Finite Group Databasebeta

← C4×#14583172 #25103484

Subgroups — C4×#14583172 #25103484

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583172C211yesmaximal, characteristic
2C4×#13063355C211yesmaximal, characteristic
3C2×C4×#10621885C211yesmaximal, characteristic, complemented
4C4×#13063332C211yesmaximal, characteristic
5#19135509C211yesmaximal, characteristic, complemented
6#19135377C211yesmaximal, characteristic, complemented
7#19135253C211yesmaximal, characteristic, complemented
8#19135249C211yesmaximal, characteristic, complemented
9#19135112C211yesmaximal, characteristic
10#19135108C211yesmaximal, characteristic
11#19134657C211yesmaximal, characteristic
12C4×#13063260C211yesmaximal, characteristic, complemented
13C4×#13063243C211yesmaximal, characteristic, complemented
14C4×#13063244C211yesmaximal, characteristic, complemented
15C4×#137×C43C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21#14583172C418yesdirect product factor
22#14583004—21no—
23#14582999—21no—
24C4×#10621885—21no—
25C4×#10621885—21no—
26C4×#10621885—21no—
27C4×#10621885—21no—
28C4×#10621885—21no—
29C4×#10621883—21no—
30C2×#13063260C2211yescharacteristic
31C2×#13063260C2211yescharacteristic
32#14582942C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34#14582907C2211yescharacteristic
35#14582900C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063244C2211yescharacteristic
39C2×#13063244C2211yescharacteristic
40C2×#13063243C2211yescharacteristic
41C2×#13063243C2211yescharacteristic
42#14582855—21no—
43#14582855—21no—
44#14582855C2211yescharacteristic
45#14582855C2211yescharacteristic
46C4×#10621877—21no—
47C4×#10621877C2211yescharacteristic
48C4×#10621877C2211yescharacteristic
49C2×C4×C43⋊C8—21no—
50C2×C4×C43⋊C8C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582663C2211yescharacteristic
56#14582663C2211yescharacteristic
57C2×#137×C43C2211yescharacteristic
58C4×#41×C43C2211yescharacteristic
59C2×C4×Q8×C43C2211yescharacteristic
60C43×#441—21no—
61C43×#440—21no—
62C4×Q16×C43—21no—
63C4×SD16×C43—21no—
64C43×#428C2211yescharacteristic
65C43×#419C2211yescharacteristic
66C43×#417C2211yescharacteristic
67C4×M16×C43C2211yescharacteristic
68C22×Dic86C2311yescharacteristic
69#13063355—22no—
70#13063355C2×C414yes—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621885—21no—
74C2×#10621885—22no—
75C2×#10621885C2×C414yescomplemented
76C2×#10621883—21no—
77#13063332—22no—
78#13063332—22no—
79#13063332—22no—
80#13063332C2×C414yes—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C22×C43⋊C8—21no—
88C22×C43⋊C8—21no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C4×Dic86—21no—
92C4×Dic86—21no—
93C4×Dic86—21no—
94C4×Dic86—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×C4×Dic43—21no—
98#13063260—22no—
99#13063260C2×C414yescomplemented
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063256—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248—21no—
110#13063248—21no—
111#13063246—21no—
112#13063244—22no—
113#13063244C2×C414yescomplemented
114#13063243—22no—
115#13063243C2×C414yescomplemented
116#13063236—21no—
117#13063236—21no—
118#13063236—21no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8D411yescharacteristic
125C4×C43⋊C8D411yescharacteristic
126C4×C43⋊C8D411yescharacteristic
127C4×C43⋊C8D411yescharacteristic
128C2×#41×C43C2311yescharacteristic
129C22×Q8×C43C2311yescharacteristic
130#137×C43—22no—
131#137×C43C2×C414yes—
132C2×Q16×C43—21no—
133C2×SD16×C43—21no—
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C4×Q8×C43—21no—
137C4×Q8×C43—21no—
138C4×Q8×C43—21no—
139C4×Q8×C43—21no—
140C4×Q8×C43D411yescharacteristic
141C4×Q8×C43D411yescharacteristic
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43D411yescharacteristic
145C4×D4×C43D411yescharacteristic
146#117×C43—21no—
147#117×C43C2311yescharacteristic
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C42×C43—21no—
151C2×C42×C43—21no—
152C2×C42×C43C2311yescharacteristic
153#107×C43—21no—
154#106×C43—21no—
155#103×C43—21no—
156#103×C43—21no—
157#103×C43—21no—
158#102×C43—21no—
159#97×C43—21no—
160C4×C8×C43—21no—
161#41×C43—21no—
162#41×C43—21no—
163#41×C43C22×C412yes—
164#41×C43#4112yes—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C22×C412yes—
171C2×Q8×C43C2×D411yescharacteristic
172C2×D4×C43—21no—
173C2×D4×C43C2×D411yescharacteristic
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43#4111yescharacteristic
180C22×C4×C43#4111yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C22×Dic43—21no—
183C22×Dic43—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86C22×C412yes—
190Q16×C43—24no—
191SD16×C43—24no—
192M16×C43—21no—
193M16×C43—21no—
194M16×C43—21no—
195M16×C43C22×C412yes—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C42×C43—21no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—41no—
213C42×C43—41no—
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C42×C43C2×D411yescharacteristic
217C42×C43C2×D411yescharacteristic
218#10621885—24no—
219#10621885—24no—
220#10621885—24no—
221#10621883—24no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224Dic43⋊C4—41no—
225Dic43⋊C4—41no—
226C4×Dic43—41no—
227C4×Dic43—41no—
228#10621877—24no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—24no—
233#10621877—21no—
234#10621877—21no—
235#10621877C22×C412yes—
236#10621877C22×C412yes—
237#10621877#4112yes—
238C2×C43⋊C8—24no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—24no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C22×C412yes—
247C2×C43⋊C8C2×D411yescharacteristic
248C2×C43⋊C8C2×D411yescharacteristic
249C2×C43⋊C8C2×D411yescharacteristic
250C2×C43⋊C8C2×D411yescharacteristic
251C2×C43⋊C8#4112yes—
252C23×C43—21no—
253C23×C43C2×#4111yescharacteristic
254Q8×C43—21no—
255Q8×C43—22no—
256Q8×C43—22no—
257Q8×C43—41no—
258Q8×C43—41no—
259Q8×C43C4×D412yes—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—21no—
263D4×C43C4×D412yes—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—41no—
272C2×C4×C43—42no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—42no—
276C2×C4×C43—41no—
277C2×C4×C43—81no—
278C2×C4×C43#12111yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×Dic43—22no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—81no—
293Dic86—22no—
294Dic86—22no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—22no—
298C8×C43—41no—
299C43⋊C8—22no—
300C43⋊C8—22no—
301C43⋊C8—21no—
302C43⋊C8—22no—
303C43⋊C8—21no—
304C43⋊C8—41no—
305C43⋊C8C4×D412yes—
306C43⋊C8C4×D412yes—
307C4×#473—431nomaximal, Sylow
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—22no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43C4×#4111yescharacteristic
314C22×C43C2×#12111yescharacteristic
315C22×C43#52911yescharacteristic
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—22no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—42no—
323C4×C43—81no—
324C4×C43#47312yescomplemented
325C4×C43C2×C4×D411yescharacteristic
326C4×C43C2×C4×D411yescharacteristic
327C4×C43#52511yescharacteristic
328C4×C43#53211yescharacteristic
329Dic43—42no—
330Dic43—81no—
331C2×#473—431no—
332C4×#137—431no—
333C4×#137D4311yescharacteristic
334C2×C4×Q16—431no—
335C4×#131—431no—
336#1979—431no—
337#1952—431no—
338#1930—431no—
339#1930—431no—
340#1908—431no—
341#1908—431no—
342#1816—431no—
343C4×#108—431no—
344C4×#101—431no—
345C4×#101—431no—
346C2×C43—21no—
347C2×C43—21no—
348C2×C43—42no—
349C2×C43C4×#12111yescharacteristic
350C2×C43C2×#47311yescharacteristic
351C2×C43#306711yescharacteristic
352C2×#137—431no—
353C2×#137C2×D4311yescharacteristic
354C22×Q16—431no—
355C2×#131—431no—
356C2×#131—431no—
357C4×#41C2×D4311yescharacteristic
358C2×C4×Q8—431no—
359C2×C4×Q8C2×D4311yescharacteristic
360#473—438no—
361#441—21no—
362#441—861no—
363#440—21no—
364#440—861no—
365C4×Q16—21no—
366C4×Q16—861no—
367C4×Q16—861no—
368C4×Q16—861no—
369C4×Q16—861no—
370C4×Q16—861no—
371C4×SD16—21no—
372C4×SD16—861no—
373C2×#108—431no—
374C2×#108—431no—
375#428—431no—
376#428C2×D4311yescharacteristic
377C2×#107—431no—
378#419—431no—
379#419C2×D4311yescharacteristic
380#417—431no—
381#417C2×D4311yescharacteristic
382C2×#103—431no—
383C2×#103—431no—
384C2×#101—431no—
385C2×#101—431no—
386C2×#101—431no—
387C2×#101—431no—
388#405—431no—
389#405—431no—
390#405—861no—
391#405—861no—
392C4×M16—431no—
393C4×M16—431no—
394C4×M16—861no—
395C4×M16C2×D4311yescharacteristic
396C2×C4×C8—431no—
397C2×C4×C8—861no—
398#343—431no—
399#343—431no—
400#343—431no—
401#343—431no—
402#341—431no—
403#341—431no—
404C43C4×#47311yescharacteristic, complemented, Sylow
405C2×#41C22×D4311yescharacteristic
406C22×Q8—431no—
407C22×Q8C22×D4311yescharacteristic
408#137—22no—
409#137—434no—
410#137—862no—
411#137C4×D4314yes—
412C2×Q16—21no—
413C2×Q16—434no—
414C2×Q16—862no—
415C2×Q16—861no—
416C2×Q16—861no—
417C2×Q16—861no—
418C2×SD16—21no—
419C2×SD16—861no—
420#131—434no—
421#131—862no—
422#131—862no—
423#131—862no—
424C2×M16—431no—
425C2×M16—431no—
426C2×M16—431no—
427C2×M16—431no—
428C2×M16—861no—
429C2×M16—861no—
430C2×M16C22×D4311yescharacteristic
431C2×M16C22×D4311yescharacteristic
432C22×C8—431no—
433C22×C8—431no—
434C22×C8—861no—
435C22×C8—861no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×Q8—21no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×Q8—861no—
443C4×Q8—861no—
444C4×Q8C22⋊D4311yescharacteristic
445C4×Q8C22⋊D4311yescharacteristic
446C4×D4—21no—
447C4×D4—21no—
448C4×D4C22⋊D4311yescharacteristic
449C4×D4C22⋊D4311yescharacteristic
450#117—21no—
451#117C22×D4311yescharacteristic
452C2×C4⋊C4—21no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—861no—
459C2×C42C22×D4311yescharacteristic
460#108—434no—
461#108—862no—
462#107—21no—
463#107—861no—
464#107—861no—
465#107—861no—
466#106—21no—
467#106—861no—
468#103—21no—
469#103—21no—
470#103—21no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#103—861no—
477#103—861no—
478#102—21no—
479#102—861no—
480#101—434no—
481#101—434no—
482#101—862no—
483#101—862no—
484#97—21no—
485#97—861no—
486#97—861no—
487#97—861no—
488#97—861no—
489C4×C8—21no—
490C4×C8—431no—
491C4×C8—431no—
492C4×C8—431no—
493C4×C8—431no—
494C4×C8—861no—
495C4×C8—861no—
496C4×C8—861no—
497C4×C8—861no—
498#41—21no—
499#41—21no—
500#41C2×C4×D4312yes—
501#41#1062189812yes—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—432no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—861no—
513C2×Q8C2×C4×D4312yes—
514C2×Q8C2×C22⋊D4311yescharacteristic
515C2×D4—21no—
516C2×D4C2×C22⋊D4311yescharacteristic
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4#1062190011yescharacteristic
525C22×C4#1062190011yescharacteristic
526C22×C4C23×D4311yescharacteristic
527Q16—24no—
528Q16—864no—
529Q16—864no—
530Q16—864no—
531SD16—24no—
532SD16—864no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—432no—
537M16—432no—
538M16—432no—
539M16—864no—
540M16—864no—
541M16—861no—
542M16—861no—
543M16—861no—
544M16—861no—
545M16—861no—
546M16C2×C4×D4312yes—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—432no—
550C2×C8—431no—
551C2×C8—431no—
552C2×C8—432no—
553C2×C8—431no—
554C2×C8—431no—
555C2×C8—864no—
556C2×C8—864no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—1721no—
572C4⋊C4—1721no—
573C4⋊C4C2×C22⋊D4311yescharacteristic
574C4⋊C4C2×C22⋊D4311yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—41no—
582C42—41no—
583C42—1721no—
584C42—1721no—
585C42D4×D4311yescharacteristic
586C42D4×D4311yescharacteristic
587C42C2×C22⋊D4311yescharacteristic
588C42C2×C22⋊D4311yescharacteristic
589C23—21no—
590C23C2×#1062190011yescharacteristic
591Q8—21no—
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—862no—
597Q8—862no—
598Q8—1721no—
599Q8—1721no—
600Q8C4×C22⋊D4312yes—
601D4—22no—
602D4—22no—
603D4—21no—
604D4C4×C22⋊D4312yes—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—81no—
619C2×C4—862no—
620C2×C4—3441no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4#1306329711yescharacteristic
625C2×C4#1306329711yescharacteristic
626C2×C4#1306329711yescharacteristic
627C2×C4#1306329711yescharacteristic
628C2×C4C22×C4×D4311yescharacteristic
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4C22×C22⋊D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4C2×#1062189811yescharacteristic
634C8—22no—
635C8—41no—
636C8—432no—
637C8—432no—
638C8—862no—
639C8—862no—
640C8—861no—
641C8—861no—
642C8—862no—
643C8—1721no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22C4×#1062190011yescharacteristic
650C22C2×#1306329711yescharacteristic
651C22#1458342911yescharacteristic
652C4—22no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4—3441no—
661C4—1722no—
662C4#1458317212yesdirect product factor
663C4C4×D4×D4311yescharacteristic
664C4C2×C4×C22⋊D4311yescharacteristic
665C4#1458340811yescharacteristic
666C4#1458344511yescharacteristic
667C2—21no—
668C2—21no—
669C2—42no—
670C2C4×#1306329711yescharacteristic
671C2C2×#1458317211yescharacteristic
672C2#1914431211yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#137×C43C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenterC4×#137D43
hypocenterC43C4×#473
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
3. C2×C4×#10621885C2semidirect
5. #19135509C2semidirect
6. #19135377C2semidirect
7. #19135253C2semidirect
8. #19135249C2semidirect
12. C4×#13063260C2semidirect
13. C4×#13063243C2semidirect
14. C4×#13063244C2semidirect
21. #14583172C4direct (N × H)
75. C2×#10621885C2×C4semidirect
99. #13063260C2×C4semidirect
113. #13063244C2×C4semidirect
115. #13063243C2×C4semidirect
324. C4×C43#473semidirect
404. C43C4×#473semidirect
662. C4#14583172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145831722
C4×#130633552
C2×C4×#106218852
C4×#130633322
#191355092
#191353772
#191352532
#191352492
#191351122
#191351082
#191346572
C4×#130632602
C4×#130632432
C4×#130632442
C4×#137×C432
C4×#47343