Finite Group Databasebeta

← C2×#19135811 #25124189

Subgroups — C2×#19135811 #25124189

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×#14583470C211yesmaximal, characteristic
2C2×#14582941C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic
4C22×#13063243C211yesmaximal, characteristic, complemented
5C2×#14582805C211yesmaximal, characteristic, complemented
6#19135811C218yesmaximal, direct product factor
7C2×#14582659C211yesmaximal, characteristic, complemented
8C22×#104×C43C211yesmaximal, characteristic
9C23×Dic86C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11#14583470—22no—
12#14583470—22no—
13#14583470—22no—
14#14583470C2214yes—
15C2×#13063323—21no—
16C2×#13063312—21no—
17C2×#13063306—22no—
18C2×#13063304—21no—
19C2×#13063304—21no—
20C2×#13063284C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22#14582941—22no—
23#14582941C2214yescomplemented
24C2×#13063259—21no—
25C2×#13063257—21no—
26#14582900—22no—
27#14582900C2214yes—
28C2×#13063249—21no—
29C2×#13063246—21no—
30C2×#13063243—24no—
31C2×#13063243C2214yescomplemented
32#14582805—22no—
33#14582805C2214yescomplemented
34C2×C43⋊#95—22no—
35#14582659C2214yescomplemented
36C22×#41×C43C2211yescharacteristic
37C22×M16×C43C2211yescharacteristic
38C22×C42×C43C2211yescharacteristic
39C2×#104×C43—24no—
40C2×#104×C43C2214yes—
41C22×Dic86—22no—
42C22×Dic86—21no—
43C22×Dic86—21no—
44C22×Dic86—21no—
45C22×Dic86—21no—
46C22×Dic86—22no—
47C22×Dic86—22no—
48C22×Dic86—22no—
49C22×Dic86D412yes—
50C22×Dic86C2312yes—
51C23×Dic43—21no—
52C23×Dic43D412yes—
53C2×#10621877—21no—
54C2×#10621877—22no—
55C2×#10621877—22no—
56C2×#10621877C2312yes—
57C22×C43⋊C8—21no—
58#13063323—24no—
59#13063323—24no—
60#13063312—24no—
61#13063312—24no—
62#13063306—28no—
63#13063306—28no—
64#13063304—24no—
65#13063304—24no—
66#13063304—24no—
67#13063304—24no—
68#13063284—21no—
69#13063284—21no—
70#13063284D412yes—
71#13063284C2312yes—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43C2312yes—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86#13063259—24no—
87#13063257—24no—
88#13063249—24no—
89#13063246—24no—
90#13063243—28no—
91C43⋊#95—28no—
92C2×#41×C43—21no—
93C2×#41×C43—21no—
94C2×#41×C43—22no—
95C2×#41×C43—22no—
96C2×#41×C43—22no—
97C2×#41×C43—22no—
98C2×#41×C43D412yes—
99C2×#41×C43C2312yes—
100C22×Q8×C43D411yescharacteristic
101C22×D4×C43—21no—
102C22×D4×C43D411yescharacteristic
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C23×C4×C43C2311yescharacteristic
106C2×M16×C43—21no—
107C2×M16×C43—22no—
108C2×M16×C43D414yes—
109C2×M16×C43C2312yes—
110C22×C8×C43—21no—
111C2×C42×C43—22no—
112C2×C42×C43—22no—
113C2×C42×C43—21no—
114C2×C42×C43C2312yes—
115#104×C43—28no—
116C24×C43—21no—
117C24×C43C2×D411yescharacteristic
118#41×C43—24no—
119#41×C43—24no—
120#41×C43—22no—
121#41×C43—22no—
122#41×C43—22no—
123#41×C43—22no—
124#41×C43—42no—
125#41×C43—42no—
126#41×C43—42no—
127#41×C43—42no—
128C2×Q8×C43—21no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43C2×D412yes—
132C2×D4×C43—21no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—42no—
138C2×D4×C43—42no—
139C2×D4×C43C2×D412yes—
140C22×C4×C43—24no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×C4×C43#4112yes—
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—24no—
164C22×Dic43—24no—
165C22×Dic43—22no—
166C22×Dic43—44no—
167C22×Dic43—41no—
168C22×Dic43—41no—
169C22×Dic43C2×D414yes—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—24no—
173C2×Dic86—24no—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—22no—
179C2×Dic86—22no—
180C2×Dic86—42no—
181C2×Dic86—42no—
182C2×Dic86—42no—
183C2×Dic86—42no—
184C2×Dic86—42no—
185C2×Dic86—42no—
186C2×Dic86—42no—
187C2×Dic86—42no—
188M16×C43—24no—
189M16×C43—22no—
190M16×C43C2×D414yes—
191C2×C8×C43—24no—
192C2×C8×C43—22no—
193C42×C43—22no—
194C42×C43—22no—
195C42×C43—42no—
196C22⋊Dic43—28no—
197C22⋊Dic43—28no—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43—41no—
205C4⋊Dic43—41no—
206C4⋊Dic43C2×D412yes—
207C4⋊Dic43C2×D412yes—
208Dic43⋊C4—28no—
209Dic43⋊C4—28no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212#10621877—22no—
213#10621877—22no—
214#10621877—42no—
215C2×C43⋊C8—22no—
216C2×C43⋊C8—42no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—42no—
223C23×C43#12011yescharacteristic
224C23×C43#12011yescharacteristic
225C23×C43#12112yes—
226C23×C43#12312yes—
227C23×C43C22×D411yescharacteristic
228Q8×C43—22no—
229Q8×C43—22no—
230Q8×C43—42no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—42no—
234D4×C43—42no—
235D4×C43—44no—
236D4×C43—42no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—42no—
240C2×C4×C43—48no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—44no—
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12011yescharacteristic
248C2×C4×C43#12112yes—
249C2×C4×C43#12112yes—
250C2×C4×C43#12112yes—
251C2×C4×C43#12112yes—
252C2×C4×C43#12112yes—
253C2×C4×C43#12312yes—
254C2×C4×C43#12312yes—
255C2×C4×C43#12312yes—
256C2×C4×C43#12412yes—
257C2×C4×C43#12412yes—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—24no—
267C2×Dic43—24no—
268C2×Dic43—24no—
269C2×Dic43—44no—
270C2×Dic43—44no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—44no—
274C2×Dic43—42no—
275C2×Dic43—82no—
276C2×Dic43—82no—
277Dic86—42no—
278Dic86—42no—
279Dic86—42no—
280Dic86—42no—
281Dic86—44no—
282Dic86—44no—
283C8×C43—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—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—84no—
296C22×C43#39412yes—
297C22×C43#39412yes—
298C22×C43#45412yes—
299C22×C43#45612yes—
300C22×C43C2×#12011yescharacteristic
301C22×C43C2×#12111yescharacteristic
302C22×C43C2×#12311yescharacteristic
303C4×C43—44no—
304C4×C43—42no—
305C4×C43#39412yes—
306C4×C43#39412yes—
307C4×C43C2×#12111yescharacteristic
308C4×C43C2×#12111yescharacteristic
309C4×C43C2×#12311yescharacteristic
310C4×C43C2×#12411yescharacteristic
311Dic43—44no—
312Dic43—42no—
313Dic43—42no—
314Dic43—82no—
315C2×#536—431no—
316C2×#428—431no—
317C22×#104D4311yescharacteristic
318C2×#417—431no—
319C22×#101—431no—
320C2×#391—431no—
321#2038—438no—
322C2×#339—431no—
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—22no—
326C2×C43—82no—
327C2×C43#203814yescomplemented
328C2×C43C2×#39411yescharacteristic
329C2×C43C2×#45411yescharacteristic
330C2×C43C2×#45611yescharacteristic
331C22×#41C2×D4311yescharacteristic
332C23×Q8—431no—
333C22×M16—431no—
334C22×M16C2×D4311yescharacteristic
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⋊C4—431no—
346C22×C42C2×D4311yescharacteristic
347#428—434no—
348#428—862no—
349C2×#107—861no—
350C2×#106—861no—
351C2×#104—24no—
352C2×#104C2×D4314yes—
353#417—434no—
354#417—862no—
355C2×#103—861no—
356C2×#102—861no—
357C2×#101—434no—
358C2×#101—864no—
359#391—434no—
360#391—862no—
361C2×#95—862no—
362#339—434no—
363C43C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41D17212yes—
371C2×#41C22×D4312yes—
372C22×Q8—432no—
373C22×Q8—432no—
374C22×Q8—861no—
375C22×Q8—861no—
376C22×Q8—862no—
377C22×Q8—861no—
378C22×Q8—861no—
379C22×Q8—862no—
380C22×Q8—862no—
381C22×Q8—862no—
382C22×Q8D17211yescharacteristic
383C22×D4—21no—
384C22×D4D17211yescharacteristic
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—432no—
388C23×C4—861no—
389C23×C4C22×D4311yescharacteristic
390C2×M16—21no—
391C2×M16—22no—
392C2×M16—432no—
393C2×M16—861no—
394C2×M16—862no—
395C2×M16—862no—
396C2×M16C22⋊D4314yes—
397C2×M16C22×D4312yes—
398C22×C8—21no—
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—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
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—28no—
435#103—864no—
436#102—864no—
437#101—868no—
438#95—868no—
439C24—21no—
440C24D4×D4311yescharacteristic
441#41—24no—
442#41—24no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—42no—
448#41—42no—
449#41—42no—
450#41—42no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—862no—
455C2×Q8—862no—
456C2×Q8—864no—
457C2×Q8—864no—
458C2×Q8—862no—
459C2×Q8—862no—
460C2×Q8—862no—
461C2×Q8—862no—
462C2×Q8—862no—
463C2×Q8—862no—
464C2×Q8—1722no—
465C2×Q8—1722no—
466C2×Q8—1722no—
467C2×Q8—1722no—
468C2×Q8—1722no—
469C2×Q8—1722no—
470C2×Q8—1722no—
471C2×Q8—1722no—
472C2×Q8C2×D17212yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4C2×D17212yes—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—434no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—862no—
495C22×C4—864no—
496C22×C4—864no—
497C22×C4—862no—
498C22×C4—1724no—
499C22×C4—1721no—
500C22×C4—1721no—
501C22×C4C2×D17211yescharacteristic
502C22×C4C2×D17211yescharacteristic
503C22×C4#1062189812yes—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4#1062190012yes—
508C22×C4#1062190012yes—
509C22×C4C2×C22⋊D4312yes—
510C22×C4C23×D4311yescharacteristic
511M16—24no—
512M16—22no—
513M16—862no—
514M16—862no—
515M16—1722no—
516M16C2×C22⋊D4314yes—
517C2×C8—24no—
518C2×C8—22no—
519C2×C8—862no—
520C2×C8—1722no—
521C4⋊C4—432no—
522C4⋊C4—432no—
523C4⋊C4—868no—
524C4⋊C4—868no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—1721no—
530C4⋊C4—1721no—
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—22no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23#1306329511yescharacteristic
547C23#1306329511yescharacteristic
548C23#1306329612yes—
549C23#1306330712yes—
550C23C2×D4×D4311yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—42no—
554Q8—1724no—
555Q8—1724no—
556Q8—1722no—
557Q8—1722no—
558Q8—1722no—
559Q8—1722no—
560D4—22no—
561D4—22no—
562D4—44no—
563D4—42no—
564D4—42no—
565D4—42no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—48no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—864no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—3442no—
581C2×C4—3442no—
582C2×C4—1724no—
583C2×C4—1722no—
584C2×C4—1724no—
585C2×C4—1724no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4#1306329511yescharacteristic
589C2×C4#1306329511yescharacteristic
590C2×C4#1306329612yes—
591C2×C4#1306329712yes—
592C2×C4#1306329712yes—
593C2×C4#1306329912yes—
594C2×C4#1306329912yes—
595C2×C4#1306330712yes—
596C2×C4#1306330912yes—
597C2×C4#1306330912yes—
598C2×C4#1306331112yes—
599C2×C4#1306331112yes—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C22×C22⋊D4311yescharacteristic
602C2×C4C22×D17211yescharacteristic
603C2×C4C2×#1062190011yescharacteristic
604C2×C4C2×#1062190011yescharacteristic
605C2×C4C2×#1062189811yescharacteristic
606C8—24no—
607C8—1722no—
608C22—21no—
609C22—21no—
610C22—24no—
611C22—24no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—84no—
618C22#1458281512yes—
619C22#1458281512yes—
620C22#1458307312yes—
621C22#1458308312yes—
622C22C2×#1306329511yescharacteristic
623C22C2×#1306329611yescharacteristic
624C22C2×#1306330711yescharacteristic
625C4—44no—
626C4—42no—
627C4—3442no—
628C4—1722no—
629C4—1724no—
630C4—1722no—
631C4#1458281512yes—
632C4#1458281512yes—
633C4C2×#1306329711yescharacteristic
634C4C2×#1306329911yescharacteristic
635C4C2×#1306330911yescharacteristic
636C4C2×#1306331111yescharacteristic
637C2—21no—
638C2—22no—
639C2—21no—
640C2—82no—
641C2#1913581114yesdirect product factor
642C2C2×#1458281511yescharacteristic
643C2C2×#1458307311yescharacteristic
644C2C2×#1458308311yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#104×C43C2
socleC23×C43#120
prime radicalC22×#41×C43C22
hypercenterC22×#104D43
hypocenterC43C2×#2038
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#14582941C2semidirect
4. C22×#13063243C2semidirect
5. C2×#14582805C2semidirect
6. #19135811C2direct (N × H)
7. C2×#14582659C2semidirect
23. #14582941C22semidirect
31. C2×#13063243C22semidirect
33. #14582805C22semidirect
35. #14582659C22semidirect
327. C2×C43#2038semidirect
363. C43C2×#2038semidirect
641. C2#19135811direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834702
C2×#145829412
C2×#145829002
C22×#130632432
C2×#145828052
#191358112
C2×#145826592
C22×#104×C432
C2×#203843