Finite Group Databasebeta

← #13074287

Subgroups — #13074287

Order 1408.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#66930C212yesmaximal, complemented
2C11×#394C211yesmaximal, characteristic
3#10622833C212yesmaximal
4#10622596C211yesmaximal, characteristic, complemented
5#10622590C211yesmaximal, characteristic, complemented
6#10622564C212yesmaximal, complemented
7#10622561C212yesmaximal, complemented
8#10622559C212yesmaximal, complemented
9#10622265C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25#66930—28no—
26C11×#95C2211yescharacteristic
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C24×C11C2312yes—
33C2×D4×C11—24no—
34C2×D4×C11—41no—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×Dic11—24no—
40C22×Dic11—24no—
41C22×Dic11—24no—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C11×C4⋊C4—41no—
47C11×C22⋊C4—24no—
48C11×C22⋊C4—24no—
49C22⋊Dic11—24no—
50C22⋊Dic11—24no—
51C22⋊Dic11—42no—
52C4⋊Dic11—41no—
53C4⋊Dic11—41no—
54Dic11⋊C4—24no—
55Dic11⋊C4—24no—
56Dic11⋊C4—24no—
57C4×Dic11—24no—
58C4×Dic11D414yescomplemented
59#2609—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11#4114yes—
67C23×C11C2411yescharacteristic
68D4×C11—44no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11C2×D412yes—
79C2×Dic11—216no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11C2×D414yes—
91C2×Dic11#4114yes—
92C2×#117—112no—
93#398—111no—
94#396—112no—
95#394D1111yescharacteristic
96#388—112no—
97#387—112no—
98#386—112no—
99#385—112no—
100#382—111no—
101C22×C11—24no—
102C22×C11—24no—
103C22×C11—24no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11C22×D411yescharacteristic
109C22×C11C2×#4112yes—
110C22×C11C2×#4112yes—
111C22×C11H(5,𝔽2)11yescharacteristic
112C22×C112−1+411yescharacteristic
113C4×C11—22no—
114C4×C11—42no—
115C4×C11—41no—
116C4×C11—41no—
117Dic11—24no—
118Dic11—24no—
119Dic11—42no—
120Dic11—42no—
121C22×D4C2×D1111yescharacteristic
122C23×C4—112no—
123#117—228no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4C2×D1111yescharacteristic
130C2×C22⋊C4—112no—
131C2×C22⋊C4—112no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4C2×D1112yes—
134C2×C22⋊C4C2×D1112yes—
135C2×C42—111no—
136C2×C42—112no—
137#95—112no—
138#95—112no—
139#95—111no—
140#95—112no—
141#95—112no—
142#95C2×D1111yescharacteristic
143C2×C11—44no—
144C2×C11#52512yes—
145C2×C11#53711yescharacteristic
146C2×C11#55111yescharacteristic
147C2×C11#55212yes—
148C2×C11#55511yescharacteristic
149C24C22×D1112yes—
150C2×D4—24no—
151C2×D4—41no—
152C22×C4—112no—
153C22×C4—112no—
154C22×C4—112no—
155C22×C4—112no—
156C22×C4—224no—
157C22×C4—224no—
158C22×C4—224no—
159C22×C4C22×D1111yescharacteristic
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1112yes—
162C22×C4C22×D1111yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—224no—
165C4⋊C4—224no—
166C4⋊C4—224no—
167C4⋊C4—441no—
168C4⋊C4—441no—
169C22⋊C4—24no—
170C22⋊C4—24no—
171C22⋊C4—224no—
172C22⋊C4—224no—
173C22⋊C4—442no—
174C42—114no—
175C42—224no—
176C11#260911yescharacteristic, complemented, Sylow
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23#434114yes—
184C23C23×D1111yescharacteristic
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—114no—
196C2×C4—114no—
197C2×C4—2216no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4D4×D1112yes—
209C22—24no—
210C22—24no—
211C22—24no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22C2×D4×D1111yescharacteristic
217C22C2×#434112yes—
218C22#6703711yescharacteristic
219C22#41×D1112yes—
220C22#6704311yescharacteristic
221C4—22no—
222C4—41no—
223C4—41no—
224C4—42no—
225C4—224no—
226C4—224no—
227C4—442no—
228C4—442no—
229C2—44no—
230C2#1062311811yescharacteristic
231C2#1062312811yescharacteristic
232C2#1062313712yes—
233C2#1062318112yes—
234C2#1062320111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC22×D4×C11C22
hypercenter#394D11
hypocenterC11#2609
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#66930C2semidirect
4. #10622596C2semidirect
5. #10622590C2semidirect
6. #10622564C2semidirect
7. #10622561C2semidirect
8. #10622559C2semidirect
9. #10622265C2semidirect
58. C4×Dic11D4semidirect
176. C11#2609semidirect

Maximal subgroups

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

subgroupindex
C2×#669302
C11×#3942
#106228332
#106225962
#106225902
#106225642
#106225612
#106225592
#106222652
#260911