Finite Group Databasebeta

← #13073099

Subgroups — #13073099

Order 1408.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×Dic11⋊C4C211yesmaximal, characteristic
2C2×#66931C211yesmaximal, characteristic
3C11×#381C211yesmaximal, characteristic
4#10622824C211yesmaximal, characteristic
5#10622556C211yesmaximal, characteristic
6#10622556C211yesmaximal, characteristic
7C22⋊C4×Dic11C211yesmaximal, characteristic
8#10622273C212yesmaximal, complemented
9#10622271C212yesmaximal, complemented
10#10622263C212yesmaximal, complemented
11#10622259C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4—24no—
22C2×Dic11⋊C4C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2212yes—
27#66931—24no—
28C11×#95C2212yes—
29C11×#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11—24no—
46C22×Dic11—22no—
47C22×Dic11—22no—
48C22×Dic11—22no—
49C22×Dic11D414yes—
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C2×Dic22—22no—
57C2×Dic22—24no—
58C11×C22⋊C4—22no—
59C11×C22⋊C4—22no—
60C22⋊Dic11—22no—
61C22⋊Dic11—22no—
62C4⋊Dic11—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—24no—
66Dic11⋊C4—24no—
67C4×Dic11—24no—
68#2503—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11—22no—
71C23×C11C2×D412yes—
72C23×C11#4112yes—
73C23×C11#4112yes—
74C23×C11C2411yescharacteristic
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—44no—
86C2×Dic11—22no—
87C2×Dic11—28no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—44no—
99C2×Dic11C2×D412yes—
100C2×Dic11C2×D412yes—
101C2×Dic11#4114yes—
102Dic22—44no—
103C2×C22⋊Q8—111no—
104C22×C4⋊C4—111no—
105#400—112no—
106#400—112no—
107#391—112no—
108#382—112no—
109#381—111no—
110#381—111no—
111#381—111no—
112#381D1111yescharacteristic
113C4×C22⋊C4—111no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—24no—
117C22×C11—24no—
118C22×C11#12414yes—
119C22×C11C22×D411yescharacteristic
120C22×C11C2×#4111yescharacteristic
121C22×C11C2×#4111yescharacteristic
122C22×C11C2×#4112yes—
123C22×C112−1+412yes—
124C4×C11—41no—
125C4×C11—42no—
126C4×C11—41no—
127C4×C11—42no—
128Dic11—22no—
129Dic11—41no—
130Dic11—42no—
131Dic11—41no—
132Dic11—42no—
133Dic11#12314yes—
134C22×Q8—111no—
135C23×C4—111no—
136C23×C4—111no—
137C23×C4C2×D1111yescharacteristic
138C22⋊Q8—224no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—111no—
142C2×C4⋊C4—111no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—224no—
145C2×C22⋊C4—111no—
146C2×C22⋊C4—111no—
147C2×C22⋊C4C2×D1111yescharacteristic
148C2×C22⋊C4C2×D1111yescharacteristic
149C2×C42—112no—
150#95—112no—
151#95—112no—
152#95—112no—
153#95—112no—
154#95—112no—
155#95—112no—
156#95—112no—
157#95C2×D1112yes—
158#95C2×D1112yes—
159C2×C11—24no—
160C2×C11C2×#12311yescharacteristic
161C2×C11C2×#12411yescharacteristic
162C2×C11#53611yescharacteristic
163C2×C11#55212yes—
164C2×C11#55212yes—
165C24C22×D1111yescharacteristic
166C2×Q8—222no—
167C2×Q8—224no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—111no—
172C22×C4—114no—
173C22×C4—111no—
174C22×C4—112no—
175C22×C4—111no—
176C22×C4—111no—
177C22×C4—112no—
178C22×C4—224no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4C22×D1112yes—
183C22×C4C22×D1111yescharacteristic
184C22×C4C22×D1111yescharacteristic
185C22×C4C22×D1112yes—
186C4⋊C4—224no—
187C4⋊C4—224no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C22⋊C4—22no—
192C22⋊C4—22no—
193C22⋊C4—222no—
194C22⋊C4—222no—
195C42—224no—
196C11#250311yescharacteristic, complemented, Sylow
197C23—22no—
198C23—22no—
199C23#433912yes—
200C23D4×D1112yes—
201C23#434112yes—
202C23C23×D1111yescharacteristic
203Q8—444no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—44no—
215C2×C4—112no—
216C2×C4—114no—
217C2×C4—112no—
218C2×C4—228no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—444no—
231C22—24no—
232C22—22no—
233C22—24no—
234C22—22no—
235C22#6693814yes—
236C22C2×#433911yescharacteristic
237C22C2×D4×D1111yescharacteristic
238C22C2×#434111yescharacteristic
239C22#41×D1112yes—
240C22#6704312yes—
241C4—42no—
242C4—41no—
243C4—42no—
244C4—41no—
245C4—114no—
246C4—222no—
247C4—442no—
248C4—442no—
249C4—441no—
250C4—441no—
251C2—24no—
252C2C2×#6693811yescharacteristic
253C2#1062306212yes—
254C2#1062317911yescharacteristic
255C2#1062318112yes—
256C2D11×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC24×C11C23
hypercenter#381D11
hypocenterC11#2503
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
8. #10622273C2semidirect
9. #10622271C2semidirect
10. #10622263C2semidirect
11. #10622259C2semidirect
196. C11#2503semidirect

Maximal subgroups

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

subgroupindex
C22×Dic11⋊C42
C2×#669312
C11×#3812
#106228242
#106225562
C22⋊C4×Dic112
#106222732
#106222712
#106222632
#106222592
#250311