Finite Group Databasebeta

← C4×#14583505 #25255708

Subgroups — C4×#14583505 #25255708

Order 11008.

2518 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583505C211yesmaximal, characteristic
2#19137384C214yesmaximal, complemented
3#19137359C214yesmaximal, complemented
4#19137337C211yesmaximal, characteristic, complemented
5#19137318C211yesmaximal, characteristic, complemented
6#19137286C212yesmaximal, complemented
7#19137234C212yesmaximal, complemented
8#19137205C211yesmaximal, characteristic, complemented
9C4×#13063322C211yesmaximal, characteristic, complemented
10C4×#13063310C214yesmaximal, complemented
11C4×#13063300C214yesmaximal, complemented
12C4×#13063300C212yesmaximal, complemented
13C4×#13063287C212yesmaximal, complemented
14C4×#13063282C211yesmaximal, characteristic, complemented
15C4×#125×C43C211yesmaximal, characteristic, complemented
16#14583505C4116yesdirect product factor
17C2×#13063322C2211yescharacteristic
18C2×#13063310C2214yes—
19C2×#13063300C2212yes—
20C2×#13063300C2214yes—
21C2×C4×D172C2212yes—
22C2×C4×D172C2214yes—
23C2×C4×D172C2214yes—
24C2×#13063287C2212yes—
25C2×#13063287C2212yes—
26C2×#13063282C2211yescharacteristic
27C2×#13063282C2211yescharacteristic
28C2×C42×D43C2211yescharacteristic
29C2×C42×D43C2214yes—
30#14582801C2212yes—
31#14582801C2214yes—
32#14582800C2214yes—
33#14582800C2212yes—
34#14582798C2214yes—
35#14582798C2212yes—
36#14582791C2214yes—
37#14582791C2214yes—
38#14582791C2214yes—
39#14582789C2214yes—
40#14582788C2214yes—
41#14582786C2214yes—
42#14582785C2214yes—
43#14582777C2214yes—
44#14582777C2214yes—
45#14582777C2214yes—
46#14582777C2214yes—
47#14582770C2214yes—
48#14582769C2211yescharacteristic
49#14582761C2214yes—
50#14582756C2212yes—
51#14582756C2214yes—
52C4⋊C4×Dic43C2212yes—
53C4⋊C4×Dic43C2212yes—
54C4×Dic43⋊C4C2212yes—
55C4×Dic43⋊C4C2212yes—
56C4×(C2×D43)⋊C4C2212yes—
57C4×(C2×D43)⋊C4C2212yes—
58C4×(C2×D43)⋊C4C2214yes—
59C4×(C2×D43)⋊C4C2214yes—
60#14582746C2214yes—
61#14582746C2214yes—
62#14582745C2211yescharacteristic
63#14582745C2211yescharacteristic
64C42×Dic43C2211yescharacteristic
65C2×#125×C43C2211yescharacteristic
66C43×#389C2212yes—
67C43×#387C2214yes—
68C43×#382C2211yescharacteristic
69C4×C4⋊C4×C43C2214yes—
70C4×C4⋊C4×C43C2212yes—
71C43×C43C2211yescharacteristic
72C22×D172C2312yes—
73C22×D172C2314yes—
74C22×D172C2314yes—
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2314yes—
77C22×C4×D43C2311yescharacteristic
78C22×C4×D43C2314yes—
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2314yes—
81#13063322C2×C418yescomplemented
82#13063310C2×C4132yescomplemented
83#13063300C2×C4132yescomplemented
84#13063300C2×C4116yescomplemented
85C4×D172—28no—
86C4×D172—48no—
87C4×D172—48no—
88#13063287—28no—
89#13063287C2×C4116yescomplemented
90#13063282—24no—
91#13063282C2×C418yescomplemented
92C2×C4⋊Dic43C2312yes—
93C2×C4⋊Dic43C2314yes—
94C2×C4⋊Dic43C2314yes—
95C2×Dic43⋊C4C2312yes—
96C2×Dic43⋊C4C2312yes—
97C2×(C2×D43)⋊C4C2314yes—
98C2×(C2×D43)⋊C4C2314yes—
99C2×(C2×D43)⋊C4C2312yes—
100C2×(C2×D43)⋊C4C2314yes—
101C2×(C2×D43)⋊C4C2314yes—
102C2×(C2×D43)⋊C4C2314yes—
103C2×(C2×D43)⋊C4C2314yes—
104C2×(C2×D43)⋊C4C2314yes—
105C2×(C2×D43)⋊C4C2314yes—
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2312yes—
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2312yes—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2314yes—
113C2×C4×Dic43C2314yes—
114C2×C4×Dic43C2312yes—
115C2×C4×Dic43C2311yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117C42×D43—24no—
118C42×D43—48no—
119C43⋊#95C2314yes—
120C43⋊#95C2312yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2312yes—
125C43⋊#95C2312yes—
126C43⋊#95C2312yes—
127#125×C43C2×C418yescomplemented
128C2×C4⋊C4×C43C2312yes—
129C2×C4⋊C4×C43C2314yes—
130C2×C4⋊C4×C43C2314yes—
131C2×C4⋊C4×C43C2312yes—
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2314yes—
134C2×C42×C43C2312yes—
135C2×C42×C43C2312yes—
136C2×C42×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138#95×C43C2314yes—
139#95×C43C2314yes—
140#95×C43C2314yes—
141C23×D43C2411yescharacteristic
142C23×D43C2414yes—
143C22×C4×C43C2414yes—
144C22×C4×C43C2412yes—
145C22×C4×C43C2412yes—
146C22×C4×C43C2414yes—
147C22×C4×C43C2411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43C2411yescharacteristic
151C22×Dic43C2411yescharacteristic
152C22×Dic43C2414yes—
153C22×Dic43C2412yes—
154C22×Dic43C2411yescharacteristic
155C22×Dic43C2412yes—
156C2×D172—24no—
157C2×D172—24no—
158C2×D172—44no—
159C2×D172—44no—
160C2×D172—44no—
161C2×D172—44no—
162C2×D172C22×C418yes—
163C2×D172C22×C4116yes—
164C2×D172C22×C4116yes—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—28no—
170C2×C4×D43—28no—
171C2×C4×D43—24no—
172C2×C4×D43—28no—
173C2×C4×D43—28no—
174C2×C4×D43—44no—
175C2×C4×D43—44no—
176C2×C4×D43—44no—
177C2×C4×D43—44no—
178C2×C4×D43—42no—
179C2×C4×D43C22×C414yes—
180C2×C4×D43C22×C4116yes—
181C4⋊C4×C43—24no—
182C4⋊C4×C43—44no—
183C4⋊C4×C43C22×C418yes—
184C4⋊C4×C43C22×C4116yes—
185C42×C43—22no—
186C42×C43—28no—
187C42×C43—24no—
188C42×C43—42no—
189C42×C43C22×C414yes—
190C42×C43#4114yes—
191(C2×D43)⋊C4—28no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—28no—
194(C2×D43)⋊C4—44no—
195(C2×D43)⋊C4—44no—
196(C2×D43)⋊C4—44no—
197(C2×D43)⋊C4—44no—
198(C2×D43)⋊C4—44no—
199(C2×D43)⋊C4C22×C418yes—
200(C2×D43)⋊C4C22×C4116yes—
201(C2×D43)⋊C4C22×C4116yes—
202C4⋊Dic43—24no—
203C4⋊Dic43—44no—
204C4⋊Dic43—44no—
205Dic43⋊C4—24no—
206Dic43⋊C4C22×C418yes—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—24no—
211C4×Dic43—44no—
212C4×Dic43—44no—
213C4×Dic43—42no—
214C4×Dic43C22×C414yes—
215C4×Dic43#4114yes—
216C23×C43C2511yescharacteristic
217C22×D43—21no—
218C22×D43—24no—
219C22×D43—24no—
220C22×D43—21no—
221C22×D43—24no—
222C22×D43—22no—
223C22×D43—24no—
224C22×D43—24no—
225C22×D43—24no—
226C22×D43—22no—
227C22×D43C23×C412yes—
228C22×D43C23×C418yes—
229C2×C4×C43—24no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—24no—
234C2×C4×C43—22no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—22no—
238C2×C4×C43—24no—
239C2×C4×C43—22no—
240C2×C4×C43C23×C414yes—
241C2×C4×C43C23×C418yes—
242C2×C4×C43C23×C412yes—
243C2×C4×C43C2×#4112yes—
244C2×C4×C43C2×#4112yes—
245C2×C4×C43C2×#4112yes—
246C2×C4×C43C2×#4112yes—
247C2×C4×C43H(5,𝔽2)14yes—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—22no—
261C2×Dic43C23×C414yes—
262C2×Dic43C23×C412yes—
263C2×Dic43C2×#4114yes—
264D172—216no—
265D172—416no—
266D172—416no—
267C4×D43—28no—
268C4×D43—416no—
269C4×D43—416no—
270C4×D43—44no—
271C4×D43—44no—
272C4×D43—416no—
273C4×#540—431nomaximal, Sylow
274C22×C43C24×C411yescharacteristic
275C22×C43C22×#4111yescharacteristic
276C22×C43C22×#4111yescharacteristic
277C22×C43C2×H(5,𝔽2)12yes—
278C22×C43#58512yes—
279C2×D43—22no—
280C2×D43—28no—
281C2×D43—28no—
282C2×D43—24no—
283C2×D43—28no—
284C2×D43—44no—
285C2×D43—41no—
286C2×D43—44no—
287C2×D43—41no—
288C2×D43—42no—
289C2×D43—44no—
290C2×D43—44no—
291C4×C43—28no—
292C4×C43—24no—
293C4×C43—22no—
294C4×C43—44no—
295C4×C43—42no—
296C4×C43C4×#4114yes—
297C4×C43#54014yescomplemented
298Dic43—22no—
299Dic43—24no—
300Dic43—24no—
301Dic43—41no—
302Dic43—44no—
303Dic43—41no—
304C2×#540—431no—
305#2335—434no—
306#2333—434no—
307#2330—431no—
308#2328—431no—
309#2324—432no—
310#2319—432no—
311#2314—431no—
312C4×#127—431no—
313C4×#125D4311yescharacteristic, complemented
314C4×#123—434no—
315C4×#121—432no—
316C4×#121—434no—
317C42×D4—432no—
318C4×#117—431no—
319C2×C43C2×C4×#4111yescharacteristic
320C2×C43C4×H(5,𝔽2)12yes—
321C2×C43C2×#54011yescharacteristic
322C2×C43#345511yescharacteristic
323C2×C43#346012yes—
324D43—42no—
325D43—48no—
326#540—4316no—
327C2×#127—431no—
328C2×#125C2×D4311yescharacteristic
329C2×#123—434no—
330C2×#121—432no—
331C2×#121—434no—
332C2×C4×D4—432no—
333C2×C4×D4—432no—
334C2×C4×D4—432no—
335C2×C4×D4—434no—
336C2×C4×D4—434no—
337C2×#117—431no—
338C2×#117—431no—
339C22×C42—431no—
340C22×C42—434no—
341#390—432no—
342#390—434no—
343#390—432no—
344#390—434no—
345#389—432no—
346#389—434no—
347#389C2×D4312yes—
348#388—434no—
349#388—434no—
350#388—434no—
351#388—434no—
352#388—434no—
353#387—434no—
354#387—434no—
355#387C2×D4314yes—
356#386—434no—
357#386—434no—
358#386—434no—
359#386—434no—
360#385—434no—
361#384—431no—
362#382C2×D4311yescharacteristic
363#381—434no—
364#380—432no—
365#380—434no—
366C4×C4⋊C4—432no—
367C4×C4⋊C4—432no—
368C4×C4⋊C4—432no—
369C4×C4⋊C4—432no—
370C4×C4⋊C4C2×D4312yes—
371C4×C4⋊C4C2×D4314yes—
372C4×C22⋊C4—432no—
373C4×C22⋊C4—432no—
374C4×C22⋊C4—434no—
375C4×C22⋊C4—434no—
376C4×C22⋊C4—434no—
377C4×C22⋊C4—434no—
378#376—431no—
379#376—431no—
380C43—431no—
381C43C2×D4311yescharacteristic
382C43C4×#54011yescharacteristic, complemented, Sylow
383C22×D4—432no—
384C22×D4—434no—
385C22×D4—434no—
386C23×C4—431no—
387C23×C4—434no—
388C23×C4—431no—
389C23×C4—434no—
390C23×C4—434no—
391C23×C4—431no—
392#127—438no—
393#125C4×D4318yescomplemented
394#123—4332no—
395#121—4332no—
396#121—4316no—
397C4×D4—4316no—
398C4×D4—868no—
399C4×D4—868no—
400C4×D4—1728no—
401C4×D4—1728no—
402#117—438no—
403#117—864no—
404C2×C4⋊C4—432no—
405C2×C4⋊C4—432no—
406C2×C4⋊C4—432no—
407C2×C4⋊C4—434no—
408C2×C4⋊C4—434no—
409C2×C4⋊C4C22×D4312yes—
410C2×C4⋊C4C22×D4314yes—
411C2×C4⋊C4C22×D4312yes—
412C2×C4⋊C4C22×D4314yes—
413C2×C22⋊C4—432no—
414C2×C22⋊C4—434no—
415C2×C22⋊C4—434no—
416C2×C22⋊C4—432no—
417C2×C22⋊C4—434no—
418C2×C22⋊C4—434no—
419C2×C22⋊C4—434no—
420C2×C22⋊C4—434no—
421C2×C22⋊C4—434no—
422C2×C22⋊C4—434no—
423C2×C22⋊C4—434no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—432no—
429C2×C42—431no—
430C2×C42—432no—
431C2×C42—434no—
432C2×C42—434no—
433C2×C42—864no—
434C2×C42—1728no—
435C2×C42C22×D4311yescharacteristic
436C2×C42C22×D4312yes—
437C2×C42C22×D4314yes—
438C2×C42C22×D4312yes—
439C2×C42C22×D4311yescharacteristic
440C2×C42C22×D4311yescharacteristic
441#95—432no—
442#95—432no—
443#95—432no—
444#95—432no—
445#95—434no—
446#95—434no—
447#95—434no—
448#95—434no—
449#95C22×D4314yes—
450#95C22×D4314yes—
451#95C22×D4314yes—
452C24—431no—
453C24—434no—
454C2×D4—438no—
455C2×D4—4316no—
456C2×D4—4316no—
457C2×D4—864no—
458C2×D4—864no—
459C2×D4—1724no—
460C2×D4—1724no—
461C2×D4—1724no—
462C2×D4—1724no—
463C22×C4—432no—
464C22×C4—432no—
465C22×C4—431no—
466C22×C4—434no—
467C22×C4—4316no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—434no—
471C22×C4—868no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—868no—
477C22×C4—868no—
478C22×C4—864no—
479C22×C4—868no—
480C22×C4—1724no—
481C22×C4—1724no—
482C22×C4—1722no—
483C22×C4—1724no—
484C22×C4—1724no—
485C22×C4C23×D4314yes—
486C22×C4C23×D4312yes—
487C22×C4C23×D4314yes—
488C22×C4C23×D4312yes—
489C22×C4C23×D4311yescharacteristic
490C22×C4C23×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492C4⋊C4—24no—
493C4⋊C4—44no—
494C4⋊C4—438no—
495C4⋊C4—864no—
496C4⋊C4—864no—
497C4⋊C4—1724no—
498C4⋊C4—1724no—
499C4⋊C4C2×C4×D4318yes—
500C4⋊C4C2×C4×D43116yes—
501C22⋊C4—438no—
502C22⋊C4—4316no—
503C22⋊C4—4316no—
504C22⋊C4—864no—
505C22⋊C4—868no—
506C22⋊C4—868no—
507C22⋊C4—1724no—
508C22⋊C4—1724no—
509C22⋊C4—1724no—
510C22⋊C4—1724no—
511C22⋊C4—1724no—
512C42—22no—
513C42—28no—
514C42—24no—
515C42—42no—
516C42—434no—
517C42—434no—
518C42—862no—
519C42—862no—
520C42—862no—
521C42—864no—
522C42—1724no—
523C42—1724no—
524C42—1722no—
525C42C2×C4×D4314yes—
526C42#1062190214yes—
527C23—432no—
528C23—438no—
529C23—861no—
530C23—864no—
531C23—864no—
532C23—861no—
533C23—864no—
534C23—862no—
535C23—864no—
536C23—864no—
537C23—862no—
538C23—864no—
539C23C24×D4311yescharacteristic
540D4—8616no—
541D4—17216no—
542D4—17216no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—434no—
555C2×C4—432no—
556C2×C4—434no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—868no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—864no—
567C2×C4—864no—
568C2×C4—862no—
569C2×C4—864no—
570C2×C4—862no—
571C2×C4—17216no—
572C2×C4—1724no—
573C2×C4—17216no—
574C2×C4—1724no—
575C2×C4—17216no—
576C2×C4C22×C4×D4314yes—
577C2×C4C22×C4×D4318yes—
578C2×C4C22×C4×D4312yes—
579C2×C4#41×D4312yes—
580C2×C4C2×#1062190212yes—
581C2×C4C2×#1062190212yes—
582C2×C4C2×#1062190212yes—
583C2×C4#1306337114yes—
584C22—862no—
585C22—868no—
586C22—868no—
587C22—864no—
588C22—868no—
589C22—1724no—
590C22—1721no—
591C22—1721no—
592C22—1724no—
593C22—1724no—
594C22—1722no—
595C22—1724no—
596C22C23×C4×D4311yescharacteristic
597C22C2×#41×D4311yescharacteristic
598C22C22×#1062190211yescharacteristic
599C22C2×#1306337112yes—
600C22#1458373512yes—
601C4—28no—
602C4—24no—
603C4—22no—
604C4—44no—
605C4—42no—
606C4—862no—
607C4—864no—
608C4—864no—
609C4—1721no—
610C4—1724no—
611C4—1721no—
612C4C4×#1062190214yes—
613C4#1458350514yesdirect product factor
614C2—1722no—
615C2—1728no—
616C2C2×C4×#1062190211yescharacteristic
617C2C4×#1306337112yes—
618C2C2×#1458350511yescharacteristic
619C2#1914798711yescharacteristic
620C2#1914801612yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC4×#125×C43C2
socle, cosocleC23×C43C25
prime radicalC2×#14583505C2
hypercenterC4×#125D43
hypocenterC43C4×#540
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. #19137384C2semidirect
3. #19137359C2semidirect
4. #19137337C2semidirect
5. #19137318C2semidirect
6. #19137286C2semidirect
7. #19137234C2semidirect
8. #19137205C2semidirect
9. C4×#13063322C2semidirect
10. C4×#13063310C2semidirect
11. C4×#13063300C2semidirect
12. C4×#13063300C2semidirect
13. C4×#13063287C2semidirect
14. C4×#13063282C2semidirect
15. C4×#125×C43C2semidirect
16. #14583505C4direct (N × H)
81. #13063322C2×C4semidirect
82. #13063310C2×C4semidirect
83. #13063300C2×C4semidirect
84. #13063300C2×C4semidirect
89. #13063287C2×C4semidirect
91. #13063282C2×C4semidirect
127. #125×C43C2×C4semidirect
297. C4×C43#540semidirect
313. C4×#125D43semidirect
382. C43C4×#540semidirect
393. #125C4×D43semidirect
613. C4#14583505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835052
#191373842
#191373592
#191373372
#191373182
#191372862
#191372342
#191372052
C4×#130633222
C4×#130633102
C4×#130633002
C4×#130632872
C4×#130632822
C4×#125×C432
C4×#54043