Finite Group Databasebeta

← #14810285

Subgroups — #14810285

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic
2C2×#10622682C211yesmaximal, characteristic, complemented
3#13073783C211yesmaximal, characteristic, complemented
4#13069821C212yesmaximal, complemented
5#13069814C212yesmaximal, complemented
6#13069538C211yesmaximal, characteristic, complemented
7#13069413C211yesmaximal, characteristic, complemented
8#13068553C212yesmaximal, complemented
9#13068553C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#478C211yesmaximal, characteristic, complemented
12C22×#4341C2212yes—
13C2×C11×#125C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66983—21no—
16C22×C4⋊Dic11—21no—
17#10623086—24no—
18#10623086—24no—
19C2×#66950C2212yes—
20C2×#66939—22no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#478—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×#66896C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34#10622682—24no—
35#10622604—21no—
36#10622603—22no—
37#10622600C2212yes—
38#10622600C2212yes—
39#10622599—21no—
40C2×#66874C2212yes—
41C2×#66874C2212yes—
42C4×C4⋊Dic11C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C22⋊D11—22no—
48C23×Dic11—22no—
49C2×#4341—24no—
50C2×#4341—24no—
51C2×#4341—24no—
52C2×#4341—24no—
53C2×#4341—42no—
54C2×#4341—42no—
55C22×D44D411yescharacteristic
56C22×C4×D11C2312yes—
57C22×Dic22C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#125—22no—
61C11×#125—22no—
62C4×D4×C11—22no—
63C4×D4×C11D414yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71#66983—28no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4D412yes—
76C2×C4⋊Dic11—28no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×C4×Dic11—21no—
83C22×C11⋊C8C2312yes—
84#66950—24no—
85#66950—24no—
86#66939—216no—
87C4×D44—22no—
88C4×D44—22no—
89#66922—22no—
90#66922D414yes—
91C11×#107—22no—
92C11×#106—22no—
93C11×C4⋊C8—22no—
94C11×#102—22no—
95C11×#102—22no—
96#66896—24no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—42no—
101(C2×D11)⋊C8—42no—
102#66880—42no—
103#66880—42no—
104#66874—24no—
105#66874—24no—
106#66867—22no—
107#25892—111nomaximal, Sylow
108C24×C11—21no—
109C23×D11C2×D412yes—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11C2×D412yes—
113C2×D4×C11#4114yes—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—44no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—28no—
123C2×C22⋊D11—44no—
124C2×C22⋊D11—44no—
125C22×Dic11—28no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—44no—
129C22×Dic11—44no—
130C22×Dic11C2×D412yes—
131#4341—48no—
132#4341—48no—
133#4341—48no—
134#4341—48no—
135C2×D44—22no—
136C2×D44—42no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22C2×D414yes—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—24no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—82no—
168C4⋊Dic11—28no—
169C4⋊Dic11—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4×Dic11—81no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×#547—111no—
179C2×#491—111no—
180C2×#478D1111yescharacteristic, complemented
181#2562—111no—
182#2036—112no—
183#2035—112no—
184#1981—111no—
185#1955—111no—
186#1788—112no—
187#1788—112no—
188#1762—111no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202D4×C11—22no—
203D4×C11—24no—
204D4×C11#12414yes—
205C2×C4×C11—22no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11#12012yes—
217C2×C4×C11#12012yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4112yes—
221C2×C4×C11H(5,𝔽2)12yes—
222C22⋊D11—416no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—416no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233D44—44no—
234C4×D11—42no—
235C4×D11—42no—
236C4×D11—42no—
237C4×D11—42no—
238Dic22—24no—
239Dic22—24no—
240Dic22—42no—
241Dic22—42no—
242C8×C11—41no—
243C8×C11—41no—
244C11⋊C8—42no—
245C22×#41—112no—
246#547—224no—
247#547—224no—
248C2×C4⋊Q8—111no—
249C2×#125C2×D1111yescharacteristic
250C2×#123—222no—
251C2×C22⋊Q8—112no—
252C2×#121—221no—
253C2×C4×D4—111no—
254C2×C4×D4C2×D1111yescharacteristic
255C22×C4⋊C4—221no—
256#491—224no—
257#478—24no—
258C2×#107C2×D1111yescharacteristic
259C2×#106C2×D1111yescharacteristic
260C2×C4⋊C8C2×D1111yescharacteristic
261C2×#103—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103—112no—
265C2×#102—112no—
266C2×#102C2×D1111yescharacteristic
267C2×#102C2×D1111yescharacteristic
268C2×C22⋊C8—112no—
269C2×C22⋊C8—112no—
270C2×#97—111no—
271#400—221no—
272#394—221no—
273#388—222no—
274#380—112no—
275#380—112no—
276C4×C4⋊C4—111no—
277#340—112no—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11C2×#12011yescharacteristic
284C22×C11#54612yes—
285C22×C11#57512yes—
286C22×C11#57711yescharacteristic
287C22×C11#57811yescharacteristic
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11C2×#12411yescharacteristic
301C4×C11#53511yescharacteristic
302C4×C11#54612yes—
303Dic11—44no—
304Dic11—42no—
305Dic11—82no—
306C2×#41—224no—
307C2×#41—224no—
308C2×#41—224no—
309C2×#41—224no—
310C2×#41—442no—
311C2×#41—442no—
312C22×Q8—112no—
313C22×D4—111no—
314C22×D4—222no—
315C22×D4C22×D1111yescharacteristic
316C23×C4—21no—
317C23×C4—112no—
318C23×C4—222no—
319C22×C8—112no—
320C22×C8C22×D1111yescharacteristic
321C22×C8C22×D1111yescharacteristic
322C4⋊Q8—114no—
323C4⋊Q8—222no—
324#125—22no—
325#125—22no—
326#123—2216no—
327C22⋊Q8—224no—
328C22⋊Q8—224no—
329#121—228no—
330C4×D4—22no—
331C4×D4—222no—
332C4×D4—222no—
333C4×D4C22⋊D1114yes—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—228no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C4⋊C4C22×D1111yescharacteristic
344C2×C4⋊C4C22×D1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—112no—
347C2×C22⋊C4—222no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C42—221no—
351C2×C42C22×D1111yescharacteristic
352#107—22no—
353#106—22no—
354C4⋊C8—22no—
355#103—224no—
356#103—224no—
357#103—442no—
358#103—442no—
359#102—22no—
360#102—22no—
361#102—224no—
362C22⋊C8—442no—
363C22⋊C8—442no—
364#97—222no—
365#95—222no—
366#95—222no—
367#95—221no—
368C2×C11—44no—
369C2×C11#243511yescharacteristic
370C2×C11#300511yescharacteristic
371C2×C11#301311yescharacteristic
372C2×C11#330712yes—
373C2×C11#331512yes—
374D11—82no—
375C24—21no—
376C24—112no—
377#41—448no—
378#41—448no—
379#41—448no—
380#41—448no—
381C2×Q8—114no—
382C2×Q8—222no—
383C2×Q8—222no—
384C2×Q8—222no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—228no—
390C2×D4—222no—
391C2×D4—442no—
392C2×D4—444no—
393C2×D4—444no—
394C2×D4#434314yes—
395C2×D4C2×C22⋊D1112yes—
396C22×C4—21no—
397C22×C4—24no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—44no—
401C22×C4—112no—
402C22×C4—228no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—444no—
412C22×C4—444no—
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4C23×D1111yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—42no—
429C4⋊C4—42no—
430C4⋊C4—228no—
431C4⋊C4—222no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4C2×C22⋊D1112yes—
437C22⋊C4—24no—
438C22⋊C4—228no—
439C22⋊C4—224no—
440C22⋊C4—444no—
441C22⋊C4—882no—
442C42—881no—
443C42D4×D1112yes—
444C42C2×C22⋊D1112yes—
445C11#2589211yescharacteristic, complemented, Sylow
446C23—22no—
447C23—24no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—222no—
452C23—222no—
453C23—222no—
454C23—222no—
455C23—222no—
456C23—222no—
457C23—222no—
458C23C2×D4×D1111yescharacteristic
459Q8—224no—
460Q8—224no—
461Q8—442no—
462Q8—442no—
463D4—22no—
464D4—24no—
465D4—444no—
466D4—4416no—
467D4#6700014yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—4416no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4#6699012yes—
494C2×C4#6699012yes—
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×#434312yes—
497C2×C4#6704212yes—
498C2×C4C22×C22⋊D1111yescharacteristic
499C8—41no—
500C8—41no—
501C8—442no—
502C22—24no—
503C22—44no—
504C22—42no—
505C22—44no—
506C22—42no—
507C22—442no—
508C22—442no—
509C22—442no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—442no—
514C22#1062316112yes—
515C22#1062330111yescharacteristic
516C22#1062330211yescharacteristic
517C22#1062330412yes—
518C22C2×#6699011yescharacteristic
519C4—22no—
520C4—22no—
521C4—42no—
522C4—81no—
523C4—81no—
524C4—442no—
525C4—444no—
526C4—882no—
527C4#1062316112yes—
528C4C2×#6700011yescharacteristic
529C4#1062336111yescharacteristic
530C2—44no—
531C2—882no—
532C2#1307226811yescharacteristic
533C2#1307785511yescharacteristic
534C2#1307792711yescharacteristic
535C2#1308058912yes—
536C2#1308070912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenterC2×#478D11
hypocenterC11#25892
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. C2×#10622682C2semidirect
3. #13073783C2semidirect
4. #13069821C2semidirect
5. #13069814C2semidirect
6. #13069538C2semidirect
7. #13069413C2semidirect
8. #13068553C2semidirect
9. #13068553C2semidirect
10. #13068441C2semidirect
11. C2×C11×#478C2semidirect
180. C2×#478D11semidirect
445. C11#25892semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106226822
#130737832
#130698212
#130698142
#130695382
#130694132
#130685532
#130684412
C2×C11×#4782
#2589211