Finite Group Databasebeta

← #13072934

Subgroups — #13072934

Order 1408.

584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×C4×C22⋊D11C211yesmaximal, characteristic
2C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
3C11×#380C211yesmaximal, characteristic, complemented
4#10622600C212yesmaximal, complemented
5#10622598C212yesmaximal, complemented
6#10622571C212yesmaximal
7#10622563C212yesmaximal, complemented
8#10622290C212yesmaximal, complemented
9#10622272C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2211yescharacteristic
12C23×Dic11C2212yes—
13C22×C4×D11C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C4×C22⋊D11—24no—
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2214yes—
20C2×C4⋊Dic11—24no—
21C2×C4⋊Dic11C2212yes—
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2214yes—
24C2×Dic11⋊C4C2211yescharacteristic
25C2×C4×Dic11C2211yescharacteristic
26C11×#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C24×C11C2311yescharacteristic
30C23×D11C2311yescharacteristic
31C22×C4×C11—24no—
32C22×C4×C11D414yes—
33C22×C4×C11C2314yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—22no—
37C2×C22⋊D11—22no—
38C2×C22⋊D11Q814yes—
39C22×Dic11—24no—
40C22×Dic11—44no—
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2314yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C2×C4×D11—22no—
46C2×C4×D11—24no—
47C11×C4⋊C4—24no—
48C11×C22⋊C4—24no—
49C22⋊Dic11—22no—
50(C2×D11)⋊C4—22no—
51(C2×D11)⋊C4—44no—
52C4⋊Dic11—24no—
53C4⋊Dic11—24no—
54C4⋊Dic11—44no—
55Dic11⋊C4—22no—
56C4×Dic11—22no—
57#2487—111nomaximal, Sylow
58C23×C11—22no—
59C23×C11—22no—
60C23×C11C2×D412yes—
61C23×C11C2×Q812yes—
62C23×C11#4112yes—
63C23×C11C2411yescharacteristic
64C22×D11—21no—
65C22×D11—22no—
66C22×D11—21no—
67C22×D11—22no—
68C22×D11C2×Q812yes—
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—28no—
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—24no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—24no—
86C2×Dic11—24no—
87C2×Dic11—48no—
88C2×Dic11C2×Q812yes—
89C4×D11—44no—
90C2×C4×D4—111no—
91C22×C4⋊C4—111no—
92#400—112no—
93#399—112no—
94#389—112no—
95#386—112no—
96#385—112no—
97#380—112no—
98#380D1111yescharacteristic, complemented
99C22×C11—22no—
100C22×C11—22no—
101C22×C11—24no—
102C22×C11—24no—
103C22×C11C22⋊Q814yes—
104C22×C11C22×D411yescharacteristic
105C22×C11C22×Q811yescharacteristic
106C22×C11C2×#4111yescharacteristic
107C22×C11C2×#4112yes—
108C22×C11H(5,𝔽2)12yes—
109C2×D11—22no—
110C2×D11—24no—
111C2×D11—41no—
112C2×D11—41no—
113C2×D11—42no—
114C4×C11—22no—
115C4×C11—44no—
116C4×C11#12314yes—
117Dic11—22no—
118Dic11—41no—
119Dic11—41no—
120Dic11—44no—
121C22×D4—111no—
122C23×C4—112no—
123C23×C4—111no—
124C23×C4C2×D1111yescharacteristic
125C4×D4—224no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—114no—
130C2×C4⋊C4—224no—
131C2×C4⋊C4C2×D1112yes—
132C2×C22⋊C4—111no—
133C2×C22⋊C4—111no—
134C2×C22⋊C4—114no—
135C2×C22⋊C4C2×D1112yes—
136C2×C42—111no—
137#95—114no—
138#95—114no—
139#95C2×D1112yes—
140C2×C11—24no—
141C2×C11C2×C22⋊Q811yescharacteristic
142C2×C11C2×#12311yescharacteristic
143C2×C11#53511yescharacteristic
144C2×C11#55312yes—
145C2×C11#55412yes—
146D11—42no—
147C24—111no—
148C24C22×D1111yescharacteristic
149C2×D4—114no—
150C2×D4—222no—
151C2×D4—222no—
152C22×C4—24no—
153C22×C4—111no—
154C22×C4—111no—
155C22×C4—114no—
156C22×C4—111no—
157C22×C4—224no—
158C22×C4—222no—
159C22×C4—224no—
160C22×C4—444no—
161C22×C4D4414yes—
162C22×C4C22×D1114yes—
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—224no—
167C4⋊C4—224no—
168C4⋊C4—222no—
169C4⋊C4—444no—
170C22⋊C4—24no—
171C22⋊C4—222no—
172C22⋊C4—222no—
173C22⋊C4—444no—
174C42—222no—
175C11#248711yescharacteristic, complemented, Sylow
176C23—22no—
177C23—22no—
178C23—112no—
179C23—221no—
180C23—222no—
181C23—221no—
182C23—222no—
183C23C2×D4412yes—
184C23#434112yes—
185C23Q8×D1112yes—
186C23C23×D1111yescharacteristic
187D4—228no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—112no—
194C2×C4—221no—
195C2×C4—221no—
196C2×C4—221no—
197C2×C4—221no—
198C2×C4—224no—
199C2×C4—222no—
200C2×C4—224no—
201C2×C4—222no—
202C2×C4—224no—
203C2×C4—448no—
204C2×C4—444no—
205C2×C4C2×D4412yes—
206C2×C4C2×D4412yes—
207C2×C4#434114yes—
208C22—22no—
209C22—22no—
210C22—24no—
211C22—24no—
212C22—222no—
213C22—224no—
214C22—441no—
215C22—441no—
216C22—442no—
217C22#6695014yes—
218C22C22×D4411yescharacteristic
219C22C2×#434112yes—
220C22C2×#434111yescharacteristic
221C22C2×Q8×D1111yescharacteristic
222C22#6704212yes—
223C4—22no—
224C4—44no—
225C4—222no—
226C4—441no—
227C4—444no—
228C4—441no—
229C4#6693914yes—
230C2—24no—
231C2—442no—
232C2C2×#6693911yescharacteristic
233C2C2×#6695011yescharacteristic
234C2#1062305611yescharacteristic
235C2#1062314912yes—
236C2#1062316612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC22×C22⋊D11C22
hypercenter#380D11
hypocenterC11#2487
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. C11×#380C2semidirect
4. #10622600C2semidirect
5. #10622598C2semidirect
7. #10622563C2semidirect
8. #10622290C2semidirect
9. #10622272C2semidirect
98. #380D11semidirect
175. C11#2487semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D112
C22×C4⋊Dic112
C11×#3802
#106226002
#106225982
#106225712
#106225632
#106222902
#106222722
#248711