Finite Group Databasebeta

← #13075543

Subgroups — #13075543

Order 1408.

504 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 129 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×#66947C212yesmaximal
2C11×#398C211yesmaximal, characteristic, complemented
3#10622602C212yesmaximal, complemented
4#10622601C211yesmaximal, characteristic
5#10622596C211yesmaximal, characteristic, complemented
6#10622585C212yesmaximal, complemented
7#10622288C212yesmaximal, complemented
8#10622288C212yesmaximal, complemented
9#10622281C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×C4×D11C2212yes—
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25#66947—28no—
26C11×#95C2212yes—
27C11×#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C23×D11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×D44—41no—
42C2×D44—41no—
43C2×D44D414yes—
44C2×C4×D11—24no—
45C2×C4×D11—42no—
46C2×C4×D11—42no—
47C11×C4⋊C4—24no—
48C11×C4⋊C4—41no—
49C11×C4⋊C4—41no—
50(C2×D11)⋊C4—24no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—24no—
55C4⋊Dic11—41no—
56Dic11⋊C4—24no—
57Dic11⋊C4—24no—
58Dic11⋊C4—42no—
59C4×Dic11—41no—
60#2724—111nomaximal, Sylow
61C23×C11C2411yescharacteristic
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—22no—
67C22×D11—22no—
68C22×D11C2×D414yes—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11C2×D412yes—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11#4114yes—
91D44—44no—
92C4×D11—48no—
93C2×#123—112no—
94#398—111no—
95#398D1111yescharacteristic, complemented
96#397—112no—
97#397—112no—
98#390—111no—
99#389—112no—
100#385—112no—
101#385—112no—
102C22×C11C22×D411yescharacteristic
103C22×C11C2×#4112yes—
104C22×C11H(5,𝔽2)11yescharacteristic
105C22×C11H(5,𝔽2)11yescharacteristic
106C22×C112−1+412yes—
107C2×D11—24no—
108C2×D11—24no—
109C2×D11—24no—
110C2×D11—42no—
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—42no—
114C4×C11—22no—
115C4×C11—42no—
116C4×C11—42no—
117C4×C11—41no—
118C4×C11—41no—
119Dic11—24no—
120Dic11—42no—
121Dic11—42no—
122C22×D4—111no—
123C23×C4—112no—
124#123—228no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4C2×D1112yes—
130C2×C4⋊C4C2×D1111yescharacteristic
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C22⋊C4—112no—
133C2×C22⋊C4—112no—
134C2×C22⋊C4—112no—
135C2×C22⋊C4—112no—
136C2×C22⋊C4—112no—
137C2×C42—111no—
138#95—112no—
139#95—112no—
140#95—112no—
141#95—111no—
142#95C2×D1112yes—
143#95C2×D1111yescharacteristic
144C2×C11#53411yescharacteristic
145C2×C11#53912yes—
146C2×C11#54712yes—
147C2×C11#55911yescharacteristic
148C2×C11#56311yescharacteristic
149D11—44no—
150C24—112no—
151C2×D4—114no—
152C2×D4—441no—
153C2×D4—441no—
154C22×C4—112no—
155C22×C4—112no—
156C22×C4—112no—
157C22×C4—224no—
158C22×C4—442no—
159C22×C4—442no—
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1112yes—
162C22×C4C22×D1111yescharacteristic
163C22×C4C22×D1112yes—
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—224no—
169C4⋊C4—224no—
170C4⋊C4—442no—
171C4⋊C4—441no—
172C22⋊C4—224no—
173C22⋊C4—224no—
174C22⋊C4—224no—
175C22⋊C4—224no—
176C22⋊C4—224no—
177C42—441no—
178C11#272411yescharacteristic, complemented, Sylow
179C23—114no—
180C23—222no—
181C23—222no—
182C23—222no—
183C23—222no—
184C23—222no—
185C23—222no—
186C23C23×D1111yescharacteristic
187D4—444no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—114no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—448no—
210C2×C4D4×D1112yes—
211C22—224no—
212C22—224no—
213C22—224no—
214C22—442no—
215C22—442no—
216C22—442no—
217C22—442no—
218C22C2×D4×D1111yescharacteristic
219C22#6703711yescharacteristic
220C22#6704012yes—
221C22#41×D1112yes—
222C22#6704211yescharacteristic
223C4—22no—
224C4—42no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—224no—
229C4—442no—
230C4—442no—
231C2—444no—
232C2#1062313611yescharacteristic
233C2#1062316212yes—
234C2#1062319511yescharacteristic
235C2#1062322312yes—
236C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC22×D44C22
hypercenter#398D11
hypocenterC11#2724
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C11×#398C2semidirect
3. #10622602C2semidirect
5. #10622596C2semidirect
6. #10622585C2semidirect
7. #10622288C2semidirect
8. #10622288C2semidirect
9. #10622281C2semidirect
95. #398D11semidirect
178. C11#2724semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C11×#3982
#106226022
#106226012
#106225962
#106225852
#106222882
#106222812
#272411