Finite Group Databasebeta

← #25102239

Subgroups — #25102239

Order 11008.

1952 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic, complemented
2C2×#14583035C211yesmaximal, characteristic
3C2×#14583010C212yesmaximal, complemented
4#19137101C211yesmaximal, characteristic, complemented
5#19134944C212yesmaximal, complemented
6#19134912C211yesmaximal, characteristic, complemented
7#19134853C212yesmaximal, complemented
8#19134525C211yesmaximal, characteristic, complemented
9#19134419C212yesmaximal, complemented
10#19134359C211yesmaximal, characteristic, complemented
11C43×#1853C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C23×C4×D43—21no—
14C22×D344C2212yes—
15C2×#13063299C2211yescharacteristic
16C2×#13063287—28no—
17C2×#13063287—21no—
18C2×#13063287—21no—
19C2×#13063287C2212yes—
20C2×#13063287C2212yes—
21C2×#13063287C2211yescharacteristic, complemented
22C2×(C22⋊D43)⋊C4—21no—
23C22×(C2×D43)⋊C4—21no—
24C22×C4×Dic43C2211yescharacteristic
25#14583035C418yescomplemented
26#14583010—28no—
27C2×#13063247C2212yes—
28C2×#13063245C2212yes—
29C2×#13063245C2212yes—
30C2×#13063245C2212yescomplemented
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2212yescomplemented
33#14582800C2211yescharacteristic, complemented
34#14582795C2211yescharacteristic, complemented
35#14582788—21no—
36#14582776—21no—
37C4⋊C4×Dic43C2211yescharacteristic, complemented
38#14582746—21no—
39#14582661C2212yescomplemented
40#14582653C2212yescomplemented
41C22×C4⋊C4×C43C2211yescharacteristic
42C2×#106×C43C2212yescomplemented
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#340C2212yescomplemented
46C24×D43—21no—
47C22×D172—21no—
48C22×D172—22no—
49C22×D172—24no—
50C22×D172—24no—
51C22×D172C2×C414yescomplemented
52C22×D172C2311yescharacteristic
53C22×D172C2312yes—
54C22×C22⋊D43—21no—
55C23×Dic43D411yescharacteristic
56C23×Dic43D411yescharacteristic
57C22×C4×D43—28no—
58C22×C4×D43—22no—
59C22×C4×D43—22no—
60C22×C4×D43—21no—
61C22×C4×D43—44no—
62C22×C4×D43—44no—
63C2×D344—24no—
64C2×D344—24no—
65C2×D344C2×C418yescomplemented
66C22×C43⋊C8C2312yes—
67#13063299—22no—
68#13063299C2×C414yescomplemented
69#13063287—28no—
70#13063287—28no—
71#13063287—24no—
72#13063287—24no—
73#13063287—24no—
74#13063287—24no—
75#13063287D418yescomplemented
76(C22⋊D43)⋊C4—44no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×(C2×D43)⋊C4—28no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—24no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063247C2×C418yescomplemented
93#13063245—24no—
94#13063245—24no—
95#13063245—24no—
96C22⋊(C43⋊C8)—22no—
97#13063235—24no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C23×C4×C43—21no—
101C23×C4×C43C2311yescharacteristic
102C22×C8×C43C2312yes—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—24no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2312yes—
108C2×C22⋊C4×C43—21no—
109#106×C43—24no—
110C22⋊C8×C43C2×C414yescomplemented
111#95×C43—21no—
112C24×C43C2×D411yescharacteristic
113C23×D43—24no—
114C23×D43—24no—
115C23×D43—24no—
116C23×D43—22no—
117C23×D43—21no—
118C23×D43—42no—
119C23×D43—42no—
120C23×D43—42no—
121C23×D43—42no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—24no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43#4112yes—
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—42no—
136C2×C22⋊D43—42no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—41no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—24no—
149C2×D172—216no—
150C2×D172—24no—
151C2×D172—24no—
152C2×D172—22no—
153C2×D172—22no—
154C2×D172—22no—
155C2×D172—216no—
156C2×D172—21no—
157C2×D172—22no—
158C2×D172—22no—
159C2×D172C22×C414yes—
160C2×D172C22×C412yescomplemented
161C2×D172C2×D414yes—
162C2×D172#4114yes—
163C2×C4×D43—28no—
164C2×C4×D43—28no—
165C2×C4×D43—432no—
166C2×C4×D43—44no—
167C2×C4×D43—44no—
168C2×C4×D43—44no—
169C2×C4×D43—44no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43C22×C414yescomplemented
176C4⋊C4×C43—24no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43C2×D414yes—
181C22⋊C4×C43—42no—
182(C2×D43)⋊C4—28no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—28no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C412yescomplemented
190Dic43⋊C4—42no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—42no—
195C4×Dic43C2×D414yes—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199D344—216no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43C4×D412yes—
205C23×C43AGL(1,ℤ/8)12yes—
206C23×C43AGL(1,ℤ/8)12yes—
207C23×C43C22×D411yescharacteristic
208C22×D43—216no—
209C22×D43—24no—
210C22×D43—24no—
211C22×D43—24no—
212C22×D43—22no—
213C22×D43—48no—
214C22×D43—48no—
215C22×D43—48no—
216C22×D43—48no—
217C22×D43—48no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—42no—
222C22×D43—48no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—48no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C4×D412yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D412yes—
246C2×C4×C43C2×#4112yes—
247C2×C4×C43C2×#4111yescharacteristic
248C22⋊D43—48no—
249C2×Dic43—28no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—44no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43#12012yes—
264C2×Dic43#12012yes—
265C2×Dic43AGL(1,ℤ/8)12yes—
266D172—216no—
267D172—24no—
268D172—24no—
269D172—24no—
270D172—24no—
271D172—42no—
272D172C4×D418yescomplemented
273C4×D43—416no—
274C4×D43—416no—
275C4×D43—84no—
276C8×C43—24no—
277C43⋊C8—42no—
278#21452—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43#44214yescomplemented
286C22×C43C2×C4×D411yescharacteristic
287C22×C43C2×#12011yescharacteristic
288C22×C43#52511yescharacteristic
289C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C43#57511yescharacteristic
293C2×D43—28no—
294C2×D43—432no—
295C2×D43—44no—
296C2×D43—44no—
297C2×D43—44no—
298C2×D43—44no—
299C2×D43—44no—
300C2×D43—44no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C4×C43—22no—
309C4×C43—44no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C2×C4×D412yes—
313C4×C43#52512yes—
314Dic43—22no—
315Dic43—22no—
316Dic43—22no—
317Dic43—42no—
318Dic43—41no—
319C22×C4×D4—431no—
320C2×#447—431no—
321C2×#442—432no—
322C4×#121—431no—
323#1879—432no—
324#1874—431no—
325#1864—432no—
326#1853D4311yescharacteristic, complemented
327#1786—431no—
328#1762—432no—
329#1749—431no—
330C2×C43—24no—
331C2×C43C4×#12011yescharacteristic
332C2×C43C2×#44211yescharacteristic
333C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
334C2×C43#300311yescharacteristic
335C2×C43#300611yescharacteristic
336C2×C43#310911yescharacteristic
337C2×C43#311411yescharacteristic
338D43—48no—
339D43—82no—
340C23×D4—431no—
341C24×C4—861no—
342C22×D8—432no—
343C2×#121—431no—
344C2×C4×D4—432no—
345C2×C4×D4—432no—
346C2×C4×D4—431no—
347C2×C4×D4—861no—
348C2×C4×D4—861no—
349C2×C4×D4—861no—
350C2×C4×D4—868no—
351C22×C4⋊C4C2×D4311yescharacteristic
352C22×C22⋊C4—861no—
353C22×C42—431no—
354#447—438no—
355#442—868no—
356C2×#106C2×D4312yescomplemented
357C2×#102—432no—
358C2×#102—432no—
359C2×#102—432no—
360C2×#102—432no—
361C2×C22⋊C8—431no—
362C2×C22⋊C8C2×D4311yescharacteristic
363C2×#97—432no—
364#390—431no—
365#389—431no—
366#388—861no—
367#386—861no—
368#380C2×D4311yescharacteristic
369C4×C4⋊C4—431no—
370C4×C22⋊C4—861no—
371#340—432no—
372#340C2×D4312yescomplemented
373#336—432no—
374C43#2145211yescharacteristic, complemented, Sylow
375C25—861no—
376C22×D4—434no—
377C22×D4—432no—
378C22×D4—431no—
379C22×D4—864no—
380C22×D4—864no—
381C22×D4—861no—
382C22×D4—861no—
383C22×D4—862no—
384C23×C4—21no—
385C23×C4—431no—
386C23×C4—431no—
387C23×C4—862no—
388C23×C4—862no—
389C23×C4—861no—
390C23×C4—868no—
391C23×C4—1724no—
392C23×C4—1724no—
393C23×C4C22×D4311yescharacteristic
394C2×D8—438no—
395C2×D8—864no—
396C2×D8—864no—
397C22×C8—432no—
398C22×C8C22×D4312yes—
399#121—434no—
400#121—862no—
401C4×D4—438no—
402C4×D4—864no—
403C4×D4—864no—
404C4×D4—864no—
405C4×D4—868no—
406C4×D4—868no—
407C4×D4—864no—
408C4×D4—1724no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4312yes—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—862no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4—868no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—864no—
429C2×C42—861no—
430#106—24no—
431#102—438no—
432#102—864no—
433#102—864no—
434#102—864no—
435C22⋊C8—862no—
436C22⋊C8C4×D4314yescomplemented
437#97—864no—
438#95—21no—
439#95—861no—
440#95—861no—
441C24—864no—
442C24—864no—
443C24—864no—
444C24—862no—
445C24—861no—
446C24—1722no—
447C24—1722no—
448C24—1722no—
449C24—1722no—
450C24D4×D4311yescharacteristic
451C2×D4—434no—
452C2×D4—432no—
453C2×D4—434no—
454C2×D4—434no—
455C2×D4—8616no—
456C2×D4—864no—
457C2×D4—864no—
458C2×D4—8616no—
459C2×D4—864no—
460C2×D4—864no—
461C2×D4—862no—
462C2×D4—862no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—862no—
466C2×D4—861no—
467C2×D4—1722no—
468C2×D4—1722no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—868no—
482C22×C4—868no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—861no—
489C22×C4—1722no—
490C22×C4—1724no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—17232no—
494C22×C4—1724no—
495C22×C4—1724no—
496C22×C4—1724no—
497C22×C4—1721no—
498C22×C4C2×C4×D4312yes—
499C22×C4D4×D4311yescharacteristic
500C22×C4#1062190212yes—
501C22×C4C23×D4311yescharacteristic
502D8—8616no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—862no—
506C2×C8—862no—
507C2×C8—862no—
508C2×C8C2×C4×D4314yescomplemented
509C4⋊C4—24no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—432no—
514C4⋊C4—861no—
515C4⋊C4—1722no—
516C4⋊C4D4×D4314yes—
517C22⋊C4—42no—
518C22⋊C4—868no—
519C22⋊C4—868no—
520C22⋊C4—864no—
521C22⋊C4—1722no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C42—434no—
525C42—862no—
526C42—862no—
527C42—862no—
528C42—1722no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—8616no—
534C23—864no—
535C23—864no—
536C23—864no—
537C23—862no—
538C23—1728no—
539C23—1728no—
540C23—1728no—
541C23—1728no—
542C23—1728no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1722no—
550C23—1722no—
551C23—1722no—
552C23—1722no—
553C23—1728no—
554C23#1306328712yes—
555C23#1306335212yes—
556C23#1306335212yes—
557C23C2×D4×D4311yescharacteristic
558D4—438no—
559D4—8616no—
560D4—864no—
561D4—864no—
562D4—864no—
563D4—864no—
564D4—1728no—
565D4—1722no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—48no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—868no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—3444no—
595C2×C4—17216no—
596C2×C4—17216no—
597C2×C4—1724no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4#1306328712yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4C2×D4×D4312yes—
603C2×C4#41×D4312yes—
604C2×C4C2×#1062190211yescharacteristic
605C8—24no—
606C8—1722no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—868no—
614C22—3441no—
615C22—3441no—
616C22—3441no—
617C22—3441no—
618C22—17232no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1724no—
623C22—1724no—
624C22—1724no—
625C22—1724no—
626C22—1724no—
627C22—1724no—
628C22#1458301014yescomplemented
629C22C2×#1306328711yescharacteristic
630C22#120×D4311yescharacteristic
631C22#1458340711yescharacteristic
632C22AGL(1,ℤ/8)×D4311yescharacteristic
633C22C2×#1306335211yescharacteristic
634C22C2×#1306335211yescharacteristic
635C22#1458369811yescharacteristic
636C4—22no—
637C4—44no—
638C4—81no—
639C4—81no—
640C4—862no—
641C4—862no—
642C4—862no—
643C4—1721no—
644C4—1722no—
645C4C4×D4×D4312yes—
646C4#1458341212yes—
647C2—24no—
648C2—3442no—
649C2—1728no—
650C2#1913709611yescharacteristic
651C2C2×#1458301011yescharacteristic
652C2#1914340211yescharacteristic
653C2#1914382311yescharacteristic
654C2#1914384611yescharacteristic
655C2#1914468311yescharacteristic
656C2#1914473611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1853C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1853D43
hypocenterC43#21452
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
1. C22×#13063287C2semidirect
3. C2×#14583010C2semidirect
4. #19137101C2semidirect
5. #19134944C2semidirect
6. #19134912C2semidirect
7. #19134853C2semidirect
8. #19134525C2semidirect
9. #19134419C2semidirect
10. #19134359C2semidirect
11. C43×#1853C2semidirect
21. C2×#13063287C22semidirect
25. #14583035C4semidirect
30. C2×#13063245C22semidirect
32. C2×#13063235C22semidirect
33. #14582800C22semidirect
34. #14582795C22semidirect
37. C4⋊C4×Dic43C22semidirect
39. #14582661C22semidirect
40. #14582653C22semidirect
42. C2×#106×C43C22semidirect
45. C43×#340C22semidirect
51. C22×D172C2×C4semidirect
65. C2×D344C2×C4semidirect
68. #13063299C2×C4semidirect
75. #13063287D4semidirect
92. #13063247C2×C4semidirect
110. C22⋊C8×C43C2×C4semidirect
160. C2×D172C22×C4semidirect
175. C2×C8×C43C22×C4semidirect
189. C4⋊Dic43C22×C4semidirect
272. D172C4×D4semidirect
285. C22×C43#442semidirect
326. #1853D43semidirect
356. C2×#106C2×D43semidirect
372. #340C2×D43semidirect
374. C43#21452semidirect
436. C22⋊C8C4×D43semidirect
508. C2×C8C2×C4×D43semidirect
628. C22#14583010semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C2×#145830352
C2×#145830102
#191371012
#191349442
#191349122
#191348532
#191345252
#191344192
#191343592
C43×#18532
#2145243