Finite Group Databasebeta

← #13076963

Subgroups — #13076963

Order 1408.

644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66999C212yesmaximal
3C2×C42×D11C211yesmaximal, characteristic
4#10622843C212yesmaximal, complemented
5#10622600C214yesmaximal
6#10622586C214yesmaximal, complemented
7#10622548C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2212yes—
9C22×C4×D11C2211yescharacteristic
10C22×C4×D11C2212yes—
11C11×C4⋊Q8—24no—
12C2×C11×C4⋊C4C2214yes—
13C2×C42×C11C2211yescharacteristic
14#66999—28no—
15C2×(C2×D11)⋊C4C2214yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2214yes—
18C2×Dic11⋊C4C2214yes—
19C2×C4×Dic11C2212yes—
20C2×C4×Dic11C2211yescharacteristic
21C42×D11—24no—
22C11⋊#95C2218yes—
23C23×D11C2311yescharacteristic
24C2×Q8×C11—24no—
25C2×Q8×C11—24no—
26C2×Q8×C11—24no—
27C22×C4×C11C2314yes—
28C22×C4×C11C2311yescharacteristic
29C22×C4×C11C2312yes—
30C22×Dic11C2314yes—
31C22×Dic11C2311yescharacteristic
32C22×Dic11C2312yes—
33C2×C4×D11—22no—
34C2×C4×D11—24no—
35C2×C4×D11—22no—
36C2×C4×D11—24no—
37C2×C4×D11D414yes—
38C2×C4×D11Q818yescomplemented
39C11×C4⋊C4—28no—
40C42×C11D414yes—
41(C2×D11)⋊C4—28no—
42C4⋊Dic11—24no—
43C4⋊Dic11—28no—
44Dic11⋊C4—28no—
45C4×Dic11—22no—
46C4×Dic11—24no—
47#2857—111nomaximal, Sylow
48C23×C11C2411yescharacteristic
49C22×D11—21no—
50C22×D11—21no—
51C22×D11—22no—
52C22×D11C2×D412yes—
53C22×D11C2×Q814yes—
54Q8×C11—48no—
55C2×C4×C11—24no—
56C2×C4×C11—24no—
57C2×C4×C11—24no—
58C2×C4×C11C2×D412yes—
59C2×C4×C11C2×D412yes—
60C2×C4×C11C2×D414yes—
61C2×C4×C11C2×Q814yes—
62C2×C4×C11#4112yes—
63C2×C4×C11#4114yes—
64C2×Dic11—21no—
65C2×Dic11—22no—
66C2×Dic11—21no—
67C2×Dic11—22no—
68C2×Dic11—24no—
69C2×Dic11—28no—
70C2×Dic11C2×D412yes—
71C2×Dic11C2×Q814yes—
72C4×D11—28no—
73C4×D11—216no—
74C2×C4⋊Q8D1111yescharacteristic, complemented
75C2×C22⋊Q8—112no—
76C22×C42—111no—
77#391—112no—
78#389—114no—
79#384—111no—
80#380—114no—
81C22×C11C22×D411yescharacteristic
82C22×C11C22×D411yescharacteristic
83C22×C11C22×Q812yes—
84C22×C11C2×#4111yescharacteristic
85C22×C11C2×#4112yes—
86C2×D11—22no—
87C2×D11—24no—
88C2×D11—22no—
89C2×D11—24no—
90C2×D11C4⋊Q814yescomplemented
91C4×C11—44no—
92C4×C11#12114yes—
93C4×C11C22⋊Q818yescomplemented
94Dic11—22no—
95Dic11—24no—
96Dic11—44no—
97C22×Q8C2×D1112yes—
98C23×C4—111no—
99C23×C4—112no—
100C4⋊Q8—24no—
101C22⋊Q8—228no—
102C2×C4⋊C4—112no—
103C2×C4⋊C4—114no—
104C2×C4⋊C4—114no—
105C2×C4⋊C4C2×D1114yes—
106C2×C22⋊C4—114no—
107C2×C42—112no—
108C2×C42—111no—
109C2×C42—224no—
110C2×C42C2×D1111yescharacteristic
111#95—118no—
112C2×C11C2×#12111yescharacteristic
113C2×C11C2×C22⋊Q812yes—
114C2×C11C2×C4⋊Q811yescharacteristic
115C2×C11#53211yescharacteristic
116C2×C11#53312yes—
117D11—24no—
118C24—111no—
119C2×Q8—24no—
120C2×Q8—24no—
121C2×Q8—24no—
122C22×C4—112no—
123C22×C4—111no—
124C22×C4—114no—
125C22×C4—118no—
126C22×C4—114no—
127C22×C4—222no—
128C22×C4—224no—
129C22×C4—222no—
130C22×C4—224no—
131C22×C4C22×D1114yes—
132C22×C4C22×D1111yescharacteristic
133C22×C4C22×D1112yes—
134C4⋊C4—28no—
135C4⋊C4—228no—
136C4⋊C4—224no—
137C4⋊C4—228no—
138C22⋊C4—228no—
139C42—222no—
140C42—224no—
141C42C22⋊D1114yes—
142C11#285711yescharacteristic, complemented, Sylow
143C23—112no—
144C23—114no—
145C23—221no—
146C23—222no—
147C23—221no—
148C23C23×D1111yescharacteristic
149Q8—48no—
150C2×C4—24no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—112no—
154C2×C4—114no—
155C2×C4—221no—
156C2×C4—222no—
157C2×C4—221no—
158C2×C4—222no—
159C2×C4—228no—
160C2×C4—2216no—
161C2×C4—224no—
162C2×C4—228no—
163C2×C4D4×D1112yes—
164C2×C4#434112yes—
165C2×C4Q8×D1114yes—
166C2×C4#434314yes—
167C2×C4C2×C22⋊D1112yes—
168C2×C4C2×C22⋊D1114yes—
169C22—114no—
170C22—222no—
171C22—224no—
172C22—222no—
173C22—224no—
174C22C2×D4×D1111yescharacteristic
175C22C2×#434111yescharacteristic
176C22C2×Q8×D1112yes—
177C22C2×#434312yes—
178C22C22×C22⋊D1111yescharacteristic
179C4—44no—
180C4—222no—
181C4—224no—
182C4—444no—
183C4#6699114yes—
184C4#6699918yescomplemented
185C2—224no—
186C2D11×C4⋊Q811yescharacteristic
187C2#1062325611yescharacteristic
188C2#1062325912yes—
189C2C2×#6699111yescharacteristic
190C2C2×#6699912yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C4⋊Q8C2
prime radicalC23×D11C23
hypercenterC2×C4⋊Q8D11
hypocenterC11#2857
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C4⋊Q8C2semidirect
4. #10622843C2semidirect
6. #10622586C2semidirect
7. #10622548C2semidirect
38. C2×C4×D11Q8semidirect
74. C2×C4⋊Q8D11semidirect
90. C2×D11C4⋊Q8semidirect
93. C4×C11C22⋊Q8semidirect
142. C11#2857semidirect
184. C4#66999semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
C2×#669992
C2×C42×D112
#106228432
#106226002
#106225862
#106225482
#285711