Finite Group Databasebeta

← #13075012

Subgroups — #13075012

Order 1408.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66990C211yesmaximal, characteristic
2C2×#66951C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic, complemented
4#10622834C211yesmaximal, characteristic, complemented
5#10622607C211yesmaximal, characteristic, complemented
6#10622574C211yesmaximal, characteristic, complemented
7#10622574C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622570C211yesmaximal, characteristic, complemented
10#10622568C211yesmaximal, characteristic, complemented
11#10622568C211yesmaximal, characteristic, complemented
12#10622564C211yesmaximal, characteristic, complemented
13#10622562C211yesmaximal, characteristic, complemented
14#10622283C211yesmaximal, characteristic, complemented
15#10622283C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic, complemented
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic, complemented
24C2×C11×C22⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic, complemented
29C2×C22⋊Dic11C2211yescharacteristic, complemented
30#66990—24no—
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic, complemented
43C2×C4⋊Dic11C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47C2×C4×Dic11C2211yescharacteristic, complemented
48#66951—24no—
49C11×#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C23×D11—22no—
56C23×D11—22no—
57C23×D11—22no—
58C23×D11—41no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11—41no—
62C23×D11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—41no—
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C11×C4⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C22⋊Dic11—22no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93C22⋊Dic11—41no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4D414yes—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—22no—
108Dic11⋊C4—41no—
109C4×Dic11—22no—
110C4×Dic11—41no—
111#2685—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11#4112yes—
126C23×C11C2411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—44no—
140C22×D11—44no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11—44no—
146C22×D11C2×D412yes—
147C22×D11#4112yes—
148D4×C11—44no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
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×C11C2×D412yes—
164C22⋊D11—44no—
165C22⋊D11—44no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
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×Dic11C2×D412yes—
184C2×#126—111no—
185C2×#120—111no—
186#399—111no—
187#396—111no—
188#394—111no—
189#394—111no—
190#394—111no—
191#394D1111yescharacteristic, complemented
192#390—111no—
193#390—111no—
194#388—111no—
195#388—111no—
196#388—111no—
197#379—111no—
198#379—111no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11C22×D411yescharacteristic
214C22×C11C2×#4111yescharacteristic
215C22×C11C2×#4111yescharacteristic
216C22×C11H(5,𝔽2)11yescharacteristic
217C22×C11H(5,𝔽2)11yescharacteristic
218C22×C11H(5,𝔽2)11yescharacteristic
219C22×C11H(5,𝔽2)11yescharacteristic
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—416no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C4×C11—22no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—41no—
240Dic11—22no—
241Dic11—41no—
242Dic11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—41no—
246C25—111no—
247C22×D4—111no—
248C22×D4—111no—
249C22×D4C2×D1111yescharacteristic
250#126—224no—
251#120—224no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4C2×D1111yescharacteristic, complemented
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4C2×D1111yescharacteristic
274C2×C22⋊C4C2×D1111yescharacteristic
275C2×C22⋊C4C2×D1111yescharacteristic, complemented
276C2×C22⋊C4C2×D1111yescharacteristic, complemented
277C2×C42—111no—
278C2×C42—111no—
279#95—111no—
280#95—111no—
281#95—111no—
282#95C2×D1111yescharacteristic, complemented
283C2×C11—42no—
284C2×C11—81no—
285C2×C11#53511yescharacteristic
286C2×C11#53811yescharacteristic
287C2×C11#53811yescharacteristic
288C2×C11#54611yescharacteristic
289C2×C11#54611yescharacteristic
290C2×C11#55111yescharacteristic
291C2×C11#56011yescharacteristic
292D11—42no—
293D11—42no—
294C24—111no—
295C24—111no—
296C24—222no—
297C24—222no—
298C24—222no—
299C24—441no—
300C24—441no—
301C24—441no—
302C24—441no—
303C24C22×D1111yescharacteristic
304C24C22×D1111yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—222no—
309C2×D4—222no—
310C2×D4—222no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—111no—
319C22×C4—111no—
320C22×C4C22×D1111yescharacteristic
321C22×C4C22×D1111yescharacteristic
322C22×C4C22×D1111yescharacteristic
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1111yescharacteristic
325C4⋊C4—22no—
326C4⋊C4—222no—
327C4⋊C4—222no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—114no—
336C22⋊C4—222no—
337C22⋊C4—222no—
338C22⋊C4—222no—
339C22⋊C4—222no—
340C22⋊C4—222no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42—222no—
351C42—441no—
352C11#268511yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—112no—
367C23—112no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23—221no—
379C23—221no—
380C23—444no—
381C23—444no—
382C23—444no—
383C23—444no—
384C23—444no—
385C23—444no—
386C23—444no—
387C23#434112yes—
388C23C23×D1111yescharacteristic
389D4—44no—
390D4—444no—
391D4—444no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—112no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4D4×D1112yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—4416no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22C2×D4×D1111yescharacteristic
455C22C2×#434111yescharacteristic
456C22#6703711yescharacteristic
457C22#6703711yescharacteristic
458C22#41×D1111yescharacteristic
459C22#6704211yescharacteristic
460C22#6704211yescharacteristic
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—222no—
467C4—441no—
468C4—441no—
469C4—441no—
470C4—441no—
471C4—441no—
472C2—42no—
473C2—81no—
474C2—442no—
475C2—442no—
476C2#1062312211yescharacteristic
477C2#1062313811yescharacteristic
478C2#1062314411yescharacteristic
479C2#1062314811yescharacteristic
480C2#1062318911yescharacteristic
481C2#1062319711yescharacteristic
482C2#1062320711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC2×#66990C2
hypercenter#394D11
hypocenterC11#2685
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66951C2semidirect
3. C11×#394C2semidirect
4. #10622834C2semidirect
5. #10622607C2semidirect
6. #10622574C2semidirect
7. #10622574C2semidirect
8. #10622572C2semidirect
9. #10622570C2semidirect
10. #10622568C2semidirect
11. #10622568C2semidirect
12. #10622564C2semidirect
13. #10622562C2semidirect
14. #10622283C2semidirect
15. #10622283C2semidirect
20. C2×C11×C4⋊C4C22semidirect
23. C2×C11×C22⋊C4C22semidirect
24. C2×C11×C22⋊C4C22semidirect
28. C2×C22⋊Dic11C22semidirect
29. C2×C22⋊Dic11C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×C4⋊Dic11C22semidirect
43. C2×C4⋊Dic11C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×C4×Dic11C22semidirect
47. C2×C4×Dic11C22semidirect
49. C11×#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
191. #394D11semidirect
257. C2×C4⋊C4C2×D11semidirect
275. C2×C22⋊C4C2×D11semidirect
276. C2×C22⋊C4C2×D11semidirect
282. #95C2×D11semidirect
352. C11#2685semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669512
C11×#3942
#106228342
#106226072
#106225742
#106225722
#106225702
#106225682
#106225642
#106225622
#106222832
#268511