Finite Group Databasebeta

← #13073079

Subgroups — #13073079

Order 1408.

568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 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×C11×#121C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic, complemented
3#10622835C214yesmaximal, complemented
4#10622834C211yesmaximal, characteristic, complemented
5#10622834C211yesmaximal, characteristic, complemented
6C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
7#10622590C211yesmaximal, characteristic, complemented
8#10622589C211yesmaximal, characteristic, complemented
9#10622557C214yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C22×D4×C11C2212yes—
12C23×C4×C11C2211yescharacteristic
13C11×#121—24no—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2214yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2214yes—
20#66979—24no—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2214yes—
24C2×C4×Dic11C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27C11⋊#95C2212yes—
28C11⋊#95C2214yes—
29C24×C11C2312yes—
30C24×C11C2311yescharacteristic
31C2×D4×C11—24no—
32C2×D4×C11—22no—
33C2×D4×C11—22no—
34C2×D4×C11—22no—
35C2×D4×C11—44no—
36C22×C4×C11—22no—
37C22×C4×C11—22no—
38C22×C4×C11D414yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C11×C4⋊C4—22no—
47C11×C22⋊C4—24no—
48C22⋊Dic11—24no—
49C22⋊Dic11—28no—
50C22⋊Dic11—24no—
51C22⋊Dic11—44no—
52C4⋊Dic11—22no—
53C4⋊Dic11—22no—
54Dic11⋊C4—44no—
55C4×Dic11—24no—
56C4×Dic11—22no—
57C4×Dic11—22no—
58#2500—111nomaximal, Sylow
59C23×C11—22no—
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—24no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—24no—
68C23×C11C2×D412yes—
69C23×C11C2411yescharacteristic
70D4×C11—48no—
71D4×C11—44no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—28no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11#4112yes—
80C2×C4×C11#4112yes—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—24no—
87C2×Dic11—22no—
88C2×Dic11—24no—
89C2×Dic11—22no—
90C2×Dic11#4114yes—
91C2×#121D1111yescharacteristic
92C2×#117—111no—
93#394—114no—
94#390—111no—
95#390—111no—
96#388—114no—
97#384—111no—
98#382—111no—
99C4×C22⋊C4—111no—
100C22×C11—22no—
101C22×C11—22no—
102C22×C11—22no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11—44no—
109C22×C11—44no—
110C22×C11C22×D411yescharacteristic
111C22×C11C2×#4111yescharacteristic
112C22×C11C2×#4111yescharacteristic
113C22×C11C2×#4112yes—
114C22×C11H(5,𝔽2)12yes—
115C4×C11—22no—
116C4×C11—42no—
117C4×C11#12314yes—
118Dic11—24no—
119Dic11—42no—
120Dic11—42no—
121Dic11—42no—
122C22×D4C2×D1111yescharacteristic
123C22×D4C2×D1112yes—
124C23×C4C2×D1111yescharacteristic
125#121—24no—
126#117—224no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—114no—
130C2×C4⋊C4C2×D1111yescharacteristic
131C2×C22⋊C4—112no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—114no—
134C2×C22⋊C4—114no—
135C2×C22⋊C4C2×D1112yes—
136C2×C42—112no—
137C2×C42—111no—
138C2×C42—111no—
139#95—112no—
140#95—114no—
141C2×C11—42no—
142C2×C11—82no—
143C2×C11C2×#12311yescharacteristic
144C2×C11#53211yescharacteristic
145C2×C11#53511yescharacteristic
146C2×C11#55312yes—
147C2×C11#55512yes—
148C24C22×D1112yes—
149C24C22×D1111yescharacteristic
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—44no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—112no—
158C22×C4—112no—
159C22×C4—112no—
160C22×C4—112no—
161C22×C4C22⋊D1114yes—
162C22×C4C22×D1112yes—
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4—444no—
169C22⋊C4—24no—
170C22⋊C4—224no—
171C22⋊C4—228no—
172C22⋊C4—224no—
173C22⋊C4—444no—
174C42—222no—
175C42—222no—
176C42—224no—
177C11#250011yescharacteristic, complemented, Sylow
178C23—21no—
179C23—21no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23—24no—
185C23—24no—
186C23—22no—
187C23C2×C22⋊D1112yes—
188C23C23×D1111yescharacteristic
189D4—48no—
190D4—44no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—114no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—224no—
202C2×C4—224no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4#434112yes—
207C2×C4#434112yes—
208C2×C4C2×C22⋊D1112yes—
209C2×C4C2×C22⋊D1112yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—44no—
219C22—44no—
220C22C2×#434111yescharacteristic
221C22C2×#434111yescharacteristic
222C22#6703712yes—
223C22#41×D1112yes—
224C22C22×C22⋊D1111yescharacteristic
225C4—22no—
226C4—42no—
227C4—224no—
228C4—442no—
229C4—442no—
230C4—442no—
231C4#6698814yes—
232C2—42no—
233C2—82no—
234C2#1062314512yes—
235C2#1062314712yes—
236C2C2×#6698811yescharacteristic
237C2#1062333611yescharacteristic
238C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2500
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66979C2semidirect
3. #10622835C2semidirect
4. #10622834C2semidirect
5. #10622834C2semidirect
6. C4×C22⋊Dic11C2semidirect
7. #10622590C2semidirect
8. #10622589C2semidirect
9. #10622557C2semidirect
177. C11#2500semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669792
#106228352
#106228342
C4×C22⋊Dic112
#106225902
#106225892
#106225572
#250011