Finite Group Databasebeta

← C2×#19135812 #25124190

Subgroups — C2×#19135812 #25124190

Order 11008.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583473C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3C22×#13063253C211yesmaximal, characteristic
4C2×#14582898C211yesmaximal, characteristic
5C22×#13063244C211yesmaximal, characteristic, complemented
6#19135812C218yesmaximal, direct product factor
7C2×#14582659C211yesmaximal, characteristic, complemented
8C2×C43×#391C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14583473—22no—
13#14583473—22no—
14#14583473—22no—
15#14583473C2214yes—
16C2×#13063323—21no—
17C2×#13063314—21no—
18C2×#13063308—22no—
19C2×#13063301—21no—
20C2×#13063301—21no—
21C2×#13063284C2211yescharacteristic
22#14582939—22no—
23#14582939C2214yescomplemented
24C2×#13063258—21no—
25C2×#13063256—21no—
26C2×#13063253—24no—
27C2×#13063253C2214yes—
28#14582898—22no—
29#14582898C2214yes—
30C2×#13063248—21no—
31C2×#13063245—21no—
32C2×#13063244—24no—
33C2×#13063244C2214yescomplemented
34#14582659C2214yescomplemented
35C23×Q8×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C43×#391—22no—
39C43×#391C2214yescomplemented
40C2×#95×C43—22no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—22no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898—22no—
47C2×#10621898D412yes—
48C2×#10621898C2312yes—
49C22×Dic86D411yescharacteristic
50C22×D172D411yescharacteristic
51C22×C22⋊D43—21no—
52C22×C4×D43—21no—
53C2×#10621877—21no—
54C2×#10621877—22no—
55C2×#10621877—21no—
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877D414yes—
59C2×#10621877C2312yes—
60C2×#10621877C2312yes—
61C22×C43⋊C8—21no—
62C22×C43⋊C8—21no—
63#13063323—24no—
64#13063323—24no—
65#13063314—24no—
66#13063314—24no—
67#13063308—28no—
68#13063308—28no—
69#13063301—24no—
70#13063301—24no—
71#13063301—24no—
72#13063301—24no—
73#13063284—21no—
74#13063284—21no—
75#13063284D412yes—
76#13063284C2312yes—
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43D411yescharacteristic
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×C4×Dic43—21no—
85#13063258—24no—
86#13063256—24no—
87#13063253—28no—
88#13063248—24no—
89#13063245—24no—
90#13063244—28no—
91C22×Q8×C43—22no—
92C22×Q8×C43—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43—21no—
95C22×Q8×C43—21no—
96C22×Q8×C43—22no—
97C22×Q8×C43—22no—
98C22×Q8×C43—22no—
99C22×Q8×C43D412yes—
100C22×Q8×C43C2312yes—
101C23×C4×C43—21no—
102C23×C4×C43—21no—
103C23×C4×C43D412yes—
104C23×C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2312yes—
111C2×C42×C43—22no—
112C2×C42×C43—22no—
113C2×C42×C43—21no—
114C2×C42×C43C2312yes—
115#95×C43—28no—
116C24×C43C2×D411yescharacteristic
117C23×D43—21no—
118C2×Q8×C43—22no—
119C2×Q8×C43—22no—
120C2×Q8×C43—24no—
121C2×Q8×C43—24no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—42no—
129C2×Q8×C43—42no—
130C2×Q8×C43—42no—
131C2×Q8×C43—42no—
132C2×Q8×C43—42no—
133C2×Q8×C43—42no—
134C2×Q8×C43—42no—
135C2×Q8×C43—42no—
136C22×C4×C43—24no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—24no—
140C22×C4×C43—24no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—42no—
144C22×C4×C43—44no—
145C22×C4×C43—41no—
146C22×C4×C43—41no—
147C22×C4×C43—42no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D414yes—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×C4×C43#4112yes—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—42no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166#10621898—24no—
167#10621898—24no—
168#10621898—22no—
169#10621898—22no—
170#10621898—22no—
171#10621898—22no—
172#10621898—42no—
173#10621898—42no—
174#10621898—42no—
175#10621898—42no—
176C2×D172—21no—
177C2×D172—22no—
178C2×D172—22no—
179C2×D172C2×D412yes—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×Dic86—22no—
185C2×Dic86—22no—
186C2×Dic86—21no—
187C2×Dic86C2×D412yes—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C42×C43—22no—
193C42×C43—22no—
194C42×C43—42no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197(C2×D43)⋊C4—28no—
198(C2×D43)⋊C4—28no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43C2×D412yes—
202C4⋊Dic43C2×D412yes—
203Dic43⋊C4—28no—
204Dic43⋊C4—28no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207#10621877—24no—
208#10621877—22no—
209#10621877—22no—
210#10621877—22no—
211#10621877—42no—
212#10621877C2×D414yes—
213C2×C43⋊C8—24no—
214C2×C43⋊C8—22no—
215C2×C43⋊C8—22no—
216C2×C43⋊C8—42no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43#12011yescharacteristic
220C23×C43#12011yescharacteristic
221C23×C43#12112yes—
222C23×C43#12312yes—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—42no—
226C22×D43—42no—
227C22×D43—42no—
228Q8×C43—42no—
229Q8×C43—42no—
230Q8×C43—42no—
231Q8×C43—42no—
232Q8×C43—44no—
233Q8×C43—44no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—42no—
239C2×C4×C43—48no—
240C2×C4×C43—42no—
241C2×C4×C43—44no—
242C2×C4×C43—44no—
243C2×C4×C43—44no—
244C2×C4×C43—42no—
245C2×C4×C43—82no—
246C2×C4×C43—82no—
247C2×C4×C43#12011yescharacteristic
248C2×C4×C43#12011yescharacteristic
249C2×C4×C43#12112yes—
250C2×C4×C43#12112yes—
251C2×C4×C43#12112yes—
252C2×C4×C43#12112yes—
253C2×C4×C43#12112yes—
254C2×C4×C43#12312yes—
255C2×C4×C43#12312yes—
256C2×C4×C43#12312yes—
257C2×C4×C43#12412yes—
258C2×C4×C43#12412yes—
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C22⋊D43—42no—
266C22⋊D43—42no—
267C22⋊D43—44no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274D172—22no—
275D172—22no—
276D172—42no—
277C4×D43—42no—
278C4×D43—42no—
279C4×D43—44no—
280Dic86—22no—
281Dic86—22no—
282Dic86—42no—
283C43⋊C8—24no—
284C43⋊C8—42no—
285C2×#2038—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—24no—
291C22×C43—24no—
292C22×C43#39412yes—
293C22×C43#39412yes—
294C22×C43#45412yes—
295C22×C43#45612yes—
296C22×C43C2×#12011yescharacteristic
297C22×C43C2×#12111yescharacteristic
298C22×C43C2×#12311yescharacteristic
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—84no—
303C4×C43—44no—
304C4×C43—44no—
305C4×C43—82no—
306C4×C43#39412yes—
307C4×C43#39412yes—
308C4×C43C2×#12111yescharacteristic
309C4×C43C2×#12111yescharacteristic
310C4×C43C2×#12311yescharacteristic
311C4×C43C2×#12411yescharacteristic
312Dic43—42no—
313Dic43—42no—
314Dic43—42no—
315C2×#536—431no—
316C2×#428—431no—
317C22×#104—431no—
318C2×#417—431no—
319C22×#101—431no—
320C2×#391D4311yescharacteristic, complemented
321#2038—438no—
322C2×#339—431no—
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—22no—
326C2×C43#203814yescomplemented
327C2×C43C2×#39411yescharacteristic
328C2×C43C2×#45411yescharacteristic
329C2×C43C2×#45611yescharacteristic
330D43—82no—
331C22×#41—431no—
332C23×Q8C2×D4311yescharacteristic
333C22×M16—431no—
334C22×M16—431no—
335#536—434no—
336#536—862no—
337#536—862no—
338#536—862no—
339C2×C4⋊Q8—861no—
340C2×#124—861no—
341C2×#123—862no—
342C2×C22⋊Q8—861no—
343C2×C22⋊Q8—861no—
344C2×#117—431no—
345C22×C4⋊C4C2×D4311yescharacteristic
346C22×C42C2×D4311yescharacteristic
347#428—434no—
348#428—862no—
349C2×#107—861no—
350C2×#106—861no—
351C2×#104—434no—
352C2×#104—864no—
353#417—434no—
354#417—862no—
355C2×#103—861no—
356C2×#102—861no—
357C2×#101—434no—
358C2×#101—864no—
359#391—22no—
360#391C2×D4314yescomplemented
361C2×#95—22no—
362#339—434no—
363C43C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—432no—
365C2×#41—432no—
366C2×#41—861no—
367C2×#41—861no—
368C2×#41—862no—
369C2×#41—862no—
370C2×#41—862no—
371C2×#41—862no—
372C22×Q8—22no—
373C22×Q8—22no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—431no—
381C22×Q8C22⋊D4312yes—
382C22×Q8C22×D4312yes—
383C22×D4—431no—
384C22×D4—861no—
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—861no—
388C23×C4C22⋊D4312yes—
389C23×C4C22×D4311yescharacteristic
390C2×M16—434no—
391C2×M16—432no—
392C2×M16—432no—
393C2×M16—862no—
394C2×M16—861no—
395C2×M16—861no—
396C2×M16—862no—
397C2×M16—862no—
398C22×C8—861no—
399C22×C8—861no—
400C4⋊Q8—864no—
401C4⋊Q8—864no—
402#124—864no—
403#124—864no—
404#123—868no—
405#123—868no—
406C22⋊Q8—864no—
407C22⋊Q8—864no—
408C22⋊Q8—864no—
409C22⋊Q8—864no—
410#117—432no—
411#117—432no—
412#117—861no—
413#117—861no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—862no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4C22×D4312yes—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—861no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—21no—
430C2×C42—861no—
431C2×C42C22×D4312yes—
432#107—864no—
433#106—864no—
434#104—868no—
435#103—864no—
436#102—864no—
437#101—868no—
438#95—28no—
439C24—861no—
440C24C2×C22⋊D4311yescharacteristic
441#41—864no—
442#41—864no—
443#41—862no—
444#41—862no—
445#41—862no—
446#41—862no—
447#41—1722no—
448#41—1722no—
449#41—1722no—
450#41—1722no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—24no—
454C2×Q8—24no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—432no—
470C2×Q8—861no—
471C2×Q8—862no—
472C2×Q8—862no—
473C2×D4—432no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—861no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—1722no—
480C2×D4—1722no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4#1062189812yes—
501C22×C4#1062189812yes—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4D4×D4312yes—
507C22×C4#1062190012yes—
508C22×C4C2×C22⋊D4314yes—
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511M16—434no—
512M16—864no—
513M16—862no—
514M16—862no—
515M16—862no—
516M16—1722no—
517C2×C8—864no—
518C2×C8—862no—
519C2×C8—862no—
520C2×C8—1722no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—432no—
526C4⋊C4—432no—
527C4⋊C4—868no—
528C4⋊C4—868no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C22⋊C4—868no—
532C22⋊C4—868no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C42—22no—
536C42—22no—
537C42—42no—
538C42—862no—
539C42—862no—
540C23—22no—
541C23—22no—
542C23—862no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23#1306329311yescharacteristic
547C23#1306329311yescharacteristic
548C23#1306329712yes—
549C23#1306330812yes—
550C23C22×C22⋊D4311yescharacteristic
551Q8—44no—
552Q8—44no—
553Q8—42no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—862no—
558Q8—862no—
559Q8—1722no—
560D4—862no—
561D4—862no—
562D4—1724no—
563D4—1722no—
564D4—1722no—
565D4—1722no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—48no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1724no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4#1306329311yescharacteristic
589C2×C4#1306329311yescharacteristic
590C2×C4#1306329712yes—
591C2×C4#1306329812yes—
592C2×C4#1306329812yes—
593C2×C4#1306329812yes—
594C2×C4#1306329812yes—
595C2×C4#1306330712yes—
596C2×C4#1306330712yes—
597C2×C4#1306330812yes—
598C2×C4#1306331112yes—
599C2×C4#1306331112yes—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C2×C4C2×#1062190011yescharacteristic
604C2×C4C2×#1062189811yescharacteristic
605C2×C4C2×#1062189811yescharacteristic
606C8—864no—
607C8—1722no—
608C22—21no—
609C22—21no—
610C22—24no—
611C22—24no—
612C22—21no—
613C22—21no—
614C22—3444no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22#1458281412yes—
619C22#1458281412yes—
620C22#1458307112yes—
621C22#1458308112yes—
622C22C2×#1306329311yescharacteristic
623C22C2×#1306329711yescharacteristic
624C22C2×#1306330811yescharacteristic
625C4—44no—
626C4—44no—
627C4—82no—
628C4—1722no—
629C4—1722no—
630C4—1722no—
631C4#1458281412yes—
632C4#1458281412yes—
633C4C2×#1306329811yescharacteristic
634C4C2×#1306329811yescharacteristic
635C4C2×#1306330711yescharacteristic
636C4C2×#1306331111yescharacteristic
637C2—21no—
638C2—22no—
639C2—21no—
640C2—3442no—
641C2#1913581214yesdirect product factor
642C2C2×#1458281411yescharacteristic
643C2C2×#1458307111yescharacteristic
644C2C2×#1458308111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#391C2
socleC23×C43#120
prime radicalC22×#10621898C22
hypercenterC2×#391D43
hypocenterC43C2×#2038
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
5. C22×#13063244C2semidirect
6. #19135812C2direct (N × H)
7. C2×#14582659C2semidirect
8. C2×C43×#391C2semidirect
23. #14582939C22semidirect
33. C2×#13063244C22semidirect
34. #14582659C22semidirect
39. C43×#391C22semidirect
320. C2×#391D43semidirect
326. C2×C43#2038semidirect
360. #391C2×D43semidirect
363. C43C2×#2038semidirect
641. C2#19135812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834732
C2×#145829392
C22×#130632532
C2×#145828982
C22×#130632442
#191358122
C2×#145826592
C2×C43×#3912
C2×#203843