Finite Group Databasebeta

← #13073972

Subgroups — #13073972

Order 1408.

564 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic11C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic, complemented
3C11×#390C211yesmaximal, characteristic
4#10622834C211yesmaximal, characteristic
5#10622598C211yesmaximal, characteristic, complemented
6#10622590C211yesmaximal, characteristic, complemented
7#10622563C212yesmaximal, complemented
8#10622562C212yesmaximal, complemented
9#10622560C212yesmaximal, complemented
10#10622559C212yesmaximal, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×Dic11C2212yes—
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22D4×Dic11—24no—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2212yes—
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32C4×Dic22—24no—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C2×D4×C11—22no—
39C2×D4×C11—22no—
40C2×D4×C11Q814yescomplemented
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11—24no—
46C22×Dic11—42no—
47C22×Dic11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C2×Dic22—22no—
55C2×Dic22—22no—
56C2×Dic22—22no—
57C11×C4⋊C4—22no—
58C11×C22⋊C4—24no—
59C11×C22⋊C4—42no—
60C42×C11—22no—
61C22⋊Dic11—24no—
62C22⋊Dic11—24no—
63C22⋊Dic11—42no—
64C4⋊Dic11—22no—
65C4⋊Dic11—22no—
66C4⋊Dic11—22no—
67C4⋊Dic11—42no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—42no—
71C4×Dic11—22no—
72C4×Dic11D414yes—
73#2580—111nomaximal, Sylow
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11C2×Q814yes—
81C23×C11C2411yescharacteristic
82D4×C11—28no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×Q812yes—
93C2×C4×C11#4112yes—
94C2×C4×C11#4112yes—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—48no—
111C2×Dic11C2×D412yes—
112C2×Dic11C2×D412yes—
113C2×Dic11#4112yes—
114Dic22—28no—
115C2×C4×Q8—111no—
116C2×C4×D4—111no—
117#399—112no—
118#393—112no—
119#390—111no—
120#390D1111yescharacteristic
121#389—111no—
122#389—111no—
123#385—112no—
124#385—112no—
125#382—111no—
126C22×C11—24no—
127C22×C11—24no—
128C22×C11—24no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11C22×D411yescharacteristic
134C22×C11C22×Q811yescharacteristic
135C22×C11C2×#4111yescharacteristic
136C22×C11C2×#4111yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C11H(5,𝔽2)11yescharacteristic
139C22×C11H(5,𝔽2)11yescharacteristic
140C4×C11—22no—
141C4×C11—41no—
142C4×C11—42no—
143C4×C11C22⋊Q814yes—
144Dic11—22no—
145Dic11—22no—
146Dic11—22no—
147Dic11—41no—
148Dic11—42no—
149Dic11—42no—
150C22×Q8—111no—
151C22×D4C2×D1111yescharacteristic
152C23×C4—112no—
153C4×Q8—224no—
154C4×D4—224no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—111no—
157C2×C4⋊C4—111no—
158C2×C4⋊C4—111no—
159C2×C4⋊C4—111no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4C2×D1111yescharacteristic
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4C2×D1112yes—
167C2×C22⋊C4C2×D1112yes—
168C2×C42—111no—
169C2×C42—111no—
170C2×C42C2×D1111yescharacteristic
171#95—112no—
172#95—112no—
173#95—112no—
174#95—112no—
175C2×C11—44no—
176C2×C11C2×C22⋊Q811yescharacteristic
177C2×C11#52511yescharacteristic
178C2×C11#53511yescharacteristic
179C2×C11#55411yescharacteristic
180C2×C11#55411yescharacteristic
181C2×C11#55911yescharacteristic
182C2×C11#55911yescharacteristic
183C24C22×D1112yes—
184C2×Q8—222no—
185C2×Q8—222no—
186C2×Q8—222no—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4Dic2214yescomplemented
190C22×C4—111no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—112no—
194C22×C4—112no—
195C22×C4—111no—
196C22×C4—224no—
197C22×C4—442no—
198C22×C4—442no—
199C22×C4C22×D1112yes—
200C22×C4C22×D1111yescharacteristic
201C22×C4C22×D1111yescharacteristic
202C22×C4C22×D1111yescharacteristic
203C4⋊C4—22no—
204C4⋊C4—222no—
205C4⋊C4—222no—
206C4⋊C4—222no—
207C4⋊C4—222no—
208C4⋊C4—222no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C22⋊C4—24no—
212C22⋊C4—42no—
213C22⋊C4—224no—
214C22⋊C4—224no—
215C22⋊C4—442no—
216C42—22no—
217C42—114no—
218C42—222no—
219C11#258011yescharacteristic, complemented, Sylow
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23C2×Dic2214yes—
227C23C23×D1111yescharacteristic
228Q8—228no—
229D4—28no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—112no—
239C2×C4—112no—
240C2×C4—112no—
241C2×C4—221no—
242C2×C4—221no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4—221no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—221no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—221no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—448no—
257C2×C4C2×Dic2212yes—
258C2×C4D4×D1112yes—
259C2×C4#434112yes—
260C2×C4#434112yes—
261C22—24no—
262C22—24no—
263C22—24no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22C22×Dic2211yescharacteristic
269C22C2×D4×D1111yescharacteristic
270C22C2×#434111yescharacteristic
271C22C2×#434111yescharacteristic
272C22#6703711yescharacteristic
273C22#41×D1111yescharacteristic
274C22#6704211yescharacteristic
275C4—22no—
276C4—42no—
277C4—41no—
278C4—222no—
279C4—222no—
280C4—222no—
281C4—442no—
282C4—441no—
283C4—442no—
284C4#6693114yes—
285C2—44no—
286C2C2×#6693111yescharacteristic
287C2#1062307011yescharacteristic
288C2#1062307411yescharacteristic
289C2#1062313711yescharacteristic
290C2#1062313811yescharacteristic
291C2#1062321211yescharacteristic
292C2#1062324411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2580
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic22C2semidirect
5. #10622598C2semidirect
6. #10622590C2semidirect
7. #10622563C2semidirect
8. #10622562C2semidirect
9. #10622560C2semidirect
10. #10622559C2semidirect
11. #10622541C2semidirect
40. C2×D4×C11Q8semidirect
189. C2×D4Dic22semidirect
219. C11#2580semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
C2×C4×Dic222
C11×#3902
#106228342
#106225982
#106225902
#106225632
#106225622
#106225602
#106225592
#106225412
#258011