Finite Group Databasebeta

← #14787662

Subgroups — #14787662

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×#10623086C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic, complemented
4#13069798C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068934C212yesmaximal, complemented
9#13068803C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2537C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C11×#121—21no—
14C2×C11×#121C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C2×#66983C2212yes—
19C22×C4⋊Dic11C2212yes—
20#10623086—24no—
21#10623086—24no—
22C2×#66950—21no—
23C2×#66939—22no—
24C2×C4×D44C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#394—22no—
27C11×#384C2211yescharacteristic
28C11×#380—21no—
29C11×#380C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C4×#4323—24no—
35#10622620—24no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2212yes—
38C2×#66871C2211yescharacteristic
39C2×#66871C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2312yes—
50C22×C22⋊D11—22no—
51C23×Dic11—22no—
52C2×#4341—28no—
53C2×#4341—44no—
54C2×#4341—44no—
55C22×D44C2311yescharacteristic
56C22×C4×D11—21no—
57C22×Dic22—21no—
58C11×#121—24no—
59C11×#121—42no—
60C11×#121—44no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D412yes—
74C2×C42×C11C2311yescharacteristic
75C2×#4323—22no—
76C2×#4323—22no—
77C2×#4323—22no—
78#66983—24no—
79#66983—24no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91#66950—28no—
92#66939—216no—
93C4×D44—22no—
94C4×D44D414yescomplemented
95#66922—22no—
96#66922D414yescomplemented
97C11×#95—22no—
98#66896—24no—
99#66896—22no—
100C22⋊(C11⋊C8)—24no—
101C22⋊(C11⋊C8)—42no—
102#66873—22no—
103#66873—42no—
104#66871—24no—
105#66871—22no—
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108#24116—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D412yes—
111C23×D11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—82no—
122C2×D4×C11D814yescomplemented
123C2×D4×C11#4112yescomplemented
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—28no—
140C2×C22⋊D11—44no—
141C2×C22⋊D11—44no—
142C22×Dic11—28no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—44no—
146C22×Dic11—44no—
147#4341—432no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44C2×D412yes—
154C2×C4×D11—24no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×Dic22—24no—
158C2×Dic22—42no—
159C2×Dic22—42no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—81no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—42no—
171C42×C11C2×D412yes—
172C42×C11C2×D412yes—
173#4323—28no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—24no—
176C4⋊Dic11—28no—
177C4⋊Dic11—24no—
178C4⋊Dic11—22no—
179C4⋊Dic11—21no—
180C4⋊Dic11C2×D414yes—
181C4⋊Dic11C2×D412yes—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8#4112yescomplemented
191C2×#547—111no—
192C2×#474—111no—
193C2×C4×D8—111no—
194#2537D1111yescharacteristic, complemented
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—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11C2×D814yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—28no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—88no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—84no—
246C2×C4×C11#12012yes—
247C2×C4×C11#12012yes—
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×C112−1+411yescharacteristic
256C22⋊D11—416no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—416no—
260C2×Dic11—42no—
261C2×Dic11—41no—
262C2×Dic11—42no—
263C2×Dic11—41no—
264D44—22no—
265D44—22no—
266D44—41no—
267D44—41no—
268C4×D11—48no—
269Dic22—48no—
270C11⋊C8—22no—
271C11⋊C8—41no—
272C11⋊C8—42no—
273C22×#41—221no—
274C22×D8—111no—
275#547—224no—
276#547—224no—
277C2×C4⋊Q8—111no—
278C2×#123—222no—
279C2×C22⋊Q8—221no—
280C2×#121—21no—
281C2×#121—112no—
282C2×#121C2×D1112yes—
283C2×C4×D4—111no—
284C2×C4×D4C2×D1111yescharacteristic
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—112no—
287#474—224no—
288C4×D8—224no—
289C2×#107—111no—
290C2×#107—112no—
291C2×C4⋊C8—111no—
292C2×#102—111no—
293C2×#102—112no—
294C2×#102—111no—
295C2×#102—112no—
296C2×C22⋊C8—112no—
297C2×C22⋊C8—112no—
298C2×C4×C8—111no—
299#394—22no—
300#384C2×D1111yescharacteristic
301#380—21no—
302#380C2×D1112yes—
303#340—112no—
304#340—112no—
305#340—112no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11C2×#12011yescharacteristic
321C22×C11#54611yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11C22×D811yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57711yescharacteristic
326C22×C11#57811yescharacteristic
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—42no—
336C4×C11—81no—
337C4×C11—82no—
338C4×C11#44714yes—
339C4×C11#52511yescharacteristic
340C4×C11#53711yescharacteristic
341C4×C11#54811yescharacteristic
342C4×C11#55011yescharacteristic
343Dic11—44no—
344Dic11—42no—
345C2×#41—228no—
346C2×#41—444no—
347C2×#41—444no—
348C22×Q8—221no—
349C22×D4—22no—
350C22×D4—111no—
351C22×D4—222no—
352C22×D4C22⋊D1111yescharacteristic
353C22×D4C22×D1111yescharacteristic
354C23×C4—21no—
355C23×C4—222no—
356C23×C4—221no—
357C23×C4C22×D1112yes—
358C2×D8—222no—
359C2×D8—222no—
360C2×D8—222no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8—112no—
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366#123—2216no—
367C22⋊Q8—228no—
368#121—24no—
369#121—42no—
370#121—44no—
371#121—224no—
372#121—224no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—114no—
378C4×D4—222no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22⋊D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1112yes—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4C22⋊D1112yes—
396C2×C42C22×D1111yescharacteristic
397#107—222no—
398#107—224no—
399C4⋊C8—222no—
400#102—222no—
401#102—222no—
402#102—224no—
403#102—442no—
404C22⋊C8—224no—
405C22⋊C8—442no—
406C4×C8—222no—
407#95—22no—
408C2×C11—44no—
409C2×C11—82no—
410C2×C11#240711yescharacteristic
411C2×C11C2×#44711yescharacteristic
412C2×C11#301311yescharacteristic
413C2×C11#329411yescharacteristic
414C2×C11#333011yescharacteristic
415C2×C11#333411yescharacteristic
416C2×C11#335411yescharacteristic
417D11—82no—
418C24—21no—
419C24—221no—
420C24C2×C22⋊D1112yes—
421#41—4432no—
422C2×Q8—224no—
423C2×Q8—442no—
424C2×Q8—442no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—82no—
435C2×D4—112no—
436C2×D4—228no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4#432314yescomplemented
445C2×D4#434112yescomplemented
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—228no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—224no—
461C22×C4—444no—
462C22×C4—444no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4C2×C22⋊D1112yes—
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469D8—228no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—222no—
475C2×C8—221no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—221no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—112no—
487C4⋊C4—114no—
488C4⋊C4—228no—
489C4⋊C4—224no—
490C4⋊C4—221no—
491C4⋊C4—222no—
492C22⋊C4—24no—
493C22⋊C4—44no—
494C22⋊C4—44no—
495C22⋊C4—42no—
496C22⋊C4—228no—
497C22⋊C4—224no—
498C42D4×D1112yes—
499C42D4×D1112yes—
500C11#2411611yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—222no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23C2×#432314yes—
522C23C22×C22⋊D1111yescharacteristic
523Q8—448no—
524D4—22no—
525D4—22no—
526D4—28no—
527D4—41no—
528D4—41no—
529D4—88no—
530D4—222no—
531D4—222no—
532D4—4416no—
533D4—441no—
534D4—441no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—84no—
551C2×C4—222no—
552C2×C4—224no—
553C2×C4—4416no—
554C2×C4—441no—
555C2×C4—442no—
556C2×C4—441no—
557C2×C4—442no—
558C2×C4—448no—
559C2×C4C2×#432312yes—
560C2×C4#6699012yes—
561C2×C4#6699012yes—
562C2×C4#6700212yes—
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4#6703711yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C2×C4#6704311yescharacteristic
569C8—222no—
570C8—442no—
571C8—441no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—442no—
587C22—442no—
588C22—442no—
589C22—881no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22C22×#432311yescharacteristic
594C22C2×#6699011yescharacteristic
595C22#1062333711yescharacteristic
596C22C2×#6700211yescharacteristic
597C22#1062335511yescharacteristic
598C22#1062336711yescharacteristic
599C22#1062336911yescharacteristic
600C4—22no—
601C4—42no—
602C4—81no—
603C4—82no—
604C4—442no—
605C4—444no—
606C4#1062264914yes—
607C4#1062312911yescharacteristic
608C4#1062313011yescharacteristic
609C4#1062313711yescharacteristic
610C4#1062313911yescharacteristic
611C2—44no—
612C2—82no—
613C2—882no—
614C2#1307195711yescharacteristic
615C2C2×#1062264911yescharacteristic
616C2#1307792811yescharacteristic
617C2#1308042911yescharacteristic
618C2#1308092111yescharacteristic
619C2#1308095911yescharacteristic
620C2#1308120511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2537C2
socleC23×C11C22×D4
hypercenter#2537D11
hypocenterC11#24116
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. C2×#10622620C2semidirect
3. C2×C4×#4323C2semidirect
4. #13069798C2semidirect
5. #13069612C2semidirect
6. #13069576C2semidirect
7. #13069411C2semidirect
8. #13068934C2semidirect
9. #13068803C2semidirect
10. #13068613C2semidirect
11. C11×#2537C2semidirect
94. C4×D44D4semidirect
96. #66922D4semidirect
122. C2×D4×C11D8semidirect
123. C2×D4×C11#41semidirect
190. C2×C11⋊C8#41semidirect
194. #2537D11semidirect
444. C2×D4#4323semidirect
445. C2×D4#4341semidirect
500. C11#24116semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106226202
C2×C4×#43232
#130697982
#130696122
#130695762
#130694112
#130689342
#130688032
#130686132
C11×#25372
#2411611