Finite Group Databasebeta

← #13072072

Subgroups — #13072072

Order 1408.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C11C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic
3C2×#66982C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#10622833C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622823C211yesmaximal, characteristic, complemented
8#10622606C211yesmaximal, characteristic, complemented
9#10622605C211yesmaximal, characteristic, complemented
10#10622572C211yesmaximal, characteristic, complemented
11#10622572C211yesmaximal, characteristic, complemented
12#10622568C211yesmaximal, characteristic, complemented
13#10622555C211yesmaximal, characteristic, complemented
14#10622553C211yesmaximal, characteristic, complemented
15#10622553C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic, complemented
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C23×Dic11C2211yescharacteristic
23C4×D4×C11—24no—
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic, complemented
27C2×C42×C11C2211yescharacteristic, complemented
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic, complemented
31C2×C22⋊Dic11C2211yescharacteristic, complemented
32#66990—24no—
33#66982—24no—
34C2×(C2×D11)⋊C4—24no—
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×Dic11⋊C4C2211yescharacteristic, complemented
48C2×Dic11⋊C4C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—41no—
63C23×D11—41no—
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11D414yes—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—41no—
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C11×C4⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C42×C11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—22no—
101C22⋊Dic11—22no—
102C22⋊Dic11—41no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4D414yescomplemented
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117#2418—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11C2×D412yes—
129C23×C11C2×D412yes—
130C23×C11#4112yes—
131C23×C11#4112yes—
132C23×C11C2411yescharacteristic
133C22×D11—28no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—44no—
147C22×D11—44no—
148C22×D11—44no—
149C22×D11—44no—
150C22×D11—44no—
151C22×D11—44no—
152C22×D11C2×D412yes—
153C22×D11#4112yes—
154D4×C11—28no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—44no—
169C2×C4×C11—44no—
170C2×C4×C11C2×D412yes—
171C2×C4×C11C2×D412yes—
172C22⋊D11—44no—
173C22⋊D11—44no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—44no—
192C2×Dic11C2×D412yes—
193C2×#123—111no—
194C2×#120—111no—
195C2×C4×D4D1111yescharacteristic, complemented
196C22×C22⋊C4—111no—
197#399—111no—
198#397—111no—
199#394—111no—
200#394—111no—
201#388—111no—
202#388—111no—
203#386—111no—
204#386—111no—
205#385—111no—
206#380—111no—
207#379—111no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11#12314yescomplemented
222C22×C11C22×D411yescharacteristic
223C22×C11C22×D411yescharacteristic
224C22×C11C2×#4111yescharacteristic
225C22×C11C2×#4111yescharacteristic
226C22×C11C2×#4111yescharacteristic
227C22×C11H(5,𝔽2)11yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—416no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249Dic11—22no—
250Dic11—41no—
251Dic11—41no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255C25—111no—
256C22×D4—111no—
257C22×D4—111no—
258C22×D4C2×D1111yescharacteristic
259C23×C4—111no—
260C23×C4C2×D1111yescharacteristic
261C23×C4C2×D1111yescharacteristic, complemented
262#123—224no—
263#120—224no—
264C4×D4—24no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4C2×D1111yescharacteristic, complemented
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—111no—
279C2×C22⋊C4—111no—
280C2×C22⋊C4—111no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—111no—
283C2×C22⋊C4—111no—
284C2×C22⋊C4—224no—
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C22⋊C4C2×D1111yescharacteristic, complemented
287C2×C42C2×D1111yescharacteristic, complemented
288#95—111no—
289#95—111no—
290#95—111no—
291#95—111no—
292#95—111no—
293#95—111no—
294C2×C11—24no—
295C2×C11—42no—
296C2×C11C2×#12311yescharacteristic
297C2×C11#52511yescharacteristic
298C2×C11#53811yescharacteristic
299C2×C11D4211yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#54611yescharacteristic
302C2×C11#55111yescharacteristic
303D11—42no—
304D11—42no—
305C24—111no—
306C24—111no—
307C24—222no—
308C24—222no—
309C24—222no—
310C24—222no—
311C24—222no—
312C24—441no—
313C24—441no—
314C24C22×D1111yescharacteristic
315C24C22×D1111yescharacteristic
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4C22⋊D1114yes—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—441no—
340C22×C4C22×D1111yescharacteristic
341C22×C4C22×D1111yescharacteristic
342C22×C4C22×D1111yescharacteristic
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—114no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—222no—
356C22⋊C4—222no—
357C22⋊C4—222no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—222no—
361C22⋊C4—222no—
362C22⋊C4—222no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C42—22no—
367C11#241811yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—112no—
379C23—112no—
380C23—228no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23—444no—
394C23—444no—
395C23—444no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23#433912yes—
400C23#433912yes—
401C23C2×C22⋊D1112yes—
402C23C2×C22⋊D1112yes—
403C23C23×D1111yescharacteristic
404D4—28no—
405D4—444no—
406D4—444no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—112no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—444no—
441C2×C4D4×D1112yes—
442C2×C4C2×C22⋊D1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—222no—
457C22—222no—
458C22—222no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—4416no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22#6698214yescomplemented
472C22C2×#433911yescharacteristic
473C22C2×#433911yescharacteristic
474C22C2×D4×D1111yescharacteristic
475C22#6703711yescharacteristic
476C22#41×D1111yescharacteristic
477C22#6704211yescharacteristic
478C22C22×C22⋊D1111yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—222no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—24no—
491C2—42no—
492C2—442no—
493C2—442no—
494C2#1062307811yescharacteristic
495C2#1062308111yescharacteristic
496C2#1062308711yescharacteristic
497C2#1062309111yescharacteristic
498C2C2×#6698211yescharacteristic
499C2D4×C22⋊D1111yescharacteristic
500C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC2×#66990C2
hypercenterC2×C4×D4D11
hypocenterC11#2418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C11C2semidirect
3. C2×#66982C2semidirect
4. C22×(C2×D11)⋊C4C2semidirect
5. #10622833C2semidirect
6. #10622826C2semidirect
7. #10622823C2semidirect
8. #10622606C2semidirect
9. #10622605C2semidirect
10. #10622572C2semidirect
11. #10622572C2semidirect
12. #10622568C2semidirect
13. #10622555C2semidirect
14. #10622553C2semidirect
15. #10622553C2semidirect
19. C23×C4×C11C22semidirect
24. C2×C11×C4⋊C4C22semidirect
26. C2×C11×C22⋊C4C22semidirect
27. C2×C42×C11C22semidirect
30. C2×C22⋊Dic11C22semidirect
31. C2×C22⋊Dic11C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×Dic11⋊C4C22semidirect
48. C2×Dic11⋊C4C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
112. (C2×D11)⋊C4D4semidirect
195. C2×C4×D4D11semidirect
221. C22×C11#123semidirect
261. C23×C4C2×D11semidirect
269. C2×C4⋊C4C2×D11semidirect
286. C2×C22⋊C4C2×D11semidirect
287. C2×C42C2×D11semidirect
367. C11#2418semidirect
471. C22#66982semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669902
C2×#669822
C22×(C2×D11)⋊C42
#106228332
#106228262
#106228232
#106226062
#106226052
#106225722
#106225682
#106225552
#106225532
#241811