Finite Group Databasebeta

← C2×#19135264 #25099178

Subgroups — C2×#19135264 #25099178

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582947C211yesmaximal, characteristic, complemented
2C2×#14582915C211yesmaximal, characteristic
3C22×#13063253C211yesmaximal, characteristic
4C2×#14582881C211yesmaximal, characteristic
5#19135264C218yesmaximal, direct product factor
6C2×#14582671C211yesmaximal, characteristic, complemented
7C2×#14582659C211yesmaximal, characteristic, complemented
8C2×C4×M16×C43C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12C2×#13063284C2211yescharacteristic
13#14582947—22no—
14#14582947C2214yescomplemented
15C2×#13063260—22no—
16#14582915—22no—
17#14582915C2214yes—
18C2×#13063253—21no—
19C2×#13063253—21no—
20C2×#13063253—22no—
21C2×#13063253C2214yes—
22C2×#13063251—22no—
23#14582881C414yescomplemented
24#14582881C2214yes—
25C2×#13063243C412yescomplemented
26C2×#13063241C412yescomplemented
27#14582671C2214yescomplemented
28#14582659C2214yescomplemented
29C22×M16×C43C2211yescharacteristic
30C22×M16×C43C2211yescharacteristic
31C22×C42×C43C2211yescharacteristic
32C4×M16×C43—22no—
33C4×M16×C43C2214yescomplemented
34C2×#97×C43—21no—
35C2×C4×C8×C43—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898C2×C412yes—
47C2×#10621898C2312yes—
48C22×Dic86C2×C411yescharacteristic
49C22×D172C2×C411yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877C2×C412yes—
61C2×#10621877C2×C412yes—
62C2×#10621877C2312yes—
63C2×#10621877C2312yes—
64C22×C43⋊C8—21no—
65C22×C43⋊C8—21no—
66#13063284—21no—
67#13063284—21no—
68#13063284—21no—
69#13063284C2312yes—
70C2×C4⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×C4×Dic43—21no—
73#13063260—28no—
74#13063253—24no—
75#13063253—24no—
76#13063251—28no—
77#13063243C2×C418yescomplemented
78#13063241C2×C418yescomplemented
79C23×C4×C43—21no—
80C23×C4×C43C2311yescharacteristic
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43—21no—
87C2×M16×C43C2×C412yes—
88C2×M16×C43C2×C412yes—
89C2×M16×C43D412yes—
90C2×M16×C43D412yes—
91C2×M16×C43C2312yes—
92C2×M16×C43C2312yes—
93C22×C8×C43—21no—
94C22×C8×C43—21no—
95C2×C42×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43D411yescharacteristic
99C2×C42×C43D411yescharacteristic
100C2×C42×C43D412yes—
101C2×C42×C43C2312yes—
102#97×C43—24no—
103C4×C8×C43—24no—
104C24×C43#4111yescharacteristic
105C23×D43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—44no—
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C22×C411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C22×C4×C43C2411yescharacteristic
125C2×C22⋊D43—22no—
126C2×C22⋊D43—22no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43—41no—
131C22×Dic43—21no—
132C22×Dic43—41no—
133#10621898—22no—
134#10621898—22no—
135#10621898—22no—
136#10621898—22no—
137#10621898—22no—
138#10621898—22no—
139#10621898—22no—
140#10621898—22no—
141#10621898—41no—
142#10621898—41no—
143#10621898—41no—
144#10621898—41no—
145#10621898—41no—
146#10621898—41no—
147#10621898—41no—
148#10621898—41no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C22×C412yes—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86C22×C412yes—
167M16×C43—22no—
168M16×C43—22no—
169M16×C43—22no—
170M16×C43—22no—
171M16×C43—22no—
172M16×C43—22no—
173M16×C43C22×C414yes—
174M16×C43C2×D414yes—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C42×C43—21no—
182C42×C43—22no—
183C42×C43—21no—
184C42×C43—22no—
185C42×C43C2×D412yes—
186C42×C43C2×D412yes—
187C22⋊Dic43—22no—
188C22⋊Dic43—41no—
189C4⋊Dic43—22no—
190C4⋊Dic43—41no—
191C4×Dic43—22no—
192C4×Dic43—41no—
193#10621877—22no—
194#10621877—22no—
195#10621877—22no—
196#10621877—22no—
197#10621877—22no—
198#10621877—41no—
199#10621877—41no—
200#10621877C22×C414yes—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—41no—
206C2×C43⋊C8—41no—
207C23×C43—42no—
208C23×C43#11711yescharacteristic
209C23×C43#11711yescharacteristic
210C23×C43#12311yescharacteristic
211C23×C43#12311yescharacteristic
212C23×C43#12411yescharacteristic
213C23×C43#12411yescharacteristic
214C23×C43C2×#4111yescharacteristic
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—82no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—44no—
223C2×C4×C43—44no—
224C2×C4×C43—42no—
225C2×C4×C43#11711yescharacteristic
226C2×C4×C43#11711yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43C4×D411yescharacteristic
231C2×C4×C43C4×D411yescharacteristic
232C2×C4×C43C4×D411yescharacteristic
233C2×C4×C43C4×D411yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12311yescharacteristic
240C2×C4×C43#12311yescharacteristic
241C2×C4×C43#12411yescharacteristic
242C2×C4×C43#12411yescharacteristic
243C2×C4×C43#12611yescharacteristic
244C2×C4×C43#12611yescharacteristic
245C2×C4×C43#12611yescharacteristic
246C2×C4×C43#12611yescharacteristic
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C22⋊D43—42no—
254C22⋊D43—42no—
255C22⋊D43—42no—
256C22⋊D43—42no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—82no—
262D172—22no—
263D172—22no—
264D172—41no—
265D172—41no—
266C4×D43—42no—
267C4×D43—42no—
268C4×D43—42no—
269C4×D43—42no—
270Dic86—22no—
271Dic86—22no—
272Dic86—41no—
273Dic86—41no—
274C8×C43—24no—
275C8×C43—24no—
276C43⋊C8—24no—
277C43⋊C8—42no—
278C2×#1932—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43#38811yescharacteristic
287C22×C43#38811yescharacteristic
288C22×C43#38811yescharacteristic
289C22×C43#38811yescharacteristic
290C22×C43C2×#11711yescharacteristic
291C22×C43C2×#12311yescharacteristic
292C22×C43C2×#12411yescharacteristic
293C2×D43—42no—
294C2×D43—82no—
295C2×D43—82no—
296C2×D43—82no—
297C4×C43—24no—
298C4×C43—42no—
299C4×C43#38811yescharacteristic
300C4×C43#38811yescharacteristic
301C4×C43#38811yescharacteristic
302C4×C43#38811yescharacteristic
303C4×C43C2×C4×D411yescharacteristic
304C4×C43C2×C4×D411yescharacteristic
305C4×C43C2×#12111yescharacteristic
306C4×C43C2×#12611yescharacteristic
307Dic43—42no—
308Dic43—82no—
309C2×#430—431no—
310C2×#421—431no—
311C22×#104—431no—
312C2×#413—431no—
313C2×C4×M16D4311yescharacteristic, complemented
314#1932—438no—
315C2×#344—431no—
316C2×#339—431no—
317C2×C43—21no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43#193212yescomplemented
324C2×C43C2×#38811yescharacteristic
325D43—82no—
326C22×#41—431no—
327C22×M16—431no—
328C22×M16—431no—
329C22×M16C2×D4311yescharacteristic
330C22×M16C2×D4311yescharacteristic
331C2×#117—431no—
332C22×C42C2×D4311yescharacteristic
333#430—434no—
334#430—862no—
335C2×#108—862no—
336#421—434no—
337#421—862no—
338C2×#104—434no—
339C2×#104—862no—
340C2×#104—861no—
341C2×#104—861no—
342C2×#104—862no—
343#413—434no—
344#413—434no—
345C2×#101—432no—
346C2×#100—432no—
347C4×M16—22no—
348C4×M16C2×D4314yescomplemented
349C2×#97—21no—
350C2×C4×C8—21no—
351#344—434no—
352#339—434no—
353C43C2×#193211yescharacteristic, complemented, Sylow
354C2×#41—432no—
355C2×#41—432no—
356C2×#41—861no—
357C2×#41—861no—
358C2×#41—861no—
359C2×#41—861no—
360C2×#41—861no—
361C2×#41—861no—
362C2×#41—861no—
363C2×#41—861no—
364C2×#41—861no—
365C2×#41—861no—
366C22×Q8—431no—
367C22×D4—431no—
368C22×D4—861no—
369C23×C4—21no—
370C23×C4—861no—
371C23×C4C22×D4311yescharacteristic
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—432no—
379C2×M16—432no—
380C2×M16—432no—
381C2×M16—432no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16—861no—
390C2×M16C4×D4312yes—
391C2×M16C4×D4312yes—
392C2×M16D17212yes—
393C2×M16D17212yes—
394C2×M16C22×D4312yes—
395C2×M16C22×D4312yes—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—861no—
399C22×C8—861no—
400#117—432no—
401#117—861no—
402#117—861no—
403#117—861no—
404C2×C4⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—861no—
410C2×C42C22⋊D4311yescharacteristic
411C2×C42C22⋊D4311yescharacteristic
412C2×C42C22⋊D4312yes—
413C2×C42C22×D4312yes—
414#108—868no—
415#104—868no—
416#104—864no—
417#104—864no—
418#101—438no—
419#100—438no—
420#97—24no—
421C4×C8—24no—
422C24—861no—
423C24#1062189811yescharacteristic
424#41—862no—
425#41—862no—
426#41—862no—
427#41—862no—
428#41—862no—
429#41—862no—
430#41—862no—
431#41—862no—
432#41—1721no—
433#41—1721no—
434#41—1721no—
435#41—1721no—
436#41—1721no—
437#41—1721no—
438#41—1721no—
439#41—1721no—
440C2×Q8—432no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×D4—432no—
447C2×D4—862no—
448C2×D4—862no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—1721no—
455C2×D4—1721no—
456C2×D4—1721no—
457C2×D4—1721no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—861no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—1721no—
467C22×C4—1721no—
468C22×C4—1721no—
469C22×C4—1721no—
470C22×C4—1721no—
471C22×C4C2×C4×D4311yescharacteristic
472C22×C4C2×C4×D4311yescharacteristic
473C22×C4C2×D17211yescharacteristic
474C22×C4C2×D17211yescharacteristic
475C22×C4#1062189811yescharacteristic
476C22×C4#1062189811yescharacteristic
477C22×C4#1062189811yescharacteristic
478C22×C4#1062189811yescharacteristic
479C22×C4#1062189811yescharacteristic
480C22×C4#1062189811yescharacteristic
481C22×C4#1062189811yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—434no—
492M16—862no—
493M16—862no—
494M16—862no—
495M16—862no—
496M16—862no—
497M16—1721no—
498M16—1721no—
499M16C2×C4×D4314yes—
500M16C2×D17214yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—862no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8—862no—
511C2×C8—1721no—
512C2×C8—1721no—
513C4⋊C4—862no—
514C4⋊C4—1721no—
515C22⋊C4—862no—
516C22⋊C4—1721no—
517C42—21no—
518C42—22no—
519C42—21no—
520C42—22no—
521C42—862no—
522C42—1721no—
523C42C2×C22⋊D4312yes—
524C42C2×C22⋊D4312yes—
525C23—42no—
526C23—862no—
527C23—3442no—
528C23—1721no—
529C23—1721no—
530C23#1306328211yescharacteristic
531C23#1306328211yescharacteristic
532C23#1306330811yescharacteristic
533C23#1306330811yescharacteristic
534C23#1306331311yescharacteristic
535C23#1306331311yescharacteristic
536C23C2×#1062189811yescharacteristic
537Q8—862no—
538Q8—862no—
539Q8—1721no—
540Q8—1721no—
541D4—862no—
542D4—862no—
543D4—1722no—
544D4—1722no—
545D4—1722no—
546D4—1722no—
547D4—1721no—
548D4—1721no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—862no—
556C2×C4—3442no—
557C2×C4—1722no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4#1306328211yescharacteristic
565C2×C4#1306328211yescharacteristic
566C2×C4C4×C22⋊D4311yescharacteristic
567C2×C4C4×C22⋊D4311yescharacteristic
568C2×C4C4×C22⋊D4311yescharacteristic
569C2×C4C4×C22⋊D4311yescharacteristic
570C2×C4C4×D17211yescharacteristic
571C2×C4C4×D17211yescharacteristic
572C2×C4C4×D17211yescharacteristic
573C2×C4C4×D17211yescharacteristic
574C2×C4#1306329911yescharacteristic
575C2×C4#1306329911yescharacteristic
576C2×C4#1306329911yescharacteristic
577C2×C4#1306329911yescharacteristic
578C2×C4#1306330811yescharacteristic
579C2×C4#1306330811yescharacteristic
580C2×C4#1306331311yescharacteristic
581C2×C4#1306331311yescharacteristic
582C2×C4#1306331911yescharacteristic
583C2×C4#1306331911yescharacteristic
584C2×C4#1306331911yescharacteristic
585C2×C4#1306331911yescharacteristic
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C22×C22⋊D4311yescharacteristic
588C2×C4C22×D17211yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4C2×#1062189811yescharacteristic
591C2×C4C2×#1062189811yescharacteristic
592C8—24no—
593C8—24no—
594C8—864no—
595C8—1722no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—3442no—
604C22—3442no—
605C22—3442no—
606C22—1722no—
607C22#1458279011yescharacteristic
608C22#1458279011yescharacteristic
609C22#1458279011yescharacteristic
610C22#1458279011yescharacteristic
611C22C2×#1306328211yescharacteristic
612C22C2×#1306330811yescharacteristic
613C22C2×#1306331311yescharacteristic
614C4—24no—
615C4—42no—
616C4—3442no—
617C4—1722no—
618C4#1458279011yescharacteristic
619C4#1458279011yescharacteristic
620C4#1458279011yescharacteristic
621C4#1458279011yescharacteristic
622C4C2×C4×C22⋊D4311yescharacteristic
623C4C2×C4×D17211yescharacteristic
624C4C2×#1306329911yescharacteristic
625C4C2×#1306331911yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—3442no—
633C2#1913526412yesdirect product factor
634C2C2×#1458279011yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×M16×C43C2
socleC22×C43#388
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×C4×M16D43
hypocenterC43C2×#1932
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#14582947C2semidirect
5. #19135264C2direct (N × H)
6. C2×#14582671C2semidirect
7. C2×#14582659C2semidirect
8. C2×C4×M16×C43C2semidirect
14. #14582947C22semidirect
23. #14582881C4semidirect
25. C2×#13063243C4semidirect
26. C2×#13063241C4semidirect
27. #14582671C22semidirect
28. #14582659C22semidirect
33. C4×M16×C43C22semidirect
77. #13063243C2×C4semidirect
78. #13063241C2×C4semidirect
313. C2×C4×M16D43semidirect
323. C2×C43#1932semidirect
348. C4×M16C2×D43semidirect
353. C43C2×#1932semidirect
633. C2#19135264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145829472
C2×#145829152
C22×#130632532
C2×#145828812
#191352642
C2×#145826712
C2×#145826592
C2×C4×M16×C432
C2×#193243