Finite Group Databasebeta

← #25125474

Subgroups — #25125474

Order 11008.

1166 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C211yesmaximal, characteristic, complemented
2C2×#14582862C211yesmaximal, characteristic
3#19136974C211yesmaximal, characteristic
4C2×#14582756C211yesmaximal, characteristic
5#19136034C212yesmaximal, complemented
6#19136033C212yesmaximal, complemented
7#19136027C212yesmaximal, complemented
8#19136022C212yesmaximal, complemented
9#19134315C211yesmaximal, characteristic, complemented
10#19134314C211yesmaximal, characteristic, complemented
11C43×#1736C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C2×#13063284C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16C22×(C2×D43)⋊C4—21no—
17#14582942—24no—
18C2×#13063258C2212yescomplemented
19C2×#13063256C2212yescomplemented
20#14582862—24no—
21C2×(C2×D43)⋊C8C2212yes—
22C2×(C2×D43)⋊C8C2212yes—
23#14582760—21no—
24#14582756—21no—
25#14582756—21no—
26#14582756C2211yescharacteristic
27#14582756C2212yes—
28#14582756C2211yescharacteristic
29#14582756C2212yes—
30#14582756C2211yescharacteristic
31#14582756C2211yescharacteristic
32#14582754—21no—
33C4×(C2×D43)⋊C4—21no—
34C4×(C2×D43)⋊C4—21no—
35C2×C43⋊#95—21no—
36#14582662C2212yescomplemented
37#14582662C2212yescomplemented
38#14582661C2212yescomplemented
39#14582661C2212yescomplemented
40C22×M16×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#340C2212yescomplemented
44C43×#340C2212yescomplemented
45C24×D43D411yescharacteristic
46C23×Dic43—21no—
47C23×Dic43D411yescharacteristic
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C22×C4×D43C2311yescharacteristic
57C22×C4×D43C2311yescharacteristic
58C2×#10621877—22no—
59C2×#10621877—22no—
60C2×#10621877D414yes—
61C22×C43⋊C8C2312yes—
62#13063284—22no—
63#13063284—22no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2312yes—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C22⋊Dic43—21no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—44no—
78C2×C4×Dic43—21no—
79#13063258—24no—
80#13063256—24no—
81(C2×D43)⋊C8—24no—
82(C2×D43)⋊C8—24no—
83C43⋊#95—22no—
84C43⋊#95—22no—
85C43⋊#95—21no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91C2×M16×C43—22no—
92C2×M16×C43—22no—
93C2×M16×C43—22no—
94C22×C8×C43C2312yes—
95#117×C43—22no—
96#117×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2312yes—
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C22⋊C4×C43—21no—
104C2×C42×C43—21no—
105C24×C43C2×D411yescharacteristic
106C23×D43—22no—
107C23×D43—22no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—41no—
112C23×D43—41no—
113C23×D43C2×D411yescharacteristic
114C23×D43C2×D411yescharacteristic
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—42no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43C2×D412yes—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43#4112yes—
124C22×C4×C43#4112yes—
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×C4×C43#4112yes—
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—22no—
135C22×Dic43—42no—
136C22×Dic43—42no—
137C22×Dic43—42no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—44no—
159C2×C4×D43—44no—
160C2×C4×D43—44no—
161C2×C4×D43—44no—
162M16×C43—44no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C42×C43—42no—
175C22⋊Dic43—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—44no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—44no—
181(C2×D43)⋊C4—42no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189C4×Dic43—42no—
190#10621877—28no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8C2×D414yes—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43#12112yes—
199C23×C43#12312yes—
200C23×C43#12312yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—28no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—44no—
216C22×D43—44no—
217C22×D43—44no—
218C22×D43—44no—
219C22×D43—44no—
220C22×D43—44no—
221C22×D43AGL(1,ℤ/8)12yes—
222C22×D43#13712yes—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—84no—
233C2×C4×C43#12112yes—
234C2×C4×C43#12312yes—
235C2×C4×C43#12314yes—
236C2×C4×C43#12312yes—
237C2×C4×C43#12414yes—
238C2×C4×C43#12614yes—
239C2×C4×C43#12614yes—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—44no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—42no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—42no—
262C2×Dic43—84no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—44no—
272C4×D43—44no—
273C8×C43—42no—
274C43⋊C8—24no—
275#23642—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43#39714yes—
283C22×C43C2×#12111yescharacteristic
284C22×C43C2×#12311yescharacteristic
285C22×C43C2×#12311yescharacteristic
286C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C43C2×#13711yescharacteristic
288C22×C43#57511yescharacteristic
289C22×C43#57511yescharacteristic
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—416no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C4×C43—82no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#39714yes—
309C4×C43C2×#12311yescharacteristic
310C4×C43C2×#12411yescharacteristic
311C4×C43C2×#12611yescharacteristic
312C4×C43C2×#12611yescharacteristic
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317Dic43—82no—
318C2×#428—431no—
319C2×#407—431no—
320#2280—431no—
321C2×#380—431no—
322#2077—432no—
323#2077—432no—
324#2076—432no—
325#2075—432no—
326#1736—431no—
327#1736—431no—
328#1736D4311yescharacteristic, complemented
329C2×C43—24no—
330C2×C43C2×#39711yescharacteristic
331C2×C43#305511yescharacteristic
332C2×C43#305611yescharacteristic
333C2×C43#309211yescharacteristic
334C2×C43#309311yescharacteristic
335C2×C43#309411yescharacteristic
336C2×C43#309511yescharacteristic
337D43—42no—
338D43—42no—
339C24×C4—431no—
340C22×M16—431no—
341C22×M16C2×D4311yescharacteristic
342C2×#117—431no—
343C2×#117C2×D4311yescharacteristic
344C22×C4⋊C4—431no—
345C22×C4⋊C4C2×D4311yescharacteristic
346C22×C22⋊C4—861no—
347#428—864no—
348C2×#107—432no—
349C2×#106—432no—
350#407—864no—
351C2×C22⋊C8—432no—
352C2×C22⋊C8—432no—
353#381—861no—
354#380—431no—
355#380—432no—
356#380—431no—
357#380—432no—
358#380—431no—
359#380—431no—
360#380—861no—
361#380—861no—
362#379—861no—
363C4×C22⋊C4—861no—
364C4×C22⋊C4—861no—
365C2×#95—861no—
366#340—432no—
367#340—432no—
368#340—432no—
369#340—432no—
370#340C2×D4312yescomplemented
371#340C2×D4312yescomplemented
372C43#2364211yescharacteristic, complemented, Sylow
373C25—431no—
374C23×C4—21no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—862no—
381C23×C4—862no—
382C23×C4—862no—
383C23×C4—862no—
384C23×C4—862no—
385C23×C4—862no—
386C23×C4—861no—
387C23×C4C22×D4311yescharacteristic
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—434no—
392C2×M16—862no—
393C2×M16—862no—
394C22×C8—432no—
395C22×C8C22×D4312yes—
396#117—22no—
397#117—22no—
398#117—862no—
399#117—862no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—432no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4312yes—
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—1724no—
421C2×C42—21no—
422C2×C42—861no—
423#107—864no—
424#106—864no—
425C22⋊C8—864no—
426C22⋊C8—864no—
427#95—862no—
428#95—862no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433C24—431no—
434C24—431no—
435C24—862no—
436C24—862no—
437C24—862no—
438C24—862no—
439C24—862no—
440C24—1721no—
441C24—1721no—
442C24D4×D4311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4—1724no—
479C22×C4—1724no—
480C22×C4—1724no—
481C22×C4—1724no—
482C22×C4#1062189812yes—
483C22×C4#1062189812yes—
484C22×C4#1062189812yes—
485C22×C4D4×D4311yescharacteristic
486C22×C4D4×D4312yes—
487C22×C4#1062190012yes—
488C22×C4#1062190212yes—
489C22×C4C23×D4311yescharacteristic
490M16—44no—
491M16—868no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—434no—
496C2×C8—862no—
497C2×C8—862no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1722no—
512C22⋊C4—42no—
513C22⋊C4—1724no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1724no—
517C22⋊C4—1722no—
518C22⋊C4—1722no—
519C22⋊C4—1722no—
520C42—42no—
521C42—1722no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—432no—
527C23—432no—
528C23—868no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23—861no—
534C23—861no—
535C23—861no—
536C23—861no—
537C23—861no—
538C23—861no—
539C23—861no—
540C23—861no—
541C23—1724no—
542C23—1724no—
543C23—1724no—
544C23—1724no—
545C23—1724no—
546C23—1724no—
547C23#1306329812yes—
548C23#1306330712yes—
549C23#1306331012yes—
550C23C2×D4×D4311yescharacteristic
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—3444no—
568C2×C4—1722no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1722no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1722no—
577C2×C4—1724no—
578C2×C4—1724no—
579C2×C4—1724no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4#1306329812yes—
589C2×C4#1306330712yes—
590C2×C4#1306331012yes—
591C2×C4#1306331014yes—
592C2×C4#1306331114yes—
593C2×C4#1306331914yes—
594C2×C4#1306332014yes—
595C2×C4C2×D4×D4311yescharacteristic
596C2×C4C2×#1062190011yescharacteristic
597C2×C4C2×#1062189811yescharacteristic
598C2×C4C2×#1062189811yescharacteristic
599C2×C4C2×#1062189811yescharacteristic
600C2×C4C2×#1062190211yescharacteristic
601C8—42no—
602C8—864no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—862no—
610C22—862no—
611C22—862no—
612C22—862no—
613C22—862no—
614C22—862no—
615C22—17216no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22—1721no—
623C22—1721no—
624C22#1458282814yes—
625C22C2×#1306329811yescharacteristic
626C22C2×#1306330711yescharacteristic
627C22C2×#1306331011yescharacteristic
628C22AGL(1,ℤ/8)×D4311yescharacteristic
629C22#137×D4311yescharacteristic
630C22#1458369511yescharacteristic
631C22#1458369811yescharacteristic
632C4—81no—
633C4—81no—
634C4—82no—
635C4—3442no—
636C4—3441no—
637C4—3441no—
638C4—1721no—
639C4—1721no—
640C4#1458282814yes—
641C4C2×#1306331011yescharacteristic
642C4C2×#1306331111yescharacteristic
643C4C2×#1306331911yescharacteristic
644C4C2×#1306332011yescharacteristic
645C2—24no—
646C2—1722no—
647C2—1722no—
648C2C2×#1458282811yescharacteristic
649C2#1914421711yescharacteristic
650C2#1914422811yescharacteristic
651C2#1914452111yescharacteristic
652C2#1914452911yescharacteristic
653C2#1914453311yescharacteristic
654C2#1914454111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#1736D43
hypocenterC43#23642
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C2×#14582942C2semidirect
5. #19136034C2semidirect
6. #19136033C2semidirect
7. #19136027C2semidirect
8. #19136022C2semidirect
9. #19134315C2semidirect
10. #19134314C2semidirect
11. C43×#1736C2semidirect
18. C2×#13063258C22semidirect
19. C2×#13063256C22semidirect
36. #14582662C22semidirect
37. #14582662C22semidirect
38. #14582661C22semidirect
39. #14582661C22semidirect
43. C43×#340C22semidirect
44. C43×#340C22semidirect
328. #1736D43semidirect
370. #340C2×D43semidirect
371. #340C2×D43semidirect
372. C43#23642semidirect

Maximal subgroups

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

subgroupindex
C2×#145829422
C2×#145828622
#191369742
C2×#145827562
#191360342
#191360332
#191360272
#191360222
#191343152
#191343142
C43×#17362
#2364243