Finite Group Databasebeta

← #13072260

Subgroups — #13072260

Order 1408.

800 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 213 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
1C23×Dic22C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3C2×#66922C212yesmaximal, complemented
4C4×C11×C22⋊C4C211yesmaximal, characteristic
5#10622563C214yesmaximal
6#10622542C212yesmaximal, complemented
7#10622269C214yesmaximal, complemented
8C23×C4×C11C2211yescharacteristic
9C23×Dic11C2212yes—
10C22×Dic22—24no—
11C22×Dic22—28no—
12C22×Dic22C2211yescharacteristic
13C22×Dic22C2212yes—
14C22×Dic22C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C42×C11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2218yes—
19C2×C4⋊Dic11C2211yescharacteristic
20#66977—24no—
21C2×Dic11⋊C4C2212yes—
22#66922—28no—
23C11×#95C2212yes—
24C11⋊#95C2218yes—
25C24×C11C2311yescharacteristic
26C22×C4×C11—24no—
27C22×C4×C11D414yes—
28C22×C4×C11C2311yescharacteristic
29C22×C4×C11C2314yes—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—28no—
32C22×Dic11—24no—
33C22×Dic11C2312yes—
34C22×Dic11C2312yes—
35C22×Dic11C2314yes—
36C2×Dic22—232no—
37C2×Dic22—28no—
38C2×Dic22—24no—
39C2×Dic22—24no—
40C2×Dic22—24no—
41C2×Dic22—24no—
42C2×Dic22—22no—
43C2×Dic22D418yes—
44C11×C22⋊C4Q818yescomplemented
45C42×C11—24no—
46C22⋊Dic11—24no—
47C4⋊Dic11—216no—
48C4⋊Dic11—22no—
49Dic11⋊C4—24no—
50#2434—111nomaximal, Sylow
51C23×C11—22no—
52C23×C11—22no—
53C23×C11C2×D412yes—
54C23×C11C2×Q814yes—
55C23×C11C2411yescharacteristic
56C2×C4×C11—24no—
57C2×C4×C11—22no—
58C2×C4×C11—24no—
59C2×C4×C11—28no—
60C2×C4×C11C2×D412yes—
61C2×C4×C11C2×D412yes—
62C2×C4×C11C2×D414yes—
63C2×C4×C11C2×Q818yescomplemented
64C2×Dic11—216no—
65C2×Dic11—24no—
66C2×Dic11—24no—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—24no—
70C2×Dic11—24no—
71C2×Dic11C2×D418yes—
72Dic22—216no—
73Dic22—216no—
74Dic22—44no—
75C23×Q8—111no—
76C2×C4⋊Q8—112no—
77C2×C22⋊Q8—111no—
78#395—114no—
79#391—112no—
80#385—114no—
81C4×C22⋊C4D1111yescharacteristic
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—28no—
85C22×C11C4⋊Q814yescomplemented
86C22×C11C22×D411yescharacteristic
87C22×C11C22×D412yes—
88C22×C11C22×Q812yes—
89C22×C112−1+412yes—
90C4×C11—22no—
91C4×C11—28no—
92C4×C11#12014yes—
93Dic11—28no—
94Dic11—42no—
95Dic11—42no—
96C22×Q8—112no—
97C22×Q8—111no—
98C22×Q8—112no—
99C22×Q8—228no—
100C22×Q8—224no—
101C23×C4—112no—
102C23×C4C2×D1111yescharacteristic
103C4⋊Q8—228no—
104C22⋊Q8—224no—
105C2×C4⋊C4—111no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—118no—
108C2×C22⋊C4—112no—
109C2×C22⋊C4C2×D1112yes—
110C2×C42C2×D1112yes—
111#95—118no—
112#95C2×D1112yes—
113C2×C11—24no—
114C2×C11C2×#12011yescharacteristic
115C2×C11C2×C4⋊Q811yescharacteristic
116C2×C11#53611yescharacteristic
117C2×C11D4×Q814yes—
118C24C22×D1111yescharacteristic
119C2×Q8—118no—
120C2×Q8—228no—
121C2×Q8—2232no—
122C2×Q8—224no—
123C2×Q8—224no—
124C2×Q8—222no—
125C2×Q8—224no—
126C2×Q8—224no—
127C22×C4—24no—
128C22×C4—114no—
129C22×C4—112no—
130C22×C4—112no—
131C22×C4—228no—
132C22×C4—224no—
133C22×C4D4414yes—
134C22×C4C22×D1114yes—
135C22×C4C22×D1111yescharacteristic
136C22×C4C22×D1111yescharacteristic
137C4⋊C4—2216no—
138C4⋊C4—224no—
139C4⋊C4—222no—
140C22⋊C4—224no—
141C22⋊C4Dic2218yescomplemented
142C42—24no—
143C11#243411yescharacteristic, complemented, Sylow
144C23—22no—
145C23—22no—
146C23C2×Dic2214yes—
147C23C2×D4412yes—
148C23C23×D1111yescharacteristic
149Q8—2216no—
150Q8—2216no—
151Q8—444no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—118no—
157C2×C4—2216no—
158C2×C4—224no—
159C2×C4—224no—
160C2×C4—222no—
161C2×C4—222no—
162C2×C4—224no—
163C2×C4—224no—
164C2×C4C2×Dic2218yescomplemented
165C2×C4C2×D4412yes—
166C2×C4C2×D4412yes—
167C2×C4D4×D1114yes—
168C22—22no—
169C22—22no—
170C22—28no—
171C22#6692214yescomplemented
172C22C22×Dic2212yes—
173C22C22×D4411yescharacteristic
174C22C2×D4×D1112yes—
175C22#6704312yes—
176C4—22no—
177C4—28no—
178C4—228no—
179C4—442no—
180C4—442no—
181C4#6693514yes—
182C2—24no—
183C2C2×#6692211yescharacteristic
184C2C2×#6693511yescharacteristic
185C2#1062305711yescharacteristic
186C2D4×Dic2214yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC24×C11C23
hypercenterC4×C22⋊C4D11
hypocenterC11#2434
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#66922C2semidirect
6. #10622542C2semidirect
7. #10622269C2semidirect
44. C11×C22⋊C4Q8semidirect
63. C2×C4×C11C2×Q8semidirect
85. C22×C11C4⋊Q8semidirect
141. C22⋊C4Dic22semidirect
143. C11#2434semidirect
164. C2×C4C2×Dic22semidirect
171. C22#66922semidirect

Maximal subgroups

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

subgroupindex
C23×Dic222
C2×#669772
C2×#669222
C4×C11×C22⋊C42
#106225632
#106225422
#106222692
#243411