Finite Group Databasebeta

← #13074959

Subgroups — #13074959

Order 1408.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66988C212yesmaximal
2C2×#66931C212yesmaximal, complemented
3C11×#394C211yesmaximal, characteristic
4#10622592C211yesmaximal, characteristic, complemented
5#10622589C211yesmaximal, characteristic, complemented
6#10622565C212yesmaximal, complemented
7#10622563C212yesmaximal, complemented
8#10622557C212yesmaximal, complemented
9#10622270C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19#66988—28no—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27#66931—28no—
28C11×#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C24×C11C2312yes—
34C2×D4×C11—24no—
35C2×D4×C11—41no—
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×Dic11—24no—
41C22×Dic11—24no—
42C22×Dic11—42no—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C2×Dic22—24no—
48C2×Dic22—41no—
49C11×C4⋊C4—41no—
50C11×C22⋊C4—24no—
51C11×C22⋊C4—24no—
52C22⋊Dic11—24no—
53C22⋊Dic11—24no—
54C22⋊Dic11D418yes—
55C4⋊Dic11—24no—
56C4⋊Dic11—41no—
57Dic11⋊C4—24no—
58Dic11⋊C4—24no—
59Dic11⋊C4—24no—
60Dic11⋊C4—24no—
61C4×Dic11—22no—
62#2680—111nomaximal, Sylow
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11C2×D414yes—
70C23×C11C2411yescharacteristic
71D4×C11—44no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11#4112yes—
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—22no—
91C2×Dic11—22no—
92C2×Dic11—48no—
93C2×Dic11C2×D414yes—
94C2×Dic11C2×D414yes—
95Dic22—44no—
96C2×#123—112no—
97C2×C22⋊Q8—112no—
98#398—112no—
99#397—112no—
100#395—111no—
101#394D1111yescharacteristic
102#388—112no—
103#385—112no—
104#384—111no—
105C22×C11—24no—
106C22×C11—24no—
107C22×C11—24no—
108C22×C11—42no—
109C22×C11—42no—
110C22×C11—42no—
111C22×C11—42no—
112C22×C11C22×D412yes—
113C22×C11C2×#4111yescharacteristic
114C22×C11H(5,𝔽2)11yescharacteristic
115C22×C112−1+411yescharacteristic
116C22×C112−1+412yes—
117C4×C11—22no—
118C4×C11—41no—
119C4×C11—41no—
120C4×C11—42no—
121Dic11—24no—
122Dic11—24no—
123Dic11—42no—
124Dic11—42no—
125C22×Q8—111no—
126C22×D4C2×D1111yescharacteristic
127C23×C4—112no—
128#123—228no—
129C22⋊Q8—228no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—112no—
135C2×C4⋊C4—111no—
136C2×C4⋊C4C2×D1111yescharacteristic
137C2×C22⋊C4—112no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—112no—
140C2×C22⋊C4C2×D1112yes—
141C2×C22⋊C4C2×D1112yes—
142C2×C42—111no—
143#95—112no—
144#95—112no—
145#95—112no—
146#95—111no—
147#95C2×D1111yescharacteristic
148C2×C11—44no—
149C2×C11#53612yes—
150C2×C11#53911yescharacteristic
151C2×C11D4211yescharacteristic
152C2×C11#54712yes—
153C2×C11#56311yescharacteristic
154C24C22×D1112yes—
155C2×Q8—224no—
156C2×Q8—441no—
157C2×D4—24no—
158C2×D4—41no—
159C22×C4—112no—
160C22×C4—112no—
161C22×C4—112no—
162C22×C4—112no—
163C22×C4—224no—
164C22×C4—224no—
165C22×C4—442no—
166C22×C4C22×D1112yes—
167C22×C4C22×D1111yescharacteristic
168C22×C4C22×D1111yescharacteristic
169C22×C4C22×D1111yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—224no—
172C4⋊C4—224no—
173C4⋊C4—224no—
174C4⋊C4—224no—
175C4⋊C4—224no—
176C4⋊C4—441no—
177C22⋊C4—24no—
178C22⋊C4—24no—
179C22⋊C4—118no—
180C22⋊C4—224no—
181C22⋊C4—224no—
182C42—222no—
183C11#268011yescharacteristic, complemented, Sylow
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23D4×D1114yes—
191C23C23×D1111yescharacteristic
192Q8—444no—
193D4—44no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—114no—
204C2×C4—114no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—448no—
216C2×C4#434112yes—
217C22—24no—
218C22—24no—
219C22—24no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×D4×D1112yes—
225C22C2×#434111yescharacteristic
226C22#6703711yescharacteristic
227C22#6704311yescharacteristic
228C22#6704312yes—
229C4—22no—
230C4—41no—
231C4—41no—
232C4—42no—
233C4—224no—
234C4—224no—
235C4—442no—
236C4—442no—
237C2—44no—
238C2#1062312111yescharacteristic
239C2#1062313311yescharacteristic
240C2#1062314212yes—
241C2#1062317912yes—
242C2#1062320311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC22×D4×C11C22
hypercenter#394D11
hypocenterC11#2680
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66931C2semidirect
4. #10622592C2semidirect
5. #10622589C2semidirect
6. #10622565C2semidirect
7. #10622563C2semidirect
8. #10622557C2semidirect
9. #10622270C2semidirect
183. C11#2680semidirect

Maximal subgroups

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

subgroupindex
C2×#669882
C2×#669312
C11×#3942
#106225922
#106225892
#106225652
#106225632
#106225572
#106222702
#268011