Finite Group Databasebeta

← #13073815

Subgroups — #13073815

Order 1408.

548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#66946C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3C11×#382C211yesmaximal, characteristic, complemented
4#10622601C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic, complemented
6#10622552C211yesmaximal, characteristic
7C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
8#10622289C214yesmaximal, complemented
9#10622281C214yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×C4×D11C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2214yes—
17C2×(C2×D11)⋊C4C2214yes—
18C2×C4⋊Dic11C2212yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2214yes—
23C2×C4×Dic11C2211yescharacteristic
24C2×C4×Dic11C2211yescharacteristic
25#66946—24no—
26#66943—24no—
27C11×#95C2214yes—
28C11⋊#95C2212yes—
29C23×D11C2312yes—
30C22×C4×C11C2312yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×Dic11C2312yes—
35C22×Dic11C2311yescharacteristic
36C22×Dic11C2311yescharacteristic
37C22×Dic11C2312yes—
38C2×D44—22no—
39C2×D44—22no—
40C2×D44Q814yes—
41C2×C4×D11—24no—
42C2×C4×D11—44no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—22no—
45C42×C11—22no—
46(C2×D11)⋊C4—24no—
47(C2×D11)⋊C4—28no—
48(C2×D11)⋊C4—44no—
49C4⋊Dic11—24no—
50C4⋊Dic11—22no—
51Dic11⋊C4—24no—
52Dic11⋊C4—24no—
53Dic11⋊C4—44no—
54C4×Dic11—22no—
55C4×Dic11D414yes—
56#2566—111nomaximal, Sylow
57C23×C11C2411yescharacteristic
58C22×D11—22no—
59C22×D11—24no—
60C22×D11—22no—
61C22×D11—24no—
62C22×D11C2×Q814yes—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—24no—
67C2×C4×C11—22no—
68C2×C4×C11—24no—
69C2×C4×C11—22no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×Q812yes—
72C2×C4×C11#4112yes—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—24no—
79C2×Dic11C2×D412yes—
80C2×Dic11C2×D412yes—
81C2×Dic11#4114yes—
82D44—28no—
83C4×D11—48no—
84C2×#125—111no—
85C2×C4×D4—111no—
86#396—114no—
87#390—111no—
88#390—111no—
89#385—114no—
90#384—111no—
91#382D1111yescharacteristic, complemented
92C4×C4⋊C4—111no—
93C22×C11C22×D411yescharacteristic
94C22×C11C22×Q811yescharacteristic
95C22×C11C2×#4111yescharacteristic
96C22×C11C2×#4112yes—
97C22×C11H(5,𝔽2)12yes—
98C2×D11—24no—
99C2×D11—28no—
100C2×D11—42no—
101C2×D11—42no—
102C2×D11—44no—
103C4×C11—42no—
104C4×C11—42no—
105C4×C11—42no—
106C4×C11C22⋊Q814yes—
107Dic11—22no—
108Dic11—22no—
109Dic11—24no—
110Dic11—42no—
111C22×D4—111no—
112C23×C4—112no—
113#125—224no—
114C4×D4—224no—
115C2×C4⋊C4—111no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—114no—
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C22⋊C4—112no—
123C2×C22⋊C4—114no—
124C2×C22⋊C4—114no—
125C2×C42—111no—
126C2×C42—111no—
127C2×C42C2×D1111yescharacteristic
128#95—112no—
129#95C2×D1114yes—
130C2×C11C2×C22⋊Q811yescharacteristic
131C2×C11#53211yescharacteristic
132C2×C11#53511yescharacteristic
133C2×C11#55312yes—
134C2×C11#55412yes—
135D11—44no—
136C24—112no—
137C2×D4—114no—
138C2×D4—222no—
139C2×D4—222no—
140C22×C4—111no—
141C22×C4—112no—
142C22×C4—111no—
143C22×C4—112no—
144C22×C4—224no—
145C22×C4—444no—
146C22×C4C22×D1112yes—
147C22×C4C22×D1112yes—
148C22×C4C22×D1112yes—
149C22×C4C22×D1111yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—224no—
153C4⋊C4—224no—
154C4⋊C4—224no—
155C4⋊C4—222no—
156C4⋊C4—444no—
157C22⋊C4—224no—
158C22⋊C4—228no—
159C22⋊C4—444no—
160C42—22no—
161C42—114no—
162C42—222no—
163C11#256611yescharacteristic, complemented, Sylow
164C23—114no—
165C23—222no—
166C23—222no—
167C23—224no—
168C23—224no—
169C23C23×D1111yescharacteristic
170D4—228no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—112no—
179C2×C4—112no—
180C2×C4—114no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—224no—
187C2×C4—448no—
188C2×C4#433912yes—
189C2×C4D4×D1112yes—
190C2×C4Q8×D1112yes—
191C22—224no—
192C22—228no—
193C22—444no—
194C22—442no—
195C22—442no—
196C22C2×#433911yescharacteristic
197C22C2×D4×D1111yescharacteristic
198C22C2×Q8×D1111yescharacteristic
199C22#41×D1112yes—
200C22#6704212yes—
201C4—42no—
202C4—42no—
203C4—42no—
204C4—224no—
205C4—222no—
206C4—222no—
207C4—442no—
208C4#6694914yes—
209C2—444no—
210C2C2×#6694911yescharacteristic
211C2#1062306112yes—
212C2#1062319911yescharacteristic
213C2#1062320511yescharacteristic
214C2#1062322112yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC22×D44C22
hypercenter#382D11
hypocenterC11#2566
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
3. C11×#382C2semidirect
5. #10622589C2semidirect
7. C4×Dic11⋊C4C2semidirect
8. #10622289C2semidirect
9. #10622281C2semidirect
91. #382D11semidirect
163. C11#2566semidirect

Maximal subgroups

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

subgroupindex
C2×#669462
C2×#669432
C11×#3822
#106226012
#106225892
#106225522
C4×Dic11⋊C42
#106222892
#106222812
#256611