Finite Group Databasebeta

← #13075007

Subgroups — #13075007

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×#67006C211yesmaximal, characteristic
2C2×#66932C211yesmaximal, characteristic, complemented
3C11×#379C211yesmaximal, characteristic, complemented
4#10622860C211yesmaximal, characteristic, complemented
5#10622574C211yesmaximal, characteristic, complemented
6#10622574C211yesmaximal, characteristic, complemented
7#10622572C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622570C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622564C211yesmaximal, characteristic, complemented
12#10622562C211yesmaximal, characteristic, complemented
13#10622561C211yesmaximal, characteristic, complemented
14#10622558C211yesmaximal, characteristic, complemented
15#10622557C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26#67006—24no—
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×C4⋊Dic11C2211yescharacteristic, complemented
41C2×C4⋊Dic11C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47C2×C4×Dic11C2211yescharacteristic, complemented
48#66932—24no—
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11—22no—
54C24×C11—22no—
55C24×C11—22no—
56C24×C11—41no—
57C24×C11—41no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11C2311yescharacteristic
61C24×C11C2311yescharacteristic
62C24×C11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—22no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—22no—
91C22⋊Dic11—22no—
92C22⋊Dic11—22no—
93C22⋊Dic11—22no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11D414yes—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103C4⋊Dic11—22no—
104C4⋊Dic11—41no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—41no—
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—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—44no—
131C23×C11—44no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—44no—
135C23×C11—44no—
136C23×C11—44no—
137C23×C11C2×D412yes—
138C23×C11#4112yes—
139C23×C11#4112yes—
140C23×C11C2411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
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—
160C22⋊D11—44no—
161C22⋊D11—44no—
162C22⋊D11—44no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
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×Dic11C2×D412yes—
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#394—111no—
192#390—111no—
193#390—111no—
194#388—111no—
195#388—111no—
196#388—111no—
197#379—111no—
198#379D1111yescharacteristic, complemented
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—416no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
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×C11C22×D411yescharacteristic
222C22×C11C2×#4111yescharacteristic
223C22×C11C2×#4111yescharacteristic
224C22×C11H(5,𝔽2)11yescharacteristic
225C22×C11H(5,𝔽2)11yescharacteristic
226C22×C11H(5,𝔽2)11yescharacteristic
227C22×C11H(5,𝔽2)11yescharacteristic
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239Dic11—22no—
240Dic11—22no—
241Dic11—41no—
242Dic11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—41no—
246C25C2×D1111yescharacteristic
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⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
272C2×C22⋊C4C2×D1111yescharacteristic
273C2×C22⋊C4C2×D1111yescharacteristic
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#95—111no—
283C2×C11—42no—
284C2×C11—42no—
285C2×C11—42no—
286C2×C11#53511yescharacteristic
287C2×C11#53811yescharacteristic
288C2×C11#53811yescharacteristic
289C2×C11#54611yescharacteristic
290C2×C11#54611yescharacteristic
291C2×C11#55111yescharacteristic
292C2×C11#56011yescharacteristic
293D11—81no—
294C24—22no—
295C24—22no—
296C24—22no—
297C24—41no—
298C24—41no—
299C24—41no—
300C24—41no—
301C24—111no—
302C24C22×D1111yescharacteristic
303C24C22×D1111yescharacteristic
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×C4—111no—
320C22×C4—111no—
321C22×C4C22×D1111yescharacteristic
322C22×C4C22×D1111yescharacteristic
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1111yescharacteristic
325C4⋊C4—222no—
326C4⋊C4—222no—
327C4⋊C4—222no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—114no—
338C22⋊C4—222no—
339C22⋊C4—222no—
340C22⋊C4—222no—
341C22⋊C4—222no—
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—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—44no—
372C23—44no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—221no—
379C23—221no—
380C23—221no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23#433912yes—
386C23D4×D1112yes—
387C23#434112yes—
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—112no—
405C2×C4—112no—
406C2×C4—221no—
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×C4—221no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—416no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22C2×#433911yescharacteristic
455C22C2×D4×D1111yescharacteristic
456C22C2×#434111yescharacteristic
457C22#6703711yescharacteristic
458C22#6703711yescharacteristic
459C22#6703711yescharacteristic
460C22#6703711yescharacteristic
461C4—41no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—222no—
466C4—222no—
467C4—441no—
468C4—441no—
469C4—441no—
470C4—441no—
471C4—441no—
472C2—42no—
473C2—42no—
474C2—42no—
475C2—881no—
476C2#1062302111yescharacteristic
477C2#1062302511yescharacteristic
478C2#1062302611yescharacteristic
479C2#1062312211yescharacteristic
480C2#1062312311yescharacteristic
481C2#1062312411yescharacteristic
482C2#1062312611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
prime radicalC2×#67006C2
hypercenter#379D11
hypocenterC11#2685
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#66932C2semidirect
3. C11×#379C2semidirect
4. #10622860C2semidirect
5. #10622574C2semidirect
6. #10622574C2semidirect
7. #10622572C2semidirect
8. #10622572C2semidirect
9. #10622570C2semidirect
10. #10622570C2semidirect
11. #10622564C2semidirect
12. #10622562C2semidirect
13. #10622561C2semidirect
14. #10622558C2semidirect
15. #10622557C2semidirect
36. C2×(C2×D11)⋊C4C22semidirect
37. C2×(C2×D11)⋊C4C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×C4⋊Dic11C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×Dic11⋊C4C22semidirect
43. C2×Dic11⋊C4C22semidirect
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
198. #379D11semidirect
352. C11#2685semidirect

Maximal subgroups

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

subgroupindex
C2×#670062
C2×#669322
C11×#3792
#106228602
#106225742
#106225722
#106225702
#106225642
#106225622
#106225612
#106225582
#106225572
#268511