Finite Group Databasebeta

← #25245438

Subgroups — #25245438

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621898C211yesmaximal, characteristic
2C2×#14583110C211yesmaximal, characteristic, complemented
3C2×#14583105C211yesmaximal, characteristic, complemented
4C2×#14583063C212yesmaximal
5#19142947C211yesmaximal, characteristic, complemented
6#19134935C212yesmaximal, complemented
7#19134928C212yesmaximal, complemented
8#19134905C212yesmaximal, complemented
9#19134601C211yesmaximal, characteristic, complemented
10#19134596C211yesmaximal, characteristic, complemented
11C43×#1797C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×Dic172C2212yes—
14C22×#10621873C2212yes—
15C2×#13063325C2211yescharacteristic
16C2×#13063304C2212yes—
17C4×#10621898—24no—
18C4×#10621898—24no—
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×C22⋊D43—21no—
24C2×C4×C22⋊D43—21no—
25C2×#13063284C2211yescharacteristic
26C2×#13063282—21no—
27C2×C42×D43—21no—
28#14583110—24no—
29#14583105—24no—
30#14583063—28no—
31C2×#13063250C2212yes—
32C2×#13063250C2212yes—
33C2×#13063250C2212yes—
34C2×#13063247C2212yes—
35#14582805C2212yes—
36#14582797—21no—
37#14582797—21no—
38#14582769C2211yescharacteristic
39#14582759—21no—
40#14582759—21no—
41#14582662C2212yes—
42#14582662C2212yes—
43C22×C42×C43C2211yescharacteristic
44C2×C4⋊C8×C43C2211yescharacteristic
45C2×C4⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2212yes—
47C43×#336C2212yes—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898D414yes—
54C22×Dic86C2312yes—
55C22×Dic86C2311yescharacteristic
56C22×D172C2311yescharacteristic
57C22×C22⋊D43—21no—
58C22×C4×D43—21no—
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C2×Dic172—24no—
62C2×Dic172—24no—
63C2×Dic172—24no—
64C2×#10621873—24no—
65C2×#10621873—24no—
66C2×#10621873—24no—
67#13063325—22no—
68#13063325—22no—
69#13063304—24no—
70#13063304—24no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C4×Dic86D414yes—
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—22no—
78C4×D172D414yes—
79C4×C22⋊D43—28no—
80C4×C22⋊D43—28no—
81#13063284—22no—
82#13063284—22no—
83#13063282—28no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2312yes—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—22no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—22no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C42×D43—28no—
102#13063250—24no—
103#13063250—24no—
104#13063250—24no—
105#13063247—24no—
106C43⋊#95—22no—
107C43⋊#95—22no—
108C23×C4×C43D411yescharacteristic
109C23×C4×C43D411yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C22×C8×C43C2312yes—
112C22×C8×C43C2312yes—
113C2×C42×C43—22no—
114C2×C42×C43—22no—
115C2×C42×C43D411yescharacteristic
116C2×C42×C43D411yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C4⋊C8×C43—22no—
120C4⋊C8×C43—22no—
121C22⋊C8×C43—24no—
122C24×C43C2×D411yescharacteristic
123C23×D43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—41no—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43#4112yes—
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—24no—
143C2×C22⋊D43—24no—
144C2×C22⋊D43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150#10621898—28no—
151#10621898—28no—
152#10621898—28no—
153#10621898—28no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C2×D412yes—
158C2×D172C2×D412yes—
159C2×D172#4112yes—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—24no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86C2×D412yes—
179C2×Dic86C2×D412yes—
180C2×Dic86#4112yes—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C2×C8×C43—22no—
186C2×C8×C43—22no—
187C42×C43—22no—
188C42×C43—22no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C2×D412yes—
192C42×C43C2×D412yes—
193C22⋊Dic43—24no—
194C22⋊Dic43—44no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—24no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—42no—
202C4⋊Dic43—42no—
203C4⋊Dic43—42no—
204C4⋊Dic43—42no—
205C4⋊Dic43C2×D412yes—
206C4⋊Dic43C2×D412yes—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209Dic43⋊C4—44no—
210C4×Dic43—24no—
211C4×Dic43—24no—
212C4×Dic43—24no—
213Dic172—48no—
214#10621873—48no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43#12112yes—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—44no—
244C2×C4×C43—44no—
245C2×C4×C43#12012yes—
246C2×C4×C43#12012yes—
247C2×C4×C43#12112yes—
248C2×C4×C43#13512yes—
249C2×C4×C43#13712yes—
250C2×C4×C43#13712yes—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C22⋊D43—216no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273D172—22no—
274D172—22no—
275D172—22no—
276D172#12114yes—
277C4×D43—216no—
278C4×D43—48no—
279C4×D43—48no—
280Dic86—22no—
281Dic86—22no—
282Dic86—22no—
283Dic86—42no—
284Dic86—42no—
285Dic86—42no—
286Dic86—42no—
287Dic86#12114yes—
288C8×C43—42no—
289C8×C43—42no—
290#32907—431nomaximal, Sylow
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43C2×#12011yescharacteristic
299C22×C43C2×#12111yescharacteristic
300C22×C43#52511yescharacteristic
301C22×C43C2×#13511yescharacteristic
302C22×C43C2×#13711yescharacteristic
303C22×C43C2×#13711yescharacteristic
304C22×C43#57511yescharacteristic
305C2×D43—24no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—22no—
315C4×C43—41no—
316C4×C43#45214yescomplemented
317C4×C43C2×#12111yescharacteristic
318C4×C43C2×#12111yescharacteristic
319C4×C43#52511yescharacteristic
320C4×C43#52511yescharacteristic
321Dic43—24no—
322Dic43—42no—
323Dic43—42no—
324Dic43—82no—
325Dic43—82no—
326C2×C4×#41—431no—
327C2×#462—431no—
328C2×#461—431no—
329C2×#452—432no—
330#2857—431no—
331#1878—432no—
332#1877—432no—
333#1873—432no—
334#1803—431no—
335#1802—431no—
336#1797D4311yescharacteristic, complemented
337C2×C43—42no—
338C2×C43#284711yescharacteristic
339C2×C43C2×#45211yescharacteristic
340C2×C43#300711yescharacteristic
341C2×C43#303511yescharacteristic
342C2×C43#303911yescharacteristic
343C2×C43#310711yescharacteristic
344C2×C43#311611yescharacteristic
345D43—44no—
346C22×#41—431no—
347C22×Q16—432no—
348C22×SD16—432no—
349C2×C4⋊Q8—431no—
350C2×C22⋊Q8—432no—
351C4×#41—864no—
352C4×#41—864no—
353C2×C4×Q8—431no—
354C2×C4×Q8—431no—
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4—861no—
358C2×C4×D4—861no—
359C2×#117—431no—
360C2×#117—861no—
361C22×C42—861no—
362C22×C42C2×D4311yescharacteristic
363#462—864no—
364#461—864no—
365#452—868no—
366C2×C4⋊C8C2×D4311yescharacteristic
367C2×C4⋊C8C2×D4311yescharacteristic
368C2×#103—432no—
369C2×#103—432no—
370C2×#103—432no—
371C2×#102—432no—
372C2×C22⋊C8C2×D4312yes—
373#391—432no—
374#389—861no—
375#389—861no—
376#384—431no—
377#380—861no—
378#380—861no—
379#340—432no—
380#340—432no—
381#336C2×D4312yes—
382C43#3290711yescharacteristic, complemented, Sylow
383C2×#41—434no—
384C2×#41—862no—
385C2×#41—862no—
386C2×#41—862no—
387C2×#41—862no—
388C2×#41—862no—
389C22×Q8—431no—
390C22×Q8—432no—
391C22×D4—431no—
392C22×D4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C23×C4—861no—
396C23×C4D17211yescharacteristic
397C23×C4D17211yescharacteristic
398C23×C4C22×D4311yescharacteristic
399C2×Q16—864no—
400C2×Q16—864no—
401C2×Q16—864no—
402C2×SD16—864no—
403C2×SD16—864no—
404C2×SD16—864no—
405C22×C8C22×D4312yes—
406C22×C8C22×D4312yes—
407C4⋊Q8—862no—
408C4⋊Q8—862no—
409C22⋊Q8—864no—
410C22⋊Q8—864no—
411C4×Q8—434no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×D4—434no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—868no—
419C4×D4—868no—
420C4×D4—862no—
421#117—868no—
422#117—862no—
423#117—862no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—862no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—868no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42D17211yescharacteristic
445C2×C42D17211yescharacteristic
446C2×C42C22×D4311yescharacteristic
447C2×C42C22×D4311yescharacteristic
448C4⋊C8—22no—
449C4⋊C8—22no—
450#103—864no—
451#103—864no—
452#103—864no—
453#102—864no—
454C22⋊C8—24no—
455#95—862no—
456#95—862no—
457C24—861no—
458C24C2×D17211yescharacteristic
459#41—868no—
460#41—868no—
461#41—868no—
462#41—868no—
463C2×Q8—432no—
464C2×Q8—432no—
465C2×Q8—432no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8—862no—
473C2×Q8—862no—
474C2×Q8—862no—
475C2×D4—432no—
476C2×D4—432no—
477C2×D4—432no—
478C2×D4—864no—
479C2×D4—864no—
480C2×D4—864no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—41no—
494C22×C4—864no—
495C22×C4—864no—
496C22×C4—864no—
497C22×C4—861no—
498C22×C4—864no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—864no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4C2×D17211yescharacteristic
509C22×C4C2×D17211yescharacteristic
510C22×C4C2×D17211yescharacteristic
511C22×C4C2×D17211yescharacteristic
512C22×C4C2×D17211yescharacteristic
513C22×C4D4×D4312yes—
514C22×C4#1062190212yes—
515C22×C4C23×D4311yescharacteristic
516Q16—1728no—
517SD16—1728no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C4⋊C4—432no—
525C4⋊C4—432no—
526C4⋊C4—864no—
527C4⋊C4—864no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1724no—
536C4⋊C4—1722no—
537C22⋊C4—864no—
538C22⋊C4—864no—
539C22⋊C4—864no—
540C22⋊C4—1724no—
541C42—22no—
542C42—22no—
543C42—21no—
544C42—21no—
545C42—864no—
546C42—864no—
547C42—864no—
548C42D4×D4312yes—
549C42D4×D4312yes—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—862no—
557C23—862no—
558C23—862no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23#1306330012yes—
564C23C22×D17211yescharacteristic
565Q8—434no—
566Q8—862no—
567Q8—862no—
568Q8—862no—
569Q8—1722no—
570Q8—1722no—
571Q8—1722no—
572Q8—1722no—
573D4—434no—
574D4—8616no—
575D4—862no—
576D4—862no—
577D4—862no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—8616no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—1728no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1728no—
611C2×C4#1306329512yes—
612C2×C4#1306329512yes—
613C2×C4#1306330012yes—
614C2×C4#1306334712yes—
615C2×C4#1306335812yes—
616C2×C4#1306335812yes—
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4C2×#1062190211yescharacteristic
623C8—42no—
624C8—42no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—864no—
633C22—1722no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22—1722no—
638C22—1722no—
639C22C2×#1306329511yescharacteristic
640C22C2×#1306330011yescharacteristic
641C22#1458341111yescharacteristic
642C22C2×#1306334711yescharacteristic
643C22C2×#1306335811yescharacteristic
644C22C2×#1306335811yescharacteristic
645C22#1458369911yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—41no—
650C4—864no—
651C4—3442no—
652C4—3442no—
653C4—1722no—
654C4—1722no—
655C4#1458306314yescomplemented
656C4#121×D4311yescharacteristic
657C4#121×D4311yescharacteristic
658C4#1458341211yescharacteristic
659C4#1458341211yescharacteristic
660C2—42no—
661C2—1724no—
662C2#1914287811yescharacteristic
663C2C2×#1458306311yescharacteristic
664C2#1914385711yescharacteristic
665C2#1914405211yescharacteristic
666C2#1914408311yescharacteristic
667C2#1914466711yescharacteristic
668C2#1914475811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1797C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenter#1797D43
hypocenterC43#32907
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#14583110C2semidirect
3. C2×#14583105C2semidirect
5. #19142947C2semidirect
6. #19134935C2semidirect
7. #19134928C2semidirect
8. #19134905C2semidirect
9. #19134601C2semidirect
10. #19134596C2semidirect
11. C43×#1797C2semidirect
316. C4×C43#452semidirect
336. #1797D43semidirect
382. C43#32907semidirect
655. C4#14583063semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106218982
C2×#145831102
C2×#145831052
C2×#145830632
#191429472
#191349352
#191349282
#191349052
#191346012
#191345962
C43×#17972
#3290743