Finite Group Databasebeta

← C4×#14583187 #25104166

Subgroups — C4×#14583187 #25104166

Order 11008.

1000 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583187C211yesmaximal, characteristic
2C4×#13063324C211yesmaximal, characteristic, complemented
3C4×D4×Dic43C211yesmaximal, characteristic
4#19135541C211yesmaximal, characteristic, complemented
5#19135357C211yesmaximal, characteristic, complemented
6#19135183C211yesmaximal, characteristic, complemented
7#19135179C211yesmaximal, characteristic, complemented
8#19134858C211yesmaximal, characteristic
9#19134854C211yesmaximal, characteristic
10#19134593C211yesmaximal, characteristic
11C4×#13063256C211yesmaximal, characteristic, complemented
12C4×#13063257C211yesmaximal, characteristic, complemented
13C4×Dic43⋊C8C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic
15C4×#102×C43C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×C4×Dic86—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C22×C4×Dic43—21no—
21#14583187C418yesdirect product factor
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582803—21no—
32#14582798C2211yescharacteristic
33#14582796—21no—
34#14582795C2211yescharacteristic
35#14582768C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4×Dic43⋊C4—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42C22⋊C4×Dic43—21no—
43C4×C22⋊Dic43—21no—
44C42×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063324—22no—
66#13063324C2×C414yescomplemented
67C4×Dic86—44no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—22no—
71D4×Dic43C2×C414yes—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—44no—
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063257—22no—
95#13063257C2×C414yescomplemented
96#13063256—22no—
97#13063256C2×C414yescomplemented
98Dic43⋊C8—22no—
99Dic43⋊C8C2×C414yescomplemented
100#13063246—22no—
101#13063246C2×C414yes—
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43Q814yescomplemented
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43C2×C414yes—
123C4×C8×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43C22×C412yes—
130C2×D4×C43C2×Q812yes—
131C2×D4×C43#4112yes—
132C22×C4×C43—24no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—24no—
142C22×Dic43—24no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×Dic86—24no—
156C2×Dic86—42no—
157C2×Dic86—42no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C412yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C412yes—
169C4⋊C4×C43C2×Q812yes—
170C22⋊C4×C43—24no—
171C42×C43—42no—
172C42×C43C2×Q812yes—
173C42×C43#4112yes—
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43C22×C412yes—
183C4⋊Dic43C22×C412yes—
184C4⋊Dic43#4112yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189C4×Dic43—22no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—22no—
193C4×Dic43—41no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43SD1614yes—
199C4×Dic43C22×C412yes—
200C4×Dic43#4112yes—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C412yes—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43C22×D411yescharacteristic
215D4×C43—22no—
216D4×C43—22no—
217D4×C43—22no—
218D4×C43C4×Q814yescomplemented
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—48no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C22⋊Q812yes—
232C2×C4×C43C22⋊Q812yes—
233C2×C4×C43C2×SD1612yes—
234C2×C4×C43AGL(1,ℤ/8)12yes—
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—48no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—48no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43C4×D412yes—
263C2×Dic43C4×D412yes—
264C2×Dic43C2×SD1612yes—
265C2×Dic43C2×SD1612yes—
266C2×Dic43#13512yes—
267Dic86—48no—
268C8×C43—22no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272C4×#476—431nomaximal, Sylow
273C22×C43—24no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×C22⋊Q811yescharacteristic
282C22×C43#52511yescharacteristic
283C22×C43C22×SD1611yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43#57511yescharacteristic
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43#47614yescomplemented
292C4×C43C2×C4×Q811yescharacteristic
293C4×C43C4×#4111yescharacteristic
294C4×C43#52911yescharacteristic
295C4×C43#53311yescharacteristic
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—41no—
300Dic43—42no—
301Dic43—42no—
302Dic43—81no—
303Dic43C4×SD1614yes—
304C2×#476—431no—
305C4×C4⋊Q8—431no—
306C42×D4—431no—
307#1987—431no—
308#1948—431no—
309#1920—431no—
310#1920—431no—
311#1864—431no—
312#1864—431no—
313#1802—431no—
314C4×#106—431no—
315C4×#106—431no—
316C4×C4⋊C8—431no—
317C4×#102—431no—
318C4×#102D4311yescharacteristic
319C2×C43—44no—
320C2×C43C4×C22⋊Q811yescharacteristic
321C2×C43C2×C4×SD1611yescharacteristic
322C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
323C2×C43C2×#47611yescharacteristic
324C2×C43#307611yescharacteristic
325C2×C43#310111yescharacteristic
326C2×C43#310611yescharacteristic
327C2×C4⋊Q8—431no—
328C2×C4×Q8—861no—
329C2×C4×D4—431no—
330C2×C4×D4—431no—
331C2×C4×D4C2×D4311yescharacteristic
332C22×C42—861no—
333#476—438no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#106—431no—
337C2×#106—431no—
338C2×C4⋊C8—431no—
339C2×C4⋊C8—431no—
340C2×#102—431no—
341C2×#102—431no—
342C2×#102C2×D4311yescharacteristic
343C2×#102C2×D4311yescharacteristic
344C2×C4×C8—431no—
345C2×C4×C8C2×D4311yescharacteristic
346#391—861no—
347#389—431no—
348#389—431no—
349#389—861no—
350#384—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—861no—
356C4×C4⋊C4C2×D4311yescharacteristic
357C4×C22⋊C4—861no—
358C4×C22⋊C4—861no—
359C4×C22⋊C4—861no—
360C43—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340C2×D4311yescharacteristic
368#340C2×D4311yescharacteristic
369#336—431no—
370#336—431no—
371C43C4×#47611yescharacteristic, complemented, Sylow
372C22×Q8—861no—
373C22×D4C22×D4311yescharacteristic
374C23×C4—21no—
375C23×C4—861no—
376C23×C4—861no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381C4⋊Q8—434no—
382C4⋊Q8—862no—
383C4×Q8—1724no—
384C4×D4—22no—
385C4×D4—434no—
386C4×D4—862no—
387C4×D4—862no—
388C4×D4—862no—
389C4×D4Dic8614yescomplemented
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C42—21no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—1724no—
417C2×C42C22×D4311yescharacteristic
418#106—434no—
419#106—434no—
420#106—862no—
421#106—862no—
422C4⋊C8—434no—
423C4⋊C8—862no—
424#102—22no—
425#102—434no—
426#102—862no—
427#102C4×D4314yes—
428C4×C8—22no—
429C4×C8—862no—
430#95—21no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437C24—21no—
438C2×Q8—864no—
439C2×Q8—1722no—
440C2×Q8—1722no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×Dic8612yes—
445C2×D4C2×C4×D4312yes—
446C2×D4#1062189812yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—864no—
458C22×C4—864no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8C2×C4×D4312yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—432no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C4⋊C4—864no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4C2×Dic8612yes—
500C4⋊C4C2×C4×D4312yes—
501C22⋊C4—24no—
502C22⋊C4—864no—
503C22⋊C4—864no—
504C42—42no—
505C42—434no—
506C42—432no—
507C42—432no—
508C42—862no—
509C42—862no—
510C42—861no—
511C42—861no—
512C42—1721no—
513C42—1722no—
514C42—1722no—
515C42—1722no—
516C42—1722no—
517C42C2×Dic8612yes—
518C42#1062190012yes—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23C2×D4×D4311yescharacteristic
527Q8—1728no—
528D4—22no—
529D4—22no—
530D4—22no—
531D4C4×Dic8614yescomplemented
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—48no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—861no—
556C2×C4—862no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—1728no—
560C2×C4—1728no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4#1306330212yes—
571C2×C4#1306330212yes—
572C2×C4SD16×D4312yes—
573C2×C4#1306334912yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4C22×Dic8611yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C8—22no—
581C8—41no—
582C8—862no—
583C8—1721no—
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22C4×D4×D4311yescharacteristic
592C22C2×#1306330211yescharacteristic
593C22#1458340811yescharacteristic
594C22C2×SD16×D4311yescharacteristic
595C22#135×D4311yescharacteristic
596C22C2×#1306334911yescharacteristic
597C22#1458369611yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—81no—
602C4—434no—
603C4—862no—
604C4—862no—
605C4—3441no—
606C4—1722no—
607C4—1722no—
608C4—1721no—
609C4—1722no—
610C4#1458318714yesdirect product factor
611C4C2×C4×Dic8611yescharacteristic
612C4C4×#1062190011yescharacteristic
613C4#1458342911yescharacteristic
614C4#1458345211yescharacteristic
615C2—44no—
616C2C4×#1306330211yescharacteristic
617C2C4×SD16×D4311yescharacteristic
618C2C4×#1306334911yescharacteristic
619C2C2×#1458318711yescharacteristic
620C2#1914437911yescharacteristic
621C2#1914460111yescharacteristic
622C2#1914465111yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43C4×#476
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C4×#13063324C2semidirect
4. #19135541C2semidirect
5. #19135357C2semidirect
6. #19135183C2semidirect
7. #19135179C2semidirect
11. C4×#13063256C2semidirect
12. C4×#13063257C2semidirect
13. C4×Dic43⋊C8C2semidirect
21. #14583187C4direct (N × H)
66. #13063324C2×C4semidirect
95. #13063257C2×C4semidirect
97. #13063256C2×C4semidirect
99. Dic43⋊C8C2×C4semidirect
114. C4×D4×C43Q8semidirect
218. D4×C43C4×Q8semidirect
291. C4×C43#476semidirect
371. C43C4×#476semidirect
389. C4×D4Dic86semidirect
531. D4C4×Dic86semidirect
610. C4#14583187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145831872
C4×#130633242
C4×D4×Dic432
#191355412
#191353572
#191351832
#191351792
#191348582
#191348542
#191345932
C4×#130632562
C4×#130632572
C4×Dic43⋊C82
C4×#130632462
C4×#102×C432
C4×#47643