Finite Group Databasebeta

← #25245431

Subgroups — #25245431

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×#10621902C211yesmaximal, characteristic
2C2×#14583101C211yesmaximal, characteristic, complemented
3C2×#14583060C212yesmaximal
4#19142942C211yesmaximal, characteristic, complemented
5#19134938C212yesmaximal, complemented
6#19134926C212yesmaximal, complemented
7#19134904C212yesmaximal, complemented
8#19134600C211yesmaximal, characteristic, complemented
9#19134596C211yesmaximal, characteristic, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C2×C43×#462C211yesmaximal, characteristic, complemented
12C22×#10621902C2211yescharacteristic
13C22×#10621884C2212yes—
14C2×#13063301C2212yes—
15C4×#10621902—24no—
16C4×#10621902—24no—
17C2×Q8×Dic43C2211yescharacteristic
18C2×C4×D172—21no—
19C2×C4×D172C2211yescharacteristic
20C2×#13063287—21no—
21C2×#13063287C2211yescharacteristic
22C2×#13063283—21no—
23C2×#13063283C2211yescharacteristic
24C2×C42×D43—21no—
25C2×C42×D43C2211yescharacteristic
26#14583101—24no—
27#14583060—28no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063249C2212yes—
30C2×#13063249C2212yes—
31C2×#13063247C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582806C2212yes—
34#14582795—21no—
35#14582795—21no—
36#14582769C2211yescharacteristic
37#14582756—21no—
38#14582756—21no—
39#14582662C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C22×Q16×C43C2212yes—
43C2×C4⋊Q8×C43C2211yescharacteristic
44C2×C4×Q8×C43C2211yescharacteristic
45C43×#462—24no—
46C2×C4⋊C8×C43C2211yescharacteristic
47C2×#103×C43C2212yes—
48C2×#10621902—22no—
49C2×#10621902—22no—
50C2×#10621902—22no—
51C2×#10621902—22no—
52C2×#10621902—22no—
53C2×#10621902D414yes—
54C22×D172—21no—
55C22×D172C2311yescharacteristic
56C22×C4×D43—21no—
57C22×C4×D43—21no—
58C22×C4×D43—21no—
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C2×#10621884—24no—
63C2×#10621884—24no—
64C2×#10621884—24no—
65C22×C43⋊C8C2312yes—
66#13063301—24no—
67#13063301—24no—
68Q8×Dic43—22no—
69Q8×Dic43—22no—
70C4×D172—28no—
71C4×D172—22no—
72C4×D172D414yes—
73#13063287—28no—
74#13063287—22no—
75#13063287—22no—
76#13063283—28no—
77#13063283—22no—
78#13063283—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2312yes—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—22no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—22no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C42×D43—28no—
95C42×D43—22no—
96C42×D43—22no—
97C4⋊(C43⋊C8)—22no—
98#13063249—24no—
99#13063249—24no—
100#13063247—24no—
101(C2×D43)⋊C8—24no—
102C43⋊#95—22no—
103C43⋊#95—22no—
104C22×Q8×C43C2312yes—
105C22×Q8×C43C2311yescharacteristic
106C2×Q16×C43—24no—
107C2×Q16×C43—24no—
108C2×Q16×C43—24no—
109C22×C8×C43C2312yes—
110C4⋊Q8×C43—22no—
111C4⋊Q8×C43—22no—
112C4×Q8×C43—22no—
113C4×Q8×C43D414yes—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C4⋊C8×C43—22no—
121#103×C43—24no—
122C23×D43—21no—
123C23×D43C2×D411yescharacteristic
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—22no—
132C2×Q8×C43—22no—
133C2×Q8×C43C2×D412yes—
134C2×Q8×C43C2×D412yes—
135C2×Q8×C43#4112yes—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147#10621902—28no—
148#10621902—28no—
149#10621902—28no—
150#10621902—28no—
151C2×D172—24no—
152C2×D172—24no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—24no—
157C2×D172C2×D412yes—
158C2×D172C2×D412yes—
159C2×D172#4112yes—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—24no—
167C2×C4×D43—24no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—24no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—41no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43C2×D412yes—
180C2×C4×D43#4112yes—
181Q16×C43—48no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C4⋊C4×C43—24no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43C2×D412yes—
190C42×C43—24no—
191C42×C43C2×D412yes—
192C42×C43C2×D412yes—
193#10621884—48no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—24no—
197(C2×D43)⋊C4—44no—
198C4⋊Dic43—24no—
199C4⋊Dic43—21no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—42no—
203C4⋊Dic43—42no—
204C4⋊Dic43C2×D412yes—
205Dic43⋊C4—44no—
206C4×Dic43—24no—
207C4×Dic43—24no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—22no—
214C2×C43⋊C8—22no—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—21no—
220C22×D43—22no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43#12112yes—
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—42no—
234Q8×C43—42no—
235Q8×C43—42no—
236Q8×C43—42no—
237Q8×C43#12114yes—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43#12012yes—
250C2×C4×C43#12012yes—
251C2×C4×C43#13512yes—
252C2×C4×C43#13712yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43#12112yes—
273C2×Dic43#13712yes—
274D172—216no—
275D172—22no—
276D172—22no—
277D172—22no—
278D172#12114yes—
279C4×D43—216no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—44no—
285C4×D43—48no—
286C4×D43—44no—
287C4×D43—48no—
288C8×C43—42no—
289C43⋊C8—42no—
290#32907—431nomaximal, Sylow
291C22×C43C2×#12011yescharacteristic
292C22×C43C2×#12111yescharacteristic
293C22×C43#52511yescharacteristic
294C22×C43C2×#13511yescharacteristic
295C22×C43C2×#13711yescharacteristic
296C22×C43C2×#13711yescharacteristic
297C22×C43#57511yescharacteristic
298C2×D43—24no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—41no—
303C2×D43—42no—
304C2×D43—41no—
305C2×D43—42no—
306C2×D43—41no—
307C2×D43—42no—
308C2×D43—41no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C4×C43—24no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—82no—
316C4×C43#45214yescomplemented
317C4×C43C2×#12111yescharacteristic
318C4×C43C2×#12111yescharacteristic
319C4×C43#52511yescharacteristic
320C4×C43#52511yescharacteristic
321Dic43—22no—
322Dic43—22no—
323Dic43—41no—
324Dic43—42no—
325Dic43—82no—
326C2×C4×#41—431no—
327C2×#462D4311yescharacteristic, complemented
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#1797—431no—
337C2×C43#284711yescharacteristic
338C2×C43C2×#45211yescharacteristic
339C2×C43#300711yescharacteristic
340C2×C43#303511yescharacteristic
341C2×C43#303911yescharacteristic
342C2×C43#310711yescharacteristic
343C2×C43#311611yescharacteristic
344D43—42no—
345D43—44no—
346C22×#41—431no—
347C22×Q16C2×D4312yes—
348C22×SD16—432no—
349C2×C4⋊Q8C2×D4311yescharacteristic
350C2×C22⋊Q8—432no—
351C4×#41—864no—
352C4×#41—864no—
353C2×C4×Q8—431no—
354C2×C4×Q8C2×D4311yescharacteristic
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4—861no—
358C2×C4×D4—861no—
359C2×#117—431no—
360C2×#117—861no—
361C22×C42—431no—
362C22×C42—861no—
363#462—24no—
364#461—864no—
365#452—868no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8C2×D4311yescharacteristic
368C2×#103—432no—
369C2×#103—432no—
370C2×#103C2×D4312yes—
371C2×#102—432no—
372C2×C22⋊C8—432no—
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#336—432no—
382C43#3290711yescharacteristic, complemented, Sylow
383C2×#41—434no—
384C2×#41—862no—
385C2×#41—862no—
386C2×#41—862no—
387C2×#41—862no—
388C2×#41—862no—
389C22×Q8C22×D4312yes—
390C22×Q8C22×D4311yescharacteristic
391C22×D4—431no—
392C22×D4—861no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—861no—
397C23×C4—861no—
398C23×C4—861no—
399C2×Q16—24no—
400C2×Q16—24no—
401C2×Q16—24no—
402C2×SD16—864no—
403C2×SD16—864no—
404C2×SD16—864no—
405C22×C8—432no—
406C22×C8C22×D4312yes—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C22⋊Q8—864no—
410C22⋊Q8—864no—
411C4×Q8—22no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8C22⋊D4314yes—
415C4×D4—434no—
416C4×D4—868no—
417C4×D4—862no—
418C4×D4—868no—
419C4×D4—862no—
420C4×D4—862no—
421#117—862no—
422#117—868no—
423#117—862no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—432no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—862no—
438C2×C42—21no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—868no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—862no—
446C2×C42—862no—
447C2×C42C22×D4311yescharacteristic
448C4⋊C8—22no—
449C4⋊C8—862no—
450#103—24no—
451#103—864no—
452#103—864no—
453#102—864no—
454C22⋊C8—864no—
455#95—862no—
456#95—862no—
457C24—431no—
458C24—861no—
459#41—868no—
460#41—868no—
461#41—868no—
462#41—868no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8D4×D4312yes—
473C2×Q8#1062190012yes—
474C2×Q8C2×C22⋊D4312yes—
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—22no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—431no—
492C22×C4—864no—
493C22×C4—862no—
494C22×C4—864no—
495C22×C4—864no—
496C22×C4—864no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—864no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—1721no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4D4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516Q16—48no—
517SD16—1728no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—862no—
522C2×C8—862no—
523C2×C8—862no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—432no—
529C4⋊C4—864no—
530C4⋊C4—861no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—1722no—
534C4⋊C4—1724no—
535C4⋊C4—1722no—
536C4⋊C4C2×C22⋊D4312yes—
537C22⋊C4—864no—
538C22⋊C4—864no—
539C22⋊C4—864no—
540C22⋊C4—1724no—
541C42—24no—
542C42—864no—
543C42—864no—
544C42—862no—
545C42—862no—
546C42—861no—
547C42—861no—
548C42D4×D4312yes—
549C42C2×C22⋊D4312yes—
550C23—432no—
551C23—862no—
552C23—861no—
553C23—862no—
554C23—862no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—861no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23C2×D4×D4311yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—42no—
569Q8—42no—
570Q8—42no—
571Q8—42no—
572Q8#1306329614yes—
573D4—434no—
574D4—8616no—
575D4—862no—
576D4—862no—
577D4—862no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—8616no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—1724no—
605C2×C4—1728no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1724no—
612C2×C4—1728no—
613C2×C4#1306329312yes—
614C2×C4#1306329312yes—
615C2×C4#1306334812yes—
616C2×C4#1306335712yes—
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C22×C22⋊D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4C2×#1062190011yescharacteristic
623C8—42no—
624C8—1722no—
625C22—862no—
626C22—862no—
627C22—864no—
628C22—862no—
629C22—1721no—
630C22—1722no—
631C22—1722no—
632C22—1721no—
633C22—1722no—
634C22—1722no—
635C22—1721no—
636C22—1722no—
637C22—1721no—
638C22—1722no—
639C22C2×#1306329311yescharacteristic
640C22#121×D4311yescharacteristic
641C22#1458340911yescharacteristic
642C22C2×#1306334811yescharacteristic
643C22#137×D4311yescharacteristic
644C22C2×#1306335711yescharacteristic
645C22#1458369811yescharacteristic
646C4—22no—
647C4—24no—
648C4—42no—
649C4—82no—
650C4—862no—
651C4—862no—
652C4—3442no—
653C4—1721no—
654C4—1722no—
655C4#1458306014yescomplemented
656C4#121×D4311yescharacteristic
657C4C2×#1306329611yescharacteristic
658C4#1458340611yescharacteristic
659C4#1458340911yescharacteristic
660C2—1722no—
661C2—1724no—
662C2#1914287411yescharacteristic
663C2C2×#1458306011yescharacteristic
664C2#1914385111yescharacteristic
665C2#1914405311yescharacteristic
666C2#1914407911yescharacteristic
667C2#1914466511yescharacteristic
668C2#1914475611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#462C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenterC2×#462D43
hypocenterC43#32907
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#14583101C2semidirect
4. #19142942C2semidirect
5. #19134938C2semidirect
6. #19134926C2semidirect
7. #19134904C2semidirect
8. #19134600C2semidirect
9. #19134596C2semidirect
10. #19134572C2semidirect
11. C2×C43×#462C2semidirect
316. C4×C43#452semidirect
327. C2×#462D43semidirect
382. C43#32907semidirect
655. C4#14583060semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
C2×#145831012
C2×#145830602
#191429422
#191349382
#191349262
#191349042
#191346002
#191345962
#191345722
C2×C43×#4622
#3290743