Finite Group Databasebeta

← #25132676

Subgroups — #25132676

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583454C211yesmaximal, characteristic, complemented
2C2×#14583190C211yesmaximal, characteristic, complemented
3C2×#14583176C211yesmaximal, characteristic, complemented
4C4×#13063300C211yesmaximal, characteristic
5#19135932C212yesmaximal, complemented
6#19135740C212yesmaximal, complemented
7#19135543C211yesmaximal, characteristic, complemented
8#19134916C212yesmaximal
9#19134795C212yesmaximal, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C43×#1988C211yesmaximal, characteristic, complemented
12#14583454—24no—
13#14583454—24no—
14C2×#13063325C2211yescharacteristic
15C2×#13063316C2212yes—
16C2×#13063305—21no—
17C2×#13063301—21no—
18C2×#13063300C2211yescharacteristic
19C2×Q8×Dic43—21no—
20C2×#13063290—21no—
21C2×C4×D172—21no—
22C2×C4×D172C2211yescharacteristic
23C2×#13063283C2212yes—
24C2×C42×D43C2211yescharacteristic
25#14583190—24no—
26#14583176—24no—
27C2×#13063258C2212yes—
28C2×#13063257C2212yes—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063247C2212yes—
31C2×#13063245C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582800C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582791—21no—
36#14582777—21no—
37#14582756C2211yescharacteristic
38C4×(C2×D43)⋊C4—21no—
39#14582661C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C2×C4⋊Q8×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C4×C4⋊C4×C43C2211yescharacteristic
45C43×#340C2212yes—
46C43×#340C2212yes—
47C22×Dic86—21no—
48C22×D172—21no—
49C22×D172C2311yescharacteristic
50C22×C4×D43—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C22×C43⋊C8C2312yes—
55#13063325—22no—
56#13063325D414yescomplemented
57#13063316—24no—
58#13063316—24no—
59#13063305—28no—
60#13063301—28no—
61#13063300—22no—
62#13063300Q814yescomplemented
63Q8×Dic43—28no—
64#13063290—28no—
65C4×D172—22no—
66C4×D172—22no—
67C4×D172—44no—
68#13063283—24no—
69#13063283—24no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2312yes—
75C2×Dic43⋊C4—22no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43—22no—
87C42×D43—22no—
88#13063258—24no—
89#13063257—24no—
90C4⋊(C43⋊C8)—22no—
91#13063247—24no—
92#13063245—24no—
93(C2×D43)⋊C8—24no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C22×Q8×C43—21no—
97C22×C8×C43C2312yes—
98C4⋊Q8×C43—22no—
99C4⋊Q8×C43D414yescomplemented
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2312yes—
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C42×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—22no—
107#95×C43—21no—
108C23×D43—21no—
109C23×D43C2×D411yescharacteristic
110C2×Q8×C43—24no—
111C2×Q8×C43—42no—
112C2×Q8×C43—42no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2411yescharacteristic
119C22×Dic43—22no—
120C22×Dic43—21no—
121C22×Dic43C2×D411yescharacteristic
122C22×Dic43C2×D411yescharacteristic
123C22×Dic43C2×D411yescharacteristic
124C2×D172—21no—
125C2×D172—24no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—42no—
131C2×D172—42no—
132C2×D172C2×Q812yes—
133C2×C4×D43—21no—
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—41no—
142C2×C4×D43—41no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×C4×D43—42no—
146C2×C4×D43C2×Q812yes—
147C2×C4×D43#4112yes—
148C2×Dic86—24no—
149C2×Dic86—42no—
150C2×Dic86—42no—
151C2×C8×C43—22no—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43C2×D414yes—
160C4⋊C4×C43C2×Q812yes—
161C42×C43—42no—
162C42×C43C2×D412yes—
163C42×C43C2×D412yes—
164(C2×D43)⋊C4—28no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—42no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170C4⋊Dic43—28no—
171C4⋊Dic43—24no—
172C4⋊Dic43—22no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—42no—
176C4⋊Dic43C2×D414yes—
177Dic43⋊C4—28no—
178C4×Dic43—28no—
179C4×Dic43—22no—
180C4×Dic43—22no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C23×C43C22×D411yescharacteristic
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—22no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43C22⋊Q812yes—
201Q8×C43—48no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—24no—
205C2×C4×C43—22no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43#12012yes—
214C2×C4×C43#12012yes—
215C2×C4×C43#13512yes—
216C2×C4×C43AGL(1,ℤ/8)12yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×Q811yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C432−1+411yescharacteristic
222C2×C4×C432−1+411yescharacteristic
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—24no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43C22⋊Q812yes—
238D172—22no—
239D172—22no—
240D172—48no—
241D172—41no—
242D172—41no—
243C4×D43—22no—
244C4×D43—22no—
245C4×D43—22no—
246C4×D43—22no—
247C4×D43—44no—
248C4×D43—44no—
249C4×D43—84no—
250Dic86—48no—
251C8×C43—42no—
252C43⋊C8—42no—
253#24300—431nomaximal, Sylow
254C22×C43C2×#12011yescharacteristic
255C22×C43C2×C22⋊Q811yescharacteristic
256C22×C43#53611yescharacteristic
257C22×C43C2×#13511yescharacteristic
258C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C43#57511yescharacteristic
260C22×C43#57511yescharacteristic
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—42no—
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C4×C43—22no—
276C4×C43—42no—
277C4×C43—44no—
278C4×C43—81no—
279C4×C43#44914yes—
280C4×C43#54811yescharacteristic
281C4×C43#54811yescharacteristic
282C4×C43D4×Q811yescharacteristic
283C4×C43D4×Q811yescharacteristic
284Dic43—22no—
285Dic43—41no—
286Dic43—44no—
287Dic43—41no—
288Dic43—81no—
289C2×#533—431no—
290C2×#476—431no—
291C2×#474—431no—
292C4×#121—431no—
293#2059—432no—
294#2025—432no—
295#1988D4311yescharacteristic, complemented
296#1987—431no—
297#1875—432no—
298#1854—432no—
299#1797—431no—
300C2×C43#240911yescharacteristic
301C2×C43C2×#44911yescharacteristic
302C2×C43#300511yescharacteristic
303C2×C43#307611yescharacteristic
304C2×C43#307711yescharacteristic
305C2×C43#323311yescharacteristic
306C2×C43#323511yescharacteristic
307D43—42no—
308D43—82no—
309#533—864no—
310#533—864no—
311C2×C4⋊Q8—431no—
312C2×C4⋊Q8C2×D4311yescharacteristic
313C2×#125—432no—
314C2×C22⋊Q8—861no—
315C2×C22⋊Q8—861no—
316C2×#121—431no—
317C2×C4×Q8—861no—
318C2×C4×Q8—861no—
319C2×C4×D4—431no—
320C2×C4×D4—861no—
321C2×#117—432no—
322C22×C42—431no—
323#476—864no—
324#474—864no—
325C2×#107—432no—
326C2×#106—432no—
327C2×C4⋊C8—431no—
328C2×C4⋊C8C2×D4311yescharacteristic
329C2×#102—432no—
330C2×#102—432no—
331C2×C22⋊C8—432no—
332#390—431no—
333#389—431no—
334#388—861no—
335#386—861no—
336#380—431no—
337C4×C4⋊C4C2×D4311yescharacteristic
338C4×C22⋊C4—861no—
339#340—432no—
340#340—432no—
341#340C2×D4312yes—
342#340C2×D4312yes—
343#336—432no—
344C43#2430011yescharacteristic, complemented, Sylow
345C22×Q8—21no—
346C22×Q8—861no—
347C22×D4—431no—
348C22×D4—861no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4—431no—
352C23×C4—861no—
353C22×C8—432no—
354C22×C8C22×D4312yes—
355C4⋊Q8—22no—
356C4⋊Q8—434no—
357C4⋊Q8—862no—
358C4⋊Q8D17214yescomplemented
359#125—864no—
360#125—864no—
361C22⋊Q8—868no—
362C22⋊Q8—868no—
363#121—434no—
364#121—862no—
365C4×Q8—868no—
366C4×Q8—868no—
367C4×D4—862no—
368C4×D4—862no—
369C4×D4—1724no—
370#117—864no—
371#117—864no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—432no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4312yes—
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—861no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C42—21no—
389C2×C42—431no—
390C2×C42—431no—
391C2×C42—431no—
392C2×C42—862no—
393C2×C42—862no—
394C2×C42—862no—
395C2×C42C22×D4311yescharacteristic
396#107—864no—
397#106—864no—
398C4⋊C8—22no—
399C4⋊C8—862no—
400#102—864no—
401#102—864no—
402C22⋊C8—864no—
403#95—21no—
404#95—861no—
405#95—861no—
406C24—431no—
407C24—861no—
408C2×Q8—24no—
409C2×Q8—42no—
410C2×Q8—42no—
411C2×Q8—864no—
412C2×Q8—1722no—
413C2×Q8—1722no—
414C2×D4—432no—
415C2×D4—864no—
416C2×D4—861no—
417C2×D4—861no—
418C2×D4—861no—
419C2×D4—861no—
420C2×D4—861no—
421C2×D4—1722no—
422C2×D4—1722no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—431no—
427C22×C4—432no—
428C22×C4—432no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—861no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4—1722no—
444C22×C4—1722no—
445C22×C4—1722no—
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4311yescharacteristic
448C22×C4C23×D4311yescharacteristic
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—862no—
453C2×C8—862no—
454C2×C8—862no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—434no—
461C4⋊C4—868no—
462C4⋊C4—868no—
463C4⋊C4—864no—
464C4⋊C4—862no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—1722no—
468C4⋊C4C2×D17214yes—
469C4⋊C4Q8×D4312yes—
470C22⋊C4—864no—
471C22⋊C4—868no—
472C22⋊C4—1722no—
473C22⋊C4—1722no—
474C22⋊C4—1722no—
475C22⋊C4—1722no—
476C42—42no—
477C42—868no—
478C42—862no—
479C42—862no—
480C42—861no—
481C42—861no—
482C42C2×D17212yes—
483C42D4×D4312yes—
484C23—432no—
485C23—861no—
486C23—861no—
487C23—861no—
488C23—861no—
489C23—861no—
490C23—861no—
491C23—862no—
492C23—1721no—
493C23—1721no—
494C23—1721no—
495C23—1721no—
496C23—1721no—
497C23—1721no—
498C23C2×D4×D4311yescharacteristic
499Q8—48no—
500Q8—1728no—
501D4—862no—
502D4—862no—
503D4—1728no—
504D4—1721no—
505D4—1721no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—432no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—864no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—3444no—
532C2×C4—1724no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1724no—
539C2×C4#1306329512yes—
540C2×C4#1306329512yes—
541C2×C4#1306334612yes—
542C2×C4#1306334912yes—
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4C22×D17211yescharacteristic
545C2×C4C2×Q8×D4311yescharacteristic
546C2×C4#41×D4311yescharacteristic
547C2×C4#1306337211yescharacteristic
548C2×C4#1306337311yescharacteristic
549C8—42no—
550C8—1722no—
551C22—862no—
552C22—862no—
553C22—862no—
554C22—3441no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22—1722no—
559C22—1722no—
560C22—1722no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22—1721no—
565C22C2×#1306329511yescharacteristic
566C22C22⋊Q8×D4311yescharacteristic
567C22#1458347211yescharacteristic
568C22C2×#1306334611yescharacteristic
569C22C2×#1306334911yescharacteristic
570C22#1458369811yescharacteristic
571C22#1458369811yescharacteristic
572C4—22no—
573C4—44no—
574C4—42no—
575C4—81no—
576C4—862no—
577C4—3441no—
578C4—1721no—
579C4—1721no—
580C4—1724no—
581C4#1458304514yes—
582C4#1458355711yescharacteristic
583C4#1458356111yescharacteristic
584C4#1458356411yescharacteristic
585C4Q8×D17211yescharacteristic
586C2—3442no—
587C2—1722no—
588C2#1913795811yescharacteristic
589C2C2×#1458304511yescharacteristic
590C2#1914384111yescharacteristic
591C2#1914437811yescharacteristic
592C2#1914438711yescharacteristic
593C2#1914577811yescharacteristic
594C2#1914579211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1988C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1988D43
hypocenterC43#24300
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×#14583454C2semidirect
2. C2×#14583190C2semidirect
3. C2×#14583176C2semidirect
5. #19135932C2semidirect
6. #19135740C2semidirect
7. #19135543C2semidirect
9. #19134795C2semidirect
10. #19134572C2semidirect
11. C43×#1988C2semidirect
56. #13063325D4semidirect
62. #13063300Q8semidirect
99. C4⋊Q8×C43D4semidirect
295. #1988D43semidirect
344. C43#24300semidirect
358. C4⋊Q8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834542
C2×#145831902
C2×#145831762
C4×#130633002
#191359322
#191357402
#191355432
#191349162
#191347952
#191345722
C43×#19882
#2430043