Finite Group Databasebeta

← C2×#19135815 #25124193

Subgroups — C2×#19135815 #25124193

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×#14583475C211yesmaximal, characteristic
2C2×#14582942C211yesmaximal, characteristic, complemented
3C22×#13063253C211yesmaximal, characteristic
4C2×#14582901C211yesmaximal, characteristic
5C22×#13063243C211yesmaximal, characteristic, complemented
6C2×#14582805C211yesmaximal, characteristic, complemented
7#19135815C218yesmaximal, direct product factor
8C2×C43×#339C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×Dic86C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14583475—22no—
13#14583475—22no—
14#14583475—22no—
15#14583475C2214yes—
16C2×#13063325—21no—
17C2×#13063313—21no—
18C2×#13063309—22no—
19C2×#13063305—21no—
20C2×#13063305—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22#14582942—22no—
23#14582942C2214yescomplemented
24C2×#13063258—21no—
25C2×#13063256—21no—
26C2×#13063253—24no—
27C2×#13063253C2214yes—
28#14582901—22no—
29#14582901C2214yes—
30C2×#13063250—21no—
31C2×#13063247—21no—
32C2×#13063243—24no—
33C2×#13063243C2214yescomplemented
34#14582805—22no—
35#14582805C2214yescomplemented
36C2×C43⋊#95—22no—
37C22×M16×C43C2211yescharacteristic
38C2×#117×C43C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C43×#339C2214yescomplemented
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—22no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898—22no—
47C2×#10621898D412yes—
48C2×#10621898C2312yes—
49C22×Dic86—22no—
50C22×Dic86—21no—
51C22×Dic86—21no—
52C22×Dic86—21no—
53C22×Dic86—21no—
54C22×Dic86—22no—
55C22×Dic86—22no—
56C22×Dic86—22no—
57C22×Dic86D412yes—
58C22×Dic86D411yescharacteristic
59C22×Dic86C2312yes—
60C22×D172D411yescharacteristic
61C22×C22⋊D43—21no—
62C23×Dic43—21no—
63C23×Dic43D412yes—
64C22×C4×D43—21no—
65C2×#10621877—21no—
66C2×#10621877—22no—
67C2×#10621877D414yes—
68C2×#10621877C2312yes—
69C22×C43⋊C8—21no—
70#13063325—24no—
71#13063325—24no—
72#13063313—24no—
73#13063313—24no—
74#13063309—28no—
75#13063309—28no—
76#13063305—24no—
77#13063305—24no—
78#13063305—24no—
79#13063305—24no—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2312yes—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90#13063258—24no—
91#13063256—24no—
92#13063253—28no—
93#13063250—24no—
94#13063247—24no—
95#13063243—28no—
96C43⋊#95—28no—
97C23×C4×C43—21no—
98C23×C4×C43C2311yescharacteristic
99C2×M16×C43—21no—
100C2×M16×C43—22no—
101C2×M16×C43—22no—
102C2×M16×C43C2312yes—
103C22×C8×C43—21no—
104#117×C43—21no—
105#117×C43—21no—
106#117×C43D412yes—
107#117×C43C2312yes—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43—22no—
113C2×C42×C43—22no—
114C2×C42×C43—21no—
115C2×C42×C43C2312yes—
116C24×C43C2×D411yescharacteristic
117C23×D43—21no—
118C22×C4×C43—24no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43#4112yes—
131C22×C4×C43#4112yes—
132C22×C4×C43#4112yes—
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—42no—
137C2×C22⋊D43—42no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—24no—
142C22×Dic43—24no—
143C22×Dic43—22no—
144C22×Dic43—44no—
145C22×Dic43—41no—
146C22×Dic43—41no—
147C22×Dic43C2×D414yes—
148#10621898—24no—
149#10621898—24no—
150#10621898—22no—
151#10621898—22no—
152#10621898—22no—
153#10621898—22no—
154#10621898—42no—
155#10621898—42no—
156#10621898—42no—
157#10621898—42no—
158C2×D172—21no—
159C2×D172—22no—
160C2×D172—22no—
161C2×D172C2×D412yes—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×Dic86—22no—
167C2×Dic86—22no—
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86—21no—
171C2×Dic86—24no—
172C2×Dic86—24no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—22no—
179C2×Dic86—42no—
180C2×Dic86—42no—
181C2×Dic86—42no—
182C2×Dic86—42no—
183C2×Dic86—42no—
184C2×Dic86—42no—
185C2×Dic86—42no—
186C2×Dic86—42no—
187C2×Dic86C2×D412yes—
188M16×C43—22no—
189M16×C43—22no—
190M16×C43—42no—
191C2×C8×C43—22no—
192C2×C8×C43—42no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D412yes—
196C4⋊C4×C43C2×D412yes—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—22no—
199C42×C43—22no—
200C42×C43—22no—
201C42×C43—22no—
202C42×C43—22no—
203C42×C43—42no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—28no—
206C4⋊Dic43—28no—
207C4⋊Dic43—28no—
208C4⋊Dic43—22no—
209C4⋊Dic43—22no—
210C4⋊Dic43—41no—
211C4⋊Dic43—41no—
212#10621877—24no—
213#10621877—22no—
214#10621877C2×D414yes—
215C2×C43⋊C8—24no—
216C2×C43⋊C8—22no—
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—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—42no—
232C2×C4×C43—48no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×C4×C43#12112yes—
239C2×C4×C43#12112yes—
240C2×C4×C43#12112yes—
241C2×C4×C43#12112yes—
242C2×C4×C43#12112yes—
243C2×C4×C43#12312yes—
244C2×C4×C43#12312yes—
245C2×C4×C43#12312yes—
246C2×C4×C43#12412yes—
247C2×C4×C43#12412yes—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C22⋊D43—42no—
255C22⋊D43—42no—
256C22⋊D43—44no—
257C2×Dic43—22no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—42no—
262C2×Dic43—44no—
263C2×Dic43—44no—
264C2×Dic43—44no—
265C2×Dic43—42no—
266C2×Dic43—82no—
267C2×Dic43—82no—
268D172—22no—
269D172—22no—
270D172—42no—
271C4×D43—42no—
272C4×D43—42no—
273C4×D43—44no—
274Dic86—22no—
275Dic86—22no—
276Dic86—42no—
277Dic86—42no—
278Dic86—42no—
279Dic86—42no—
280Dic86—44no—
281Dic86—44no—
282Dic86—42no—
283C8×C43—42no—
284C43⋊C8—24no—
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—42no—
305C4×C43—42no—
306C4×C43#39412yes—
307C4×C43#39412yes—
308C4×C43C2×#12111yescharacteristic
309C4×C43C2×#12111yescharacteristic
310C4×C43C2×#12311yescharacteristic
311C4×C43C2×#12411yescharacteristic
312Dic43—42no—
313Dic43—44no—
314Dic43—82no—
315C2×#536—431no—
316C2×#428—431no—
317C22×#104—431no—
318C2×#417—431no—
319C22×#101—431no—
320C2×#391—431no—
321#2038—438no—
322C2×#339D4311yescharacteristic, complemented
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×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×#117C2×D4311yescharacteristic
345C22×C4⋊C4—431no—
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—434no—
360#391—862no—
361C2×#95—862no—
362#339C2×D4314yescomplemented
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—432no—
373C22×Q8—432no—
374C22×Q8—431no—
375C22×Q8—861no—
376C22×Q8—861no—
377C22×Q8—862no—
378C22×Q8—862no—
379C22×Q8—861no—
380C22×Q8—861no—
381C22×Q8—862no—
382C22×Q8—862no—
383C22×D4—431no—
384C22×D4—861no—
385C23×C4—21no—
386C23×C4—432no—
387C23×C4—861no—
388C23×C4—861no—
389C23×C4C22×D4311yescharacteristic
390C2×M16—21no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—434no—
394C2×M16—432no—
395C2×M16—861no—
396C2×M16—862no—
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—21no—
411#117—21no—
412#117D17212yes—
413#117C22×D4312yes—
414C2×C4⋊C4—432no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4D17211yescharacteristic
423C2×C4⋊C4D17211yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—862no—
427C2×C42—21no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—21no—
431C2×C42C22×D4312yes—
432#107—864no—
433#106—864no—
434#104—868no—
435#103—864no—
436#102—864no—
437#101—868no—
438#95—868no—
439C24—861no—
440C24D4×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—432no—
452C2×Q8—862no—
453C2×Q8—862no—
454C2×Q8—861no—
455C2×Q8—864no—
456C2×Q8—864no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×Q8—862no—
460C2×Q8—862no—
461C2×Q8—862no—
462C2×Q8—862no—
463C2×Q8—862no—
464C2×Q8—862no—
465C2×Q8—1722no—
466C2×Q8—1722no—
467C2×Q8—1722no—
468C2×Q8—1722no—
469C2×Q8—1722no—
470C2×Q8—1722no—
471C2×Q8—1722no—
472C2×Q8—1722no—
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—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—434no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—861no—
491C22×C4—864no—
492C22×C4—864no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—1724no—
497C22×C4—1721no—
498C22×C4—1721no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4C2×D17211yescharacteristic
502C22×C4C2×D17211yescharacteristic
503C22×C4#1062189812yes—
504C22×C4#1062189812yes—
505C22×C4D4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4312yes—
509C22×C4#1062190212yes—
510C22×C4C23×D4311yescharacteristic
511M16—22no—
512M16—22no—
513M16—42no—
514M16—434no—
515M16—864no—
516M16—862no—
517C2×C8—22no—
518C2×C8—42no—
519C2×C8—864no—
520C2×C8—862no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—868no—
524C4⋊C4—868no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—1721no—
528C4⋊C4—1721no—
529C4⋊C4C2×D17212yes—
530C4⋊C4C2×D17212yes—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—868no—
534C22⋊C4—868no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—42no—
540C23—22no—
541C23—22no—
542C23—862no—
543C23—1722no—
544C23—1722no—
545C23—1722no—
546C23#1306329511yescharacteristic
547C23#1306329511yescharacteristic
548C23#1306329812yes—
549C23#1306331012yes—
550C23C2×D4×D4311yescharacteristic
551Q8—862no—
552Q8—862no—
553Q8—1724no—
554Q8—1724no—
555Q8—1722no—
556Q8—1722no—
557Q8—1722no—
558Q8—1722no—
559Q8—1722no—
560D4—862no—
561D4—862no—
562D4—1724no—
563D4—1722no—
564D4—1722no—
565D4—1722no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—864no—
575C2×C4—862no—
576C2×C4—864no—
577C2×C4—864no—
578C2×C4—3442no—
579C2×C4—3442no—
580C2×C4—1724no—
581C2×C4—1722no—
582C2×C4—1724no—
583C2×C4—1724no—
584C2×C4—1722no—
585C2×C4—1724no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4#1306329511yescharacteristic
589C2×C4#1306329511yescharacteristic
590C2×C4#1306329812yes—
591C2×C4#1306329812yes—
592C2×C4#1306329812yes—
593C2×C4#1306330012yes—
594C2×C4#1306330012yes—
595C2×C4#1306331012yes—
596C2×C4#1306331012yes—
597C2×C4#1306331012yes—
598C2×C4#1306331312yes—
599C2×C4#1306331312yes—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C22×D17211yescharacteristic
603C2×C4C2×#1062189811yescharacteristic
604C2×C4C2×#1062189811yescharacteristic
605C2×C4C2×#1062190211yescharacteristic
606C8—42no—
607C8—864no—
608C22—21no—
609C22—21no—
610C22—24no—
611C22—24no—
612C22—21no—
613C22—21no—
614C22—3444no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22#1458281712yes—
619C22#1458281712yes—
620C22#1458307312yes—
621C22#1458308312yes—
622C22C2×#1306329511yescharacteristic
623C22C2×#1306329811yescharacteristic
624C22C2×#1306331011yescharacteristic
625C4—44no—
626C4—42no—
627C4—42no—
628C4—3442no—
629C4—1724no—
630C4—1722no—
631C4#1458281712yes—
632C4#1458281712yes—
633C4C2×#1306329811yescharacteristic
634C4C2×#1306330011yescharacteristic
635C4C2×#1306331011yescharacteristic
636C4C2×#1306331311yescharacteristic
637C2—21no—
638C2—22no—
639C2—21no—
640C2—3442no—
641C2#1913581514yesdirect product factor
642C2C2×#1458281711yescharacteristic
643C2C2×#1458307311yescharacteristic
644C2C2×#1458308311yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#339C2
socleC23×C43#120
prime radicalC22×#10621898C22
hypercenterC2×#339D43
hypocenterC43C2×#2038
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
2. C2×#14582942C2semidirect
5. C22×#13063243C2semidirect
6. C2×#14582805C2semidirect
7. #19135815C2direct (N × H)
8. C2×C43×#339C2semidirect
23. #14582942C22semidirect
33. C2×#13063243C22semidirect
35. #14582805C22semidirect
40. C43×#339C22semidirect
322. C2×#339D43semidirect
326. C2×C43#2038semidirect
362. #339C2×D43semidirect
363. C43C2×#2038semidirect
641. C2#19135815direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834752
C2×#145829422
C22×#130632532
C2×#145829012
C22×#130632432
C2×#145828052
#191358152
C2×C43×#3392
C2×#203843