Finite Group Databasebeta

← #13073546

Subgroups — #13073546

Order 1408.

900 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 169 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×#66992C211yesmaximal, characteristic, complemented
3C2×#66990C211yesmaximal, characteristic, complemented
4C2×#66982C211yesmaximal, characteristic, complemented
5C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6C2×#66935C211yesmaximal, characteristic, complemented
7#10622605C212yesmaximal, complemented
8#10622601C212yesmaximal, complemented
9#10622573C212yesmaximal, complemented
10#10622570C212yesmaximal, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C24×D11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C22×C22⋊D11C2212yes—
17C22×C22⋊D11C2211yescharacteristic, complemented
18C23×Dic11C2211yescharacteristic
19C22×D44C2212yes—
20C11×#123—24no—
21C2×C11×C4⋊C4C2212yescomplemented
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2212yescomplemented
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic, complemented
26#66992—24no—
27#66990—24no—
28#66982—24no—
29C2×(C2×D11)⋊C4—24no—
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×(C2×D11)⋊C4C2212yes—
33C2×(C2×D11)⋊C4C2212yes—
34C2×(C2×D11)⋊C4C2212yescomplemented
35C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
36C2×Dic11⋊C4C2212yescomplemented
37C2×Dic11⋊C4C2211yescharacteristic, complemented
38C2×C4×Dic11C2212yescomplemented
39#66935—24no—
40C11⋊#95C2212yescomplemented
41C24×C11C2311yescharacteristic
42C24×C11C2311yescharacteristic
43C23×D11—22no—
44C23×D11—24no—
45C23×D11—22no—
46C23×D11—22no—
47C23×D11—42no—
48C23×D11C2311yescharacteristic
49C23×D11C2312yes—
50C2×D4×C11—22no—
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11C2312yes—
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2312yes—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—22no—
61C2×C22⋊D11—22no—
62C2×C22⋊D11—22no—
63C2×C22⋊D11—22no—
64C2×C22⋊D11—24no—
65C2×C22⋊D11—42no—
66C2×C22⋊D11—42no—
67C22×Dic11—42no—
68C22×Dic11D414yescomplemented
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2312yes—
72C22×Dic11C2311yescharacteristic
73C2×D44—24no—
74C2×D44—24no—
75C2×D44—42no—
76C11×C4⋊C4—24no—
77C11×C22⋊C4—24no—
78C11×C22⋊C4D414yescomplemented
79C22⋊Dic11—22no—
80C22⋊Dic11D414yescomplemented
81(C2×D11)⋊C4—24no—
82(C2×D11)⋊C4—24no—
83(C2×D11)⋊C4—24no—
84(C2×D11)⋊C4—24no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—24no—
87Dic11⋊C4—24no—
88Dic11⋊C4—22no—
89C4×Dic11—42no—
90#2539—111nomaximal, Sylow
91C23×C11—22no—
92C23×C11—22no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11C2×D412yes—
99C23×C11C2×D412yes—
100C23×C11C2×D412yes—
101C23×C11C2411yescharacteristic
102C22×D11—28no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—22no—
106C22×D11—22no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—22no—
113C22×D11—22no—
114C22×D11—48no—
115C22×D11—48no—
116C22×D11—44no—
117C22×D11—44no—
118C22×D11#4114yes—
119D4×C11—44no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—21no—
128C2×C4×C11—44no—
129C2×C4×C11C2×D414yes—
130C22⋊D11—48no—
131C22⋊D11—44no—
132C22⋊D11—44no—
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—44no—
141C2×Dic11C2×D414yes—
142C2×Dic11C2×D412yes—
143C2×Dic11C2×D412yes—
144D44—48no—
145C2×#123—111no—
146C2×#123D1111yescharacteristic, complemented
147C2×#121—111no—
148C2×#120—111no—
149C2×#120—111no—
150C22×C22⋊C4—111no—
151#399—112no—
152#392—112no—
153#390—112no—
154#390—112no—
155C4×C22⋊C4—111no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—24no—
159C22×C11—24no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—42no—
164C22×C11—42no—
165C22×C11#12714yes—
166C22×C11C22×D411yescharacteristic
167C22×C11C22×D411yescharacteristic
168C22×C11C22×D411yescharacteristic
169C22×C11C2×#4112yes—
170C22×C11H(5,𝔽2)12yes—
171C2×D11—24no—
172C2×D11—24no—
173C2×D11—24no—
174C2×D11—416no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—42no—
183C2×D11—42no—
184C4×C11—24no—
185C4×C11—42no—
186C4×C11—41no—
187Dic11—22no—
188Dic11—22no—
189Dic11—24no—
190Dic11—41no—
191C25—111no—
192C22×D4—111no—
193C22×D4—112no—
194C22×D4—111no—
195C22×D4—112no—
196C22×D4C2×D1111yescharacteristic
197C23×C4—111no—
198C23×C4C2×D1111yescharacteristic
199#123—24no—
200#123—224no—
201#121—224no—
202#120—224no—
203#120—224no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—112no—
206C2×C4⋊C4C2×D1112yescomplemented
207C2×C22⋊C4—111no—
208C2×C22⋊C4—111no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4—112no—
212C2×C22⋊C4—112no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—112no—
215C2×C22⋊C4—224no—
216C2×C22⋊C4C2×D1111yescharacteristic
217C2×C22⋊C4C2×D1112yescomplemented
218C2×C42—112no—
219#95—112no—
220C2×C11—24no—
221C2×C11—81no—
222C2×C11#52511yescharacteristic
223C2×C11C2×#12711yescharacteristic
224C2×C11#53411yescharacteristic
225C2×C11#54612yes—
226C2×C11#54612yes—
227D11—44no—
228D11—81no—
229C24—112no—
230C24—111no—
231C24—224no—
232C24—222no—
233C24—222no—
234C24—222no—
235C24—442no—
236C24C22×D1111yescharacteristic
237C24C22×D1111yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—224no—
242C2×D4—224no—
243C2×D4—222no—
244C2×D4—224no—
245C2×D4—222no—
246C2×D4—222no—
247C2×D4—222no—
248C2×D4—224no—
249C2×D4—442no—
250C2×D4—442no—
251C2×D4—442no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—111no—
256C22×C4—112no—
257C22×C4—111no—
258C22×C4—114no—
259C22×C4—111no—
260C22×C4—442no—
261C22×C4C22×D1112yes—
262C22×C4C22×D1111yescharacteristic
263C22×C4C22×D1112yes—
264C4⋊C4—24no—
265C4⋊C4—222no—
266C4⋊C4—224no—
267C22⋊C4—24no—
268C22⋊C4—114no—
269C22⋊C4—224no—
270C22⋊C4—224no—
271C22⋊C4—224no—
272C22⋊C4—222no—
273C22⋊C4—224no—
274C22⋊C4—222no—
275C22⋊C4—224no—
276C22⋊C4C22⋊D1114yescomplemented
277C42—442no—
278C11#253911yescharacteristic, complemented, Sylow
279C23—22no—
280C23—22no—
281C23—21no—
282C23—21no—
283C23—22no—
284C23—22no—
285C23—21no—
286C23—114no—
287C23—228no—
288C23—222no—
289C23—222no—
290C23—222no—
291C23—222no—
292C23—222no—
293C23—222no—
294C23—221no—
295C23—221no—
296C23—222no—
297C23—222no—
298C23—221no—
299C23—448no—
300C23—448no—
301C23—444no—
302C23—444no—
303C23D4×D1112yes—
304C23D4×D1112yes—
305C23C2×C22⋊D1112yes—
306C23C23×D1111yescharacteristic
307D4—44no—
308D4—448no—
309D4—448no—
310D4—444no—
311D4—444no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—114no—
322C2×C4—112no—
323C2×C4—112no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—444no—
332C2×C4C2×C22⋊D1114yes—
333C22—24no—
334C22—22no—
335C22—24no—
336C22—22no—
337C22—41no—
338C22—42no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22—224no—
343C22—224no—
344C22—224no—
345C22—4416no—
346C22—442no—
347C22—442no—
348C22—442no—
349C22—442no—
350C22—441no—
351C22—442no—
352C22—441no—
353C22—442no—
354C22—441no—
355C22#6699314yes—
356C22C2×D4×D1111yescharacteristic
357C22C2×D4×D1111yescharacteristic
358C22#41×D1112yes—
359C22#6704212yes—
360C22C22×C22⋊D1111yescharacteristic
361C4—24no—
362C4—42no—
363C4—41no—
364C4—222no—
365C4—222no—
366C4—224no—
367C4—441no—
368C2—24no—
369C2—81no—
370C2—444no—
371C2—881no—
372C2#1062318411yescharacteristic
373C2#1062318512yes—
374C2#1062318711yescharacteristic
375C2C2×#6699311yescharacteristic
376C2#1062336012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#123C2
hypercenterC2×#123D11
hypocenterC11#2539
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
2. C2×#66992C2semidirect
3. C2×#66990C2semidirect
4. C2×#66982C2semidirect
5. C22×(C2×D11)⋊C4C2semidirect
6. C2×#66935C2semidirect
7. #10622605C2semidirect
8. #10622601C2semidirect
9. #10622573C2semidirect
10. #10622570C2semidirect
11. C22⋊C4×Dic11C2semidirect
17. C22×C22⋊D11C22semidirect
21. C2×C11×C4⋊C4C22semidirect
23. C2×C11×C22⋊C4C22semidirect
25. C2×C22⋊Dic11C22semidirect
34. C2×(C2×D11)⋊C4C22semidirect
35. C2×(C2×D11)⋊C4C22semidirect
36. C2×Dic11⋊C4C22semidirect
37. C2×Dic11⋊C4C22semidirect
38. C2×C4×Dic11C22semidirect
40. C11⋊#95C22semidirect
68. C22×Dic11D4semidirect
78. C11×C22⋊C4D4semidirect
80. C22⋊Dic11D4semidirect
146. C2×#123D11semidirect
206. C2×C4⋊C4C2×D11semidirect
217. C2×C22⋊C4C2×D11semidirect
276. C22⋊C4C22⋊D11semidirect
278. C11#2539semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×#669922
C2×#669902
C2×#669822
C22×(C2×D11)⋊C42
C2×#669352
#106226052
#106226012
#106225732
#106225702
C22⋊C4×Dic112
#253911