Finite Group Databasebeta

← #13072007

Subgroups — #13072007

Order 1408.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66990C211yesmaximal, characteristic
2C2×#66936C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6#10622835C211yesmaximal, characteristic, complemented
7#10622602C211yesmaximal, characteristic, complemented
8#10622600C211yesmaximal, characteristic, complemented
9#10622569C211yesmaximal, characteristic, complemented
10#10622569C211yesmaximal, characteristic, complemented
11#10622569C211yesmaximal, characteristic, complemented
12#10622566C211yesmaximal, characteristic, complemented
13#10622565C211yesmaximal, characteristic, complemented
14#10622280C211yesmaximal, characteristic, complemented
15#10622277C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic, complemented
28C2×C11×C22⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic, complemented
33C2×C22⋊Dic11C2211yescharacteristic, complemented
34#66990—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×C4⋊Dic11C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44#66936—24no—
45C22⋊C4×D11—24no—
46C22⋊C4×D11—24no—
47C11×#95C2211yescharacteristic, complemented
48C11⋊#95C2211yescharacteristic, 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—41no—
62C23×D11—41no—
63C23×D11D414yes—
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C2×C4×D11—22no—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—22no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—41no—
103C22⋊Dic11—22no—
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106C22⋊Dic11—22no—
107C22⋊Dic11—41no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4D414yescomplemented
114C4⋊Dic11—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—41no—
117#2412—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×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11C2×D412yes—
132C23×C11C2411yescharacteristic
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—28no—
142C22×D11—28no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11—44no—
146C22×D11—44no—
147C22×D11—44no—
148C22×D11C2×D412yes—
149C22×D11C2×D412yes—
150C22×D11C2×D412yes—
151C22×D11#4112yes—
152C22×D11#4112yes—
153C22×D11#4112yes—
154D4×C11—44no—
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—21no—
169C2×C4×C11C2×D412yes—
170C22⋊D11—44no—
171C22⋊D11—44no—
172C2×Dic11—21no—
173C2×Dic11—21no—
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×Dic11C2×D412yes—
190C4×D11—44no—
191C4×D11—44no—
192C4×D11—44no—
193C4×D11—44no—
194C2×#123—111no—
195C2×#120—111no—
196C22×C22⋊C4—111no—
197C22×C22⋊C4—111no—
198#397—111no—
199#397—111no—
200#394—111no—
201#394D1111yescharacteristic, complemented
202#386—111no—
203#386—111no—
204#386—111no—
205#385—111no—
206#381—111no—
207#380—111no—
208#380—111no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11C22×D411yescharacteristic
224C22×C11C22×D411yescharacteristic
225C22×C11C2×#4111yescharacteristic
226C22×C11C2×#4111yescharacteristic
227C22×C11C2×#4111yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C22×C11H(5,𝔽2)11yescharacteristic
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—22no—
239C2×D11—22no—
240C2×D11—22no—
241C2×D11—22no—
242C2×D11—416no—
243C2×D11#12114yes—
244C2×D11#12314yescomplemented
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—41no—
250Dic11—22no—
251Dic11—41no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255Dic11—41no—
256C25—111no—
257C22×D4—111no—
258C22×D4—111no—
259C22×D4C2×D1111yescharacteristic
260C23×C4—111no—
261C23×C4—111no—
262C23×C4—111no—
263C23×C4—111no—
264#123—224no—
265#120—224no—
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—224no—
282C2×C22⋊C4—224no—
283C2×C22⋊C4C2×D1111yescharacteristic
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic, complemented
286C2×C22⋊C4C2×D1111yescharacteristic, complemented
287#95—111no—
288#95—111no—
289#95—111no—
290#95—111no—
291#95—111no—
292#95—111no—
293#95—111no—
294#95C2×D1111yescharacteristic, complemented
295C2×C11—42no—
296C2×C11—81no—
297C2×C11C2×#12111yescharacteristic
298C2×C11C2×#12311yescharacteristic
299C2×C11#53411yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#54611yescharacteristic
302C2×C11#55111yescharacteristic
303C2×C11#55111yescharacteristic
304D11—24no—
305D11—24no—
306C24—111no—
307C24—111no—
308C24—114no—
309C24—222no—
310C24—222no—
311C24—222no—
312C24—222no—
313C24—441no—
314C24—441no—
315C24C22×D1111yescharacteristic
316C24C22×D1111yescharacteristic
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—222no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—222no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4C22×D1111yescharacteristic
345C22×C4C22×D1111yescharacteristic
346C22×C4C22×D1111yescharacteristic
347C22×C4C22×D1111yescharacteristic
348C22×C4C22×D1111yescharacteristic
349C4⋊C4—41no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—441no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—41no—
357C22⋊C4—114no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—222no—
361C22⋊C4—222no—
362C22⋊C4—222no—
363C22⋊C4—222no—
364C22⋊C4—222no—
365C22⋊C4—222no—
366C22⋊C4—222no—
367C22⋊C4—441no—
368C11#241211yescharacteristic, complemented, Sylow
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—112no—
383C23—112no—
384C23—112no—
385C23—112no—
386C23—112no—
387C23—112no—
388C23—228no—
389C23—228no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23—444no—
402C23—444no—
403C23D4×D1112yes—
404C23C23×D1111yescharacteristic
405D4—44no—
406D4—444no—
407D4—444no—
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—21no—
421C2×C4—21no—
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×C4—444no—
442C2×C4—444no—
443C2×C4—444no—
444C2×C4D4×D1112yes—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—114no—
460C22—114no—
461C22—222no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—222no—
466C22—222no—
467C22—222no—
468C22—222no—
469C22—222no—
470C22—222no—
471C22—222no—
472C22—222no—
473C22—4416no—
474C22C2×D4×D1111yescharacteristic
475C22C2×D4×D1111yescharacteristic
476C22#6703711yescharacteristic
477C22#6703711yescharacteristic
478C22#41×D1111yescharacteristic
479C22#41×D1111yescharacteristic
480C22#41×D1111yescharacteristic
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—222no—
487C4—441no—
488C4—441no—
489C4—441no—
490C4—441no—
491C4—441no—
492C2—42no—
493C2—81no—
494C2—224no—
495C2—224no—
496C2#1062312011yescharacteristic
497C2D11×#12111yescharacteristic
498C2#1062314111yescharacteristic
499C2#1062314311yescharacteristic
500C2D11×#12311yescharacteristic
501C2#1062319011yescharacteristic
502C2#1062321011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC2×#66990C2
hypercenter#394D11
hypocenterC11#2412
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66936C2semidirect
3. C2×C22⋊C4×D11C2semidirect
4. C2×C22⋊C4×D11C2semidirect
5. C11×#394C2semidirect
6. #10622835C2semidirect
7. #10622602C2semidirect
8. #10622600C2semidirect
9. #10622569C2semidirect
10. #10622569C2semidirect
11. #10622569C2semidirect
12. #10622566C2semidirect
13. #10622565C2semidirect
14. #10622280C2semidirect
15. #10622277C2semidirect
24. C2×C11×C4⋊C4C22semidirect
27. C2×C11×C22⋊C4C22semidirect
28. C2×C11×C22⋊C4C22semidirect
32. C2×C22⋊Dic11C22semidirect
33. C2×C22⋊Dic11C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×Dic11⋊C4C22semidirect
43. C2×Dic11⋊C4C22semidirect
47. C11×#95C22semidirect
48. C11⋊#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
113. (C2×D11)⋊C4D4semidirect
201. #394D11semidirect
244. C2×D11#123semidirect
269. C2×C4⋊C4C2×D11semidirect
285. C2×C22⋊C4C2×D11semidirect
286. C2×C22⋊C4C2×D11semidirect
294. #95C2×D11semidirect
368. C11#2412semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669362
C2×C22⋊C4×D112
C11×#3942
#106228352
#106226022
#106226002
#106225692
#106225662
#106225652
#106222802
#106222772
#241211