Finite Group Databasebeta

← #25099299

Subgroups — #25099299

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582900C211yesmaximal, characteristic
2C2×M16×Dic43C211yesmaximal, characteristic, complemented
3#19137086C211yesmaximal, characteristic
4C2×#14582795C211yesmaximal, characteristic, complemented
5#19135289C212yesmaximal, complemented
6#19135282C212yesmaximal, complemented
7#19135275C212yesmaximal, complemented
8#19135268C212yesmaximal, complemented
9#19134315C211yesmaximal, characteristic, complemented
10#19134314C211yesmaximal, characteristic, complemented
11C2×C43×#417C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C2×#13063284C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4—21no—
16C22×C4×Dic43C2211yescharacteristic
17#14582900C418yescomplemented
18C2×#13063249C2212yes—
19C2×#13063246C2212yes—
20M16×Dic43—24no—
21C2×#13063235C2212yes—
22C2×C8×Dic43C2212yes—
23#14582806C2211yescharacteristic
24#14582806C2211yescharacteristic
25#14582802C2211yescharacteristic
26#14582802C2211yescharacteristic
27#14582795—21no—
28#14582795—21no—
29#14582795C2212yes—
30#14582795C2212yes—
31#14582779—21no—
32#14582779—21no—
33C4×C22⋊Dic43—21no—
34C4×C22⋊Dic43—21no—
35C2×C43⋊#95—21no—
36#14582662C2212yes—
37#14582662C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40C22×#41×C43C2211yescharacteristic
41C22×M16×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#417—24no—
44C2×#103×C43C2212yes—
45C2×#102×C43C2212yes—
46C23×Dic43—21no—
47C23×Dic43D411yescharacteristic
48C23×Dic43D411yescharacteristic
49C2×#10621877—22no—
50C2×#10621877—22no—
51C2×#10621877C2×C414yes—
52C22×C43⋊C8C2312yes—
53#13063284—22no—
54#13063284—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43C2×C414yes—
58C2×C4⋊Dic43C2311yescharacteristic
59C2×C4⋊Dic43C2311yescharacteristic
60C2×C4⋊Dic43C2312yes—
61C2×Dic43⋊C4—22no—
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4—44no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43—21no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43D411yescharacteristic
73C2×C4×Dic43D411yescharacteristic
74C2×C4×Dic43C2311yescharacteristic
75C2×C4×Dic43C2311yescharacteristic
76#13063249C2×C418yescomplemented
77#13063246C2×C418yescomplemented
78#13063235—24no—
79C8×Dic43—24no—
80C43⋊#95—22no—
81C43⋊#95—22no—
82C43⋊#95—21no—
83C43⋊#95—21no—
84C43⋊#95—21no—
85C43⋊#95—21no—
86C2×#41×C43—22no—
87C2×#41×C43—22no—
88C2×#41×C43—22no—
89C2×#41×C43—22no—
90C2×#41×C43—22no—
91C2×#41×C43C2×C414yes—
92C22×Q8×C43C2311yescharacteristic
93C22×D4×C43—21no—
94C22×D4×C43C2311yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43—21no—
97C23×C4×C43C2311yescharacteristic
98C2×M16×C43—22no—
99C2×M16×C43—22no—
100C2×M16×C43D414yes—
101C22×C8×C43C2312yes—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2312yes—
106#103×C43—24no—
107#102×C43—24no—
108C24×C43—21no—
109C24×C43C2×D411yescharacteristic
110#41×C43—28no—
111#41×C43—28no—
112#41×C43—44no—
113#41×C43—44no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43C22×C412yes—
120C2×D4×C43—21no—
121C2×D4×C43—24no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C2×D4×C43C22×C412yes—
129C22×C4×C43—24no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43#4112yes—
141C22×C4×C43#4112yes—
142C22×C4×C43#4112yes—
143C22×C4×C43#4112yes—
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—24no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161M16×C43—28no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43C2×D414yes—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—42no—
168C22⋊Dic43—42no—
169C22⋊Dic43—42no—
170C22⋊Dic43—42no—
171C22⋊Dic43—42no—
172C22⋊Dic43—42no—
173C4⋊Dic43—24no—
174C4⋊Dic43—22no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43C22×C414yes—
180Dic43⋊C4—44no—
181Dic43⋊C4—44no—
182C4×Dic43—22no—
183C4×Dic43—22no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—42no—
189#10621877—28no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8C22×C414yes—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—22no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43C4×D412yes—
205C23×C43#12112yes—
206C23×C43#12412yes—
207C23×C43C22×D411yescharacteristic
208Q8×C43—22no—
209Q8×C43—22no—
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—22no—
213D4×C43—22no—
214D4×C43—48no—
215D4×C43—41no—
216D4×C43—41no—
217C2×C4×C43—22no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—48no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—84no—
225C2×C4×C43#11714yes—
226C2×C4×C43C4×D412yes—
227C2×C4×C43C4×D414yes—
228C2×C4×C43#12112yes—
229C2×C4×C43#12314yes—
230C2×C4×C43#12412yes—
231C2×C4×C43#12614yes—
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—24no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—44no—
250C2×Dic43—44no—
251C2×Dic43—48no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43AGL(1,ℤ/8)12yes—
261C2×Dic43#13712yes—
262C8×C43—24no—
263C43⋊C8—24no—
264#21093—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43#38814yes—
279C22×C43C2×C4×D411yescharacteristic
280C22×C43C2×#12111yescharacteristic
281C22×C43C2×#12411yescharacteristic
282C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57511yescharacteristic
286C4×C43—42no—
287C4×C43—82no—
288C4×C43#38814yes—
289C4×C43C2×#11711yescharacteristic
290C4×C43C2×C4×D411yescharacteristic
291C4×C43C2×#12311yescharacteristic
292C4×C43C2×#12611yescharacteristic
293Dic43—22no—
294Dic43—22no—
295Dic43—44no—
296Dic43—41no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300C2×#417—431no—
301C2×#417D4311yescharacteristic
302C2×C4×M16—431no—
303#2297—431no—
304C2×#389—431no—
305#1936—432no—
306#1935—432no—
307#1934—432no—
308#1933—432no—
309#1736—431no—
310#1736—431no—
311C2×C43—24no—
312C2×C43—82no—
313C2×C43C2×#38811yescharacteristic
314C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
315C2×C43C4×#13711yescharacteristic
316C2×C43#305511yescharacteristic
317C2×C43#305611yescharacteristic
318C2×C43#314111yescharacteristic
319C2×C43#314211yescharacteristic
320C22×#41C2×D4311yescharacteristic
321C22×M16—431no—
322C22×M16C2×D4311yescharacteristic
323C2×#117—431no—
324C22×C4⋊C4—431no—
325C22×C4⋊C4—861no—
326C22×C4⋊C4C2×D4311yescharacteristic
327C22×C42—431no—
328#417—24no—
329#417—438no—
330C2×#103—432no—
331C2×#103C2×D4312yes—
332C2×#102—432no—
333C2×#102C2×D4312yes—
334C4×M16—864no—
335C2×#97—432no—
336C2×C4×C8—432no—
337#391—431no—
338#391—431no—
339#390—431no—
340#390—431no—
341#389—432no—
342#389—432no—
343#389—861no—
344#389—861no—
345#386—861no—
346#386—861no—
347C4×C22⋊C4—861no—
348C4×C22⋊C4—861no—
349C2×#95—861no—
350#340—432no—
351#340—432no—
352#340—432no—
353#340—432no—
354C43#2109311yescharacteristic, complemented, Sylow
355C2×#41—22no—
356C2×#41—22no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41C4×D4314yes—
361C22×Q8C22×D4311yescharacteristic
362C22×D4—21no—
363C22×D4C22×D4311yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—861no—
369C23×C4C22×D4311yescharacteristic
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—434no—
373C2×M16—862no—
374C2×M16—862no—
375C2×M16C22⋊D4314yes—
376C22×C8—432no—
377C22×C8C22×D4312yes—
378#117—862no—
379#117—862no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—434no—
384C2×C4⋊C4—432no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—1724no—
392C2×C4⋊C4C22×D4312yes—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—862no—
403C2×C42—862no—
404C2×C42—861no—
405#103—24no—
406#103—438no—
407#102—24no—
408#102—438no—
409#97—864no—
410C4×C8—864no—
411#95—862no—
412#95—862no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—21no—
418C24D4×D4311yescharacteristic
419#41—28no—
420#41—28no—
421#41—44no—
422#41—44no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×C4×D4312yes—
429C2×D4—24no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4C2×C4×D4312yes—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—864no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4—1722no—
461C22×C4—1722no—
462C22×C4C2×C4×D4312yes—
463C22×C4#1062189812yes—
464C22×C4D4×D4311yescharacteristic
465C22×C4#1062190012yes—
466C22×C4#1062190012yes—
467C22×C4#1062190012yes—
468C22×C4C2×C22⋊D4312yes—
469C22×C4C23×D4311yescharacteristic
470M16—28no—
471M16—868no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—434no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8C2×C22⋊D4314yes—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—42no—
481C4⋊C4—434no—
482C4⋊C4—864no—
483C4⋊C4—862no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—1724no—
489C4⋊C4—1724no—
490C22⋊C4—1722no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C22⋊C4—1722no—
494C22⋊C4—1722no—
495C42—862no—
496C42—862no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42—861no—
501C42—1722no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23(C22⋊D43)⋊C412yes—
514C23#1306329612yes—
515C23#1306331112yes—
516C23C2×D4×D4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521D4—22no—
522D4—22no—
523D4—48no—
524D4—41no—
525D4—41no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—864no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—1724no—
548C2×C4—1724no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1728no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4#1306328114yes—
559C2×C4(C22⋊D43)⋊C412yes—
560C2×C4C4×C22⋊D4314yes—
561C2×C4#1306329612yes—
562C2×C4#1306330614yes—
563C2×C4#1306331112yes—
564C2×C4#1306331814yes—
565C2×C4C22×C4×D4311yescharacteristic
566C2×C4C22×C22⋊D4311yescharacteristic
567C2×C4C2×#1062190011yescharacteristic
568C2×C4C2×#1062190011yescharacteristic
569C2×C4C2×#1062190011yescharacteristic
570C2×C4C2×#1062189811yescharacteristic
571C8—24no—
572C8—864no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22#1458278714yes—
587C22C2×(C22⋊D43)⋊C411yescharacteristic
588C22C2×#1306329611yescharacteristic
589C22C2×#1306331111yescharacteristic
590C22AGL(1,ℤ/8)×D4311yescharacteristic
591C22#137×D4311yescharacteristic
592C22#1458369511yescharacteristic
593C22#1458369811yescharacteristic
594C4—42no—
595C4—82no—
596C4—862no—
597C4—862no—
598C4—3441no—
599C4—3441no—
600C4—1721no—
601C4—1721no—
602C4—1724no—
603C4#1458278714yes—
604C4C2×#1306328111yescharacteristic
605C4C2×C4×C22⋊D4311yescharacteristic
606C4C2×#1306330611yescharacteristic
607C4C2×#1306331811yescharacteristic
608C2—24no—
609C2—82no—
610C2C2×#1458278711yescharacteristic
611C2#1914340811yescharacteristic
612C2#1914341911yescharacteristic
613C2#1914420811yescharacteristic
614C2#1914421911yescharacteristic
615C2#1914498611yescharacteristic
616C2#1914499311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#21093
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×M16×Dic43C2semidirect
4. C2×#14582795C2semidirect
5. #19135289C2semidirect
6. #19135282C2semidirect
7. #19135275C2semidirect
8. #19135268C2semidirect
9. #19134315C2semidirect
10. #19134314C2semidirect
17. #14582900C4semidirect
76. #13063249C2×C4semidirect
77. #13063246C2×C4semidirect
354. C43#21093semidirect

Maximal subgroups

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

subgroupindex
C2×#145829002
C2×M16×Dic432
#191370862
C2×#145827952
#191352892
#191352822
#191352752
#191352682
#191343152
#191343142
C2×C43×#4172
#2109343