Finite Group Databasebeta

← C2×#19134963 #25098086

Subgroups — C2×#19134963 #25098086

Order 11008.

1802 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063358C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic
3C22×#13063251C211yesmaximal, characteristic
4C2×#14582909C211yesmaximal, characteristic, complemented
5C2×#14582804C211yesmaximal, characteristic, complemented
6#19134963C218yesmaximal, direct product factor
7C2×#14582660C211yesmaximal, characteristic, complemented
8C2×C43×#343C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×Dic86C2211yescharacteristic
11C2×#13063358—24no—
12C2×#13063358—22no—
13C2×#13063358C418yescomplemented
14C2×#13063358C2214yes—
15C22×Dic172—21no—
16C22×#10621873—21no—
17#14583380—22no—
18#14583380—22no—
19#14583380—22no—
20#14583380C2214yes—
21C2×#13063290—21no—
22C2×#13063287—21no—
23C2×C4×C22⋊D43—22no—
24C2×#13063284C2211yescharacteristic
25C2×#13063283—21no—
26C2×C4⋊C4×D43—21no—
27C22×C4×Dic43C2211yescharacteristic
28C2×#13063251—24no—
29C2×#13063251C2214yes—
30#14582909—22no—
31#14582909C2214yescomplemented
32C2×#13063250—21no—
33C2×#13063250—21no—
34#14582804—22no—
35#14582804C2214yescomplemented
36C2×C43⋊#95—22no—
37#14582660C2214yescomplemented
38C22×M16×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C22×C4⋊C4×C43C2211yescharacteristic
41C43×#343C2214yescomplemented
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898C2×C414yes—
47C2×#10621898D414yes—
48C2×#10621898D412yes—
49C2×#10621898C2312yes—
50C22×Dic86—21no—
51C22×Dic86—21no—
52C22×Dic86—21no—
53C22×Dic86—22no—
54C22×Dic86—21no—
55C22×Dic86—22no—
56C22×Dic86—21no—
57C22×Dic86—22no—
58C22×Dic86C2×C414yescomplemented
59C22×Dic86D411yescharacteristic
60C22×Dic86C2312yes—
61C22×D172D411yescharacteristic
62C22×C22⋊D43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—22no—
67#13063358—216no—
68#13063358—28no—
69#13063358C2×C4116yescomplemented
70C2×Dic172—28no—
71C2×Dic172—24no—
72C2×#10621873—28no—
73C2×#10621873—24no—
74#13063290—24no—
75#13063290—24no—
76#13063287—24no—
77#13063287—24no—
78C4×C22⋊D43—28no—
79C4×C22⋊D43—28no—
80#13063284—21no—
81#13063284—21no—
82#13063284D412yes—
83#13063284C2312yes—
84#13063283—24no—
85#13063283—24no—
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43D411yescharacteristic
88C2×Dic43⋊C4—22no—
89C4⋊C4×D43—24no—
90C4⋊C4×D43—24no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—22no—
93C2×C4×Dic43—22no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2312yes—
99#13063251—28no—
100#13063250—24no—
101#13063250—24no—
102C43⋊#95—28no—
103C23×C4×C43D412yes—
104C23×C4×C43C2311yescharacteristic
105C2×M16×C43—22no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43—22no—
109C2×M16×C43—22no—
110C2×M16×C43C2×C414yescomplemented
111C2×M16×C43C2312yes—
112C2×M16×C43C2312yes—
113C22×C8×C43—21no—
114C22×C8×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43D412yes—
120C2×C4⋊C4×C43C2312yes—
121C24×C43C2×D411yescharacteristic
122C23×D43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—44no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D414yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43#4112yes—
135C22×C4×C43#4112yes—
136C22×C4×C43C2411yescharacteristic
137C2×C22⋊D43—24no—
138C2×C22⋊D43—22no—
139C2×C22⋊D43—24no—
140C2×C22⋊D43—22no—
141C22×Dic43—24no—
142C22×Dic43—24no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153#10621898—24no—
154#10621898—24no—
155#10621898—24no—
156#10621898—24no—
157#10621898—24no—
158#10621898—22no—
159#10621898—22no—
160#10621898C22⋊C418yes—
161#10621898C22×C414yes—
162#10621898C2×D414yes—
163C2×D172—21no—
164C2×D172—22no—
165C2×D172C22⋊C414yes—
166C2×D172C2×D412yes—
167C2×C4×D43—24no—
168C2×C4×D43—22no—
169C2×C4×D43—24no—
170C2×C4×D43—22no—
171C2×C4×D43—28no—
172C2×C4×D43—84no—
173C2×Dic86—21no—
174C2×Dic86—22no—
175C2×Dic86—24no—
176C2×Dic86—24no—
177C2×Dic86—24no—
178C2×Dic86—24no—
179C2×Dic86—22no—
180C2×Dic86—22no—
181C2×Dic86—22no—
182C2×Dic86—22no—
183C2×Dic86—24no—
184C2×Dic86—22no—
185C2×Dic86—41no—
186C2×Dic86—41no—
187C2×Dic86—42no—
188C2×Dic86—42no—
189C2×Dic86—42no—
190C2×Dic86—42no—
191C2×Dic86—42no—
192C2×Dic86C22⋊C414yes—
193C2×Dic86C22×C414yescomplemented
194C2×Dic86C2×D412yes—
195M16×C43—24no—
196M16×C43—22no—
197M16×C43—22no—
198M16×C43—22no—
199M16×C43—42no—
200M16×C43C22×C414yescomplemented
201C2×C8×C43—24no—
202C2×C8×C43—22no—
203C2×C8×C43—22no—
204C2×C8×C43—42no—
205C4⋊C4×C43—22no—
206C4⋊C4×C43—22no—
207C4⋊C4×C43—22no—
208C4⋊C4×C43—22no—
209C22⋊Dic43—22no—
210C22⋊Dic43—22no—
211(C2×D43)⋊C4—28no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C2×D412yes—
215C4⋊Dic43C2×D412yes—
216Dic43⋊C4—28no—
217C4×Dic43—28no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—42no—
223Dic172—216no—
224#10621873—216no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43C4×D412yes—
228C23×C43#12011yescharacteristic
229C23×C43#12011yescharacteristic
230C23×C43#12112yes—
231C23×C43C22×D411yescharacteristic
232C22×D43—22no—
233C22×D43—24no—
234C22×D43—42no—
235C22×D43—42no—
236C2×C4×C43—24no—
237C2×C4×C43—44no—
238C2×C4×C43—44no—
239C2×C4×C43—82no—
240C2×C4×C43C2×C22⋊C412yes—
241C2×C4×C43C2×C22⋊C412yes—
242C2×C4×C43C4×D412yes—
243C2×C4×C43C4×D412yes—
244C2×C4×C43C4×D412yes—
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12112yes—
248C2×C4×C43#12112yes—
249C2×C4×C43#12112yes—
250C2×C4×C43#12312yes—
251C2×C4×C43#12312yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C22⋊D43—24no—
259C22⋊D43—24no—
260C22⋊D43—28no—
261C2×Dic43—22no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—24no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—48no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—44no—
273C2×Dic43—44no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276D172—22no—
277D172—24no—
278D172C2×C22⋊C414yes—
279C4×D43—24no—
280C4×D43—24no—
281C4×D43—28no—
282C4×D43—88no—
283Dic86—22no—
284Dic86—24no—
285Dic86—24no—
286Dic86—24no—
287Dic86—42no—
288Dic86—42no—
289Dic86—44no—
290Dic86—44no—
291Dic86C2×C22⋊C414yes—
292C8×C43—24no—
293C8×C43—42no—
294C2×#1882—431nomaximal, Sylow
295C22×C43—24no—
296C22×C43—24no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43#38612yes—
302C22×C43#38612yes—
303C22×C43#45512yes—
304C22×C43#45612yes—
305C22×C43C2×C4×D411yescharacteristic
306C22×C43C2×#12011yescharacteristic
307C22×C43C2×#12111yescharacteristic
308C2×D43—24no—
309C2×D43—48no—
310C2×D43—42no—
311C2×D43—42no—
312C4×C43—44no—
313C4×C43#38612yes—
314C4×C43#38612yes—
315C4×C43C22×C22⋊C411yescharacteristic
316C4×C43C2×C4×D411yescharacteristic
317C4×C43C2×#12111yescharacteristic
318C4×C43C2×#12311yescharacteristic
319Dic43—24no—
320Dic43—44no—
321Dic43—42no—
322Dic43—42no—
323Dic43—44no—
324C22×#137—431no—
325C2×#520—431no—
326C22×#104—431no—
327C2×#419—431no—
328C2×#391—431no—
329#1882—438no—
330C2×#343D4311yescharacteristic, complemented
331C2×#339—431no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—22no—
335C2×C43#188214yescomplemented
336C2×C43C2×#38611yescharacteristic
337C2×C43C2×#45511yescharacteristic
338C2×C43C2×#45611yescharacteristic
339D43—44no—
340C22×#41—431no—
341C23×Q8—431no—
342C2×#137—434no—
343C2×#137—438no—
344C2×#137—862no—
345C2×#137—864no—
346C22×Q16—861no—
347C22×SD16—861no—
348C22×M16C2×D4311yescharacteristic
349C22×M16C2×D4311yescharacteristic
350#520—434no—
351#520—862no—
352#520—862no—
353#520—862no—
354C2×C4×Q8—861no—
355C2×C4×D4—861no—
356C2×C4×D4—862no—
357C2×#117—431no—
358C2×#117—861no—
359C22×C4⋊C4—861no—
360C22×C4⋊C4C2×D4311yescharacteristic
361C22×C42—431no—
362C2×#104—434no—
363C2×#104—864no—
364#419—434no—
365#419—862no—
366C2×#103—861no—
367C2×#103—861no—
368#391—434no—
369#391—862no—
370C2×#95—862no—
371#343C2×D4314yescomplemented
372#339—434no—
373C43C2×#188211yescharacteristic, complemented, Sylow
374C2×#41—434no—
375C2×#41—432no—
376C2×#41—434no—
377C2×#41—432no—
378C2×#41—861no—
379C2×#41—862no—
380C2×#41—861no—
381C2×#41—862no—
382C22×Q8—434no—
383C22×Q8—431no—
384C22×Q8—432no—
385C22×Q8—861no—
386C22×Q8—862no—
387C22×Q8—861no—
388C22×Q8—861no—
389C22×Q8—862no—
390C22×Q8—861no—
391C22×Q8—861no—
392C22×Q8—862no—
393C22×D4—431no—
394C22×D4—861no—
395C23×C4—862no—
396C23×C4—861no—
397C23×C4—861no—
398C23×C4—861no—
399C23×C4D17212yes—
400C23×C4C22×D4311yescharacteristic
401#137—4316no—
402#137—8616no—
403#137—868no—
404C2×Q16—868no—
405C2×Q16—864no—
406C2×SD16—868no—
407C2×SD16—864no—
408C2×M16—22no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C4×D4314yescomplemented
414C2×M16C22×D4312yes—
415C2×M16C22×D4312yes—
416C22×C8—21no—
417C22×C8—21no—
418C4×Q8—864no—
419C4×Q8—864no—
420C4×D4—864no—
421C4×D4—864no—
422C4×D4—868no—
423C4×D4—868no—
424#117—432no—
425#117—432no—
426#117—864no—
427#117—864no—
428#117—861no—
429#117—861no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—864no—
437C2×C4⋊C4—864no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4D17212yes—
440C2×C4⋊C4C22×D4312yes—
441C2×C22⋊C4—862no—
442C2×C22⋊C4—861no—
443C2×C42—432no—
444C2×C42—862no—
445C2×C42—861no—
446C2×C42—862no—
447C2×C42—862no—
448C2×C42—861no—
449#104—868no—
450#103—864no—
451#103—864no—
452#95—868no—
453C24—861no—
454C24C2×D17211yescharacteristic
455#41—438no—
456#41—434no—
457#41—434no—
458#41—864no—
459#41—864no—
460#41—864no—
461#41—864no—
462#41—864no—
463#41—862no—
464#41—862no—
465C2×Q8—434no—
466C2×Q8—434no—
467C2×Q8—432no—
468C2×Q8—864no—
469C2×Q8—861no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8—864no—
473C2×Q8—864no—
474C2×Q8—864no—
475C2×Q8—864no—
476C2×Q8—862no—
477C2×Q8—862no—
478C2×Q8—862no—
479C2×Q8—862no—
480C2×Q8—1721no—
481C2×Q8—1721no—
482C2×Q8—1722no—
483C2×Q8—1722no—
484C2×Q8—1722no—
485C2×Q8—1722no—
486C2×Q8—1722no—
487C2×D4—434no—
488C2×D4—432no—
489C2×D4—864no—
490C2×D4—862no—
491C2×D4—864no—
492C2×D4—862no—
493C2×D4—861no—
494C2×D4—862no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—44no—
498C22×C4—868no—
499C22×C4—861no—
500C22×C4—864no—
501C22×C4—862no—
502C22×C4—864no—
503C22×C4—862no—
504C22×C4—864no—
505C22×C4—864no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—3444no—
511C22×C4—1722no—
512C22×C4—1721no—
513C22×C4—1721no—
514C22×C4—1722no—
515C22×C4—1722no—
516C22×C4C2×C4×D4312yes—
517C22×C4C2×D17214yes—
518C22×C4C2×D17211yescharacteristic
519C22×C4#1062189812yes—
520C22×C4D4×D4311yescharacteristic
521C22×C4D4×D4311yescharacteristic
522C22×C4D4×D4312yes—
523C22×C4D4×D4311yescharacteristic
524C22×C4D4×D4311yescharacteristic
525C22×C4#1062190212yes—
526C22×C4C23×D4311yescharacteristic
527Q16—8616no—
528SD16—8616no—
529M16—24no—
530M16—22no—
531M16—22no—
532M16—22no—
533M16—42no—
534M16C2×C4×D4314yescomplemented
535C2×C8—24no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—42no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—432no—
544C4⋊C4—432no—
545C4⋊C4—868no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C22⋊C4—868no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C42—868no—
552C42—862no—
553C42—862no—
554C42—862no—
555C42—862no—
556C42—1722no—
557C23—22no—
558C23—22no—
559C23—862no—
560C23—864no—
561C23—1722no—
562C23—1722no—
563C23C4×D17212yes—
564C23#1306329511yescharacteristic
565C23#1306329511yescharacteristic
566C23#1306330012yes—
567C23C22×D17211yescharacteristic
568Q8—434no—
569Q8—862no—
570Q8—864no—
571Q8—864no—
572Q8—864no—
573Q8—1722no—
574Q8—1722no—
575Q8—1724no—
576Q8—1724no—
577D4—434no—
578D4—864no—
579D4—864no—
580D4—868no—
581D4—862no—
582D4—864no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—82no—
587C2×C4—862no—
588C2×C4—864no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—868no—
592C2×C4—864no—
593C2×C4—864no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—3448no—
597C2×C4—1728no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1724no—
605C2×C4—1724no—
606C2×C4C22⋊C4×D4312yes—
607C2×C4C22⋊C4×D4312yes—
608C2×C4#1306328712yes—
609C2×C4#1306328712yes—
610C2×C4C4×D17212yes—
611C2×C4#1306329511yescharacteristic
612C2×C4#1306329511yescharacteristic
613C2×C4#1306329812yes—
614C2×C4#1306329812yes—
615C2×C4#1306330012yes—
616C2×C4#1306331012yes—
617C2×C4#1306331012yes—
618C2×C4C22×C4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C2×C4C2×D4×D4311yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4C2×#1062189811yescharacteristic
623C2×C4C2×#1062190211yescharacteristic
624C8—24no—
625C8—42no—
626C22—21no—
627C22—21no—
628C22—24no—
629C22—24no—
630C22—21no—
631C22—21no—
632C22—864no—
633C22—1722no—
634C22—1728no—
635C22—1722no—
636C22#1458277712yes—
637C22#1458277712yes—
638C22#1458307912yes—
639C22#1458308412yes—
640C22C2×C4×D17211yescharacteristic
641C22C2×#1306329511yescharacteristic
642C22C2×#1306330011yescharacteristic
643C4—44no—
644C4—864no—
645C4—1724no—
646C4—1722no—
647C4—1724no—
648C4—1722no—
649C4#1458277712yes—
650C4#1458277712yes—
651C4C2×C22⋊C4×D4311yescharacteristic
652C4C2×#1306328711yescharacteristic
653C4C2×#1306329811yescharacteristic
654C4C2×#1306331011yescharacteristic
655C2—21no—
656C2—21no—
657C2—22no—
658C2—1724no—
659C2#1913496314yesdirect product factor
660C2C2×#1458277711yescharacteristic
661C2C2×#1458307911yescharacteristic
662C2C2×#1458308411yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#343C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#343D43
hypocenterC43C2×#1882
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×#14582909C2semidirect
5. C2×#14582804C2semidirect
6. #19134963C2direct (N × H)
7. C2×#14582660C2semidirect
8. C2×C43×#343C2semidirect
13. C2×#13063358C4semidirect
31. #14582909C22semidirect
35. #14582804C22semidirect
37. #14582660C22semidirect
41. C43×#343C22semidirect
58. C22×Dic86C2×C4semidirect
69. #13063358C2×C4semidirect
110. C2×M16×C43C2×C4semidirect
193. C2×Dic86C22×C4semidirect
200. M16×C43C22×C4semidirect
330. C2×#343D43semidirect
335. C2×C43#1882semidirect
371. #343C2×D43semidirect
373. C43C2×#1882semidirect
413. C2×M16C4×D43semidirect
534. M16C2×C4×D43semidirect
659. C2#19134963direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633582
C2×#145833802
C22×#130632512
C2×#145829092
C2×#145828042
#191349632
C2×#145826602
C2×C43×#3432
C2×#188243