Finite Group Databasebeta

← #14787668

Subgroups — #14787668

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic, complemented
4#13069800C212yesmaximal, complemented
5#13069613C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069409C211yesmaximal, characteristic, complemented
8#13068930C212yesmaximal, complemented
9#13068802C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic, complemented
11C2×C11×#474C211yesmaximal, characteristic, complemented
12C22×#4343—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66999—21no—
16C2×#66991C2212yes—
17C22×#4323C2211yescharacteristic
18C2×#66983—21no—
19#10623257—24no—
20#10623257—24no—
21C2×#66948C2212yes—
22C2×#66947—22no—
23C2×C4⋊C4×D11C2212yes—
24C2×C4×D44C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C11×#474—24no—
27C2×C11×#107C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×#66896C2211yescharacteristic
31#10622825—21no—
32C2×#66885C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C4×#4323—24no—
36#10622600C2212yes—
37C2×#66873C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622574—22no—
40#10622548C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622189C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—22no—
49C2×#4343—28no—
50C2×#4343—44no—
51C2×#4343—44no—
52C22×D44—22no—
53C22×D44D411yescharacteristic
54C22×D44C2311yescharacteristic
55C22×C4×D11—22no—
56C22×C4×D11—21no—
57C22×C4×D11C2312yes—
58C22×C8×C11C2312yes—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8D414yescomplemented
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69#66999—28no—
70#66991—24no—
71#66991—42no—
72C2×#4323—22no—
73C2×#4323—22no—
74C2×#4323—22no—
75#66983—44no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4D412yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—22no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88#66948—24no—
89#66948—24no—
90#66947—216no—
91C4⋊C4×D11—24no—
92C4⋊C4×D11—24no—
93C4×D44—22no—
94C4×D44—22no—
95C4×D44—22no—
96C4×D44D414yescomplemented
97C11×#107—24no—
98C11×C4⋊C8—22no—
99C11×#102—24no—
100#66896—22no—
101C11⋊#95—22no—
102#66885—42no—
103(C2×D11)⋊C8—24no—
104(C2×D11)⋊C8—42no—
105#66873—22no—
106#66871—22no—
107C4×C11⋊C8—22no—
108#24116—111nomaximal, Sylow
109C24×C11—21no—
110C23×D11—21no—
111C23×D11C2×D412yes—
112C2×Q8×C11—24no—
113C2×Q8×C11—42no—
114C2×Q8×C11—42no—
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—22no—
122C22×C4×C11—21no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—44no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—82no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11C2×D412yes—
135#4343—432no—
136C2×D44—28no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—44no—
145C2×D44—44no—
146C2×D44D814yescomplemented
147C2×D44C2×D412yes—
148C2×C4×D11—28no—
149C2×C4×D11—24no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—44no—
157C2×C4×D11—44no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C2×D414yes—
168C11×C22⋊C4—42no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171C22⋊Dic11—44no—
172#4323—28no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—44no—
177C4⋊Dic11—22no—
178C4⋊Dic11—21no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—42no—
182C4⋊Dic11—81no—
183C4⋊Dic11C2×D412yes—
184Dic11⋊C4—28no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8#4112yescomplemented
191C2×#547—111no—
192C2×#474D1111yescharacteristic, complemented
193C2×C4×D8—111no—
194#2537—111no—
195#2033—112no—
196#1999—112no—
197#1990—111no—
198#1954—111no—
199#1874—112no—
200#1852—112no—
201#1802—111no—
202C23×C11—22no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11C22×D411yescharacteristic
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11C2×D814yes—
224Q8×C11—48no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—24no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—84no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12012yes—
240C2×C4×C11C2×D812yes—
241C2×C4×C11AGL(1,ℤ/8)12yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C22⋊D11—88no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258D44—22no—
259D44—22no—
260D44—28no—
261D44—416no—
262D44—41no—
263D44—41no—
264C4×D11—416no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—42no—
269C4×D11—48no—
270C8×C11—42no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C22×#41—221no—
274C22×D8—111no—
275#547—224no—
276#547—224no—
277C2×C4⋊Q8C2×D1111yescharacteristic
278C2×#123—222no—
279C2×C22⋊Q8—221no—
280C2×#121—112no—
281C2×#121—112no—
282C2×#121—221no—
283C2×C4×D4—111no—
284C2×C4×D4—111no—
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—112no—
287#474—24no—
288C4×D8—224no—
289C2×#107—111no—
290C2×#107C2×D1112yes—
291C2×C4⋊C8C2×D1111yescharacteristic
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—112no—
295C2×#102C2×D1112yes—
296C2×C22⋊C8—112no—
297C2×C22⋊C8—112no—
298C2×C4×C8—111no—
299#394—222no—
300#384—111no—
301#380—112no—
302#380—221no—
303#340—112no—
304#340—112no—
305#340—112no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11C2×#12011yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11#54711yescharacteristic
316C22×C11C22×D811yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57811yescharacteristic
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—24no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—22no—
335C4×C11—44no—
336C4×C11—81no—
337C4×C11#44714yes—
338C4×C11#52511yescharacteristic
339C4×C11#53711yescharacteristic
340C4×C11#54811yescharacteristic
341C4×C11#55011yescharacteristic
342Dic11—42no—
343Dic11—42no—
344Dic11—82no—
345C2×#41—228no—
346C2×#41—444no—
347C2×#41—444no—
348C22×Q8—21no—
349C22×D4—111no—
350C22×D4—111no—
351C22×D4—222no—
352C22×D4—222no—
353C22×D4C22×D1111yescharacteristic
354C23×C4—21no—
355C23×C4—112no—
356C23×C4—222no—
357C23×C4—221no—
358C2×D8—222no—
359C2×D8—222no—
360C2×D8—222no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8C22×D1112yes—
364C4⋊Q8—22no—
365C4⋊Q8C22⋊D1114yescomplemented
366#123—2216no—
367C22⋊Q8—228no—
368#121—224no—
369#121—224no—
370#121—224no—
371#121—442no—
372#121—444no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—114no—
376C4×D4—222no—
377C4×D4—222no—
378C4×D4—222no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1112yes—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C42C22×D1111yescharacteristic
397#107—24no—
398#107—222no—
399C4⋊C8—22no—
400#102—24no—
401#102—222no—
402#102—222no—
403#102—442no—
404C22⋊C8—224no—
405C22⋊C8—442no—
406C4×C8—222no—
407#95—222no—
408C2×C11—82no—
409C2×C11#240711yescharacteristic
410C2×C11C2×#44711yescharacteristic
411C2×C11#301311yescharacteristic
412C2×C11#329411yescharacteristic
413C2×C11#333011yescharacteristic
414C2×C11#333411yescharacteristic
415C2×C11#335411yescharacteristic
416D11—44no—
417D11—82no—
418C24—21no—
419C24—112no—
420C24—221no—
421#41—4432no—
422C2×Q8—24no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—114no—
431C2×D4—112no—
432C2×D4—228no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—444no—
441C2×D4—444no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—882no—
445C2×D4#434312yescomplemented
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—112no—
452C22×C4—228no—
453C22×C4—221no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—444no—
463C22×C4—444no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469D8—228no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—112no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—112no—
484C4⋊C4—228no—
485C4⋊C4—222no—
486C4⋊C4—221no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—442no—
490C4⋊C4—881no—
491C4⋊C4C2×C22⋊D1114yes—
492C22⋊C4—42no—
493C22⋊C4—228no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C22⋊C4—444no—
497C22⋊C4—444no—
498C42D4×D1112yes—
499C42C2×C22⋊D1112yes—
500C11#2411611yescharacteristic, complemented, Sylow
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—114no—
509C23—222no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—222no—
514C23—222no—
515C23—222no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23C2×D4×D1111yescharacteristic
523Q8—48no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528D4—228no—
529D4—222no—
530D4—222no—
531D4—4416no—
532D4—441no—
533D4—441no—
534D4—888no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—84no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—4416no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—448no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4D8×D1112yes—
560C2×C4#6696412yes—
561C2×C4#6699012yes—
562C2×C4#6699012yes—
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×#434311yescharacteristic
565C2×C4#6704011yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#6704211yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C8—42no—
570C8—222no—
571C8—441no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—224no—
580C22—224no—
581C22—224no—
582C22—442no—
583C22—442no—
584C22—442no—
585C22—442no—
586C22—442no—
587C22—442no—
588C22—442no—
589C22—881no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22#1062316111yescharacteristic
594C22#1062316211yescharacteristic
595C22C2×D8×D1111yescharacteristic
596C22C2×#6696411yescharacteristic
597C22#1062330911yescharacteristic
598C22#1062331011yescharacteristic
599C22C2×#6699011yescharacteristic
600C4—22no—
601C4—44no—
602C4—81no—
603C4—442no—
604C4—442no—
605C4—882no—
606C4#1062276914yes—
607C4#1062315811yescharacteristic
608C4#1062316011yescharacteristic
609C4#1062334811yescharacteristic
610C4#1062336511yescharacteristic
611C2—82no—
612C2—444no—
613C2—882no—
614C2#1307196311yescharacteristic
615C2C2×#1062276911yescharacteristic
616C2#1307793011yescharacteristic
617C2#1308042611yescharacteristic
618C2#1308091811yescharacteristic
619C2#1308096211yescharacteristic
620C2#1308121411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
hypercenterC2×#474D11
hypocenterC11#24116
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623257C2semidirect
2. C2×C4×#4323C2semidirect
3. #13073529C2semidirect
4. #13069800C2semidirect
5. #13069613C2semidirect
6. #13069578C2semidirect
7. #13069409C2semidirect
8. #13068930C2semidirect
9. #13068802C2semidirect
10. #13068617C2semidirect
11. C2×C11×#474C2semidirect
60. C11×C4⋊Q8D4semidirect
96. C4×D44D4semidirect
120. C2×D4×C11#41semidirect
146. C2×D44D8semidirect
190. C2×C11⋊C8#41semidirect
192. C2×#474D11semidirect
365. C4⋊Q8C22⋊D11semidirect
445. C2×D4#4343semidirect
500. C11#24116semidirect

Maximal subgroups

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

subgroupindex
C2×#106232572
C2×C4×#43232
#130735292
#130698002
#130696132
#130695782
#130694092
#130689302
#130688022
#130686172
C2×C11×#4742
#2411611