Finite Group Databasebeta

← #25099628

Subgroups — #25099628

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583009C211yesmaximal, characteristic
2#19137059C211yesmaximal, characteristic, complemented
3#19135222C211yesmaximal, characteristic, complemented
4#19135215C211yesmaximal, characteristic, complemented
5#19135180C211yesmaximal, characteristic, complemented
6#19135173C211yesmaximal, characteristic, complemented
7#19134943C211yesmaximal, characteristic
8#19134943C211yesmaximal, characteristic
9#19134856C211yesmaximal, characteristic, complemented
10#19134842C211yesmaximal, characteristic, complemented
11#19134493C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic, complemented
14#19134344C211yesmaximal, characteristic, complemented
15C42×D4×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063282—21no—
19#14583009C418yescomplemented
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582790—21no—
36#14582790—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38C4×(C2×D43)⋊C4—21no—
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C22×C42×C43—21no—
53C4×C4⋊C4×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C22⋊C4×C43—21no—
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43—21no—
59C43×C43C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621882—22no—
63C2×#10621882—22no—
64C2×#10621882C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C4×D172—22no—
70C4×D172C2×C414yescomplemented
71#13063282—44no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
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—21no—
83#13063258—22no—
84#13063256—22no—
85#13063256C2×C414yescomplemented
86#13063246—22no—
87#13063246—22no—
88#13063246C2×C414yes—
89#13063245—22no—
90#13063245—22no—
91#13063245C2×C414yescomplemented
92#13063236—22no—
93#13063236C2×C414yescomplemented
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×D4×C43C2311yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43—21no—
100C23×C4×C43—21no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106C4×D4×C43C2×C414yes—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—44no—
117C2×C42×C43D411yescharacteristic
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43D411yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C2×D4×C43#4112yes—
134C2×D4×C43#4112yes—
135C22×C4×C43—24no—
136C22×C4×C43—24no—
137C22×C4×C43—24no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C22×C412yes—
163C2×C4×D43—24no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C412yes—
170C4⋊C4×C43#4112yes—
171C4⋊C4×C43#4112yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—24no—
175C42×C43—22no—
176C42×C43—22no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43—41no—
183C42×C43—42no—
184C42×C43—42no—
185C42×C43—42no—
186C42×C43C22×C412yes—
187C42×C43#4112yes—
188#10621882—28no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202C4×Dic43—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C22×C412yes—
214C2×C43⋊C8C22×C412yes—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43#11714yescomplemented
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—48no—
252C2×C4×C43—48no—
253C2×C4×C43—48no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43C4×D412yes—
261C2×C4×C43C4×D412yes—
262C2×C4×C43AGL(1,ℤ/8)12yes—
263C2×C4×C43AGL(1,ℤ/8)12yes—
264C2×C4×C43C23×C411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×Dic43—22no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283C4×D43—48no—
284C43⋊C8—22no—
285C43⋊C8—22no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#21122—431nomaximal, Sylow
289C22×C43—24no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43#52511yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57511yescharacteristic
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—41no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—42no—
319C4×C43C2×#11711yescharacteristic
320C4×C43C4×#4111yescharacteristic
321C4×C43#52911yescharacteristic
322C4×C43#52911yescharacteristic
323Dic43—42no—
324Dic43—81no—
325Dic43—81no—
326C2×#442—431no—
327#2293—431no—
328C42×D4D4311yescharacteristic, complemented
329#1926—431no—
330#1925—431no—
331#1920—431no—
332#1919—431no—
333#1879—431no—
334#1879—431no—
335#1864—431no—
336#1862—431no—
337#1776—431no—
338#1762—431no—
339#1762—431no—
340#1745—431no—
341C2×C43—44no—
342C2×C43#229011yescharacteristic
343C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
344C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
345C2×C43#310911yescharacteristic
346C2×C43#311111yescharacteristic
347C2×C43#311411yescharacteristic
348C2×C43#311511yescharacteristic
349D43—82no—
350C22×D8—431no—
351C2×C4×D4—431no—
352C2×C4×D4C2×D4311yescharacteristic
353C2×C4×D4C2×D4311yescharacteristic
354C2×C4×D4C2×D4311yescharacteristic
355C2×#117—861no—
356C22×C42—21no—
357#442—438no—
358C2×#107—431no—
359C2×#106—431no—
360C2×#106—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#97—431no—
368C2×#97—431no—
369#390—431no—
370#390—431no—
371#389—431no—
372#389—431no—
373#388—861no—
374#388—861no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4C2×D4311yescharacteristic
377C4×C4⋊C4C2×D4311yescharacteristic
378C4×C4⋊C4C2×D4311yescharacteristic
379C4×C22⋊C4—21no—
380C4×C22⋊C4—21no—
381C4×C22⋊C4—21no—
382C4×C22⋊C4—861no—
383C43C2×D4311yescharacteristic
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#336—431no—
391#336—431no—
392#336—431no—
393#336—431no—
394C43#2112211yescharacteristic, complemented, Sylow
395C22×D4—431no—
396C22×D4C22×D4311yescharacteristic
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—861no—
401C2×D8—434no—
402C2×D8—862no—
403C2×D8—862no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8—431no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—434no—
414C4×D4—862no—
415C4×D4C4×D4314yes—
416#117—1724no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—44no—
437C2×C42—861no—
438C2×C42C22⋊D4311yescharacteristic
439C2×C42C22⋊D4311yescharacteristic
440C2×C42C22⋊D4311yescharacteristic
441C2×C42C22⋊D4311yescharacteristic
442C2×C42C22×D4311yescharacteristic
443C2×C42C22×D4311yescharacteristic
444C2×C42C22×D4311yescharacteristic
445#107—862no—
446#106—434no—
447#106—862no—
448#102—434no—
449#102—434no—
450#102—862no—
451#102—862no—
452#102—862no—
453#102—862no—
454#97—434no—
455#97—862no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—21no—
463C24—861no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—432no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4C2×C4×D4312yes—
474C2×D4#1062189812yes—
475C2×D4#1062189812yes—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—861no—
489C22×C4—864no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C2×C22⋊D4311yescharacteristic
500C22×C4C23×D4311yescharacteristic
501D8—868no—
502C2×C8—432no—
503C2×C8—432no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—432no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4C2×C4×D4312yes—
526C4⋊C4#1062189812yes—
527C4⋊C4#1062189812yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—864no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C42—22no—
537C42—22no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—41no—
543C42—41no—
544C42—42no—
545C42—42no—
546C42—42no—
547C42—1722no—
548C42C2×C4×D4312yes—
549C42#1062189812yes—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—862no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23C22×C22⋊D4311yescharacteristic
565D4—22no—
566D4—22no—
567D4—22no—
568D4—862no—
569D4—862no—
570D4—1721no—
571D4—1721no—
572D4#1306328214yescomplemented
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—48no—
591C2×C4—48no—
592C2×C4—48no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—862no—
600C2×C4—1728no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4C4×C22⋊D4312yes—
610C2×C4C4×C22⋊D4312yes—
611C2×C4#1306335012yes—
612C2×C4#1306335112yes—
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4C2×#1062189811yescharacteristic
615C2×C4C2×#1062189811yescharacteristic
616C2×C4C2×#1062189811yescharacteristic
617C2×C4C2×#1062189811yescharacteristic
618C2×C4C2×#1062189811yescharacteristic
619C8—862no—
620C8—862no—
621C8—1721no—
622C8—1721no—
623C22—24no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—3441no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22C2×C4×C22⋊D4311yescharacteristic
638C22#1458341011yescharacteristic
639C22#1458341011yescharacteristic
640C22C2×#1306335011yescharacteristic
641C22C2×#1306335111yescharacteristic
642C22#1458369711yescharacteristic
643C22#1458369711yescharacteristic
644C4—22no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—3441no—
654C4—3441no—
655C4—1722no—
656C4C2×#1306328211yescharacteristic
657C4C4×#1062189811yescharacteristic
658C4#1458343311yescharacteristic
659C4#1458343311yescharacteristic
660C2—44no—
661C2—3442no—
662C2#1913703811yescharacteristic
663C2C4×#1306335011yescharacteristic
664C2C4×#1306335111yescharacteristic
665C2#1914468611yescharacteristic
666C2#1914470411yescharacteristic
667C2#1914473311yescharacteristic
668C2#1914474611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC42×D4×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenterC42×D4D43
hypocenterC43#21122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. #19137059C2semidirect
3. #19135222C2semidirect
4. #19135215C2semidirect
5. #19135180C2semidirect
6. #19135173C2semidirect
9. #19134856C2semidirect
10. #19134842C2semidirect
11. #19134493C2semidirect
12. #19134423C2semidirect
13. #19134420C2semidirect
14. #19134344C2semidirect
15. C42×D4×C43C2semidirect
19. #14583009C4semidirect
70. C4×D172C2×C4semidirect
85. #13063256C2×C4semidirect
91. #13063245C2×C4semidirect
93. #13063236C2×C4semidirect
233. D4×C43#117semidirect
328. C42×D4D43semidirect
394. C43#21122semidirect
572. D4#13063282semidirect

Maximal subgroups

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

subgroupindex
C2×#145830092
#191370592
#191352222
#191352152
#191351802
#191351732
#191349432
#191348562
#191348422
#191344932
#191344232
#191344202
#191343442
C42×D4×C432
#2112243