Finite Group Databasebeta

← #25133159

Subgroups — #25133159

Order 11008.

1248 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic86C211yesmaximal, characteristic
2C2×#14583193C211yesmaximal, characteristic, complemented
3C2×#14582996C211yesmaximal, characteristic
4#19139963C211yesmaximal, characteristic, complemented
5#19135923C211yesmaximal, characteristic, complemented
6#19135921C211yesmaximal, characteristic, complemented
7#19135737C211yesmaximal, characteristic, complemented
8#19135735C211yesmaximal, characteristic, complemented
9#19135566C211yesmaximal, characteristic, complemented
10#19135533C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic
12#19134927C211yesmaximal, characteristic
13#19134840C211yesmaximal, characteristic
14#19134603C211yesmaximal, characteristic
15C43×#1862C211yesmaximal, characteristic
16C23×Dic86—21no—
17C22×#10621883C2211yescharacteristic
18D4×Dic86—24no—
19D4×Dic86—24no—
20C2×#13063325C2211yescharacteristic
21C2×#13063324C2211yescharacteristic
22C2×#13063324C2211yescharacteristic
23C2×#13063304—21no—
24C2×#13063302—21no—
25C2×#13063302—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30#14583193—24no—
31#14582996—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×Dic43⋊C8C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063235C2211yescharacteristic
40#14582840—21no—
41#14582819—21no—
42#14582805C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582785—21no—
46#14582781—21no—
47#14582764C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—28no—
64C22×Dic86—21no—
65C22×Dic86—21no—
66C22×Dic86—21no—
67C22×Dic86—44no—
68C22×Dic86—44no—
69C22×Dic86D411yescharacteristic
70C22×Dic86C2311yescharacteristic
71C23×Dic43—21no—
72C23×Dic43—21no—
73C2×#10621883—22no—
74C2×#10621883—22no—
75C2×#10621883Q814yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063325—22no—
79#13063325—22no—
80#13063324—22no—
81#13063324—22no—
82#13063324—22no—
83#13063324D414yes—
84#13063304—28no—
85#13063302—28no—
86#13063302—28no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89#13063290—22no—
90#13063290—22no—
91D4×Dic43—22no—
92D4×Dic43—22no—
93D4×Dic43—22no—
94D4×Dic43D414yes—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43D411yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4D411yescharacteristic
105C2×Dic43⋊C4D411yescharacteristic
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111#13063258—22no—
112#13063258—22no—
113Dic43⋊C8—22no—
114#13063250—22no—
115#13063250—22no—
116#13063248—22no—
117#13063246—22no—
118#13063235—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#107×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#95×C43—21no—
142C24×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43C2×D412yes—
147C2×D4×C43C2×Q812yes—
148C2×D4×C43#4112yes—
149C22×C4×C43—24no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—24no—
159C22×Dic43—24no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—24no—
180C2×Dic86—24no—
181C2×Dic86—21no—
182C2×Dic86—24no—
183C2×Dic86—432no—
184C2×Dic86—42no—
185C2×Dic86—42no—
186C2×Dic86—42no—
187C2×Dic86—42no—
188C2×Dic86—42no—
189C2×Dic86—42no—
190C2×Dic86C2×Q812yescomplemented
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—42no—
203C4⋊C4×C43C2×D412yes—
204C22⋊C4×C43—24no—
205C42×C43—21no—
206C42×C43—21no—
207C22⋊Dic43—24no—
208C22⋊Dic43—24no—
209#10621883—28no—
210C4⋊Dic43—24no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—22no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43C2×D412yes—
217C4⋊Dic43C2×D412yes—
218Dic43⋊C4—24no—
219Dic43⋊C4—24no—
220Dic43⋊C4—22no—
221Dic43⋊C4—22no—
222Dic43⋊C4—42no—
223Dic43⋊C4—42no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—42no—
227C4×Dic43C2×D412yes—
228C4×Dic43C2×D412yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C2×Q812yescomplemented
235C23×C43—22no—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43C22×D411yescharacteristic
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—22no—
246D4×C43C22⋊Q814yes—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—48no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43AGL(1,ℤ/8)12yes—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×Q811yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—48no—
282C2×Dic43—48no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43#12012yes—
293C2×Dic43#12012yes—
294C2×Dic43AGL(1,ℤ/8)12yes—
295Dic86—28no—
296Dic86—22no—
297Dic86—22no—
298Dic86—48no—
299Dic86—48no—
300Dic86—48no—
301Dic86—41no—
302Dic86—41no—
303C8×C43—41no—
304C8×C43—41no—
305C43⋊C8—22no—
306C43⋊C8—41no—
307#24342—431nomaximal, Sylow
308C22×C43—24no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43—42no—
312C22×C43—42no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43C2×#12011yescharacteristic
316C22×C43#54811yescharacteristic
317C22×C43D4×Q811yescharacteristic
318C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C43#57811yescharacteristic
321C22×C43#57811yescharacteristic
322C4×C43—22no—
323C4×C43—42no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43C2×C22⋊Q811yescharacteristic
328C4×C43#53611yescharacteristic
329C4×C43#54811yescharacteristic
330C4×C43D4×Q811yescharacteristic
331Dic43—22no—
332Dic43—22no—
333Dic43—22no—
334Dic43—42no—
335Dic43—42no—
336Dic43—42no—
337Dic43—41no—
338Dic43—81no—
339C2×D4×Q8—431no—
340C2×#477—431no—
341C2×#440—431no—
342#2581—431no—
343#2057—431no—
344#2057—431no—
345#2024—431no—
346#2024—431no—
347#1993—431no—
348#1985—431no—
349#1877—431no—
350#1877—431no—
351#1862—431no—
352#1862D4311yescharacteristic
353#1804—431no—
354C2×C43—44no—
355C2×C43#240911yescharacteristic
356C2×C43#300311yescharacteristic
357C2×C43#301111yescharacteristic
358C2×C43#336711yescharacteristic
359C2×C43#336711yescharacteristic
360C2×C43#338611yescharacteristic
361C2×C43#338611yescharacteristic
362C23×Q8—861no—
363C22×SD16—431no—
364D4×Q8—864no—
365D4×Q8—864no—
366C2×C4⋊Q8—431no—
367C2×C4⋊Q8—431no—
368C2×C4⋊Q8—431no—
369C2×C22⋊Q8—861no—
370C2×C22⋊Q8—861no—
371C2×C22⋊Q8—861no—
372C2×C4×Q8—431no—
373C2×C4×Q8—431no—
374C2×C4×D4—431no—
375C2×C4×D4—431no—
376C2×C4×D4C2×D4311yescharacteristic
377#477—864no—
378#440—864no—
379C2×#107—431no—
380C2×#107—431no—
381C2×#107C2×D4311yescharacteristic
382C2×C4⋊C8—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#102—431no—
387C2×#102C2×D4311yescharacteristic
388C2×#102C2×D4311yescharacteristic
389C2×#97—431no—
390#400—861no—
391#395—861no—
392#391—431no—
393#391—431no—
394#389—431no—
395#389C2×D4311yescharacteristic
396#387—861no—
397#387—861no—
398#382—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340C2×D4311yescharacteristic
405#336—431no—
406#336—431no—
407#336—431no—
408#336C2×D4311yescharacteristic
409C43#2434211yescharacteristic, complemented, Sylow
410C22×Q8—431no—
411C22×Q8—431no—
412C22×Q8—861no—
413C22×Q8—861no—
414C22×Q8—868no—
415C22×Q8—861no—
416C22×Q8—1724no—
417C22×Q8—1724no—
418C22×D4C22×D4311yescharacteristic
419C23×C4—21no—
420C23×C4—861no—
421C23×C4—861no—
422C2×SD16—434no—
423C2×SD16—862no—
424C2×SD16—862no—
425C22×C8—431no—
426C22×C8—431no—
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C4⋊Q8—434no—
430C4⋊Q8—862no—
431C4⋊Q8—862no—
432C4⋊Q8—862no—
433C4⋊Q8—862no—
434C4⋊Q8—862no—
435C22⋊Q8—868no—
436C22⋊Q8—868no—
437C22⋊Q8—868no—
438C4×Q8—862no—
439C4×Q8—862no—
440C4×Q8—862no—
441C4×Q8—862no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—434no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—861no—
469C2×C42C22×D4311yescharacteristic
470#107—22no—
471#107—862no—
472#107—862no—
473C4⋊C8—862no—
474#103—862no—
475#103—862no—
476#103—862no—
477#102—22no—
478#102—22no—
479#102—862no—
480#97—862no—
481#95—21no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487#95—861no—
488#95—861no—
489C24—21no—
490C2×Q8—432no—
491C2×Q8—862no—
492C2×Q8—862no—
493C2×Q8—864no—
494C2×Q8—864no—
495C2×Q8—864no—
496C2×Q8—862no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—1722no—
503C2×Q8—1722no—
504C2×Q8—1722no—
505C2×Q8—1722no—
506C2×Q8—1722no—
507C2×Q8—17232no—
508C2×Q8—1722no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4#1062189812yes—
513C2×D4D4×D4312yes—
514C2×D4Q8×D4312yes—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—864no—
526C22×C4—864no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—1722no—
532C22×C4—1722no—
533C22×C4—1722no—
534C22×C4—1722no—
535C22×C4D4×D4311yescharacteristic
536C22×C4D4×D4311yescharacteristic
537C22×C4C23×D4311yescharacteristic
538SD16—868no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—432no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—432no—
558C4⋊C4—432no—
559C4⋊C4—862no—
560C4⋊C4—862no—
561C4⋊C4—862no—
562C4⋊C4—864no—
563C4⋊C4—864no—
564C4⋊C4—864no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—1722no—
570C4⋊C4—1722no—
571C4⋊C4D4×D4312yes—
572C22⋊C4—24no—
573C22⋊C4—864no—
574C22⋊C4—864no—
575C42—21no—
576C42—21no—
577C42—432no—
578C42—432no—
579C42—861no—
580C42—861no—
581C42—1722no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C2×D4×D4311yescharacteristic
590Q8—868no—
591Q8—862no—
592Q8—862no—
593Q8—1728no—
594Q8—1728no—
595Q8—1728no—
596Q8—1721no—
597Q8—1721no—
598D4—22no—
599D4—22no—
600D4—22no—
601D4#1306330314yes—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—48no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—432no—
618C2×C4—432no—
619C2×C4—432no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—862no—
627C2×C4—861no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—1728no—
633C2×C4—1728no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4#1306334912yes—
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4C2×Q8×D4311yescharacteristic
647C2×C4C2×#1062189811yescharacteristic
648C2×C4#1306337211yescharacteristic
649C2×C4#1306337211yescharacteristic
650C8—41no—
651C8—41no—
652C8—862no—
653C8—1721no—
654C22—24no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22#120×D4311yescharacteristic
662C22#1458355811yescharacteristic
663C22#1458356211yescharacteristic
664C22AGL(1,ℤ/8)×D4311yescharacteristic
665C22C2×#1306334911yescharacteristic
666C22#1458371311yescharacteristic
667C22#1458371511yescharacteristic
668C4—22no—
669C4—42no—
670C4—41no—
671C4—81no—
672C4—81no—
673C4—862no—
674C4—862no—
675C4—862no—
676C4—3441no—
677C4—1722no—
678C4—1722no—
679C4—1722no—
680C4—1721no—
681C4C2×#1306330311yescharacteristic
682C4#1458347111yescharacteristic
683C4#1458355811yescharacteristic
684C4#1458356211yescharacteristic
685C2—44no—
686C2#1913795911yescharacteristic
687C2#1914381911yescharacteristic
688C2#1914388711yescharacteristic
689C2#1914731111yescharacteristic
690C2#1914731411yescharacteristic
691C2#1914751111yescharacteristic
692C2#1914752011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1862D43
hypocenterC43#24342
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#14583193C2semidirect
4. #19139963C2semidirect
5. #19135923C2semidirect
6. #19135921C2semidirect
7. #19135737C2semidirect
8. #19135735C2semidirect
9. #19135566C2semidirect
10. #19135533C2semidirect
75. C2×#10621883Q8semidirect
190. C2×Dic86C2×Q8semidirect
234. C2×C43⋊C8C2×Q8semidirect
409. C43#24342semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145831932
C2×#145829962
#191399632
#191359232
#191359212
#191357372
#191357352
#191355662
#191355332
#191349292
#191349272
#191348402
#191346032
C43×#18622
#2434243