Finite Group Databasebeta

← #25106315

Subgroups — #25106315

Order 11008.

1394 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C211yesmaximal, characteristic
2C2×#14582953C211yesmaximal, characteristic, complemented
3C2×#14582764C211yesmaximal, characteristic, complemented
4#19135566C212yesmaximal, complemented
5#19135417C212yesmaximal, complemented
6#19134913C211yesmaximal, characteristic, complemented
7#19134912C211yesmaximal, characteristic, complemented
8#19134910C211yesmaximal, characteristic, complemented
9#19134604C212yesmaximal, complemented
10#19134603C212yesmaximal, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13#14583444—24no—
14#14583444C418yescomplemented
15C2×#13063324C2211yescharacteristic
16C2×#13063321C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063299C2211yescharacteristic
19C2×#13063297—21no—
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25#14582953—24no—
26C2×Dic43⋊C8C2212yes—
27C2×#13063247C2212yes—
28C2×#13063246C2212yes—
29C2×#13063245C2212yes—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063235C2212yes—
32#14582764—21no—
33#14582764—21no—
34#14582764C2212yes—
35#14582764C2212yes—
36C2×C43⋊#95—21no—
37C2×C43⋊#95—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×#121×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C2×C22⋊C8×C43C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621900—28no—
47C2×#10621900—44no—
48C2×#10621900—44no—
49C22×Dic86—21no—
50C22×D172C2311yescharacteristic
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C23×Dic43D411yescharacteristic
57C23×Dic43D411yescharacteristic
58C22×C4×D43—21no—
59C22×C43⋊C8C2312yes—
60#13063324—22no—
61#13063324C2×C414yescomplemented
62#13063321—22no—
63#13063321C2×C414yescomplemented
64#13063311—28no—
65#13063299—22no—
66#13063299C2×C414yes—
67#13063297—28no—
68D4×Dic43—22no—
69D4×Dic43C2×C414yescomplemented
70#13063287—22no—
71#13063287C2×C414yescomplemented
72(C22⋊D43)⋊C4—28no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—42no—
75C2×C4⋊Dic43C2312yes—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43C2×C414yes—
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D414yes—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87Dic43⋊C8—24no—
88#13063247—42no—
89#13063246—42no—
90#13063245—42no—
91C22⋊(C43⋊C8)—22no—
92#13063235—24no—
93C43⋊#95—22no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C22×D4×C43—21no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101C22×C8×C43C2312yes—
102#121×C43—22no—
103#121×C43C2×C414yes—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—42no—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C22⋊C4×C43—21no—
109#102×C43—42no—
110C22⋊C8×C43—22no—
111C24×C43—21no—
112C24×C43C2×D411yescharacteristic
113C23×D43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—24no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—42no—
119C2×D4×C43—42no—
120C2×D4×C43C22×C412yes—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—24no—
133C2×C22⋊D43—24no—
134C2×C22⋊D43—24no—
135C2×C22⋊D43—42no—
136C2×C22⋊D43—42no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C22×Dic43—24no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—22no—
146C22×Dic43—41no—
147C22×Dic43—41no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43C22⋊C414yes—
154C22×Dic43C22⋊C414yes—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159#10621900—432no—
160C2×D172—21no—
161C2×D172—22no—
162C2×D172—22no—
163C2×D172C22×C412yes—
164C2×C4×D43—24no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×Dic86—24no—
168C2×Dic86—42no—
169C2×Dic86—42no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43C22×C412yes—
178C22⋊C4×C43—24no—
179C22⋊Dic43—24no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—42no—
186C4⋊Dic43C22×C412yes—
187Dic43⋊C4—24no—
188C4×Dic43C22⋊C414yes—
189C4×Dic43C22⋊C414yes—
190C4×Dic43C22×C412yes—
191C4×Dic43C22×C412yes—
192C4×Dic43C2×D412yes—
193C4×Dic43C2×D412yes—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—22no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43C2×C22⋊C412yes—
209C23×C43AGL(1,ℤ/8)12yes—
210C23×C43AGL(1,ℤ/8)12yes—
211C23×C43C22×D411yescharacteristic
212C22×D43—22no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219D4×C43—24no—
220D4×C43—48no—
221D4×C43—42no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—84no—
233C2×C4×C43C2×C22⋊C412yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43H(5,𝔽2)12yes—
237C2×C4×C432−1+412yes—
238C22⋊D43—48no—
239C22⋊D43—48no—
240C22⋊D43—48no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—28no—
250C2×Dic43—22no—
251C2×Dic43—44no—
252C2×Dic43—48no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—84no—
259C2×Dic43C2×C22⋊C412yes—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263D172—24no—
264D172—42no—
265C4×D43—48no—
266Dic86—48no—
267C8×C43—42no—
268C43⋊C8—42no—
269#21865—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43#41814yes—
284C22×C43C22×C22⋊C411yescharacteristic
285C22×C43#53511yescharacteristic
286C22×C43#53611yescharacteristic
287C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C43#57511yescharacteristic
290C22×C43#57511yescharacteristic
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C4×C43—22no—
299C4×C43—42no—
300C4×C43—82no—
301C4×C43#52012yes—
302C4×C43#53712yes—
303Dic43—22no—
304Dic43—22no—
305Dic43—22no—
306Dic43—22no—
307Dic43—42no—
308Dic43—82no—
309C2×#532—431no—
310C2×#432—431no—
311C2×#382—431no—
312#1993—432no—
313#1961—432no—
314#1874—431no—
315#1874—431no—
316#1874—431no—
317#1874D4311yescharacteristic, complemented
318#1804—432no—
319#1804—432no—
320C2×C43—24no—
321C2×C43—82no—
322C2×C43#231111yescharacteristic
323C2×C43C2×#41811yescharacteristic
324C2×C43#289611yescharacteristic
325C2×C43#321311yescharacteristic
326C2×C43#321311yescharacteristic
327C2×C43#323411yescharacteristic
328C2×C43#323411yescharacteristic
329D43—82no—
330C22×#41—861no—
331#532—438no—
332#532—864no—
333C2×C4⋊Q8—431no—
334C2×#127—431no—
335C2×#124—861no—
336C2×#121—431no—
337C2×#121—861no—
338C2×#121C2×D4311yescharacteristic
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C2×C4×D4—861no—
342C22×C4⋊C4—431no—
343C22×C4⋊C4C2×D4311yescharacteristic
344C22×C42—431no—
345#432—864no—
346C2×C4⋊C8—432no—
347C2×#102—432no—
348C2×#102—432no—
349C2×#102—432no—
350C2×#102C2×D4312yes—
351C2×C22⋊C8—431no—
352C2×C22⋊C8C2×D4311yescharacteristic
353C2×#97—432no—
354#382—432no—
355#382—432no—
356#382—861no—
357#382—861no—
358C2×#95—861no—
359C2×#95—861no—
360#340—432no—
361#340—432no—
362#340—432no—
363#340C2×D4312yes—
364C43#2186511yescharacteristic, complemented, Sylow
365C2×#41—868no—
366C2×#41—1724no—
367C2×#41—1724no—
368C22×Q8—861no—
369C22×D4—21no—
370C22×D4—431no—
371C22×D4—861no—
372C22×D4—861no—
373C22×D4—861no—
374C22×D4C22×D4311yescharacteristic
375C23×C4—21no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—861no—
379C23×C4—861no—
380C23×C4—861no—
381C23×C4C22×D4311yescharacteristic
382C22×C8—432no—
383C22×C8C22×D4312yes—
384C4⋊Q8—434no—
385C4⋊Q8—862no—
386#127—434no—
387#127—862no—
388#124—868no—
389#121—22no—
390#121—434no—
391#121—868no—
392#121—862no—
393#121C4×D4314yes—
394C4×D4—434no—
395C4×D4—434no—
396C4×D4—868no—
397C4×D4—862no—
398C4×D4—862no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—432no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—1722no—
406C2×C4⋊C4C22×D4312yes—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—434no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—434no—
416C2×C42—431no—
417C2×C42—431no—
418C4⋊C8—864no—
419#102—42no—
420#102—1722no—
421#102—1722no—
422#102—1722no—
423C22⋊C8—22no—
424C22⋊C8—862no—
425#97—864no—
426#95—862no—
427#95—862no—
428#95—862no—
429#95—862no—
430C24—21no—
431C24—861no—
432C24D4×D4311yescharacteristic
433#41—17232no—
434C2×Q8—864no—
435C2×Q8—1722no—
436C2×Q8—1722no—
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—432no—
444C2×D4—864no—
445C2×D4—864no—
446C2×D4—864no—
447C2×D4—861no—
448C2×D4—862no—
449C2×D4—862no—
450C2×D4—1722no—
451C2×D4—1722no—
452C2×D4—1722no—
453C2×D4—1722no—
454C2×D4—1722no—
455C2×D4—1722no—
456C2×D4C2×C4×D4312yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—434no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—434no—
470C22×C4—864no—
471C22×C4—864no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—861no—
475C22×C4—862no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4—1721no—
479C22×C4—1721no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4C2×C4×D4312yes—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4312yes—
488C22×C4C23×D4311yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—862no—
493C2×C8—862no—
494C2×C8—862no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—42no—
499C4⋊C4—432no—
500C4⋊C4—864no—
501C4⋊C4—861no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—1722no—
505C4⋊C4C2×C4×D4312yes—
506C22⋊C4—24no—
507C22⋊C4—864no—
508C22⋊C4—864no—
509C22⋊C4—864no—
510C42—434no—
511C42—434no—
512C42—432no—
513C42—432no—
514C42—432no—
515C42—432no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—862no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23C22⋊C4×D4312yes—
535C23#1306334912yes—
536C23#1306335212yes—
537C23C2×D4×D4311yescharacteristic
538Q8—1728no—
539D4—24no—
540D4—48no—
541D4—42no—
542D4—864no—
543D4—1728no—
544D4—1728no—
545D4—1728no—
546D4—1722no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—84no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—868no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—3444no—
573C2×C4—1728no—
574C2×C4—1724no—
575C2×C4—1728no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4C22⋊C4×D4312yes—
582C2×C4C22×C4×D4311yescharacteristic
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4#1306337012yes—
585C2×C4#1306337212yes—
586C8—42no—
587C8—1722no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—3441no—
605C22—1722no—
606C22—1722no—
607C22—1722no—
608C22#1458290214yes—
609C22C2×C22⋊C4×D4311yescharacteristic
610C22#1458346411yescharacteristic
611C22#1458347111yescharacteristic
612C22C2×#1306334911yescharacteristic
613C22C2×#1306335211yescharacteristic
614C22#1458369511yescharacteristic
615C22#1458369811yescharacteristic
616C4—22no—
617C4—42no—
618C4—82no—
619C4—862no—
620C4—862no—
621C4—862no—
622C4—862no—
623C4—3442no—
624C4—1722no—
625C4#1458337812yes—
626C4#1458347612yes—
627C2—24no—
628C2—82no—
629C2—3442no—
630C2#1913718211yescharacteristic
631C2C2×#1458290211yescharacteristic
632C2#1914311111yescharacteristic
633C2#1914557911yescharacteristic
634C2#1914558111yescharacteristic
635C2#1914578211yescharacteristic
636C2#1914578411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583444C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43#21865
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#14582953C2semidirect
3. C2×#14582764C2semidirect
4. #19135566C2semidirect
5. #19135417C2semidirect
6. #19134913C2semidirect
7. #19134912C2semidirect
8. #19134910C2semidirect
9. #19134604C2semidirect
10. #19134603C2semidirect
11. C43×#1874C2semidirect
14. #14583444C4semidirect
61. #13063324C2×C4semidirect
63. #13063321C2×C4semidirect
69. D4×Dic43C2×C4semidirect
71. #13063287C2×C4semidirect
317. #1874D43semidirect
364. C43#21865semidirect

Maximal subgroups

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

subgroupindex
C2×#145834442
C2×#145829532
C2×#145827642
#191355662
#191354172
#191349132
#191349122
#191349102
#191346042
#191346032
C43×#18742
#2186543