Finite Group Databasebeta

← #14804222

Subgroups — #14804222

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622686C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3C2×#10622685C212yesmaximal, complemented
4#13071680C211yesmaximal, characteristic, complemented
5#13069926C212yesmaximal, complemented
6#13069687C212yesmaximal, complemented
7#13069544C211yesmaximal, characteristic, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13068967C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#2541C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#127C2212yes—
14C2×C11×#121—21no—
15C2×C11×#121—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4323C2212yes—
18C22×#4323C2212yes—
19C22×#4323C2212yes—
20C2×#66946—21no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44C2212yes—
23C11×#392—22no—
24C11×#390C2212yes—
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2211yescharacteristic
28C2×#66896C2212yes—
29C2×#66896C2211yescharacteristic
30#10622686—24no—
31#10622685—28no—
32#10622628—24no—
33#10622601—21no—
34C2×#66873C2212yes—
35#10622552C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622278—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44C2312yes—
54C22×C4×D11—22no—
55C11×#127—24no—
56C11×#127—22no—
57C11×#127—22no—
58C11×#127—42no—
59C11×#121—44no—
60C11×#121—44no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11C2312yes—
70C2×C42×C11C2311yescharacteristic
71C2×#4323—24no—
72C2×#4323—24no—
73C2×#4323—24no—
74C2×#4323—24no—
75C2×#4323—24no—
76C2×#4323—24no—
77C2×#4323—42no—
78C2×#4323—42no—
79C2×#4323—42no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89#66946—44no—
90#66927—22no—
91#66927D414yescomplemented
92C4×D44—24no—
93C4×D44—42no—
94C11×#95D412yes—
95#66896—24no—
96#66896—22no—
97#66896—42no—
98#66896D414yescomplemented
99C11⋊#95—21no—
100#66873—24no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)—24no—
103C4×C11⋊C8—22no—
104#25364—111nomaximal, Sylow
105C24×C11—21no—
106C24×C11—22no—
107C23×D11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—82no—
128C2×D4×C11—81no—
129C2×D4×C11—81no—
130C2×D4×C11—82no—
131C2×D4×C11C2×D412yes—
132C22×C4×C11—21no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44—81no—
153C2×D44—81no—
154C2×D44C2×D414yes—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×C4×D11—82no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4D814yescomplemented
162C11×C22⋊C4—44no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—44no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11C2×D412yes—
168C42×C11#4112yes—
169#4323—48no—
170#4323—48no—
171#4323—48no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—82no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11C2×D412yes—
179C4×Dic11—42no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2×D412yes—
188C2×C11⋊C8#4112yes—
189C2×#493—111no—
190C2×#459—112no—
191C2×#459—111no—
192#2541D1111yescharacteristic, complemented
193#2366—111no—
194#2054—112no—
195#2011—112no—
196#1982—111no—
197#1939—111no—
198#1879—112no—
199C4×#102—111no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11C22×D411yescharacteristic
215C22×D11—24no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—42no—
225D4×C11—41no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—42no—
230D4×C11—88no—
231D4×C11—84no—
232D4×C11—88no—
233D4×C11—84no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—84no—
245C2×C4×C11#12112yes—
246C2×C4×C11#12112yes—
247C2×C4×C11C2×D814yes—
248C2×C4×C11C2×D812yes—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262D44—24no—
263D44—24no—
264D44—42no—
265D44—42no—
266D44—48no—
267D44—84no—
268C4×D11—88no—
269C11⋊C8—22no—
270C11⋊C8—22no—
271C11⋊C8—42no—
272C22×D8—112no—
273C22×D8—112no—
274C22×D8—112no—
275C2×#127—111no—
276C2×#127C2×D1111yescharacteristic
277C2×#127C2×D1112yes—
278C2×#121—21no—
279C2×#121—21no—
280C2×C4×D4—112no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283#493—224no—
284#459—228no—
285#459—224no—
286C2×C4⋊C8—112no—
287C2×C4⋊C8—111no—
288C2×#102—111no—
289C2×#102—112no—
290C2×#102—111no—
291C2×#102—112no—
292C2×#102—112no—
293C2×C4×C8—111no—
294#392—22no—
295#390—112no—
296#390—221no—
297#390C2×D1112yes—
298#386—222no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—111no—
302#340—111no—
303#336—112no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11C2×#12111yescharacteristic
319C22×C11D4211yescharacteristic
320C22×C11#55011yescharacteristic
321C22×C11C22×D811yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11#57611yescharacteristic
324C22×C11#57611yescharacteristic
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C4×C11—24no—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—81no—
336C4×C11#45914yescomplemented
337C4×C11#53211yescharacteristic
338C4×C11#54011yescharacteristic
339C4×C11D4211yescharacteristic
340C4×C11#54611yescharacteristic
341Dic11—42no—
342Dic11—81no—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—21no—
347C22×D4—112no—
348C22×D4—221no—
349C22×D4—221no—
350C22×D4C22×D1112yes—
351C22×D4C22×D1111yescharacteristic
352C23×C4—21no—
353C23×C4—222no—
354C2×D8—224no—
355C2×D8—224no—
356C2×D8—224no—
357C2×D8—224no—
358C2×D8—224no—
359C2×D8—224no—
360C2×D8—442no—
361C2×D8—442no—
362C2×D8—442no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—112no—
366#127—24no—
367#127—22no—
368#127—22no—
369#127—42no—
370#127—114no—
371#127—222no—
372#121—44no—
373#121—44no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—224no—
377C4×D4—442no—
378C4×D4—444no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22⋊D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—222no—
390C2×C42—221no—
391C2×C42C22×D1112yes—
392C2×C42C22×D1111yescharacteristic
393C4⋊C8—224no—
394C4⋊C8—222no—
395#102—114no—
396#102—224no—
397#102—224no—
398#102—222no—
399#102—442no—
400C4×C8—222no—
401#95—221no—
402#95C22⋊D1112yes—
403C2×C11—82no—
404C2×C11—162no—
405C2×C11#242811yescharacteristic
406C2×C11C2×#45911yescharacteristic
407C2×C11#304111yescharacteristic
408C2×C11#327411yescharacteristic
409C2×C11D4×D811yescharacteristic
410C2×C11#339111yescharacteristic
411C2×C11#339911yescharacteristic
412D11—84no—
413C24—21no—
414C24—22no—
415C24—222no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—82no—
436C2×D4—81no—
437C2×D4—81no—
438C2×D4—82no—
439C2×D4—114no—
440C2×D4—224no—
441C2×D4—224no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—442no—
448C2×D4—442no—
449C2×D4—881no—
450C2×D4—881no—
451C2×D4D4×D1112yes—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—444no—
459C22×C4—444no—
460C22×C4—882no—
461C22×C4C2×C22⋊D1112yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C23×D1111yescharacteristic
466D8—448no—
467D8—448no—
468D8—448no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—112no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4#432314yescomplemented
486C22⋊C4—44no—
487C22⋊C4—44no—
488C22⋊C4—42no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C22⋊C4—882no—
492C42—22no—
493C42—22no—
494C42—442no—
495C42D4×D1112yes—
496C42#434112yes—
497C11#2536411yescharacteristic, complemented, Sylow
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—224no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23C22×C22⋊D1111yescharacteristic
520D4—22no—
521D4—22no—
522D4—42no—
523D4—42no—
524D4—41no—
525D4—42no—
526D4—41no—
527D4—42no—
528D4—88no—
529D4—84no—
530D4—88no—
531D4—84no—
532D4—224no—
533D4—224no—
534D4—442no—
535D4—442no—
536D4—448no—
537D4—884no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4—222no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—888no—
556C2×C4C2×#432314yes—
557C2×C4C2×#432312yes—
558C2×C4#6698512yes—
559C2×C4#6699112yes—
560C2×C4#6699112yes—
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×#434111yescharacteristic
564C2×C4#6703711yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C2×C4#6704211yescharacteristic
567C8—222no—
568C8—222no—
569C8—442no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—444no—
585C22—444no—
586C22—444no—
587C22—882no—
588C22—882no—
589C22—882no—
590C22—882no—
591C22C22×#432311yescharacteristic
592C22C2×#6698511yescharacteristic
593C22C2×#6699111yescharacteristic
594C22D4×C22⋊D1111yescharacteristic
595C22#1062336511yescharacteristic
596C22#1062336611yescharacteristic
597C22#1062336611yescharacteristic
598C4—22no—
599C4—24no—
600C4—42no—
601C4—81no—
602C4—442no—
603C4—881no—
604C4#1062268514yescomplemented
605C4#1062312711yescharacteristic
606C4#1062314011yescharacteristic
607C4#1062314311yescharacteristic
608C4#1062315011yescharacteristic
609C2—82no—
610C2—162no—
611C2—884no—
612C2#1307220011yescharacteristic
613C2C2×#1062268511yescharacteristic
614C2#1307811511yescharacteristic
615C2#1308023211yescharacteristic
616C2D4×#432311yescharacteristic
617C2#1308158811yescharacteristic
618C2#1308165811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2541C2
socleC23×C11C22×D4
hypercenter#2541D11
hypocenterC11#25364
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#10622686C2semidirect
2. C2×#10622628C2semidirect
3. C2×#10622685C2semidirect
4. #13071680C2semidirect
5. #13069926C2semidirect
6. #13069687C2semidirect
7. #13069544C2semidirect
8. #13069335C2semidirect
9. #13068967C2semidirect
10. C4×#66896C2semidirect
11. C11×#2541C2semidirect
91. #66927D4semidirect
98. #66896D4semidirect
161. C11×C4⋊C4D8semidirect
192. #2541D11semidirect
336. C4×C11#459semidirect
485. C4⋊C4#4323semidirect
497. C11#25364semidirect
604. C4#10622685semidirect

Maximal subgroups

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

subgroupindex
C2×#106226862
C2×#106226282
C2×#106226852
#130716802
#130699262
#130696872
#130695442
#130693352
#130689672
C4×#668962
C11×#25412
#2536411