Finite Group Databasebeta

← #24986259

Subgroups — #24986259

Order 11008.

954 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582861C211yesmaximal, characteristic
2C2×C22⋊C8×D43C211yesmaximal, characteristic
3#19136976C211yesmaximal, characteristic
4#19132443C211yesmaximal, characteristic, complemented
5#19132442C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1282C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621872—21no—
10C22×C8×D43C412yescomplemented
11C2×#13063282—21no—
12#14582861—21no—
13#14582861—21no—
14#14582861C412yescomplemented
15#14582861C412yescomplemented
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18C2×(C2×D43)⋊C8—21no—
19C2×(C2×D43)⋊C8C412yescomplemented
20C22⋊C8×D43—21no—
21C22⋊C8×D43—21no—
22C22⋊C8×D43—21no—
23C22⋊C8×D43—21no—
24#14582761—21no—
25#14582758—21no—
26#14582757C412yes—
27#14582754C412yes—
28C4×(C2×D43)⋊C4—21no—
29C4×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊C8×C43C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C4×C22⋊C4×C43C2211yescharacteristic
33C24×D43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C22×C4×D43—44no—
36C22×C4×D43C2×C411yescharacteristic
37C22×C4×D43C2×C411yescharacteristic
38C22×C4×D43C2×C411yescharacteristic
39C22×C4×D43C2×C411yescharacteristic
40C22×C4×D43D411yescharacteristic
41C22×C4×D43D411yescharacteristic
42C22×C4×D43D411yescharacteristic
43C22×C4×D43D411yescharacteristic
44C22×C4×D43D411yescharacteristic
45C22×C4×D43D411yescharacteristic
46C22×C4×D43Q811yescharacteristic
47C22×C4×D43Q811yescharacteristic
48C2×#10621872—22no—
49C2×#10621872—22no—
50C2×#10621872—44no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8C2×C412yes—
53C2×C8×D43—22no—
54C2×C8×D43—22no—
55C2×C8×D43—44no—
56#13063282—44no—
57C2×Dic43⋊C4—22no—
58C2×C22⋊Dic43C2×C412yes—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×C4×Dic43—21no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)C2×C412yes—
66(C2×D43)⋊C8—22no—
67(C2×D43)⋊C8—22no—
68(C2×D43)⋊C8—22no—
69(C2×D43)⋊C8—22no—
70C43⋊#95—21no—
71C43⋊#95—22no—
72C23×C4×C43C2311yescharacteristic
73C22×C8×C43—21no—
74C22×C8×C43C2×C412yes—
75C2×C22⋊C4×C43C2×C412yes—
76C2×C42×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43C2×C412yes—
81#95×C43—21no—
82C24×C43C22×C411yescharacteristic
83C23×D43—22no—
84C23×D43—22no—
85C23×D43—42no—
86C23×D43—42no—
87C23×D43C4211yescharacteristic
88C23×D43C4211yescharacteristic
89C23×D43C22⋊C411yescharacteristic
90C23×D43C22⋊C411yescharacteristic
91C23×D43C4⋊C411yescharacteristic
92C23×D43C4⋊C411yescharacteristic
93C22×C4×C43—22no—
94C22×C4×C43—42no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×Q811yescharacteristic
101C22×Dic43—22no—
102C22×Dic43—42no—
103C22×Dic43C4211yescharacteristic
104C22×Dic43C4211yescharacteristic
105C22×Dic43C22⋊C411yescharacteristic
106C22×Dic43C22⋊C411yescharacteristic
107C22×Dic43C4⋊C411yescharacteristic
108C22×Dic43C4⋊C411yescharacteristic
109C2×C4×D43—24no—
110C2×C4×D43—24no—
111C2×C4×D43—24no—
112C2×C4×D43—42no—
113C2×C4×D43—42no—
114C2×C4×D43—42no—
115C2×C4×D43—42no—
116C2×C4×D43—42no—
117C2×C4×D43—42no—
118C2×C4×D43—42no—
119C2×C4×D43—42no—
120C2×C4×D43—42no—
121C2×C4×D43C22⋊C411yescharacteristic
122C2×C4×D43C22⋊C411yescharacteristic
123C2×C4×D43C22⋊C411yescharacteristic
124C2×C4×D43C22⋊C411yescharacteristic
125C2×C4×D43C22⋊C411yescharacteristic
126C2×C4×D43C22⋊C411yescharacteristic
127C2×C4×D43C22⋊C411yescharacteristic
128C2×C4×D43C22⋊C411yescharacteristic
129C2×C4×D43C4⋊C411yescharacteristic
130C2×C4×D43C4⋊C411yescharacteristic
131C2×C4×D43C4⋊C411yescharacteristic
132C2×C4×D43C4⋊C411yescharacteristic
133C2×C4×D43C4⋊C411yescharacteristic
134C2×C4×D43C4⋊C411yescharacteristic
135C2×C4×D43C4⋊C411yescharacteristic
136C2×C4×D43C4⋊C411yescharacteristic
137C2×C8×C43—22no—
138C2×C8×C43—22no—
139C2×C8×C43—42no—
140C2×C8×C43—42no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—22no—
143C42×C43—42no—
144C22⋊Dic43—22no—
145C22⋊Dic43—22no—
146(C2×D43)⋊C4—44no—
147(C2×D43)⋊C4—44no—
148Dic43⋊C4—44no—
149C4×Dic43—42no—
150C2×C43⋊C8—22no—
151C2×C43⋊C8—22no—
152C2×C43⋊C8—42no—
153C2×C43⋊C8—42no—
154#10621872—44no—
155#10621872—44no—
156C8×D43—44no—
157C8×D43—44no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43C2×C4211yescharacteristic
161C23×C43C2×C22⋊C411yescharacteristic
162C23×C43C2×C4⋊C411yescharacteristic
163C23×C43#13112yes—
164C23×C43#13112yes—
165C22×D43—21no—
166C22×D43—21no—
167C22×D43—22no—
168C22×D43—22no—
169C22×D43—21no—
170C22×D43—21no—
171C22×D43—22no—
172C22×D43—22no—
173C22×D43—22no—
174C22×D43—22no—
175C22×D43—22no—
176C22×D43—22no—
177C22×D43—22no—
178C22×D43—22no—
179C22×D43—41no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—48no—
186C22×D43—48no—
187C22×D43#9511yescharacteristic
188C22×D43#9511yescharacteristic
189C22×D43#9511yescharacteristic
190C22×D43#9511yescharacteristic
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43C2×C22⋊C411yescharacteristic
201C2×C4×C43C2×C22⋊C411yescharacteristic
202C2×C4×C43C2×C4⋊C411yescharacteristic
203C2×C4×C43C2×C4⋊C411yescharacteristic
204C2×Dic43—22no—
205C2×Dic43—22no—
206C2×Dic43—22no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—42no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43#9511yescharacteristic
214C2×Dic43#9511yescharacteristic
215C2×Dic43#9511yescharacteristic
216C2×Dic43#9511yescharacteristic
217C4×D43—22no—
218C4×D43—22no—
219C4×D43—22no—
220C4×D43—22no—
221C4×D43—22no—
222C4×D43—22no—
223C4×D43—22no—
224C4×D43—22no—
225C4×D43—22no—
226C4×D43—41no—
227C4×D43—41no—
228C4×D43—41no—
229C4×D43—41no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43#9914yes—
233C8×C43—42no—
234C8×C43—42no—
235C43⋊C8—42no—
236C43⋊C8—42no—
237#7927—431nomaximal, Sylow
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—42no—
245C22×C43—42no—
246C22×C43C2×#9511yescharacteristic
247C22×C43#40511yescharacteristic
248C22×C43#40511yescharacteristic
249C22×C43#40812yes—
250C22×C43#42412yes—
251C2×D43—24no—
252C2×D43—24no—
253C2×D43—21no—
254C2×D43—21no—
255C2×D43—21no—
256C2×D43—21no—
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—21no—
262C2×D43—21no—
263C2×D43—44no—
264C2×D43—44no—
265C2×D43—44no—
266C2×D43—44no—
267C2×D43—42no—
268C2×D43—42no—
269C2×D43#34212yes—
270C2×D43#34412yes—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—82no—
275C4×C43C2×#9912yes—
276Dic43—21no—
277Dic43—21no—
278Dic43—21no—
279Dic43—82no—
280Dic43#34212yes—
281C2×#407—431no—
282C22×C22⋊C8—431no—
283#2280—431no—
284#1282—431no—
285#1282—431no—
286#1282—431no—
287#1282D4311yescharacteristic, complemented
288C2×C43—22no—
289C2×C43—21no—
290C2×C43—21no—
291C2×C43—22no—
292C2×C43#172911yescharacteristic
293C2×C43C2×#34211yescharacteristic
294C2×C43C2×#34411yescharacteristic
295D43—22no—
296D43—22no—
297D43—41no—
298D43—41no—
299C24×C4—431no—
300C22×M16—861no—
301C23×C8—432no—
302C2×#117—861no—
303#407—432no—
304#407—432no—
305#407—861no—
306#407—861no—
307C2×C22⋊C8—431no—
308C2×C22⋊C8—431no—
309C2×C22⋊C8—432no—
310C2×C22⋊C8—861no—
311C2×C22⋊C8—861no—
312C2×C22⋊C8—861no—
313C2×C22⋊C8—861no—
314C2×C22⋊C8—861no—
315C2×C22⋊C8C2×D4311yescharacteristic
316C2×C22⋊C8C2×D4311yescharacteristic
317#381—861no—
318#380—432no—
319#380—861no—
320#379—432no—
321C4×C22⋊C4—431no—
322C4×C22⋊C4—861no—
323C4×C22⋊C4C2×D4311yescharacteristic
324C43#792711yescharacteristic, complemented, Sylow
325C25—431no—
326C23×C4—431no—
327C23×C4—431no—
328C23×C4—431no—
329C23×C4—431no—
330C23×C4—431no—
331C23×C4—431no—
332C23×C4—431no—
333C23×C4—431no—
334C23×C4—431no—
335C23×C4—431no—
336C23×C4—431no—
337C23×C4—431no—
338C23×C4—431no—
339C23×C4—1724no—
340C23×C4C22×D4311yescharacteristic
341C2×M16—862no—
342C2×M16—862no—
343C2×M16—1724no—
344C22×C8—21no—
345C22×C8—432no—
346C22×C8—862no—
347C22×C8—862no—
348C22×C8—861no—
349C22×C8—1724no—
350C22×C8C4×D4312yes—
351#117—1724no—
352C2×C4⋊C4—862no—
353C2×C22⋊C4—432no—
354C2×C22⋊C4—862no—
355C2×C22⋊C4—862no—
356C2×C22⋊C4C4×D4312yes—
357C2×C42—21no—
358C2×C42—861no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—432no—
363C22⋊C8—862no—
364C22⋊C8—862no—
365C22⋊C8—862no—
366C22⋊C8—862no—
367C22⋊C8—861no—
368C22⋊C8—861no—
369C22⋊C8—861no—
370C22⋊C8C4×D4312yes—
371#95—21no—
372#95—862no—
373#95—861no—
374C24—431no—
375C24—431no—
376C24—431no—
377C24—431no—
378C24—431no—
379C24—431no—
380C24—862no—
381C24—862no—
382C24—1722no—
383C24—1722no—
384C24C2×C4×D4311yescharacteristic
385C22×C4—22no—
386C22×C4—42no—
387C22×C4—431no—
388C22×C4—431no—
389C22×C4—431no—
390C22×C4—431no—
391C22×C4—431no—
392C22×C4—431no—
393C22×C4—431no—
394C22×C4—431no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—431no—
401C22×C4—431no—
402C22×C4—431no—
403C22×C4—431no—
404C22×C4—431no—
405C22×C4—431no—
406C22×C4—431no—
407C22×C4—431no—
408C22×C4—431no—
409C22×C4—864no—
410C22×C4—864no—
411C22×C4—864no—
412C22×C4—862no—
413C22×C4—1722no—
414C22×C4—1722no—
415C22×C4—1722no—
416C22×C4—1722no—
417C22×C4—1722no—
418C22×C4—1722no—
419C22×C4—1722no—
420C22×C4—1722no—
421C22×C4—1722no—
422C22×C4—1722no—
423C22×C4C2×C4×D4311yescharacteristic
424C22×C4C2×C4×D4311yescharacteristic
425C22×C4D4×D4311yescharacteristic
426C22×C4D4×D4311yescharacteristic
427C22×C4D4×D4311yescharacteristic
428C22×C4Q8×D4311yescharacteristic
429M16—1724no—
430M16—1724no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—42no—
434C2×C8—42no—
435C2×C8—862no—
436C2×C8—862no—
437C2×C8—1724no—
438C2×C8—1724no—
439C2×C8—1722no—
440C2×C8—1722no—
441C4⋊C4—1724no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—862no—
445C22⋊C4—862no—
446C22⋊C4—1724no—
447C22⋊C4—1724no—
448C42—42no—
449C42—1722no—
450C23—41no—
451C23—41no—
452C23—431no—
453C23—431no—
454C23—431no—
455C23—431no—
456C23—862no—
457C23—862no—
458C23—862no—
459C23—862no—
460C23—862no—
461C23—862no—
462C23—861no—
463C23—861no—
464C23—861no—
465C23—861no—
466C23—862no—
467C23—862no—
468C23—862no—
469C23—862no—
470C23—1721no—
471C23—1721no—
472C23—1721no—
473C23—1721no—
474C23—1721no—
475C23—1721no—
476C23—1728no—
477C23—1728no—
478C23C42×D4311yescharacteristic
479C23C22⋊C4×D4311yescharacteristic
480C23C4⋊C4×D4311yescharacteristic
481C23#1306333112yes—
482C23#1306333312yes—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—431no—
493C2×C4—434no—
494C2×C4—431no—
495C2×C4—431no—
496C2×C4—431no—
497C2×C4—862no—
498C2×C4—862no—
499C2×C4—862no—
500C2×C4—862no—
501C2×C4—862no—
502C2×C4—862no—
503C2×C4—862no—
504C2×C4—862no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4C22⋊C4×D4311yescharacteristic
522C2×C4C22⋊C4×D4311yescharacteristic
523C2×C4C4⋊C4×D4311yescharacteristic
524C2×C4C4⋊C4×D4311yescharacteristic
525C8—42no—
526C8—42no—
527C8—1722no—
528C8—1722no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—42no—
536C22—42no—
537C22—432no—
538C22—432no—
539C22—864no—
540C22—864no—
541C22—861no—
542C22—861no—
543C22—861no—
544C22—861no—
545C22—861no—
546C22—861no—
547C22—861no—
548C22—861no—
549C22—861no—
550C22—861no—
551C22—1724no—
552C22—1724no—
553C22—1724no—
554C22—1724no—
555C22—1722no—
556C22—1722no—
557C22#95×D4311yescharacteristic
558C22#1458285311yescharacteristic
559C22#1458285611yescharacteristic
560C22#1458286412yes—
561C22#1458292412yes—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—82no—
566C4—432no—
567C4—861no—
568C4—861no—
569C4—861no—
570C4—3442no—
571C4#99×D4312yes—
572C2—22no—
573C2—21no—
574C2—21no—
575C2—22no—
576C2—862no—
577C2—862no—
578C2—1721no—
579C2—1721no—
580C2#1913429011yescharacteristic
581C2#342×D4311yescharacteristic
582C2#344×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1282C2
socleC22×C43C2×#95
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1282D43
hypocenterC43#7927
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
4. #19132443C2semidirect
5. #19132442C2semidirect
6. #19132441C2semidirect
7. C43×#1282C2semidirect
10. C22×C8×D43C4semidirect
14. #14582861C4semidirect
15. #14582861C4semidirect
19. C2×(C2×D43)⋊C8C4semidirect
287. #1282D43semidirect
324. C43#7927semidirect

Maximal subgroups

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

subgroupindex
C2×#145828612
C2×C22⋊C8×D432
#191369762
#191324432
#191324422
#191324412
C43×#12822
#792743