Finite Group Databasebeta

← #13074829

Subgroups — #13074829

Order 1408.

932 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 157 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×#127C211yesmaximal, characteristic, complemented
2C2×#66992C212yesmaximal, complemented
3C2×#66990C211yesmaximal, characteristic, complemented
4C2×#66990C212yesmaximal, complemented
5#10622836C212yesmaximal, complemented
6#10622836C212yesmaximal, complemented
7#10622835C212yesmaximal, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622553C212yesmaximal, complemented
10C24×D11C2211yescharacteristic
11C22×D4×C11C2212yes—
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yescomplemented
14C22×D4×C11C2211yescharacteristic, complemented
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2212yes—
17C22×C22⋊D11C2212yes—
18C23×Dic11C2211yescharacteristic, complemented
19C11×#127—24no—
20C2×C42×C11C2211yescharacteristic, complemented
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2212yescomplemented
24C2×C22⋊Dic11C2211yescharacteristic, complemented
25C2×C22⋊Dic11C2212yescomplemented
26#66992—28no—
27#66990—24no—
28#66990—28no—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×Dic11⋊C4C2212yescomplemented
33C11⋊#95C2212yescomplemented
34C11⋊#95C2212yescomplemented
35C24×C11C2312yes—
36C24×C11C2311yescharacteristic
37C24×C11C2311yescharacteristic
38C23×D11—22no—
39C23×D11—24no—
40C23×D11—41no—
41C23×D11—42no—
42C23×D11—41no—
43C23×D11C2312yes—
44C2×D4×C11—24no—
45C2×D4×C11—24no—
46C2×D4×C11—24no—
47C2×D4×C11—24no—
48C2×D4×C11—22no—
49C2×D4×C11—41no—
50C2×D4×C11—41no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11D414yescomplemented
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2312yes—
58C2×C22⋊D11—24no—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—24no—
61C2×C22⋊D11—24no—
62C2×C22⋊D11—24no—
63C2×C22⋊D11—42no—
64C2×C22⋊D11—42no—
65C2×C22⋊D11—42no—
66C2×C22⋊D11—42no—
67C22×Dic11—24no—
68C22×Dic11—41no—
69C22×Dic11C2312yes—
70C22×Dic11C2312yes—
71C22×Dic11C2312yes—
72C42×C11—22no—
73C22⋊Dic11—24no—
74C22⋊Dic11—24no—
75C22⋊Dic11—22no—
76C22⋊Dic11—41no—
77C22⋊Dic11—42no—
78(C2×D11)⋊C4—24no—
79(C2×D11)⋊C4—24no—
80(C2×D11)⋊C4D418yescomplemented
81Dic11⋊C4—24no—
82#2669—111nomaximal, Sylow
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—22no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—22no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11C2×D412yes—
99C23×C11C2×D412yes—
100C23×C11C2411yescharacteristic
101C22×D11—22no—
102C22×D11—22no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—22no—
106C22×D11—22no—
107C22×D11—44no—
108C22×D11—48no—
109C22×D11—48no—
110C22×D11—44no—
111C22×D11—44no—
112C22×D11C2×D414yes—
113D4×C11—44no—
114D4×C11—48no—
115D4×C11—48no—
116D4×C11—44no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11C2×D414yes—
122C2×C4×C11C2×D412yes—
123C22⋊D11—48no—
124C22⋊D11—48no—
125C22⋊D11—48no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—44no—
135C2×Dic11C2×D414yes—
136C2×#127D1111yescharacteristic, complemented
137C2×#121—112no—
138C2×#120—112no—
139C2×#120—111no—
140#394—112no—
141#392—112no—
142#392—112no—
143#388—112no—
144#386—111no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—24no—
148C22×C11—24no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11C22×D412yes—
163C22×C11C22×D411yescharacteristic
164C22×C11H(5,𝔽2)11yescharacteristic
165C22×C11H(5,𝔽2)11yescharacteristic
166C22×C11H(5,𝔽2)12yes—
167C2×D11—24no—
168C2×D11—24no—
169C2×D11—24no—
170C2×D11—416no—
171C2×D11—42no—
172C2×D11—42no—
173C2×D11—42no—
174C2×D11—42no—
175C4×C11—22no—
176C4×C11—24no—
177Dic11—24no—
178Dic11—42no—
179Dic11—42no—
180C25—111no—
181C22×D4—112no—
182C22×D4—112no—
183C22×D4—112no—
184C22×D4C2×D1112yes—
185C22×D4C2×D1111yescharacteristic
186C22×D4C2×D1112yescomplemented
187C22×D4C2×D1111yescharacteristic, complemented
188C23×C4—111no—
189#127—24no—
190#121—228no—
191#120—228no—
192#120—224no—
193C2×C4⋊C4—112no—
194C2×C22⋊C4—112no—
195C2×C22⋊C4—112no—
196C2×C22⋊C4—111no—
197C2×C22⋊C4—112no—
198C2×C22⋊C4—112no—
199C2×C22⋊C4—112no—
200C2×C22⋊C4—111no—
201C2×C22⋊C4—112no—
202C2×C42C2×D1111yescharacteristic, complemented
203#95—112no—
204#95—112no—
205C2×C11—42no—
206C2×C11—42no—
207C2×C11—82no—
208C2×C11#53411yescharacteristic
209C2×C11#53512yes—
210C2×C11D4211yescharacteristic
211C2×C11D4212yes—
212C2×C11#56011yescharacteristic
213D11—44no—
214C24—112no—
215C24—224no—
216C24—222no—
217C24—442no—
218C24—441no—
219C24—441no—
220C24C22×D1112yes—
221C24C22×D1111yescharacteristic
222C24C22×D1111yescharacteristic
223C2×D4—24no—
224C2×D4—24no—
225C2×D4—24no—
226C2×D4—24no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—42no—
231C2×D4—42no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—224no—
235C2×D4—224no—
236C2×D4—224no—
237C2×D4—224no—
238C2×D4—224no—
239C2×D4—442no—
240C2×D4—442no—
241C2×D4—442no—
242C2×D4—442no—
243C2×D4C22⋊D1114yescomplemented
244C22×C4—112no—
245C22×C4—112no—
246C22×C4—112no—
247C22×C4—224no—
248C22×C4—441no—
249C22×C4C22×D1112yes—
250C22×C4C22×D1111yescharacteristic
251C4⋊C4—224no—
252C22⋊C4—118no—
253C22⋊C4—224no—
254C22⋊C4—224no—
255C22⋊C4—222no—
256C22⋊C4—224no—
257C22⋊C4—224no—
258C22⋊C4—441no—
259C22⋊C4—442no—
260C42—22no—
261C11#266911yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23—21no—
265C23—21no—
266C23—22no—
267C23—22no—
268C23—21no—
269C23—21no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—114no—
278C23—222no—
279C23—222no—
280C23—222no—
281C23—222no—
282C23—222no—
283C23—222no—
284C23—448no—
285C23—444no—
286C23—444no—
287C23—448no—
288C23—444no—
289C23C2×C22⋊D1112yes—
290C23C2×C22⋊D1112yes—
291C23C23×D1111yescharacteristic
292D4—44no—
293D4—48no—
294D4—48no—
295D4—44no—
296D4—448no—
297D4—448no—
298D4—448no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—114no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—444no—
313C2×C4D4×D1114yes—
314C2×C4C2×C22⋊D1112yes—
315C22—24no—
316C22—24no—
317C22—22no—
318C22—22no—
319C22—42no—
320C22—42no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—224no—
333C22—224no—
334C22—224no—
335C22—4416no—
336C22—442no—
337C22—442no—
338C22—442no—
339C22—442no—
340C22C2×D4×D1112yes—
341C22#6703711yescharacteristic
342C22#6703712yes—
343C22#6703711yescharacteristic
344C22C22×C22⋊D1111yescharacteristic
345C4—24no—
346C4—22no—
347C4—224no—
348C4—442no—
349C4—442no—
350C2—42no—
351C2—42no—
352C2—82no—
353C2—444no—
354C2#1062324612yes—
355C2#1062324811yescharacteristic
356C2#1062325111yescharacteristic
357C2D4×C22⋊D1112yes—
358C2#1062333511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#127C2
hypercenterC2×#127D11
hypocenterC11#2669
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×C11×#127C2semidirect
2. C2×#66992C2semidirect
3. C2×#66990C2semidirect
4. C2×#66990C2semidirect
5. #10622836C2semidirect
6. #10622836C2semidirect
7. #10622835C2semidirect
8. #10622833C2semidirect
9. #10622553C2semidirect
13. C22×D4×C11C22semidirect
14. C22×D4×C11C22semidirect
18. C23×Dic11C22semidirect
20. C2×C42×C11C22semidirect
23. C2×C22⋊Dic11C22semidirect
24. C2×C22⋊Dic11C22semidirect
25. C2×C22⋊Dic11C22semidirect
32. C2×Dic11⋊C4C22semidirect
33. C11⋊#95C22semidirect
34. C11⋊#95C22semidirect
55. C2×D4×C11D4semidirect
80. (C2×D11)⋊C4D4semidirect
136. C2×#127D11semidirect
186. C22×D4C2×D11semidirect
187. C22×D4C2×D11semidirect
202. C2×C42C2×D11semidirect
243. C2×D4C22⋊D11semidirect
261. C11#2669semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1272
C2×#669922
C2×#669902
#106228362
#106228352
#106228332
#106225532
#266911