Finite Group Databasebeta

← #13076948

Subgroups — #13076948

Order 1408.

688 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 177 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×#66983C211yesmaximal, characteristic
2C22×C4×Dic11C211yesmaximal, characteristic, complemented
3C2×#66939C212yesmaximal, complemented
4C11×#380C211yesmaximal, characteristic, complemented
5#10622601C212yesmaximal, complemented
6#10622598C212yesmaximal, complemented
7#10622571C212yesmaximal, complemented
8#10622283C214yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C22×C22⋊D11C2212yes—
11C23×Dic11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16#66983—24no—
17C2×(C2×D11)⋊C4C2214yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×C4⋊Dic11C2214yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4×Dic11—24no—
23C2×C4×Dic11C2212yes—
24C2×C4×Dic11C2212yes—
25#66939—28no—
26C11×#95C2212yes—
27C11⋊#95C2214yes—
28C24×C11C2311yescharacteristic
29C23×D11C2312yes—
30C22×C4×C11—24no—
31C22×C4×C11D414yes—
32C22×C4×C11C2314yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C2×C22⋊D11—24no—
36C2×C22⋊D11—24no—
37C2×C22⋊D11—24no—
38C22×Dic11—24no—
39C22×Dic11—22no—
40C22×Dic11—22no—
41C22×Dic11—22no—
42C22×Dic11D414yescomplemented
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C2×D44—22no—
47C2×D44—24no—
48C11×C4⋊C4—24no—
49C11×C22⋊C4—24no—
50(C2×D11)⋊C4—28no—
51(C2×D11)⋊C4—28no—
52(C2×D11)⋊C4—24no—
53C4⋊Dic11—28no—
54C4⋊Dic11—22no—
55C4×Dic11—24no—
56C4×Dic11—24no—
57#2854—111nomaximal, Sylow
58C23×C11—22no—
59C23×C11—22no—
60C23×C11C2×D412yes—
61C23×C11C2×D412yes—
62C23×C11#4112yes—
63C23×C11C2411yescharacteristic
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—24no—
67C22×D11—24no—
68C22×D11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—28no—
71C2×C4×C11—24no—
72C2×C4×C11—24no—
73C2×C4×C11—24no—
74C2×C4×C11C2×D412yes—
75C2×C4×C11C2×D412yes—
76C2×C4×C11#4114yes—
77C22⋊D11—48no—
78C2×Dic11—28no—
79C2×Dic11—28no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11C2×D414yes—
88C2×Dic11#4114yes—
89D44—44no—
90C2×#123—112no—
91C2×#121—111no—
92C22×C42—111no—
93#390—112no—
94#389—112no—
95#388—114no—
96#386—112no—
97#380D1111yescharacteristic, complemented
98C22×C11—22no—
99C22×C11—22no—
100C22×C11—24no—
101C22×C11—24no—
102C22×C11#12114yes—
103C22×C11C22×D411yescharacteristic
104C22×C11C22×D411yescharacteristic
105C22×C11C2×#4112yes—
106C22×C11C2×#4111yescharacteristic
107C22×C11C2×#4112yes—
108C2×D11—42no—
109C2×D11—42no—
110C2×D11—42no—
111C2×D11—44no—
112C2×D11—44no—
113C4×C11—22no—
114C4×C11—44no—
115C4×C11#12314yescomplemented
116Dic11—24no—
117Dic11—24no—
118Dic11—42no—
119C22×D4—112no—
120C22×D4—111no—
121C23×C4—111no—
122C23×C4—111no—
123C23×C4C2×D1111yescharacteristic
124#123—228no—
125#121—224no—
126C2×C4⋊C4—111no—
127C2×C4⋊C4—114no—
128C2×C4⋊C4C2×D1112yes—
129C2×C22⋊C4—112no—
130C2×C22⋊C4—114no—
131C2×C22⋊C4—114no—
132C2×C22⋊C4C2×D1112yes—
133C2×C42—112no—
134C2×C42—112no—
135C2×C42—224no—
136#95—114no—
137#95C2×D1112yes—
138C2×C11—24no—
139C2×C11C2×#12111yescharacteristic
140C2×C11C2×#12311yescharacteristic
141C2×C11#52511yescharacteristic
142C2×C11#52912yes—
143C2×C11#53212yes—
144D11—82no—
145C24—112no—
146C24C22×D1111yescharacteristic
147C2×D4—224no—
148C2×D4—224no—
149C2×D4—224no—
150C2×D4—222no—
151C2×D4—224no—
152C22×C4—24no—
153C22×C4—114no—
154C22×C4—112no—
155C22×C4—112no—
156C22×C4—112no—
157C22×C4—224no—
158C22×C4—222no—
159C22×C4—222no—
160C22×C4—222no—
161C22×C4D4414yes—
162C22×C4C22×D1114yes—
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—228no—
167C4⋊C4—222no—
168C22⋊C4—24no—
169C22⋊C4—228no—
170C22⋊C4—228no—
171C22⋊C4—224no—
172C42—224no—
173C42—224no—
174C11#285411yescharacteristic, complemented, Sylow
175C23—22no—
176C23—22no—
177C23—222no—
178C23—222no—
179C23—224no—
180C23—222no—
181C23—224no—
182C23C2×D4412yes—
183C23D4×D1112yes—
184C23#434312yes—
185C23C23×D1111yescharacteristic
186D4—448no—
187D4—444no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—114no—
194C2×C4—114no—
195C2×C4—228no—
196C2×C4—228no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4C2×D4412yes—
205C2×C4C2×D4412yes—
206C2×C4#434114yes—
207C22—22no—
208C22—22no—
209C22—24no—
210C22—24no—
211C22—442no—
212C22—442no—
213C22—442no—
214C22—444no—
215C22—444no—
216C22#6694814yes—
217C22C22×D4411yescharacteristic
218C22C2×D4×D1111yescharacteristic
219C22C2×#434112yes—
220C22C2×#434311yescharacteristic
221C22#41×D1112yes—
222C4—22no—
223C4—44no—
224C4—224no—
225C4—224no—
226C4—442no—
227C4#6693914yescomplemented
228C2—24no—
229C2—882no—
230C2C2×#6693911yescharacteristic
231C2C2×#6694811yescharacteristic
232C2#1062305511yescharacteristic
233C2#1062312712yes—
234C2#1062315512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC2×#66983C2
hypercenter#380D11
hypocenterC11#2854
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic11C2semidirect
3. C2×#66939C2semidirect
4. C11×#380C2semidirect
5. #10622601C2semidirect
6. #10622598C2semidirect
7. #10622571C2semidirect
8. #10622283C2semidirect
42. C22×Dic11D4semidirect
97. #380D11semidirect
115. C4×C11#123semidirect
174. C11#2854semidirect
227. C4#66939semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C22×C4×Dic112
C2×#669392
C11×#3802
#106226012
#106225982
#106225712
#106222832
#285411