Finite Group Databasebeta

← #25105639

Subgroups — #25105639

Order 11008.

1590 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583411C211yesmaximal, characteristic
2C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
3#380×D43C211yesmaximal, characteristic, complemented
4#19135022C212yesmaximal, complemented
5#19135017C212yesmaximal, complemented
6#19134911C212yesmaximal, complemented
7#19134901C212yesmaximal, complemented
8#19134690C211yesmaximal, characteristic, complemented
9#19134536C211yesmaximal, characteristic, complemented
10#19134533C211yesmaximal, characteristic, complemented
11C43×#1825C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×C8×D43C2212yes—
15#14583411—24no—
16#14583411C418yescomplemented
17C2×#13063309—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063300C2211yescharacteristic
21C2×#13063300C2211yescharacteristic
22C2×#13063295—21no—
23C2×C4×D172—21no—
24C2×C4×D172—21no—
25C2×C4⋊C4×D43C2212yes—
26C2×C22⋊C4×D43—21no—
27C2×#13063250C2212yescomplemented
28C2×#13063248C2212yescomplemented
29C2×#13063247C2212yescomplemented
30C2×#13063245C2212yescomplemented
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×(C2×D43)⋊C8C2212yes—
33C22⋊C8×D43—24no—
34#14582759C2211yescharacteristic
35#14582758—21no—
36#14582757—21no—
37#14582756C2212yes—
38#95×D43—21no—
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C2×#117×C43C2211yescharacteristic
42C2×C22⋊C8×C43C2211yescharacteristic
43C43×#380C2211yescharacteristic
44C43×#340C2212yescomplemented
45C43×#340C2212yescomplemented
46C24×D43D411yescharacteristic
47C2×#10621898—22no—
48C2×#10621898—42no—
49C2×#10621898—42no—
50C2×#10621898C2×C414yescomplemented
51C22×Dic86C2311yescharacteristic
52C22×D172—21no—
53C22×D172—21no—
54C22×D172C2311yescharacteristic
55C22×C22⋊D43—21no—
56C23×Dic43D411yescharacteristic
57C22×C4×D43—21no—
58C22×C4×D43—22no—
59C22×C4×D43—42no—
60C22×C4×D43—42no—
61C22×C4×D43C2×C414yes—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D414yes—
65C22×C4×D43C2311yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C22×C43⋊C8C2312yes—
68C2×C8×D43—24no—
69C2×C8×D43—42no—
70C2×C8×D43—42no—
71#13063309—28no—
72#13063305—22no—
73#13063305—22no—
74#13063305C2×C414yes—
75#13063305C2×C414yescomplemented
76#13063300—22no—
77#13063300—22no—
78#13063300C2×C414yes—
79#13063300C2×C414yescomplemented
80#13063295—28no—
81C4×D172—28no—
82C4×D172—28no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2312yes—
86C2×Dic43⋊C4—22no—
87C4⋊C4×D43—42no—
88C4⋊C4×D43—42no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—22no—
95C22⋊C4×D43—44no—
96#13063250—42no—
97#13063248—42no—
98#13063247—42no—
99#13063245—42no—
100C22⋊(C43⋊C8)—22no—
101(C2×D43)⋊C8—24no—
102C43⋊#95—21no—
103C43⋊#95—22no—
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43C2312yes—
106#117×C43—22no—
107#117×C43C2×C414yescomplemented
108C2×C4⋊C4×C43C2312yes—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114C22⋊C8×C43—22no—
115#95×C43—21no—
116C24×C43C2×D411yescharacteristic
117C23×D43—24no—
118C23×D43—22no—
119C23×D43—22no—
120C23×D43—21no—
121C23×D43—42no—
122C23×D43C22⋊C414yes—
123C23×D43C2×D411yescharacteristic
124C23×D43C2×D411yescharacteristic
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—44no—
136C22×Dic43—21no—
137C22×Dic43—22no—
138C22×Dic43—42no—
139C22×Dic43C22⋊C414yes—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142#10621898—44no—
143#10621898—44no—
144#10621898—48no—
145C2×D172—21no—
146C2×D172—24no—
147C2×D172—24no—
148C2×D172—22no—
149C2×D172—22no—
150C2×D172—44no—
151C2×D172—42no—
152C2×D172—42no—
153C2×D172C22×C412yes—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—24no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—44no—
162C2×C4×D43—44no—
163C2×C4×D43—44no—
164C2×C4×D43—44no—
165C2×C4×D43—48no—
166C2×C4×D43—44no—
167C2×C4×D43—44no—
168C2×C4×D43C22⋊C414yes—
169C2×C4×D43C22⋊C414yes—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C22×C412yes—
172C2×C4×D43C2×D412yes—
173C2×C4×D43C2×D412yes—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—21no—
177C2×Dic86C22×C412yes—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43C22×C412yes—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—24no—
188C22⋊C4×C43—42no—
189C42×C43—24no—
190C22⋊Dic43—42no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—44no—
196C4⋊Dic43—24no—
197C4⋊Dic43—24no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200Dic43⋊C4—44no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C8×D43—48no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43C2×C22⋊C412yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—28no—
217C22×D43—28no—
218C22×D43—22no—
219C22×D43—44no—
220C22×D43—48no—
221C22×D43—48no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43C2×C22⋊C412yes—
227C22×D43C2×C22⋊C412yes—
228C22×D43#13514yes—
229C22×D43AGL(1,ℤ/8)12yes—
230C22×D43#13712yes—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43C2×C22⋊C412yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43H(5,𝔽2)12yes—
247C2×C4×C43H(5,𝔽2)12yes—
248C22⋊D43—48no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—44no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43C2×C22⋊C412yes—
258C2×Dic43C2×C22⋊C412yes—
259D172—22no—
260D172—22no—
261D172—48no—
262D172—48no—
263D172—42no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—24no—
269C4×D43—24no—
270C4×D43—44no—
271C4×D43—44no—
272C4×D43—48no—
273C4×D43—88no—
274Dic86—22no—
275Dic86—22no—
276Dic86—42no—
277C8×C43—42no—
278C43⋊C8—42no—
279#21763—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43C22×C22⋊C411yescharacteristic
286C22×C43#53412yes—
287C22×C43C2×#13512yes—
288C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C43C2×#13711yescharacteristic
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43—24no—
297C2×D43—24no—
298C2×D43—416no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—82no—
303C2×D43—82no—
304C2×D43#41614yes—
305C2×D43#41714yes—
306C4×C43—22no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—82no—
310C4×C43#51811yescharacteristic
311C4×C43#51811yescharacteristic
312C4×C43#53412yes—
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—82no—
317C2×#525—431no—
318C22×C22⋊C8—431no—
319C2×#380—431no—
320#1893—432no—
321#1892—432no—
322#1874—432no—
323#1872—432no—
324#1825—431no—
325#1825D4311yescharacteristic, complemented
326#1788—431no—
327#1788—431no—
328C2×C43—42no—
329C2×C43#230811yescharacteristic
330C2×C43C2×#41611yescharacteristic
331C2×C43C2×#41711yescharacteristic
332C2×C43#318812yes—
333C2×C43#319012yes—
334D43—24no—
335D43—24no—
336D43—82no—
337C22×#41—431no—
338C24×C4—431no—
339C23×C8—432no—
340#525—438no—
341#525—864no—
342C2×#123—861no—
343C2×C22⋊Q8—431no—
344C2×C22⋊Q8—431no—
345C2×#121—431no—
346C2×#121—431no—
347C2×#120—861no—
348C2×C4×D4—861no—
349C2×C4×D4—861no—
350C2×#117C2×D4311yescharacteristic
351C22×C4⋊C4—432no—
352C22×C22⋊C4—861no—
353C2×#103—432no—
354C2×#103—432no—
355C2×#102—432no—
356C2×#102—432no—
357C2×C22⋊C8—431no—
358C2×C22⋊C8—432no—
359C2×C22⋊C8—864no—
360C2×C22⋊C8C2×D4311yescharacteristic
361#380—431no—
362#380—432no—
363#380—861no—
364#380—861no—
365#380C2×D4311yescharacteristic
366C2×#95—861no—
367#340—432no—
368#340—432no—
369#340C2×D4312yescomplemented
370#340C2×D4312yescomplemented
371C43#2176311yescharacteristic, complemented, Sylow
372C25—431no—
373C2×#41—434no—
374C2×#41—862no—
375C2×#41—1722no—
376C2×#41—1722no—
377C22×Q8—431no—
378C22×D4—431no—
379C22×D4—861no—
380C22×D4—861no—
381C22×D4—861no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—431no—
385C23×C4—434no—
386C23×C4—431no—
387C23×C4—431no—
388C23×C4—434no—
389C23×C4—862no—
390C23×C4—861no—
391C23×C4—1722no—
392C23×C4—1722no—
393C23×C4C22×D4311yescharacteristic
394C22×C8—432no—
395C22×C8—864no—
396C22×C8—1722no—
397C22×C8—1722no—
398C22×C8C22×D4312yes—
399#123—868no—
400C22⋊Q8—434no—
401C22⋊Q8—434no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404#121—434no—
405#121—434no—
406#121—862no—
407#121—862no—
408#120—868no—
409C4×D4—868no—
410C4×D4—868no—
411#117—22no—
412#117C4×D4314yescomplemented
413C2×C4⋊C4—432no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—1722no—
418C2×C4⋊C4—1722no—
419C2×C4⋊C4C22×D4312yes—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—1724no—
431C2×C42—21no—
432#103—1722no—
433#103—1722no—
434#102—1722no—
435#102—1722no—
436C22⋊C8—22no—
437C22⋊C8—864no—
438C22⋊C8—862no—
439#95—21no—
440#95—862no—
441#95—861no—
442C24—431no—
443C24—431no—
444C24—434no—
445C24—862no—
446C24—864no—
447C24—862no—
448C24—861no—
449C24—1722no—
450C24D4×D4311yescharacteristic
451#41—1724no—
452#41—1724no—
453#41—1728no—
454C2×Q8—432no—
455C2×Q8—861no—
456C2×Q8—862no—
457C2×Q8—862no—
458C2×D4—432no—
459C2×D4—864no—
460C2×D4—864no—
461C2×D4—864no—
462C2×D4—861no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—1724no—
466C2×D4—1722no—
467C2×D4—1722no—
468C2×D4—1724no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—434no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—434no—
482C22×C4—434no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—861no—
488C22×C4—864no—
489C22×C4—862no—
490C22×C4—1724no—
491C22×C4—1724no—
492C22×C4—1728no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1724no—
496C22×C4—1724no—
497C22×C4—1724no—
498C22×C4—1724no—
499C22×C4—1722no—
500C22×C4C2×C4×D4312yes—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4312yes—
503C22×C4C23×D4311yescharacteristic
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—862no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8—1728no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—864no—
516C4⋊C4—864no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—1724no—
520C4⋊C4C2×C4×D4312yes—
521C4⋊C4C2×C4×D4312yes—
522C22⋊C4—24no—
523C22⋊C4—42no—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—864no—
527C22⋊C4—864no—
528C22⋊C4—1724no—
529C22⋊C4—1722no—
530C42—24no—
531C23—22no—
532C23—21no—
533C23—21no—
534C23—22no—
535C23—432no—
536C23—432no—
537C23—434no—
538C23—432no—
539C23—432no—
540C23—868no—
541C23—868no—
542C23—862no—
543C23—861no—
544C23—861no—
545C23—862no—
546C23—862no—
547C23—862no—
548C23—1724no—
549C23—1728no—
550C23—1728no—
551C23—1722no—
552C23—1721no—
553C23—1721no—
554C23—1722no—
555C23C22⋊C4×D4312yes—
556C23C2×D4×D4311yescharacteristic
557Q8—862no—
558Q8—862no—
559Q8—1722no—
560D4—862no—
561D4—862no—
562D4—1728no—
563D4—1728no—
564D4—1728no—
565D4—1722no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—432no—
579C2×C4—432no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—864no—
587C2×C4—864no—
588C2×C4—862no—
589C2×C4—3448no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1728no—
593C2×C4—1724no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4C22⋊C4×D4312yes—
599C2×C4C22×C4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4#1306337112yes—
602C2×C4#1306337112yes—
603C8—42no—
604C8—1722no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—42no—
609C22—42no—
610C22—434no—
611C22—434no—
612C22—862no—
613C22—862no—
614C22—864no—
615C22—864no—
616C22—864no—
617C22—864no—
618C22—862no—
619C22—862no—
620C22—3442no—
621C22—3442no—
622C22—17216no—
623C22—1722no—
624C22—1722no—
625C22—1722no—
626C22C2×C22⋊C4×D4311yescharacteristic
627C22#1458346012yes—
628C22#135×D4312yes—
629C22AGL(1,ℤ/8)×D4311yescharacteristic
630C22#137×D4311yescharacteristic
631C4—22no—
632C4—42no—
633C4—42no—
634C4—82no—
635C4—862no—
636C4—862no—
637C4—3442no—
638C4—1722no—
639C4#1458337311yescharacteristic
640C4#1458337311yescharacteristic
641C4#1458346012yes—
642C2—42no—
643C2—864no—
644C2—864no—
645C2—3442no—
646C2#1913717211yescharacteristic
647C2#416×D4311yescharacteristic
648C2#417×D4311yescharacteristic
649C2#1914536412yes—
650C2#1914538012yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1825C2
socleC23×C43C22×D4
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenter#1825D43
hypocenterC43#21763
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D43C2semidirect
3. #380×D43C2semidirect
4. #19135022C2semidirect
5. #19135017C2semidirect
6. #19134911C2semidirect
7. #19134901C2semidirect
8. #19134690C2semidirect
9. #19134536C2semidirect
10. #19134533C2semidirect
11. C43×#1825C2semidirect
16. #14583411C4semidirect
27. C2×#13063250C22semidirect
28. C2×#13063248C22semidirect
29. C2×#13063247C22semidirect
30. C2×#13063245C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
44. C43×#340C22semidirect
45. C43×#340C22semidirect
50. C2×#10621898C2×C4semidirect
75. #13063305C2×C4semidirect
79. #13063300C2×C4semidirect
107. #117×C43C2×C4semidirect
325. #1825D43semidirect
369. #340C2×D43semidirect
370. #340C2×D43semidirect
371. C43#21763semidirect
412. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834112
C2×C22⋊C8×D432
#380×D432
#191350222
#191350172
#191349112
#191349012
#191346902
#191345362
#191345332
C43×#18252
#2176343