Finite Group Databasebeta

← #14788806

Subgroups — #14788806

Order 2816.

2202 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
1C22×#66927C211yesmaximal, characteristic, complemented
2C2×#10622628C212yesmaximal, complemented
3C2×#10622649C212yesmaximal, complemented
4#13069850C212yesmaximal, complemented
5#13069686C212yesmaximal, complemented
6#13069543C212yesmaximal, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068546C212yesmaximal, complemented
9C4×C11×#121C211yesmaximal, characteristic, complemented
10C23×D44—21no—
11C23×D44—21no—
12C23×D44C2212yes—
13C2×C11×#121C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C22×#4323C2214yescomplemented
18C2×#66927—21no—
19C2×#66927—21no—
20C2×#66927—28no—
21C2×#66927C2212yes—
22C2×#66927C2212yes—
23C11×#390C2211yescharacteristic, complemented
24C11×#389C2211yescharacteristic, complemented
25C11×#388—21no—
26C11×#386—21no—
27C11×#380C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic, complemented
29C4×C11×C22⋊C4—21no—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622649—28no—
32#10622628—28no—
33C2×#66873C2214yescomplemented
34C2×#66873C2214yescomplemented
35C2×#66873C2214yescomplemented
36C2×C4⋊(C11⋊C8)C2212yescomplemented
37#10622162C2212yescomplemented
38C24×D11—22no—
39C22×D4×C11—21no—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×D44—28no—
46C22×D44—28no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—28no—
53C22×D44—24no—
54C22×D44—24no—
55C22×D44—44no—
56C22×D44—44no—
57C22×D44—44no—
58C22×D44—44no—
59C22×D44—44no—
60C22×D44C2314yes—
61C11×#121—22no—
62C11×#121D414yescomplemented
63C4×D4×C11—24no—
64C4×D4×C11—44no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—24no—
75C2×C42×C11—21no—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×#4323—28no—
81C2×#4323—28no—
82C2×#4323—44no—
83C22×C11⋊C8C2314yes—
84#66927—28no—
85#66927—28no—
86#66927—28no—
87#66927—24no—
88#66927D418yescomplemented
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C22⋊(C11⋊C8)—24no—
93#66873—28no—
94#66873—28no—
95#66873—44no—
96C4⋊(C11⋊C8)—24no—
97#24208—111nomaximal, Sylow
98C24×C11—21no—
99C24×C11C2×D411yescharacteristic
100C23×D11—28no—
101C23×D11—24no—
102C23×D11—44no—
103C23×D11—44no—
104C23×D11—44no—
105C23×D11—44no—
106C23×D11—44no—
107C23×D11—44no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11C2×D412yescomplemented
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11D814yescomplemented
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C2×D44—28no—
138C2×D44—28no—
139C2×D44—28no—
140C2×D44—28no—
141C2×D44—28no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44—24no—
146C2×D44—24no—
147C2×D44—416no—
148C2×D44—416no—
149C2×D44—432no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44—44no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—432no—
156C2×D44—44no—
157C2×D44—44no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—44no—
161C2×D44C2×D418yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4C2×D412yescomplemented
167C11×C22⋊C4—24no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—42no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—42no—
176C42×C11C2×D414yes—
177#4323—416no—
178C2×C11⋊C8—24no—
179C2×C11⋊C8—24no—
180C2×C11⋊C8—24no—
181C22×#127—111no—
182C2×#459—112no—
183C2×#447—112no—
184C4×#121D1111yescharacteristic, complemented
185#2041—112no—
186#2011—112no—
187#1982—112no—
188#1797—111no—
189#1786—112no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11#12112yes—
202C23×C11C2×D812yes—
203C23×C11AGL(1,ℤ/8)12yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—28no—
206C22×D11—416no—
207C22×D11—416no—
208C22×D11—416no—
209C22×D11—44no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—88no—
216C22×D11—88no—
217C22×D11—88no—
218C22×D11—88no—
219D4×C11—24no—
220D4×C11—48no—
221D4×C11—42no—
222C2×C4×C11—28no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—28no—
234C2×C4×C11—22no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—84no—
244C2×C4×C11#12012yes—
245C2×C4×C11#12012yes—
246C2×C4×C11#12112yes—
247C2×C4×C11C2×D812yes—
248C2×C4×C11C2×D812yes—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11AGL(1,ℤ/8)12yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D412yes—
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)12yes—
255D44—28no—
256D44—28no—
257D44—416no—
258D44—416no—
259D44—416no—
260D44—416no—
261D44—44no—
262D44—44no—
263D44—416no—
264C11⋊C8—44no—
265C23×D4—112no—
266C23×D4—221no—
267C23×D4—221no—
268C22×D8—114no—
269C2×#127—112no—
270C2×#127—112no—
271C2×#127—228no—
272C2×#127—221no—
273C2×#127—221no—
274C2×#121C2×D1111yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4C2×D1111yescharacteristic, complemented
277C22×C42C2×D1111yescharacteristic
278#459—228no—
279#447—228no—
280C2×C4⋊C8—112no—
281C2×#102—114no—
282C2×#102—114no—
283C2×#102—114no—
284C2×C22⋊C8—112no—
285#390C2×D1111yescharacteristic, complemented
286#389C2×D1111yescharacteristic, complemented
287#388—21no—
288#386—21no—
289#380C2×D1111yescharacteristic
290C4×C4⋊C4C2×D1111yescharacteristic, complemented
291C4×C22⋊C4—21no—
292#336—112no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11#45914yescomplemented
307C22×C11C2×#12011yescharacteristic
308C22×C11C2×#12111yescharacteristic
309C22×C11#53511yescharacteristic
310C22×C11C22×D811yescharacteristic
311C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C2×D11—48no—
315C2×D11—48no—
316C2×D11—48no—
317C2×D11—832no—
318C2×D11—84no—
319C2×D11—84no—
320C2×D11—84no—
321C2×D11—84no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11#44714yescomplemented
330C4×C11D4212yes—
331C4×C11#54612yes—
332C25—222no—
333C22×D4—21no—
334C22×D4—114no—
335C22×D4—228no—
336C22×D4—228no—
337C22×D4—228no—
338C22×D4—224no—
339C22×D4—224no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4—444no—
346C22×D4—444no—
347C22×D4—444no—
348C22×D4—444no—
349C22×D4—444no—
350C22×D4C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4C22⋊D1111yescharacteristic
353C23×C4C22⋊D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C2×D8—228no—
356C2×D8—228no—
357C2×D8—444no—
358C22×C8—114no—
359#127—118no—
360#127—228no—
361#127—228no—
362#127—228no—
363#127—224no—
364#121—22no—
365#121D4414yescomplemented
366C4×D4—24no—
367C4×D4—44no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—24no—
378C2×C42—21no—
379C2×C42C22⋊D1111yescharacteristic
380C2×C42C22⋊D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—224no—
384#102—228no—
385#102—228no—
386#102—444no—
387C22⋊C8—224no—
388#95—21no—
389#95—21no—
390#95—21no—
391C2×C11—24no—
392C2×C11—82no—
393C2×C11#240811yescharacteristic
394C2×C11C2×#44711yescharacteristic
395C2×C11#300311yescharacteristic
396C2×C11C2×#45911yescharacteristic
397C2×C11#303811yescharacteristic
398C2×C11#320511yescharacteristic
399C2×C11#321711yescharacteristic
400D11—88no—
401C24—21no—
402C24—228no—
403C24—224no—
404C24—444no—
405C24—444no—
406C24—444no—
407C24—444no—
408C24—444no—
409C24—444no—
410C24C2×C22⋊D1111yescharacteristic
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—118no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—228no—
422C2×D4—228no—
423C2×D4—224no—
424C2×D4—224no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—4416no—
429C2×D4—4416no—
430C2×D4—4432no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—444no—
435C2×D4—444no—
436C2×D4—4432no—
437C2×D4—444no—
438C2×D4—444no—
439C2×D4—444no—
440C2×D4—444no—
441C2×D4—444no—
442C2×D4C2×D4412yescomplemented
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4#432314yescomplemented
457C22×C4C2×D4412yes—
458C22×C4#433912yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465D8—4416no—
466C2×C8—224no—
467C2×C8—224no—
468C2×C8—224no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—42no—
473C4⋊C4C2×D4412yescomplemented
474C22⋊C4—24no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C42—22no—
480C42—22no—
481C42—22no—
482C42—42no—
483C42D4×D1114yes—
484C11#2420811yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—228no—
497C23—4416no—
498C23—4416no—
499C23—4416no—
500C23—444no—
501C23—444no—
502C23—444no—
503C23—444no—
504C23—444no—
505C23—444no—
506C23—888no—
507C23—888no—
508C23—888no—
509C23—888no—
510C23#6698312yes—
511C23C2×#432312yes—
512C23#6700212yes—
513C23C22×C22⋊D1111yescharacteristic
514D4—24no—
515D4—48no—
516D4—42no—
517D4—228no—
518D4—228no—
519D4—4416no—
520D4—4416no—
521D4—4416no—
522D4—4416no—
523D4—444no—
524D4—444no—
525D4—4416no—
526C2×C4—28no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—28no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—84no—
548C2×C4#6698312yes—
549C2×C4C2×#432312yes—
550C2×C4C2×#432312yes—
551C2×C4#6699012yes—
552C2×C4#6699012yes—
553C2×C4#6700212yes—
554C2×C4#6700212yes—
555C2×C4C22×D4411yescharacteristic
556C2×C4C2×#433911yescharacteristic
557C2×C4C2×D4×D1112yes—
558C2×C4#6704212yes—
559C8—444no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—448no—
574C22—448no—
575C22—448no—
576C22—8832no—
577C22—884no—
578C22—884no—
579C22—884no—
580C22—884no—
581C22#1062262814yescomplemented
582C22C2×#6698311yescharacteristic
583C22C22×#432311yescharacteristic
584C22C2×#6699011yescharacteristic
585C22C2×#6700211yescharacteristic
586C22C2×#6700211yescharacteristic
587C22C2×#6700211yescharacteristic
588C22#1062336111yescharacteristic
589C4—22no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4#1062264914yescomplemented
597C4D4×D4412yes—
598C4#1062308112yes—
599C2—24no—
600C2—82no—
601C2—888no—
602C2#1307197211yescharacteristic
603C2C2×#1062264911yescharacteristic
604C2#1307784211yescharacteristic
605C2C2×#1062262811yescharacteristic
606C2#1307809611yescharacteristic
607C2#1307953111yescharacteristic
608C2#1307963111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
hypercenterC4×#121D11
hypocenterC11#24208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66927C2semidirect
2. C2×#10622628C2semidirect
3. C2×#10622649C2semidirect
4. #13069850C2semidirect
5. #13069686C2semidirect
6. #13069543C2semidirect
7. #13068596C2semidirect
8. #13068546C2semidirect
9. C4×C11×#121C2semidirect
15. C2×C4×D4×C11C22semidirect
17. C22×#4323C22semidirect
23. C11×#390C22semidirect
24. C11×#389C22semidirect
28. C4×C11×C4⋊C4C22semidirect
33. C2×#66873C22semidirect
34. C2×#66873C22semidirect
35. C2×#66873C22semidirect
36. C2×C4⋊(C11⋊C8)C22semidirect
37. #10622162C22semidirect
62. C11×#121D4semidirect
88. #66927D4semidirect
114. C2×D4×C11C2×D4semidirect
128. C22×C4×C11D8semidirect
166. C11×C4⋊C4C2×D4semidirect
184. C4×#121D11semidirect
276. C2×C4×D4C2×D11semidirect
285. #390C2×D11semidirect
286. #389C2×D11semidirect
290. C4×C4⋊C4C2×D11semidirect
306. C22×C11#459semidirect
329. C4×C11#447semidirect
365. #121D44semidirect
442. C2×D4C2×D44semidirect
456. C22×C4#4323semidirect
473. C4⋊C4C2×D44semidirect
484. C11#24208semidirect
581. C22#10622628semidirect
596. C4#10622649semidirect

Maximal subgroups

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

subgroupindex
C22×#669272
C2×#106226282
C2×#106226492
#130698502
#130696862
#130695432
#130685962
#130685462
C4×C11×#1212
#2420811