Finite Group Databasebeta

← #14770914

Subgroups — #14770914

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071485C211yesmaximal, characteristic, complemented
2D4×C22⋊Dic11C211yesmaximal, characteristic
3#13069301C212yesmaximal, complemented
4#13069238C212yesmaximal, complemented
5#13068865C212yesmaximal, complemented
6#13068702C211yesmaximal, characteristic, complemented
7#13068645C211yesmaximal, characteristic, complemented
8#13068547C211yesmaximal, characteristic
9#102×Dic11C212yesmaximal, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C22×C11×#102C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C22⋊Dic11—21no—
16C2×D4×Dic11C2212yes—
17C2×#66979—21no—
18C2×C11×#102C418yescomplemented
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23#10622860—21no—
24#10622834C2212yes—
25#10622833—22no—
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622824—21no—
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66882C2212yescomplemented
34C2×C8×Dic11C2212yescomplemented
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—
72#66979—44no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2312yes—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8C2312yes—
79C11×#102C2×C414yes—
80C11×#102C2×C414yes—
81C11×#102C2×C414yescomplemented
82C11×#102C2×C414yescomplemented
83#66896—24no—
84#66896—42no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95D412yes—
90C22⋊(C11⋊C8)—22no—
91#66882—42no—
92C8×Dic11—42no—
93#22570—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—24no—
97C24×C11—44no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—82no—
101C24×C11C2×D411yescharacteristic
102C2×D4×C11—28no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—44no—
110C2×D4×C11—48no—
111C2×D4×C11—44no—
112C2×D4×C11C22×C412yes—
113C2×D4×C11C22×C412yes—
114C2×D4×C11#4114yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—44no—
129C22×Dic11—44no—
130C22×Dic11—82no—
131C22×Dic11C2×D412yes—
132C22×Dic11C2×D412yes—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—44no—
136C2×C8×C11C22×C412yes—
137C2×C8×C11C22×C412yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C22×C412yes—
142C11×C4⋊C4C22×C412yes—
143C22⋊Dic11—22no—
144C22⋊Dic11—44no—
145C22⋊Dic11—44no—
146C22⋊Dic11—42no—
147C22⋊Dic11—42no—
148C22⋊Dic11—82no—
149C22⋊Dic11D814yes—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—44no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—44no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C22×#102D1111yescharacteristic
162#2344—111no—
163D4×C22⋊C4—111no—
164#1934—112no—
165#1925—112no—
166#1862—112no—
167#1823—111no—
168#1808—111no—
169#1786—111no—
170C4×#102—112no—
171C8×C22⋊C4—111no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—24no—
176C23×C11—22no—
177C23×C11—48no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—48no—
186C23×C11—84no—
187C23×C11—88no—
188C23×C11—88no—
189C23×C11C4×D412yes—
190C23×C11C2×D812yes—
191C23×C11#13512yes—
192C23×C11C22×D411yescharacteristic
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—24no—
197D4×C11—48no—
198D4×C11—42no—
199D4×C11#11714yescomplemented
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—48no—
211C2×C4×C11C4×D412yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C2×#4112yes—
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11H(5,𝔽2)12yes—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—88no—
228C2×Dic11C2×D814yes—
229C8×C11—22no—
230C8×C11—22no—
231C11⋊C8—42no—
232C23×D4C2×D1111yescharacteristic
233C23×C8C2×D1111yescharacteristic
234C2×C4×D4—112no—
235C2×#117—221no—
236C22×C4⋊C4C2×D1111yescharacteristic
237C22×C22⋊C4—221no—
238C2×#107—112no—
239C2×#102—112no—
240C2×#102—112no—
241C2×#102Dic1118yescomplemented
242C2×#102C2×D1111yescharacteristic
243C2×#102C2×D1111yescharacteristic
244C2×#102C2×D1111yescharacteristic
245C2×#102C2×D1111yescharacteristic
246C2×C22⋊C8—111no—
247C2×C4×C8—112no—
248#390—112no—
249#389—112no—
250#387—222no—
251#386—222no—
252#381—221no—
253#380—111no—
254#380—111no—
255#379—221no—
256C4×C4⋊C4—112no—
257C4×C22⋊C4—111no—
258#340—112no—
259#340—112no—
260#340—112no—
261#336—112no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—816no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11C4×D814yes—
278C22×C11C2×C4×D411yescharacteristic
279C22×C11#54612yes—
280C22×C11C22×D811yescharacteristic
281C22×C11C2×#13511yescharacteristic
282C22×C11#57712yes—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11C2×#11711yescharacteristic
287C4×C11#51811yescharacteristic
288C4×C11#55112yes—
289Dic11—24no—
290Dic11—42no—
291Dic11—82no—
292Dic11—82no—
293C25—21no—
294C22×D4—24no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—42no—
298C22×D4C2×Dic1114yes—
299C22×D4C22×D1111yescharacteristic
300C22×D4C22×D1111yescharacteristic
301C23×C4—21no—
302C23×C4—222no—
303C23×C4C22×D1111yescharacteristic
304C22×C8—42no—
305C22×C8—112no—
306C22×C8C2×Dic1114yescomplemented
307C22×C8C22×D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C4×D4—224no—
310C4×D4—442no—
311#117—444no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4C2×Dic1114yescomplemented
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4—111no—
321C2×C22⋊C4—111no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—444no—
328C2×C42—112no—
329C2×C42—222no—
330#107—442no—
331#102—224no—
332#102—442no—
333#102C2×Dic1114yes—
334#102C2×Dic1114yes—
335#102C2×Dic1114yescomplemented
336#102C2×Dic1114yescomplemented
337C22⋊C8—222no—
338C4×C8—442no—
339#95—112no—
340#95—222no—
341#95—222no—
342#95—221no—
343#95—221no—
344C2×C11—24no—
345C2×C11—44no—
346C2×C11—82no—
347C2×C11#234211yescharacteristic
348C2×C11C2×C4×D811yescharacteristic
349C2×C11#294911yescharacteristic
350C2×C11#329412yes—
351C2×C11#329612yes—
352C24—21no—
353C24—21no—
354C24—24no—
355C24—44no—
356C24—42no—
357C24—42no—
358C24—82no—
359C24D4×D1111yescharacteristic
360C2×D4—28no—
361C2×D4—24no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—44no—
368C2×D4—48no—
369C2×D4—44no—
370C2×D4#433914yes—
371C2×D4C22×Dic1112yes—
372C2×D4C22×Dic1112yes—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—444no—
385C22×C4—444no—
386C22×C4—882no—
387C22×C4D4×D1111yescharacteristic
388C22×C4#434112yes—
389C22×C4C22×Dic1112yes—
390C22×C4C23×D1111yescharacteristic
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—44no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8C22×Dic1112yes—
398C2×C8C22×Dic1112yes—
399C4⋊C4—24no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—444no—
407C4⋊C4C22×Dic1112yes—
408C4⋊C4C22×Dic1112yes—
409C22⋊C4—114no—
410C22⋊C4—222no—
411C22⋊C4—444no—
412C22⋊C4—444no—
413C22⋊C4—442no—
414C22⋊C4—442no—
415C22⋊C4—882no—
416C42—222no—
417C42—222no—
418C42—444no—
419C11#2257011yescharacteristic, complemented, Sylow
420C23—22no—
421C23—22no—
422C23—24no—
423C23—22no—
424C23—22no—
425C23—48no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—48no—
430C23—42no—
431C23—41no—
432C23—41no—
433C23—42no—
434C23—84no—
435C23—88no—
436C23—88no—
437C23D8×D1112yes—
438C23#6696512yes—
439C23D4×Dic1112yes—
440C23C2×D4×D1111yescharacteristic
441D4—24no—
442D4—22no—
443D4—22no—
444D4—22no—
445D4—48no—
446D4—42no—
447D4#6697914yescomplemented
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—48no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—114no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—888no—
472C2×C4D4×Dic1112yes—
473C2×C4C2×#433912yes—
474C2×C4C2×#434111yescharacteristic
475C2×C4#6703712yes—
476C2×C4C23×Dic1111yescharacteristic
477C8—22no—
478C8—22no—
479C8—442no—
480C22—22no—
481C22—24no—
482C22—24no—
483C22—22no—
484C22—24no—
485C22—44no—
486C22—42no—
487C22—44no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—816no—
493C22—82no—
494C22—82no—
495C22D8×Dic1114yes—
496C22#1062302112yes—
497C22C2×D8×D1111yescharacteristic
498C22C2×#6696511yescharacteristic
499C22#1062329312yes—
500C22C2×D4×Dic1111yescharacteristic
501C4—22no—
502C4—42no—
503C4—42no—
504C4—224no—
505C4—442no—
506C4—882no—
507C4—882no—
508C4#1062302612yes—
509C4C2×#6697911yescharacteristic
510C4#1062332911yescharacteristic
511C2—24no—
512C2—44no—
513C2—82no—
514C2#1307146511yescharacteristic
515C2C2×D8×Dic1111yescharacteristic
516C2#1307747611yescharacteristic
517C2#1308042512yes—
518C2#1308044712yes—
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#22570
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. #13071485C2semidirect
3. #13069301C2semidirect
4. #13069238C2semidirect
5. #13068865C2semidirect
6. #13068702C2semidirect
7. #13068645C2semidirect
9. #102×Dic11C2semidirect
10. C8×C22⋊Dic11C2semidirect
18. C2×C11×#102C4semidirect
33. C2×#66882C22semidirect
34. C2×C8×Dic11C22semidirect
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
81. C11×#102C2×C4semidirect
82. C11×#102C2×C4semidirect
199. D4×C11#117semidirect
241. C2×#102Dic11semidirect
306. C22×C8C2×Dic11semidirect
317. C2×C4⋊C4C2×Dic11semidirect
335. #102C2×Dic11semidirect
336. #102C2×Dic11semidirect
419. C11#22570semidirect
447. D4#66979semidirect

Maximal subgroups

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

subgroupindex
#130714852
D4×C22⋊Dic112
#130693012
#130692382
#130688652
#130687022
#130686452
#130685472
#102×Dic112
C8×C22⋊Dic112
C22×C11×#1022
#2257011