Finite Group Databasebeta

← #13078742

Subgroups — #13078742

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
1C11×#533C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic
3#10622707C212yesmaximal, complemented
4#10622703C212yesmaximal, complemented
5#10622663C212yesmaximal
6#10622656C212yesmaximal
7#10622643C214yesmaximal, complemented
8#10622539C211yesmaximal, characteristic
9C22×Dic22C2211yescharacteristic
10C11×C4⋊Q8C2211yescharacteristic
11C11×C4⋊Q8C2211yescharacteristic
12C11×#125—21no—
13C11×C22⋊Q8—21no—
14C11×C22⋊Q8C2212yes—
15C4×Q8×C11—21no—
16C4×Q8×C11C2212yes—
17C11×#117—21no—
18C2×C42×C11C2211yescharacteristic
19C2×#4326C2214yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4—21no—
22C2×C4×Dic11—21no—
23C4×Dic22—21no—
24C4×Dic22—21no—
25C4×Dic22C2212yes—
26C4×Dic22C2212yes—
27#66899C2214yes—
28C22⋊(C11⋊C8)C2212yes—
29#66874C2214yes—
30#66872C2214yes—
31C4⋊(C11⋊C8)C2212yes—
32#66867C2212yes—
33C2×Q8×C11—21no—
34C2×Q8×C11C2312yes—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×Dic11—21no—
39C22×Dic11—21no—
40C2×Dic22—24no—
41C2×Dic22—21no—
42C2×Dic22C2312yes—
43C11×C4⋊C4—21no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4C2312yes—
49C11×C22⋊C4—22no—
50C42×C11—22no—
51C42×C11D411yescharacteristic
52C42×C11D411yescharacteristic
53C42×C11C2311yescharacteristic
54C42×C11C2311yescharacteristic
55#4326—28no—
56C4⋊Dic11—21no—
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61C4×Dic11—22no—
62C2×C11⋊C8C2314yes—
63#3113—111nomaximal, Sylow
64C23×C11C2×D411yescharacteristic
65Q8×C11—24no—
66Q8×C11—42no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2411yescharacteristic
78C2×Dic11—24no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—42no—
82Dic22—24no—
83Dic22—22no—
84Dic22#4114yes—
85C11⋊C8—24no—
86#533D1111yescharacteristic
87C2×C4×Q8—111no—
88#483—112no—
89#475—112no—
90#462—112no—
91#451—112no—
92#441—114no—
93#432—111no—
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—42no—
103C4×C11—42no—
104C4×C11#13712yes—
105C4×C11C2×#4112yes—
106Dic11—24no—
107Dic11—42no—
108C22×Q8—111no—
109C2×Q16—114no—
110C4⋊Q8C2×D1111yescharacteristic
111C4⋊Q8C2×D1111yescharacteristic
112#125—21no—
113C22⋊Q8—21no—
114C22⋊Q8C2×D1112yes—
115C4×Q8—21no—
116C4×Q8—112no—
117C4×Q8—112no—
118C4×Q8—221no—
119C4×Q8—221no—
120C4×Q8C2×D1112yes—
121#117—21no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—221no—
124C2×C42—221no—
125C2×C42C2×D1111yescharacteristic
126#106—114no—
127C4⋊C8—112no—
128#103—114no—
129#103—114no—
130C22⋊C8—112no—
131#97—112no—
132C2×C11—22no—
133C2×C11#52511yescharacteristic
134C2×C11C2×#13711yescharacteristic
135C2×C11C2×#13711yescharacteristic
136C2×Q8—21no—
137C2×Q8—112no—
138C2×Q8—224no—
139C2×Q8—221no—
140C2×Q8C22×D1112yes—
141C22×C4—221no—
142C22×C4—221no—
143C22×C4C22⋊D1111yescharacteristic
144C22×C4C22⋊D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146Q16—228no—
147C2×C8—114no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—112no—
154C4⋊C4—221no—
155C4⋊C4—222no—
156C4⋊C4—222no—
157C4⋊C4C22×D1112yes—
158C22⋊C4—22no—
159C42—22no—
160C42—222no—
161C42—222no—
162C42C22⋊D1111yescharacteristic
163C42C22⋊D1111yescharacteristic
164C42C22×D1111yescharacteristic
165C42C22×D1111yescharacteristic
166C11#311311yescharacteristic, complemented, Sylow
167C23C2×C22⋊D1111yescharacteristic
168Q8—24no—
169Q8—42no—
170Q8—114no—
171Q8—224no—
172Q8—222no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—224no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—442no—
182C2×C4C2×C22⋊D1111yescharacteristic
183C2×C4C2×C22⋊D1111yescharacteristic
184C2×C4C2×C22⋊D1111yescharacteristic
185C2×C4C2×C22⋊D1111yescharacteristic
186C2×C4C2×C22⋊D1111yescharacteristic
187C2×C4C23×D1111yescharacteristic
188C8—224no—
189C22—21no—
190C22—21no—
191C22#6699512yes—
192C22C22×C22⋊D1111yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—224no—
200C4—442no—
201C4#6700412yes—
202C4#41×D1112yes—
203C2—22no—
204C2C2×#6699511yescharacteristic
205C2C2×#6700411yescharacteristic
206C2#1062335911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#533D11
hypocenterC11#3113
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #10622707C2semidirect
4. #10622703C2semidirect
7. #10622643C2semidirect
166. C11#3113semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
C2×C4×Dic222
#106227072
#106227032
#106226632
#106226562
#106226432
#106225392
#311311