Finite Group Databasebeta

← #13072377

Subgroups — #13072377

Order 1408.

696 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#127C211yesmaximal, characteristic
2C2×#66988C212yesmaximal, complemented
3C2×D4×Dic11C211yesmaximal, characteristic, complemented
4#10622835C212yesmaximal, complemented
5#10622835C212yesmaximal, complemented
6#10622834C211yesmaximal, characteristic, complemented
7#10622834C211yesmaximal, characteristic, complemented
8#10622834C211yesmaximal, characteristic, complemented
9#10622833C212yesmaximal, complemented
10C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C22×D4×C11C2212yes—
15C22×D4×C11C2211yescharacteristic
16C23×Dic11C2212yes—
17C11×#127—24no—
18C2×C42×C11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2212yes—
26#66988—28no—
27D4×Dic11—24no—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34C2×C4×Dic11C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C24×C11C2312yes—
39C24×C11C2312yes—
40C2×D4×C11—24no—
41C2×D4×C11—24no—
42C2×D4×C11—24no—
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—24no—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C2×D4×C11D414yes—
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×Dic11—24no—
56C22×Dic11—24no—
57C22×Dic11—42no—
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2312yes—
61C22×Dic11C2312yes—
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C42×C11—22no—
65C22⋊Dic11—24no—
66C22⋊Dic11—24no—
67C22⋊Dic11—24no—
68C22⋊Dic11—24no—
69C22⋊Dic11—42no—
70C22⋊Dic11—42no—
71C22⋊Dic11—42no—
72C4⋊Dic11—22no—
73C4⋊Dic11—22no—
74Dic11⋊C4—24no—
75Dic11⋊C4—22no—
76Dic11⋊C4D414yescomplemented
77C4×Dic11—22no—
78C4×Dic11—22no—
79#2445—111nomaximal, Sylow
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—22no—
93C23×C11C2×D414yes—
94C23×C11C2411yescharacteristic
95D4×C11—28no—
96D4×C11—48no—
97D4×C11—48no—
98D4×C11—44no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11C2×D412yes—
104C2×C4×C11C2×D412yes—
105C2×C4×C11#4112yes—
106C2×C4×C11#4112yes—
107C2×C4×C11#4112yes—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—22no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—48no—
125C2×Dic11C2×D412yes—
126C2×Dic11C2×D412yes—
127C2×#127D1111yescharacteristic
128C2×#123—112no—
129C2×C4×D4—111no—
130#394—112no—
131#394—112no—
132#390—111no—
133#390—111no—
134#390—111no—
135#389—111no—
136#386—112no—
137C4×C4⋊C4—111no—
138C22×C11—24no—
139C22×C11—24no—
140C22×C11—24no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11C22×D411yescharacteristic
153C22×C11C22×D411yescharacteristic
154C22×C11C2×#4111yescharacteristic
155C22×C11C2×#4111yescharacteristic
156C22×C11C2×#4111yescharacteristic
157C22×C11H(5,𝔽2)11yescharacteristic
158C22×C11H(5,𝔽2)11yescharacteristic
159C4×C11—22no—
160C4×C11—22no—
161C4×C11#12314yescomplemented
162Dic11—22no—
163Dic11—22no—
164Dic11—41no—
165Dic11—42no—
166Dic11—41no—
167Dic11—42no—
168C22×D4C2×D1111yescharacteristic
169C22×D4C2×D1112yes—
170C22×D4C2×D1112yes—
171C22×D4C2×D1111yescharacteristic
172C23×C4—112no—
173#127—24no—
174#123—228no—
175C4×D4—224no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4—111no—
180C2×C4⋊C4—111no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—112no—
186C2×C22⋊C4—112no—
187C2×C22⋊C4—112no—
188C2×C42—111no—
189C2×C42—111no—
190C2×C42C2×D1111yescharacteristic
191#95—111no—
192#95—111no—
193#95—112no—
194C2×C11—44no—
195C2×C11—82no—
196C2×C11C2×#12311yescharacteristic
197C2×C11#53211yescharacteristic
198C2×C11#54011yescharacteristic
199C2×C11D4211yescharacteristic
200C2×C11#54611yescharacteristic
201C2×C11#55011yescharacteristic
202C2×C11#55911yescharacteristic
203C24C22×D1112yes—
204C24C22×D1112yes—
205C2×D4—24no—
206C2×D4—24no—
207C2×D4—24no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—24no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4C22⋊D1114yes—
217C22×C4—111no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—111no—
221C22×C4—112no—
222C22×C4—112no—
223C22×C4—224no—
224C22×C4—224no—
225C22×C4—442no—
226C22×C4C22×D1111yescharacteristic
227C22×C4C22×D1111yescharacteristic
228C22×C4C22×D1111yescharacteristic
229C4⋊C4—114no—
230C4⋊C4—224no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C4⋊C4—222no—
234C22⋊C4—224no—
235C22⋊C4—224no—
236C22⋊C4—224no—
237C22⋊C4—224no—
238C22⋊C4—442no—
239C22⋊C4—442no—
240C22⋊C4—442no—
241C42—22no—
242C42—222no—
243C42—222no—
244C11#244511yescharacteristic, complemented, Sylow
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23C2×C22⋊D1114yes—
259C23C23×D1111yescharacteristic
260D4—28no—
261D4—48no—
262D4—48no—
263D4—44no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—112no—
269C2×C4—112no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4—221no—
277C2×C4—222no—
278C2×C4—221no—
279C2×C4—222no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—222no—
284C2×C4—221no—
285C2×C4—222no—
286C2×C4—448no—
287C2×C4D4×D1112yes—
288C2×C4#434112yes—
289C2×C4#434112yes—
290C2×C4#434112yes—
291C2×C4C2×C22⋊D1112yes—
292C22—24no—
293C22—24no—
294C22—24no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22C2×D4×D1111yescharacteristic
307C22C2×#434111yescharacteristic
308C22C2×#434111yescharacteristic
309C22C2×#434111yescharacteristic
310C22#6703711yescharacteristic
311C22#6703711yescharacteristic
312C22C22×C22⋊D1111yescharacteristic
313C4—22no—
314C4—22no—
315C4—222no—
316C4—222no—
317C4—442no—
318C4—441no—
319C4—442no—
320C4—441no—
321C4#6698814yescomplemented
322C2—44no—
323C2—82no—
324C2#1062324411yescharacteristic
325C2#1062324711yescharacteristic
326C2#1062324911yescharacteristic
327C2#1062325011yescharacteristic
328C2C2×#6698811yescharacteristic
329C2D4×C22⋊D1111yescharacteristic
330C2#1062333711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#127C2
hypercenterC2×#127D11
hypocenterC11#2445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C2×D4×Dic11C2semidirect
4. #10622835C2semidirect
5. #10622835C2semidirect
6. #10622834C2semidirect
7. #10622834C2semidirect
8. #10622834C2semidirect
9. #10622833C2semidirect
10. C4×Dic11⋊C4C2semidirect
11. #10622541C2semidirect
76. Dic11⋊C4D4semidirect
161. C4×C11#123semidirect
244. C11#2445semidirect
321. C4#66988semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1272
C2×#669882
C2×D4×Dic112
#106228352
#106228342
#106228332
C4×Dic11⋊C42
#106225412
#244511