Finite Group Databasebeta

← #13073819

Subgroups — #13073819

Order 1408.

548 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 161 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×D4×Dic11C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3C11×#390C211yesmaximal, characteristic
4#10622834C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic, complemented
6#10622561C214yesmaximal, complemented
7#10622559C214yesmaximal, complemented
8#10622549C211yesmaximal, characteristic, complemented
9C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2214yes—
14C2×C42×C11C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2214yes—
17D4×Dic11—24no—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2214yes—
24C2×C4×Dic11C2211yescharacteristic
25C2×C4×Dic11C2211yescharacteristic
26#66943—24no—
27C11⋊#95C2212yes—
28C11⋊#95C2214yes—
29C24×C11C2312yes—
30C2×D4×C11—22no—
31C2×D4×C11—22no—
32C2×D4×C11Q814yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—24no—
37C22×Dic11—44no—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2311yescharacteristic
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2312yes—
43C11×C4⋊C4—22no—
44C11×C22⋊C4—44no—
45C42×C11—22no—
46C22⋊Dic11—24no—
47C22⋊Dic11—28no—
48C4⋊Dic11—24no—
49C4⋊Dic11—22no—
50C4⋊Dic11—22no—
51Dic11⋊C4—24no—
52Dic11⋊C4—24no—
53Dic11⋊C4—44no—
54C4×Dic11—22no—
55C4×Dic11D414yes—
56#2566—111nomaximal, Sylow
57C23×C11—22no—
58C23×C11—24no—
59C23×C11—22no—
60C23×C11—24no—
61C23×C11C2×Q814yes—
62C23×C11C2411yescharacteristic
63D4×C11—28no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—24no—
68C2×C4×C11—22no—
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×Q812yes—
71C2×C4×C11#4112yes—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—24no—
79C2×Dic11—24no—
80C2×Dic11—48no—
81C2×Dic11C2×D412yes—
82C2×Dic11C2×D412yes—
83C2×Dic11#4114yes—
84C2×#125—111no—
85C2×C4×D4—111no—
86#396—114no—
87#390—111no—
88#390D1111yescharacteristic
89#385—114no—
90#384—111no—
91#382—111no—
92C4×C4⋊C4—111no—
93C22×C11—24no—
94C22×C11—28no—
95C22×C11—42no—
96C22×C11—42no—
97C22×C11—44no—
98C22×C11C22×D411yescharacteristic
99C22×C11C22×Q811yescharacteristic
100C22×C11C2×#4111yescharacteristic
101C22×C11C2×#4112yes—
102C22×C11H(5,𝔽2)12yes—
103C4×C11—42no—
104C4×C11—42no—
105C4×C11C22⋊Q814yes—
106Dic11—22no—
107Dic11—22no—
108Dic11—24no—
109Dic11—42no—
110Dic11—42no—
111C22×D4C2×D1111yescharacteristic
112C23×C4—112no—
113#125—224no—
114C4×D4—224no—
115C2×C4⋊C4—111no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—114no—
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C22⋊C4—112no—
123C2×C22⋊C4—114no—
124C2×C22⋊C4C2×D1114yes—
125C2×C42—111no—
126C2×C42—111no—
127C2×C42C2×D1111yescharacteristic
128#95—112no—
129#95—114no—
130C2×C11—44no—
131C2×C11C2×C22⋊Q811yescharacteristic
132C2×C11#53211yescharacteristic
133C2×C11#53511yescharacteristic
134C2×C11#55312yes—
135C2×C11#55412yes—
136C24C22×D1112yes—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4Dic2214yes—
140C22×C4—111no—
141C22×C4—112no—
142C22×C4—111no—
143C22×C4—112no—
144C22×C4—112no—
145C22×C4—224no—
146C22×C4—444no—
147C22×C4C22×D1112yes—
148C22×C4C22×D1112yes—
149C22×C4C22×D1111yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—224no—
152C4⋊C4—224no—
153C4⋊C4—224no—
154C4⋊C4—222no—
155C4⋊C4—222no—
156C4⋊C4—444no—
157C22⋊C4—44no—
158C22⋊C4—224no—
159C22⋊C4—228no—
160C42—22no—
161C42—114no—
162C42—222no—
163C11#256611yescharacteristic, complemented, Sylow
164C23—22no—
165C23—22no—
166C23—24no—
167C23—24no—
168C23C2×Dic2214yes—
169C23C23×D1111yescharacteristic
170D4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—112no—
177C2×C4—112no—
178C2×C4—114no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—224no—
186C2×C4—224no—
187C2×C4—448no—
188C2×C4C2×Dic2212yes—
189C2×C4D4×D1112yes—
190C2×C4#434112yes—
191C22—24no—
192C22—28no—
193C22—42no—
194C22—44no—
195C22—42no—
196C22C22×Dic2211yescharacteristic
197C22C2×D4×D1111yescharacteristic
198C22C2×#434111yescharacteristic
199C22#6703712yes—
200C22#41×D1112yes—
201C4—42no—
202C4—42no—
203C4—222no—
204C4—224no—
205C4—222no—
206C4—442no—
207C4—442no—
208C4#6693114yes—
209C2—44no—
210C2C2×#6693111yescharacteristic
211C2#1062307012yes—
212C2#1062314512yes—
213C2#1062319911yescharacteristic
214C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2566
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
5. #10622589C2semidirect
6. #10622561C2semidirect
7. #10622559C2semidirect
8. #10622549C2semidirect
9. C4×Dic11⋊C4C2semidirect
163. C11#2566semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
C2×#669432
C11×#3902
#106228342
#106225892
#106225612
#106225592
#106225492
C4×Dic11⋊C42
#256611