Finite Group Databasebeta

← #25130501

Subgroups — #25130501

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583614C211yesmaximal, characteristic, complemented
2C2×#14583189C211yesmaximal, characteristic, complemented
3#19139508C211yesmaximal, characteristic, complemented
4#19135782C212yesmaximal, complemented
5#19135590C212yesmaximal, complemented
6#19135556C211yesmaximal, characteristic, complemented
7#19135389C211yesmaximal, characteristic, complemented
8#19134914C212yesmaximal, complemented
9#19134791C212yesmaximal, complemented
10#19134595C211yesmaximal, characteristic, complemented
11C2×C4×D8×C43C211yesmaximal, characteristic, complemented
12#14583614—24no—
13#14583614—24no—
14C2×#13063325C2211yescharacteristic
15C2×#13063311—22no—
16C2×#13063299—21no—
17C2×#13063299—21no—
18C2×#13063296C2212yes—
19C2×#13063296C2212yes—
20C2×C4×D172C2211yescharacteristic
21C2×#13063284—21no—
22C2×#13063283C2212yes—
23#14583189—24no—
24C2×#13063256C2212yes—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063246C2212yes—
27C2×#13063246C2212yes—
28C2×(C2×D43)⋊C8C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30#14582815—22no—
31#14582769C2211yescharacteristic
32#14582759—21no—
33#14582756C2212yes—
34#14582662C2212yes—
35#14582662C2212yes—
36#14582661C2212yes—
37C22×D8×C43C2211yescharacteristic
38C2×C4×D4×C43C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C4×D8×C43—24no—
41C2×#107×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×C4×C8×C43C2211yescharacteristic
45C22×Dic86—21no—
46C22×D172D411yescharacteristic
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C4×D43C2312yes—
50C22×C43⋊C8C2312yes—
51#13063325—22no—
52#13063325D414yescomplemented
53#13063311—216no—
54#13063299—28no—
55#13063299—44no—
56#13063296—24no—
57#13063296—24no—
58#13063296—24no—
59#13063296—42no—
60C4×D172—22no—
61C4×D172—22no—
62#13063284—28no—
63#13063283—24no—
64#13063283—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43C2312yes—
70C2×C4⋊Dic43C2312yes—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4D412yes—
76C2×C4×Dic43—22no—
77#13063256—24no—
78C4⋊(C43⋊C8)—22no—
79#13063246—24no—
80#13063246—42no—
81(C2×D43)⋊C8—24no—
82(C2×D43)⋊C8—42no—
83C43⋊#95—22no—
84C22×D4×C43C2311yescharacteristic
85C22×D4×C43C2311yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C2×D8×C43—22no—
89C2×D8×C43—22no—
90C2×D8×C43—22no—
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43D414yescomplemented
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#107×C43—22no—
103#102×C43—22no—
104#102×C43—22no—
105C4×C8×C43—22no—
106C24×C43—21no—
107C24×C43—21no—
108C23×D43C2×D412yes—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43C2×D412yes—
120C2×D4×C43#4112yes—
121C22×C4×C43—24no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—28no—
133C2×C22⋊D43—44no—
134C2×C22⋊D43—44no—
135C2×C22⋊D43—82no—
136C2×C22⋊D43—82no—
137C2×C22⋊D43—82no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43C2×D412yes—
141C2×D172—22no—
142C2×D172—22no—
143C2×D172—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×Dic86—24no—
151C2×Dic86—81no—
152C2×Dic86—81no—
153D8×C43—28no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43#4112yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43C2×D412yes—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—42no—
166C42×C43C2×D412yes—
167C42×C43C2×D412yes—
168C22⋊Dic43—28no—
169C22⋊Dic43—44no—
170(C2×D43)⋊C4—28no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—44no—
173C4⋊Dic43—24no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—42no—
179C4⋊Dic43—81no—
180C4⋊Dic43C2×D414yes—
181C4×Dic43—28no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—22no—
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—22no—
210D4×C43—22no—
211D4×C43—41no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—48no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—84no—
225C2×C4×C43#12012yes—
226C2×C4×C43#12012yes—
227C2×C4×C43#13512yes—
228C2×C4×C43AGL(1,ℤ/8)12yes—
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×C4×C432−1+411yescharacteristic
235C22⋊D43—88no—
236C22⋊D43—88no—
237C2×Dic43—22no—
238C2×Dic43—24no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246D172—44no—
247C4×D43—42no—
248C4×D43—42no—
249C4×D43—42no—
250C4×D43—42no—
251Dic86—84no—
252C8×C43—22no—
253C8×C43—41no—
254C43⋊C8—42no—
255#24117—431nomaximal, Sylow
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43C2×#12011yescharacteristic
271C22×C43#54611yescharacteristic
272C22×C43#54711yescharacteristic
273C22×C43C2×#13511yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C43#57611yescharacteristic
276C22×C43#57711yescharacteristic
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—42no—
282C2×D43—42no—
283C2×D43—42no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43#44914yes—
288C4×C43#52511yescharacteristic
289C4×C43#53711yescharacteristic
290C4×C43#54811yescharacteristic
291C4×C43#55011yescharacteristic
292Dic43—42no—
293Dic43—44no—
294Dic43—82no—
295C2×#555—431no—
296C2×#476—431no—
297C2×C4×D8D4311yescharacteristic, complemented
298#2537—431no—
299#2034—432no—
300#1999—432no—
301#1990—431no—
302#1954—431no—
303#1875—432no—
304#1854—432no—
305#1802—431no—
306C2×C43—82no—
307C2×C43—82no—
308C2×C43#240711yescharacteristic
309C2×C43C2×#44911yescharacteristic
310C2×C43#301211yescharacteristic
311C2×C43#330311yescharacteristic
312C2×C43#332511yescharacteristic
313C2×C43#334111yescharacteristic
314C2×C43#335411yescharacteristic
315D43—82no—
316C22×D8C2×D4311yescharacteristic
317#555—864no—
318#555—864no—
319C2×C4⋊Q8—431no—
320C2×#124—862no—
321C2×#121—432no—
322C2×#121—432no—
323C2×#121—861no—
324C2×#121—861no—
325C2×C4×D4—431no—
326C2×C4×D4C2×D4311yescharacteristic
327C2×C4×D4C2×D4311yescharacteristic
328C2×#117—432no—
329C2×#117—861no—
330#476—864no—
331C4×D8—24no—
332C2×#107C2×D4311yescharacteristic
333C2×#106—432no—
334C2×C4⋊C8—431no—
335C2×#102—432no—
336C2×#102—432no—
337C2×#102C2×D4311yescharacteristic
338C2×#102C2×D4311yescharacteristic
339C2×C22⋊C8—432no—
340C2×C22⋊C8—432no—
341C2×C4×C8C2×D4311yescharacteristic
342#394—862no—
343#384—431no—
344#380—432no—
345#380—861no—
346#340—432no—
347#340—432no—
348#340—432no—
349C43#2411711yescharacteristic, complemented, Sylow
350C22×Q8—861no—
351C22×D4—431no—
352C22×D4—862no—
353C22×D4—862no—
354C22×D4C22×D4311yescharacteristic
355C22×D4C22×D4311yescharacteristic
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—432no—
359C2×D8—22no—
360C2×D8—22no—
361C2×D8—22no—
362C22×C8—432no—
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365C4⋊Q8—434no—
366C4⋊Q8—862no—
367#124—8616no—
368#121—864no—
369#121—868no—
370#121—864no—
371#121—864no—
372#121—1722no—
373#121—1724no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—862no—
378C4×D4—862no—
379C4×D4C22⋊D4314yescomplemented
380#117—864no—
381#117—868no—
382#117—864no—
383C2×C4⋊C4—432no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—432no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—432no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4—862no—
397C2×C22⋊C4—862no—
398C2×C42—862no—
399C2×C42C22×D4311yescharacteristic
400#107—22no—
401#106—864no—
402C4⋊C8—862no—
403#102—22no—
404#102—22no—
405#102—864no—
406#102—1722no—
407C22⋊C8—864no—
408C22⋊C8—1722no—
409C4×C8—22no—
410#95—862no—
411C24—21no—
412C24—21no—
413C24—432no—
414C2×Q8—864no—
415C2×Q8—3441no—
416C2×Q8—3441no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—868no—
428C2×D4—862no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—3442no—
432C2×D4—3442no—
433C2×D4—3442no—
434C2×D4—1724no—
435C2×D4—1724no—
436C2×D4#1062189812yes—
437C2×D4C2×C22⋊D4312yes—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—432no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458D8—28no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—862no—
465C2×C8—862no—
466C2×C8—862no—
467C2×C8#1062189812yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—434no—
472C4⋊C4—862no—
473C4⋊C4—864no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—3441no—
478C4⋊C4—1722no—
479C4⋊C4C2×C22⋊D4312yes—
480C22⋊C4—24no—
481C22⋊C4—42no—
482C22⋊C4—868no—
483C22⋊C4—868no—
484C22⋊C4—864no—
485C22⋊C4—1724no—
486C22⋊C4—1724no—
487C42—868no—
488C42D4×D4312yes—
489C42C2×C22⋊D4312yes—
490C23—22no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—862no—
505C23—862no—
506C23—862no—
507C23—862no—
508C23—862no—
509C23—862no—
510C23—862no—
511C23C2×D4×D4311yescharacteristic
512Q8—3444no—
513D4—22no—
514D4—22no—
515D4—22no—
516D4—22no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—3448no—
522D4—3448no—
523D4—1724no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—864no—
537C2×C4—862no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4#1306329312yes—
548C2×C4#1306329312yes—
549C2×C4#1306334412yes—
550C2×C4#1306334912yes—
551C2×C4C2×D4×D4311yescharacteristic
552C2×C4C22×C22⋊D4311yescharacteristic
553C2×C4C2×#1062189811yescharacteristic
554C2×C4C2×#1062189811yescharacteristic
555C2×C4#1306337111yescharacteristic
556C2×C4#1306337211yescharacteristic
557C8—22no—
558C8—41no—
559C8—1722no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—1722no—
575C22—1722no—
576C22—1722no—
577C22—1722no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22C2×#1306329311yescharacteristic
582C22#1458354511yescharacteristic
583C22#1458355411yescharacteristic
584C22C2×#1306334411yescharacteristic
585C22C2×#1306334911yescharacteristic
586C22#1458370111yescharacteristic
587C22#1458370611yescharacteristic
588C4—22no—
589C4—42no—
590C4—81no—
591C4—3442no—
592C4—1722no—
593C4—1724no—
594C4#1458304114yes—
595C4#1458341011yescharacteristic
596C4#1458347711yescharacteristic
597C4#1458355811yescharacteristic
598C4#1458357011yescharacteristic
599C2—82no—
600C2—82no—
601C2—3442no—
602C2#1913794011yescharacteristic
603C2C2×#1458304111yescharacteristic
604C2#1914389511yescharacteristic
605C2#1914652511yescharacteristic
606C2#1914683911yescharacteristic
607C2#1914701911yescharacteristic
608C2#1914719211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
hypercenterC2×C4×D8D43
hypocenterC43#24117
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583614C2semidirect
2. C2×#14583189C2semidirect
3. #19139508C2semidirect
4. #19135782C2semidirect
5. #19135590C2semidirect
6. #19135556C2semidirect
7. #19135389C2semidirect
8. #19134914C2semidirect
9. #19134791C2semidirect
10. #19134595C2semidirect
11. C2×C4×D8×C43C2semidirect
52. #13063325D4semidirect
96. C4×D4×C43D4semidirect
297. C2×C4×D8D43semidirect
349. C43#24117semidirect
379. C4×D4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145831892
#191395082
#191357822
#191355902
#191355562
#191353892
#191349142
#191347912
#191345952
C2×C4×D8×C432
#2411743