Finite Group Databasebeta

← #25099533

Subgroups — #25099533

Order 11008.

978 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic43C211yesmaximal, characteristic
2#19137070C211yesmaximal, characteristic, complemented
3C4×D4×Dic43C211yesmaximal, characteristic
4#19135239C211yesmaximal, characteristic, complemented
5#19135233C211yesmaximal, characteristic, complemented
6#19135174C211yesmaximal, characteristic, complemented
7#19135172C211yesmaximal, characteristic, complemented
8#19134931C211yesmaximal, characteristic
9#19134842C211yesmaximal, characteristic
10#19134840C211yesmaximal, characteristic
11#19134487C211yesmaximal, characteristic, complemented
12#103×Dic43C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic
14#19134339C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C22×C4×Dic43—21no—
20SD16×Dic43C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582784—21no—
34#14582782—21no—
35C4⋊C4×Dic43C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4×C4⋊Dic43C2211yescharacteristic
39#14582750—21no—
40C22⋊C4×Dic43—21no—
41C22⋊C4×Dic43—21no—
42C4×C22⋊Dic43—21no—
43#14582744—21no—
44C42×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64Q8×Dic43—22no—
65Q8×Dic43C2×C414yescomplemented
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43C2×C414yes—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—44no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—22no—
92#13063258—22no—
93#13063257C2×C414yescomplemented
94#13063249—22no—
95#13063249C2×C414yescomplemented
96#13063246—22no—
97#13063246C2×C414yes—
98C8×Dic43—22no—
99C8×Dic43C2×C414yescomplemented
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43C2×C414yes—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×D4×C43—22no—
117C4×D4×C43—22no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#103×C43—22no—
123#102×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C22×C412yes—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43C22×C412yes—
137C2×D4×C43#4112yes—
138C2×D4×C43#4112yes—
139C22×C4×C43—24no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—24no—
149C22×Dic43—24no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162SD16×C43—28no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C22×C412yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—24no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—24no—
177C22⋊Dic43—24no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43C22×C412yes—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189C4×Dic43—22no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—24no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—42no—
200C4×Dic43C22×C412yes—
201C4×Dic43#4112yes—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C22×C412yes—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—41no—
219Q8×C43—41no—
220D4×C43—22no—
221D4×C43—22no—
222D4×C43—22no—
223D4×C43#11714yes—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—48no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43#13512yes—
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—48no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—48no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43C4×D412yes—
268C2×Dic43C4×D412yes—
269C2×Dic43#13512yes—
270C2×Dic43AGL(1,ℤ/8)12yes—
271C2×Dic43#13712yes—
272C8×C43—22no—
273C8×C43—41no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276#21114—431nomaximal, Sylow
277C22×C43—24no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43C2×C4×D411yescharacteristic
285C22×C43#52511yescharacteristic
286C22×C43#52511yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C43C2×#13711yescharacteristic
291C4×C43—22no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—42no—
295C4×C43—81no—
296C4×C43C2×#11711yescharacteristic
297C4×C43C4×#4111yescharacteristic
298C4×C43#52911yescharacteristic
299C4×C43#52911yescharacteristic
300Dic43—22no—
301Dic43—22no—
302Dic43—42no—
303Dic43—41no—
304Dic43—42no—
305Dic43—42no—
306Dic43—81no—
307Dic43#44014yes—
308C2×C4×SD16—431no—
309#2295—431no—
310C42×D4—431no—
311#1928—431no—
312#1928—431no—
313#1919—431no—
314#1919—431no—
315#1877—431no—
316#1877D4311yescharacteristic
317#1862—431no—
318#1862—431no—
319C4×#107—431no—
320C4×#103—431no—
321C4×#102—431no—
322#1744—431no—
323C2×C43—44no—
324C2×C43#229011yescharacteristic
325C2×C43C4×#13511yescharacteristic
326C2×C43C2×#44011yescharacteristic
327C2×C43#310511yescharacteristic
328C2×C43#310511yescharacteristic
329C2×C43#310711yescharacteristic
330C2×C43#310711yescharacteristic
331C22×SD16C2×D4311yescharacteristic
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×C4×D4—431no—
335C2×C4×D4C2×D4311yescharacteristic
336C22×C42—861no—
337C4×SD16—438no—
338C2×#107—431no—
339C2×#107—431no—
340C2×#106—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103C2×D4311yescharacteristic
344C2×#102—431no—
345C2×#102—431no—
346C2×#102C2×D4311yescharacteristic
347C2×C4×C8—431no—
348C2×C4×C8—431no—
349#391—431no—
350#391C2×D4311yescharacteristic
351#389—431no—
352#389—431no—
353#387—861no—
354#387—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—861no—
360C4×C22⋊C4—861no—
361C4×C22⋊C4—861no—
362C4×C22⋊C4—861no—
363#376—861no—
364C43—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#336—431no—
372#336—431no—
373#336—431no—
374#336C2×D4311yescharacteristic
375C43#2111411yescharacteristic, complemented, Sylow
376C22×Q8C22×D4311yescharacteristic
377C22×D4C22×D4311yescharacteristic
378C23×C4—21no—
379C23×C4—861no—
380C23×C4—861no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16C4×D4314yes—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C4×Q8—434no—
389C4×Q8—862no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—434no—
393C4×D4—862no—
394C4×D4—862no—
395C4×D4—862no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42—1724no—
420C2×C42C22×D4311yescharacteristic
421#107—862no—
422#107—862no—
423#106—434no—
424#103—22no—
425#103—434no—
426#103—862no—
427#102—22no—
428#102—434no—
429#102—862no—
430C4×C8—434no—
431C4×C8—862no—
432#95—21no—
433#95—21no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×C4×D4312yes—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4C2×C4×D4312yes—
453C2×D4#1062190012yes—
454C2×D4#1062190012yes—
455C22×C4—24no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—864no—
466C22×C4—864no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—28no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—432no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8C2×C4×D4312yes—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—432no—
495C4⋊C4—432no—
496C4⋊C4—432no—
497C4⋊C4—864no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4#1062190012yes—
506C22⋊C4—24no—
507C22⋊C4—864no—
508C22⋊C4—864no—
509C42—21no—
510C42—21no—
511C42—432no—
512C42—432no—
513C42—862no—
514C42—862no—
515C42—862no—
516C42—864no—
517C42—862no—
518C42—861no—
519C42—861no—
520C42—1722no—
521C42—1722no—
522C42—1722no—
523C42—1722no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23C2×D4×D4311yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536D4—22no—
537D4—22no—
538D4—22no—
539D4#1306328114yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—48no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—432no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—861no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—1728no—
571C2×C4—1728no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4#1306334612yes—
582C2×C4C22×C4×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4C2×#1062190011yescharacteristic
586C2×C4C2×#1062190011yescharacteristic
587C2×C4C2×#1062190011yescharacteristic
588C8—22no—
589C8—41no—
590C8—862no—
591C8—1721no—
592C22—24no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22C4×D4×D4311yescharacteristic
600C22#1458340511yescharacteristic
601C22#1458340911yescharacteristic
602C22#135×D4311yescharacteristic
603C22C2×#1306334611yescharacteristic
604C22AGL(1,ℤ/8)×D4311yescharacteristic
605C22#137×D4311yescharacteristic
606C4—22no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—81no—
611C4—434no—
612C4—862no—
613C4—862no—
614C4—3441no—
615C4—1722no—
616C4—1722no—
617C4—1722no—
618C4—1721no—
619C4C2×#1306328111yescharacteristic
620C4C4×#1062190011yescharacteristic
621C4#1458342611yescharacteristic
622C4#1458343011yescharacteristic
623C2—44no—
624C2#1913703511yescharacteristic
625C2C4×#1306334611yescharacteristic
626C2#440×D4311yescharacteristic
627C2#1914464111yescharacteristic
628C2#1914464311yescharacteristic
629C2#1914465911yescharacteristic
630C2#1914466311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1877D43
hypocenterC43#21114
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
2. #19137070C2semidirect
4. #19135239C2semidirect
5. #19135233C2semidirect
6. #19135174C2semidirect
7. #19135172C2semidirect
11. #19134487C2semidirect
12. #103×Dic43C2semidirect
14. #19134339C2semidirect
20. SD16×Dic43C4semidirect
65. Q8×Dic43C2×C4semidirect
93. #13063257C2×C4semidirect
95. #13063249C2×C4semidirect
99. C8×Dic43C2×C4semidirect
375. C43#21114semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic432
#191370702
C4×D4×Dic432
#191352392
#191352332
#191351742
#191351722
#191349312
#191348422
#191348402
#191344872
#103×Dic432
#102×Dic432
#191343392
C43×#18772
#2111443