Finite Group Databasebeta

← C2×#19135263 #25099177

Subgroups — C2×#19135263 #25099177

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×#14582915C211yesmaximal, characteristic
2C22×#13063251C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4C2×M16×Dic43C211yesmaximal, characteristic, complemented
5#19135263C218yesmaximal, direct product factor
6C2×#14582670C211yesmaximal, characteristic, complemented
7C2×#14582660C211yesmaximal, characteristic, complemented
8C2×C43×#430C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12C22×C4×Dic43C2211yescharacteristic
13#14582915—22no—
14#14582915C2214yes—
15C2×#13063251—21no—
16C2×#13063251—21no—
17C2×#13063251—22no—
18C2×#13063251—22no—
19C2×#13063251C2214yes—
20#14582881C414yescomplemented
21#14582881C2214yes—
22C2×#13063243C412yescomplemented
23C2×#13063241C412yescomplemented
24M16×Dic43—22no—
25M16×Dic43C2214yescomplemented
26C2×#13063235—21no—
27C2×C8×Dic43—21no—
28#14582670C2214yescomplemented
29#14582660C2214yescomplemented
30C22×M16×C43C2211yescharacteristic
31C22×M16×C43C2211yescharacteristic
32C22×M16×C43C2211yescharacteristic
33C43×#430—22no—
34C43×#430C2214yescomplemented
35C2×#108×C43—22no—
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—
51C23×Dic43—21no—
52C22×C4×D43—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877C2×C412yes—
57C2×#10621877C2×C412yes—
58C2×#10621877C2312yes—
59C22×C43⋊C8—21no—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284C2312yes—
64C2×C4⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43D411yescharacteristic
71C2×C4×Dic43D411yescharacteristic
72C2×C4×Dic43D412yes—
73C2×C4×Dic43C2312yes—
74#13063251—28no—
75#13063251—24no—
76#13063251—24no—
77#13063243C2×C418yescomplemented
78#13063241C2×C418yescomplemented
79#13063235—24no—
80C8×Dic43—24no—
81C23×C4×C43C2311yescharacteristic
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43C2×C412yes—
94C2×M16×C43C2×C412yes—
95C2×M16×C43D412yes—
96C2×M16×C43D412yes—
97C2×M16×C43C2312yes—
98C2×M16×C43C2312yes—
99C2×M16×C43C2312yes—
100C22×C8×C43—21no—
101C22×C8×C43—21no—
102C22×C8×C43—21no—
103#108×C43—28no—
104C24×C43#4111yescharacteristic
105C23×D43—21no—
106C22×C4×C43C22×C411yescharacteristic
107C22×C4×C43C22×C411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43C2411yescharacteristic
120C2×C22⋊D43—22no—
121C2×C22⋊D43—22no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—44no—
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×C43—22no—
174M16×C43—22no—
175M16×C43—41no—
176M16×C43—41no—
177M16×C43C22×C414yes—
178M16×C43C2×D414yes—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C2×C8×C43—22no—
186C2×C8×C43—41no—
187C2×C8×C43—41no—
188C22⋊Dic43—22no—
189C22⋊Dic43—41no—
190C4⋊Dic43—22no—
191C4⋊Dic43—41no—
192C4×Dic43—21no—
193C4×Dic43—22no—
194C4×Dic43—21no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C4×Dic43—41no—
198C4×Dic43C2×D412yes—
199C4×Dic43C2×D412yes—
200#10621877—22no—
201#10621877—22no—
202#10621877—22no—
203#10621877C22×C414yes—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
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#11711yescharacteristic
220C2×C4×C43#11711yescharacteristic
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12311yescharacteristic
234C2×C4×C43#12311yescharacteristic
235C2×C4×C43#12411yescharacteristic
236C2×C4×C43#12411yescharacteristic
237C2×C4×C43#12611yescharacteristic
238C2×C4×C43#12611yescharacteristic
239C2×C4×C43#12611yescharacteristic
240C2×C4×C43#12611yescharacteristic
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—42no—
248C22⋊D43—42no—
249C22⋊D43—42no—
250C22⋊D43—42no—
251C2×Dic43—24no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—44no—
256C2×Dic43—44no—
257C2×Dic43—42no—
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—
276C8×C43—42no—
277C43⋊C8—24no—
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#38811yescharacteristic
298C4×C43#38811yescharacteristic
299C4×C43#38811yescharacteristic
300C4×C43#38811yescharacteristic
301C4×C43C2×C4×D411yescharacteristic
302C4×C43C2×C4×D411yescharacteristic
303C4×C43C2×#12111yescharacteristic
304C4×C43C2×#12611yescharacteristic
305Dic43—24no—
306Dic43—42no—
307Dic43—42no—
308Dic43—82no—
309C2×#430D4311yescharacteristic, complemented
310C2×#421—431no—
311C22×#104—431no—
312C2×#413—431no—
313C2×C4×M16—431no—
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×M16C2×D4311yescharacteristic
329C22×M16C2×D4311yescharacteristic
330C22×M16C2×D4311yescharacteristic
331C2×#117—431no—
332C22×C42—431no—
333#430—22no—
334#430C2×D4314yescomplemented
335C2×#108—22no—
336#421—434no—
337#421—862no—
338C2×#104—434no—
339C2×#104—861no—
340C2×#104—861no—
341C2×#104—862no—
342C2×#104—862no—
343#413—434no—
344#413—434no—
345C2×#101—432no—
346C2×#100—432no—
347C4×M16—434no—
348C4×M16—862no—
349C2×#97—861no—
350C2×C4×C8—861no—
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—861no—
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—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—432no—
384C2×M16—432no—
385C2×M16—432no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16C4×D4312yes—
390C2×M16C4×D4312yes—
391C2×M16C22⋊D4312yes—
392C2×M16C22⋊D4312yes—
393C2×M16C22×D4312yes—
394C2×M16C22×D4312yes—
395C2×M16C22×D4312yes—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—21no—
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—431no—
407C2×C42—431no—
408C2×C42—432no—
409C2×C42—432no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—861no—
414#108—28no—
415#104—864no—
416#104—864no—
417#104—868no—
418#101—438no—
419#100—438no—
420#97—864no—
421C4×C8—864no—
422C24—861no—
423C24#1062190211yescharacteristic
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—861no—
459C22×C4—861no—
460C22×C4—862no—
461C22×C4—861no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—1724no—
466C22×C4—1721no—
467C22×C4—1721no—
468C22×C4—1721no—
469C22×C4—1721no—
470C22×C4—1721no—
471C22×C4C2×C4×D4311yescharacteristic
472C22×C4C2×C4×D4311yescharacteristic
473C22×C4#1062189811yescharacteristic
474C22×C4#1062189811yescharacteristic
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4#1062190011yescharacteristic
478C22×C4#1062190011yescharacteristic
479C22×C4#1062190211yescharacteristic
480C22×C4#1062190211yescharacteristic
481C22×C4#1062190211yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—22no—
492M16—22no—
493M16—41no—
494M16—41no—
495M16—434no—
496M16—862no—
497M16—862no—
498M16—862no—
499M16C2×C4×D4314yes—
500M16C2×C22⋊D4314yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—862no—
511C2×C8—862no—
512C2×C8—862no—
513C4⋊C4—862no—
514C4⋊C4—1721no—
515C22⋊C4—862no—
516C22⋊C4—1721no—
517C42—432no—
518C42—432no—
519C42—861no—
520C42—862no—
521C42—861no—
522C42—862no—
523C42—862no—
524C42—1721no—
525C23—42no—
526C23—862no—
527C23—3442no—
528C23—1721no—
529C23—1721no—
530C23#1306328311yescharacteristic
531C23#1306328311yescharacteristic
532C23#1306331011yescharacteristic
533C23#1306331011yescharacteristic
534C23#1306331411yescharacteristic
535C23#1306331411yescharacteristic
536C23C2×#1062190211yescharacteristic
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—864no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—3442no—
554C2×C4—1724no—
555C2×C4—1724no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4#1306328311yescharacteristic
565C2×C4#1306328311yescharacteristic
566C2×C4C4×C22⋊D4311yescharacteristic
567C2×C4C4×C22⋊D4311yescharacteristic
568C2×C4C4×C22⋊D4311yescharacteristic
569C2×C4C4×C22⋊D4311yescharacteristic
570C2×C4#1306328711yescharacteristic
571C2×C4#1306328711yescharacteristic
572C2×C4#1306328711yescharacteristic
573C2×C4#1306328711yescharacteristic
574C2×C4#1306329711yescharacteristic
575C2×C4#1306329711yescharacteristic
576C2×C4#1306329711yescharacteristic
577C2×C4#1306329711yescharacteristic
578C2×C4#1306331011yescharacteristic
579C2×C4#1306331011yescharacteristic
580C2×C4#1306331411yescharacteristic
581C2×C4#1306331411yescharacteristic
582C2×C4#1306332011yescharacteristic
583C2×C4#1306332011yescharacteristic
584C2×C4#1306332011yescharacteristic
585C2×C4#1306332011yescharacteristic
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C22×C22⋊D4311yescharacteristic
589C2×C4C2×#1062190011yescharacteristic
590C2×C4C2×#1062189811yescharacteristic
591C2×C4C2×#1062190211yescharacteristic
592C8—24no—
593C8—24no—
594C8—42no—
595C8—864no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—3442no—
604C22—3442no—
605C22—3442no—
606C22—1722no—
607C22#1458278911yescharacteristic
608C22#1458278911yescharacteristic
609C22#1458278911yescharacteristic
610C22#1458278911yescharacteristic
611C22C2×#1306328311yescharacteristic
612C22C2×#1306331011yescharacteristic
613C22C2×#1306331411yescharacteristic
614C4—864no—
615C4—3442no—
616C4—1722no—
617C4—1722no—
618C4#1458278911yescharacteristic
619C4#1458278911yescharacteristic
620C4#1458278911yescharacteristic
621C4#1458278911yescharacteristic
622C4C2×C4×C22⋊D4311yescharacteristic
623C4C2×#1306328711yescharacteristic
624C4C2×#1306329711yescharacteristic
625C4C2×#1306332011yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—3442no—
633C2#1913526312yesdirect product factor
634C2C2×#1458278911yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#430C2
socleC22×C43#388
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#430D43
hypocenterC43C2×#1932
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
4. C2×M16×Dic43C2semidirect
5. #19135263C2direct (N × H)
6. C2×#14582670C2semidirect
7. C2×#14582660C2semidirect
8. C2×C43×#430C2semidirect
20. #14582881C4semidirect
22. C2×#13063243C4semidirect
23. C2×#13063241C4semidirect
25. M16×Dic43C22semidirect
28. #14582670C22semidirect
29. #14582660C22semidirect
34. C43×#430C22semidirect
77. #13063243C2×C4semidirect
78. #13063241C2×C4semidirect
309. C2×#430D43semidirect
323. C2×C43#1932semidirect
334. #430C2×D43semidirect
353. C43C2×#1932semidirect
633. C2#19135263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145829152
C22×#130632512
C2×#145828812
C2×M16×Dic432
#191352632
C2×#145826702
C2×#145826602
C2×C43×#4302
C2×#193243