Finite Group Databasebeta

← #13072855

Subgroups — #13072855

Order 1408.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D11C211yesmaximal, characteristic
2C2×#66932C211yesmaximal, characteristic, complemented
3C11×#397C211yesmaximal, characteristic, complemented
4#10622607C211yesmaximal, characteristic, complemented
5#10622602C211yesmaximal, characteristic, complemented
6#10622568C211yesmaximal, characteristic
7#10622568C211yesmaximal, characteristic
8#10622565C211yesmaximal, characteristic, complemented
9#10622557C211yesmaximal, characteristic, complemented
10#10622288C211yesmaximal, characteristic, complemented
11#10622282C211yesmaximal, characteristic, complemented
12#10622282C211yesmaximal, characteristic, complemented
13#10622281C211yesmaximal, characteristic, complemented
14#10622280C211yesmaximal, characteristic, complemented
15#10622279C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×C4⋊Dic11C2211yescharacteristic, complemented
37C2×Dic11⋊C4C2211yescharacteristic, complemented
38C2×Dic11⋊C4C2211yescharacteristic, complemented
39C2×Dic11⋊C4C2211yescharacteristic, complemented
40C2×Dic11⋊C4C2211yescharacteristic, complemented
41C2×C4×Dic11C2211yescharacteristic, complemented
42C2×C4×Dic11C2211yescharacteristic, complemented
43C22⋊C4×D11—24no—
44#66932—24no—
45C11×#95C2211yescharacteristic, complemented
46C11×#95C2211yescharacteristic, complemented
47C11×#95C2211yescharacteristic, complemented
48C11⋊#95C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11C2311yescharacteristic
54C23×D11—22no—
55C23×D11—22no—
56C23×D11—22no—
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11C2311yescharacteristic
62C23×D11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—41no—
85C22⋊Dic11—22no—
86C22⋊Dic11—41no—
87C22⋊Dic11D414yes—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—22no—
92(C2×D11)⋊C4—22no—
93(C2×D11)⋊C4—22no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98C4⋊Dic11—22no—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—22no—
104C4×Dic11—41no—
105#2480—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11C2×D412yes—
113C23×C11C2411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—28no—
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—44no—
126C22×D11—44no—
127C22×D11—44no—
128C22×D11—44no—
129C22×D11—44no—
130C22×D11—44no—
131C22×D11#4112yes—
132C22×D11#4112yes—
133C22×D11#4112yes—
134C22×D11#4112yes—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11C2×D412yes—
170C2×Dic11C2×D412yes—
171C4×D11—44no—
172C4×D11—44no—
173C2×#126—111no—
174C22×C22⋊C4—111no—
175#397—111no—
176#397—111no—
177#397D1111yescharacteristic, complemented
178#396—111no—
179#388—111no—
180#388—111no—
181#388—111no—
182#385—111no—
183#385—111no—
184#380—111no—
185#379—111no—
186#379—111no—
187C4×C22⋊C4—111no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11C22×D411yescharacteristic
196C22×C11C2×#4111yescharacteristic
197C22×C11C2×#4111yescharacteristic
198C22×C11C2×#4111yescharacteristic
199C22×C11C2×#4111yescharacteristic
200C22×C11H(5,𝔽2)11yescharacteristic
201C22×C11H(5,𝔽2)11yescharacteristic
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—22no—
210C2×D11—22no—
211C2×D11—416no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11#12614yescomplemented
217C4×C11—41no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—41no—
223Dic11—22no—
224Dic11—22no—
225Dic11—41no—
226Dic11—41no—
227Dic11—41no—
228Dic11—41no—
229C25—111no—
230C23×C4—111no—
231C23×C4—111no—
232#126—224no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4C2×D1111yescharacteristic, complemented
239C2×C22⋊C4—111no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—111no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—111no—
250C2×C22⋊C4—111no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—224no—
253C2×C22⋊C4C2×D1111yescharacteristic
254C2×C22⋊C4C2×D1111yescharacteristic
255C2×C22⋊C4C2×D1111yescharacteristic
256C2×C42—111no—
257C2×C42—111no—
258#95—111no—
259#95—111no—
260#95—111no—
261#95—111no—
262#95—111no—
263#95C2×D1111yescharacteristic, complemented
264#95C2×D1111yescharacteristic, complemented
265#95C2×D1111yescharacteristic, complemented
266C2×C11—42no—
267C2×C11#52511yescharacteristic
268C2×C11C2×#12611yescharacteristic
269C2×C11#53811yescharacteristic
270C2×C11#54611yescharacteristic
271C2×C11#54611yescharacteristic
272C2×C11#55111yescharacteristic
273C2×C11#55111yescharacteristic
274D11—24no—
275D11—42no—
276C24—111no—
277C24—111no—
278C24—222no—
279C24—222no—
280C24—222no—
281C24—222no—
282C24—222no—
283C24—441no—
284C24—441no—
285C24C22×D1111yescharacteristic
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—111no—
292C22×C4—222no—
293C22×C4—222no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4C22×D1111yescharacteristic
299C22×C4C22×D1111yescharacteristic
300C22×C4C22×D1111yescharacteristic
301C22×C4C22×D1111yescharacteristic
302C22×C4C22×D1111yescharacteristic
303C22×C4C22×D1111yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—41no—
313C22⋊C4—114no—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C22⋊C4—222no—
317C22⋊C4—222no—
318C22⋊C4—222no—
319C22⋊C4—222no—
320C22⋊C4—222no—
321C22⋊C4—222no—
322C22⋊C4—222no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C42—222no—
327C42—441no—
328C11#248011yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—112no—
336C23—112no—
337C23—112no—
338C23—112no—
339C23—228no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23—221no—
345C23—221no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—444no—
351C23—444no—
352C23—444no—
353C23—444no—
354C23—444no—
355C23—444no—
356C23D4×D1112yes—
357C23C23×D1111yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—112no—
377C2×C4—112no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—444no—
395C2×C4—444no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—114no—
404C22—222no—
405C22—222no—
406C22—222no—
407C22—222no—
408C22—222no—
409C22—222no—
410C22—222no—
411C22—222no—
412C22—222no—
413C22—4416no—
414C22—441no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22C2×D4×D1111yescharacteristic
419C22#6703711yescharacteristic
420C22#41×D1111yescharacteristic
421C22#41×D1111yescharacteristic
422C22#41×D1111yescharacteristic
423C22#41×D1111yescharacteristic
424C22#6704211yescharacteristic
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—222no—
432C4—222no—
433C4—441no—
434C4—441no—
435C4—441no—
436C4—441no—
437C2—42no—
438C2—224no—
439C2—442no—
440C2#1062314111yescharacteristic
441C2#1062318511yescharacteristic
442C2#1062318711yescharacteristic
443C2#1062318811yescharacteristic
444C2#1062321011yescharacteristic
445C2D11×#12611yescharacteristic
446C2#1062323611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×D11C22
hypercenter#397D11
hypocenterC11#2480
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#66932C2semidirect
3. C11×#397C2semidirect
4. #10622607C2semidirect
5. #10622602C2semidirect
8. #10622565C2semidirect
9. #10622557C2semidirect
10. #10622288C2semidirect
11. #10622282C2semidirect
12. #10622282C2semidirect
13. #10622281C2semidirect
14. #10622280C2semidirect
15. #10622279C2semidirect
19. C2×C11×C4⋊C4C22semidirect
36. C2×C4⋊Dic11C22semidirect
37. C2×Dic11⋊C4C22semidirect
38. C2×Dic11⋊C4C22semidirect
39. C2×Dic11⋊C4C22semidirect
40. C2×Dic11⋊C4C22semidirect
41. C2×C4×Dic11C22semidirect
42. C2×C4×Dic11C22semidirect
45. C11×#95C22semidirect
46. C11×#95C22semidirect
47. C11×#95C22semidirect
48. C11⋊#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
177. #397D11semidirect
216. C2×D11#126semidirect
238. C2×C4⋊C4C2×D11semidirect
263. #95C2×D11semidirect
264. #95C2×D11semidirect
265. #95C2×D11semidirect
328. C11#2480semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D112
C2×#669322
C11×#3972
#106226072
#106226022
#106225682
#106225652
#106225572
#106222882
#106222822
#106222812
#106222802
#106222792
#248011