Finite Group Databasebeta

← #13075000

Subgroups — #13075000

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×#66951C211yesmaximal, characteristic, complemented
2C2×#66935C211yesmaximal, characteristic
3C11×#399C211yesmaximal, characteristic, complemented
4#10622607C211yesmaximal, characteristic, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622603C211yesmaximal, characteristic, complemented
8#10622601C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622568C211yesmaximal, characteristic, complemented
12#10622568C211yesmaximal, characteristic, complemented
13#10622558C211yesmaximal, characteristic, complemented
14#10622285C211yesmaximal, characteristic, complemented
15#10622282C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic, complemented
21C2×C11×C4⋊C4C2211yescharacteristic, complemented
22C2×C11×C4⋊C4C2211yescharacteristic, complemented
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C2×C4⋊Dic11C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic11C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47#66951—24no—
48#66935—24no—
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—41no—
58C23×D11—41no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11C2311yescharacteristic
62C23×D11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—41no—
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—22no—
91C22⋊Dic11—41no—
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—
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)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4D414yes—
106C4⋊Dic11—22no—
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#4112yes—
119C23×C11C2411yescharacteristic
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
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—
148C2×C4×C11—21no—
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×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11C2×D412yes—
166C22⋊D11—44no—
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×Dic11C2×D412yes—
182D44—44no—
183D44—44no—
184C2×#126—111no—
185C2×#120—111no—
186#399D1111yescharacteristic, complemented
187#396—111no—
188#394—111no—
189#394—111no—
190#394—111no—
191#394—111no—
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×C11C22×D411yescharacteristic
207C22×C11C2×#4111yescharacteristic
208C22×C11C2×#4111yescharacteristic
209C22×C11H(5,𝔽2)11yescharacteristic
210C22×C11H(5,𝔽2)11yescharacteristic
211C22×C11H(5,𝔽2)11yescharacteristic
212C22×C11H(5,𝔽2)11yescharacteristic
213C2×D11—22no—
214C2×D11—22no—
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—416no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—41no—
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—
240C4×C11—41no—
241Dic11—22no—
242Dic11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—41no—
246C25—111no—
247C22×D4—111no—
248C22×D4—111no—
249C22×D4—111no—
250#126—224no—
251#120—224no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4C2×D1111yescharacteristic, complemented
256C2×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—111no—
274C2×C22⋊C4C2×D1111yescharacteristic
275C2×C22⋊C4C2×D1111yescharacteristic
276C2×C22⋊C4C2×D1111yescharacteristic
277C2×C42—111no—
278C2×C42—111no—
279#95—111no—
280#95—111no—
281#95—111no—
282#95C2×D1111yescharacteristic, complemented
283C2×C11—42no—
284C2×C11#53511yescharacteristic
285C2×C11#53811yescharacteristic
286C2×C11#53811yescharacteristic
287C2×C11#54611yescharacteristic
288C2×C11#54611yescharacteristic
289C2×C11#55111yescharacteristic
290C2×C11#56011yescharacteristic
291D11—42no—
292D11—42no—
293D11—81no—
294C24—111no—
295C24—111no—
296C24—111no—
297C24—222no—
298C24—222no—
299C24—222no—
300C24—441no—
301C24—441no—
302C24—441no—
303C24—441no—
304C24C22×D1111yescharacteristic
305C2×D4—222no—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—222no—
310C2×D4—441no—
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×C4C22×D1111yescharacteristic
320C22×C4C22×D1111yescharacteristic
321C22×C4C22×D1111yescharacteristic
322C22×C4C22×D1111yescharacteristic
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1111yescharacteristic
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—441no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—114no—
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⋊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—112no—
360C23—112no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
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#434312yes—
388C23C23×D1111yescharacteristic
389D4—444no—
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—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—112no—
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—222no—
433C22—222no—
434C22—222no—
435C22—222no—
436C22—222no—
437C22—222no—
438C22—4416no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22—441no—
443C22—441no—
444C22—441no—
445C22—441no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22C2×D4×D1111yescharacteristic
455C22#6703711yescharacteristic
456C22#6703711yescharacteristic
457C22C2×#434311yescharacteristic
458C22#41×D1111yescharacteristic
459C22#6704211yescharacteristic
460C22#6704211yescharacteristic
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—222no—
468C4—441no—
469C4—441no—
470C4—441no—
471C4—441no—
472C2—42no—
473C2—442no—
474C2—442no—
475C2—881no—
476C2#1062316111yescharacteristic
477C2#1062316811yescharacteristic
478C2#1062317511yescharacteristic
479C2#1062318511yescharacteristic
480C2#1062318811yescharacteristic
481C2#1062319711yescharacteristic
482C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC2×#66935C2
hypercenter#399D11
hypocenterC11#2685
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66951C2semidirect
3. C11×#399C2semidirect
4. #10622607C2semidirect
5. #10622604C2semidirect
6. #10622604C2semidirect
7. #10622603C2semidirect
8. #10622601C2semidirect
9. #10622574C2semidirect
10. #10622570C2semidirect
11. #10622568C2semidirect
12. #10622568C2semidirect
13. #10622558C2semidirect
14. #10622285C2semidirect
15. #10622282C2semidirect
20. C2×C11×C4⋊C4C22semidirect
21. C2×C11×C4⋊C4C22semidirect
22. C2×C11×C4⋊C4C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×C4⋊Dic11C22semidirect
43. C2×Dic11⋊C4C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×C4×Dic11C22semidirect
46. C2×C4×Dic11C22semidirect
49. C11×#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
186. #399D11semidirect
255. C2×C4⋊C4C2×D11semidirect
256. C2×C4⋊C4C2×D11semidirect
257. C2×C4⋊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×#669512
C2×#669352
C11×#3992
#106226072
#106226042
#106226032
#106226012
#106225742
#106225702
#106225682
#106225582
#106222852
#106222822
#268511