Finite Group Databasebeta

← #25096639

Subgroups — #25096639

Order 11008.

1782 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2C2×#14582954C211yesmaximal, characteristic, complemented
3#19136999C211yesmaximal, characteristic, complemented
4#19134684C212yesmaximal, complemented
5#19134594C212yesmaximal, complemented
6#19134593C212yesmaximal, complemented
7#19134524C212yesmaximal
8#19134423C211yesmaximal, characteristic, complemented
9#19134421C211yesmaximal, characteristic, complemented
10#19134420C211yesmaximal, characteristic, complemented
11C43×#1762C211yesmaximal, characteristic, complemented
12C22×D4×D43C2211yescharacteristic
13C23×C4×D43—21no—
14C2×C4×D172C2211yescharacteristic
15C2×D4×Dic43C2211yescharacteristic
16C2×#13063287C2211yescharacteristic
17C2×C4×C22⋊D43—21no—
18C2×(C22⋊D43)⋊C4—21no—
19C4×D4×D43—24no—
20C4×D4×D43C418yescomplemented
21C2×#13063282—21no—
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C22⋊C4×D43—21no—
24C2×C42×D43C2211yescharacteristic
25#14582954—24no—
26C2×Dic43⋊C8C2212yescomplemented
27C2×#13063247C2212yes—
28C2×#13063246C2212yes—
29C2×#13063245C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×#13063236C2211yescharacteristic, complemented
32#14582768C2212yescomplemented
33#14582763—21no—
34#14582758—21no—
35#14582756C2212yes—
36C4×Dic43⋊C4—21no—
37C4×C4⋊Dic43C2211yescharacteristic, complemented
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C2×C4×D4×C43C2211yescharacteristic
42C2×#102×C43C2212yes—
43C2×#97×C43C2211yescharacteristic, complemented
44C4×C4⋊C4×C43C2211yescharacteristic, complemented
45C43×#340C2212yescomplemented
46C24×D43—21no—
47C22×D172C2311yescharacteristic
48C22×C22⋊D43—21no—
49C2×D4×D43—24no—
50C2×D4×D43—24no—
51C2×D4×D43—22no—
52C2×D4×D43C2×C414yes—
53C23×Dic43—21no—
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—21no—
57C22×C4×D43—28no—
58C22×C4×D43—48no—
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2312yes—
63C4×D172—22no—
64C4×D172C2×C414yes—
65D4×Dic43—22no—
66D4×Dic43C2×C414yes—
67#13063287—22no—
68#13063287C2×C414yes—
69C4×C22⋊D43—28no—
70(C22⋊D43)⋊C4—28no—
71#13063282—44no—
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C4⋊C4×D43—22no—
78C4⋊C4×D43C2×C414yes—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C22⋊C4×D43—28no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43C2×C414yes—
89C42×D43D414yes—
90Dic43⋊C8—24no—
91#13063247—24no—
92#13063246—24no—
93#13063245—24no—
94(C2×D43)⋊C8—24no—
95#13063236—22no—
96C43⋊#95—21no—
97C43⋊#95—22no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C22×C8×C43C2312yes—
101C4×D4×C43—22no—
102C4×D4×C43C2×C414yes—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C22⋊C4×C43—21no—
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108#102×C43—24no—
109#97×C43—22no—
110#95×C43—21no—
111C24×C43—21no—
112C23×D43—28no—
113C23×D43—21no—
114C23×D43—24no—
115C23×D43—44no—
116C23×D43—42no—
117C23×D43—42no—
118C23×D43C2×D411yescharacteristic
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43C22×C412yes—
122C2×D4×C43#4114yes—
123C22×C4×C43—24no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—44no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C2×C22⋊D43—28no—
131C2×C22⋊D43—24no—
132C22×Dic43—24no—
133C22×Dic43—21no—
134C22×Dic43—22no—
135C22×Dic43—44no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139D4×D43—216no—
140D4×D43—28no—
141D4×D43—28no—
142C2×D172—21no—
143C2×D172—22no—
144C2×D172C22×C412yes—
145C2×D172#4114yes—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—24no—
149C2×C4×D43—24no—
150C2×C4×D43—24no—
151C2×C4×D43—24no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—44no—
155C2×C4×D43—432no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43C22⋊C414yes—
159C2×C4×D43C22⋊C414yes—
160C2×C4×D43C22×C412yes—
161C2×C4×D43C2×D412yes—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43C22×C412yes—
169C22⋊C4×C43—24no—
170C42×C43—42no—
171C42×C43C22×C412yes—
172C42×C43C2×D412yes—
173C22⋊Dic43—24no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—44no—
177C4⋊Dic43—21no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43C22×C412yes—
181Dic43⋊C4—24no—
182Dic43⋊C4—44no—
183Dic43⋊C4—44no—
184C4×Dic43—42no—
185C4×Dic43C22⋊C414yes—
186C4×Dic43C22⋊C414yes—
187C4×Dic43C22×C412yes—
188C4×Dic43C2×D412yes—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C23×C43—22no—
193C23×C43—24no—
194C23×C43—42no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43C22×D411yescharacteristic
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—216no—
201C22×D43—22no—
202C22×D43—24no—
203C22×D43—48no—
204C22×D43—416no—
205C22×D43—416no—
206C22×D43—42no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—48no—
210C22×D43C2×C22⋊C412yes—
211C22×D43AGL(1,ℤ/8)12yes—
212C22×D43#13712yes—
213D4×C43—22no—
214D4×C43—24no—
215D4×C43#11714yescomplemented
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—48no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43C2×C22⋊C412yes—
226C2×C4×C43C2×C22⋊C412yes—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4112yes—
230C2×C4×C43C2×#4112yes—
231C22⋊D43—216no—
232C2×Dic43—22no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—42no—
237C2×Dic43—48no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43C2×C22⋊C412yes—
242C2×Dic43C2×C22⋊C412yes—
243C2×Dic43C2×C22⋊C412yes—
244C2×Dic43AGL(1,ℤ/8)14yes—
245D172—22no—
246D172—24no—
247D172#11714yescomplemented
248C4×D43—28no—
249C4×D43—22no—
250C4×D43—22no—
251C4×D43—24no—
252C4×D43—28no—
253C4×D43—48no—
254C4×D43—48no—
255C4×D43—48no—
256C8×C43—42no—
257C43⋊C8—42no—
258#20738—431nomaximal, Sylow
259C22×C43—24no—
260C22×C43—44no—
261C22×C43—44no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43C22×C22⋊C411yescharacteristic
265C22×C43#52512yes—
266C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C43C2×AGL(1,ℤ/8)12yes—
268C22×C43C2×#13711yescharacteristic
269C2×D43—24no—
270C2×D43—24no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—24no—
274C2×D43—432no—
275C2×D43—44no—
276C2×D43—44no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43#41714yes—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—42no—
283C4×C43—82no—
284C4×C43C2×#11711yescharacteristic
285C4×C43C2×#11711yescharacteristic
286C4×C43#52512yes—
287Dic43—22no—
288Dic43—22no—
289Dic43—42no—
290Dic43—82no—
291Dic43#41814yes—
292C22×C4×D4—431no—
293C2×#432—431no—
294#2285—431no—
295#1824—432no—
296#1802—432no—
297#1802—432no—
298#1786—432no—
299#1762—431no—
300#1762—431no—
301#1762—431no—
302#1762D4311yescharacteristic, complemented
303C2×C43—44no—
304C2×C43#228011yescharacteristic
305C2×C43C2×#41811yescharacteristic
306C2×C43C2×#41711yescharacteristic
307C2×C43#310912yes—
308C2×C43#311012yes—
309D43—24no—
310D43—44no—
311C23×D4—431no—
312C24×C4—861no—
313C2×C4×D4—431no—
314C2×C4×D4—438no—
315C2×C4×D4—431no—
316C2×C4×D4—431no—
317C2×C4×D4—861no—
318C2×C4×D4—864no—
319C2×C4×D4—861no—
320C2×C4×D4C2×D4311yescharacteristic
321C2×#117—861no—
322C22×C4⋊C4—431no—
323C22×C22⋊C4—861no—
324C22×C42—431no—
325#432—864no—
326C2×C4⋊C8—432no—
327C2×#102—432no—
328C2×#102—432no—
329C2×#102—432no—
330C2×#102C2×D4312yes—
331C2×C22⋊C8—432no—
332C2×#97—431no—
333C2×#97C2×D4311yescharacteristic, complemented
334#384—432no—
335#382—861no—
336#380—432no—
337#380—861no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4—861no—
340C4×C4⋊C4C2×D4311yescharacteristic, complemented
341#340—432no—
342#340—432no—
343#340—432no—
344#340C2×D4312yescomplemented
345C43#2073811yescharacteristic, complemented, Sylow
346C25—861no—
347C22×D4—434no—
348C22×D4—431no—
349C22×D4—862no—
350C22×D4—861no—
351C22×D4—864no—
352C22×D4—864no—
353C22×D4C22×D4311yescharacteristic
354C23×C4—21no—
355C23×C4—431no—
356C23×C4—431no—
357C23×C4—431no—
358C23×C4—861no—
359C23×C4—868no—
360C23×C4—861no—
361C23×C4—861no—
362C23×C4—861no—
363C23×C4—1728no—
364C22×C8—432no—
365C22×C8C22×D4312yes—
366C4×D4—22no—
367C4×D4—434no—
368C4×D4—434no—
369C4×D4—434no—
370C4×D4—868no—
371C4×D4—862no—
372C4×D4—868no—
373C4×D4—862no—
374C4×D4—862no—
375C4×D4C4×D4314yes—
376#117—1724no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—434no—
379C2×C4⋊C4—432no—
380C2×C4⋊C4—862no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4C22×D4312yes—
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—868no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—862no—
392C2×C42—21no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—434no—
397C2×C42—434no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400C4⋊C8—864no—
401#102—24no—
402#102—864no—
403#102—864no—
404#102—864no—
405C22⋊C8—864no—
406#97—22no—
407#97—862no—
408#95—21no—
409#95—862no—
410#95—861no—
411C24—21no—
412C24—431no—
413C24—864no—
414C24—868no—
415C24—861no—
416C24—1722no—
417C24—1722no—
418C24—1724no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—432no—
422C2×D4—434no—
423C2×D4—864no—
424C2×D4—868no—
425C2×D4—8616no—
426C2×D4—868no—
427C2×D4—868no—
428C2×D4—861no—
429C2×D4—862no—
430C2×D4C2×C4×D4312yes—
431C2×D4#1062189814yes—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—44no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—434no—
440C22×C4—434no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—864no—
444C22×C4—864no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—864no—
448C22×C4—864no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—864no—
453C22×C4—862no—
454C22×C4—1724no—
455C22×C4—1724no—
456C22×C4—17232no—
457C22×C4—1724no—
458C22×C4—1724no—
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—862no—
466C2×C8—862no—
467C2×C8—862no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—432no—
472C4⋊C4—864no—
473C4⋊C4—861no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—1724no—
477C4⋊C4—1724no—
478C4⋊C4C2×C4×D4312yes—
479C22⋊C4—24no—
480C22⋊C4—864no—
481C22⋊C4—864no—
482C22⋊C4—864no—
483C22⋊C4—1724no—
484C42—42no—
485C42—434no—
486C42—434no—
487C42—432no—
488C42—432no—
489C42—1722no—
490C42C2×C4×D4312yes—
491C42D4×D4312yes—
492C23—22no—
493C23—24no—
494C23—42no—
495C23—41no—
496C23—41no—
497C23—432no—
498C23—432no—
499C23—432no—
500C23—8616no—
501C23—862no—
502C23—862no—
503C23—862no—
504C23—864no—
505C23—1728no—
506C23—1728no—
507C23—17216no—
508C23—17216no—
509C23—1722no—
510C23—1721no—
511C23—1721no—
512C23C2×D4×D4311yescharacteristic
513D4—22no—
514D4—24no—
515D4—434no—
516D4—8616no—
517D4—862no—
518D4—864no—
519D4#1306328214yescomplemented
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—48no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—432no—
530C2×C4—434no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—868no—
534C2×C4—868no—
535C2×C4—862no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—864no—
541C2×C4—862no—
542C2×C4—1728no—
543C2×C4—1728no—
544C2×C4—1728no—
545C2×C4—1728no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4C22⋊C4×D4312yes—
551C2×C4C22⋊C4×D4312yes—
552C2×C4C22×C4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4#41×D4312yes—
555C2×C4C2×#1062189812yes—
556C8—42no—
557C8—1722no—
558C22—24no—
559C22—42no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—434no—
564C22—862no—
565C22—862no—
566C22—864no—
567C22—864no—
568C22—864no—
569C22—17232no—
570C22—1722no—
571C22—1722no—
572C22—1724no—
573C22—1724no—
574C22C2×C22⋊C4×D4311yescharacteristic
575C22#1458340812yes—
576C22AGL(1,ℤ/8)×D4312yes—
577C22AGL(1,ℤ/8)×D4311yescharacteristic
578C22#137×D4311yescharacteristic
579C4—22no—
580C4—22no—
581C4—42no—
582C4—82no—
583C4—434no—
584C4—862no—
585C4—862no—
586C4—3442no—
587C4—1722no—
588C4#117×D4311yescharacteristic
589C4C2×#1306328211yescharacteristic
590C4#1458340812yes—
591C2—44no—
592C2—864no—
593C2—1724no—
594C2#1913697611yescharacteristic
595C2#418×D4311yescharacteristic
596C2#417×D4311yescharacteristic
597C2#1914468412yes—
598C2#1914469212yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#20738
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14582954C2semidirect
3. #19136999C2semidirect
4. #19134684C2semidirect
5. #19134594C2semidirect
6. #19134593C2semidirect
8. #19134423C2semidirect
9. #19134421C2semidirect
10. #19134420C2semidirect
11. C43×#1762C2semidirect
20. C4×D4×D43C4semidirect
26. C2×Dic43⋊C8C22semidirect
31. C2×#13063236C22semidirect
32. #14582768C22semidirect
37. C4×C4⋊Dic43C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
43. C2×#97×C43C22semidirect
44. C4×C4⋊C4×C43C22semidirect
45. C43×#340C22semidirect
215. D4×C43#117semidirect
247. D172#117semidirect
302. #1762D43semidirect
333. C2×#97C2×D43semidirect
340. C4×C4⋊C4C2×D43semidirect
344. #340C2×D43semidirect
345. C43#20738semidirect
519. D4#13063282semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C2×#145829542
#191369992
#191346842
#191345942
#191345932
#191345242
#191344232
#191344212
#191344202
C43×#17622
#2073843