Finite Group Databasebeta

← #14804496

Subgroups — #14804496

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622651C212yesmaximal, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4#13073562C211yesmaximal, characteristic, complemented
5#13069798C212yesmaximal, complemented
6#13069612C212yesmaximal, complemented
7#13069421C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13069042C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#2537C211yesmaximal, characteristic, complemented
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66993—21no—
17C22×#4323C2212yes—
18C2×#66983C2212yes—
19C2×#66983C2212yes—
20C23×C11⋊C8C2212yes—
21C2×#66927C2211yescharacteristic
22C11×#394—22no—
23C11×#384C2211yescharacteristic
24C11×#380—21no—
25C11×#380C2212yes—
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622651—28no—
30#10622628—24no—
31D4×C11⋊C8—24no—
32#10622601—21no—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×#66873C2212yes—
36C2×#66871C2212yes—
37#10622573—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2312yes—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44C2312yes—
54C11×#121—24no—
55C11×#121—42no—
56C11×#121—44no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11C2311yescharacteristic
71#66993—44no—
72C2×#4323—24no—
73C2×#4323—24no—
74C2×#4323—42no—
75#66983—24no—
76#66983—24no—
77#66983—42no—
78#66983—42no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4×Dic11—21no—
84C22×C11⋊C8—24no—
85C22×C11⋊C8—24no—
86C22×C11⋊C8—42no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90#66927—22no—
91#66927—22no—
92C11×#95—22no—
93#66896—22no—
94#66896D414yescomplemented
95C11⋊#95—21no—
96C22⋊(C11⋊C8)—24no—
97#66873—24no—
98#66873—24no—
99#66873—42no—
100#66871—24no—
101C4⋊(C11⋊C8)D414yescomplemented
102C4×C11⋊C8—22no—
103#25384—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11C2×D412yes—
106C23×D11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—82no—
117C2×D4×C11D814yescomplemented
118C2×D4×C11C2×D412yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C2×C22⋊D11—44no—
138C2×C22⋊D11—82no—
139C2×C22⋊D11—82no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44—81no—
153C2×D44—81no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—81no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—42no—
165C42×C11C2×D412yes—
166C42×C11#4112yes—
167#4323—48no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4—44no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11C2×D412yes—
173C4⋊Dic11#4112yes—
174C4×Dic11—42no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—48no—
183C2×C11⋊C8C2×D414yes—
184C2×C11⋊C8C2×D412yes—
185C2×#466—112no—
186C2×#459—111no—
187C2×C8×D4—111no—
188#2541—111no—
189#2537D1111yescharacteristic, complemented
190#2033—112no—
191#1999—112no—
192#1957—111no—
193#1947—111no—
194#1893—112no—
195C4×#102—111no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11C2×D814yes—
210C23×C11C22×D411yescharacteristic
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—28no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—88no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—84no—
240C2×C4×C11#12112yes—
241C2×C4×C11#12112yes—
242C2×C4×C11C2×D812yes—
243C2×C4×C11#13512yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C22⋊D11—88no—
251C22⋊D11—88no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258D44—42no—
259D44—42no—
260D44—42no—
261D44—42no—
262D44—84no—
263D44—84no—
264C11⋊C8—22no—
265C11⋊C8—24no—
266C11⋊C8—41no—
267C22×D8—112no—
268C23×C8—112no—
269C2×#127—111no—
270C2×#127—221no—
271C2×#121—21no—
272C2×#121—112no—
273C2×#121—112no—
274C2×#121C2×D1112yes—
275C2×C4×D4C2×D1111yescharacteristic
276C2×C4×D4C2×D1111yescharacteristic
277#466—228no—
278#459—224no—
279C8×D4—224no—
280C2×#107—112no—
281C2×C4⋊C8—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#102—112no—
285C2×#102—112no—
286C2×#102—112no—
287C2×C22⋊C8—112no—
288C2×C4×C8—111no—
289#394—22no—
290#392—222no—
291#390—221no—
292#384C2×D1111yescharacteristic
293#380—21no—
294#380C2×D1112yes—
295C4×C4⋊C4—111no—
296#340—111no—
297#340—112no—
298#340—111no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11C2×#12111yescharacteristic
314C22×C11D4211yescharacteristic
315C22×C11#54611yescharacteristic
316C22×C11C22×D811yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—82no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—82no—
327C4×C11—22no—
328C4×C11—42no—
329C4×C11—82no—
330C4×C11—81no—
331C4×C11#46614yescomplemented
332C4×C11#53211yescharacteristic
333C4×C11#54011yescharacteristic
334C4×C11D4211yescharacteristic
335C4×C11#55011yescharacteristic
336Dic11—42no—
337Dic11—42no—
338C22×D4—22no—
339C22×D4—112no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—221no—
343C22×D4—221no—
344C22×D4C22⋊D1111yescharacteristic
345C22×D4C22×D1111yescharacteristic
346C23×C4—21no—
347C23×C4C22×D1112yes—
348C2×D8—224no—
349C2×D8—224no—
350C2×D8—442no—
351C22×C8—111no—
352C22×C8—112no—
353C22×C8—111no—
354C22×C8—224no—
355C22×C8—224no—
356C22×C8—442no—
357#127—222no—
358#127—222no—
359#127—444no—
360#121—24no—
361#121—42no—
362#121—44no—
363#121—224no—
364#121—224no—
365#121—442no—
366#121—442no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4C22⋊D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1112yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4C22⋊D1112yes—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—224no—
387C4⋊C8—114no—
388#102—114no—
389#102—224no—
390#102—224no—
391#102—222no—
392#102—442no—
393C22⋊C8—224no—
394C4×C8—222no—
395#95—22no—
396#95—221no—
397C2×C11—44no—
398C2×C11—82no—
399C2×C11#242811yescharacteristic
400C2×C11C2×#46611yescharacteristic
401C2×C11#306211yescharacteristic
402C2×C11D4×D811yescharacteristic
403C2×C11#328411yescharacteristic
404C2×C11#329411yescharacteristic
405C2×C11#330511yescharacteristic
406D11—162no—
407C24—21no—
408C24—222no—
409C24C2×C22⋊D1112yes—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—82no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—442no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—442no—
434C2×D4—881no—
435C2×D4—881no—
436C2×D4—882no—
437C2×D4—882no—
438C2×D4#432314yescomplemented
439C2×D4D4×D1112yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457D8—448no—
458C2×C8—114no—
459C2×C8—112no—
460C2×C8—221no—
461C2×C8—222no—
462C2×C8—221no—
463C2×C8—222no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—448no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—112no—
476C4⋊C4—112no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C22⋊C4—24no—
480C22⋊C4—44no—
481C22⋊C4—44no—
482C22⋊C4—42no—
483C22⋊C4—444no—
484C22⋊C4—444no—
485C42—442no—
486C42D4×D1112yes—
487C42#434112yes—
488C11#2538411yescharacteristic, complemented, Sylow
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23C2×#432314yes—
510C23C22×C22⋊D1111yescharacteristic
511D4—22no—
512D4—22no—
513D4—28no—
514D4—41no—
515D4—41no—
516D4—88no—
517D4—442no—
518D4—442no—
519D4—442no—
520D4—442no—
521D4—884no—
522D4—888no—
523D4—888no—
524D4—884no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—84no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4C2×#432312yes—
548C2×C4#6699212yes—
549C2×C4#6699212yes—
550C2×C4#6700312yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#6704211yescharacteristic
557C8—222no—
558C8—224no—
559C8—441no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—882no—
575C22—882no—
576C22—882no—
577C22—882no—
578C22—882no—
579C22—882no—
580C22—882no—
581C22C22×#432311yescharacteristic
582C22D4×C22⋊D1111yescharacteristic
583C22C2×#6699211yescharacteristic
584C22C2×#6700311yescharacteristic
585C22#1062336011yescharacteristic
586C22#1062336611yescharacteristic
587C22#1062336811yescharacteristic
588C4—22no—
589C4—42no—
590C4—81no—
591C4—82no—
592C4—442no—
593C4—442no—
594C4#1062265114yescomplemented
595C4#1062312711yescharacteristic
596C4#1062313011yescharacteristic
597C4#1062314011yescharacteristic
598C4#1062315011yescharacteristic
599C2—44no—
600C2—82no—
601C2—1762no—
602C2#1307220611yescharacteristic
603C2C2×#1062265111yescharacteristic
604C2#1307829811yescharacteristic
605C2D4×#432311yescharacteristic
606C2#1308034211yescharacteristic
607C2#1308042311yescharacteristic
608C2#1308056011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2537C2
socleC23×C11C22×D4
hypercenter#2537D11
hypocenterC11#25384
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#10622651C2semidirect
2. C2×#10622628C2semidirect
3. C2×D4×C11⋊C8C2semidirect
4. #13073562C2semidirect
5. #13069798C2semidirect
6. #13069612C2semidirect
7. #13069421C2semidirect
8. #13069372C2semidirect
9. #13069042C2semidirect
10. C4×#66896C2semidirect
11. C11×#2537C2semidirect
94. #66896D4semidirect
101. C4⋊(C11⋊C8)D4semidirect
117. C2×D4×C11D8semidirect
189. #2537D11semidirect
331. C4×C11#466semidirect
438. C2×D4#4323semidirect
488. C11#25384semidirect
594. C4#10622651semidirect

Maximal subgroups

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

subgroupindex
C2×#106226512
C2×#106226282
C2×D4×C11⋊C82
#130735622
#130697982
#130696122
#130694212
#130693722
#130690422
C4×#668962
C11×#25372
#2538411