Finite Group Databasebeta

← #13078747

Subgroups — #13078747

Order 1408.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#10623001C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic
3C11×#432C211yesmaximal, characteristic
4#10622464C212yesmaximal, complemented
5#10622462C212yesmaximal, complemented
6#10622352C212yesmaximal
7#10622334C212yesmaximal
8#10622329C214yesmaximal, complemented
9C22×Dic22C2211yescharacteristic
10C2×C42×C11C2211yescharacteristic
11#66979—21no—
12C2×C4⋊Dic11C2211yescharacteristic
13#66977—21no—
14#66977C2212yes—
15C2×Dic11⋊C4—21no—
16C2×C4×Dic11—21no—
17C2×Dic44C2214yes—
18#66923—21no—
19#66922C2211yescharacteristic
20#66922C2211yescharacteristic
21C4×Dic22—21no—
22C4×Dic22—21no—
23C4×Dic22—21no—
24C4×Dic22C2212yes—
25C4×Dic22C2212yes—
26C4×Dic22C2212yes—
27C11×C4⋊C8C2212yes—
28C11×C22⋊C8C2212yes—
29C11×#97C2212yes—
30#66881C2214yes—
31#66880C2214yes—
32#66880C2214yes—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D411yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—21no—
37C22×Dic11—21no—
38C2×Dic22—24no—
39C2×Dic22—21no—
40C2×Dic22—21no—
41C2×Dic22C2312yes—
42C2×Dic22C2312yes—
43C2×C8×C11C2314yes—
44C42×C11D411yescharacteristic
45C42×C11D411yescharacteristic
46C42×C11C2311yescharacteristic
47C42×C11C2311yescharacteristic
48C22⋊Dic11—22no—
49C4⋊Dic11—21no—
50C4⋊Dic11—21no—
51C4⋊Dic11—21no—
52C4⋊Dic11—21no—
53C4⋊Dic11C2312yes—
54C4⋊Dic11C2312yes—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59C4×Dic11—22no—
60C4×Dic11—22no—
61C4×Dic11—22no—
62Dic44—28no—
63#3113—111nomaximal, Sylow
64C23×C11C2×D411yescharacteristic
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2411yescharacteristic
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—42no—
80Dic22—24no—
81Dic22—22no—
82Dic22—24no—
83Dic22—42no—
84Dic22#4114yes—
85C8×C11—24no—
86#533—111no—
87C2×C4×Q8—111no—
88#483—112no—
89#475—112no—
90#462—112no—
91#451—112no—
92#441—114no—
93#432D1111yescharacteristic
94C22×C11—21no—
95C22×C11—21no—
96C22×C11#13712yes—
97C22×C11C22×D411yescharacteristic
98C4×C11—21no—
99C4×C11—21no—
100C4×C11—21no—
101C4×C11—21no—
102C4×C11#13712yes—
103C4×C11C2×#4112yes—
104Dic11—24no—
105Dic11—42no—
106Dic11—42no—
107Dic11—42no—
108C22×Q8—111no—
109C2×Q16—114no—
110C4⋊Q8—111no—
111C4⋊Q8—111no—
112#125—221no—
113C22⋊Q8—112no—
114C22⋊Q8—221no—
115C4×Q8—112no—
116C4×Q8—112no—
117C4×Q8—112no—
118C4×Q8—221no—
119C4×Q8—221no—
120C4×Q8—221no—
121#117—221no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—221no—
124C2×C42—221no—
125C2×C42C2×D1111yescharacteristic
126#106—114no—
127C4⋊C8C2×D1112yes—
128#103—114no—
129#103—114no—
130C22⋊C8C2×D1112yes—
131#97C2×D1112yes—
132C2×C11—22no—
133C2×C11#52511yescharacteristic
134C2×C11C2×#13711yescharacteristic
135C2×C11C2×#13711yescharacteristic
136C2×Q8—112no—
137C2×Q8—112no—
138C2×Q8—224no—
139C2×Q8—221no—
140C2×Q8—221no—
141C22×C4—221no—
142C22×C4—221no—
143C22×C4D4411yescharacteristic
144C22×C4D4411yescharacteristic
145C22×C4C22×D1111yescharacteristic
146Q16—228no—
147C2×C8C22×D1114yes—
148C4⋊C4—112no—
149C4⋊C4—112no—
150C4⋊C4—221no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—221no—
154C4⋊C4—221no—
155C4⋊C4—222no—
156C4⋊C4—222no—
157C4⋊C4—221no—
158C22⋊C4—222no—
159C42—222no—
160C42—222no—
161C42—222no—
162C42D4411yescharacteristic
163C42D4411yescharacteristic
164C42C22×D1111yescharacteristic
165C42C22×D1111yescharacteristic
166C11#311311yescharacteristic, complemented, Sylow
167C23C2×D4411yescharacteristic
168Q8—114no—
169Q8—224no—
170Q8—222no—
171Q8—224no—
172Q8—442no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—224no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—442no—
182C2×C4C2×D4411yescharacteristic
183C2×C4C2×D4411yescharacteristic
184C2×C4C2×D4411yescharacteristic
185C2×C4C2×D4411yescharacteristic
186C2×C4C2×D4411yescharacteristic
187C2×C4C23×D1111yescharacteristic
188C8—24no—
189C22—21no—
190C22—21no—
191C22#6696212yes—
192C22C22×D4411yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—224no—
198C4—442no—
199C4—442no—
200C4—442no—
201C4#6696212yes—
202C4#41×D1112yes—
203C2—22no—
204C2#1062305511yescharacteristic
205C2C2×#6696211yescharacteristic
206C2C2×#6696211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#432C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#432D11
hypocenterC11#3113
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
4. #10622464C2semidirect
5. #10622462C2semidirect
8. #10622329C2semidirect
166. C11#3113semidirect

Maximal subgroups

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

subgroupindex
#106230012
C2×C4×Dic222
C11×#4322
#106224642
#106224622
#106223522
#106223342
#106223292
#311311