Finite Group Databasebeta

← #25067626

Subgroups — #25067626

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144640C211yesmaximal, characteristic
2#19143596C211yesmaximal, characteristic, complemented
3D4×#10621872C211yesmaximal, characteristic, complemented
4#19133506C211yesmaximal, characteristic, complemented
5#19133487C211yesmaximal, characteristic, complemented
6#19133472C211yesmaximal, characteristic, complemented
7#19133460C211yesmaximal, characteristic, complemented
8#19133431C211yesmaximal, characteristic, complemented
9#19133424C211yesmaximal, characteristic, complemented
10#19133404C211yesmaximal, characteristic, complemented
11#19133385C211yesmaximal, characteristic, complemented
12#19133057C211yesmaximal, characteristic, complemented
13#19132984C211yesmaximal, characteristic, complemented
14#19132889C211yesmaximal, characteristic, complemented
15C8×D8×C43C211yesmaximal, characteristic, complemented
16C22×#10621872—21no—
17#14583431C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583236C411yescharacteristic
20#14583216C411yescharacteristic
21#14583202C411yescharacteristic
22#14583201C411yescharacteristic
23#14583113C411yescharacteristic
24#14583112C411yescharacteristic
25#14583051C411yescharacteristic
26#14583031C411yescharacteristic
27#14583029C2211yescharacteristic, complemented
28#14583023C2211yescharacteristic, complemented
29C4×#10621873C2211yescharacteristic
30C4×#10621883C2211yescharacteristic
31C4×#10621882C2211yescharacteristic
32#14582978C2211yescharacteristic
33#14582977C2211yescharacteristic, complemented
34#14582976C2211yescharacteristic
35#14582974—21no—
36#14582970—21no—
37#14582970—21no—
38#14582967—21no—
39D4×C43⋊C8C2211yescharacteristic
40#14582957—21no—
41#14582951C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582921C2211yescharacteristic
45#14582861—21no—
46#14582854—21no—
47C4×#10621872C2211yescharacteristic
48#14582651C2211yescharacteristic, complemented
49#14582650C2211yescharacteristic, 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#14582621C2211yescharacteristic, complemented
59#14582620C2211yescharacteristic, complemented
60C4×D8×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic, complemented
63C43×#335C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C82×C43C2211yescharacteristic, complemented
67C2×D4×D43C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×#10621872—44no—
77C2×#10621872D411yescharacteristic
78C2×#10621872D411yescharacteristic
79C22×C43⋊C8—21no—
80#13063318—21no—
81#13063316C2×C411yescharacteristic
82#13063312C2×C411yescharacteristic
83#13063307—21no—
84#13063305C2×C411yescharacteristic
85#13063296C2×C411yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172C2311yescharacteristic
88D4×Dic43C2×C411yescharacteristic
89#13063287C2×C411yescharacteristic
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063284—21no—
94C4⋊C4×D43C2×C411yescharacteristic
95C22⋊C4×D43—21no—
96C42×D43C2311yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8C2×C411yescharacteristic
107Dic43⋊C8C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063248C2×C411yescharacteristic
110#13063247C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113#13063245C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊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#13063235—21no—
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×D8×C43C2×C411yescharacteristic
131C22×C8×C43—21no—
132C22×C8×C43—21no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43C2×C411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C22×Dic43—21no—
153D4×D43—22no—
154D4×D43—41no—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43C22×C411yescharacteristic
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43#4111yescharacteristic
164C2×Dic86C22×C411yescharacteristic
165D8×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C2×C8×C43—42no—
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181C22⋊Dic43—21no—
182C22⋊Dic43—21no—
183C22⋊Dic43—21no—
184#10621883—22no—
185#10621882—41no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C22×C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43C22×C411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200#10621877—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621873—41no—
210#10621872—22no—
211#10621872—41no—
212#10621872—42no—
213#10621872—42no—
214#10621872—42no—
215C23×C43—21no—
216C23×C43—21no—
217C22×D43—21no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—81no—
221C22×D43C4×D411yescharacteristic
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43#13112yes—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—42no—
236C22⋊D43—81no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—42no—
241C2×Dic43C4×D411yescharacteristic
242C2×Dic43C4×D411yescharacteristic
243C2×Dic43C4×D411yescharacteristic
244D172—21no—
245D172—21no—
246C4×D43—21no—
247C4×D43—21no—
248C4×D43—21no—
249C4×D43—21no—
250C4×D43—41no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—41no—
254C4×D43—41no—
255Dic86—21no—
256Dic86—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43AGL(1,ℤ/8)12yes—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#18006—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4×D411yescharacteristic
279C2×D43—21no—
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—84no—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43C2×#13111yescharacteristic
290C4×C43#56811yescharacteristic
291C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C43#57511yescharacteristic
293Dic43—21no—
294Dic43—21no—
295Dic43—21no—
296Dic43—41no—
297Dic43—41no—
298Dic43—41no—
299#3105—431no—
300#2969—431no—
301D4×M16—431no—
302#1594—431no—
303#1590—431no—
304#1588—431no—
305#1586—431no—
306#1582—431no—
307#1581—431no—
308SD16⋊C8—431no—
309C8×D8D4311yescharacteristic, complemented
310#1574—431no—
311#1495—431no—
312#1478—431no—
313#1453—431no—
314C2×C43—42no—
315C2×C43—81no—
316C2×C43#293311yescharacteristic
317C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C43#295711yescharacteristic
319D43—41no—
320D43—81no—
321C22×M16—861no—
322#529—431no—
323C2×C4×D4—431no—
324#484—431no—
325#481—431no—
326#478—431no—
327#478—431no—
328#463—431no—
329#463—431no—
330#450—431no—
331#447—431no—
332#446—431no—
333C8×Q8—431no—
334C4×SD16—431no—
335C4×SD16—431no—
336C4×D8—431no—
337C4×D8C2×D4311yescharacteristic
338#436—431no—
339#436—431no—
340#436—431no—
341#436—861no—
342#435—861no—
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4C2×D4311yescharacteristic
347C8×D4C2×D4311yescharacteristic, complemented
348#433—861no—
349#431—431no—
350#431—431no—
351#431—431no—
352#423—431no—
353#407—861no—
354#405—861no—
355C4×M16—431no—
356#335—431no—
357#335C2×D4311yescharacteristic, complemented
358#334—431no—
359#334—431no—
360Q8⋊C8—431no—
361Q8⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8C2×D4311yescharacteristic
367D4⋊C8C2×D4311yescharacteristic, complemented
368#322—431no—
369#322—431no—
370#322—431no—
371C82C2×D4311yescharacteristic, complemented
372C43#1800611yescharacteristic, complemented, Sylow
373C22×D4—431no—
374C23×C4—861no—
375C2×SD16—431no—
376C2×SD16—431no—
377C2×D8—431no—
378C2×D8C4×D4311yescharacteristic
379C2×M16—431no—
380C2×M16—431no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—1724no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—861no—
389#126—861no—
390#125—431no—
391#124—431no—
392#123—861no—
393C22⋊Q8—431no—
394#121—431no—
395C4×Q8—431no—
396C4×D4—431no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4C22×D4311yescharacteristic
403C4×D4C22×D4311yescharacteristic
404#117—861no—
405C2×C4⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C42—431no—
408#107—431no—
409#107C4×D4311yescharacteristic
410#106—431no—
411#106—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422#103—431no—
423#103—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427#102—431no—
428#102C4×D4311yescharacteristic
429#102C4×D4311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—431no—
433C22⋊C8—431no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440#97—431no—
441#97—431no—
442#97—861no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8—861no—
448C4×C8C22×D4311yescharacteristic
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C24—861no—
452C2×Q8—431no—
453C2×D4—431no—
454C2×D4—861no—
455C2×D4—862no—
456C2×D4—861no—
457C2×D4—1721no—
458C2×D4C2×C4×D4311yescharacteristic
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—1722no—
470C22×C4—1722no—
471SD16—862no—
472SD16—1721no—
473D8—22no—
474D8—1721no—
475M16—862no—
476M16—1721no—
477M16—1722no—
478M16—1722no—
479M16—1722no—
480M16—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—1722no—
494C2×C8C2×C4×D4311yescharacteristic
495C2×C8C2×C4×D4311yescharacteristic
496C2×C8D4×D4311yescharacteristic
497C2×C8D4×D4311yescharacteristic
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4C2×C4×D4311yescharacteristic
506C4⋊C4C2×C4×D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—431no—
517C42—431no—
518C42—431no—
519C42—861no—
520C42C23×D4311yescharacteristic
521C23—21no—
522C23—21no—
523C23—431no—
524C23—861no—
525C23—3441no—
526C23—1722no—
527C23—1722no—
528Q8—861no—
529Q8—861no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—861no—
534D4—861no—
535D4—3441no—
536D4—1722no—
537D4#1306333112yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—431no—
545C2×C4—431no—
546C2×C4—431no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—1721no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—861no—
570C8—861no—
571C8—861no—
572C8—861no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C8#1306334912yes—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—861no—
584C22—861no—
585C22—861no—
586C22—3444no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22C4×D4×D4311yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—861no—
595C4—861no—
596C4—861no—
597C4—1721no—
598C4—1721no—
599C4—1721no—
600C4C2×#1306333111yescharacteristic
601C4#1458366411yescharacteristic
602C4C2×#1306334911yescharacteristic
603C4#1458369611yescharacteristic
604C2—42no—
605C2—81no—
606C2—3441no—
607C2—1721no—
608C2#1914331511yescharacteristic
609C2C4×#1306334911yescharacteristic
610C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×D8×C43C2
socleC22×C43C2×C4×D4
prime radical#14583031C4
cosocleC42×C43C24
hypercenterC8×D8D43
hypocenterC43#18006
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #19143596C2semidirect
3. D4×#10621872C2semidirect
4. #19133506C2semidirect
5. #19133487C2semidirect
6. #19133472C2semidirect
7. #19133460C2semidirect
8. #19133431C2semidirect
9. #19133424C2semidirect
10. #19133404C2semidirect
11. #19133385C2semidirect
12. #19133057C2semidirect
13. #19132984C2semidirect
14. #19132889C2semidirect
15. C8×D8×C43C2semidirect
27. #14583029C22semidirect
28. #14583023C22semidirect
33. #14582977C22semidirect
48. #14582651C22semidirect
49. #14582650C22semidirect
50. #14582649C22semidirect
51. #14582631C22semidirect
52. #14582629C22semidirect
55. D4⋊(C43⋊C8)C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582620C22semidirect
62. C8×D4×C43C22semidirect
63. C43×#335C22semidirect
65. C43×D4⋊C8C22semidirect
66. C82×C43C22semidirect
309. C8×D8D43semidirect
347. C8×D4C2×D43semidirect
357. #335C2×D43semidirect
367. D4⋊C8C2×D43semidirect
371. C82C2×D43semidirect
372. C43#18006semidirect

Maximal subgroups

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

subgroupindex
#191446402
#191435962
D4×#106218722
#191335062
#191334872
#191334722
#191334602
#191334312
#191334242
#191334042
#191333852
#191330572
#191329842
#191328892
C8×D8×C432
#1800643