Finite Group Databasebeta

← C2×#19134821 #25097451

Subgroups — C2×#19134821 #25097451

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C211yesmaximal, characteristic, complemented
2C22×#13063252C211yesmaximal, characteristic
3C2×#14582900C211yesmaximal, characteristic
4C2×#14582768C211yesmaximal, characteristic, complemented
5#19134821C218yesmaximal, direct product factor
6C2×#14582668C211yesmaximal, characteristic, complemented
7C2×#14582658C211yesmaximal, characteristic, complemented
8C2×C43×#520C211yesmaximal, characteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×Dic43⋊C4—22no—
13C22×C4×Dic43C2211yescharacteristic
14#14582942—22no—
15#14582942C2214yescomplemented
16C2×#13063258—21no—
17C2×#13063256—21no—
18C2×#13063252C418yescomplemented
19C2×#13063252C2214yes—
20#14582900—22no—
21#14582900C2214yes—
22C2×#13063249—21no—
23C2×#13063246—21no—
24#14582768—22no—
25#14582768C2214yescomplemented
26#14582668C2214yescomplemented
27#14582658C2214yescomplemented
28C22×#41×C43C2211yescharacteristic
29C43×#520—22no—
30C43×#520—22no—
31C43×#520—22no—
32C43×#520C2214yes—
33C2×C4×Q8×C43—21no—
34C2×C4×D4×C43—21no—
35C2×C4×D4×C43—22no—
36C2×#117×C43—21no—
37C2×#117×C43C2211yescharacteristic
38C22×C4⋊C4×C43—21no—
39C22×C4⋊C4×C43C2211yescharacteristic
40C23×Dic43—21no—
41C23×Dic43—21no—
42C2×#10621877—21no—
43C2×#10621877—22no—
44C2×#10621877—21no—
45C2×#10621877—22no—
46C2×#10621877—22no—
47C2×#10621877C2×C414yescomplemented
48C2×#10621877C2312yes—
49C2×#10621877C2312yes—
50C22×C43⋊C8—21no—
51C22×C43⋊C8—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43C2312yes—
58C2×Dic43⋊C4—28no—
59C2×Dic43⋊C4—48no—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—22no—
62C2×C4×Dic43C2×C414yescomplemented
63C2×C4×Dic43C2312yes—
64#13063258—24no—
65#13063256—24no—
66#13063252C2×C4116yescomplemented
67#13063249—24no—
68#13063246—24no—
69C2×#41×C43—21no—
70C2×#41×C43—21no—
71C2×#41×C43—22no—
72C2×#41×C43—22no—
73C2×#41×C43C2×C414yes—
74C2×#41×C43D412yes—
75C2×#41×C43Q814yes—
76C2×#41×C43C2312yes—
77C22×Q8×C43D411yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43D411yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43—22no—
82C23×C4×C43D412yes—
83C23×C4×C43C2311yescharacteristic
84C4×Q8×C43—24no—
85C4×Q8×C43—24no—
86C4×D4×C43—28no—
87C4×D4×C43—24no—
88C4×D4×C43—24no—
89C4×D4×C43—28no—
90#117×C43—24no—
91#117×C43—21no—
92#117×C43—21no—
93#117×C43—24no—
94#117×C43D412yes—
95#117×C43C2312yes—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—24no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—24no—
103C2×C4⋊C4×C43D412yes—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43—22no—
110C2×C42×C43—21no—
111C24×C43—21no—
112C24×C43C2×D411yescharacteristic
113#41×C43—24no—
114#41×C43—24no—
115#41×C43—24no—
116#41×C43—24no—
117#41×C43—24no—
118#41×C43—22no—
119#41×C43—22no—
120#41×C43C4⋊C418yescomplemented
121#41×C43C22×C414yes—
122#41×C43C2×Q814yes—
123C2×Q8×C43—21no—
124C2×Q8×C43—22no—
125C2×Q8×C43C4⋊C414yescomplemented
126C2×Q8×C43C2×D412yes—
127C2×D4×C43—21no—
128C2×D4×C43—22no—
129C2×D4×C43—24no—
130C2×D4×C43—22no—
131C2×D4×C43—24no—
132C2×D4×C43—22no—
133C2×D4×C43C4⋊C414yescomplemented
134C2×D4×C43C2×D412yes—
135C22×C4×C43—24no—
136C22×C4×C43—22no—
137C22×C4×C43—24no—
138C22×C4×C43—22no—
139C22×C4×C43—28no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—44no—
146C22×C4×C43—84no—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D414yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×Q812yes—
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—24no—
159C22×Dic43—24no—
160C22×Dic43—24no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—44no—
164C22×Dic43—41no—
165C22×Dic43—41no—
166C4⋊C4×C43—28no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43C2×D412yes—
174C4⋊C4×C43C2×D412yes—
175C22⋊C4×C43—28no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C42×C43—28no—
179C42×C43—22no—
180C42×C43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43—22no—
183C4⋊Dic43—41no—
184C4⋊Dic43—41no—
185Dic43⋊C4—416no—
186C4×Dic43—24no—
187C4×Dic43—22no—
188C4×Dic43C22×C414yescomplemented
189#10621877—24no—
190#10621877—22no—
191#10621877—22no—
192#10621877—22no—
193#10621877—42no—
194#10621877C22×C414yescomplemented
195C2×C43⋊C8—24no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—42no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—24no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43C4×D412yes—
206C23×C43#12011yescharacteristic
207C23×C43#12011yescharacteristic
208C23×C43C22⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210Q8×C43—22no—
211Q8×C43—24no—
212Q8×C43C2×C4⋊C414yescomplemented
213D4×C43—24no—
214D4×C43—24no—
215D4×C43—28no—
216D4×C43—22no—
217D4×C43—24no—
218D4×C43C2×C4⋊C414yescomplemented
219C2×C4×C43—22no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—28no—
224C2×C4×C43—22no—
225C2×C4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—44no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—44no—
231C2×C4×C43—82no—
232C2×C4×C43—88no—
233C2×C4×C43C2×C4⋊C412yes—
234C2×C4×C43C2×C4⋊C412yes—
235C2×C4×C43C4×D412yes—
236C2×C4×C43C4×D412yes—
237C2×C4×C43C4×D412yes—
238C2×C4×C43#12011yescharacteristic
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43C22⋊Q812yes—
241C2×C4×C43C22⋊Q812yes—
242C2×C4×C43C22⋊Q812yes—
243C2×C4×C43#12312yes—
244C2×C4×C43#12312yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×Q811yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×Dic43—24no—
252C2×Dic43—216no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—44no—
256C2×Dic43—42no—
257C2×Dic43—82no—
258C2×Dic43—82no—
259C43⋊C8—24no—
260C43⋊C8—42no—
261C2×#1859—431nomaximal, Sylow
262C22×C43—24no—
263C22×C43—24no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—24no—
269C22×C43—48no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43#38512yes—
273C22×C43#38512yes—
274C22×C43#45312yes—
275C22×C43#45612yes—
276C22×C43C2×C4×D411yescharacteristic
277C22×C43C2×#12011yescharacteristic
278C22×C43C2×C22⋊Q811yescharacteristic
279C4×C43—24no—
280C4×C43—44no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43#38512yes—
284C4×C43#38512yes—
285C4×C43C22×C4⋊C411yescharacteristic
286C4×C43C2×C4×D411yescharacteristic
287C4×C43C2×C22⋊Q811yescharacteristic
288C4×C43C2×#12311yescharacteristic
289Dic43—28no—
290Dic43—82no—
291C2×#520D4311yescharacteristic
292C2×#428—431no—
293C22×#104—431no—
294C2×#417—431no—
295C2×#384—431no—
296#1859—438no—
297C2×#343—431no—
298C2×#339—431no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—22no—
302C2×C43—44no—
303C2×C43#185914yescomplemented
304C2×C43C2×#38511yescharacteristic
305C2×C43C2×#45311yescharacteristic
306C2×C43C2×#45611yescharacteristic
307C22×#41C2×D4311yescharacteristic
308C22×M16—431no—
309C22×M16—431no—
310#520—22no—
311#520—22no—
312#520—22no—
313#520C2×D4314yes—
314C2×C4×Q8—21no—
315C2×C4×D4—21no—
316C2×C4×D4—22no—
317C2×#117—21no—
318C2×#117C2×D4311yescharacteristic
319C22×C4⋊C4—21no—
320C22×C4⋊C4—431no—
321C22×C4⋊C4—862no—
322C22×C4⋊C4C2×D4311yescharacteristic
323C22×C42—431no—
324#428—434no—
325#428—862no—
326C2×#107—861no—
327C2×#106—861no—
328C2×#104—434no—
329C2×#104—438no—
330#417—434no—
331#417—862no—
332C2×#103—861no—
333C2×#102—861no—
334#384—434no—
335#384—862no—
336#343—434no—
337#339—434no—
338C43C2×#185911yescharacteristic, complemented, Sylow
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41Dic8614yes—
344C2×#41C4×D4314yes—
345C2×#41C22⋊D4312yes—
346C2×#41C22×D4312yes—
347C22×Q8C22⋊D4311yescharacteristic
348C22×D4—21no—
349C22×D4C22⋊D4311yescharacteristic
350C23×C4—21no—
351C23×C4—22no—
352C23×C4—861no—
353C23×C4—861no—
354C23×C4C22⋊D4312yes—
355C23×C4C22×D4311yescharacteristic
356C2×M16—434no—
357C2×M16—432no—
358C2×M16—432no—
359C2×M16—862no—
360C2×M16—861no—
361C2×M16—861no—
362C2×M16—862no—
363C2×M16—862no—
364C22×C8—861no—
365C22×C8—861no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×D4—28no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—28no—
372#117—24no—
373#117—21no—
374#117—21no—
375#117—24no—
376#117C22⋊D4312yes—
377#117C22×D4312yes—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—432no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—868no—
392C2×C4⋊C4—1728no—
393C2×C4⋊C4C22⋊D4312yes—
394C2×C4⋊C4C22⋊D4311yescharacteristic
395C2×C4⋊C4C22⋊D4311yescharacteristic
396C2×C4⋊C4C22×D4312yes—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—21no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42—434no—
402C2×C42—432no—
403C2×C42—862no—
404C2×C42—861no—
405#107—864no—
406#106—864no—
407#104—4316no—
408#103—864no—
409#102—864no—
410C24—21no—
411C24C2×C22⋊D4311yescharacteristic
412#41—24no—
413#41—24no—
414#41—24no—
415#41—24no—
416#41—24no—
417#41—22no—
418#41—22no—
419#41Dic43⋊C418yescomplemented
420#41C2×Dic8614yes—
421#41C2×C4×D4314yes—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8Dic43⋊C414yescomplemented
425C2×Q8C2×C22⋊D4312yes—
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—24no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4Dic43⋊C414yescomplemented
433C2×D4C2×C22⋊D4312yes—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—28no—
443C22×C4—22no—
444C22×C4—44no—
445C22×C4—84no—
446C22×C4—864no—
447C22×C4—864no—
448C22×C4—864no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—1724no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4C2×Dic8612yes—
455C22×C4C2×C4×D4312yes—
456C22×C4#1062189812yes—
457C22×C4#1062189812yes—
458C22×C4C2×C22⋊D4314yes—
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C23×D4311yescharacteristic
465M16—434no—
466M16—864no—
467M16—862no—
468M16—862no—
469M16—862no—
470M16—1722no—
471C2×C8—864no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—1722no—
475C4⋊C4—28no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—17216no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4C2×C22⋊D4312yes—
488C4⋊C4C2×C22⋊D4312yes—
489C22⋊C4—28no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C42—28no—
493C42—22no—
494C42—22no—
495C42—434no—
496C42—864no—
497C42—862no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—42no—
503C23—42no—
504C23C4×C22⋊D4312yes—
505C23#1306329411yescharacteristic
506C23#1306329411yescharacteristic
507C23#1306330412yes—
508C23C22×C22⋊D4311yescharacteristic
509Q8—22no—
510Q8—24no—
511Q8C2×Dic43⋊C414yescomplemented
512D4—24no—
513D4—24no—
514D4—28no—
515D4—22no—
516D4—24no—
517D4C2×Dic43⋊C414yescomplemented
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—28no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—82no—
531C2×C4—88no—
532C2×C4—864no—
533C2×C4—864no—
534C2×C4—8616no—
535C2×C4—864no—
536C2×C4—3442no—
537C2×C4—3442no—
538C2×C4—1724no—
539C2×C4—1722no—
540C2×C4C2×Dic43⋊C412yes—
541C2×C4C2×Dic43⋊C412yes—
542C2×C4C4×C22⋊D4312yes—
543C2×C4C4×C22⋊D4312yes—
544C2×C4C4×C22⋊D4312yes—
545C2×C4#1306329411yescharacteristic
546C2×C4#1306329411yescharacteristic
547C2×C4#1306330412yes—
548C2×C4#1306330412yes—
549C2×C4#1306330412yes—
550C2×C4#1306330812yes—
551C2×C4#1306330812yes—
552C2×C4C22×C4×D4311yescharacteristic
553C2×C4C22×C22⋊D4311yescharacteristic
554C2×C4C22×C22⋊D4311yescharacteristic
555C2×C4C22×Dic8611yescharacteristic
556C2×C4C2×#1062189811yescharacteristic
557C2×C4C2×#1062189811yescharacteristic
558C8—864no—
559C8—1722no—
560C22—21no—
561C22—21no—
562C22—24no—
563C22—24no—
564C22—21no—
565C22—21no—
566C22—24no—
567C22—42no—
568C22—48no—
569C22—42no—
570C22#1458277212yes—
571C22#1458277212yes—
572C22#1458306712yes—
573C22#1458308212yes—
574C22C2×C4×C22⋊D4311yescharacteristic
575C22C2×#1306329411yescharacteristic
576C22C2×#1306330411yescharacteristic
577C4—24no—
578C4—42no—
579C4—44no—
580C4—42no—
581C4—868no—
582C4—3442no—
583C4#1458277212yes—
584C4#1458277212yes—
585C4C22×Dic43⋊C411yescharacteristic
586C4C2×C4×C22⋊D4311yescharacteristic
587C4C2×#1306330411yescharacteristic
588C4C2×#1306330811yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—44no—
593C2#1913482114yesdirect product factor
594C2C2×#1458277211yescharacteristic
595C2C2×#1458306711yescharacteristic
596C2C2×#1458308211yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#520C2
socleC23×C43#120
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#520D43
hypocenterC43C2×#1859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#14582942C2semidirect
4. C2×#14582768C2semidirect
5. #19134821C2direct (N × H)
6. C2×#14582668C2semidirect
7. C2×#14582658C2semidirect
15. #14582942C22semidirect
18. C2×#13063252C4semidirect
25. #14582768C22semidirect
26. #14582668C22semidirect
27. #14582658C22semidirect
47. C2×#10621877C2×C4semidirect
62. C2×C4×Dic43C2×C4semidirect
66. #13063252C2×C4semidirect
120. #41×C43C4⋊C4semidirect
125. C2×Q8×C43C4⋊C4semidirect
133. C2×D4×C43C4⋊C4semidirect
188. C4×Dic43C22×C4semidirect
194. #10621877C22×C4semidirect
212. Q8×C43C2×C4⋊C4semidirect
218. D4×C43C2×C4⋊C4semidirect
303. C2×C43#1859semidirect
338. C43C2×#1859semidirect
419. #41Dic43⋊C4semidirect
424. C2×Q8Dic43⋊C4semidirect
432. C2×D4Dic43⋊C4semidirect
511. Q8C2×Dic43⋊C4semidirect
517. D4C2×Dic43⋊C4semidirect
593. C2#19134821direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145829422
C22×#130632522
C2×#145829002
C2×#145827682
#191348212
C2×#145826682
C2×#145826582
C2×C43×#5202
C2×#185943