Finite Group Databasebeta

← #25115757

Subgroups — #25115757

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582984C211yesmaximal, characteristic
2#19137540C211yesmaximal, characteristic
3Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
4#19135292C211yesmaximal, characteristic
5#19135290C211yesmaximal, characteristic
6#19135173C211yesmaximal, characteristic, complemented
7#19135171C211yesmaximal, characteristic, complemented
8#19134950C211yesmaximal, characteristic
9#19134948C211yesmaximal, characteristic
10#19134721C211yesmaximal, characteristic, complemented
11#19134598C211yesmaximal, characteristic, complemented
12#19134594C211yesmaximal, characteristic
13#19134463C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063282—21no—
21#14582984C418yescomplemented
22C2×#13063256C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582801C2211yescharacteristic
31#14582800C2211yescharacteristic
32#14582797—21no—
33#14582797C2211yescharacteristic
34#14582795—21no—
35#14582795C2211yescharacteristic
36#14582790—21no—
37#14582788—21no—
38#14582768—21no—
39#14582768C2211yescharacteristic
40#14582768C2211yescharacteristic
41#14582758—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67Q8×Dic43—22no—
68Q8×Dic43—22no—
69Q8×Dic43—41no—
70Q8×Dic43C2×C414yes—
71#13063287—22no—
72#13063287C2×C414yes—
73#13063282—44no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C2×Dic43⋊C4D411yescharacteristic
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063256C2×C414yes—
98Dic43⋊C8—22no—
99#13063249—22no—
100#13063247—41no—
101#13063247C2×C414yes—
102#13063245—41no—
103#13063235—41no—
104C8×Dic43C2×C414yes—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×Q8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×Q8×C43—22no—
114C4×Q8×C43—41no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#103×C43—22no—
123#103×C43C2×C414yes—
124#97×C43—41no—
125#95×C43—21no—
126C23×D43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C22×C412yes—
131C2×Q8×C43#4112yes—
132C2×Q8×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C22×C412yes—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C412yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43C22×C412yes—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—42no—
172C42×C43—42no—
173#10621884—28no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—81no—
178(C2×D43)⋊C4—81no—
179C4⋊Dic43—21no—
180C4⋊Dic43—24no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—42no—
186C4⋊Dic43C22×C412yes—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—24no—
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×C43C22×D411yescharacteristic
209C22×D43—22no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—22no—
219Q8×C43#11714yescomplemented
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
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×C43C23×C411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43C4×D412yes—
262C2×Dic43C4×D412yes—
263C2×Dic43AGL(1,ℤ/8)12yes—
264C2×Dic43#13712yes—
265D172—22no—
266D172—22no—
267D172—41no—
268D172—41no—
269C4×D43—48no—
270C8×C43—22no—
271C8×C43—41no—
272C43⋊C8—22no—
273C43⋊C8—41no—
274#22759—431nomaximal, Sylow
275C22×C43C2×C4×D411yescharacteristic
276C22×C43#54611yescharacteristic
277C22×C43#54811yescharacteristic
278C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C43C2×#13711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57711yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C4×C43—24no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43C2×#11711yescharacteristic
296C4×C43#52011yescharacteristic
297C4×C43#55211yescharacteristic
298C4×C43#55311yescharacteristic
299Dic43—22no—
300Dic43—41no—
301Dic43—41no—
302Dic43—42no—
303Dic43—81no—
304Dic43—81no—
305Dic43#44014yes—
306C2×C4×SD16—431no—
307#2354—431no—
308Q8×C4⋊C4—431no—
309#1936—431no—
310#1936—431no—
311#1919—431no—
312#1919—431no—
313#1880—431no—
314#1880—431no—
315#1834—431no—
316#1803—431no—
317#1802—431no—
318#1770—431no—
319#1763—431no—
320#1763D4311yescharacteristic, complemented
321C2×C43#235211yescharacteristic
322C2×C43C2×#44011yescharacteristic
323C2×C43#295211yescharacteristic
324C2×C43#332911yescharacteristic
325C2×C43#333211yescharacteristic
326C2×C43#336811yescharacteristic
327C2×C43#336911yescharacteristic
328D43—82no—
329C22×SD16—431no—
330C2×C4×Q8—431no—
331C2×C4×Q8—431no—
332C2×C4×Q8C2×D4311yescharacteristic
333C2×C4×D4—431no—
334C2×#117—861no—
335C4×SD16—438no—
336C2×#106—431no—
337C2×C4⋊C8—431no—
338C2×#103—431no—
339C2×#103C2×D4311yescharacteristic
340C2×#103C2×D4311yescharacteristic
341C2×#102—431no—
342C2×#102—431no—
343C2×#102—431no—
344C2×#97—431no—
345C2×#97C2×D4311yescharacteristic
346C2×C4×C8—431no—
347#390—431no—
348#390—431no—
349#389—431no—
350#389—431no—
351#389—861no—
352#389—861no—
353#388—861no—
354#388—861no—
355#384—431no—
356#384—431no—
357#384—861no—
358#380—861no—
359C4×C4⋊C4—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—861no—
362C4×C4⋊C4C2×D4311yescharacteristic
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340C2×D4311yescharacteristic
370#340C2×D4311yescharacteristic
371#336—431no—
372#336—431no—
373C43#2275911yescharacteristic, complemented, Sylow
374C22×Q8C22×D4311yescharacteristic
375C22×D4—431no—
376C23×C4—861no—
377C2×SD16—434no—
378C2×SD16—862no—
379C2×SD16—862no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C4×Q8—22no—
385C4×Q8—41no—
386C4×Q8—434no—
387C4×Q8—862no—
388C4×Q8—862no—
389C4×Q8—1721no—
390C4×D4—434no—
391C4×D4—862no—
392#117—1724no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42C22×D4311yescharacteristic
423#106—434no—
424C4⋊C8—862no—
425#103—22no—
426#103—862no—
427#103C4×D4314yes—
428#102—434no—
429#102—1721no—
430#102—1721no—
431#97—41no—
432#97—1721no—
433C4×C8—434no—
434#95—21no—
435#95—431no—
436#95—431no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—861no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×C4×D4312yes—
445C2×Q8#1062189812yes—
446C2×Q8#1062189812yes—
447C2×D4—432no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—864no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470SD16—868no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—432no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8C2×C4×D4312yes—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—432no—
490C4⋊C4—862no—
491C4⋊C4—862no—
492C4⋊C4—864no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—3441no—
499C4⋊C4—3441no—
500C4⋊C4—3441no—
501C4⋊C4—3441no—
502C4⋊C4—1722no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4C2×C4×D4312yes—
506C22⋊C4—864no—
507C22⋊C4—3441no—
508C22⋊C4—3441no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—42no—
515C42—432no—
516C42—432no—
517C42—864no—
518C42—861no—
519C42—861no—
520C42—1722no—
521C42—1722no—
522C23—862no—
523C23—1721no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23—1721no—
528C23—1721no—
529C23C2×D4×D4311yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8#1306328214yescomplemented
534D4—862no—
535D4—862no—
536D4—1721no—
537D4—1721no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—862no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—1728no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C22×C4×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4C2×#1062189811yescharacteristic
581C2×C4C2×#1062189811yescharacteristic
582C2×C4#1306337011yescharacteristic
583C2×C4#1306337211yescharacteristic
584C8—22no—
585C8—41no—
586C8—862no—
587C8—1721no—
588C22—3441no—
589C22—3441no—
590C22—3441no—
591C22—3441no—
592C22—1722no—
593C22—1722no—
594C22—1722no—
595C22C4×D4×D4311yescharacteristic
596C22#1458353911yescharacteristic
597C22#1458355811yescharacteristic
598C22AGL(1,ℤ/8)×D4311yescharacteristic
599C22#137×D4311yescharacteristic
600C22#1458370811yescharacteristic
601C22#1458370811yescharacteristic
602C4—24no—
603C4—41no—
604C4—41no—
605C4—42no—
606C4—81no—
607C4—81no—
608C4—434no—
609C4—862no—
610C4—3441no—
611C4—3441no—
612C4—1722no—
613C4—1721no—
614C4—1721no—
615C4C2×#1306328211yescharacteristic
616C4#1458337811yescharacteristic
617C4#1458358211yescharacteristic
618C4#1458359811yescharacteristic
619C2—3442no—
620C2#1913751811yescharacteristic
621C2#440×D4311yescharacteristic
622C2#1914347511yescharacteristic
623C2#1914688511yescharacteristic
624C2#1914691811yescharacteristic
625C2#1914732511yescharacteristic
626C2#1914733611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1763D43
hypocenterC43#22759
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
3. Q8×Dic43⋊C4C2semidirect
6. #19135173C2semidirect
7. #19135171C2semidirect
10. #19134721C2semidirect
11. #19134598C2semidirect
13. #19134463C2semidirect
14. #19134427C2semidirect
15. C43×#1763C2semidirect
21. #14582984C4semidirect
219. Q8×C43#117semidirect
320. #1763D43semidirect
373. C43#22759semidirect
533. Q8#13063282semidirect

Maximal subgroups

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

subgroupindex
C2×#145829842
#191375402
Q8×Dic43⋊C42
#191352922
#191352902
#191351732
#191351712
#191349502
#191349482
#191347212
#191345982
#191345942
#191344632
#191344272
C43×#17632
#2275943