Finite Group Databasebeta

← #25103755

Subgroups — #25103755

Order 11008.

972 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583221C211yesmaximal, characteristic
2#19137111C211yesmaximal, characteristic
3C4×#13063283C211yesmaximal, characteristic, complemented
4#19135219C211yesmaximal, characteristic, complemented
5#19135188C211yesmaximal, characteristic, complemented
6#19135180C211yesmaximal, characteristic, complemented
7#19134914C211yesmaximal, characteristic
8#19134791C211yesmaximal, characteristic, complemented
9#19134688C211yesmaximal, characteristic, complemented
10#107×Dic43C211yesmaximal, characteristic, complemented
11#19134483C211yesmaximal, characteristic, complemented
12#102×Dic43C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×(C22⋊D43)⋊C4—21no—
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22#14583221C418yescomplemented
23C2×#13063259C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582793—21no—
34#14582775—21no—
35#14582756C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C22⋊C4×Dic43—21no—
41C4×(C2×D43)⋊C4—21no—
42#14582746—21no—
43#14582744—21no—
44C42×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×C22⋊D43—21no—
61C23×Dic43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063296—22no—
68#13063296C2×C414yes—
69D4×Dic43—22no—
70D4×Dic43—22no—
71(C22⋊D43)⋊C4—44no—
72#13063283—22no—
73#13063283—22no—
74#13063283—22no—
75#13063283C2×C414yescomplemented
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C42×D43—22no—
96C42×D43—22no—
97#13063259C2×C414yescomplemented
98#13063256—22no—
99#13063256C2×C414yescomplemented
100#13063246—22no—
101#13063246C2×C414yescomplemented
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8C2×C414yescomplemented
104C8×Dic43—22no—
105C8×Dic43—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#107×C43—22no—
123#102×C43—22no—
124#102×C43C2×C414yescomplemented
125#95×C43—21no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43C22×C412yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—24no—
141C2×C22⋊D43—42no—
142C2×C22⋊D43—42no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—41no—
163C2×C4×D43C22×C412yes—
164C2×C4×D43#4112yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C412yes—
176C4⋊C4×C43#4112yes—
177C22⋊C4×C43—42no—
178C22⋊C4×C43—42no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—42no—
182C22⋊Dic43—24no—
183C22⋊Dic43—42no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C22×C412yes—
193C4⋊Dic43C22×C412yes—
194C4⋊Dic43#4112yes—
195Dic43⋊C4—42no—
196C4×Dic43—24no—
197C4×Dic43—24no—
198C4×Dic43—22no—
199C4×Dic43—22no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C4×Dic43#4112yes—
205C4×Dic43#4112yes—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C22×C412yes—
212C23×C43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43C4×D412yes—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—41no—
230D4×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
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#13512yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C22⋊D43—48no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—41no—
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—84no—
270C2×Dic43C4×D412yes—
271C2×Dic43#12312yes—
272C2×Dic43#12312yes—
273C2×Dic43#13512yes—
274C2×Dic43AGL(1,ℤ/8)12yes—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—44no—
280C4×D43—44no—
281C8×C43—22no—
282C8×C43—41no—
283C43⋊C8—22no—
284C43⋊C8—41no—
285C4×#482—431nomaximal, Sylow
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43C2×#12311yescharacteristic
295C22×C43#52511yescharacteristic
296C22×C43C2×#13511yescharacteristic
297C22×C43C2×#13511yescharacteristic
298C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C43#57511yescharacteristic
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C4×C43—22no—
308C4×C43—41no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43C4×#4111yescharacteristic
313C4×C43C4×#4111yescharacteristic
314C4×C43#52911yescharacteristic
315C4×C43#52911yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—42no—
319Dic43—42no—
320Dic43—42no—
321Dic43—81no—
322Dic43#48214yescomplemented
323C2×#482—431no—
324C4×#121—431no—
325C4×#117—431no—
326#1926—431no—
327#1925D4311yescharacteristic, complemented
328#1921—431no—
329#1920—431no—
330#1875—431no—
331#1854—431no—
332#1825—431no—
333C4×#107—431no—
334C4×#106—431no—
335C4×#102—431no—
336C4×#102—431no—
337C4×C22⋊C8—431no—
338C2×C43—82no—
339C2×C43C4×#12311yescharacteristic
340C2×C43C4×#13511yescharacteristic
341C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C43C2×#48211yescharacteristic
343C2×C43#309111yescharacteristic
344C2×C43#310211yescharacteristic
345C2×C43#310611yescharacteristic
346D43—42no—
347C2×#121—431no—
348C2×C4×D4—431no—
349C2×C4×D4—861no—
350C2×#117—431no—
351C2×#117—431no—
352C22×C42—431no—
353#482—438no—
354C2×#107—431no—
355C2×#107C2×D4311yescharacteristic
356C2×#106—431no—
357C2×#106—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102C2×D4311yescharacteristic
361C2×#102C2×D4311yescharacteristic
362C2×C22⋊C8—431no—
363C2×C22⋊C8—431no—
364C2×C4×C8—431no—
365C2×C4×C8—431no—
366#390C2×D4311yescharacteristic
367#389—431no—
368#388—861no—
369#386—861no—
370#380—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4C2×D4311yescharacteristic
376C4×C22⋊C4—861no—
377C4×C22⋊C4—861no—
378C4×C22⋊C4—861no—
379#376—861no—
380C43—861no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#336—431no—
390#336C2×D4311yescharacteristic
391C43C4×#48211yescharacteristic, complemented, Sylow
392C22×D4—861no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—861no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402#121—434no—
403#121—862no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—1724no—
407#117—434no—
408#117—862no—
409#117—862no—
410#117—862no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—21no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—862no—
431C2×C42—862no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439#107—22no—
440#107—434no—
441#106—434no—
442#106—862no—
443#102—22no—
444#102—434no—
445#102—862no—
446#102C4×D4314yescomplemented
447C22⋊C8—434no—
448C22⋊C8—862no—
449C4×C8—862no—
450C4×C8—862no—
451#95—21no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—21no—
459C24—431no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—864no—
466C2×D4—1722no—
467C2×D4—1722no—
468C2×D4C2×C4×D4312yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—862no—
489C22×C4—861no—
490C22×C4—1721no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—432no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8C2×C4×D4312yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—1722no—
522C4⋊C4C2×C4×D4312yes—
523C4⋊C4#1062190012yes—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—864no—
527C22⋊C4—864no—
528C22⋊C4—864no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C42—21no—
532C42—21no—
533C42—42no—
534C42—432no—
535C42—432no—
536C42—862no—
537C42—862no—
538C42—864no—
539C42—864no—
540C42—1722no—
541C42—1722no—
542C42—1722no—
543C42—1722no—
544C23—22no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—432no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23C2×D4×D4311yescharacteristic
559D4—22no—
560D4—22no—
561D4—41no—
562D4—41no—
563D4—1728no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—432no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—3444no—
595C2×C4—1724no—
596C2×C4—1724no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4#1306334412yes—
607C2×C4C22×C4×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#41×D4311yescharacteristic
612C2×C4C2×#1062190011yescharacteristic
613C8—22no—
614C8—41no—
615C8—862no—
616C8—1721no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—862no—
625C22—862no—
626C22—862no—
627C22—1721no—
628C22—1721no—
629C22—1721no—
630C22—1721no—
631C22C4×D4×D4311yescharacteristic
632C22#123×D4311yescharacteristic
633C22#1458340911yescharacteristic
634C22#135×D4311yescharacteristic
635C22C2×#1306334411yescharacteristic
636C22AGL(1,ℤ/8)×D4311yescharacteristic
637C22#1458369811yescharacteristic
638C4—22no—
639C4—41no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—434no—
644C4—862no—
645C4—862no—
646C4—3441no—
647C4—1722no—
648C4—1722no—
649C4—1722no—
650C4C4×#1062190011yescharacteristic
651C4#1458336711yescharacteristic
652C4#1458342811yescharacteristic
653C4#1458343211yescharacteristic
654C2—82no—
655C2—1722no—
656C2#1913712211yescharacteristic
657C2C4×#1306334411yescharacteristic
658C2#1914340011yescharacteristic
659C2#482×D4311yescharacteristic
660C2#1914450311yescharacteristic
661C2#1914461211yescharacteristic
662C2#1914465211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1925D43
hypocenterC43C4×#482
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
3. C4×#13063283C2semidirect
4. #19135219C2semidirect
5. #19135188C2semidirect
6. #19135180C2semidirect
8. #19134791C2semidirect
9. #19134688C2semidirect
10. #107×Dic43C2semidirect
11. #19134483C2semidirect
12. #102×Dic43C2semidirect
13. #102×Dic43C2semidirect
14. #19134352C2semidirect
15. C43×#1925C2semidirect
22. #14583221C4semidirect
75. #13063283C2×C4semidirect
97. #13063259C2×C4semidirect
99. #13063256C2×C4semidirect
101. #13063246C2×C4semidirect
103. (C2×D43)⋊C8C2×C4semidirect
124. #102×C43C2×C4semidirect
322. Dic43#482semidirect
327. #1925D43semidirect
391. C43C4×#482semidirect
446. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832212
#191371112
C4×#130632832
#191352192
#191351882
#191351802
#191349142
#191347912
#191346882
#107×Dic432
#191344832
#102×Dic432
#191343522
C43×#19252
C4×#48243