Finite Group Databasebeta

← #14788081

Subgroups — #14788081

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic, complemented
3C2×#10622456C211yesmaximal, characteristic, complemented
4C4×#66983C211yesmaximal, characteristic, complemented
5#13069799C212yesmaximal, complemented
6#13069614C212yesmaximal, complemented
7#13069567C211yesmaximal, characteristic, complemented
8#13069542C211yesmaximal, characteristic, complemented
9#13068963C212yesmaximal, complemented
10#13068866C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C22×C42×C11C2211yescharacteristic
14C2×#66983—21no—
15C2×#66983C2211yescharacteristic
16C2×#66983C2212yes—
17C2×C4×C22⋊D11—21no—
18C22×D88C2212yes—
19#10623008—24no—
20#10623008—24no—
21C2×#66928—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C4×D44C2211yescharacteristic
25C2×C4×D44C2212yes—
26C2×#66922C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2212yes—
30#10622826—21no—
31#10622825C2211yescharacteristic
32C2×#66885C2212yes—
33C2×#66885C2212yes—
34C2×#66885C2212yes—
35C2×#66885C2212yes—
36C2×#66882C2212yes—
37#10622553—21no—
38#10622552C2211yescharacteristic
39C4×(C2×D11)⋊C4—21no—
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622459—24no—
43#10622456—24no—
44C11×#336C2212yes—
45#10622189C2212yes—
46#10622189C2212yes—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C22×C22⋊D11—22no—
52C2×#4339—28no—
53C2×#4339—44no—
54C2×#4339—44no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2312yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—22no—
60C22×C4×D11—21no—
61C22×Dic22—21no—
62C22×C8×C11C2312yes—
63C22×C8×C11C2312yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71#66983—28no—
72#66983—24no—
73#66983—22no—
74#66983—24no—
75#66983—22no—
76C4×C22⋊D11—44no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×D88—24no—
91C2×D88—24no—
92C2×D88—42no—
93#66928—28no—
94#66927—22no—
95#66927D414yescomplemented
96C4×D44—28no—
97C4×D44—24no—
98C4×D44—22no—
99C4×D44—22no—
100C4×D44—24no—
101#66922—22no—
102#66922D414yescomplemented
103C11×C4⋊C8—22no—
104C11×C4⋊C8—22no—
105C11×C22⋊C8—42no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109#66885—24no—
110#66885—24no—
111#66885—24no—
112#66885—42no—
113#66882—24no—
114#24150—111nomaximal, Sylow
115C24×C11C2×D411yescharacteristic
116C23×D11—21no—
117C23×D11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11D814yescomplemented
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—28no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—42no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—44no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146#4339—432no—
147C2×D44—24no—
148C2×D44—24no—
149C2×D44—22no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—21no—
157C2×D44—22no—
158C2×D44—21no—
159C2×D44—42no—
160C2×D44—42no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44C2×D414yes—
164C2×D44#4112yescomplemented
165C2×C4×D11—28no—
166C2×C4×D11—44no—
167C2×C4×D11—42no—
168C2×C4×D11—44no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×Dic22—24no—
172C2×Dic22—42no—
173C2×Dic22—42no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D412yes—
185C42×C11C2×D412yes—
186C22⋊Dic11—42no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—24no—
194C4⋊Dic11—22no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D414yes—
201C4⋊Dic11#4112yescomplemented
202Dic11⋊C4—42no—
203C4×Dic11—42no—
204D88—48no—
205C2×#532—111no—
206C2×#474—111no—
207C2×#459—111no—
208C4×#121—111no—
209#2033—112no—
210#1999—112no—
211#1988—111no—
212#1982—111no—
213#1879—112no—
214#1862—112no—
215#1797D1111yescharacteristic, complemented
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11C2×D812yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—41no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—41no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—28no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—44no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11#12012yes—
255C2×C4×C11#12012yes—
256C2×C4×C11C2×D812yes—
257C2×C4×C11C2×D812yes—
258C2×C4×C11AGL(1,ℤ/8)12yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C22⋊D11—416no—
266C22⋊D11—48no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279D44—22no—
280D44—24no—
281D44—24no—
282D44—22no—
283D44—48no—
284D44—41no—
285D44—42no—
286D44—42no—
287D44—41no—
288D44—48no—
289C4×D11—416no—
290C4×D11—84no—
291Dic22—48no—
292C8×C11—42no—
293C8×C11—42no—
294C22×#41—221no—
295C22×D8—112no—
296#532—224no—
297#532—224no—
298C2×C4⋊Q8—111no—
299C2×#127—111no—
300C2×#124—221no—
301C2×#121—112no—
302C2×#121—111no—
303C2×#121—221no—
304C2×C4×D4—112no—
305C2×C4×D4—111no—
306C2×C4×D4—221no—
307C2×C4×D4—221no—
308C22×C42C2×D1111yescharacteristic
309#474—224no—
310#459—224no—
311C2×#107—112no—
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×C4⋊C8C2×D1111yescharacteristic
314C2×#102—112no—
315C2×#102—112no—
316C2×#102—112no—
317C2×#102—112no—
318C2×C22⋊C8C2×D1112yes—
319#390—111no—
320#389—111no—
321#388—221no—
322#386—221no—
323#380—111no—
324C4×C4⋊C4—111no—
325C4×C22⋊C4—221no—
326#340—112no—
327#340—112no—
328#336C2×D1112yes—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×#12011yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11#53711yescharacteristic
339C22×C11C22×D811yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11#57511yescharacteristic
342C22×C11#57511yescharacteristic
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—44no—
346C2×D11—42no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—82no—
350C2×D11—82no—
351C2×D11—81no—
352C2×D11—82no—
353C2×D11—82no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11#44714yes—
362C4×C11#54611yescharacteristic
363C4×C11#54711yescharacteristic
364C4×C11#54811yescharacteristic
365C4×C11#55011yescharacteristic
366Dic11—42no—
367Dic11—44no—
368Dic11—81no—
369Dic11—81no—
370C2×#41—228no—
371C2×#41—444no—
372C2×#41—444no—
373C22×Q8—221no—
374C22×D4—112no—
375C22×D4—111no—
376C22×D4—221no—
377C22×D4—222no—
378C22×D4—221no—
379C22×D4—221no—
380C23×C4—222no—
381C23×C4—221no—
382C23×C4D4411yescharacteristic
383C23×C4D4411yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C2×D8—224no—
386C2×D8—224no—
387C2×D8—442no—
388C22×C8C22×D1112yes—
389C22×C8C22×D1112yes—
390C4⋊Q8—114no—
391C4⋊Q8—222no—
392#127—114no—
393#127—222no—
394#124—228no—
395#121—224no—
396#121—222no—
397#121—224no—
398#121—222no—
399#121—228no—
400C4×D4—224no—
401C4×D4—224no—
402C4×D4—228no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—444no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—221no—
422C2×C42D4411yescharacteristic
423C2×C42D4411yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426#107—224no—
427C4⋊C8—22no—
428C4⋊C8—22no—
429#102—224no—
430#102—224no—
431#102—224no—
432#102—442no—
433C22⋊C8—42no—
434#95—221no—
435#95—221no—
436#95—221no—
437C2×C11—42no—
438C2×C11#240711yescharacteristic
439C2×C11C2×#44711yescharacteristic
440C2×C11#300511yescharacteristic
441C2×C11#310011yescharacteristic
442C2×C11#311511yescharacteristic
443C2×C11#324511yescharacteristic
444C2×C11#325111yescharacteristic
445D11—82no—
446D11—84no—
447C24—221no—
448C24—222no—
449C24C2×D4411yescharacteristic
450#41—4432no—
451C2×Q8—224no—
452C2×Q8—442no—
453C2×Q8—442no—
454C2×D4—114no—
455C2×D4—112no—
456C2×D4—228no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—224no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—222no—
463C2×D4—222no—
464C2×D4—221no—
465C2×D4—222no—
466C2×D4—221no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—221no—
470C2×D4—442no—
471C2×D4—442no—
472C2×D4—444no—
473C2×D4—442no—
474C2×D4—442no—
475C2×D4—444no—
476C2×D4—442no—
477C2×D4—442no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—228no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—444no—
495C22×C4—444no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4D8814yescomplemented
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4C2×D4411yescharacteristic
505C22×C4C23×D1111yescharacteristic
506D8—448no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C4⋊C4—114no—
514C4⋊C4—112no—
515C4⋊C4—224no—
516C4⋊C4—222no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C22⋊C4—228no—
524C22⋊C4—228no—
525C22⋊C4—224no—
526C22⋊C4—442no—
527C22⋊C4—442no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C42—22no—
531C42—22no—
532C42—21no—
533C42—21no—
534C42—442no—
535C42D4×D1112yes—
536C42D4×D1112yes—
537C11#2415011yescharacteristic, complemented, Sylow
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—224no—
545C23—222no—
546C23—441no—
547C23—442no—
548C23—441no—
549C23—442no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—441no—
557C23—442no—
558C23C2×D8812yes—
559C23C22×D4411yescharacteristic
560Q8—448no—
561D4—222no—
562D4—224no—
563D4—224no—
564D4—222no—
565D4—448no—
566D4—4416no—
567D4—448no—
568D4—448no—
569D4—441no—
570D4—442no—
571D4—441no—
572D4—442no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—28no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—44no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—224no—
590C2×C4—222no—
591C2×C4—4416no—
592C2×C4—441no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—884no—
603C2×C4#6693512yes—
604C2×C4#6693512yes—
605C2×C4C2×D8812yes—
606C2×C4C2×D8812yes—
607C2×C4#6696112yes—
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#6704011yescharacteristic
612C2×C4#41×D1111yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C8—42no—
615C8—42no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—444no—
624C22—442no—
625C22—442no—
626C22—444no—
627C22—444no—
628C22—442no—
629C22—881no—
630C22—882no—
631C22—881no—
632C22—881no—
633C22—882no—
634C22—882no—
635C22—881no—
636C22—882no—
637C22C2×#6693511yescharacteristic
638C22#1062304111yescharacteristic
639C22#1062305511yescharacteristic
640C22C22×D8811yescharacteristic
641C22C2×#6696111yescharacteristic
642C22#1062327911yescharacteristic
643C22#1062327911yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—41no—
648C4—444no—
649C4—442no—
650C4—881no—
651C4—881no—
652C4#1062234514yes—
653C4#1062313011yescharacteristic
654C4#1062314311yescharacteristic
655C4#1062316211yescharacteristic
656C4#1062316411yescharacteristic
657C2—42no—
658C2—884no—
659C2—882no—
660C2#1307196211yescharacteristic
661C2C2×#1062234511yescharacteristic
662C2#1307786111yescharacteristic
663C2#1307861711yescharacteristic
664C2#1307876811yescharacteristic
665C2#1307992611yescharacteristic
666C2#1307997911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1797C2
socleC23×C11C22×D4
hypercenter#1797D11
hypocenterC11#24150
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10622459C2semidirect
3. C2×#10622456C2semidirect
4. C4×#66983C2semidirect
5. #13069799C2semidirect
6. #13069614C2semidirect
7. #13069567C2semidirect
8. #13069542C2semidirect
9. #13068963C2semidirect
10. #13068866C2semidirect
11. C11×#1797C2semidirect
95. #66927D4semidirect
102. #66922D4semidirect
129. C22×C4×C11D8semidirect
164. C2×D44#41semidirect
201. C4⋊Dic11#41semidirect
215. #1797D11semidirect
499. C22×C4D88semidirect
537. C11#24150semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106224592
C2×#106224562
C4×#669832
#130697992
#130696142
#130695672
#130695422
#130689632
#130688662
C11×#17972
#2415011