Finite Group Databasebeta

← C4×#14583292 #25105148

Subgroups — C4×#14583292 #25105148

Order 11008.

1094 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583292C211yesmaximal, characteristic
2C2×C4×#10621885C211yesmaximal, characteristic, complemented
3C2×C4×#10621873C211yesmaximal, characteristic
4C2×C4×#10621884C211yesmaximal, characteristic
5C4×#13063323C211yesmaximal, characteristic, complemented
6C4×#13063314C211yesmaximal, characteristic
7#19135474C211yesmaximal, characteristic
8#19135473C211yesmaximal, characteristic
9#19135467C211yesmaximal, characteristic, complemented
10#19135463C211yesmaximal, characteristic, complemented
11#19135413C211yesmaximal, characteristic, complemented
12#19135408C211yesmaximal, characteristic
13#19134762C211yesmaximal, characteristic, complemented
14C4×#13063235C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063314C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583292C418yesdirect product factor
24C4×#10621885—24no—
25C4×#10621873—24no—
26C4×#10621884—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39C2×#13063235C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582806C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582794—22no—
46#14582789—22no—
47#14582768C2211yescharacteristic
48#14582764C2211yescharacteristic
49C4×Dic43⋊C4—22no—
50C4×(C2×D43)⋊C4—22no—
51C42×Dic43C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C4×Q16×C43—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×C4×C8×C43C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885C2×C414yescomplemented
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873C2×C414yes—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063323—22no—
75#13063323C2×C414yescomplemented
76#13063314—22no—
77#13063314C2×C414yes—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C4×D172—22no—
81C4×D172—22no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—22no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D412yes—
92C2×C4×Dic43D412yes—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063258—22no—
96#13063257—22no—
97#13063256—22no—
98#13063250—22no—
99#13063249—22no—
100#13063249—22no—
101#13063248—22no—
102#13063247—22no—
103#13063245—22no—
104#13063235—22no—
105#13063235—22no—
106#13063235—22no—
107#13063235C2×C414yescomplemented
108C4×C43⋊C8D414yes—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C22×Q8×C43C2311yescharacteristic
114C22×Q8×C43C2311yescharacteristic
115C2×Q16×C43—22no—
116C2×Q16×C43—22no—
117C2×Q16×C43C2×C414yescomplemented
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4×Q8×C43—22no—
121C4×Q8×C43—22no—
122C4×Q8×C43—22no—
123C4×Q8×C43—22no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132#103×C43—22no—
133#103×C43—22no—
134C4×C8×C43D414yes—
135C23×D43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C22×C412yes—
147C2×Q8×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43C2×D412yes—
159C22×Dic43C2×D412yes—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172C22×C412yes—
166C2×C4×D43—42no—
167C2×C4×D43—44no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86C22×C412yes—
174Q16×C43—28no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C22×C412yes—
178C2×C8×C43C2×D412yes—
179C2×C8×C43C2×D412yes—
180C2×C8×C43#4112yes—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—42no—
187C42×C43—42no—
188C42×C43—42no—
189C42×C43C2×D412yes—
190C42×C43C2×D412yes—
191#10621885—28no—
192#10621884—28no—
193(C2×D43)⋊C4—28no—
194(C2×D43)⋊C4—44no—
195(C2×D43)⋊C4—42no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200Dic43⋊C4—28no—
201Dic43⋊C4—44no—
202Dic43⋊C4—42no—
203C4×Dic43—24no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C4×Dic43C22×C412yes—
209C4×Dic43#4112yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C22×C412yes—
213C2×C43⋊C8C2×D412yes—
214C2×C43⋊C8C2×D412yes—
215C2×C43⋊C8#4112yes—
216#10621873—28no—
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—42no—
222C22×D43—42no—
223Q8×C43—22no—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43#12712yes—
243C2×C4×C43#12712yes—
244C2×C4×C43#13714yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43C4×D414yes—
264D172—22no—
265D172—22no—
266D172—41no—
267D172—41no—
268C4×D43—84no—
269Dic86—22no—
270Dic86—22no—
271Dic86—41no—
272Dic86—41no—
273C8×C43—22no—
274C8×C43C4×D414yes—
275C43⋊C8—22no—
276C43⋊C8C4×D414yes—
277C4×#497—431nomaximal, Sylow
278C22×C43C2×C4×D411yescharacteristic
279C22×C43C2×#12711yescharacteristic
280C22×C43#53211yescharacteristic
281C22×C43C2×#13712yes—
282C22×C43#57512yes—
283C2×D43—42no—
284C2×D43—44no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—82no—
288C4×C43—22no—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#49714yescomplemented
294C4×C43C2×C4×D411yescharacteristic
295C4×C43C2×C4×D411yescharacteristic
296C4×C43#53211yescharacteristic
297C4×C43#53211yescharacteristic
298Dic43—24no—
299Dic43—42no—
300Dic43—42no—
301Dic43—81no—
302Dic43—81no—
303C2×#497—431no—
304C2×C4×Q16—431no—
305C2×C4×Q16D4311yescharacteristic, complemented
306C2×C4×SD16—431no—
307C2×C4×SD16—431no—
308C4×C4⋊Q8—431no—
309C4×#124—431no—
310#1973—431no—
311#1973—431no—
312#1971—431no—
313#1971—431no—
314#1960—431no—
315#1959—431no—
316#1847—431no—
317C4×#97—431no—
318C2×C43C4×#12711yescharacteristic
319C2×C43C4×#13712yes—
320C2×C43C2×#49711yescharacteristic
321C2×C43#315011yescharacteristic
322C2×C43#317212yes—
323D43—82no—
324C22×Q16—431no—
325C22×Q16C2×D4311yescharacteristic
326C22×SD16—431no—
327C22×SD16—431no—
328C2×C4⋊Q8—431no—
329C2×#124—431no—
330C2×C4×Q8—431no—
331C2×C4×Q8C2×D4311yescharacteristic
332C2×C4×Q8C2×D4311yescharacteristic
333C2×C4×D4—431no—
334#497—438no—
335C4×Q16—24no—
336C4×Q16—864no—
337C4×SD16—864no—
338C4×SD16—864no—
339C2×#107—431no—
340C2×#107C2×D4311yescharacteristic
341C2×#106—431no—
342C2×#106—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103C2×D4311yescharacteristic
348C2×#103C2×D4311yescharacteristic
349C2×#102—431no—
350C2×#102—431no—
351C2×#97—431no—
352C2×#97—431no—
353C2×#97—431no—
354C2×#97—431no—
355C2×C4×C8—431no—
356C2×C4×C8C2×D4311yescharacteristic
357#391—431no—
358#391—431no—
359#391—431no—
360#390—431no—
361#389—862no—
362#388—862no—
363#384—431no—
364#382—431no—
365C4×C4⋊C4—862no—
366C4×C22⋊C4—862no—
367C43—431no—
368C43C4×#49711yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×Q8C22×D4311yescharacteristic
371C22×Q8C22×D4311yescharacteristic
372C22×D4—431no—
373C23×C4—861no—
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—434no—
377C2×Q16—862no—
378C2×Q16—862no—
379C2×Q16C4×D4314yescomplemented
380C2×SD16—434no—
381C2×SD16—434no—
382C2×SD16—862no—
383C2×SD16—862no—
384C2×SD16—862no—
385C2×SD16—862no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C4⋊Q8—434no—
391C4⋊Q8—862no—
392#124—434no—
393#124—862no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×D4—862no—
401C4×D4—862no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—862no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—861no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—431no—
417C2×C42—432no—
418C2×C42—431no—
419C2×C42—432no—
420C2×C42—861no—
421C2×C42C22×D4311yescharacteristic
422#107—22no—
423#107—862no—
424#106—862no—
425#106—862no—
426#103—22no—
427#103—22no—
428#103—862no—
429#103—862no—
430#103—862no—
431#103—862no—
432#102—862no—
433#102—862no—
434#97—434no—
435#97—862no—
436#97—862no—
437#97—862no—
438C4×C8—434no—
439C4×C8C22⋊D4314yes—
440#95—862no—
441#95—862no—
442#95—862no—
443#95—862no—
444C24—861no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—432no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8C2×C4×D4312yes—
462C2×Q8C2×C4×D4312yes—
463C2×D4—432no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—432no—
474C22×C4—432no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—1722no—
479C22×C4—1724no—
480C22×C4D4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4C23×D4311yescharacteristic
483Q16—28no—
484Q16—868no—
485SD16—868no—
486SD16—868no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—432no—
490C2×C8—432no—
491C2×C8—432no—
492C2×C8—432no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8C2×C4×D4312yes—
496C2×C8#1062189812yes—
497C2×C8C2×C22⋊D4312yes—
498C2×C8C2×C22⋊D4312yes—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—868no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—1724no—
511C4⋊C4—1722no—
512C22⋊C4—868no—
513C22⋊C4—1724no—
514C22⋊C4—1722no—
515C42—42no—
516C42—42no—
517C42—432no—
518C42—432no—
519C42—864no—
520C42—861no—
521C42—861no—
522C42—1722no—
523C42—1722no—
524C42D4×D4312yes—
525C42C2×C22⋊D4312yes—
526C23—862no—
527C23—1722no—
528C23—1721no—
529C23—1722no—
530C23—1721no—
531C23C2×D4×D4311yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—862no—
541Q8—862no—
542Q8—1721no—
543Q8—1721no—
544D4—862no—
545D4—862no—
546D4—1721no—
547D4—1721no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—434no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—3444no—
567C2×C4—1722no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1722no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4#1306332112yes—
574C2×C4#1306332112yes—
575C2×C4#1306335714yes—
576C2×C4C22×C4×D4311yescharacteristic
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4C2×#1062189811yescharacteristic
582C8—22no—
583C8—434no—
584C8—862no—
585C8C4×C22⋊D4314yes—
586C22—3441no—
587C22—3441no—
588C22—3442no—
589C22—1722no—
590C22—1724no—
591C22C4×D4×D4311yescharacteristic
592C22C2×#1306332111yescharacteristic
593C22#1458344611yescharacteristic
594C22C2×#1306335712yes—
595C22#1458369612yes—
596C4—22no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—864no—
602C4—3441no—
603C4—3441no—
604C4—1722no—
605C4—1722no—
606C4#1458329214yesdirect product factor
607C4C4×D4×D4311yescharacteristic
608C4C2×C4×C22⋊D4311yescharacteristic
609C4#1458344511yescharacteristic
610C4#1458344611yescharacteristic
611C2—3442no—
612C2C4×#1306332111yescharacteristic
613C2C4×#1306335712yes—
614C2C2×#1458329211yescharacteristic
615C2#1914503811yescharacteristic
616C2#1914519912yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC2×C4×Q16D43
hypocenterC43C4×#497
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621885C2semidirect
5. C4×#13063323C2semidirect
9. #19135467C2semidirect
10. #19135463C2semidirect
11. #19135413C2semidirect
13. #19134762C2semidirect
14. C4×#13063235C2semidirect
15. C2×C4×Q16×C43C2semidirect
23. #14583292C4direct (N × H)
65. C2×#10621885C2×C4semidirect
75. #13063323C2×C4semidirect
107. #13063235C2×C4semidirect
117. C2×Q16×C43C2×C4semidirect
293. C4×C43#497semidirect
305. C2×C4×Q16D43semidirect
368. C43C4×#497semidirect
379. C2×Q16C4×D43semidirect
606. C4#14583292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832922
C2×C4×#106218852
C2×C4×#106218732
C2×C4×#106218842
C4×#130633232
C4×#130633142
#191354742
#191354732
#191354672
#191354632
#191354132
#191354082
#191347622
C4×#130632352
C2×C4×Q16×C432
C4×#49743