Finite Group Databasebeta

← #13073596

Subgroups — #13073596

Order 1408.

576 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 165 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×#66928C211yesmaximal, characteristic
2C2×#66928C211yesmaximal, characteristic
3C2×#66922C211yesmaximal, characteristic, complemented
4C2×C4×Dic22C211yesmaximal, characteristic, complemented
5C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6#10622607C214yesmaximal, complemented
7#10622552C211yesmaximal, characteristic
8#10622542C211yesmaximal, characteristic, complemented
9#10622283C214yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2212yes—
14C2×C42×C11C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2214yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2214yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25#66928—24no—
26#66928—24no—
27#66922—24no—
28C4×Dic22—24no—
29C11×#95C2212yes—
30C11⋊#95C2214yes—
31C23×D11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×D44—22no—
41C2×D44—22no—
42C2×D44—22no—
43C2×Dic22—22no—
44C2×Dic22—22no—
45C2×Dic22—22no—
46C2×Dic22—22no—
47C2×Dic22—22no—
48C2×Dic22D414yes—
49C11×C4⋊C4—24no—
50C42×C11—22no—
51C42×C11—22no—
52C42×C11D414yes—
53(C2×D11)⋊C4—28no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—28no—
57C4⋊Dic11—28no—
58C4⋊Dic11—22no—
59Dic11⋊C4—24no—
60C4×Dic11—24no—
61#2545—111nomaximal, Sylow
62C23×C11C2411yescharacteristic
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—24no—
66C22×D11—22no—
67C22×D11—24no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11#4114yes—
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×Dic11C2×D414yes—
89D44—44no—
90Dic22—28no—
91Dic22—44no—
92C2×C4⋊Q8—111no—
93C2×#124—111no—
94C2×#124—111no—
95C2×C4×Q8—111no—
96#396—114no—
97#391—111no—
98#390—111no—
99#388—114no—
100C4×C4⋊C4D1111yescharacteristic, complemented
101C22×C11C22×D411yescharacteristic
102C22×C11C22×D411yescharacteristic
103C22×C11C2×#4112yes—
104C22×C11C2×#4111yescharacteristic
105C22×C112−1+412yes—
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—44no—
110C2×D11—44no—
111C4×C11—22no—
112C4×C11—22no—
113C4×C11—24no—
114C4×C11—42no—
115C4×C11#12114yes—
116Dic11—24no—
117Dic11—42no—
118Dic11—42no—
119C22×Q8—111no—
120C22×Q8—111no—
121C22×D4—111no—
122C4⋊Q8—224no—
123#124—224no—
124#124—224no—
125C4×Q8—224no—
126C2×C4⋊C4—111no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—114no—
129C2×C4⋊C4C2×D1112yes—
130C2×C22⋊C4—112no—
131C2×C22⋊C4—114no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—114no—
134C2×C42—112no—
135C2×C42C2×D1111yescharacteristic
136C2×C42C2×D1111yescharacteristic
137C2×C42C2×D1111yescharacteristic
138#95—114no—
139#95C2×D1112yes—
140C2×C11C2×#12111yescharacteristic
141C2×C11#53211yescharacteristic
142C2×C11#53611yescharacteristic
143C2×C11#54812yes—
144C2×C11#55612yes—
145D11—82no—
146C24—112no—
147C2×Q8—114no—
148C2×Q8—222no—
149C2×Q8—222no—
150C2×Q8—222no—
151C2×Q8—222no—
152C2×Q8—222no—
153C2×D4—222no—
154C2×D4—222no—
155C2×D4—222no—
156C22×C4—112no—
157C22×C4—112no—
158C22×C4—112no—
159C22×C4C22×D1112yes—
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1112yes—
163C22×C4C22×D1111yescharacteristic
164C4⋊C4—24no—
165C4⋊C4—228no—
166C4⋊C4—224no—
167C4⋊C4—222no—
168C22⋊C4—228no—
169C22⋊C4—224no—
170C22⋊C4—224no—
171C22⋊C4—228no—
172C42—22no—
173C42—22no—
174C42—224no—
175C42D4414yes—
176C11#254511yescharacteristic, complemented, Sylow
177C23—222no—
178C23—224no—
179C23—222no—
180C23—222no—
181C23—224no—
182C23C23×D1111yescharacteristic
183Q8—228no—
184Q8—444no—
185D4—444no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—114no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—224no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4C2×D4412yes—
202C2×C4C2×D4412yes—
203C2×C4C2×D4412yes—
204C2×C4#433914yes—
205C2×C4D4×D1112yes—
206C2×C4#434312yes—
207C22—442no—
208C22—442no—
209C22—442no—
210C22—444no—
211C22—444no—
212C22C22×D4411yescharacteristic
213C22C2×#433912yes—
214C22C2×D4×D1111yescharacteristic
215C22C2×#434311yescharacteristic
216C22#6704312yes—
217C4—22no—
218C4—22no—
219C4—24no—
220C4—42no—
221C4—224no—
222C4—442no—
223C4—442no—
224C4#6694814yes—
225C2—882no—
226C2#1062300811yescharacteristic
227C2C2×#6694811yescharacteristic
228C2#1062305711yescharacteristic
229C2#1062308312yes—
230C2#1062311512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
prime radicalC22×D44C22
hypercenterC4×C4⋊C4D11
hypocenterC11#2545
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#66922C2semidirect
4. C2×C4×Dic22C2semidirect
5. C4×C11×C4⋊C4C2semidirect
6. #10622607C2semidirect
8. #10622542C2semidirect
9. #10622283C2semidirect
100. C4×C4⋊C4D11semidirect
176. C11#2545semidirect

Maximal subgroups

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

subgroupindex
C2×#669282
C2×#669222
C2×C4×Dic222
C4×C11×C4⋊C42
#106226072
#106225522
#106225422
#106222832
#254511