Finite Group Databasebeta

← #25135339

Subgroups — #25135339

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583040C211yesmaximal, characteristic
2C2×#14582953C211yesmaximal, characteristic, complemented
3#19142927C211yesmaximal, characteristic
4C2×#14582804C211yesmaximal, characteristic, complemented
5#19135985C212yesmaximal, complemented
6#19135914C212yesmaximal, complemented
7#19135474C212yesmaximal, complemented
8#19135286C212yesmaximal, complemented
9#19134912C211yesmaximal, characteristic
10#19134529C211yesmaximal, characteristic, complemented
11C43×#1852C211yesmaximal, characteristic, complemented
12C23×Dic86C2211yescharacteristic
13C22×#10621873C2212yes—
14C2×#13063309—21no—
15C2×#13063299C2211yescharacteristic
16C22×C4×Dic43C2211yescharacteristic
17#14583040—24no—
18#14582953—24no—
19C2×Dic43⋊C8C2212yes—
20C2×#13063250C2212yes—
21C2×#13063248C2212yes—
22C2×#13063248C2212yes—
23C2×#13063245C2212yes—
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063235C2212yes—
26#14582804—21no—
27#14582804—21no—
28#14582804C2212yes—
29#14582804C2212yes—
30#14582800C2211yescharacteristic
31#14582800C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582791—21no—
35#14582791—21no—
36#14582776—21no—
37C2×C43⋊#95—21no—
38C2×C43⋊#95—21no—
39#14582661C2212yes—
40C22×C4⋊C4×C43C2211yescharacteristic
41C2×#107×C43C2212yes—
42C2×C22⋊C8×C43C2211yescharacteristic
43C43×#380C2211yescharacteristic
44C43×#340C2212yes—
45C22×Dic86—21no—
46C22×Dic86—24no—
47C22×Dic86—22no—
48C22×Dic86—22no—
49C22×Dic86—42no—
50C22×Dic86C2312yes—
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C23×Dic43—21no—
54C23×Dic43D411yescharacteristic
55C23×Dic43D411yescharacteristic
56C2×#10621873—24no—
57C2×#10621873—24no—
58C2×#10621873—42no—
59C22×C43⋊C8C2312yes—
60#13063309—44no—
61#13063299—22no—
62#13063299—22no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2311yescharacteristic
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68C2×(C2×D43)⋊C4—21no—
69C2×(C2×D43)⋊C4—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×C4×Dic43—22no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43D411yescharacteristic
74C2×C4×Dic43D411yescharacteristic
75C2×C4×Dic43C2311yescharacteristic
76C2×C4×Dic43C2311yescharacteristic
77Dic43⋊C8—24no—
78#13063250—24no—
79#13063248—24no—
80#13063248—42no—
81#13063245—42no—
82C22⋊(C43⋊C8)—22no—
83#13063235—24no—
84C43⋊#95—21no—
85C43⋊#95—21no—
86C43⋊#95—22no—
87C43⋊#95—22no—
88C43⋊#95—22no—
89C43⋊#95—22no—
90C23×C4×C43—21no—
91C23×C4×C43C2311yescharacteristic
92C22×C8×C43C2312yes—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—42no—
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2312yes—
98C2×C22⋊C4×C43—21no—
99#107×C43—42no—
100C22⋊C8×C43D414yes—
101#95×C43—21no—
102C24×C43C2×D411yescharacteristic
103C23×D43—21no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—42no—
110C22×C4×C43—42no—
111C22×C4×C43—42no—
112C22×C4×C43C2×D412yes—
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43#4112yes—
115C22×C4×C43C2411yescharacteristic
116C2×C22⋊D43—42no—
117C2×C22⋊D43—42no—
118C2×C22⋊D43—42no—
119C22×Dic43—24no—
120C22×Dic43—22no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—21no—
127C22×Dic43—41no—
128C22×Dic43—42no—
129C22×Dic43—42no—
130C22×Dic43C2×D411yescharacteristic
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—22no—
137C2×D172—22no—
138C2×Dic86—22no—
139C2×Dic86—22no—
140C2×Dic86—22no—
141C2×Dic86—22no—
142C2×Dic86—24no—
143C2×Dic86—22no—
144C2×Dic86—48no—
145C2×Dic86—48no—
146C2×Dic86—42no—
147C2×Dic86—42no—
148C2×Dic86#4114yes—
149C2×C8×C43—22no—
150C2×C8×C43—22no—
151C2×C8×C43C2×D414yes—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—42no—
157C22⋊C4×C43—42no—
158(C2×D43)⋊C4—42no—
159(C2×D43)⋊C4—42no—
160(C2×D43)⋊C4—42no—
161(C2×D43)⋊C4—42no—
162(C2×D43)⋊C4—42no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—42no—
166C4⋊Dic43—42no—
167C4×Dic43—22no—
168C4×Dic43—22no—
169C4×Dic43—21no—
170C4×Dic43—21no—
171C4×Dic43—21no—
172C4×Dic43—21no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176#10621873—48no—
177C23×C43—21no—
178C23×C43—21no—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43#12112yes—
182C23×C43AGL(1,ℤ/8)12yes—
183C23×C43#13712yes—
184C23×C43C22×D411yescharacteristic
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—24no—
195C2×C4×C43—24no—
196C2×C4×C43—41no—
197C2×C4×C43—42no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—84no—
206C2×C4×C43#12112yes—
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C2×#4112yes—
209C2×C4×C43C2×#4111yescharacteristic
210C2×C4×C43H(5,𝔽2)12yes—
211C22⋊D43—84no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—24no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—44no—
225C2×Dic43—48no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—44no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43#13712yes—
233D172—42no—
234D172—42no—
235Dic86—24no—
236Dic86—24no—
237Dic86—48no—
238Dic86—42no—
239Dic86—42no—
240C8×C43—24no—
241C43⋊C8—42no—
242#24509—431nomaximal, Sylow
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—22no—
248C22×C43—22no—
249C22×C43#46814yes—
250C22×C43C2×#12111yescharacteristic
251C22×C43#52511yescharacteristic
252C22×C43#53511yescharacteristic
253C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
254C22×C43C2×#13711yescharacteristic
255C22×C43C2×#13711yescharacteristic
256C22×C43#57511yescharacteristic
257C2×D43—81no—
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C4×C43—22no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43—82no—
268C4×C43#54612yes—
269C4×C43#55112yes—
270Dic43—22no—
271Dic43—44no—
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275Dic43—81no—
276C2×#448—431no—
277C2×#432—431no—
278#2854—431no—
279C2×#391—431no—
280#2068—432no—
281#2055—432no—
282#1973—432no—
283#1935—432no—
284#1874—431no—
285#1852D4311yescharacteristic, complemented
286#1787—431no—
287C2×C43—24no—
288C2×C43#241111yescharacteristic
289C2×C43C2×#46811yescharacteristic
290C2×C43#305611yescharacteristic
291C2×C43#311211yescharacteristic
292C2×C43#311711yescharacteristic
293C2×C43#321311yescharacteristic
294C2×C43#321811yescharacteristic
295D43—161no—
296C23×Q8—431no—
297C22×SD16—432no—
298C2×#123—861no—
299C2×#121—431no—
300C22×C4⋊C4C2×D4311yescharacteristic
301C22×C42—431no—
302#448—864no—
303#432—864no—
304C2×#107C2×D4312yes—
305C2×C4⋊C8—432no—
306C2×#103—432no—
307C2×#103—432no—
308C2×#103—432no—
309C2×#102—432no—
310C2×C22⋊C8—431no—
311C2×C22⋊C8C2×D4311yescharacteristic
312C2×#97—432no—
313#391—432no—
314#391—432no—
315#391—861no—
316#391—861no—
317#390—431no—
318#390—431no—
319#389—431no—
320#389—431no—
321#388—861no—
322#388—861no—
323#386—861no—
324#380C2×D4311yescharacteristic
325C2×#95—861no—
326C2×#95—861no—
327#340—432no—
328#340C2×D4312yes—
329C43#2450911yescharacteristic, complemented, Sylow
330C22×Q8—432no—
331C22×Q8—864no—
332C22×Q8—861no—
333C22×Q8—862no—
334C22×Q8—862no—
335C22×Q8—1722no—
336C22×D4—431no—
337C22×D4—861no—
338C23×C4—21no—
339C23×C4—431no—
340C23×C4—431no—
341C23×C4—861no—
342C23×C4C22×D4311yescharacteristic
343C2×SD16—864no—
344C2×SD16—864no—
345C2×SD16—1722no—
346C22×C8—432no—
347C22×C8C22×D4312yes—
348#123—1724no—
349#121—862no—
350#121—862no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—431no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4C22×D4312yes—
357C2×C4⋊C4C22×D4311yescharacteristic
358C2×C4⋊C4C22×D4311yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—861no—
361C2×C22⋊C4—861no—
362C2×C22⋊C4—861no—
363C2×C22⋊C4—861no—
364C2×C22⋊C4—861no—
365C2×C42—431no—
366C2×C42—431no—
367C2×C42—431no—
368C2×C42—431no—
369C2×C42—862no—
370C2×C42—862no—
371#107—42no—
372C4⋊C8—864no—
373#103—864no—
374#103—864no—
375#103—1722no—
376#102—1722no—
377C22⋊C8—862no—
378C22⋊C8D17214yes—
379#97—864no—
380#95—21no—
381#95—862no—
382#95—862no—
383#95—862no—
384#95—862no—
385#95—861no—
386#95—861no—
387C24—861no—
388C24D4×D4311yescharacteristic
389C2×Q8—434no—
390C2×Q8—864no—
391C2×Q8—862no—
392C2×Q8—862no—
393C2×Q8—862no—
394C2×Q8—862no—
395C2×Q8—862no—
396C2×Q8—1728no—
397C2×Q8—1728no—
398C2×Q8—1722no—
399C2×Q8—1722no—
400C2×D4—861no—
401C2×D4—862no—
402C2×D4—861no—
403C2×D4—862no—
404C2×D4—1722no—
405C2×D4—1722no—
406C2×D4—1722no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—431no—
416C22×C4—431no—
417C22×C4—431no—
418C22×C4—431no—
419C22×C4—862no—
420C22×C4—864no—
421C22×C4—862no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—861no—
427C22×C4—1721no—
428C22×C4—1722no—
429C22×C4—1722no—
430C22×C4C2×D17212yes—
431C22×C4D4×D4311yescharacteristic
432C22×C4#1062190212yes—
433C22×C4C23×D4311yescharacteristic
434SD16—1728no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—862no—
438C2×C8—862no—
439C2×C8—862no—
440C2×C8C2×D17214yes—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—42no—
446C4⋊C4—861no—
447C4⋊C4—861no—
448C4⋊C4—1722no—
449C4⋊C4—1722no—
450C22⋊C4—42no—
451C22⋊C4—1722no—
452C22⋊C4—1722no—
453C22⋊C4—1722no—
454C22⋊C4—1722no—
455C22⋊C4—1722no—
456C42—862no—
457C42—862no—
458C42—861no—
459C42—861no—
460C42—861no—
461C42—861no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—1721no—
467C23—1721no—
468C23—1721no—
469C23—1721no—
470C23—1721no—
471C23—1721no—
472C23—1721no—
473C23#1306330012yes—
474C23#1306334912yes—
475C23#1306335712yes—
476C23C2×D4×D4311yescharacteristic
477Q8—864no—
478Q8—864no—
479Q8—1728no—
480Q8—1722no—
481Q8—1722no—
482D4—3444no—
483D4—1722no—
484D4—1722no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—84no—
499C2×C4—432no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—864no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—1724no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1728no—
517C2×C4—1722no—
518C2×C4—1724no—
519C2×C4—1722no—
520C2×C4#1306330012yes—
521C2×C4C22×D17211yescharacteristic
522C2×C4#41×D4312yes—
523C2×C4C2×#1062190211yescharacteristic
524C2×C4#1306337012yes—
525C8—24no—
526C8—1722no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—3441no—
534C22—3441no—
535C22—3441no—
536C22—3441no—
537C22—3441no—
538C22—3441no—
539C22—3441no—
540C22#1458314614yes—
541C22C2×#1306330011yescharacteristic
542C22#1458340711yescharacteristic
543C22#1458346411yescharacteristic
544C22C2×#1306334911yescharacteristic
545C22#137×D4311yescharacteristic
546C22C2×#1306335711yescharacteristic
547C22#1458369511yescharacteristic
548C4—22no—
549C4—81no—
550C4—82no—
551C4—81no—
552C4—862no—
553C4—3441no—
554C4—1721no—
555C4—1724no—
556C4—1721no—
557C4—1721no—
558C4#1458354412yes—
559C4#1458357612yes—
560C2—24no—
561C2—6881no—
562C2#1913797811yescharacteristic
563C2C2×#1458314611yescharacteristic
564C2#1914422611yescharacteristic
565C2#1914471411yescharacteristic
566C2#1914476911yescharacteristic
567C2#1914557911yescharacteristic
568C2#1914562511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1852C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1852D43
hypocenterC43#24509
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#14582953C2semidirect
4. C2×#14582804C2semidirect
5. #19135985C2semidirect
6. #19135914C2semidirect
7. #19135474C2semidirect
8. #19135286C2semidirect
10. #19134529C2semidirect
11. C43×#1852C2semidirect
285. #1852D43semidirect
329. C43#24509semidirect

Maximal subgroups

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

subgroupindex
C2×#145830402
C2×#145829532
#191429272
C2×#145828042
#191359852
#191359142
#191354742
#191352862
#191349122
#191345292
C43×#18522
#2450943