Finite Group Databasebeta

← #13074521

Subgroups — #13074521

Order 1408.

450 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 133 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×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#66932C211yesmaximal, characteristic
3C11×#393C211yesmaximal, characteristic
4#10622842C211yesmaximal, characteristic, complemented
5#10622566C211yesmaximal, characteristic
6#10622564C212yesmaximal
7#10622561C212yesmaximal
8#10622274C211yesmaximal, characteristic, complemented
9#10622274C212yesmaximal, complemented
10#10622265C212yesmaximal, complemented
11#10622263C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×C11×C22⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C22⋊Dic11C2212yes—
18Q8×Dic11—24no—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29#66932—24no—
30C11×#95C2211yescharacteristic
31C11×#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C2×Q8×C11—22no—
39C2×Q8×C11—24no—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C11×C22⋊C4—22no—
51C11×C22⋊C4—24no—
52C22⋊Dic11—22no—
53C22⋊Dic11—22no—
54C22⋊Dic11—42no—
55C4⋊Dic11—22no—
56C4⋊Dic11—24no—
57C4⋊Dic11—22no—
58C4⋊Dic11—42no—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—24no—
62Dic11⋊C4—42no—
63C4×Dic11—24no—
64C4×Dic11D414yes—
65#2637—111nomaximal, Sylow
66C23×C11—21no—
67C23×C11—22no—
68C23×C11—21no—
69C23×C11—21no—
70C23×C11—22no—
71C23×C11C2411yescharacteristic
72Q8×C11—28no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D412yes—
82C2×C4×C11#4114yes—
83C2×Dic11—21no—
84C2×Dic11—21no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11C2×D412yes—
98C2×Dic11C2×D412yes—
99C2×#126—111no—
100C2×C4×Q8—111no—
101#398—111no—
102#398—112no—
103#397—111no—
104#396—112no—
105#395—111no—
106#393D1111yescharacteristic
107#388—112no—
108#387—112no—
109#382—111no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11C22×D411yescharacteristic
116C22×C11C2×#4112yes—
117C22×C11H(5,𝔽2)11yescharacteristic
118C22×C112−1+411yescharacteristic
119C22×C112−1+412yes—
120C4×C11—22no—
121C4×C11—24no—
122C4×C11—41no—
123C4×C11—42no—
124Dic11—22no—
125Dic11—22no—
126Dic11—41no—
127Dic11—42no—
128Dic11—41no—
129Dic11—42no—
130C22×Q8C2×D1111yescharacteristic
131#126—224no—
132C4×Q8—224no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—111no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4—112no—
141C2×C22⋊C4—111no—
142C2×C22⋊C4—111no—
143C2×C22⋊C4—112no—
144C2×C22⋊C4C2×D1111yescharacteristic
145C2×C22⋊C4C2×D1112yes—
146C2×C42—111no—
147C2×C42—112no—
148#95—112no—
149#95—111no—
150#95—112no—
151#95—112no—
152#95—112no—
153#95C2×D1111yescharacteristic
154#95C2×D1112yes—
155C2×C11—81no—
156C2×C11#52511yescharacteristic
157C2×C11#53611yescharacteristic
158C2×C11#53711yescharacteristic
159C2×C11#54112yes—
160C2×C11#54212yes—
161C24C22×D1111yescharacteristic
162C2×Q8—22no—
163C2×Q8—24no—
164C22×C4—111no—
165C22×C4—111no—
166C22×C4—112no—
167C22×C4—112no—
168C22×C4—111no—
169C22×C4—111no—
170C22×C4C22×D1111yescharacteristic
171C22×C4C22×D1112yes—
172C22×C4C22×D1111yescharacteristic
173C22×C4C22×D1112yes—
174C4⋊C4—224no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4—224no—
180C4⋊C4—442no—
181C4⋊C4—442no—
182C22⋊C4—22no—
183C22⋊C4—24no—
184C22⋊C4—222no—
185C22⋊C4—222no—
186C22⋊C4—442no—
187C42—114no—
188C42—224no—
189C11#263711yescharacteristic, complemented, Sylow
190C23—21no—
191C23—22no—
192C23—21no—
193C23—21no—
194C23—22no—
195C23C23×D1111yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—112no—
206C2×C4—112no—
207C2×C4—221no—
208C2×C4—221no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—221no—
212C2×C4—221no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—221no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—221no—
220C2×C4—222no—
221C2×C4D4×D1112yes—
222C2×C4#434114yes—
223C22—41no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22C2×D4×D1111yescharacteristic
229C22C2×#434112yes—
230C22#6704011yescharacteristic
231C22#6704211yescharacteristic
232C22#6704312yes—
233C4—22no—
234C4—24no—
235C4—41no—
236C4—42no—
237C4—222no—
238C4—222no—
239C4—441no—
240C4—442no—
241C4—441no—
242C4—442no—
243C2—81no—
244C2#1062311711yescharacteristic
245C2#1062315612yes—
246C2#1062316011yescharacteristic
247C2#1062320611yescharacteristic
248C2#1062321312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC24×C11C23
hypercenter#393D11
hypocenterC11#2637
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic11C2semidirect
4. #10622842C2semidirect
8. #10622274C2semidirect
9. #10622274C2semidirect
10. #10622265C2semidirect
11. #10622263C2semidirect
189. C11#2637semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
C2×#669322
C11×#3932
#106228422
#106225662
#106225642
#106225612
#106222742
#106222652
#106222632
#263711