Finite Group Databasebeta

← C2×#19134819 #25097449

Subgroups — C2×#19134819 #25097449

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×#14583382C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3C22×#13063252C211yesmaximal, characteristic
4C2×#14582768C211yesmaximal, characteristic, complemented
5#19134819C218yesmaximal, direct product factor
6C2×#14582667C211yesmaximal, characteristic, complemented
7C2×#14582660C211yesmaximal, characteristic, complemented
8C2×C43×#417C211yesmaximal, characteristic
9C22×#10621877C2211yescharacteristic
10#14583382—22no—
11#14583382—22no—
12#14583382—22no—
13#14583382C2214yes—
14C2×Q8×Dic43—21no—
15C2×D4×Dic43—22no—
16C2×D4×Dic43—21no—
17C2×#13063284—21no—
18C2×#13063284C2211yescharacteristic
19C22×C4⋊Dic43—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4—22no—
22C22×C4×Dic43C2211yescharacteristic
23#14582939—22no—
24#14582939C2214yescomplemented
25C2×#13063258—21no—
26C2×#13063256—21no—
27C2×#13063252C418yescomplemented
28C2×#13063252C2214yes—
29#14582768—22no—
30#14582768C2214yescomplemented
31#14582667C2214yescomplemented
32#14582660C2214yescomplemented
33C22×#41×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#417—22no—
37C43×#417C2214yes—
38C2×#103×C43—21no—
39C2×#102×C43—21no—
40C23×Dic43—21no—
41C23×Dic43—22no—
42C23×Dic43D412yes—
43C2×#10621877—21no—
44C2×#10621877—22no—
45C2×#10621877C2×C414yescomplemented
46C2×#10621877C2312yes—
47C22×C43⋊C8—21no—
48Q8×Dic43—24no—
49Q8×Dic43—24no—
50D4×Dic43—28no—
51D4×Dic43—24no—
52D4×Dic43—24no—
53D4×Dic43—28no—
54#13063284—24no—
55#13063284—21no—
56#13063284—21no—
57#13063284—24no—
58#13063284D412yes—
59#13063284C2312yes—
60C2×C4⋊Dic43—22no—
61C2×C4⋊Dic43—24no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—24no—
67C2×C4⋊Dic43D412yes—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2312yes—
71C2×Dic43⋊C4—28no—
72C2×Dic43⋊C4—48no—
73C2×C22⋊Dic43—22no—
74C2×C22⋊Dic43—21no—
75C2×C4×Dic43—22no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—22no—
79C2×C4×Dic43C2×C414yescomplemented
80C2×C4×Dic43C2312yes—
81#13063258—24no—
82#13063256—24no—
83#13063252C2×C4116yescomplemented
84C2×#41×C43—21no—
85C2×#41×C43—21no—
86C2×#41×C43—22no—
87C2×#41×C43—22no—
88C2×#41×C43C2×C414yes—
89C2×#41×C43D412yes—
90C2×#41×C43Q814yes—
91C2×#41×C43C2312yes—
92C22×Q8×C43D411yescharacteristic
93C22×D4×C43—21no—
94C22×D4×C43D411yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43—21no—
97C23×C4×C43C2311yescharacteristic
98C2×M16×C43—21no—
99C2×M16×C43—22no—
100C2×M16×C43—22no—
101C2×M16×C43C2312yes—
102C22×C8×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2312yes—
109#103×C43—24no—
110#102×C43—24no—
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—21no—
140C22×C4×C43—22no—
141C22×C4×C43—44no—
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43C22×C412yes—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×Q812yes—
151C22×C4×C43#4112yes—
152C22×C4×C43#4112yes—
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—24no—
155C22×Dic43—24no—
156C22×Dic43—28no—
157C22×Dic43—24no—
158C22×Dic43—21no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—44no—
164C22×Dic43—84no—
165C22×Dic43C2×D414yes—
166M16×C43—22no—
167M16×C43—22no—
168M16×C43—42no—
169C2×C8×C43—22no—
170C2×C8×C43—42no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C22⋊Dic43—28no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C4⋊Dic43—28no—
179C4⋊Dic43—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43—22no—
182C4⋊Dic43—21no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43C2×D412yes—
186C4⋊Dic43C2×D412yes—
187Dic43⋊C4—416no—
188C4×Dic43—28no—
189C4×Dic43—24no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43C22×C414yescomplemented
194#10621877—24no—
195#10621877—22no—
196#10621877C22×C414yescomplemented
197C2×C43⋊C8—24no—
198C2×C43⋊C8—22no—
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—44no—
225C2×C4×C43—42no—
226C2×C4×C43—82no—
227C2×C4×C43—82no—
228C2×C4×C43C2×C4⋊C412yes—
229C2×C4×C43C2×C4⋊C412yes—
230C2×C4×C43C4×D412yes—
231C2×C4×C43C4×D412yes—
232C2×C4×C43C4×D412yes—
233C2×C4×C43#12011yescharacteristic
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43C22⋊Q812yes—
236C2×C4×C43C22⋊Q812yes—
237C2×C4×C43C22⋊Q812yes—
238C2×C4×C43#12312yes—
239C2×C4×C43#12312yes—
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×Q811yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×Dic43—24no—
247C2×Dic43—216no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—22no—
251C2×Dic43—24no—
252C2×Dic43—22no—
253C2×Dic43—44no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—44no—
257C2×Dic43—82no—
258C2×Dic43—88no—
259C8×C43—42no—
260C43⋊C8—24no—
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—82no—
281C4×C43#38512yes—
282C4×C43#38512yes—
283C4×C43C22×C4⋊C411yescharacteristic
284C4×C43C2×C4×D411yescharacteristic
285C4×C43C2×C22⋊Q811yescharacteristic
286C4×C43C2×#12311yescharacteristic
287Dic43—28no—
288Dic43—44no—
289Dic43—42no—
290Dic43—42no—
291C2×#520—431no—
292C2×#428—431no—
293C22×#104—431no—
294C2×#417D4311yescharacteristic
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×M16C2×D4311yescharacteristic
310#520—434no—
311#520—862no—
312#520—862no—
313#520—862no—
314C2×C4×Q8—861no—
315C2×C4×D4—862no—
316C2×C4×D4—861no—
317C2×#117—431no—
318C2×#117—861no—
319C22×C4⋊C4—431no—
320C22×C4⋊C4—861no—
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—22no—
331#417C2×D4314yes—
332C2×#103—21no—
333C2×#102—21no—
334#384—434no—
335#384—862no—
336#343—434no—
337#339—434no—
338C43C2×#185911yescharacteristic, complemented, Sylow
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—22no—
342C2×#41—22no—
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—21no—
352C23×C4—432no—
353C23×C4—861no—
354C23×C4—862no—
355C23×C4C22×D4311yescharacteristic
356C2×M16—21no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—434no—
360C2×M16—432no—
361C2×M16—861no—
362C2×M16—862no—
363C2×M16C22×D4312yes—
364C22×C8—21no—
365C22×C8—861no—
366C4×Q8—864no—
367C4×Q8—864no—
368C4×D4—868no—
369C4×D4—868no—
370C4×D4—864no—
371C4×D4—864no—
372#117—432no—
373#117—432no—
374#117—864no—
375#117—864no—
376#117—861no—
377#117—861no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—432no—
386C2×C4⋊C4—432no—
387C2×C4⋊C4—864no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—864no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—868no—
395C2×C4⋊C4—1728no—
396C2×C4⋊C4C22×D4312yes—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—861no—
399C2×C42—434no—
400C2×C42—432no—
401C2×C42—862no—
402C2×C42—861no—
403C2×C42—862no—
404C2×C42—861no—
405#107—864no—
406#106—864no—
407#104—4316no—
408#103—24no—
409#102—24no—
410C24—21no—
411C24D4×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—22no—
440C22×C4—44no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—434no—
444C22×C4—864no—
445C22×C4—864no—
446C22×C4—864no—
447C22×C4—862no—
448C22×C4—868no—
449C22×C4—862no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—862no—
453C22×C4—3444no—
454C22×C4—1724no—
455C22×C4C2×Dic8612yes—
456C22×C4C2×C4×D4312yes—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460C22×C4#1062190012yes—
461C22×C4#1062190012yes—
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C23×D4311yescharacteristic
465M16—22no—
466M16—22no—
467M16—42no—
468M16—434no—
469M16—864no—
470M16—862no—
471C2×C8—22no—
472C2×C8—42no—
473C2×C8—864no—
474C2×C8—862no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—432no—
480C4⋊C4—432no—
481C4⋊C4—868no—
482C4⋊C4—861no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—861no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—17216no—
489C22⋊C4—868no—
490C22⋊C4—862no—
491C22⋊C4—862no—
492C42—434no—
493C42—868no—
494C42—864no—
495C42—862no—
496C42—862no—
497C42—862no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—42no—
503C23—42no—
504C23(C22⋊D43)⋊C412yes—
505C23#1306329311yescharacteristic
506C23#1306329311yescharacteristic
507C23#1306330212yes—
508C23C2×D4×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—44no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—864no—
528C2×C4—8616no—
529C2×C4—864no—
530C2×C4—864no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—864no—
534C2×C4—3442no—
535C2×C4—3448no—
536C2×C4—1722no—
537C2×C4—1724no—
538C2×C4—1722no—
539C2×C4—1724no—
540C2×C4C2×Dic43⋊C412yes—
541C2×C4C2×Dic43⋊C412yes—
542C2×C4(C22⋊D43)⋊C412yes—
543C2×C4(C22⋊D43)⋊C412yes—
544C2×C4(C22⋊D43)⋊C412yes—
545C2×C4#1306329311yescharacteristic
546C2×C4#1306329311yescharacteristic
547C2×C4#1306330212yes—
548C2×C4#1306330212yes—
549C2×C4#1306330212yes—
550C2×C4#1306330612yes—
551C2×C4#1306330612yes—
552C2×C4C22×C4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C22×C22⋊D4311yescharacteristic
555C2×C4C22×Dic8611yescharacteristic
556C2×C4C2×#1062190011yescharacteristic
557C2×C4C2×#1062190011yescharacteristic
558C8—42no—
559C8—864no—
560C22—24no—
561C22—24no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—24no—
567C22—48no—
568C22—42no—
569C22—42no—
570C22#1458277112yes—
571C22#1458277112yes—
572C22#1458306512yes—
573C22#1458308012yes—
574C22C2×(C22⋊D43)⋊C411yescharacteristic
575C22C2×#1306329311yescharacteristic
576C22C2×#1306330211yescharacteristic
577C4—24no—
578C4—82no—
579C4—868no—
580C4—1722no—
581C4—1724no—
582C4—1722no—
583C4#1458277112yes—
584C4#1458277112yes—
585C4C22×Dic43⋊C411yescharacteristic
586C4C2×(C22⋊D43)⋊C411yescharacteristic
587C4C2×#1306330211yescharacteristic
588C4C2×#1306330611yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—44no—
593C2#1913481914yesdirect product factor
594C2C2×#1458277111yescharacteristic
595C2C2×#1458306511yescharacteristic
596C2C2×#1458308011yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43#120
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43C2×#1859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
4. C2×#14582768C2semidirect
5. #19134819C2direct (N × H)
6. C2×#14582667C2semidirect
7. C2×#14582660C2semidirect
24. #14582939C22semidirect
27. C2×#13063252C4semidirect
30. #14582768C22semidirect
31. #14582667C22semidirect
32. #14582660C22semidirect
45. C2×#10621877C2×C4semidirect
79. C2×C4×Dic43C2×C4semidirect
83. #13063252C2×C4semidirect
120. #41×C43C4⋊C4semidirect
125. C2×Q8×C43C4⋊C4semidirect
133. C2×D4×C43C4⋊C4semidirect
193. C4×Dic43C22×C4semidirect
196. #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#19134819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833822
C2×#145829392
C22×#130632522
C2×#145827682
#191348192
C2×#145826672
C2×#145826602
C2×C43×#4172
C2×#185943