Finite Group Databasebeta

← #13071908

Subgroups — #13071908

Order 1408.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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×#66940C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic
4#10622593C211yesmaximal, characteristic
5#10622592C212yesmaximal
6#10622592C211yesmaximal, characteristic
7C4⋊C4×Dic11C212yesmaximal
8#10622270C212yesmaximal
9#10622269C211yesmaximal, characteristic
10#10622262C212yesmaximal
11#10622261C211yesmaximal, characteristic
12C22×Dic22C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2212yes—
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2211yescharacteristic
19C2×Dic11⋊C4C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24C2×C4×Dic11C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27C2×C4×Dic11C2212yes—
28#66940—24no—
29#66940—24no—
30C11×#95C2211yescharacteristic
31C11×#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2311yescharacteristic
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48C2×Dic22—22no—
49C2×Dic22—22no—
50C2×Dic22—24no—
51C2×Dic22—22no—
52C2×Dic22—22no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—24no—
56C4⋊Dic11—24no—
57Dic11⋊C4—24no—
58Dic11⋊C4—22no—
59Dic11⋊C4—24no—
60Dic11⋊C4—24no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63C4×Dic11—22no—
64C4×Dic11—24no—
65C4×Dic11D414yes—
66C4×Dic11Q818yescomplemented
67#2399—111nomaximal, Sylow
68C23×C11C2411yescharacteristic
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×Q814yes—
81C2×C4×C11#4112yes—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11C2×D412yes—
93C2×Dic11C2×D412yes—
94C2×Dic11C2×Q814yes—
95C2×Dic11C2×Q814yes—
96C2×Dic11#4112yes—
97C2×Dic11#4114yes—
98Dic22—28no—
99Dic22—28no—
100C2×C4×Q8—111no—
101C2×C4×Q8—111no—
102#398—111no—
103#398—112no—
104#398D1111yescharacteristic
105#395—112no—
106#395—111no—
107#395—111no—
108C4×C4⋊C4—112no—
109C4×C4⋊C4—112no—
110#376—111no—
111C22×C11C22×D411yescharacteristic
112C22×C11C22×Q812yes—
113C22×C11C2×#4111yescharacteristic
114C22×C11C2×#4111yescharacteristic
115C22×C11C2×#4112yes—
116C4×C11—22no—
117C4×C11—22no—
118C4×C11—24no—
119C4×C11—42no—
120C4×C11—41no—
121Dic11—22no—
122Dic11—22no—
123Dic11—24no—
124Dic11—24no—
125Dic11—41no—
126Dic11C4⋊Q814yes—
127C22×Q8—111no—
128C22×Q8—111no—
129C4×Q8—224no—
130C4×Q8—224no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4—111no—
134C2×C4⋊C4—112no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4C2×D1111yescharacteristic
138C2×C4⋊C4C2×D1111yescharacteristic
139C2×C4⋊C4C2×D1112yes—
140C2×C42—111no—
141C2×C42—112no—
142C2×C42—112no—
143C2×C42—111no—
144C2×C42—111no—
145#95—111no—
146#95—112no—
147#95—112no—
148#95—112no—
149#95—112no—
150#95C2×D1111yescharacteristic
151#95C2×D1112yes—
152C2×C11#52511yescharacteristic
153C2×C11#52511yescharacteristic
154C2×C11C2×C4⋊Q811yescharacteristic
155C2×C11#53312yes—
156C2×C11#53312yes—
157C2×Q8—222no—
158C2×Q8—222no—
159C2×Q8—224no—
160C2×Q8—222no—
161C2×Q8—222no—
162C22×C4—111no—
163C22×C4—112no—
164C22×C4—111no—
165C22×C4—111no—
166C22×C4—112no—
167C22×C4—111no—
168C22×C4C22×D1112yes—
169C22×C4C22×D1111yescharacteristic
170C22×C4C22×D1111yescharacteristic
171C22×C4C22×D1111yescharacteristic
172C22×C4C22×D1112yes—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—224no—
177C4⋊C4—222no—
178C4⋊C4—224no—
179C4⋊C4—224no—
180C4⋊C4—224no—
181C4⋊C4—222no—
182C42—114no—
183C42—118no—
184C42—222no—
185C42—224no—
186C42—222no—
187C11#239911yescharacteristic, complemented, Sylow
188C23C23×D1111yescharacteristic
189Q8—228no—
190Q8—228no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—112no—
202C2×C4—114no—
203C2×C4—112no—
204C2×C4—114no—
205C2×C4—112no—
206C2×C4—114no—
207C2×C4—221no—
208C2×C4—222no—
209C2×C4—221no—
210C2×C4—221no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—221no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4—222no—
217C2×C4D4×D1112yes—
218C2×C4#434112yes—
219C2×C4Q8×D1114yes—
220C22C2×D4×D1111yescharacteristic
221C22C2×#434111yescharacteristic
222C22C2×Q8×D1112yes—
223C22#41×D1111yescharacteristic
224C22#41×D1112yes—
225C4—22no—
226C4—24no—
227C4—22no—
228C4—42no—
229C4—41no—
230C4—114no—
231C4—222no—
232C4—222no—
233C4—224no—
234C4—224no—
235C4—441no—
236C2#1062313711yescharacteristic
237C2#1062315312yes—
238C2#1062318711yescharacteristic
239C2#1062321912yes—
240C2D11×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2399
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
66. C4×Dic11Q8semidirect
187. C11#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#669402
C11×#3982
#106225932
#106225922
C4⋊C4×Dic112
#106222702
#106222692
#106222622
#106222612
#239911