Finite Group Databasebeta

← #25130545

Subgroups — #25130545

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583614C211yesmaximal, characteristic
2C2×#14583194C211yesmaximal, characteristic, complemented
3#19139513C211yesmaximal, characteristic, complemented
4#19135775C212yesmaximal, complemented
5#19135595C212yesmaximal, complemented
6#19135556C211yesmaximal, characteristic, complemented
7#19135389C211yesmaximal, characteristic, complemented
8#19134904C212yesmaximal, complemented
9#19134793C212yesmaximal, complemented
10#19134595C211yesmaximal, characteristic, complemented
11C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
12#14583614—24no—
13#14583614—24no—
14C2×#13063325C2211yescharacteristic
15C2×#13063311—22no—
16C2×#13063301C2212yes—
17C2×#13063299—21no—
18C2×#13063296C2212yes—
19C2×C4×D172C2211yescharacteristic
20C2×#13063284—21no—
21C2×#13063283C2212yes—
22#14583194—24no—
23C2×#13063258C2212yes—
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2212yes—
26C2×#13063246C2212yes—
27C2×(C2×D43)⋊C8C2212yes—
28C2×(C2×D43)⋊C8C2212yes—
29#14582821—22no—
30#14582801—21no—
31#14582797—21no—
32#14582769C2211yescharacteristic
33#14582756C2212yes—
34#14582662C2212yes—
35#14582662C2212yes—
36#14582661C2212yes—
37C22×SD16×C43C2211yescharacteristic
38C2×C4×Q8×C43C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C4×SD16×C43—24no—
41C2×#106×C43C2211yescharacteristic
42C2×#103×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×C4×C8×C43C2211yescharacteristic
45C22×Dic86—21no—
46C22×D172D411yescharacteristic
47C22×C22⋊D43—22no—
48C22×C4×D43C2312yes—
49C22×C43⋊C8C2312yes—
50#13063325—22no—
51#13063325D414yes—
52#13063311—216no—
53#13063301—24no—
54#13063301—42no—
55#13063299—28no—
56#13063296—24no—
57#13063296—24no—
58C4×D172—22no—
59C4×D172—22no—
60#13063284—28no—
61#13063283—24no—
62#13063283—24no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×C4⋊Dic43C2312yes—
68C2×C4⋊Dic43C2312yes—
69C2×Dic43⋊C4—22no—
70C2×C22⋊Dic43—22no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4D412yes—
75C2×C4×Dic43—22no—
76#13063258—24no—
77C4⋊(C43⋊C8)—22no—
78#13063249—24no—
79#13063246—42no—
80(C2×D43)⋊C8—24no—
81(C2×D43)⋊C8—42no—
82C43⋊#95—22no—
83C22×Q8×C43C2311yescharacteristic
84C22×D4×C43C2311yescharacteristic
85C23×C4×C43—21no—
86C2×SD16×C43—22no—
87C2×SD16×C43—22no—
88C2×SD16×C43—22no—
89C22×C8×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91C4×Q8×C43—22no—
92C4×Q8×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43D414yes—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43C2311yescharacteristic
101#106×C43—22no—
102#103×C43—22no—
103#102×C43—22no—
104C4×C8×C43—22no—
105C24×C43—21no—
106C23×D43C2×D412yes—
107C2×Q8×C43—21no—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43#4112yes—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43C2×D412yes—
119C22×C4×C43—24no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—28no—
129C2×C22⋊D43—82no—
130C2×C22⋊D43—82no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43C2×D412yes—
134C2×D172—22no—
135C2×D172—22no—
136C2×D172—22no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×Dic86—24no—
144C2×Dic86—81no—
145C2×Dic86—81no—
146SD16×C43—28no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43#4112yes—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43C2×D412yes—
158C22⋊C4×C43—24no—
159C42×C43—42no—
160C42×C43C2×D412yes—
161C42×C43C2×D412yes—
162C22⋊Dic43—28no—
163(C2×D43)⋊C4—28no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—44no—
166(C2×D43)⋊C4—82no—
167C4⋊Dic43—24no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43—22no—
171C4⋊Dic43—22no—
172C4⋊Dic43—42no—
173C4⋊Dic43—81no—
174C4⋊Dic43C2×D414yes—
175Dic43⋊C4—44no—
176C4×Dic43—28no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C23×C43—22no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43C22×D411yescharacteristic
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—22no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—22no—
195Q8×C43—22no—
196Q8×C43—22no—
197Q8×C43—41no—
198Q8×C43—41no—
199D4×C43—22no—
200D4×C43—22no—
201D4×C43—41no—
202D4×C43—41no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—48no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43#12012yes—
216C2×C4×C43#12012yes—
217C2×C4×C43#13512yes—
218C2×C4×C43#13712yes—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43H(5,𝔽2)11yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C22⋊D43—88no—
226C2×Dic43—22no—
227C2×Dic43—24no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235D172—44no—
236C4×D43—42no—
237C4×D43—42no—
238C4×D43—42no—
239C4×D43—42no—
240Dic86—84no—
241C8×C43—22no—
242C8×C43—41no—
243C43⋊C8—42no—
244#24121—431nomaximal, Sylow
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43C2×#12011yescharacteristic
253C22×C43#54611yescharacteristic
254C22×C43#54711yescharacteristic
255C22×C43C2×#13511yescharacteristic
256C22×C43C2×#13711yescharacteristic
257C22×C43#57611yescharacteristic
258C22×C43#57711yescharacteristic
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C4×C43—22no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—81no—
270C4×C43#45214yes—
271C4×C43#52511yescharacteristic
272C4×C43#53711yescharacteristic
273C4×C43#54811yescharacteristic
274C4×C43#55011yescharacteristic
275Dic43—42no—
276Dic43—44no—
277Dic43—82no—
278C2×#555—431no—
279C2×#477—431no—
280C2×C4×SD16D4311yescharacteristic, complemented
281#2538—431no—
282#2033—432no—
283#2000—432no—
284#1990—431no—
285#1954—431no—
286#1873—432no—
287#1854—432no—
288#1802—431no—
289C2×C43—82no—
290C2×C43#240711yescharacteristic
291C2×C43C2×#45211yescharacteristic
292C2×C43#301211yescharacteristic
293C2×C43#330511yescharacteristic
294C2×C43#332911yescharacteristic
295C2×C43#334011yescharacteristic
296C2×C43#335711yescharacteristic
297D43—82no—
298C22×SD16C2×D4311yescharacteristic
299#555—864no—
300#555—864no—
301C2×C4⋊Q8—431no—
302C2×#124—862no—
303C2×C22⋊Q8—432no—
304C2×#121—432no—
305C2×#121—861no—
306C2×C4×Q8C2×D4311yescharacteristic
307C2×C4×D4—431no—
308C2×C4×D4C2×D4311yescharacteristic
309C2×#117—432no—
310C2×#117—861no—
311#477—864no—
312C4×SD16—24no—
313C2×#107—432no—
314C2×#106C2×D4311yescharacteristic
315C2×C4⋊C8—431no—
316C2×#103—432no—
317C2×#103C2×D4311yescharacteristic
318C2×#102—432no—
319C2×#102C2×D4311yescharacteristic
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×C4×C8C2×D4311yescharacteristic
323#396—862no—
324#390—861no—
325#389—861no—
326#384—431no—
327#380—432no—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2412111yescharacteristic, complemented, Sylow
332C22×Q8—861no—
333C22×Q8C22×D4311yescharacteristic
334C22×D4—431no—
335C22×D4—862no—
336C22×D4C22×D4311yescharacteristic
337C23×C4—21no—
338C23×C4—432no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C22×C8—432no—
343C22×C8C22×D4311yescharacteristic
344C22×C8C22×D4311yescharacteristic
345C4⋊Q8—434no—
346C4⋊Q8—862no—
347#124—8616no—
348C22⋊Q8—864no—
349C22⋊Q8—1722no—
350#121—864no—
351#121—868no—
352#121—864no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—22no—
356C4×D4—862no—
357C4×D4—862no—
358C4×D4C22⋊D4314yes—
359#117—864no—
360#117—868no—
361#117—864no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—432no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C4⋊C4C22×D4311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—432no—
374C2×C22⋊C4—862no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C42—21no—
379C2×C42—862no—
380C2×C42C22×D4311yescharacteristic
381#107—864no—
382#106—22no—
383C4⋊C8—862no—
384#103—22no—
385#103—864no—
386#102—22no—
387#102—1722no—
388C22⋊C8—864no—
389C22⋊C8—1722no—
390C4×C8—22no—
391#95—862no—
392C24—21no—
393C24—432no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—864no—
400C2×Q8—3441no—
401C2×Q8—3441no—
402C2×Q8#1062189812yes—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—868no—
409C2×D4—862no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—3442no—
413C2×D4—3442no—
414C2×D4C2×C22⋊D4312yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—432no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4D4×D4311yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4C23×D4311yescharacteristic
433SD16—28no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—862no—
440C2×C8—862no—
441C2×C8—862no—
442C2×C8#1062189812yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—42no—
447C4⋊C4—434no—
448C4⋊C4—862no—
449C4⋊C4—864no—
450C4⋊C4—862no—
451C4⋊C4—862no—
452C4⋊C4—862no—
453C4⋊C4—3441no—
454C4⋊C4—1724no—
455C4⋊C4—1722no—
456C4⋊C4C2×C22⋊D4312yes—
457C22⋊C4—24no—
458C22⋊C4—868no—
459C22⋊C4—868no—
460C22⋊C4—864no—
461C22⋊C4—3442no—
462C22⋊C4—1724no—
463C42—42no—
464C42—868no—
465C42D4×D4312yes—
466C42C2×C22⋊D4312yes—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—862no—
475C23—862no—
476C23—862no—
477C23—862no—
478C23—862no—
479C23—862no—
480C23—862no—
481C23C2×D4×D4311yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—3444no—
487D4—22no—
488D4—22no—
489D4—41no—
490D4—41no—
491D4—3448no—
492D4—1724no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—48no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—864no—
508C2×C4—862no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4—1722no—
512C2×C4—1722no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4#1306329312yes—
519C2×C4#1306329312yes—
520C2×C4#1306334612yes—
521C2×C4#1306335412yes—
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4C2×#1062189811yescharacteristic
525C2×C4C2×#1062189811yescharacteristic
526C2×C4#1306337111yescharacteristic
527C2×C4#1306337211yescharacteristic
528C8—22no—
529C8—41no—
530C8—1722no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—1722no—
539C22—1722no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22C2×#1306329311yescharacteristic
546C22#1458354511yescharacteristic
547C22#1458355411yescharacteristic
548C22C2×#1306334611yescharacteristic
549C22C2×#1306335411yescharacteristic
550C22#1458370111yescharacteristic
551C22#1458370611yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—3442no—
557C4—1722no—
558C4—1724no—
559C4#1458305814yes—
560C4#1458341011yescharacteristic
561C4#1458347711yescharacteristic
562C4#1458355811yescharacteristic
563C4#1458357011yescharacteristic
564C2—82no—
565C2—3442no—
566C2#1913794011yescharacteristic
567C2C2×#1458305811yescharacteristic
568C2#1914389511yescharacteristic
569C2#1914654711yescharacteristic
570C2#1914689111yescharacteristic
571C2#1914701011yescharacteristic
572C2#1914722311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583614C2
hypercenterC2×C4×SD16D43
hypocenterC43#24121
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14583194C2semidirect
3. #19139513C2semidirect
4. #19135775C2semidirect
5. #19135595C2semidirect
6. #19135556C2semidirect
7. #19135389C2semidirect
8. #19134904C2semidirect
9. #19134793C2semidirect
10. #19134595C2semidirect
11. C2×C4×SD16×C43C2semidirect
280. C2×C4×SD16D43semidirect
331. C43#24121semidirect

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145831942
#191395132
#191357752
#191355952
#191355562
#191353892
#191349042
#191347932
#191345952
C2×C4×SD16×C432
#2412143