Finite Group Databasebeta

← #14788512

Subgroups — #14788512

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic, complemented
4#13069850C212yesmaximal, complemented
5#13069686C212yesmaximal, complemented
6#13069553C211yesmaximal, characteristic, complemented
7#13069421C211yesmaximal, characteristic, complemented
8#13068967C212yesmaximal, complemented
9#13068862C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic, complemented
12C22×#4343—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4323C2211yescharacteristic
17C22×#4323C2212yes—
18#10623108—24no—
19#10623108—24no—
20C2×#66948—21no—
21C2×#66948—22no—
22C2×#66927C2212yes—
23C2×#66927C2211yescharacteristic
24C2×C4×D44C2212yes—
25C2×C4×D44C2211yescharacteristic
26C11×#396—22no—
27C11×#390C2212yes—
28C11×#389C2212yes—
29C11×#384C2211yescharacteristic
30C11×#380—21no—
31C2×#66896C2211yescharacteristic
32#10622628—24no—
33C4×#4323—24no—
34C2×#66873C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39C2×#66871C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C2×#4343—28no—
49C2×#4343—44no—
50C2×#4343—44no—
51C22×D44—22no—
52C22×D44—21no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44C2312yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—22no—
58C22×C4×D11—21no—
59C11×C22⋊Q8—44no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C2×#4323—22no—
77C2×#4323—22no—
78C2×#4323—24no—
79C2×#4323—24no—
80C2×#4323—22no—
81C2×#4323—42no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88#66948—28no—
89#66948—216no—
90#66927—24no—
91#66927—24no—
92#66927—22no—
93#66927D414yes—
94C4×D44—24no—
95C4×D44—22no—
96C4×D44—24no—
97C4×D44D414yes—
98C11×#95—22no—
99#66896—22no—
100#66873—22no—
101#66873—24no—
102#66873—24no—
103#66873—42no—
104#66873—42no—
105#66871—22no—
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108#24184—111nomaximal, Sylow
109C24×C11—21no—
110C23×D11—22no—
111C23×D11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11D814yescomplemented
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11#4112yescomplemented
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132#4343—432no—
133C2×D44—28no—
134C2×D44—28no—
135C2×D44—24no—
136C2×D44—24no—
137C2×D44—22no—
138C2×D44—21no—
139C2×D44—22no—
140C2×D44—21no—
141C2×D44—22no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—22no—
145C2×D44—21no—
146C2×D44—22no—
147C2×D44—44no—
148C2×D44—44no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—81no—
152C2×D44—81no—
153C2×D44—82no—
154C2×D44—82no—
155C2×D44C2×D414yes—
156C2×D44C2×D412yes—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—44no—
160C2×C4×D11—44no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—44no—
171C11×C4⋊C4—81no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—82no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11C2×D412yes—
178C42×C11C2×D412yes—
179#4323—28no—
180#4323—48no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—24no—
183C4⋊Dic11—21no—
184C4⋊Dic11C2×D412yes—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8#4112yescomplemented
194C2×#550—111no—
195C2×#459—111no—
196C2×C4×D8—111no—
197#2538D1111yescharacteristic, complemented
198#2041—112no—
199#2011—112no—
200#1984—111no—
201#1957—111no—
202#1879—112no—
203#1862—112no—
204#1802—111no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—41no—
219C22×D11—42no—
220C22×D11—41no—
221C22×D11—42no—
222C22×D11—41no—
223C22×D11—42no—
224C22×D11—41no—
225C22×D11—42no—
226C22×D11—41no—
227Q8×C11—28no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—84no—
246C2×C4×C11#12012yes—
247C2×C4×C11#12012yes—
248C2×C4×C11C2×D814yes—
249C2×C4×C11C2×D812yes—
250C2×C4×C11AGL(1,ℤ/8)12yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260D44—22no—
261D44—22no—
262D44—24no—
263D44—24no—
264D44—416no—
265D44—42no—
266D44—42no—
267D44—41no—
268D44—41no—
269D44—48no—
270D44—84no—
271D44—88no—
272C4×D11—416no—
273C4×D11—48no—
274C11⋊C8—22no—
275C11⋊C8—41no—
276C11⋊C8—42no—
277C22×#41—221no—
278C22×D8—111no—
279C22×D8—112no—
280#550—224no—
281#550—224no—
282C2×#127—111no—
283C2×#127—112no—
284C2×C22⋊Q8—21no—
285C2×#121—221no—
286C2×#121—222no—
287C2×C4×Q8C2×D1111yescharacteristic
288C2×C4×D4—111no—
289C2×C4×D4—112no—
290C2×C4×D4C2×D1111yescharacteristic
291#459—224no—
292C4×D8—224no—
293C2×#107—111no—
294C2×C4⋊C8—111no—
295C2×#102—111no—
296C2×#102—112no—
297C2×#102—112no—
298C2×#102—111no—
299C2×#102—112no—
300C2×#102—112no—
301C2×C4×C8—111no—
302#396—22no—
303#390C2×D1112yes—
304#389C2×D1112yes—
305#384C2×D1111yescharacteristic
306#380—21no—
307#340—112no—
308#336—112no—
309#336—112no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11C2×#12011yescharacteristic
318C22×C11#54811yescharacteristic
319C22×C11#55011yescharacteristic
320C22×C11C22×D811yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11#57611yescharacteristic
323C22×C11#57711yescharacteristic
324C2×D11—42no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—42no—
328C2×D11—44no—
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—81no—
334C2×D11—82no—
335C2×D11—81no—
336C2×D11—82no—
337C2×D11—81no—
338C4×C11—24no—
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—82no—
342C4×C11—81no—
343C4×C11#44714yes—
344C4×C11#52511yescharacteristic
345C4×C11#53711yescharacteristic
346C4×C11#54611yescharacteristic
347C4×C11#54711yescharacteristic
348Dic11—42no—
349C2×#41—228no—
350C2×#41—444no—
351C2×#41—444no—
352C22×Q8C22⋊D1111yescharacteristic
353C22×D4—111no—
354C22×D4—112no—
355C22×D4—222no—
356C22×D4—221no—
357C22×D4—222no—
358C22×D4—221no—
359C22×D4C22×D1111yescharacteristic
360C23×C4—21no—
361C23×C4—222no—
362C23×C4—221no—
363C2×D8—222no—
364C2×D8—222no—
365C2×D8—222no—
366C2×D8—224no—
367C2×D8—224no—
368C2×D8—442no—
369C22×C8—111no—
370C22×C8—112no—
371C22×C8—111no—
372#127—114no—
373#127—224no—
374#127—224no—
375#127—222no—
376C22⋊Q8—44no—
377#121—228no—
378#121—2216no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—114no—
384C4×D4—224no—
385C4×D4—224no—
386C4×D4—222no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4C22⋊D1111yescharacteristic
392C2×C4⋊C4C22⋊D1112yes—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1112yes—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—221no—
400C2×C42C22×D1112yes—
401C2×C42C22×D1111yescharacteristic
402#107—222no—
403C4⋊C8—222no—
404#102—224no—
405#102—222no—
406#102—224no—
407#102—222no—
408#102—442no—
409#102—442no—
410C4×C8—222no—
411#95—22no—
412C2×C11—82no—
413C2×C11#240711yescharacteristic
414C2×C11C2×#44711yescharacteristic
415C2×C11#301211yescharacteristic
416C2×C11#335811yescharacteristic
417C2×C11#336611yescharacteristic
418C2×C11#339111yescharacteristic
419C2×C11#339711yescharacteristic
420D11—82no—
421D11—84no—
422C24—21no—
423C24—222no—
424C24—221no—
425#41—4432no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8#432314yescomplemented
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—112no—
435C2×D4—114no—
436C2×D4—228no—
437C2×D4—228no—
438C2×D4—224no—
439C2×D4—224no—
440C2×D4—222no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—222no—
444C2×D4—221no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—222no—
450C2×D4—444no—
451C2×D4—444no—
452C2×D4—442no—
453C2×D4—442no—
454C2×D4—881no—
455C2×D4—881no—
456C2×D4—882no—
457C2×D4—882no—
458C2×D4#434312yescomplemented
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—228no—
465C22×C4—221no—
466C22×C4—224no—
467C22×C4—444no—
468C22×C4—444no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476D8—228no—
477D8—448no—
478C2×C8—112no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—222no—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—42no—
494C4⋊C4—44no—
495C4⋊C4—81no—
496C4⋊C4—112no—
497C4⋊C4—221no—
498C22⋊C4—44no—
499C22⋊C4—42no—
500C22⋊C4—82no—
501C22⋊C4—228no—
502C22⋊C4—224no—
503C42—22no—
504C42—22no—
505C42D4×D1112yes—
506C42D4×D1112yes—
507C11#2418411yescharacteristic, complemented, Sylow
508C23—22no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—224no—
516C23—222no—
517C23—442no—
518C23—441no—
519C23—441no—
520C23—442no—
521C23—442no—
522C23—441no—
523C23—442no—
524C23—441no—
525C23—442no—
526C23—441no—
527C23—442no—
528C23—441no—
529C23C22×C22⋊D1111yescharacteristic
530Q8—28no—
531D4—22no—
532D4—22no—
533D4—41no—
534D4—41no—
535D4—222no—
536D4—222no—
537D4—224no—
538D4—224no—
539D4—4416no—
540D4—442no—
541D4—442no—
542D4—448no—
543D4—441no—
544D4—441no—
545D4—884no—
546D4—888no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—84no—
561C2×C4—222no—
562C2×C4—4416no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—448no—
566C2×C4C2×#432314yes—
567C2×C4C2×#432312yes—
568C2×C4#6699012yes—
569C2×C4#6699012yes—
570C2×C4#6700212yes—
571C2×C4C2×D4×D1111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×#434311yescharacteristic
574C2×C4#6704011yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C2×C4#6704211yescharacteristic
577C8—222no—
578C8—441no—
579C8—442no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—444no—
588C22—442no—
589C22—442no—
590C22—444no—
591C22—444no—
592C22—442no—
593C22—882no—
594C22—881no—
595C22—882no—
596C22—881no—
597C22—882no—
598C22—881no—
599C22—882no—
600C22—881no—
601C22C22×#432311yescharacteristic
602C22C2×#6699011yescharacteristic
603C22#1062334811yescharacteristic
604C22C2×#6700211yescharacteristic
605C22#1062336511yescharacteristic
606C22#1062336611yescharacteristic
607C22#1062336811yescharacteristic
608C4—24no—
609C4—22no—
610C4—42no—
611C4—81no—
612C4—82no—
613C4—442no—
614C4#1062264914yes—
615C4#1062315811yescharacteristic
616C4#1062316011yescharacteristic
617C4#1062316111yescharacteristic
618C4#1062316211yescharacteristic
619C2—82no—
620C2—884no—
621C2—882no—
622C2#1307196311yescharacteristic
623C2C2×#1062264911yescharacteristic
624C2#1307791711yescharacteristic
625C2#1308125111yescharacteristic
626C2#1308132311yescharacteristic
627C2#1308158811yescharacteristic
628C2#1308163611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
hypercenter#2538D11
hypocenterC11#24184
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#10623108C2semidirect
2. C2×#10622628C2semidirect
3. C2×C4×#4323C2semidirect
4. #13069850C2semidirect
5. #13069686C2semidirect
6. #13069553C2semidirect
7. #13069421C2semidirect
8. #13068967C2semidirect
9. #13068862C2semidirect
10. #13068613C2semidirect
11. C11×#2538C2semidirect
114. C2×Q8×C11D8semidirect
120. C2×D4×C11#41semidirect
193. C2×C11⋊C8#41semidirect
197. #2538D11semidirect
428. C2×Q8#4323semidirect
458. C2×D4#4343semidirect
507. C11#24184semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106226282
C2×C4×#43232
#130698502
#130696862
#130695532
#130694212
#130689672
#130688622
#130686132
C11×#25382
#2418411