Finite Group Databasebeta

← #25129038

Subgroups — #25129038

Order 11008.

1228 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2C2×#14583057C211yesmaximal, characteristic, complemented
3C2×#14582909C211yesmaximal, characteristic, complemented
4#19137960C211yesmaximal, characteristic
5#19135747C212yesmaximal, complemented
6#19135605C212yesmaximal, complemented
7#19135028C211yesmaximal, characteristic, complemented
8#19134935C212yesmaximal, complemented
9#19134900C212yesmaximal, complemented
10#19134691C211yesmaximal, characteristic, complemented
11C43×#1870C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C22×Dic172C2212yes—
14#14583589—24no—
15#14583589—24no—
16C2×#13063318—21no—
17C2×#13063317C2211yescharacteristic
18C2×#13063315—21no—
19C2×#13063306—21no—
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2212yes—
22C2×#13063304C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×#13063284C2211yescharacteristic
25C2×#13063281—21no—
26C22×C4⋊Dic43C2211yescharacteristic
27#14583057—24no—
28#14582909—24no—
29C2×#13063250C2212yes—
30C2×#13063250C2212yes—
31C2×#13063250C2212yes—
32C2×#13063250C2212yes—
33#14582819—21no—
34#14582811—21no—
35#14582805C2212yes—
36#14582779—21no—
37#14582771—21no—
38#14582759C2211yescharacteristic
39#14582662C2212yes—
40#14582662C2212yes—
41#14582662C2212yes—
42C22×M16×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2212yes—
46C43×#336C2212yes—
47C22×Dic86—22no—
48C22×Dic86—24no—
49C22×Dic86—22no—
50C22×Dic86—21no—
51C22×Dic86—42no—
52C22×Dic86C2311yescharacteristic
53C22×Dic86C2312yes—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C2×Dic172—24no—
57C2×Dic172—24no—
58C2×Dic172—42no—
59#13063318—28no—
60#13063317—22no—
61#13063317—22no—
62#13063315—28no—
63#13063306—28no—
64#13063304—22no—
65#13063304—22no—
66#13063304—22no—
67#13063304—24no—
68#13063304—42no—
69#13063304D414yes—
70C4×Dic86—22no—
71C4×Dic86—22no—
72#13063284—22no—
73#13063284D414yes—
74#13063281—28no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43C2312yes—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—22no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95#13063250—24no—
96#13063250—24no—
97#13063250—24no—
98#13063250—42no—
99C43⋊#95—22no—
100C43⋊#95—22no—
101C43⋊#95—21no—
102C22×D4×C43D411yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C2×M16×C43—22no—
106C2×M16×C43—42no—
107C22×C8×C43C2312yes—
108C22×C8×C43C2312yes—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C22⋊C8×C43—22no—
116C22⋊C8×C43—42no—
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—41no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—24no—
136C22×Dic43—22no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—44no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C2×Dic86—28no—
147C2×Dic86—22no—
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—22no—
153C2×Dic86—21no—
154C2×Dic86—22no—
155C2×Dic86—48no—
156C2×Dic86—44no—
157C2×Dic86—44no—
158C2×Dic86—42no—
159C2×Dic86C2×D412yes—
160C2×Dic86#4114yes—
161M16×C43—44no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C4⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C42×C43—21no—
172C42×C43—21no—
173C22⋊Dic43—24no—
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176C22⋊Dic43—44no—
177C22⋊Dic43—42no—
178C4⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43C2×D412yes—
185C4⋊Dic43C2×D412yes—
186C4⋊Dic43C2×D412yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—24no—
189Dic43⋊C4—24no—
190Dic43⋊C4—24no—
191Dic43⋊C4—24no—
192Dic43⋊C4—44no—
193C4×Dic43—24no—
194C4×Dic43—24no—
195Dic172—48no—
196C23×C43—21no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43#12012yes—
205C23×C43#13712yes—
206C23×C43C22×D411yescharacteristic
207D4×C43—44no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—24no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—42no—
222C2×C4×C43#12012yes—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4112yes—
226C2×C4×C43H(5,𝔽2)12yes—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—24no—
232C2×Dic43—48no—
233C2×Dic43—48no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245Dic86—24no—
246Dic86—24no—
247Dic86—24no—
248Dic86—48no—
249Dic86—41no—
250Dic86—41no—
251Dic86—42no—
252Dic86—42no—
253C8×C43—42no—
254C8×C43—42no—
255#23983—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—24no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43C2×#12011yescharacteristic
267C22×C43#54612yes—
268C22×C43C2×#13711yescharacteristic
269C22×C43#57511yescharacteristic
270C22×C43#57812yes—
271C4×C43—22no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43#52511yescharacteristic
276C4×C43#53511yescharacteristic
277C4×C43#54612yes—
278Dic43—44no—
279Dic43—42no—
280Dic43—42no—
281Dic43—42no—
282Dic43—42no—
283Dic43—82no—
284C2×#552—431no—
285C2×#451—431no—
286C2×#419—431no—
287#2409—431no—
288#2026—432no—
289#2001—432no—
290#1894—431no—
291#1878—432no—
292#1872—432no—
293#1870D4311yescharacteristic
294#1825—431no—
295C2×C43—42no—
296C2×C43—42no—
297C2×C43#240411yescharacteristic
298C2×C43#300711yescharacteristic
299C2×C43#301111yescharacteristic
300C2×C43#331212yes—
301C2×C43#332712yes—
302C23×Q8—431no—
303C22×Q16—432no—
304C22×M16C2×D4311yescharacteristic
305#552—864no—
306#552—864no—
307C2×#126—861no—
308C2×#125—431no—
309C2×#125—861no—
310C2×#123—861no—
311C2×C22⋊Q8—431no—
312C2×C22⋊Q8—431no—
313C2×C22⋊Q8—432no—
314C2×C4×Q8—431no—
315C2×C4×D4C2×D4311yescharacteristic
316C2×#117—431no—
317C2×#117—861no—
318C22×C4⋊C4—431no—
319#451—864no—
320#419—864no—
321C2×#103—432no—
322C2×#103—432no—
323C2×#103—432no—
324C2×#103—432no—
325C2×C22⋊C8C2×D4311yescharacteristic
326C2×C22⋊C8C2×D4312yes—
327#395—861no—
328#393—861no—
329#391—432no—
330#386—861no—
331#385—861no—
332#380—431no—
333#340—432no—
334#340—432no—
335#340—432no—
336#336C2×D4312yes—
337C43#2398311yescharacteristic, complemented, Sylow
338C22×Q8—431no—
339C22×Q8—432no—
340C22×Q8—864no—
341C22×Q8—861no—
342C22×Q8—862no—
343C22×Q8—862no—
344C22×Q8—1722no—
345C22×D4D17211yescharacteristic
346C23×C4—861no—
347C23×C4—861no—
348C23×C4C22×D4311yescharacteristic
349C23×C4C22×D4311yescharacteristic
350C2×Q16—864no—
351C2×Q16—864no—
352C2×Q16—1722no—
353C2×M16—22no—
354C2×M16—42no—
355C22×C8C22×D4312yes—
356C22×C8C22×D4312yes—
357#126—868no—
358#125—862no—
359#125—862no—
360#125—868no—
361#123—868no—
362C22⋊Q8—434no—
363C22⋊Q8—862no—
364C22⋊Q8—862no—
365C22⋊Q8—862no—
366C22⋊Q8—864no—
367C22⋊Q8—1722no—
368C4×Q8—862no—
369C4×Q8—862no—
370C4×D4—22no—
371C4×D4—22no—
372#117—434no—
373#117—868no—
374#117—862no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—432no—
379C2×C4⋊C4—862no—
380C2×C4⋊C4—862no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4D17211yescharacteristic
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4D17211yescharacteristic
395C2×C22⋊C4D17211yescharacteristic
396C2×C42—861no—
397C2×C42—861no—
398C2×C42C22×D4311yescharacteristic
399#103—864no—
400#103—864no—
401#103—864no—
402#103—1722no—
403C22⋊C8—22no—
404C22⋊C8—42no—
405#95—861no—
406#95—862no—
407#95—862no—
408C24C2×D17211yescharacteristic
409C24C2×D17211yescharacteristic
410C2×Q8—432no—
411C2×Q8—434no—
412C2×Q8—868no—
413C2×Q8—861no—
414C2×Q8—862no—
415C2×Q8—862no—
416C2×Q8—862no—
417C2×Q8—862no—
418C2×Q8—862no—
419C2×Q8—862no—
420C2×Q8—862no—
421C2×Q8—1724no—
422C2×Q8—1728no—
423C2×Q8—1724no—
424C2×Q8—1722no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—41no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—864no—
435C22×C4—862no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—862no—
441C22×C4—1724no—
442C22×C4—1722no—
443C22×C4—1722no—
444C22×C4—1722no—
445C22×C4C2×D17211yescharacteristic
446C22×C4C2×D17211yescharacteristic
447C22×C4C2×D17211yescharacteristic
448C22×C4C2×D17211yescharacteristic
449C22×C4D4×D4312yes—
450C22×C4D4×D4312yes—
451C22×C4C23×D4311yescharacteristic
452Q16—1728no—
453M16—44no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C4⋊C4—22no—
461C4⋊C4—432no—
462C4⋊C4—432no—
463C4⋊C4—432no—
464C4⋊C4—864no—
465C4⋊C4—864no—
466C4⋊C4—864no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—864no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4—1724no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—864no—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—1724no—
482C22⋊C4—1722no—
483C42—21no—
484C42—21no—
485C42—864no—
486C42—864no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23#1306329512yes—
496C23#1306335812yes—
497C23C22×D17211yescharacteristic
498Q8—864no—
499Q8—864no—
500Q8—864no—
501Q8—1728no—
502Q8—1721no—
503Q8—1722no—
504Q8—1721no—
505Q8—1722no—
506D4—44no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—864no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1728no—
530C2×C4—1728no—
531C2×C4—1722no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4#1306329512yes—
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4#41×D4312yes—
543C2×C4#1306337012yes—
544C8—42no—
545C8—42no—
546C22—22no—
547C22—24no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—42no—
555C22—41no—
556C22C2×#1306329511yescharacteristic
557C22#1458354412yes—
558C22C2×#1306335811yescharacteristic
559C22#1458369911yescharacteristic
560C22#1458371612yes—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—3442no—
566C4—1724no—
567C4—1722no—
568C4—1722no—
569C4—1722no—
570C4—1722no—
571C4#1458340711yescharacteristic
572C4#1458346411yescharacteristic
573C4#1458353812yes—
574C2—42no—
575C2—42no—
576C2#1913791311yescharacteristic
577C2#1914385711yescharacteristic
578C2#1914389211yescharacteristic
579C2#1914664812yes—
580C2#1914686512yes—
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1870C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#1870D43
hypocenterC43#23983
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#14583057C2semidirect
3. C2×#14582909C2semidirect
5. #19135747C2semidirect
6. #19135605C2semidirect
7. #19135028C2semidirect
8. #19134935C2semidirect
9. #19134900C2semidirect
10. #19134691C2semidirect
337. C43#23983semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145830572
C2×#145829092
#191379602
#191357472
#191356052
#191350282
#191349352
#191349002
#191346912
C43×#18702
#2398343