Finite Group Databasebeta

← #13072736

Subgroups — #13072736

Order 1408.

786 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
1C22×C11×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic
3C2×#66977C211yesmaximal, characteristic, complemented
4C2×#66938C211yesmaximal, characteristic, complemented
5#10622860C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622826C211yesmaximal, characteristic, complemented
8C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622572C211yesmaximal, characteristic, complemented
11#10622570C211yesmaximal, characteristic, complemented
12#10622565C211yesmaximal, characteristic, complemented
13#10622564C211yesmaximal, characteristic, complemented
14#10622560C211yesmaximal, characteristic, complemented
15#10622557C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×Dic22C2211yescharacteristic, complemented
23C2×C11×C22⋊C4—24no—
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28#67006—24no—
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C2×C4⋊Dic11C2211yescharacteristic, complemented
43#66977—24no—
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47C2×C4×Dic11C2211yescharacteristic, complemented
48#66938—24no—
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11—22no—
56C24×C11—22no—
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—22no—
60C24×C11—41no—
61C24×C11—41no—
62C24×C11C2311yescharacteristic
63C24×C11C2311yescharacteristic
64C24×C11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C2×Dic22—22no—
93C2×Dic22—22no—
94C2×Dic22—41no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4D414yescomplemented
99C22⋊Dic11—22no—
100C22⋊Dic11—22no—
101C22⋊Dic11—22no—
102C22⋊Dic11—22no—
103C22⋊Dic11—22no—
104C22⋊Dic11—22no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C22⋊Dic11D414yes—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115C4×Dic11—22no—
116C4×Dic11—41no—
117#2472—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—28no—
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×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—44no—
136C23×C11—44no—
137C23×C11—44no—
138C23×C11—44no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11C2×D412yes—
142C23×C11C2×D412yes—
143C23×C11#4112yes—
144C23×C11#4112yes—
145C23×C11#4112yes—
146C23×C11C2411yescharacteristic
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—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—44no—
165C2×C4×C11—44no—
166C2×C4×C11C2×D412yes—
167C2×C4×C11C2×D412yes—
168C22⋊D11—44no—
169C22⋊D11—44no—
170C22⋊D11—44no—
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×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11C2×D412yes—
191C2×Dic11C2×D412yes—
192Dic22—44no—
193C2×#124—111no—
194C2×C22⋊Q8—111no—
195C2×#120—111no—
196C22×C22⋊C4D1111yescharacteristic, complemented
197#397—111no—
198#394—111no—
199#394—111no—
200#393—111no—
201#390—111no—
202#388—111no—
203#388—111no—
204#386—111no—
205#386—111no—
206#379—111no—
207C4×C22⋊C4—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—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—416no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11#12414yescomplemented
230C22×C11C22×D411yescharacteristic
231C22×C11C22×D411yescharacteristic
232C22×C11C2×#4111yescharacteristic
233C22×C11C2×#4111yescharacteristic
234C22×C11C2×#4111yescharacteristic
235C22×C11H(5,𝔽2)11yescharacteristic
236C22×C11H(5,𝔽2)11yescharacteristic
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—
248Dic11—22no—
249Dic11—22no—
250Dic11—41no—
251Dic11—41no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255C25C2×D1111yescharacteristic
256C22×Q8—111no—
257C22×D4—111no—
258C22×D4—111no—
259C22×D4—111no—
260C23×C4C2×D1111yescharacteristic
261C23×C4C2×D1111yescharacteristic
262#124—224no—
263C22⋊Q8—224no—
264#120—224no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
283C2×C22⋊C4C2×D1111yescharacteristic
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C42—111no—
287C2×C42—111no—
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×C11—42no—
297C2×C11#52511yescharacteristic
298C2×C11C2×#12411yescharacteristic
299C2×C11#53811yescharacteristic
300C2×C11D4211yescharacteristic
301C2×C11#54611yescharacteristic
302C2×C11#54611yescharacteristic
303C2×C11#55111yescharacteristic
304D11—81no—
305C24—22no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—41no—
311C24—41no—
312C24—111no—
313C24C22×D1111yescharacteristic
314C24C22×D1111yescharacteristic
315C24C22×D1111yescharacteristic
316C2×Q8—222no—
317C2×Q8—222no—
318C2×Q8—441no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—441no—
327C2×D4—441no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4C22×D1111yescharacteristic
342C22×C4C22×D1111yescharacteristic
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—114no—
352C22⋊C4—222no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—222no—
356C22⋊C4—222no—
357C22⋊C4—222no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4C22⋊D1114yescomplemented
365C42—222no—
366C42—441no—
367C11#247211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23#433912yes—
399C23#433912yes—
400C23D4×D1112yes—
401C23#434112yes—
402C23C2×C22⋊D1112yes—
403C23C23×D1111yescharacteristic
404Q8—444no—
405D4—444no—
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—44no—
419C2×C4—44no—
420C2×C4—112no—
421C2×C4—112no—
422C2×C4—221no—
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—221no—
441C2×C4C2×C22⋊D1112yes—
442C2×C4C2×C22⋊D1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22#6693814yescomplemented
472C22C2×#433911yescharacteristic
473C22C2×#433911yescharacteristic
474C22C2×D4×D1111yescharacteristic
475C22C2×#434111yescharacteristic
476C22#6703711yescharacteristic
477C22#6703711yescharacteristic
478C22C22×C22⋊D1111yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—222no—
484C4—222no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—881no—
494C2#1062302111yescharacteristic
495C2C2×#6693811yescharacteristic
496C2#1062302511yescharacteristic
497C2#1062302611yescharacteristic
498C2#1062332211yescharacteristic
499C2D4×C22⋊D1111yescharacteristic
500C2#1062333711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×C22⋊C4C2
prime radicalC2×#67006C2
hypercenterC22×C22⋊C4D11
hypocenterC11#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C11×C22⋊C4C2semidirect
3. C2×#66977C2semidirect
4. C2×#66938C2semidirect
5. #10622860C2semidirect
6. #10622826C2semidirect
7. #10622826C2semidirect
8. C4×C22⋊Dic11C2semidirect
9. #10622574C2semidirect
10. #10622572C2semidirect
11. #10622570C2semidirect
12. #10622565C2semidirect
13. #10622564C2semidirect
14. #10622560C2semidirect
15. #10622557C2semidirect
22. C22×Dic22C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. 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
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
98. C11×C22⋊C4D4semidirect
196. C22×C22⋊C4D11semidirect
229. C22×C11#124semidirect
364. C22⋊C4C22⋊D11semidirect
367. C11#2472semidirect
471. C22#66938semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊C42
C2×#670062
C2×#669772
C2×#669382
#106228602
#106228262
C4×C22⋊Dic112
#106225742
#106225722
#106225702
#106225652
#106225642
#106225602
#106225572
#247211