocenterC11#2049
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
4. C2×#66888C2semidirect
5. #10622737C2semidirect
6. #10622733C2semidirect
7. #10622194C2semidirect
163. C11#2049semidirect

Maximal subgroups

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

subgroupindex
C2×#670042
C11×#4132
#106228492
C2×#668882
#106227372
#106227332
#106221942
#204911