Finite Group Databasebeta

← C4×#14583714 #25960840

Subgroups — C4×#14583714 #25960840

Order 11008.

2658 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×#14583714C211yesmaximal, characteristic
2C4×#13063372C211yesmaximal, characteristic, complemented
3#19143468C213yesmaximal, complemented
4#19143461C213yesmaximal, complemented
5#19143438C213yesmaximal, complemented
6#19143434C213yesmaximal, complemented
7C4×#13063356C213yesmaximal, complemented
8C4×#13063355C213yesmaximal, complemented
9C4×#13063345C213yesmaximal, complemented
10C2×C4×#10621885C213yesmaximal, complemented
11#19143193C211yesmaximal, characteristic, complemented
12#19143128C211yesmaximal, characteristic, complemented
13#19143125C211yesmaximal, characteristic, complemented
14C4×#13063332C211yesmaximal, characteristic, complemented
15C4×2−1+4×C43C211yesmaximal, characteristic, complemented
16C2×#13063372C2211yescharacteristic
17#14583714C4116yesdirect product factor
18C2×#13063356C2213yes—
19C2×#13063355C2213yes—
20C2×#13063345C2213yes—
21C22×#10621885C2213yes—
22C2×#13063332C2211yescharacteristic
23C2×#13063332C2211yescharacteristic
24#14583382C2211yescharacteristic
25#14583379C2213yes—
26#14583378—23no—
27#14583376C2213yes—
28#14583375—21no—
29C4×#10621898C2213yes—
30C4×#10621900—23no—
31C2×C4×Dic86C2213yes—
32C4×Q8×D43—21no—
33#14583004C2216yes—
34#14583004C2216yes—
35#14582999C2216yes—
36#14582997C2216yes—
37C4×#10621885C2216yes—
38C4×#10621885C2213yes—
39C4×#10621885C2216yes—
40C4×#10621885C2213yes—
41C4×#10621885C2216yes—
42C4×#10621884C2213yes—
43C4×#10621884C2213yes—
44C4×#10621883C2213yes—
45C4×#10621883C2213yes—
46C4×#10621882C2213yes—
47C4×#10621882C2211yescharacteristic
48#14582942C2213yes—
49#14582939C2213yes—
50#14582935C2213yes—
51C2×#13063258C2213yes—
52#14582908C2213yes—
53#14582907C2213yes—
54#14582900C2213yes—
55#14582898C2213yes—
56#14582895C2213yes—
57#14582893C2213yes—
58C2×#13063249C2213yes—
59C2×#13063248C2213yes—
60#14582855C2213yes—
61#14582855C2213yes—
62C4×#10621877C2213yes—
63C2×C4×C43⋊C8C2213yes—
64C2×2−1+4×C43C2211yescharacteristic
65C43×#520—23no—
66C43×#520C2213yes—
67C43×#520C2211yescharacteristic
68C43×#519—21no—
69C43×#519C2213yes—
70C4×#41×C43—23no—
71C4×#41×C43C2213yes—
72C4×#41×C43C2211yescharacteristic
73C2×C4×Q8×C43—21no—
74C2×C4×Q8×C43C2213yes—
75#13063372—24no—
76#13063372C2×C418yescomplemented
77C2×#10621898C2313yes—
78C2×#10621900—23no—
79C22×Dic86C2313yes—
80C2×Q8×D43—21no—
81#13063356C2×C4124yescomplemented
82#13063355C2×C4124yescomplemented
83#13063345C2×C4124yescomplemented
84C2×#10621885C2×C4124yescomplemented
85C2×#10621885C2313yes—
86C2×#10621885C2316yes—
87C2×#10621883C2313yes—
88C2×#10621884C2313yes—
89C2×#10621882C2311yescharacteristic
90#13063332—24no—
91#13063332C2×C418yescomplemented
92C2×#10621877C2313yes—
93C2×#10621877C2313yes—
94C22×C43⋊C8C2313yes—
95C22×C43⋊C8C2313yes—
96Q8×Dic43—21no—
97C4×Dic86—23no—
98C4×Dic86—23no—
99C4×Dic86C2313yes—
100C4×Dic86C2316yes—
101C4×Dic86C2313yes—
102#13063290—23no—
103#13063290—23no—
104C4×D172C2311yescharacteristic
105C4×D172C2313yes—
106D4×Dic43—23no—
107C4×C22⋊D43—23no—
108C4×C22⋊D43—23no—
109(C22⋊D43)⋊C4—26no—
110#13063284C2313yes—
111#13063283—23no—
112#13063282—23no—
113#13063281—26no—
114C2×C4⋊Dic43C2313yes—
115C2×Dic43⋊C4—23no—
116C4⋊C4×D43—23no—
117C2×C4×Dic43—23no—
118C42×D43—23no—
119#13063258C2313yes—
120#13063258C2316yes—
121#13063258C2311yescharacteristic
122#13063256C2313yes—
123#13063256C2313yes—
124#13063249C2313yes—
125#13063249C2316yes—
126#13063249C2313yes—
127#13063248C2313yes—
128#13063248C2316yes—
129#13063248C2313yes—
130#13063246C2311yescharacteristic
131#13063246C2313yes—
132#13063245C2311yescharacteristic
133#13063245C2313yes—
134#13063236C2316yes—
135C4×C43⋊C8C2311yescharacteristic
136C4×C43⋊C8C2313yes—
137C4×C43⋊C8C2313yes—
138C4×C43⋊C8C2313yes—
1392−1+4×C43—24no—
1402−1+4×C43C2×C418yescomplemented
141C2×#41×C43—23no—
142C2×#41×C43C2313yes—
143C2×#41×C43C2311yescharacteristic
144C22×Q8×C43—21no—
145C22×Q8×C43C2313yes—
146C4×Q8×C43—21no—
147C4×Q8×C43—23no—
148C4×Q8×C43—23no—
149C4×Q8×C43—23no—
150C4×Q8×C43—23no—
151C4×Q8×C43D411yescharacteristic
152C4×Q8×C43D411yescharacteristic
153C4×Q8×C43C2313yes—
154C4×Q8×C43C2316yes—
155C4×Q8×C43C2313yes—
156C4×D4×C43—23no—
157C4×D4×C43—23no—
158C4×D4×C43—23no—
159C4×D4×C43—26no—
160C4×D4×C43D413yes—
161C4×D4×C43D413yes—
162C4×D4×C43C2311yescharacteristic
163C4×D4×C43C2313yes—
164#117×C43—23no—
165#117×C43—26no—
166#117×C43—23no—
167#117×C43C2313yes—
168#117×C43C2313yes—
169C2×C4⋊C4×C43—23no—
170C2×C4⋊C4×C43—23no—
171C2×C4⋊C4×C43C2313yes—
172C2×C42×C43—23no—
173C2×C42×C43—23no—
174C2×C42×C43C2313yes—
175#41×C43—224no—
176#41×C43—26no—
177#41×C43C22×C4112yes—
178#41×C43C22×C414yes—
179#41×C43#4114yes—
180C2×Q8×C43—28no—
181C2×Q8×C43—23no—
182C2×Q8×C43—26no—
183C2×Q8×C43C22×C4112yes—
184C2×Q8×C43C2×D411yescharacteristic
185C2×Q8×C43C2413yes—
186C2×D4×C43—23no—
187C2×D4×C43C2×D413yes—
188C2×D4×C43C2411yescharacteristic
189C22×C4×C43—23no—
190C22×C4×C43—21no—
191C22×C4×C43—23no—
192C22×C4×C43—23no—
193C22×C4×C43—23no—
194C22×C4×C43C2×D413yes—
195C22×C4×C43C2×D413yes—
196C22×C4×C43C2413yes—
197C2×C22⋊D43—23no—
198C22×Dic43—23no—
199C22×Dic43—23no—
200Q8×D43—28no—
201#10621900—224no—
202#10621898—26no—
203#10621898C22×C4112yes—
204C2×D172C2411yescharacteristic
205C2×C4×D43—23no—
206C2×C4×D43—21no—
207C2×C4×D43—23no—
208C2×Dic86—23no—
209C2×Dic86—26no—
210C2×Dic86C22×C4112yes—
211C2×Dic86C2413yes—
212C4⋊C4×C43—26no—
213C4⋊C4×C43—23no—
214C4⋊C4×C43—23no—
215C4⋊C4×C43—23no—
216C4⋊C4×C43C2×D413yes—
217C4⋊C4×C43C2×D413yes—
218C4⋊C4×C43C2413yes—
219C4⋊C4×C43C2411yescharacteristic
220C22⋊C4×C43—21no—
221C22⋊C4×C43—23no—
222C22⋊C4×C43—23no—
223C22⋊C4×C43C2×D416yes—
224C42×C43—23no—
225C42×C43—23no—
226C42×C43—26no—
227C42×C43—23no—
228C42×C43C2×D413yes—
229C42×C43C2×D413yes—
230C42×C43C2411yescharacteristic
231C42×C43C2413yes—
232C22⋊Dic43—23no—
233#10621885C22×C4112yes—
234#10621885C22×C4124yes—
235#10621884C22×C4112yes—
236#10621883C22×C4112yes—
237#10621882C22×C414yes—
238(C2×D43)⋊C4—21no—
239(C2×D43)⋊C4—23no—
240C4⋊Dic43—23no—
241C4⋊Dic43C2411yescharacteristic
242C4⋊Dic43C2413yes—
243Dic43⋊C4—26no—
244Dic43⋊C4—23no—
245Dic43⋊C4—23no—
246C4×Dic43—23no—
247C4×Dic43—23no—
248C4×Dic43—23no—
249C4×Dic43—26no—
250#10621877—26no—
251#10621877C22×C4112yes—
252C2×C43⋊C8—26no—
253C2×C43⋊C8C22×C4112yes—
254C2×C43⋊C8C2411yescharacteristic
255C2×C43⋊C8C2413yes—
256C2×C43⋊C8C2411yescharacteristic
257C2×C43⋊C8C2413yes—
258C23×C43—21no—
259C23×C43C22×D413yes—
260C22×D43—21no—
261Q8×C43—212no—
262Q8×C43—23no—
263Q8×C43C4×D414yes—
264Q8×C43C23×C416yes—
265D4×C43—212no—
266D4×C43—21no—
267D4×C43C4×D4112yes—
268D4×C43C23×C412yes—
269C2×C4×C43—212no—
270C2×C4×C43—23no—
271C2×C4×C43—212no—
272C2×C4×C43—26no—
273C2×C4×C43—21no—
274C2×C4×C43—23no—
275C2×C4×C43—43no—
276C2×C4×C43—42no—
277C2×C4×C43—83no—
278C2×C4×C43—83no—
279C2×C4×C43C23×C416yes—
280C2×C4×C43C22×D413yes—
281C2×C4×C43C22×D413yes—
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C22×D413yes—
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4116yes—
286C2×C4×C43C2511yescharacteristic
287C22⋊D43—212no—
288C2×Dic43—212no—
289C2×Dic43—23no—
290C2×Dic43—21no—
291C2×Dic43—23no—
292C2×Dic43—83no—
293D172—21no—
294D172C23×C412yes—
295C4×D43—212no—
296C4×D43—42no—
297C4×D43—83no—
298Dic86—212no—
299Dic86—23no—
300Dic86C23×C416yes—
301C43⋊C8—21no—
302C43⋊C8—23no—
303C43⋊C8C23×C412yes—
304C43⋊C8C23×C416yes—
305C4×#578—431nomaximal, Sylow
306C22×C43—23no—
307C22×C43—23no—
308C22×C43—22no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43C2×C4×D416yes—
312C22×C43C23×D411yescharacteristic
313C2×D43—22no—
314C2×D43—41no—
315C2×D43—41no—
316C4×C43—23no—
317C4×C43—21no—
318C4×C43—26no—
319C4×C43—23no—
320C4×C43—43no—
321C4×C43—41no—
322C4×C43C2×C4×D416yes—
323C4×C43#57812yescomplemented
324C4×C43C24×C411yescharacteristic
325C4×C43C22×#4111yescharacteristic
326Dic43—26no—
327Dic43—43no—
328Dic43—41no—
329C2×#578—431no—
330C4×2−1+4—431no—
331C4×2−1+4D4311yescharacteristic, complemented
332#2951—433no—
333#2950—433no—
334#2947—433no—
335#2947—433no—
336C4×#137—433no—
337C4×#137—433no—
338C4×#135—433no—
339C2×C4×Q16—433no—
340#2913—431no—
341#2898—431no—
342#2898—431no—
343C4×#131—431no—
344C2×C43—26no—
345C2×C43—42no—
346C2×C43C22×C4×D411yescharacteristic
347C2×C43C2×#57811yescharacteristic
348C2×C43#358411yescharacteristic
349D43—42no—
350C2×2−1+4—431no—
351C2×2−1+4C2×D4311yescharacteristic
352#578—4316no—
353C2×#137—433no—
354C2×#137—433no—
355C2×#135—433no—
356C22×Q16—433no—
357C2×#131—431no—
358C2×#131—431no—
359#520—23no—
360#520—431no—
361#520—433no—
362#520—863no—
363#520C2×D4313yes—
364#520C2×D4311yescharacteristic
365#519—21no—
366#519—433no—
367#519—861no—
368#519C2×D4313yes—
369C4×#41—23no—
370C4×#41—433no—
371C4×#41—863no—
372C4×#41C2×D4313yes—
373C4×#41C2×D4311yescharacteristic
374C2×C4×Q8—21no—
375C2×C4×Q8—433no—
376C2×C4×Q8—861no—
377C2×C4×Q8C2×D4313yes—
378#441—436no—
379#441—436no—
380#440—436no—
381#440—436no—
382C4×Q16—433no—
383C4×Q16—436no—
384C4×Q16—436no—
385C4×Q16—436no—
386C4×Q16—433no—
387C4×SD16—433no—
388C4×SD16—433no—
389C4×SD16—433no—
390C4×SD16—433no—
391C4×D8—431no—
392C4×D8—433no—
393#428—433no—
394#428—433no—
395#427—433no—
396C2×#107—433no—
397#419—433no—
398#419—433no—
399#417—433no—
400#417—433no—
401#416—433no—
402#416—433no—
403C2×#103—433no—
404C2×#103—433no—
405#405—433no—
406#405—433no—
407C4×M16—433no—
408C2×C4×C8—433no—
409C43C4×#57811yescharacteristic, complemented, Sylow
4102−1+4—24no—
4112−1+4—438no—
4122−1+4—864no—
4132−1+4C4×D4318yescomplemented
414C2×#41—23no—
415C2×#41—433no—
416C2×#41—863no—
417C2×#41C22×D4313yes—
418C2×#41C22×D4311yescharacteristic
419C22×Q8—21no—
420C22×Q8—433no—
421C22×Q8—861no—
422C22×Q8C22×D4313yes—
423#137—4324no—
424#137—4324no—
425#135—4324no—
426C2×Q16—4324no—
427C2×Q16—433no—
428C2×Q16—436no—
429C2×SD16—433no—
430C2×SD16—433no—
431C2×D8—431no—
432#131—438no—
433#131—864no—
434C2×M16—433no—
435C2×M16—433no—
436C22×C8—433no—
437C22×C8—433no—
438C4×Q8—21no—
439C4×Q8—23no—
440C4×Q8—23no—
441C4×Q8—23no—
442C4×Q8—23no—
443C4×Q8—433no—
444C4×Q8—436no—
445C4×Q8—433no—
446C4×Q8—861no—
447C4×Q8—863no—
448C4×Q8—863no—
449C4×Q8—863no—
450C4×Q8—863no—
451C4×Q8C22⋊D4311yescharacteristic
452C4×Q8C22⋊D4311yescharacteristic
453C4×Q8C22×D4313yes—
454C4×Q8C22×D4316yes—
455C4×Q8C22×D4313yes—
456C4×D4—23no—
457C4×D4—23no—
458C4×D4—23no—
459C4×D4—26no—
460C4×D4—431no—
461C4×D4—433no—
462C4×D4—863no—
463C4×D4—863no—
464C4×D4—863no—
465C4×D4—866no—
466C4×D4C22⋊D4313yes—
467C4×D4C22⋊D4313yes—
468C4×D4C22×D4311yescharacteristic
469C4×D4C22×D4313yes—
470#117—23no—
471#117—26no—
472#117—23no—
473#117—433no—
474#117—863no—
475#117—866no—
476#117—863no—
477#117C22×D4313yes—
478#117C22×D4313yes—
479C2×C4⋊C4—23no—
480C2×C4⋊C4—23no—
481C2×C4⋊C4—433no—
482C2×C4⋊C4—863no—
483C2×C4⋊C4—863no—
484C2×C4⋊C4C22×D4313yes—
485C2×C42—23no—
486C2×C42—23no—
487C2×C42—863no—
488C2×C42—863no—
489C2×C42C22×D4313yes—
490#107—433no—
491#107—436no—
492#107—431no—
493#106—433no—
494#106—433no—
495#103—433no—
496#103—436no—
497#103—433no—
498#103—433no—
499#103—436no—
500#103—433no—
501#102—431no—
502#102—433no—
503#102—431no—
504#102—433no—
505#97—436no—
506C4×C8—431no—
507C4×C8—433no—
508C4×C8—433no—
509C4×C8—433no—
510#41—224no—
511#41—26no—
512#41—4312no—
513#41—8624no—
514#41—866no—
515#41C2×C4×D43112yes—
516#41C2×C4×D4314yes—
517#41#1062189814yes—
518C2×Q8—28no—
519C2×Q8—23no—
520C2×Q8—26no—
521C2×Q8—4312no—
522C2×Q8—433no—
523C2×Q8—868no—
524C2×Q8—863no—
525C2×Q8—866no—
526C2×Q8C2×C4×D43112yes—
527C2×Q8C2×C22⋊D4311yescharacteristic
528C2×Q8C23×D4313yes—
529C2×D4—23no—
530C2×D4—431no—
531C2×D4—863no—
532C2×D4C2×C22⋊D4313yes—
533C2×D4C23×D4311yescharacteristic
534C22×C4—23no—
535C22×C4—23no—
536C22×C4—23no—
537C22×C4—21no—
538C22×C4—23no—
539C22×C4—863no—
540C22×C4—863no—
541C22×C4—863no—
542C22×C4—863no—
543C22×C4—861no—
544C22×C4C2×C22⋊D4313yes—
545C22×C4C2×C22⋊D4313yes—
546C22×C4C23×D4313yes—
547Q16—4312no—
548Q16—4324no—
549SD16—4312no—
550SD16—4312no—
551D8—434no—
552M16—4312no—
553M16—866no—
554C2×C8—4312no—
555C2×C8—431no—
556C2×C8—433no—
557C2×C8—431no—
558C2×C8—433no—
559C2×C8—866no—
560C4⋊C4—26no—
561C4⋊C4—23no—
562C4⋊C4—23no—
563C4⋊C4—23no—
564C4⋊C4—431no—
565C4⋊C4—433no—
566C4⋊C4—863no—
567C4⋊C4—866no—
568C4⋊C4—863no—
569C4⋊C4—863no—
570C4⋊C4C2×C22⋊D4313yes—
571C4⋊C4C2×C22⋊D4313yes—
572C4⋊C4C23×D4311yescharacteristic
573C4⋊C4C23×D4313yes—
574C22⋊C4—23no—
575C22⋊C4—21no—
576C22⋊C4—23no—
577C22⋊C4—863no—
578C22⋊C4—861no—
579C22⋊C4—863no—
580C22⋊C4C2×C22⋊D4316yes—
581C42—23no—
582C42—26no—
583C42—23no—
584C42—23no—
585C42—863no—
586C42—863no—
587C42—866no—
588C42—863no—
589C42C2×C22⋊D4313yes—
590C42C2×C22⋊D4313yes—
591C42C23×D4313yes—
592C42C23×D4311yescharacteristic
593C23—21no—
594C23—861no—
595C23C22×C22⋊D4313yes—
596Q8—212no—
597Q8—23no—
598Q8—436no—
599Q8—8612no—
600Q8—863no—
601Q8C4×C22⋊D4314yes—
602Q8C22×C4×D4316yes—
603D4—212no—
604D4—21no—
605D4—432no—
606D4—8612no—
607D4—861no—
608D4C4×C22⋊D43112yes—
609D4C22×C4×D4312yes—
610C2×C4—212no—
611C2×C4—23no—
612C2×C4—212no—
613C2×C4—26no—
614C2×C4—21no—
615C2×C4—23no—
616C2×C4—43no—
617C2×C4—42no—
618C2×C4—83no—
619C2×C4—83no—
620C2×C4—8612no—
621C2×C4—863no—
622C2×C4—8612no—
623C2×C4—861no—
624C2×C4—863no—
625C2×C4—3443no—
626C2×C4—3443no—
627C2×C4—1722no—
628C2×C4C22×C4×D4316yes—
629C2×C4C22×C22⋊D4313yes—
630C2×C4C22×C22⋊D4313yes—
631C2×C4C22×C22⋊D4311yescharacteristic
632C2×C4C22×C22⋊D4313yes—
633C2×C4C22×C22⋊D4311yescharacteristic
634C2×C4C2×#1062189816yes—
635C2×C4C24×D4311yescharacteristic
636C8—432no—
637C8—436no—
638C8—861no—
639C8—863no—
640C22—23no—
641C22—23no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—862no—
646C22—1721no—
647C22—1721no—
648C22C2×C4×C22⋊D4316yes—
649C22C23×C22⋊D4311yescharacteristic
650C4—23no—
651C4—21no—
652C4—23no—
653C4—26no—
654C4—41no—
655C4—43no—
656C4—866no—
657C4—1721no—
658C4—1723no—
659C4C2×C4×C22⋊D4316yes—
660C4#1458371412yesdirect product factor
661C4C23×C4×D4311yescharacteristic
662C4C22×#1062189811yescharacteristic
663C2—26no—
664C2—42no—
665C2—1722no—
666C2C22×C4×C22⋊D4311yescharacteristic
667C2C2×#1458371411yescharacteristic
668C2#1914936611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC4×2−1+4×C43C2
socleC22×C43C23×D4
prime radicalC2×#14583714C2
cosocleC2×C4×C43C25
hypercenterC4×2−1+4D43
hypocenterC43C4×#578
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#13063372C2semidirect
3. #19143468C2semidirect
4. #19143461C2semidirect
5. #19143438C2semidirect
6. #19143434C2semidirect
7. C4×#13063356C2semidirect
8. C4×#13063355C2semidirect
9. C4×#13063345C2semidirect
10. C2×C4×#10621885C2semidirect
11. #19143193C2semidirect
12. #19143128C2semidirect
13. #19143125C2semidirect
14. C4×#13063332C2semidirect
15. C4×2−1+4×C43C2semidirect
17. #14583714C4direct (N × H)
76. #13063372C2×C4semidirect
81. #13063356C2×C4semidirect
82. #13063355C2×C4semidirect
83. #13063345C2×C4semidirect
84. C2×#10621885C2×C4semidirect
91. #13063332C2×C4semidirect
140. 2−1+4×C43C2×C4semidirect
323. C4×C43#578semidirect
331. C4×2−1+4D43semidirect
409. C43C4×#578semidirect
413. 2−1+4C4×D43semidirect
660. C4#14583714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837142
C4×#130633722
#191434682
#191434612
#191434382
#191434342
C4×#130633562
C4×#130633552
C4×#130633452
C2×C4×#106218852
#191431932
#191431282
#191431252
C4×#130633322
C4×2−1+4×C432
C4×#57843