Finite Group Databasebeta

← #13072008

Subgroups — #13072008

Order 1408.

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

normal subgroups only

This group has 814 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×C11×#123C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic
3C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#10622833C211yesmaximal, characteristic, complemented
6#10622824C211yesmaximal, characteristic, complemented
7#10622606C212yesmaximal, complemented
8#10622600C212yesmaximal, complemented
9#10622574C212yesmaximal, complemented
10#10622569C212yesmaximal, complemented
11#10622563C211yesmaximal, characteristic, complemented
12C24×D11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C22×C22⋊D11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C22×C4×D11C2212yes—
19C11×#123—24no—
20C2×C11×C4⋊C4C2212yescomplemented
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2212yescomplemented
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2212yescomplemented
26#66990—24no—
27C2×(C2×D11)⋊C4—24no—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×C4⋊Dic11C2212yescomplemented
34C22⋊C4×D11—24no—
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C11⋊#95C2212yescomplemented
38C11⋊#95C2212yescomplemented
39C24×C11C2311yescharacteristic
40C24×C11C2311yescharacteristic
41C23×D11—22no—
42C23×D11—22no—
43C23×D11—24no—
44C23×D11—42no—
45C23×D11D414yes—
46C23×D11C2311yescharacteristic
47C23×D11C2311yescharacteristic
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11C2312yes—
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2312yes—
57C2×C22⋊D11—22no—
58C2×C22⋊D11—22no—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—42no—
61C22×Dic11—22no—
62C22×Dic11—42no—
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2312yes—
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2312yes—
67C2×C4×D11—24no—
68C2×C4×D11—24no—
69C2×C4×D11—42no—
70C11×C4⋊C4—24no—
71C11×C22⋊C4—24no—
72C11×C22⋊C4D414yescomplemented
73C22⋊Dic11—22no—
74C22⋊Dic11—22no—
75C22⋊Dic11—42no—
76(C2×D11)⋊C4—24no—
77(C2×D11)⋊C4—24no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—24no—
81C4⋊Dic11—42no—
82#2412—111nomaximal, Sylow
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—22no—
88C23×C11—21no—
89C23×C11—22no—
90C23×C11C2×D412yes—
91C23×C11C2×D412yes—
92C23×C11#4112yes—
93C23×C11C2411yescharacteristic
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—22no—
97C22×D11—28no—
98C22×D11—21no—
99C22×D11—21no—
100C22×D11—22no—
101C22×D11—22no—
102C22×D11—28no—
103C22×D11—44no—
104C22×D11—48no—
105C22×D11—48no—
106C22×D11C2×D412yes—
107C22×D11C2×D412yes—
108C22×D11#4114yes—
109D4×C11—44no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11—44no—
119C2×C4×C11C2×D414yes—
120C22⋊D11—44no—
121C22⋊D11—44no—
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—44no—
133C4×D11—48no—
134C2×#123D1111yescharacteristic, complemented
135C2×#120—111no—
136C22×C22⋊C4—111no—
137C22×C22⋊C4—111no—
138#397—112no—
139#394—112no—
140#386—111no—
141#386—112no—
142#385—111no—
143#381—111no—
144#380—112no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—24no—
148C22×C11—24no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11#12114yes—
155C22×C11C22×D411yescharacteristic
156C22×C11C22×D411yescharacteristic
157C22×C11C2×#4111yescharacteristic
158C22×C11C2×#4112yes—
159C22×C11H(5,𝔽2)12yes—
160C2×D11—22no—
161C2×D11—22no—
162C2×D11—24no—
163C2×D11—24no—
164C2×D11—22no—
165C2×D11—22no—
166C2×D11—22no—
167C2×D11—416no—
168C2×D11—42no—
169C2×D11—42no—
170C2×D11#12314yescomplemented
171C4×C11—24no—
172C4×C11—42no—
173C4×C11—41no—
174Dic11—41no—
175Dic11—42no—
176Dic11—41no—
177Dic11—42no—
178C25—111no—
179C22×D4—111no—
180C22×D4—111no—
181C22×D4C2×D1111yescharacteristic
182C23×C4—111no—
183C23×C4—112no—
184C23×C4C2×D1111yescharacteristic
185#123—24no—
186#120—224no—
187C2×C4⋊C4—112no—
188C2×C4⋊C4C2×D1112yescomplemented
189C2×C22⋊C4—111no—
190C2×C22⋊C4—111no—
191C2×C22⋊C4—112no—
192C2×C22⋊C4—112no—
193C2×C22⋊C4—112no—
194C2×C22⋊C4—111no—
195C2×C22⋊C4—111no—
196C2×C22⋊C4—112no—
197C2×C22⋊C4—224no—
198C2×C22⋊C4—224no—
199C2×C22⋊C4C2×D1111yescharacteristic
200C2×C22⋊C4C2×D1112yescomplemented
201#95—112no—
202#95—112no—
203#95—112no—
204#95—112no—
205C2×C11—24no—
206C2×C11—81no—
207C2×C11C2×#12111yescharacteristic
208C2×C11C2×#12311yescharacteristic
209C2×C11#53411yescharacteristic
210C2×C11#54612yes—
211C2×C11#55112yes—
212D11—24no—
213D11—42no—
214C24—111no—
215C24—111no—
216C24—114no—
217C24—224no—
218C24—222no—
219C24—222no—
220C24—442no—
221C24C22×D1111yescharacteristic
222C24C22×D1111yescharacteristic
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—222no—
227C2×D4—222no—
228C2×D4—224no—
229C2×D4—442no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—111no—
234C22×C4—112no—
235C22×C4—112no—
236C22×C4—111no—
237C22×C4—224no—
238C22×C4—222no—
239C22×C4—224no—
240C22×C4—442no—
241C22×C4—442no—
242C22×C4C22×D1112yes—
243C22×C4C22×D1111yescharacteristic
244C22×C4C22×D1112yes—
245C4⋊C4—24no—
246C4⋊C4—442no—
247C22⋊C4—24no—
248C22⋊C4—224no—
249C22⋊C4—224no—
250C22⋊C4—222no—
251C22⋊C4—222no—
252C22⋊C4—222no—
253C22⋊C4—222no—
254C22⋊C4—224no—
255C22⋊C4—442no—
256C22⋊C4C22⋊D1114yescomplemented
257C11#241211yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23—21no—
261C23—21no—
262C23—22no—
263C23—22no—
264C23—21no—
265C23—112no—
266C23—114no—
267C23—112no—
268C23—228no—
269C23—221no—
270C23—222no—
271C23—221no—
272C23—228no—
273C23—221no—
274C23—222no—
275C23—222no—
276C23—221no—
277C23—444no—
278C23—448no—
279C23—448no—
280C23D4×D1112yes—
281C23#434112yes—
282C23C2×C22⋊D1112yes—
283C23C23×D1111yescharacteristic
284D4—44no—
285D4—444no—
286D4—444no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—44no—
296C2×C4—222no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—222no—
300C2×C4—222no—
301C2×C4—222no—
302C2×C4—222no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—448no—
307C2×C4—444no—
308C2×C4C2×C22⋊D1114yes—
309C22—24no—
310C22—22no—
311C22—22no—
312C22—24no—
313C22—41no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—42no—
318C22—114no—
319C22—222no—
320C22—224no—
321C22—222no—
322C22—224no—
323C22—222no—
324C22—222no—
325C22—222no—
326C22—4416no—
327C22—442no—
328C22—442no—
329C22#6699114yes—
330C22C2×D4×D1111yescharacteristic
331C22C2×#434111yescharacteristic
332C22#41×D1112yes—
333C22#6704212yes—
334C22C22×C22⋊D1111yescharacteristic
335C4—24no—
336C4—42no—
337C4—41no—
338C4—442no—
339C4—441no—
340C4—442no—
341C4—441no—
342C2—24no—
343C2—81no—
344C2—224no—
345C2—442no—
346C2D11×#12311yescharacteristic
347C2#1062318411yescharacteristic
348C2#1062318912yes—
349C2C2×#6699111yescharacteristic
350C2#1062336012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#123C2
prime radicalC2×#66990C2
hypercenterC2×#123D11
hypocenterC11#2412
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
3. C22×(C2×D11)⋊C4C2semidirect
4. C2×C22⋊C4×D11C2semidirect
5. #10622833C2semidirect
6. #10622824C2semidirect
7. #10622606C2semidirect
8. #10622600C2semidirect
9. #10622574C2semidirect
10. #10622569C2semidirect
11. #10622563C2semidirect
20. C2×C11×C4⋊C4C22semidirect
22. C2×C11×C22⋊C4C22semidirect
25. C2×C22⋊Dic11C22semidirect
33. C2×C4⋊Dic11C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
37. C11⋊#95C22semidirect
38. C11⋊#95C22semidirect
72. C11×C22⋊C4D4semidirect
134. C2×#123D11semidirect
170. C2×D11#123semidirect
188. C2×C4⋊C4C2×D11semidirect
200. C2×C22⋊C4C2×D11semidirect
256. C22⋊C4C22⋊D11semidirect
257. C11#2412semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×#669902
C22×(C2×D11)⋊C42
C2×C22⋊C4×D112
#106228332
#106228242
#106226062
#106226002
#106225742
#106225692
#106225632
#241211