Finite Group Databasebeta

← #14770870

Subgroups — #14770870

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071493C211yesmaximal, characteristic, complemented
2D4×C22⋊Dic11C211yesmaximal, characteristic
3#13069315C212yesmaximal, complemented
4#13069238C212yesmaximal, complemented
5#13068865C212yesmaximal, complemented
6#13068706C211yesmaximal, characteristic, complemented
7#13068645C211yesmaximal, characteristic, complemented
8#13068547C211yesmaximal, characteristic
9#13068443C212yesmaximal, complemented
10#13068392C211yesmaximal, characteristic, complemented
11C22×C11×#102C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C22⋊Dic11—21no—
16C2×D4×Dic11C2212yes—
17C2×C11×#102C418yescomplemented
18C2×C11×#102C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22#10622860—21no—
23#10622834C2212yes—
24#10622833—22no—
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27#10622825—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11—21no—
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66882C2212yescomplemented
34C2×#66879C2212yescomplemented
35#10622598C2212yescomplemented
36#10622594—22no—
37C4⋊C4×Dic11C2212yescomplemented
38#10622189C2212yescomplemented
39#10622188C2212yescomplemented
40#10622167C2212yescomplemented
41#10622167C2212yescomplemented
42C25×C11—21no—
43C22×D4×C11—24no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—42no—
47C22×D4×C11C2×C414yes—
48C22×D4×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—22no—
53C22×C8×C11—42no—
54C22×C8×C11C2×C414yescomplemented
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2×C414yescomplemented
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—44no—
68C2×C22⋊Dic11D411yescharacteristic
69C2×C22⋊Dic11D411yescharacteristic
70D4×Dic11—24no—
71D4×Dic11—42no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×C4×Dic11—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78C11×#102C2×C414yes—
79C11×#102C2×C414yes—
80C11×#102C2×C414yescomplemented
81C11×#102C2×C414yescomplemented
82#66896—24no—
83#66896—42no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95D412yes—
89C22⋊(C11⋊C8)—22no—
90#66882—42no—
91#66879—42no—
92#22566—111nomaximal, Sylow
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—24no—
96C24×C11—44no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—82no—
100C24×C11C2×D411yescharacteristic
101C2×D4×C11—28no—
102C2×D4×C11—24no—
103C2×D4×C11—21no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—44no—
109C2×D4×C11—48no—
110C2×D4×C11—44no—
111C2×D4×C11C22×C412yes—
112C2×D4×C11C22×C412yes—
113C2×D4×C11#4114yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—24no—
119C22×C4×C11—82no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—44no—
127C22×Dic11—44no—
128C22×Dic11—82no—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—44no—
134C2×C8×C11C22×C412yes—
135C2×C8×C11C22×C412yes—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4C22×C412yes—
141C22⋊Dic11—22no—
142C22⋊Dic11—22no—
143C22⋊Dic11—44no—
144C22⋊Dic11—44no—
145C22⋊Dic11—42no—
146C22⋊Dic11—42no—
147C22⋊Dic11—82no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—82no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—82no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C22×#102D1111yescharacteristic
160#2345—111no—
161D4×C22⋊C4—111no—
162#1936—112no—
163#1925—112no—
164#1862—112no—
165#1824—111no—
166#1808—111no—
167#1786—111no—
168#1762—112no—
169#1752—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—24no—
174C23×C11—22no—
175C23×C11—48no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—48no—
184C23×C11—84no—
185C23×C11—88no—
186C23×C11—88no—
187C23×C11C4×D412yes—
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11#13712yes—
190C23×C11C22×D411yescharacteristic
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—24no—
195D4×C11—48no—
196D4×C11—42no—
197D4×C11#11714yes—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—84no—
207C2×C4×C11C4×D412yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C2×#4112yes—
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)12yes—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—88no—
225C8×C11—22no—
226C8×C11—22no—
227C11⋊C8—42no—
228C23×D4C2×D1111yescharacteristic
229C23×C8C2×D1111yescharacteristic
230C2×C4×D4—112no—
231C22×C4⋊C4C2×D1111yescharacteristic
232C22×C22⋊C4—221no—
233C2×#107—112no—
234C2×#102—112no—
235C2×#102—112no—
236C2×#102Dic1118yescomplemented
237C2×#102C2×D1111yescharacteristic
238C2×#102C2×D1111yescharacteristic
239C2×#102C2×D1111yescharacteristic
240C2×#102C2×D1111yescharacteristic
241C2×C22⋊C8—111no—
242C2×#97—112no—
243#390—112no—
244#389—112no—
245#387—222no—
246#386—222no—
247#380—111no—
248#380—111no—
249#380—221no—
250#379—221no—
251C4×C4⋊C4—112no—
252C4×C22⋊C4—111no—
253C4×C22⋊C4—221no—
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—816no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11#44014yes—
274C22×C11C2×C4×D411yescharacteristic
275C22×C11#54612yes—
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11C2×#13711yescharacteristic
278C22×C11#57612yes—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11C2×#11711yescharacteristic
283C4×C11#51811yescharacteristic
284C4×C11#55112yes—
285Dic11—42no—
286Dic11—42no—
287Dic11—82no—
288Dic11—82no—
289C25—21no—
290C22×D4—24no—
291C22×D4—21no—
292C22×D4—22no—
293C22×D4—42no—
294C22×D4C2×Dic1114yes—
295C22×D4C22×D1111yescharacteristic
296C22×D4C22×D1111yescharacteristic
297C23×C4—21no—
298C23×C4—222no—
299C23×C4C22×D1111yescharacteristic
300C22×C8—42no—
301C22×C8—112no—
302C22×C8C2×Dic1114yescomplemented
303C22×C8C22×D1111yescharacteristic
304C22×C8C22×D1111yescharacteristic
305C4×D4—224no—
306C4×D4—442no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4C2×Dic1114yescomplemented
313C2×C4⋊C4C22×D1111yescharacteristic
314C2×C4⋊C4C22×D1111yescharacteristic
315C2×C22⋊C4—111no—
316C2×C22⋊C4—111no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—444no—
323C2×C42—112no—
324C2×C42—222no—
325#107—442no—
326#102—224no—
327#102—442no—
328#102C2×Dic1114yes—
329#102C2×Dic1114yes—
330#102C2×Dic1114yescomplemented
331#102C2×Dic1114yescomplemented
332C22⋊C8—222no—
333#97—442no—
334#95—112no—
335#95—222no—
336#95—222no—
337#95—221no—
338#95—221no—
339C2×C11—24no—
340C2×C11—44no—
341C2×C11—82no—
342C2×C11#234211yescharacteristic
343C2×C11C2×#44011yescharacteristic
344C2×C11#294811yescharacteristic
345C2×C11#331412yes—
346C2×C11#331812yes—
347C24—21no—
348C24—21no—
349C24—24no—
350C24—44no—
351C24—42no—
352C24—42no—
353C24—82no—
354C24D4×D1111yescharacteristic
355C2×D4—28no—
356C2×D4—24no—
357C2×D4—22no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—44no—
363C2×D4—48no—
364C2×D4—44no—
365C2×D4#433914yes—
366C2×D4C22×Dic1112yes—
367C2×D4C22×Dic1112yes—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—24no—
373C22×C4—82no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—444no—
379C22×C4—444no—
380C22×C4—882no—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434112yes—
383C22×C4C22×Dic1112yes—
384C22×C4C23×D1111yescharacteristic
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—44no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8C22×Dic1112yes—
392C2×C8C22×Dic1112yes—
393C4⋊C4—24no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—882no—
401C4⋊C4C22×Dic1112yes—
402C4⋊C4C22×Dic1112yes—
403C22⋊C4—222no—
404C22⋊C4—222no—
405C22⋊C4—444no—
406C22⋊C4—444no—
407C22⋊C4—442no—
408C22⋊C4—442no—
409C22⋊C4—882no—
410C42—222no—
411C42—222no—
412C42—882no—
413C11#2256611yescharacteristic, complemented, Sylow
414C23—22no—
415C23—22no—
416C23—24no—
417C23—22no—
418C23—22no—
419C23—48no—
420C23—42no—
421C23—41no—
422C23—41no—
423C23—42no—
424C23—42no—
425C23—48no—
426C23—41no—
427C23—41no—
428C23—84no—
429C23—88no—
430C23—88no—
431C23#6696712yes—
432C23#6696812yes—
433C23D4×Dic1112yes—
434C23C2×D4×D1111yescharacteristic
435D4—24no—
436D4—22no—
437D4—22no—
438D4—22no—
439D4—48no—
440D4—42no—
441D4#6697914yes—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—84no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—888no—
464C2×C4D4×Dic1112yes—
465C2×C4C2×#433912yes—
466C2×C4C2×#434111yescharacteristic
467C2×C4#6703712yes—
468C2×C4C23×Dic1111yescharacteristic
469C8—22no—
470C8—22no—
471C8—442no—
472C22—22no—
473C22—24no—
474C22—24no—
475C22—22no—
476C22—24no—
477C22—44no—
478C22—42no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—816no—
485C22—82no—
486C22—82no—
487C22#1062277714yes—
488C22#1062302112yes—
489C22#1062328812yes—
490C22C2×#6696711yescharacteristic
491C22C2×#6696811yescharacteristic
492C22C2×D4×Dic1111yescharacteristic
493C4—22no—
494C4—42no—
495C4—42no—
496C4—442no—
497C4—442no—
498C4—882no—
499C4—882no—
500C4#1062302612yes—
501C4C2×#6697911yescharacteristic
502C4#1062332911yescharacteristic
503C2—24no—
504C2—44no—
505C2—82no—
506C2#1307146511yescharacteristic
507C2C2×#1062277711yescharacteristic
508C2#1307746811yescharacteristic
509C2#1308069312yes—
510C2#1308075312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11#22566
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. #13071493C2semidirect
3. #13069315C2semidirect
4. #13069238C2semidirect
5. #13068865C2semidirect
6. #13068706C2semidirect
7. #13068645C2semidirect
9. #13068443C2semidirect
10. #13068392C2semidirect
17. C2×C11×#102C4semidirect
33. C2×#66882C22semidirect
34. C2×#66879C22semidirect
35. #10622598C22semidirect
37. C4⋊C4×Dic11C22semidirect
38. #10622189C22semidirect
39. #10622188C22semidirect
40. #10622167C22semidirect
41. #10622167C22semidirect
54. C22×C8×C11C2×C4semidirect
59. C2×C11×C4⋊C4C2×C4semidirect
80. C11×#102C2×C4semidirect
81. C11×#102C2×C4semidirect
236. C2×#102Dic11semidirect
302. C22×C8C2×Dic11semidirect
312. C2×C4⋊C4C2×Dic11semidirect
330. #102C2×Dic11semidirect
331. #102C2×Dic11semidirect
413. C11#22566semidirect

Maximal subgroups

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

subgroupindex
#130714932
D4×C22⋊Dic112
#130693152
#130692382
#130688652
#130687062
#130686452
#130685472
#130684432
#130683922
C22×C11×#1022
#2256611