Finite Group Databasebeta

← #25066694

Subgroups — #25066694

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144653C211yesmaximal, characteristic
2#19143705C211yesmaximal, characteristic, complemented
3#19143672C211yesmaximal, characteristic, complemented
4#19133473C211yesmaximal, characteristic, complemented
5#19133457C211yesmaximal, characteristic, complemented
6#19133426C211yesmaximal, characteristic, complemented
7#19133418C211yesmaximal, characteristic, complemented
8SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
9#19133392C211yesmaximal, characteristic, complemented
10#19133387C211yesmaximal, characteristic, complemented
11#19133377C211yesmaximal, characteristic, complemented
12#19133028C211yesmaximal, characteristic, complemented
13#19132992C211yesmaximal, characteristic, complemented
14#19132896C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16#14583446C2211yescharacteristic
17C4×#10621902C2211yescharacteristic
18#14583225C411yescharacteristic
19#14583221C411yescharacteristic
20#14583192C411yescharacteristic
21#14583188C411yescharacteristic
22#14583097C411yescharacteristic
23#14583093C411yescharacteristic
24#14583047C411yescharacteristic
25#14583043C411yescharacteristic
26Q8×C43⋊C8C2211yescharacteristic
27C4×#10621884C2211yescharacteristic
28C4×D344C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30#14582978C2211yescharacteristic
31#14582968—21no—
32#14582967—21no—
33C8×D172—21no—
34C8×D172C2211yescharacteristic
35D4×C43⋊C8C2211yescharacteristic
36#14582964—21no—
37#14582964C2211yescharacteristic
38#14582964C2211yescharacteristic
39#14582955C2211yescharacteristic
40#14582950—21no—
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582950C2211yescharacteristic
44C4⋊C8×D43—21no—
45C4⋊C8×D43C2211yescharacteristic
46#14582867—21no—
47#14582864—21no—
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582628C2211yescharacteristic
53#14582628C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×#10621898—21no—
69C2×#10621884C2×C411yescharacteristic
70C2×D344C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621872—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78#13063324C2×C411yescharacteristic
79#13063321C2×C411yescharacteristic
80#13063311—21no—
81#13063300C2×C411yescharacteristic
82#13063298—21no—
83#13063296C2×C411yescharacteristic
84Q8×Dic43C2×C411yescharacteristic
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87C4×D172C2311yescharacteristic
88#13063287—21no—
89#13063287C2×C411yescharacteristic
90C4×C22⋊D43—21no—
91#13063283—21no—
92#13063283C2×C411yescharacteristic
93C42×D43—21no—
94C42×D43C2311yescharacteristic
95#13063259C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063245C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8C2×C411yescharacteristic
121(C2×D43)⋊C8C2×C411yescharacteristic
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124#13063235—21no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C2×SD16×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150#10621902—22no—
151#10621902—22no—
152#10621898—81no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C22×C411yescharacteristic
157C2×D172C22×C411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43C22×C411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165C2×Dic86—21no—
166SD16×C43—22no—
167M16×C43—81no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43C22×C411yescharacteristic
177C4⋊C4×C43C22×C411yescharacteristic
178C22⋊C4×C43—21no—
179C42×C43—21no—
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182#10621884—22no—
183#10621882—22no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C411yescharacteristic
191C4⋊Dic43C22×C411yescharacteristic
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43C22×C411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206D344—22no—
207#10621872—81no—
208C8×D43—81no—
209C8×D43—81no—
210C8×D43—81no—
211C8×D43—81no—
212C23×C43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43C4×D411yescharacteristic
216Q8×C43—21no—
217Q8×C43#13112yes—
218D4×C43—21no—
219D4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—81no—
229C22⋊D43—81no—
230C22⋊D43—81no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43C4×D411yescharacteristic
234C2×Dic43C4×D411yescharacteristic
235C2×Dic43C4×D411yescharacteristic
236D172—24no—
237D172—21no—
238D172—21no—
239D172—21no—
240D172—81no—
241D172#13112yes—
242C4×D43—24no—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—81no—
253Dic86—81no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17920—431nomaximal, Sylow
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×C4×D411yescharacteristic
273C2×D43—22no—
274C2×D43—21no—
275C2×D43—21no—
276C2×D43—21no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—22no—
283C4×C43—21no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43C2×#13111yescharacteristic
287C4×C43C2×#13111yescharacteristic
288C4×C43#57611yescharacteristic
289C4×C43#57711yescharacteristic
290Dic43—21no—
291Dic43—21no—
292Dic43—21no—
293Dic43—41no—
294Dic43—41no—
295#3106—431no—
296#2988—431no—
297#2981—431no—
298#1588—431no—
299#1586—431no—
300#1583D4311yescharacteristic, complemented
301#1581—431no—
302#1580—431no—
303SD16⋊C8—431no—
304C8×SD16—431no—
305C8×D8—431no—
306#1573—431no—
307#1488—431no—
308#1480—431no—
309#1454—431no—
310C2×C43—81no—
311C2×C43#292911yescharacteristic
312C2×C43#294611yescharacteristic
313C2×C43#295711yescharacteristic
314D43—41no—
315D43—42no—
316D43—81no—
317#532—431no—
318C4×#41—431no—
319#482—431no—
320#482—431no—
321#477—431no—
322#476—431no—
323#460—431no—
324#459—431no—
325#449—431no—
326#449—431no—
327C8×Q8—431no—
328C8×Q8C2×D4311yescharacteristic
329C4×SD16—431no—
330C4×SD16C2×D4311yescharacteristic
331C4×D8—431no—
332C4×D8—431no—
333#436—431no—
334#436C2×D4311yescharacteristic
335#435—861no—
336#435—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432—431no—
344#431—431no—
345#431—431no—
346#431—431no—
347#431—861no—
348C2×C4⋊C8—431no—
349C2×C4⋊C8—861no—
350#408—861no—
351#408—861no—
352#335—431no—
353#335—431no—
354#334—431no—
355#334C2×D4311yescharacteristic
356Q8⋊C8—431no—
357Q8⋊C8C2×D4311yescharacteristic
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8C2×D4311yescharacteristic
364#322—431no—
365#322—431no—
366#322C2×D4311yescharacteristic
367C82—431no—
368C43#1792011yescharacteristic, complemented, Sylow
369C2×#41—431no—
370C2×#41—861no—
371C2×SD16—431no—
372C2×SD16C4×D4311yescharacteristic
373C2×D8—431no—
374C2×D8—431no—
375C2×M16—21no—
376C2×M16—861no—
377C22×C8—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—431no—
383#127—431no—
384#124—861no—
385#121—431no—
386#121—431no—
387#121—861no—
388C4×Q8—431no—
389C4×Q8C22×D4311yescharacteristic
390C4×D4—431no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397#117—431no—
398#117—861no—
399C2×C42—431no—
400C2×C42—861no—
401#107—431no—
402#107—431no—
403#106—431no—
404#106C4×D4311yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417#103—431no—
418#103C4×D4311yescharacteristic
419#102—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102C4×D4311yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—431no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437#97—861no—
438C4×C8—21no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446#41—862no—
447#41—862no—
448#41—3441no—
449#41—3441no—
450C2×Q8—861no—
451C2×Q8C2×C4×D4311yescharacteristic
452C2×D4—431no—
453C2×D4—431no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468SD16—22no—
469SD16—862no—
470D8—862no—
471D8—862no—
472M16—81no—
473M16—3441no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—3441no—
485C2×C8—3441no—
486C2×C8—3441no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8C2×C4×D4311yescharacteristic
490C2×C8C2×C4×D4311yescharacteristic
491C2×C8D4×D4311yescharacteristic
492C2×C8D4×D4311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×C4×D4311yescharacteristic
499C4⋊C4C2×C4×D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C42—21no—
508C42—431no—
509C42—431no—
510C42—431no—
511C42—861no—
512C42—861no—
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—431no—
516C23—861no—
517C23—861no—
518Q8—21no—
519Q8—3441no—
520Q8#1306333312yes—
521D4—21no—
522D4—21no—
523D4—432no—
524D4—864no—
525D4—861no—
526D4—861no—
527D4—861no—
528D4—3441no—
529D4—3441no—
530D4—3441no—
531D4—3441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—431no—
538C2×C4—431no—
539C2×C4—431no—
540C2×C4—864no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—3441no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—861no—
574C22—862no—
575C22—861no—
576C22—861no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22C4×D4×D4311yescharacteristic
583C4—21no—
584C4—22no—
585C4—41no—
586C4—41no—
587C4—861no—
588C4—861no—
589C4—861no—
590C4—1721no—
591C4—1721no—
592C4#131×D4311yescharacteristic
593C4C2×#1306333311yescharacteristic
594C4#1458370111yescharacteristic
595C4#1458370511yescharacteristic
596C2—81no—
597C2—3441no—
598C2—1721no—
599C2—1722no—
600C2#1914328611yescharacteristic
601C2#1914342211yescharacteristic
602C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1583C2
socleC22×C43C2×C4×D4
prime radical#19144653C2
cosocleC42×C43C24
hypercenter#1583D43
hypocenterC43#17920
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #19143705C2semidirect
3. #19143672C2semidirect
4. #19133473C2semidirect
5. #19133457C2semidirect
6. #19133426C2semidirect
7. #19133418C2semidirect
8. SD16⋊(C43⋊C8)C2semidirect
9. #19133392C2semidirect
10. #19133387C2semidirect
11. #19133377C2semidirect
12. #19133028C2semidirect
13. #19132992C2semidirect
14. #19132896C2semidirect
15. C43×#1583C2semidirect
300. #1583D43semidirect
368. C43#17920semidirect

Maximal subgroups

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

subgroupindex
#191446532
#191437052
#191436722
#191334732
#191334572
#191334262
#191334182
SD16⋊(C43⋊C8)2
#191333922
#191333872
#191333772
#191330282
#191329922
#191328962
C43×#15832
#1792043