Finite Group Databasebeta

← #13073518

Subgroups — #13073518

Order 1408.

732 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 161 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×#66948C212yesmaximal, complemented
2C2×C4×D44C211yesmaximal, characteristic, complemented
3C2×C4×D44C211yesmaximal, characteristic, complemented
4C11×#382C211yesmaximal, characteristic, complemented
5#10622600C212yesmaximal, complemented
6#10622287C212yesmaximal, complemented
7#10622284C212yesmaximal, complemented
8#10622278C214yesmaximal, complemented
9C22×D44C2211yescharacteristic
10C22×D44C2214yes—
11C22×D44C2211yescharacteristic
12C22×C4×D11C2212yes—
13C22×C4×D11C2212yes—
14C2×C11×C4⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2214yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22#66948—28no—
23C4×D44—24no—
24C4×D44—24no—
25C11×#95C2212yes—
26C11×#95C2212yes—
27C11⋊#95C2214yes—
28C23×D11C2312yes—
29C23×D11C2312yes—
30C22×C4×C11C2314yes—
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×Dic11C2312yes—
35C22×Dic11C2312yes—
36C2×D44—28no—
37C2×D44—24no—
38C2×D44—28no—
39C2×D44—22no—
40C2×D44—22no—
41C2×D44—22no—
42C2×D44—44no—
43C2×D44D414yescomplemented
44C2×C4×D11—24no—
45C2×C4×D11—24no—
46C2×C4×D11—24no—
47C2×C4×D11—24no—
48C2×C4×D11—44no—
49C11×C4⋊C4—24no—
50C42×C11D414yescomplemented
51(C2×D11)⋊C4—28no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—24no—
54(C2×D11)⋊C4—44no—
55C4⋊Dic11—22no—
56C4⋊Dic11—22no—
57#2535—111nomaximal, Sylow
58C23×C11C2411yescharacteristic
59C22×D11—22no—
60C22×D11—22no—
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—24no—
66C22×D11—22no—
67C22×D11—24no—
68C22×D11—22no—
69C22×D11C2×D414yes—
70C22×D11#4114yes—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—24no—
74C2×C4×C11—24no—
75C2×C4×C11—24no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2×D412yes—
80C2×C4×C11#4112yes—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—24no—
86D44—28no—
87D44—28no—
88D44—416no—
89C4×D11—48no—
90C4×D11—48no—
91C2×#121—112no—
92C2×C4×D4—111no—
93C2×C4×D4—111no—
94#397—112no—
95#392—112no—
96#386—114no—
97#382D1111yescharacteristic, complemented
98#380—112no—
99C22×C11C22×D411yescharacteristic
100C22×C11C22×D411yescharacteristic
101C22×C11C2×#4111yescharacteristic
102C22×C11C2×#4112yes—
103C22×C11H(5,𝔽2)12yes—
104C2×D11—24no—
105C2×D11—24no—
106C2×D11—28no—
107C2×D11—24no—
108C2×D11—24no—
109C2×D11—42no—
110C2×D11—42no—
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—44no—
116C4×C11—22no—
117C4×C11—22no—
118C4×C11—44no—
119C4×C11#12114yes—
120Dic11—42no—
121Dic11—42no—
122C22×D4—111no—
123C22×D4—111no—
124C22×D4—114no—
125C23×C4—112no—
126C23×C4—112no—
127#121—228no—
128C4×D4—224no—
129C4×D4—224no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—111no—
132C2×C4⋊C4C2×D1112yes—
133C2×C22⋊C4—112no—
134C2×C22⋊C4—112no—
135C2×C22⋊C4—114no—
136C2×C22⋊C4—114no—
137C2×C42C2×D1111yescharacteristic
138#95—114no—
139#95C2×D1112yes—
140#95C2×D1112yes—
141C2×C11C2×#12111yescharacteristic
142C2×C11#52511yescharacteristic
143C2×C11#53511yescharacteristic
144C2×C11#54612yes—
145C2×C11#55312yes—
146D11—44no—
147D11—44no—
148C24—112no—
149C24—112no—
150C2×D4—114no—
151C2×D4—224no—
152C2×D4—228no—
153C2×D4—228no—
154C2×D4—222no—
155C2×D4—222no—
156C2×D4—222no—
157C2×D4—444no—
158C22×C4—112no—
159C22×C4—112no—
160C22×C4—224no—
161C22×C4—224no—
162C22×C4—224no—
163C22×C4—224no—
164C22×C4—444no—
165C22×C4C22×D1114yes—
166C22×C4C22×D1111yescharacteristic
167C22×C4C22×D1111yescharacteristic
168C22×C4C22×D1111yescharacteristic
169C4⋊C4—24no—
170C4⋊C4—222no—
171C4⋊C4—222no—
172C22⋊C4—228no—
173C22⋊C4—224no—
174C22⋊C4—224no—
175C22⋊C4—444no—
176C42D4414yescomplemented
177C11#253511yescharacteristic, complemented, Sylow
178C23—114no—
179C23—114no—
180C23—222no—
181C23—222no—
182C23—222no—
183C23—222no—
184C23—222no—
185C23—222no—
186C23—224no—
187C23—222no—
188C23—224no—
189C23—222no—
190C23C23×D1111yescharacteristic
191D4—228no—
192D4—228no—
193D4—4416no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—224no—
204C2×C4—448no—
205C2×C4—448no—
206C2×C4C2×D4412yes—
207C2×C4C2×D4412yes—
208C2×C4C2×D4412yes—
209C2×C4D4×D1112yes—
210C2×C4#434312yes—
211C22—224no—
212C22—224no—
213C22—224no—
214C22—228no—
215C22—224no—
216C22—442no—
217C22—442no—
218C22—442no—
219C22—442no—
220C22—442no—
221C22—442no—
222C22—444no—
223C22C22×D4411yescharacteristic
224C22C2×D4×D1111yescharacteristic
225C22C2×#434311yescharacteristic
226C22#41×D1112yes—
227C22#6704212yes—
228C4—22no—
229C4—22no—
230C4—44no—
231C4—442no—
232C4—442no—
233C4#6694814yes—
234C2—444no—
235C2—444no—
236C2C2×#6694811yescharacteristic
237C2#1062305511yescharacteristic
238C2#1062305611yescharacteristic
239C2#1062320712yes—
240C2#1062322612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
hypercenter#382D11
hypocenterC11#2535
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×C4×D44C2semidirect
3. C2×C4×D44C2semidirect
4. C11×#382C2semidirect
5. #10622600C2semidirect
6. #10622287C2semidirect
7. #10622284C2semidirect
8. #10622278C2semidirect
43. C2×D44D4semidirect
50. C42×C11D4semidirect
97. #382D11semidirect
176. C42D44semidirect
177. C11#2535semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×C4×D442
C11×#3822
#106226002
#106222872
#106222842
#106222782
#253511