Finite Group Databasebeta

← #25130900

Subgroups — #25130900

Order 11008.

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×#14583447C211yesmaximal, characteristic, complemented
2C2×#14583179C211yesmaximal, characteristic, complemented
3C4×#13063296C211yesmaximal, characteristic, complemented
4#19135775C212yesmaximal, complemented
5#19135590C212yesmaximal, complemented
6#19135546C211yesmaximal, characteristic, complemented
7#19135523C211yesmaximal, characteristic, complemented
8#19134945C212yesmaximal, complemented
9#19134840C212yesmaximal, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C2×C43×#459C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13#14583447—24no—
14#14583447—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063312—21no—
17C2×#13063296—21no—
18C2×#13063296C2212yes—
19C2×#13063296C2211yescharacteristic
20C2×D4×Dic43—21no—
21C2×D4×Dic43C2212yes—
22C2×C4×C22⋊D43—21no—
23C2×C42×D43C2211yescharacteristic
24#14583179—24no—
25C2×#13063258C2212yes—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063246C2212yes—
28C2×#13063246C2212yes—
29C2×#13063246C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31#14582802C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582787—21no—
34#14582775—21no—
35#14582756C2211yescharacteristic
36C4×C4⋊Dic43C2211yescharacteristic
37C4×C22⋊Dic43—21no—
38#14582662C2212yes—
39#14582662C2212yes—
40#14582653C2212yes—
41C22×D8×C43C2212yes—
42C2×#127×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C43×#459—24no—
45C2×C4⋊C8×C43C2211yescharacteristic
46C2×#102×C43C2212yes—
47C2×#10621900—28no—
48C2×#10621900—44no—
49C2×#10621900—44no—
50C22×Dic86—21no—
51C22×C22⋊D43—21no—
52C22×C22⋊D43—22no—
53C23×Dic43—22no—
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C22×C4×D43C2311yescharacteristic
57C22×C43⋊C8C2312yes—
58#13063325—22no—
59#13063325D414yescomplemented
60#13063312—28no—
61#13063296—28no—
62#13063296—24no—
63#13063296—22no—
64#13063296—24no—
65#13063296—22no—
66D4×Dic43—28no—
67D4×Dic43—24no—
68D4×Dic43—24no—
69C4×C22⋊D43—44no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85C42×D43—22no—
86C42×D43—22no—
87#13063258—24no—
88C4⋊(C43⋊C8)—22no—
89#13063246—24no—
90#13063246—24no—
91#13063246—42no—
92(C2×D43)⋊C8—42no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C22×D4×C43—21no—
97C22×D4×C43—21no—
98C22×D4×C43C2312yes—
99C22×D4×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C2×D8×C43—24no—
102C2×D8×C43—24no—
103C2×D8×C43—42no—
104C22×C8×C43C2312yes—
105#127×C43—22no—
106#127×C43D414yescomplemented
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C42×C43C2311yescharacteristic
112C4⋊C8×C43—22no—
113#102×C43—24no—
114C24×C43—21no—
115C24×C43—22no—
116C23×D43C2×D411yescharacteristic
117C2×D4×C43—24no—
118C2×D4×C43—24no—
119C2×D4×C43—22no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—21no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43—42no—
132C2×D4×C43—42no—
133C2×D4×C43C2×D414yes—
134C2×D4×C43#4112yescomplemented
135C22×C4×C43—21no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—28no—
143C2×C22⋊D43—24no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—44no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—44no—
148C22×Dic43—28no—
149C22×Dic43—21no—
150C22×Dic43—22no—
151C22×Dic43—21no—
152C22×Dic43—44no—
153C22×Dic43—44no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157#10621900—432no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×C4×D43D814yescomplemented
170C2×Dic86—24no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173D8×C43—48no—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C22⋊C4×C43—42no—
180C42×C43C2×D412yes—
181C42×C43C2×D412yes—
182C22⋊Dic43—28no—
183C22⋊Dic43—28no—
184C22⋊Dic43—24no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187(C2×D43)⋊C4—42no—
188C4⋊Dic43—24no—
189C4⋊Dic43—22no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C2×D414yes—
194C4⋊Dic43#4112yescomplemented
195Dic43⋊C4—42no—
196C4×Dic43—22no—
197C4×Dic43—22no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—42no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C23×C43—24no—
205C23×C43—22no—
206C23×C43—41no—
207C23×C43—42no—
208C23×C43—41no—
209C23×C43—42no—
210C23×C43—41no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43C22×D411yescharacteristic
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43C2×D812yes—
226D4×C43—22no—
227D4×C43—24no—
228D4×C43—24no—
229D4×C43—22no—
230D4×C43—48no—
231D4×C43—41no—
232D4×C43—42no—
233D4×C43—42no—
234D4×C43—41no—
235D4×C43—48no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—84no—
242C2×C4×C43#12012yes—
243C2×C4×C43#12012yes—
244C2×C4×C43C2×D812yes—
245C2×C4×C43AGL(1,ℤ/8)12yes—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C22⋊D43—416no—
253C22⋊D43—48no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—24no—
259C2×Dic43—22no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—416no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43C2×D812yes—
273C4×D43—28no—
274C4×D43—44no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279Dic86—48no—
280C8×C43—42no—
281C43⋊C8—42no—
282#24150—431nomaximal, Sylow
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—44no—
286C22×C43—42no—
287C22×C43—44no—
288C22×C43—44no—
289C22×C43—82no—
290C22×C43—82no—
291C22×C43—81no—
292C22×C43—82no—
293C22×C43—82no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43C2×#12011yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43#53711yescharacteristic
300C22×C43C22×D811yescharacteristic
301C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C43#57511yescharacteristic
303C22×C43#57511yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C4×C43—22no—
312C4×C43—81no—
313C4×C43#44714yes—
314C4×C43#54611yescharacteristic
315C4×C43#54711yescharacteristic
316C4×C43#54811yescharacteristic
317C4×C43#55011yescharacteristic
318Dic43—22no—
319Dic43—42no—
320Dic43—41no—
321Dic43—44no—
322Dic43—41no—
323Dic43—81no—
324C2×#532—431no—
325C2×#474—431no—
326C2×#459D4311yescharacteristic, complemented
327C4×#121—431no—
328#2033—432no—
329#1999—432no—
330#1988—431no—
331#1982—431no—
332#1879—432no—
333#1862—432no—
334#1797—431no—
335C2×C43—82no—
336C2×C43—84no—
337C2×C43#240711yescharacteristic
338C2×C43C2×#44711yescharacteristic
339C2×C43#300511yescharacteristic
340C2×C43#310011yescharacteristic
341C2×C43#311511yescharacteristic
342C2×C43#324511yescharacteristic
343C2×C43#325111yescharacteristic
344D43—42no—
345C22×#41—861no—
346C22×D8C2×D4312yes—
347#532—864no—
348#532—864no—
349C2×C4⋊Q8—431no—
350C2×#127C2×D4311yescharacteristic
351C2×#124—861no—
352C2×#121—432no—
353C2×#121—431no—
354C2×#121—861no—
355C2×C4×D4—432no—
356C2×C4×D4—861no—
357C2×C4×D4—861no—
358C2×C4×D4C2×D4311yescharacteristic
359C22×C42—431no—
360#474—864no—
361#459—24no—
362C2×#107—432no—
363C2×C4⋊C8—431no—
364C2×C4⋊C8C2×D4311yescharacteristic
365C2×#102—432no—
366C2×#102—432no—
367C2×#102—432no—
368C2×#102C2×D4312yes—
369C2×C22⋊C8—432no—
370#390—431no—
371#389—431no—
372#388—861no—
373#386—861no—
374#380—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—861no—
377#340—432no—
378#340—432no—
379#336—432no—
380C43#2415011yescharacteristic, complemented, Sylow
381C2×#41—868no—
382C2×#41—1724no—
383C2×#41—1724no—
384C22×Q8—861no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—861no—
388C22×D4—862no—
389C22×D4C22×D4311yescharacteristic
390C22×D4C22×D4312yes—
391C23×C4—21no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—862no—
396C2×D8—24no—
397C2×D8—24no—
398C2×D8—42no—
399C22×C8—432no—
400C22×C8C22×D4312yes—
401C4⋊Q8—434no—
402C4⋊Q8—862no—
403#127—22no—
404#127C22⋊D4314yescomplemented
405#124—868no—
406#121—864no—
407#121—862no—
408#121—868no—
409#121—862no—
410#121—864no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—864no—
414C4×D4—868no—
415C4×D4—864no—
416C4×D4—1724no—
417C2×C4⋊C4—432no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—862no—
434C2×C42—862no—
435C2×C42—861no—
436C2×C42C22×D4311yescharacteristic
437#107—864no—
438C4⋊C8—22no—
439C4⋊C8—862no—
440#102—24no—
441#102—864no—
442#102—864no—
443#102—1722no—
444C22⋊C8—1722no—
445#95—861no—
446#95—861no—
447#95—861no—
448C24—21no—
449C24—22no—
450C24—431no—
451#41—17232no—
452C2×Q8—864no—
453C2×Q8—1722no—
454C2×Q8—1722no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—868no—
472C2×D4—864no—
473C2×D4—1722no—
474C2×D4—1724no—
475C2×D4—1724no—
476C2×D4—1722no—
477C2×D4#1062190012yescomplemented
478C2×D4C2×C22⋊D4314yes—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—431no—
484C22×C4—434no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—868no—
490C22×C4—861no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—1721no—
501C22×C4—1721no—
502C22×C4—1724no—
503C22×C4—1724no—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507D8—48no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—862no—
512C2×C8—862no—
513C2×C8—862no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—434no—
517C4⋊C4—432no—
518C4⋊C4—864no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—1722no—
524C22⋊C4—42no—
525C22⋊C4—868no—
526C22⋊C4—868no—
527C22⋊C4—864no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C42—862no—
532C42—862no—
533C42—861no—
534C42—861no—
535C42—1722no—
536C42D4×D4312yes—
537C42C2×C22⋊D4312yes—
538C23—24no—
539C23—22no—
540C23—41no—
541C23—42no—
542C23—41no—
543C23—42no—
544C23—41no—
545C23—42no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—41no—
550C23—42no—
551C23—41no—
552C23—432no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23C2×D4×D4311yescharacteristic
560Q8—1728no—
561D4—22no—
562D4—22no—
563D4—24no—
564D4—24no—
565D4—48no—
566D4—42no—
567D4—41no—
568D4—42no—
569D4—48no—
570D4—41no—
571D4—17216no—
572D4—1728no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—84no—
579C2×C4—432no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—868no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—864no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—1724no—
592C2×C4—17216no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4#1306329312yes—
605C2×C4#1306329312yes—
606C2×C4D8×D4312yes—
607C2×C4#1306334912yes—
608C2×C4C2×D4×D4311yescharacteristic
609C2×C4C22×C22⋊D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4C2×#1062190011yescharacteristic
612C2×C4#1306337011yescharacteristic
613C2×C4#1306337211yescharacteristic
614C8—42no—
615C8—1722no—
616C22—42no—
617C22—44no—
618C22—42no—
619C22—44no—
620C22—42no—
621C22—44no—
622C22—82no—
623C22—81no—
624C22—82no—
625C22—81no—
626C22—81no—
627C22—82no—
628C22—81no—
629C22—82no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22C2×#1306329311yescharacteristic
638C22#1458340911yescharacteristic
639C22#1458347811yescharacteristic
640C22C2×D8×D4311yescharacteristic
641C22C2×#1306334911yescharacteristic
642C22#1458369511yescharacteristic
643C22#1458369511yescharacteristic
644C4—22no—
645C4—81no—
646C4—862no—
647C4—3441no—
648C4—1724no—
649C4—1721no—
650C4—1722no—
651C4—1721no—
652C4#1458303114yes—
653C4#1458354311yescharacteristic
654C4#1458354811yescharacteristic
655C4#1458355511yescharacteristic
656C4#1458356711yescharacteristic
657C2—82no—
658C2—84no—
659C2—1722no—
660C2#1913793611yescharacteristic
661C2C2×#1458303111yescharacteristic
662C2#1914383411yescharacteristic
663C2#1914459411yescharacteristic
664C2#1914474311yescharacteristic
665C2#1914590311yescharacteristic
666C2#1914595311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#459C2
socleC23×C43C22×D4
hypercenterC2×#459D43
hypocenterC43#24150
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#14583447C2semidirect
2. C2×#14583179C2semidirect
3. C4×#13063296C2semidirect
4. #19135775C2semidirect
5. #19135590C2semidirect
6. #19135546C2semidirect
7. #19135523C2semidirect
8. #19134945C2semidirect
9. #19134840C2semidirect
10. #19134572C2semidirect
11. C2×C43×#459C2semidirect
59. #13063325D4semidirect
106. #127×C43D4semidirect
134. C2×D4×C43#41semidirect
169. C2×C4×D43D8semidirect
194. C4⋊Dic43#41semidirect
326. C2×#459D43semidirect
380. C43#24150semidirect
404. #127C22⋊D43semidirect
477. C2×D4#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145834472
C2×#145831792
C4×#130632962
#191357752
#191355902
#191355462
#191355232
#191349452
#191348402
#191345722
C2×C43×#4592
#2415043