Finite Group Databasebeta

← #25196567

Subgroups — #25196567

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142946C211yesmaximal, characteristic, complemented
2C4×#13063300C211yesmaximal, characteristic
3#19136161C211yesmaximal, characteristic, complemented
4#19136125C211yesmaximal, characteristic, complemented
5#19135927C211yesmaximal, characteristic, complemented
6#19135730C211yesmaximal, characteristic, complemented
7#19135180C211yesmaximal, characteristic, complemented
8#19135022C211yesmaximal, characteristic
9#19135022C211yesmaximal, characteristic
10#19134859C211yesmaximal, characteristic, complemented
11#19134855C211yesmaximal, characteristic, complemented
12#19134619C211yesmaximal, characteristic, complemented
13#19134617C211yesmaximal, characteristic, complemented
14#336×D43C211yesmaximal, characteristic, complemented
15C43×#1920C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063303—21no—
20C2×#13063300C2211yescharacteristic
21C2×C4×D172—21no—
22C2×C4×D172C2211yescharacteristic
23C2×C42×D43C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31#14582803—21no—
32#14582800C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582794—21no—
36#14582791—21no—
37#14582777—21no—
38#14582768C2211yescharacteristic
39#14582758—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4×(C2×D43)⋊C4—21no—
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C2×C8×D43—22no—
69C2×C8×D43—22no—
70C2×C8×D43—22no—
71C2×C8×D43—22no—
72C2×C8×D43—41no—
73C2×C8×D43—41no—
74#13063324—41no—
75#13063324—41no—
76#13063303—44no—
77#13063300—22no—
78#13063300Q814yescomplemented
79C4×D172—41no—
80C4×D172—41no—
81C4×D172—44no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—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—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C42×D43—41no—
101C42×D43—41no—
102#13063257—41no—
103#13063256—22no—
104#13063256—41no—
105#13063247—22no—
106#13063247—41no—
107#13063245—22no—
108#13063245—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#106×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C23×D43C2×D411yescharacteristic
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×D172—21no—
142C2×D172—24no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—42no—
148C2×D172—42no—
149C2×D172C2×Q812yes—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43SD1614yes—
163C2×C4×D43C2×Q812yes—
164C2×C4×D43#4112yes—
165C2×Dic86—42no—
166C2×Dic86—42no—
167C2×Dic86—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43#4112yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43C2×Q812yes—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—42no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8#4112yes—
214C8×D43—44no—
215C8×D43—44no—
216C23×C43C22×D411yescharacteristic
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—22no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43C22⋊Q812yes—
229C22×D43C2×SD1612yes—
230C22×D43AGL(1,ℤ/8)12yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C2×SD1612yes—
249C2×C4×C43C22×Q811yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43C22⋊Q812yes—
271C2×Dic43C2×SD1612yes—
272C2×Dic43#13512yes—
273D172—22no—
274D172—22no—
275D172—48no—
276D172—41no—
277D172—41no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—44no—
283C4×D43—44no—
284C4×D43—84no—
285Dic86—84no—
286C8×C43—22no—
287C8×C43—41no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290#29156—431nomaximal, Sylow
291C22×C43C2×C22⋊Q811yescharacteristic
292C22×C43#53211yescharacteristic
293C22×C43#53411yescharacteristic
294C22×C43C22×SD1611yescharacteristic
295C22×C43C2×#13511yescharacteristic
296C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C43#57511yescharacteristic
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43#47614yes—
312C4×C43—22no—
313C4×C43—41no—
314C4×C43—42no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43#55111yescharacteristic
319C4×C43#55111yescharacteristic
320C4×C43#55411yescharacteristic
321C4×C43#55411yescharacteristic
322Dic43—22no—
323Dic43—22no—
324Dic43—22no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328#2857—431no—
329C4×#121—431no—
330#2100—431no—
331#2094—431no—
332#2058—431no—
333#2023—431no—
334#1920—431no—
335#1920D4311yescharacteristic, complemented
336#1893—431no—
337#1893—431no—
338#1864—431no—
339#1864—431no—
340#1807—431no—
341#1807—431no—
342C2×#336—431no—
343C2×C43#256411yescharacteristic
344C2×C43C2×#47611yescharacteristic
345C2×C43#307611yescharacteristic
346C2×C43#316711yescharacteristic
347C2×C43#318011yescharacteristic
348C2×C43#318711yescharacteristic
349C2×C43#318811yescharacteristic
350D43—24no—
351D43—82no—
352C23×C8—431no—
353C23×C8—431no—
354C2×C4⋊Q8—431no—
355C2×C22⋊Q8—861no—
356C2×#121—431no—
357C2×C4×D4—431no—
358C2×C4×D4—861no—
359C22×C42—431no—
360C2×#106—431no—
361C2×#106—431no—
362C2×#106—431no—
363C2×#106C2×D4311yescharacteristic
364C2×#102—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368#391—861no—
369#390—431no—
370#389—431no—
371#389—431no—
372#389—861no—
373#389C2×D4311yescharacteristic
374#388—861no—
375#386—861no—
376#384—431no—
377#380—431no—
378#380—431no—
379#380—431no—
380#380—861no—
381C4×C4⋊C4C2×D4311yescharacteristic
382C4×C22⋊C4—861no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#340C2×D4311yescharacteristic
390#340C2×D4311yescharacteristic
391#336—431no—
392#336—431no—
393#336—431no—
394#336C2×D4311yescharacteristic
395C43#2915611yescharacteristic, complemented, Sylow
396C22×Q8—861no—
397C22×D4—431no—
398C22×D4—861no—
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—861no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—862no—
406C22×C8—862no—
407C22×C8—862no—
408C22×C8—862no—
409C22×C8—1721no—
410C22×C8—1721no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413C4⋊Q8—1721no—
414C4⋊Q8—1721no—
415C22⋊Q8—1724no—
416#121—434no—
417#121—862no—
418C4×D4—1721no—
419C4×D4—1721no—
420C4×D4—1724no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—1721no—
446C2×C42—1721no—
447C2×C42C22×D4311yescharacteristic
448#106—22no—
449#106—862no—
450#106—1721no—
451#106—1721no—
452#102—862no—
453#102—862no—
454#102—1721no—
455#102—1721no—
456#95—21no—
457#95—21no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463C24—431no—
464C24—861no—
465C2×Q8—1722no—
466C2×Q8—1722no—
467C2×Q8—1722no—
468C2×D4—432no—
469C2×D4—864no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—1722no—
476C2×D4—1722no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—434no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—1721no—
497C22×C4—1721no—
498C22×C4—1721no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—432no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—1724no—
517C2×C8—1724no—
518C2×C8#1062189812yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4Q8×D4312yes—
539C22⋊C4—864no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C42—21no—
547C42—21no—
548C42—42no—
549C42—861no—
550C42—861no—
551C42—1721no—
552C42—1721no—
553C23—432no—
554C23—432no—
555C23—432no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—862no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23C2×D4×D4311yescharacteristic
568Q8—3444no—
569D4—862no—
570D4—862no—
571D4—1728no—
572D4—1721no—
573D4—1721no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—3444no—
605C2×C4—1724no—
606C2×C4—1724no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4SD16×D4312yes—
617C2×C4C2×Q8×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4#1306337111yescharacteristic
622C2×C4#1306337111yescharacteristic
623C8—22no—
624C8—41no—
625C8—862no—
626C8—1721no—
627C22—434no—
628C22—862no—
629C22—862no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—862no—
634C22—3441no—
635C22—3441no—
636C22—3441no—
637C22—3441no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22C22⋊Q8×D4311yescharacteristic
642C22#1458344611yescharacteristic
643C22#1458346011yescharacteristic
644C22C2×SD16×D4311yescharacteristic
645C22#135×D4311yescharacteristic
646C22AGL(1,ℤ/8)×D4311yescharacteristic
647C22#1458369811yescharacteristic
648C4—22no—
649C4—41no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—862no—
655C4—862no—
656C4—862no—
657C4—3441no—
658C4—3441no—
659C4—3441no—
660C4#1458357311yescharacteristic
661C4#1458357411yescharacteristic
662C4#1458360511yescharacteristic
663C4#1458360911yescharacteristic
664C2—864no—
665C2—3442no—
666C2#1913977411yescharacteristic
667C2#476×D4311yescharacteristic
668C2#1914438211yescharacteristic
669C2#1914515111yescharacteristic
670C2#1914528911yescharacteristic
671C2#1914535111yescharacteristic
672C2#1914536411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1920D43
hypocenterC43#29156
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
1. #19142946C2semidirect
3. #19136161C2semidirect
4. #19136125C2semidirect
5. #19135927C2semidirect
6. #19135730C2semidirect
7. #19135180C2semidirect
10. #19134859C2semidirect
11. #19134855C2semidirect
12. #19134619C2semidirect
13. #19134617C2semidirect
14. #336×D43C2semidirect
15. C43×#1920C2semidirect
78. #13063300Q8semidirect
335. #1920D43semidirect
395. C43#29156semidirect

Maximal subgroups

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

subgroupindex
#191429462
C4×#130633002
#191361612
#191361252
#191359272
#191357302
#191351802
#191350222
#191348592
#191348552
#191346192
#191346172
#336×D432
C43×#19202
#2915643