Finite Group Databasebeta

← #14788504

Subgroups — #14788504

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×#10622685C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069687C212yesmaximal, complemented
6#13069553C211yesmaximal, characteristic, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068863C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C11×#550—24no—
14C11×#550—24no—
15C2×C11×#127C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66999—21no—
23C22×#4323C2211yescharacteristic
24C22×#4323C2212yes—
25C2×C4×D44C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2211yescharacteristic
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622685—24no—
32C4×#4323—24no—
33#10622607—22no—
34#10622600—21no—
35C2×#66873C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622552C2212yes—
38#10622548C2211yescharacteristic
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11C2312yes—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—21no—
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
59C11×#127—24no—
60C11×#127—24no—
61C11×#127—22no—
62C11×#127D414yes—
63C11×#121—28no—
64C11×#121—216no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—22no—
70C4×D4×C11D414yes—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2312yes—
77C2×C42×C11C2311yescharacteristic
78#66999—44no—
79C2×#4323—22no—
80C2×#4323—22no—
81C2×#4323—24no—
82C2×#4323—24no—
83C2×#4323—22no—
84C2×#4323—42no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×Dic11⋊C4—22no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96C4×D44—22no—
97C4×D44—22no—
98#66896—22no—
99#66896—24no—
100#66896—24no—
101#66896—42no—
102#66896—42no—
103C11⋊#95—22no—
104#66873—22no—
105#66871—22no—
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108#24184—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—21no—
111C23×D11—21no—
112C11×#41—432no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11D814yescomplemented
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11—81no—
135C2×D4×C11—81no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D414yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—28no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—22no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44#4112yescomplemented
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—24no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D412yes—
172C42×C11C2×D412yes—
173#4323—28no—
174#4323—48no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—44no—
177(C2×D11)⋊C4—82no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—42no—
183C4⋊Dic11—81no—
184Dic11⋊C4—44no—
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×#550D1111yescharacteristic, complemented
195C2×#459—111no—
196C2×C4×D8—111no—
197#2538—111no—
198#2041—112no—
199#2011—112no—
200#1984—111no—
201#1957—111no—
202#1879—112no—
203#1862—112no—
204#1802—111no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227Q8×C11—28no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—24no—
231D4×C11—24no—
232D4×C11—416no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—48no—
238D4×C11—84no—
239D4×C11—88no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—416no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—48no—
252C2×C4×C11#12012yes—
253C2×C4×C11#12012yes—
254C2×C4×C11C2×D814yes—
255C2×C4×C11C2×D812yes—
256C2×C4×C11AGL(1,ℤ/8)12yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—41no—
264C2×Dic11—42no—
265C2×Dic11—41no—
266C2×Dic11—42no—
267C2×Dic11—41no—
268C2×Dic11—42no—
269D44—22no—
270D44—22no—
271D44—41no—
272D44—41no—
273C4×D11—84no—
274C11⋊C8—22no—
275C11⋊C8—41no—
276C11⋊C8—42no—
277C22×#41—21no—
278C22×D8—111no—
279C22×D8—112no—
280#550—24no—
281#550—24no—
282C2×#127C2×D1112yes—
283C2×#127C2×D1111yescharacteristic
284C2×C22⋊Q8—221no—
285C2×#121—21no—
286C2×#121—22no—
287C2×C4×Q8C2×D1111yescharacteristic
288C2×C4×D4—111no—
289C2×C4×D4C2×D1112yes—
290C2×C4×D4C2×D1111yescharacteristic
291#459—224no—
292C4×D8—224no—
293C2×#107—111no—
294C2×C4⋊C8—111no—
295C2×#102—112no—
296C2×#102—112no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—112no—
300C2×#102—112no—
301C2×C4×C8—111no—
302#396—222no—
303#390—112no—
304#389—112no—
305#384—111no—
306#380—221no—
307#340—112no—
308#336—112no—
309#336—112no—
310C22×C11—42no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—42no—
316C22×C11—81no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—81no—
320C22×C11—82no—
321C22×C11—81no—
322C22×C11—82no—
323C22×C11—81no—
324C22×C11C2×#12011yescharacteristic
325C22×C11#54811yescharacteristic
326C22×C11#55011yescharacteristic
327C22×C11C22×D811yescharacteristic
328C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C11#57611yescharacteristic
330C22×C11#57711yescharacteristic
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C4×C11—24no—
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11#44714yes—
343C4×C11#52511yescharacteristic
344C4×C11#53711yescharacteristic
345C4×C11#54611yescharacteristic
346C4×C11#54711yescharacteristic
347Dic11—82no—
348Dic11—81no—
349C2×#41—28no—
350C2×#41—44no—
351C2×#41—44no—
352C22×Q8C22⋊D1111yescharacteristic
353C22×D4—22no—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—111no—
358C22×D4C22×D1112yes—
359C22×D4C22×D1111yescharacteristic
360C23×C4—22no—
361C23×C4—21no—
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—24no—
373#127—24no—
374#127—22no—
375#127C22⋊D1114yes—
376C22⋊Q8—444no—
377#121—28no—
378#121—216no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4—222no—
385C4×D4—222no—
386C4×D4C22⋊D1114yes—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C22⋊D1111yescharacteristic
393C2×C4⋊C4C22⋊D1112yes—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—222no—
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—222no—
412C2×C11—82no—
413C2×C11—84no—
414C2×C11#240711yescharacteristic
415C2×C11C2×#44711yescharacteristic
416C2×C11#301211yescharacteristic
417C2×C11#335811yescharacteristic
418C2×C11#336611yescharacteristic
419C2×C11#339111yescharacteristic
420C2×C11#339711yescharacteristic
421D11—82no—
422C24—22no—
423C24—21no—
424C24—221no—
425#41—432no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8#432314yescomplemented
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4—112no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4C2×C22⋊D1114yes—
458C2×D4C2×C22⋊D1112yes—
459C22×C4—28no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—442no—
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—222no—
482C2×C8—221no—
483C2×C8—222no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—222no—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—444no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4C2×C22⋊D1112yes—
498C22⋊C4—28no—
499C22⋊C4—24no—
500C22⋊C4—444no—
501C22⋊C4—442no—
502C22⋊C4—882no—
503C42—22no—
504C42—22no—
505C42C2×C22⋊D1112yes—
506C42C2×C22⋊D1112yes—
507C11#2418411yescharacteristic, complemented, Sylow
508C23—24no—
509C23—22no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—41no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—222no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23—441no—
528C23—441no—
529C23C22×C22⋊D1111yescharacteristic
530Q8—28no—
531D4—24no—
532D4—22no—
533D4—24no—
534D4—22no—
535D4—416no—
536D4—48no—
537D4—41no—
538D4—42no—
539D4—41no—
540D4—42no—
541D4—84no—
542D4—88no—
543D4—222no—
544D4—222no—
545D4—441no—
546D4—441no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—416no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—48no—
559C2×C4—442no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—441no—
565C2×C4—884no—
566C2×C4C2×#432314yes—
567C2×C4C2×#432312yes—
568C2×C4#6698512yes—
569C2×C4#6700612yes—
570C2×C4#6700612yes—
571C2×C4#41×D1111yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#6704211yescharacteristic
574C2×C4#6704311yescharacteristic
575C2×C4C22×C22⋊D1111yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—222no—
578C8—442no—
579C8—441no—
580C22—44no—
581C22—42no—
582C22—44no—
583C22—42no—
584C22—44no—
585C22—42no—
586C22—82no—
587C22—81no—
588C22—82no—
589C22—81no—
590C22—82no—
591C22—81no—
592C22—82no—
593C22—81no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—881no—
598C22—881no—
599C22—881no—
600C22—881no—
601C22C22×#432311yescharacteristic
602C22C2×#6698511yescharacteristic
603C22#1062336211yescharacteristic
604C22#1062336511yescharacteristic
605C22#1062336611yescharacteristic
606C22#1062336711yescharacteristic
607C22C2×#6700611yescharacteristic
608C4—24no—
609C4—22no—
610C4—42no—
611C4—42no—
612C4—881no—
613C4—882no—
614C4#1062283014yes—
615C4#1062335511yescharacteristic
616C4#1062335911yescharacteristic
617C4#1062336011yescharacteristic
618C4#1062336411yescharacteristic
619C2—84no—
620C2—82no—
621C2—882no—
622C2#1307195511yescharacteristic
623C2C2×#1062283011yescharacteristic
624C2#1307792011yescharacteristic
625C2#1308124711yescharacteristic
626C2#1308131911yescharacteristic
627C2#1308158811yescharacteristic
628C2#1308163211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11#24184
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622685C2semidirect
2. C2×C4×#4323C2semidirect
3. #13073534C2semidirect
4. #13069847C2semidirect
5. #13069687C2semidirect
6. #13069553C2semidirect
7. #13069423C2semidirect
8. #13068964C2semidirect
9. #13068863C2semidirect
10. #13068616C2semidirect
11. C2×C11×#550C2semidirect
115. C2×Q8×C11D8semidirect
159. C2×D44#41semidirect
193. C2×C11⋊C8#41semidirect
194. C2×#550D11semidirect
428. C2×Q8#4323semidirect
507. C11#24184semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
C2×C4×#43232
#130735342
#130698472
#130696872
#130695532
#130694232
#130689642
#130688632
#130686162
C2×C11×#5502
#2418411