Finite Group Databasebeta

← #14925890

Subgroups — #14925890

Order 2816.

3394 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C212yesmaximal, complemented
2#13074197C214yesmaximal, complemented
3#13073960C214yesmaximal, complemented
4#13073503C214yesmaximal, complemented
5#13072897C211yesmaximal, characteristic, complemented
6#13071939C212yesmaximal, complemented
7#13071851C214yesmaximal, complemented
8#13071141C214yesmaximal, complemented
9#120×Dic11C214yesmaximal, complemented
10#13070994C211yesmaximal, characteristic, complemented
11C11×#2403C211yesmaximal, characteristic
12C23×D4×C11C2212yes—
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2212yescomplemented
15C2×C11×#120C2214yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yescomplemented
18C2×#66988C2214yes—
19C2×D4×Dic11—216no—
20C2×D4×Dic11C2214yes—
21C2×D4×Dic11C2214yes—
22C2×D4×Dic11C2214yescomplemented
23C2×D4×Dic11C2214yescomplemented
24C2×D4×Dic11C2214yescomplemented
25C22×C4⋊Dic11C2212yescomplemented
26C22×C4×Dic11C2212yescomplemented
27C2×#66930C2212yescomplemented
28C11×#392C2214yes—
29C11×#386C2214yes—
30C11×#379C2211yescharacteristic
31#10622860C2211yescharacteristic
32#10622860C2214yescomplemented
33#10622835C2218yescomplemented
34#10622835C2214yescomplemented
35#10622833C2214yes—
36#10622833C2218yescomplemented
37#10622823C2214yescomplemented
38#10622566C2214yescomplemented
39#10622563C2214yescomplemented
40#10622563C2218yescomplemented
41#10622561C2218yescomplemented
42#10622558C2218yescomplemented
43#10622556C2214yescomplemented
44#10622556C2212yescomplemented
45#10622555C2214yescomplemented
46C22⋊C4×Dic11C2214yescomplemented
47C22⋊C4×Dic11C2218yescomplemented
48#10622274C2214yescomplemented
49#10622268C2218yescomplemented
50#10622262C2214yescomplemented
51C25×C11C2312yes—
52C25×C11C2311yescharacteristic
53C22×D4×C11—28no—
54C22×D4×C11—216no—
55C22×D4×C11C2314yes—
56C22×D4×C11C2314yes—
57C22×D4×C11C2314yes—
58C23×C4×C11C2312yes—
59C23×Dic11—28no—
60C23×Dic11—44no—
61C23×Dic11—48no—
62C23×Dic11D418yescomplemented
63C23×Dic11C2312yes—
64C23×Dic11C2314yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C23×Dic11C2314yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C11×#120—216no—
72C2×C11×C22⋊C4C2314yes—
73C2×C11×C22⋊C4C2318yes—
74C2×C11×C22⋊C4C2312yes—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11C2314yes—
78C2×C22⋊Dic11C2318yes—
79C2×C22⋊Dic11C2314yes—
80C2×C22⋊Dic11C2314yes—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2314yes—
83C2×C22⋊Dic11C2312yes—
84C2×C22⋊Dic11C2318yes—
85#66988—216no—
86D4×Dic11—216no—
87D4×Dic11—216no—
88D4×Dic11—216no—
89D4×Dic11—216no—
90D4×Dic11—48no—
91C2×C4⋊Dic11—28no—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2314yes—
97C2×C4×Dic11—28no—
98C2×C4×Dic11C2314yes—
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2314yes—
101#66930—44no—
102C11×#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107#34956—111nomaximal, Sylow
108C24×C11—24no—
109C24×C11—28no—
110C24×C11—28no—
111C24×C11—28no—
112C24×C11—42no—
113C24×C11—44no—
114C24×C11C2×D414yes—
115C24×C11C2411yescharacteristic
116C24×C11C2414yes—
117C24×C11C2412yes—
118C2×D4×C11—264no—
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—216no—
124C2×D4×C11—28no—
125C2×D4×C11—44no—
126C2×D4×C11#41116yes—
127C22×C4×C11—24no—
128C22×C4×C11—28no—
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×Dic11—24no—
132C22×Dic11—28no—
133C22×Dic11—28no—
134C22×Dic11—28no—
135C22×Dic11—216no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—28no—
139C22×Dic11—44no—
140C22×Dic11—44no—
141C22×Dic11—42no—
142C22×Dic11—48no—
143C22×Dic11—416no—
144C22×Dic11—432no—
145C22×Dic11C2×D418yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D418yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2414yes—
150C22×Dic11C2414yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2411yescharacteristic
154C22×Dic11C2411yescharacteristic
155C11×C22⋊C4—28no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—42no—
158C22⋊Dic11—28no—
159C22⋊Dic11—28no—
160C22⋊Dic11—28no—
161C22⋊Dic11—28no—
162C22⋊Dic11—216no—
163C22⋊Dic11—28no—
164C22⋊Dic11—42no—
165C22⋊Dic11—48no—
166C4⋊Dic11—28no—
167C4⋊Dic11—28no—
168C4⋊Dic11—44no—
169Dic11⋊C4—216no—
170Dic11⋊C4—44no—
171C4×Dic11—28no—
172C4×Dic11—28no—
173C4×Dic11—28no—
174C22×C4×D4—112no—
175#2600—114no—
176#2579—114no—
177#2534—114no—
178#2483—111no—
179#2405—112no—
180#2403D1111yescharacteristic
181#2392—114no—
182C4×#123—114no—
183C4×#120—114no—
184#2280—111no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—216no—
188C23×C11—216no—
189C23×C11—24no—
190C23×C11—28no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—28no—
195C23×C11—44no—
196C23×C11—416no—
197C23×C11—432no—
198C23×C11—48no—
199C23×C11—48no—
200C23×C11C22×D412yes—
201C23×C11C22×D414yes—
202C23×C11C2×#4118yes—
203C23×C11C2×#4118yes—
204C23×C11C2511yescharacteristic
205D4×C11—232no—
206D4×C11—232no—
207D4×C11—416no—
208C2×C4×C11—216no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—28no—
212C2×C4×C11—24no—
213C2×C4×C11C2×#4118yes—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—216no—
217C2×Dic11—28no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—28no—
221C2×Dic11—28no—
222C2×Dic11—24no—
223C2×Dic11—28no—
224C2×Dic11—44no—
225C2×Dic11—48no—
226C2×Dic11—416no—
227C2×Dic11—48no—
228C2×Dic11—48no—
229C2×Dic11—416no—
230C2×Dic11C22×D414yes—
231C2×Dic11C22×D412yes—
232C2×Dic11C22×D412yes—
233C2×Dic11H(5,𝔽2)14yes—
234C23×D4C2×D1112yes—
235C24×C4—111no—
236C24×C4—112no—
237C2×#123—114no—
238C2×#120C2×D1114yes—
239C2×C4×D4—114no—
240C2×C4×D4—114no—
241C2×C4×D4—114no—
242C2×C4×D4—114no—
243C2×C4×D4—114no—
244C2×C4×D4—2216no—
245C2×#117—112no—
246C22×C4⋊C4—112no—
247C22×C22⋊C4—112no—
248C22×C22⋊C4—112no—
249C22×C42—112no—
250#398—114no—
251#397—114no—
252#396—118no—
253#394—118no—
254#394—114no—
255#392C2×D1114yes—
256#388—118no—
257#387—118no—
258#386—114no—
259#386—118no—
260#386C2×D1114yes—
261#385—114no—
262#385—118no—
263#385—114no—
264#381—112no—
265#381—114no—
266#380—114no—
267#379—111no—
268#379—114no—
269#379C2×D1111yescharacteristic
270C4×C4⋊C4—114no—
271C4×C22⋊C4—118no—
272C4×C22⋊C4—114no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—216no—
276C22×C11—24no—
277C22×C11—28no—
278C22×C11—22no—
279C22×C11—216no—
280C22×C11—416no—
281C22×C11—432no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—48no—
285C22×C11—44no—
286C22×C11#52518yes—
287C22×C11C23×D411yescharacteristic
288C22×C11C22×#4114yes—
289C22×C11C2×H(5,𝔽2)12yes—
290C4×C11—28no—
291C4×C11—44no—
292Dic11—24no—
293Dic11—22no—
294Dic11—44no—
295Dic11—44no—
296Dic11—44no—
297Dic11#53414yes—
298C25C22×D1112yes—
299C25C22×D1111yescharacteristic
300C22×D4—28no—
301C22×D4—216no—
302C22×D4C22×D1114yes—
303C22×D4C22×D1114yes—
304C22×D4C22×D1114yes—
305C23×C4—111no—
306C23×C4—112no—
307C23×C4—118no—
308C23×C4—112no—
309C23×C4—111no—
310C23×C4—112no—
311C23×C4—114no—
312C23×C4—112no—
313C23×C4—114no—
314C23×C4—228no—
315C23×C4—444no—
316C23×C4—448no—
317C23×C4C22×D1112yes—
318#123—2216no—
319#120—216no—
320C4×D4—2216no—
321C4×D4—2216no—
322C4×D4—2216no—
323C4×D4—2216no—
324C4×D4—448no—
325#117—444no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—114no—
328C2×C4⋊C4—118no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—228no—
332C2×C22⋊C4—114no—
333C2×C22⋊C4—114no—
334C2×C22⋊C4—114no—
335C2×C22⋊C4—114no—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—118no—
338C2×C22⋊C4—112no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—228no—
341C2×C22⋊C4—228no—
342C2×C22⋊C4C22×D1114yes—
343C2×C22⋊C4C22×D1118yes—
344C2×C22⋊C4C22×D1112yes—
345C2×C42—114no—
346C2×C42—114no—
347C2×C42—114no—
348C2×C42—228no—
349#95—118no—
350#95—118no—
351#95—118no—
352#95—114no—
353#95C22×D1114yes—
354C2×C11—28no—
355C2×C11—42no—
356C2×C11—48no—
357C2×C11C2×#52512yes—
358C2×C11C2×#53411yescharacteristic
359C2×C11#348114yes—
360C24—24no—
361C24—28no—
362C24—28no—
363C24—28no—
364C24—42no—
365C24—44no—
366C24D4×D1114yes—
367C24C23×D1111yescharacteristic
368C24C23×D1114yes—
369C24C23×D1112yes—
370C2×D4—264no—
371C2×D4—28no—
372C2×D4—28no—
373C2×D4—28no—
374C2×D4—28no—
375C2×D4—216no—
376C2×D4—28no—
377C2×D4—44no—
378C2×D4#4341116yes—
379C22×C4—24no—
380C22×C4—28no—
381C22×C4—111no—
382C22×C4—118no—
383C22×C4—114no—
384C22×C4—112no—
385C22×C4—111no—
386C22×C4—118no—
387C22×C4—114no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—224no—
392C22×C4—228no—
393C22×C4—228no—
394C22×C4—228no—
395C22×C4—2216no—
396C22×C4—224no—
397C22×C4—224no—
398C22×C4—228no—
399C22×C4—4416no—
400C22×C4—444no—
401C22×C4—442no—
402C22×C4—448no—
403C22×C4—444no—
404C22×C4—4432no—
405C22×C4C23×D1114yes—
406C22×C4C23×D1114yes—
407C4⋊C4—228no—
408C4⋊C4—228no—
409C4⋊C4—2216no—
410C4⋊C4—444no—
411C4⋊C4—444no—
412C22⋊C4—28no—
413C22⋊C4—216no—
414C22⋊C4—42no—
415C22⋊C4—228no—
416C22⋊C4—228no—
417C22⋊C4—228no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C22⋊C4—2216no—
421C22⋊C4—442no—
422C22⋊C4—448no—
423C42—228no—
424C42—228no—
425C42—228no—
426C11#3495611yescharacteristic, complemented, Sylow
427C23—24no—
428C23—24no—
429C23—216no—
430C23—216no—
431C23—24no—
432C23—28no—
433C23—24no—
434C23—24no—
435C23—22no—
436C23—28no—
437C23—44no—
438C23—416no—
439C23—432no—
440C23—48no—
441C23—48no—
442C23C2×D4×D1112yes—
443C23C2×D4×D1114yes—
444C23C2×#434118yes—
445C23C2×#434118yes—
446C23C24×D1111yescharacteristic
447D4—232no—
448D4—232no—
449D4—416no—
450C2×C4—216no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—28no—
454C2×C4—24no—
455C2×C4—112no—
456C2×C4—114no—
457C2×C4—114no—
458C2×C4—112no—
459C2×C4—2216no—
460C2×C4—228no—
461C2×C4—222no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—228no—
466C2×C4—228no—
467C2×C4—224no—
468C2×C4—228no—
469C2×C4—4416no—
470C2×C4—444no—
471C2×C4—448no—
472C2×C4—4416no—
473C2×C4—448no—
474C2×C4—448no—
475C2×C4C2×#434118yes—
476C22—24no—
477C22—216no—
478C22—24no—
479C22—22no—
480C22—216no—
481C22—24no—
482C22—28no—
483C22—416no—
484C22—432no—
485C22—44no—
486C22—48no—
487C22—44no—
488C22—44no—
489C22#1062311718yes—
490C22C22×D4×D1111yescharacteristic
491C22C22×#434114yes—
492C22D11×H(5,𝔽2)12yes—
493C4—28no—
494C4—44no—
495C4—114no—
496C4—224no—
497C4—222no—
498C4—444no—
499C4—444no—
500C4—444no—
501C2—28no—
502C2—42no—
503C2—48no—
504C2C2×#1062311712yes—
505C2D11×#53411yescharacteristic
506C2#1308221714yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
Fitting, prime radicalC11×#2403C2
hypercenter#2403D11
hypocenterC11#34956
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2403

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. #13074197C2semidirect
3. #13073960C2semidirect
4. #13073503C2semidirect
5. #13072897C2semidirect
6. #13071939C2semidirect
7. #13071851C2semidirect
8. #13071141C2semidirect
9. #120×Dic11C2semidirect
10. #13070994C2semidirect
14. C24×Dic11C22semidirect
17. C22×C22⋊Dic11C22semidirect
22. C2×D4×Dic11C22semidirect
23. C2×D4×Dic11C22semidirect
24. C2×D4×Dic11C22semidirect
25. C22×C4⋊Dic11C22semidirect
26. C22×C4×Dic11C22semidirect
27. C2×#66930C22semidirect
32. #10622860C22semidirect
33. #10622835C22semidirect
34. #10622835C22semidirect
36. #10622833C22semidirect
37. #10622823C22semidirect
38. #10622566C22semidirect
39. #10622563C22semidirect
40. #10622563C22semidirect
41. #10622561C22semidirect
42. #10622558C22semidirect
43. #10622556C22semidirect
44. #10622556C22semidirect
45. #10622555C22semidirect
46. C22⋊C4×Dic11C22semidirect
47. C22⋊C4×Dic11C22semidirect
48. #10622274C22semidirect
49. #10622268C22semidirect
50. #10622262C22semidirect
62. C23×Dic11D4semidirect
426. C11#34956semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
#130741972
#130739602
#130735032
#130728972
#130719392
#130718512
#130711412
#120×Dic112
#130709942
C11×#24032
#3495611