Finite Group Databasebeta

← #25066660

Subgroups — #25066660

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144640C211yesmaximal, characteristic
2#19143739C211yesmaximal, characteristic, complemented
3#19143616C211yesmaximal, characteristic, complemented
4#19133454C211yesmaximal, characteristic, complemented
5#19133431C211yesmaximal, characteristic, complemented
6#19133422C211yesmaximal, characteristic, complemented
7#19133416C211yesmaximal, characteristic, complemented
8#19133404C211yesmaximal, characteristic, complemented
9#19133394C211yesmaximal, characteristic, complemented
10D8×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133382C211yesmaximal, characteristic, complemented
12#19133018C211yesmaximal, characteristic, complemented
13#19133000C211yesmaximal, characteristic, complemented
14#19132896C211yesmaximal, characteristic, complemented
15C43×#1586C211yesmaximal, characteristic, complemented
16#14583431C2211yescharacteristic
17C4×D4×D43C2211yescharacteristic
18#14583236C411yescharacteristic
19#14583216C411yescharacteristic
20#14583202C411yescharacteristic
21#14583201C411yescharacteristic
22#14583113C411yescharacteristic
23#14583112C411yescharacteristic
24#14583051C411yescharacteristic
25#14583031C411yescharacteristic
26#14583029C2211yescharacteristic, complemented
27#14583023C2211yescharacteristic, complemented
28C4×#10621873C2211yescharacteristic
29C4×#10621883C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582975—21no—
32#14582967—21no—
33C8×D172C2211yescharacteristic
34D4×C43⋊C8C2211yescharacteristic
35D4×C43⋊C8C2211yescharacteristic, complemented
36#14582964C2211yescharacteristic
37C8×C22⋊D43—21no—
38(C22⋊D43)⋊C8—21no—
39#14582957—21no—
40#14582951C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582927—21no—
45#14582921C2211yescharacteristic
46C2×(C2×D43)⋊C8—21no—
47C22⋊C8×D43—21no—
48#14582652C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51#14582631C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53#14582628C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic, complemented
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic, complemented
58#14582620C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic, complemented
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×D4×D43C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621872—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77#13063318—21no—
78#13063316C2×C411yescharacteristic
79#13063312C2×C411yescharacteristic
80#13063307—21no—
81#13063305C2×C411yescharacteristic
82#13063296C2×C411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172C2311yescharacteristic
85D4×Dic43C2×C411yescharacteristic
86#13063287C2×C411yescharacteristic
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89(C22⋊D43)⋊C4—21no—
90#13063284—21no—
91C4⋊C4×D43C2×C411yescharacteristic
92C22⋊C4×D43—21no—
93C42×D43C2311yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063257C2×C411yescharacteristic
96#13063256C2×C411yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊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)⋊C8C2×C411yescharacteristic
120(C2×D43)⋊C8C2×C411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122(C2×D43)⋊C8D411yescharacteristic
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×D8×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43C2×C411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×D4×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152D4×D43—22no—
153D4×D43—22no—
154C2×D172C22×C411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—81no—
159C2×C4×D43—81no—
160C2×C4×D43C22×C411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86C22×C411yescharacteristic
164D8×C43—22no—
165M16×C43—81no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180C22⋊Dic43—21no—
181C22⋊Dic43—21no—
182C22⋊Dic43—21no—
183#10621883—22no—
184#10621882—22no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C411yescharacteristic
191C4⋊Dic43C22×C411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208#10621873—22no—
209#10621872—81no—
210C8×D43—81no—
211C8×D43—81no—
212C23×C43—21no—
213C23×C43—21no—
214C22×D43—21no—
215C22×D43—24no—
216C22×D43—81no—
217C22×D43—81no—
218C22×D43C4×D411yescharacteristic
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43#13112yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—24no—
233C22⋊D43—81no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—81no—
238C2×Dic43C4×D411yescharacteristic
239C2×Dic43C4×D411yescharacteristic
240C2×Dic43C4×D411yescharacteristic
241D172—21no—
242D172#13112yes—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—81no—
251C4×D43—81no—
252Dic86—21no—
253Dic86—21no—
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#17918—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43C2×C4×D411yescharacteristic
276C2×D43—21no—
277C2×D43—22no—
278C2×D43—21no—
279C2×D43—21no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—84no—
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—
295Dic43—41no—
296#3105—431no—
297#2993—431no—
298#2972—431no—
299#1586D4311yescharacteristic, complemented
300#1585—431no—
301#1582—431no—
302#1581—431no—
303#1580—431no—
304SD16⋊C8—431no—
305C8×SD16—431no—
306C8×D8—431no—
307#1574—431no—
308#1486—431no—
309#1482—431no—
310#1454—431no—
311C2×C43—42no—
312C2×C43—81no—
313C2×C43#292911yescharacteristic
314C2×C43#294611yescharacteristic
315C2×C43#295711yescharacteristic
316D43—41no—
317D43—42no—
318#529—431no—
319C2×C4×D4—431no—
320#484—431no—
321#481—431no—
322#478—431no—
323#478—431no—
324#463—431no—
325#463—431no—
326#450—431no—
327#447—431no—
328#446—431no—
329C8×Q8—431no—
330C4×SD16—431no—
331C4×SD16—431no—
332C4×D8—431no—
333C4×D8C2×D4311yescharacteristic
334#436—861no—
335#436C2×D4311yescharacteristic, complemented
336#435—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343C8×D4C2×D4311yescharacteristic
344#433—861no—
345#431—431no—
346#431—431no—
347#431—431no—
348#431—431no—
349#424—861no—
350#423—431no—
351C2×C22⋊C8—861no—
352C2×C22⋊C8—861no—
353#335—431no—
354#335—431no—
355#334—431no—
356#334C2×D4311yescharacteristic, complemented
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8C2×D4311yescharacteristic
364D4⋊C8C2×D4311yescharacteristic, complemented
365#322—431no—
366#322—431no—
367#322C2×D4311yescharacteristic, complemented
368C82—431no—
369C43#1791811yescharacteristic, complemented, Sylow
370C22×D4—431no—
371C23×C4—861no—
372C2×SD16—431no—
373C2×SD16—431no—
374C2×D8—431no—
375C2×D8C4×D4311yescharacteristic
376C2×M16—21no—
377C2×M16—861no—
378C22×C8—21no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383#126—861no—
384#125—431no—
385#124—431no—
386#123—861no—
387C22⋊Q8—431no—
388#121—431no—
389C4×Q8—431no—
390C4×D4—431no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397C4×D4C22×D4311yescharacteristic
398#117—861no—
399C2×C4⋊C4—431no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402#107—431no—
403#107C4×D4311yescharacteristic
404#106—431no—
405#106—431no—
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⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418#103—431no—
419#103—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102C4×D4311yescharacteristic
425#102C4×D4311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C22⋊C8—431no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438#97—861no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447C24—861no—
448C2×Q8—431no—
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4—861no—
454C2×D4C2×C4×D4311yescharacteristic
455C2×D4C2×C4×D4311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—3441no—
466C22×C4—3441no—
467SD16—862no—
468SD16—862no—
469D8—22no—
470D8—862no—
471M16—81no—
472M16—3441no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
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×C8C2×C4×D4311yescharacteristic
489C2×C8C2×C4×D4311yescharacteristic
490C2×C8D4×D4311yescharacteristic
491C2×C8D4×D4311yescharacteristic
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4C2×C4×D4311yescharacteristic
500C4⋊C4C2×C4×D4311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C42—431no—
511C42—431no—
512C42—431no—
513C42—861no—
514C42C23×D4311yescharacteristic
515C23—21no—
516C23—21no—
517C23—431no—
518C23—864no—
519C23—861no—
520C23—3441no—
521C23—3441no—
522Q8—861no—
523Q8—861no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—432no—
528D4—864no—
529D4—861no—
530D4—3441no—
531D4#1306333312yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—431no—
539C2×C4—431no—
540C2×C4—431no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—3441no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4C22×C4×D4311yescharacteristic
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4#41×D4311yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C8—1721no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—861no—
578C22—861no—
579C22—861no—
580C22—862no—
581C22—3444no—
582C22—1721no—
583C22—1721no—
584C22C4×D4×D4311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—861no—
589C4—861no—
590C4—861no—
591C4—1721no—
592C4—1721no—
593C4—1721no—
594C4#131×D4311yescharacteristic
595C4C2×#1306333311yescharacteristic
596C4#1458370311yescharacteristic
597C4#1458370911yescharacteristic
598C2—42no—
599C2—81no—
600C2—1721no—
601C2—1722no—
602C2#1914328611yescharacteristic
603C2#1914342411yescharacteristic
604C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1586C2
socleC22×C43C2×C4×D4
prime radical#14583031C4
cosocleC42×C43C24
hypercenter#1586D43
hypocenterC43#17918
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #19143739C2semidirect
3. #19143616C2semidirect
4. #19133454C2semidirect
5. #19133431C2semidirect
6. #19133422C2semidirect
7. #19133416C2semidirect
8. #19133404C2semidirect
9. #19133394C2semidirect
10. D8×C43⋊C8C2semidirect
11. #19133382C2semidirect
12. #19133018C2semidirect
13. #19133000C2semidirect
14. #19132896C2semidirect
15. C43×#1586C2semidirect
26. #14583029C22semidirect
27. #14583023C22semidirect
35. D4×C43⋊C8C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582649C22semidirect
51. #14582631C22semidirect
52. #14582629C22semidirect
55. D4⋊(C43⋊C8)C22semidirect
57. #14582621C22semidirect
58. #14582620C22semidirect
59. C8×C43⋊C8C22semidirect
61. C43×#436C22semidirect
63. C43×#334C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
299. #1586D43semidirect
335. #436C2×D43semidirect
356. #334C2×D43semidirect
364. D4⋊C8C2×D43semidirect
367. #322C2×D43semidirect
369. C43#17918semidirect

Maximal subgroups

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

subgroupindex
#191446402
#191437392
#191436162
#191334542
#191334312
#191334222
#191334162
#191334042
#191333942
D8×C43⋊C82
#191333822
#191330182
#191330002
#191328962
C43×#15862
#1791843