Finite Group Databasebeta

← C4×#14583040 #25102192

Subgroups — C4×#14583040 #25102192

Order 11008.

1532 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic86C211yesmaximal, characteristic, complemented
2C2×#14583040C211yesmaximal, characteristic
3C2×C4×#10621873C212yesmaximal, complemented
4C4×#13063299C211yesmaximal, characteristic
5#19134949C212yesmaximal, complemented
6#19134910C211yesmaximal, characteristic
7#19134866C212yesmaximal, complemented
8#19134790C211yesmaximal, characteristic, complemented
9#19134531C211yesmaximal, characteristic, complemented
10C4×#13063250C212yesmaximal, complemented
11C4×C22⋊C8×C43C211yesmaximal, characteristic, complemented
12C23×Dic86C2211yescharacteristic
13C22×#10621873C2212yes—
14C2×#13063299C2211yescharacteristic
15C2×C4×Dic86—28no—
16C2×C4×Dic86—21no—
17C2×C4×Dic86—21no—
18C2×C4×Dic86C2212yes—
19C2×C4×Dic86C2212yes—
20C2×C4×D172C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4—21no—
24C22×C4×Dic43—21no—
25#14583040C418yesdirect product factor
26C4×#10621873—28no—
27C2×#13063257C2212yes—
28C2×#13063250C2212yes—
29C2×#13063250C2212yes—
30C2×#13063250C2212yes—
31C2×#13063247C2212yes—
32#14582801C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582790—21no—
35#14582778—21no—
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38C4×(C2×D43)⋊C4—21no—
39#14582662C2212yes—
40#14582662C2212yes—
41C22×C42×C43C2211yescharacteristic
42C2×C22⋊C8×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×C4×C8×C43C2212yes—
45C43×#336C2212yes—
46C22×Dic86—21no—
47C22×Dic86—22no—
48C22×Dic86—24no—
49C22×Dic86—24no—
50C22×Dic86C2×C414yescomplemented
51C22×Dic86C2312yes—
52C22×D172C2311yescharacteristic
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C22×C4×D43—21no—
57C2×#10621873—24no—
58C2×#10621873—24no—
59C2×#10621873C2×C418yescomplemented
60#13063299—22no—
61#13063299C2×C414yes—
62C4×Dic86—28no—
63C4×Dic86—28no—
64C4×Dic86—24no—
65C4×Dic86—24no—
66C4×Dic86—24no—
67C4×Dic86D418yescomplemented
68C4×D172—24no—
69C4×C22⋊D43—44no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—24no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2312yes—
76C2×Dic43⋊C4—28no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—28no—
86C2×C4×Dic43—22no—
87C2×C4×Dic43—22no—
88C2×C4×Dic43—21no—
89#13063257—24no—
90#13063250—24no—
91#13063250—24no—
92#13063250C2×C418yescomplemented
93#13063247—24no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C23×C4×C43D411yescharacteristic
98C23×C4×C43D411yescharacteristic
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43C2312yes—
101C22×C8×C43C2312yes—
102C2×C42×C43—24no—
103C2×C42×C43D411yescharacteristic
104C2×C42×C43D411yescharacteristic
105C2×C42×C43C2311yescharacteristic
106C2×C42×C43C2311yescharacteristic
107C22⋊C8×C43—22no—
108C22⋊C8×C43C2×C414yescomplemented
109C4×C8×C43—24no—
110C24×C43C2×D411yescharacteristic
111C23×D43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—41no—
119C22×C4×C43SD1614yescomplemented
120C22×C4×C43C22×C412yes—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4112yes—
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—24no—
129C2×C22⋊D43—42no—
130C2×C22⋊D43—42no—
131C22×Dic43—24no—
132C22×Dic43—24no—
133C22×Dic43—24no—
134C22×Dic43—24no—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—22no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—42no—
141C22×Dic43—42no—
142C2×D172—21no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172C22×C412yes—
146C2×C4×D43—42no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×Dic86—24no—
150C2×Dic86—24no—
151C2×Dic86—216no—
152C2×Dic86—24no—
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86—22no—
156C2×Dic86—216no—
157C2×Dic86C22×C414yes—
158C2×Dic86C2×D414yes—
159C2×Dic86#4114yes—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43C22×C414yes—
166C42×C43—22no—
167C42×C43—22no—
168C42×C43—22no—
169C42×C43C2×D414yes—
170C22⋊Dic43—42no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175C4⋊Dic43—24no—
176C4⋊Dic43—22no—
177C4⋊Dic43—21no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43C22×C412yes—
181C4⋊Dic43C2×D414yes—
182Dic43⋊C4—28no—
183Dic43⋊C4—28no—
184Dic43⋊C4—42no—
185C4×Dic43—28no—
186C4×Dic43—28no—
187C4×Dic43—42no—
188#10621873—216no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43C4×D412yes—
194C23×C43C2×SD1612yes—
195C23×C43#13512yes—
196C23×C43C22×D411yescharacteristic
197C22×D43—22no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—28no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—44no—
217C2×C4×C43C4×D412yes—
218C2×C4×C43#12012yes—
219C2×C4×C43#12012yes—
220C2×C4×C43C2×SD1612yes—
221C2×C4×C43C2×SD1612yes—
222C2×C4×C43#13712yes—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×D412yes—
225C2×C4×C43C2×#4112yes—
226C2×C4×C43C2×#4111yescharacteristic
227C22⋊D43—48no—
228C2×Dic43—216no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—22no—
233C2×Dic43—24no—
234C2×Dic43—48no—
235C2×Dic43—41no—
236C2×Dic43—42no—
237C2×Dic43—41no—
238C2×Dic43—42no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245D172—24no—
246D172—42no—
247C4×D43—84no—
248Dic86—216no—
249Dic86—24no—
250Dic86—24no—
251Dic86—24no—
252Dic86C4×D418yescomplemented
253C8×C43—24no—
254C8×C43—42no—
255C4×#448—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43C4×SD1614yescomplemented
263C22×C43C2×C4×D411yescharacteristic
264C22×C43C2×#12011yescharacteristic
265C22×C43#52511yescharacteristic
266C22×C43C22×SD1611yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13711yescharacteristic
269C22×C43#57511yescharacteristic
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—81no—
277C4×C43—22no—
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—41no—
281C4×C43#44814yescomplemented
282C4×C43C2×C4×D412yes—
283C4×C43#52512yes—
284Dic43—28no—
285Dic43—42no—
286Dic43—44no—
287Dic43—81no—
288Dic43—81no—
289C22×C4×Q8—431no—
290C2×#448—431no—
291C2×C4×SD16—432no—
292C4×#121—431no—
293#1880—432no—
294#1874—431no—
295#1865—432no—
296#1853—431no—
297#1787—431no—
298C4×#103—432no—
299C4×C22⋊C8D4311yescharacteristic, complemented
300C2×C43—24no—
301C2×C43C4×#12011yescharacteristic
302C2×C43C2×C4×SD1611yescharacteristic
303C2×C43C4×#13711yescharacteristic
304C2×C43C2×#44811yescharacteristic
305C2×C43#300211yescharacteristic
306C2×C43#310311yescharacteristic
307C2×C43#310811yescharacteristic
308D43—82no—
309C23×Q8—431no—
310C22×SD16—432no—
311C2×#121—431no—
312C2×C4×Q8—432no—
313C2×C4×Q8—432no—
314C2×C4×Q8—868no—
315C2×C4×Q8—861no—
316C2×C4×Q8—861no—
317C2×C4×D4—431no—
318C2×C4×D4—861no—
319C22×C4⋊C4—431no—
320C22×C4⋊C4—861no—
321C22×C42—861no—
322C22×C42C2×D4311yescharacteristic
323#448—438no—
324C4×SD16—868no—
325C2×#106—432no—
326C2×#103—432no—
327C2×#103—432no—
328C2×#103—432no—
329C2×#102—432no—
330C2×C22⋊C8C2×D4311yescharacteristic
331C2×C22⋊C8C2×D4311yescharacteristic
332C2×C4×C8C2×D4312yes—
333#390—431no—
334#389—431no—
335#388—861no—
336#386—861no—
337#380—431no—
338C4×C4⋊C4—431no—
339C4×C22⋊C4—861no—
340#340—432no—
341#340—432no—
342#336C2×D4312yes—
343C43C4×#44811yescharacteristic, complemented, Sylow
344C22×Q8—434no—
345C22×Q8—432no—
346C22×Q8—864no—
347C22×Q8—864no—
348C22×Q8—861no—
349C22×Q8—862no—
350C22×D4—431no—
351C22×D4—861no—
352C23×C4—861no—
353C23×C4—861no—
354C23×C4—861no—
355C23×C4D17211yescharacteristic
356C23×C4D17211yescharacteristic
357C23×C4C22×D4311yescharacteristic
358C2×SD16—438no—
359C2×SD16—864no—
360C2×SD16—864no—
361C22×C8C22×D4312yes—
362C22×C8C22×D4312yes—
363#121—434no—
364#121—862no—
365C4×Q8—438no—
366C4×Q8—864no—
367C4×Q8—864no—
368C4×Q8—868no—
369C4×Q8—868no—
370C4×Q8—864no—
371C4×D4—864no—
372C4×D4—1724no—
373C2×C4⋊C4—432no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—864no—
378C2×C4⋊C4—868no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—862no—
381C2×C4⋊C4—862no—
382C2×C4⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C42—24no—
389C2×C42—868no—
390C2×C42—862no—
391C2×C42—862no—
392C2×C42—861no—
393C2×C42D17211yescharacteristic
394C2×C42D17211yescharacteristic
395C2×C42C22×D4311yescharacteristic
396C2×C42C22×D4311yescharacteristic
397#106—864no—
398#103—438no—
399#103—864no—
400#103—864no—
401#102—864no—
402C22⋊C8—22no—
403C22⋊C8C4×D4314yescomplemented
404C4×C8—24no—
405#95—861no—
406#95—861no—
407#95—861no—
408C24—861no—
409C24C2×D17211yescharacteristic
410C2×Q8—434no—
411C2×Q8—434no—
412C2×Q8—434no—
413C2×Q8—8616no—
414C2×Q8—864no—
415C2×Q8—864no—
416C2×Q8—8616no—
417C2×Q8—864no—
418C2×Q8—862no—
419C2×Q8—862no—
420C2×Q8—862no—
421C2×D4—432no—
422C2×D4—864no—
423C2×D4—862no—
424C2×D4—862no—
425C2×D4—861no—
426C2×D4—1722no—
427C2×D4—1722no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—41no—
435C22×C4—864no—
436C22×C4—864no—
437C22×C4—864no—
438C22×C4—862no—
439C22×C4—864no—
440C22×C4—861no—
441C22×C4—862no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—1722no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4—1722no—
449C22×C4#1062187314yescomplemented
450C22×C4C2×C4×D4312yes—
451C22×C4C2×D17211yescharacteristic
452C22×C4C2×D17211yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4C2×D17211yescharacteristic
455C22×C4C2×D17211yescharacteristic
456C22×C4#1062189812yes—
457C22×C4C23×D4311yescharacteristic
458SD16—8616no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8C2×C4×D4314yes—
465C4⋊C4—432no—
466C4⋊C4—434no—
467C4⋊C4—868no—
468C4⋊C4—864no—
469C4⋊C4—868no—
470C4⋊C4—862no—
471C4⋊C4—861no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—1722no—
475C22⋊C4—864no—
476C22⋊C4—1722no—
477C22⋊C4—1722no—
478C22⋊C4—1722no—
479C22⋊C4—1722no—
480C42—22no—
481C42—22no—
482C42—22no—
483C42—868no—
484C42—868no—
485C42—1722no—
486C42D4×D4314yes—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—862no—
492C23—1721no—
493C23—1721no—
494C23—1721no—
495C23—1721no—
496C23—1721no—
497C23—1721no—
498C23C4×D17212yes—
499C23C2×#1062187312yes—
500C23#1306334712yes—
501C23C22×D17211yescharacteristic
502Q8—438no—
503Q8—8616no—
504Q8—864no—
505Q8—864no—
506Q8—864no—
507D4—864no—
508D4—1728no—
509D4—1722no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—44no—
523C2×C4—8616no—
524C2×C4—864no—
525C2×C4—864no—
526C2×C4—864no—
527C2×C4—862no—
528C2×C4—864no—
529C2×C4—3444no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1728no—
537C2×C4—1721no—
538C2×C4—1722no—
539C2×C4—1721no—
540C2×C4—1722no—
541C2×C4C4×D17212yes—
542C2×C4#1306329512yes—
543C2×C4#1306329512yes—
544C2×C4C2×#1062187312yes—
545C2×C4C2×#1062187312yes—
546C2×C4#1306335812yes—
547C2×C4C22×C4×D4311yescharacteristic
548C2×C4C2×D4×D4312yes—
549C2×C4#41×D4312yes—
550C2×C4C2×#1062189811yescharacteristic
551C8—24no—
552C8—42no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—3441no—
560C22—3441no—
561C22—3441no—
562C22—3441no—
563C22—1722no—
564C22—1722no—
565C22—1722no—
566C22C4×#1062187314yescomplemented
567C22C2×C4×D17211yescharacteristic
568C22C2×#1306329511yescharacteristic
569C22#1458341111yescharacteristic
570C22C22×#1062187311yescharacteristic
571C22C2×#1306334711yescharacteristic
572C22C2×#1306335811yescharacteristic
573C22#1458369911yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—868no—
579C4—3441no—
580C4—3441no—
581C4—1724no—
582C4—1722no—
583C4#1458304014yesdirect product factor
584C4C4×D4×D4312yes—
585C4#1458340812yes—
586C2—24no—
587C2—3442no—
588C2C4×#1306329511yescharacteristic
589C2C2×C4×#1062187311yescharacteristic
590C2C4×#1306335811yescharacteristic
591C2C2×#1458304011yescharacteristic
592C2#1914381711yescharacteristic
593C2#1914462711yescharacteristic
594C2#1914467711yescharacteristic
subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×C22⋊C8×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenterC4×C22⋊C8D43
hypocenterC43C4×#448
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic86C2semidirect
3. C2×C4×#10621873C2semidirect
5. #19134949C2semidirect
7. #19134866C2semidirect
8. #19134790C2semidirect
9. #19134531C2semidirect
10. C4×#13063250C2semidirect
11. C4×C22⋊C8×C43C2semidirect
25. #14583040C4direct (N × H)
50. C22×Dic86C2×C4semidirect
59. C2×#10621873C2×C4semidirect
67. C4×Dic86D4semidirect
92. #13063250C2×C4semidirect
108. C22⋊C8×C43C2×C4semidirect
119. C22×C4×C43SD16semidirect
252. Dic86C4×D4semidirect
262. C22×C43C4×SD16semidirect
281. C4×C43#448semidirect
299. C4×C22⋊C8D43semidirect
343. C43C4×#448semidirect
403. C22⋊C8C4×D43semidirect
449. C22×C4#10621873semidirect
566. C22C4×#10621873semidirect
583. C4#14583040direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic862
C2×#145830402
C2×C4×#106218732
C4×#130632992
#191349492
#191349102
#191348662
#191347902
#191345312
C4×#130632502
C4×C22⋊C8×C432
C4×#44843