Finite Group Databasebeta

← #13076965

Subgroups — #13076965

Order 1408.

644 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 189 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×#66999C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic, complemented
3C2×#66950C211yesmaximal, characteristic
4C2×C42×D11C211yesmaximal, characteristic
5C11×#391C211yesmaximal, characteristic, complemented
6#10622589C211yesmaximal, characteristic, complemented
7#10622542C211yesmaximal, characteristic, complemented
8#10622280C214yesmaximal
9#10622260C214yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×C4×D11C2211yescharacteristic
12C22×C4×D11C2212yes—
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16#66999—24no—
17#66997—24no—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2214yes—
24C2×Dic11⋊C4C2214yes—
25C2×C4×Dic11C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27#66950—24no—
28C42×D11—24no—
29C11×#95C2214yes—
30C11⋊#95C2214yes—
31C23×D11C2311yescharacteristic
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C22×C4×C11C2312yes—
36C22×C4×C11C2312yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2312yes—
43C2×C4×D11—24no—
44C2×C4×D11—24no—
45C2×C4×D11—22no—
46C2×C4×D11—22no—
47C2×C4×D11D414yes—
48C2×C4×D11Q818yescomplemented
49C2×Dic22—22no—
50C2×Dic22—22no—
51C2×Dic22—22no—
52C11×C4⋊C4—22no—
53C42×C11—22no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56C4⋊Dic11—24no—
57C4⋊Dic11—22no—
58Dic11⋊C4—28no—
59Dic11⋊C4—24no—
60Dic11⋊C4—28no—
61C4×Dic11—24no—
62C4×Dic11D414yes—
63#2857—111nomaximal, Sylow
64C23×C11C2411yescharacteristic
65C22×D11—21no—
66C22×D11—21no—
67C22×D11—22no—
68C22×D11C2×D412yes—
69C22×D11C2×Q814yes—
70Q8×C11—44no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11—22no—
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×Q814yes—
81C2×C4×C11#4112yes—
82C2×Dic11—21no—
83C2×Dic11—21no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—24no—
88C2×Dic11—22no—
89C2×Dic11C2×D412yes—
90C2×Dic11C2×D414yes—
91C2×Dic11C2×Q814yes—
92C2×Dic11#4114yes—
93C4×D11—28no—
94C4×D11—216no—
95Dic22—44no—
96C2×C4⋊Q8—111no—
97C2×C22⋊Q8—111no—
98C2×C22⋊Q8—111no—
99C22×C42—111no—
100#391—111no—
101#391D1111yescharacteristic, complemented
102#389—114no—
103#384—111no—
104#380—114no—
105C22×C11C22×D411yescharacteristic
106C22×C11C22×D411yescharacteristic
107C22×C11C22×Q812yes—
108C22×C11C2×#4111yescharacteristic
109C22×C11C2×#4112yes—
110C2×D11—22no—
111C2×D11—24no—
112C2×D11—22no—
113C2×D11—24no—
114C2×D11C4⋊Q814yescomplemented
115C4×C11—24no—
116C4×C11—42no—
117C4×C11—42no—
118C4×C11#12114yes—
119Dic11—22no—
120Dic11—42no—
121Dic11—42no—
122Dic11C22⋊Q818yescomplemented
123C22×Q8—111no—
124C22×Q8C2×D1111yescharacteristic
125C23×C4—111no—
126C23×C4—112no—
127C4⋊Q8—224no—
128C22⋊Q8—224no—
129C22⋊Q8—224no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4—114no—
134C2×C4⋊C4—114no—
135C2×C4⋊C4C2×D1111yescharacteristic
136C2×C22⋊C4—112no—
137C2×C22⋊C4—112no—
138C2×C42—111no—
139C2×C42—112no—
140C2×C42—224no—
141C2×C42C2×D1111yescharacteristic
142#95—114no—
143#95C2×D1114yes—
144C2×C11C2×#12111yescharacteristic
145C2×C11C2×C22⋊Q812yes—
146C2×C11C2×C4⋊Q811yescharacteristic
147C2×C11#53211yescharacteristic
148C2×C11#53312yes—
149D11—24no—
150C24—111no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—22no—
154C2×Q8—222no—
155C2×Q8—222no—
156C2×Q8—222no—
157C22×C4—112no—
158C22×C4—111no—
159C22×C4—114no—
160C22×C4—118no—
161C22×C4—112no—
162C22×C4—112no—
163C22×C4—224no—
164C22×C4—224no—
165C22×C4—222no—
166C22×C4—222no—
167C22×C4C22×D1112yes—
168C22×C4C22×D1112yes—
169C22×C4C22×D1112yes—
170C22×C4C22×D1111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—224no—
173C4⋊C4—224no—
174C4⋊C4—228no—
175C4⋊C4—228no—
176C4⋊C4—222no—
177C22⋊C4—224no—
178C22⋊C4—224no—
179C42—22no—
180C42—114no—
181C42—224no—
182C11#285711yescharacteristic, complemented, Sylow
183C23—112no—
184C23—114no—
185C23—221no—
186C23—221no—
187C23—222no—
188C23C23×D1111yescharacteristic
189Q8—44no—
190Q8—444no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—24no—
198C2×C4—114no—
199C2×C4—114no—
200C2×C4—114no—
201C2×C4—112no—
202C2×C4—2216no—
203C2×C4—221no—
204C2×C4—221no—
205C2×C4—228no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—224no—
211C2×C4#433912yes—
212C2×C4D4×D1112yes—
213C2×C4D4×D1112yes—
214C2×C4Q8×D1114yes—
215C22—114no—
216C22—222no—
217C22—224no—
218C22—224no—
219C22—222no—
220C22C2×#433911yescharacteristic
221C22C2×D4×D1111yescharacteristic
222C22C2×D4×D1111yescharacteristic
223C22C2×Q8×D1112yes—
224C22#41×D1112yes—
225C4—24no—
226C4—42no—
227C4—42no—
228C4—118no—
229C4—222no—
230C4—442no—
231C4—442no—
232C4#6693714yes—
233C2—224no—
234C2C2×#6693711yescharacteristic
235C2#1062310912yes—
236C2D11×C22⋊Q812yes—
237C2#1062319911yescharacteristic
238C2D11×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC23×D11C23
hypercenter#391D11
hypocenterC11#2857
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#66997C2semidirect
5. C11×#391C2semidirect
6. #10622589C2semidirect
7. #10622542C2semidirect
9. #10622260C2semidirect
48. C2×C4×D11Q8semidirect
101. #391D11semidirect
114. C2×D11C4⋊Q8semidirect
122. Dic11C22⋊Q8semidirect
182. C11#2857semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×#669972
C2×#669502
C2×C42×D112
C11×#3912
#106225892
#106225422
#106222802
#106222602
#285711