Finite Group Databasebeta

← #25130525

Subgroups — #25130525

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583623C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19139508C211yesmaximal, characteristic
4#19135800C212yesmaximal, complemented
5#19135599C212yesmaximal, complemented
6#19135557C211yesmaximal, characteristic, complemented
7#19135388C211yesmaximal, characteristic, complemented
8#19134914C212yesmaximal, complemented
9#19134791C212yesmaximal, complemented
10#19134601C211yesmaximal, characteristic, complemented
11C2×C43×#474C211yesmaximal, characteristic, complemented
12C22×#10621883C2211yescharacteristic
13#14583623—24no—
14#14583623—24no—
15C2×#13063320—22no—
16C2×#13063314—21no—
17C2×#13063305C2212yes—
18C2×#13063299—21no—
19C2×#13063296C2212yes—
20C2×Q8×Dic43—21no—
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×#13063283C2212yes—
24C4×#10621883—24no—
25C2×#13063256C2211yescharacteristic
26C2×#13063250C2212yes—
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×(C2×D43)⋊C8C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582815—22no—
33#14582769C2211yescharacteristic
34#14582759—21no—
35#14582756C2212yes—
36#14582662C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×C4×D4×C43C2211yescharacteristic
41C43×#474—24no—
42C2×#107×C43C2212yes—
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×#102×C43C2212yes—
45C22×Dic86C2311yescharacteristic
46C22×D172D411yescharacteristic
47C22×C22⋊D43—22no—
48C22×C4×D43C2312yes—
49C2×#10621883—22no—
50C2×#10621883—22no—
51C2×#10621883—22no—
52C22×C43⋊C8C2311yescharacteristic
53C22×C43⋊C8C2311yescharacteristic
54#13063320—216no—
55#13063314—28no—
56#13063305—24no—
57#13063305—24no—
58#13063299—44no—
59#13063296—24no—
60#13063296—42no—
61Q8×Dic43—28no—
62C4×Dic86—22no—
63C4×Dic86D414yescomplemented
64C4×D172—22no—
65C4×D172—22no—
66#13063283—24no—
67#13063283—24no—
68C2×C4⋊Dic43—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—22no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4D412yes—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—22no—
82#13063256—22no—
83#13063250—42no—
84#13063248—22no—
85#13063246—22no—
86(C2×D43)⋊C8—24no—
87(C2×D43)⋊C8—42no—
88C4×C43⋊C8—22no—
89C43⋊#95—22no—
90C22×Q8×C43—21no—
91C22×D4×C43C2311yescharacteristic
92C23×C4×C43—21no—
93C22×C8×C43C2312yes—
94C4⋊Q8×C43—22no—
95C4⋊Q8×C43D414yescomplemented
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2312yes—
101C2×C22⋊C4×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—24no—
104C4⋊C8×C43—22no—
105#102×C43—24no—
106C24×C43—21no—
107C23×D43C2×D412yes—
108C2×Q8×C43—24no—
109C2×Q8×C43—42no—
110C2×Q8×C43—42no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43#4112yes—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2411yescharacteristic
125C2×C22⋊D43—44no—
126C2×C22⋊D43—44no—
127C2×C22⋊D43—82no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—22no—
131C22×Dic43C2×D412yes—
132C2×D172—22no—
133C2×D172—22no—
134C2×D172—22no—
135C2×C4×D43—22no—
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86C2×D412yes—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43—22no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43C2×D414yes—
155C22⋊C4×C43—42no—
156C42×C43C2×D412yes—
157C42×C43C2×D412yes—
158C22⋊Dic43—44no—
159#10621883—28no—
160(C2×D43)⋊C4—28no—
161(C2×D43)⋊C4—28no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—44no—
164C4⋊Dic43—28no—
165C4⋊Dic43—22no—
166C4⋊Dic43—21no—
167C4⋊Dic43—22no—
168C4⋊Dic43—22no—
169C4⋊Dic43—42no—
170C4⋊Dic43—81no—
171C4⋊Dic43C2×D412yes—
172Dic43⋊C4—24no—
173C4×Dic43—28no—
174C4×Dic43—24no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8#4112yes—
181C23×C43—22no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43C22×D411yescharacteristic
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—22no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196Q8×C43—48no—
197D4×C43—22no—
198D4×C43—22no—
199D4×C43—41no—
200D4×C43—41no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—24no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—84no—
210C2×C4×C43#12012yes—
211C2×C4×C43#12012yes—
212C2×C4×C43#13512yes—
213C2×C4×C43AGL(1,ℤ/8)12yes—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43H(5,𝔽2)11yescharacteristic
219C2×C4×C432−1+411yescharacteristic
220C22⋊D43—88no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233D172—44no—
234C4×D43—42no—
235C4×D43—42no—
236C4×D43—42no—
237C4×D43—42no—
238Dic86—22no—
239Dic86—22no—
240Dic86—41no—
241Dic86—41no—
242C8×C43—42no—
243C43⋊C8—22no—
244C43⋊C8—41no—
245#24119—431nomaximal, Sylow
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43C2×#12011yescharacteristic
254C22×C43#54611yescharacteristic
255C22×C43#54711yescharacteristic
256C22×C43C2×#13511yescharacteristic
257C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C43#57711yescharacteristic
259C22×C43#57811yescharacteristic
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—42no—
267C4×C43—22no—
268C4×C43—44no—
269C4×C43—81no—
270C4×C43#44914yes—
271C4×C43#52511yescharacteristic
272C4×C43#53711yescharacteristic
273C4×C43#54811yescharacteristic
274C4×C43#55011yescharacteristic
275Dic43—42no—
276Dic43—42no—
277Dic43—42no—
278Dic43—82no—
279C2×#556—431no—
280C2×#474D4311yescharacteristic, complemented
281C2×C4×SD16—431no—
282#2537—431no—
283#2036—432no—
284#2000—432no—
285#1990—431no—
286#1954—431no—
287#1875—432no—
288#1854—432no—
289#1803—431no—
290C2×C43—82no—
291C2×C43#240711yescharacteristic
292C2×C43C2×#44911yescharacteristic
293C2×C43#301311yescharacteristic
294C2×C43#330211yescharacteristic
295C2×C43#332411yescharacteristic
296C2×C43#334011yescharacteristic
297C2×C43#335311yescharacteristic
298D43—82no—
299C22×SD16—431no—
300#556—864no—
301#556—864no—
302C2×C4⋊Q8C2×D4311yescharacteristic
303C2×#126—862no—
304C2×#124—861no—
305C2×C22⋊Q8—432no—
306C2×#121—432no—
307C2×#121—861no—
308C2×C4×Q8—431no—
309C2×C4×Q8—861no—
310C2×C4×D4—431no—
311C2×C4×D4C2×D4311yescharacteristic
312C2×#117—432no—
313#474—24no—
314C4×SD16—864no—
315C2×#107C2×D4312yes—
316C2×#106—431no—
317C2×C4⋊C8C2×D4311yescharacteristic
318C2×#103—431no—
319C2×#103—432no—
320C2×#102—431no—
321C2×#102C2×D4312yes—
322C2×C22⋊C8—432no—
323C2×C22⋊C8—432no—
324C2×C4×C8—431no—
325#394—862no—
326#384—431no—
327#380—432no—
328#380—861no—
329#340—432no—
330#340—432no—
331#340—432no—
332C43#2411911yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×Q8—431no—
335C22×D4—431no—
336C22×D4—862no—
337C22×D4C22×D4311yescharacteristic
338C23×C4—21no—
339C23×C4—432no—
340C2×SD16—862no—
341C2×SD16—862no—
342C2×SD16—862no—
343C22×C8—431no—
344C22×C8—431no—
345C22×C8C22×D4312yes—
346C4⋊Q8—22no—
347C4⋊Q8C22⋊D4314yescomplemented
348#126—8616no—
349#124—868no—
350C22⋊Q8—864no—
351C22⋊Q8—864no—
352#121—864no—
353#121—1722no—
354#121—1724no—
355C4×Q8—434no—
356C4×Q8—868no—
357C4×Q8—862no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—862no—
361C4×D4—862no—
362#117—864no—
363#117—864no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C4⋊C4C22×D4312yes—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—432no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4—862no—
379C2×C22⋊C4—862no—
380C2×C42—862no—
381C2×C42—861no—
382C2×C42C22×D4311yescharacteristic
383#107—24no—
384#106—862no—
385C4⋊C8—22no—
386#103—862no—
387#103—1722no—
388#102—24no—
389#102—862no—
390C22⋊C8—864no—
391C22⋊C8—1722no—
392C4×C8—862no—
393#95—862no—
394C24—21no—
395C24—432no—
396C2×Q8—24no—
397C2×Q8—42no—
398C2×Q8—42no—
399C2×Q8—432no—
400C2×Q8—861no—
401C2×Q8—861no—
402C2×Q8—861no—
403C2×Q8—861no—
404C2×Q8—861no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—862no—
413C2×D4—3442no—
414C2×D4—1724no—
415C2×D4—1724no—
416C2×D4#1062190212yes—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—432no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4C23×D4311yescharacteristic
435SD16—868no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—432no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—432no—
450C4⋊C4—868no—
451C4⋊C4—862no—
452C4⋊C4—864no—
453C4⋊C4—861no—
454C4⋊C4—862no—
455C4⋊C4—862no—
456C4⋊C4—3441no—
457C4⋊C4—1722no—
458C4⋊C4C2×C22⋊D4314yes—
459C22⋊C4—42no—
460C22⋊C4—868no—
461C22⋊C4—868no—
462C22⋊C4—864no—
463C22⋊C4—1724no—
464C22⋊C4—1724no—
465C42—868no—
466C42—864no—
467C42D4×D4312yes—
468C42C2×C22⋊D4312yes—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—862no—
477C23—862no—
478C23—862no—
479C23—862no—
480C23—862no—
481C23—862no—
482C23—862no—
483C23C2×D4×D4311yescharacteristic
484Q8—48no—
485Q8—862no—
486Q8—862no—
487Q8—1721no—
488Q8—1721no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—3448no—
494D4—1724no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—84no—
504C2×C4—862no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4—1722no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4#1306329312yes—
521C2×C4#1306329312yes—
522C2×C4#1306334412yes—
523C2×C4#1306334912yes—
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4C22×C22⋊D4311yescharacteristic
526C2×C4#41×D4311yescharacteristic
527C2×C4C2×#1062190211yescharacteristic
528C2×C4#1306337111yescharacteristic
529C2×C4#1306337311yescharacteristic
530C8—42no—
531C8—862no—
532C8—1721no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22—1722no—
546C22—1722no—
547C22C2×#1306329311yescharacteristic
548C22#1458354011yescharacteristic
549C22#1458355111yescharacteristic
550C22C2×#1306334411yescharacteristic
551C22C2×#1306334911yescharacteristic
552C22#1458370811yescharacteristic
553C22#1458371511yescharacteristic
554C4—22no—
555C4—44no—
556C4—81no—
557C4—3442no—
558C4—1722no—
559C4—1722no—
560C4—1722no—
561C4#1458304114yes—
562C4#1458341211yescharacteristic
563C4#1458347911yescharacteristic
564C4#1458356011yescharacteristic
565C4#1458356811yescharacteristic
566C2—82no—
567C2—3442no—
568C2#1913794211yescharacteristic
569C2C2×#1458304111yescharacteristic
570C2#1914390911yescharacteristic
571C2#1914650911yescharacteristic
572C2#1914682311yescharacteristic
573C2#1914700511yescharacteristic
574C2#1914717611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#474C2
socleC23×C43C22×D4
prime radical#19139508C2
hypercenterC2×#474D43
hypocenterC43#24119
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#14583623C2semidirect
2. C2×C4×#10621883C2semidirect
4. #19135800C2semidirect
5. #19135599C2semidirect
6. #19135557C2semidirect
7. #19135388C2semidirect
8. #19134914C2semidirect
9. #19134791C2semidirect
10. #19134601C2semidirect
11. C2×C43×#474C2semidirect
63. C4×Dic86D4semidirect
95. C4⋊Q8×C43D4semidirect
280. C2×#474D43semidirect
332. C43#24119semidirect
347. C4⋊Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836232
C2×C4×#106218832
#191395082
#191358002
#191355992
#191355572
#191353882
#191349142
#191347912
#191346012
C2×C43×#4742
#2411943