Finite Group Databasebeta

← C2×#10572 #241128

Subgroups — C2×#10572 #241128

Order 512.

1532 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2646C211yesmaximal, characteristic
2C2×#1853C211yesmaximal, characteristic
3C2×#1852C211yesmaximal, characteristic
4C2×#1444C211yesmaximal, characteristic
5#10572C218yesmaximal, direct product factor
6C2×#1294C211yesmaximal, characteristic
7C2×#1294C211yesmaximal, characteristic
8C2×#1280C211yesmaximal, characteristic
9C23×C4⋊C4—21no—
10C23×C4⋊C4C2211yescharacteristic
11C22×#107—21no—
12C22×#106—21no—
13C22×C22⋊C8C2211yescharacteristic
14C22×C22⋊C8C2211yescharacteristic
15#2646—22no—
16#2646—22no—
17#2646—22no—
18#2646C2214yes—
19C2×#400—21no—
20C2×#400—21no—
21C2×#398—21no—
22C2×#398—21no—
23C2×#385—21no—
24C2×#385—21no—
25C2×#380C2211yescharacteristic
26C2×#380C2211yescharacteristic
27C22×#95—21no—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30#1853—22no—
31#1853C2214yes—
32#1852—22no—
33#1852C2214yes—
34C2×#340—21no—
35C2×#340—21no—
36#1444—22no—
37#1444C2214yes—
38#1294C2214yes—
39#1294C2214yes—
40#1280C2214yes—
41C24×C4—21no—
42C24×C4—21no—
43C24×C4D411yescharacteristic
44C24×C4D411yescharacteristic
45C24×C4C2311yescharacteristic
46C23×C8—21no—
47C23×C8—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—44no—
59C22×C4⋊C4—44no—
60C22×C4⋊C4—44no—
61C22×C4⋊C4—44no—
62C22×C4⋊C4D411yescharacteristic
63C22×C4⋊C4D411yescharacteristic
64C22×C4⋊C4D411yescharacteristic
65C22×C4⋊C4D411yescharacteristic
66C22×C4⋊C4C2312yes—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C2×#107—24no—
70C2×#107—44no—
71C2×#106—24no—
72C2×#106—44no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—22no—
76C2×C22⋊C8—22no—
77C2×C22⋊C8Q814yes—
78C2×C22⋊C8Q814yes—
79C2×C22⋊C8C2312yes—
80C2×C22⋊C8C2312yes—
81#400—24no—
82#400—24no—
83#400—24no—
84#400—24no—
85#398—24no—
86#398—24no—
87#398—24no—
88#398—24no—
89#385—24no—
90#385—24no—
91#385—24no—
92#385—24no—
93#380—21no—
94#380—21no—
95#380—21no—
96#380—21no—
97#380D412yes—
98#380D412yes—
99#380C2312yes—
100#380C2312yes—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95—22no—
113C2×#95—24no—
114C2×#95—44no—
115C2×#95D412yes—
116C2×#95Q814yes—
117C2×#95C2312yes—
118C2×#95C2312yes—
119#340—24no—
120#340—24no—
121C25C2×D411yescharacteristic
122C23×C4—24no—
123C23×C4—24no—
124C23×C4—24no—
125C23×C4—22no—
126C23×C4—24no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—42no—
141C23×C4—42no—
142C23×C4—42no—
143C23×C4—42no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—42no—
147C23×C4—42no—
148C23×C4—42no—
149C23×C4—42no—
150C23×C4—42no—
151C23×C4—42no—
152C23×C4—42no—
153C23×C4—41no—
154C23×C4—41no—
155C23×C4—42no—
156C23×C4—42no—
157C23×C4C2×D411yescharacteristic
158C23×C4C2×D411yescharacteristic
159C23×C4C2×D412yes—
160C23×C4C2×D412yes—
161C23×C4C2×D411yescharacteristic
162C23×C4C2×D411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C23×C4C2×Q812yes—
165C23×C4C2×Q812yes—
166C23×C4C2×Q812yes—
167C23×C4#4112yes—
168C23×C4C2411yescharacteristic
169C22×C8—24no—
170C22×C8—24no—
171C22×C8—22no—
172C22×C8—22no—
173C22×C8—42no—
174C22×C8—42no—
175C22×C8—42no—
176C22×C8—42no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4—44no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—48no—
196C2×C4⋊C4—48no—
197C2×C4⋊C4—48no—
198C2×C4⋊C4—432no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4—82no—
206C2×C4⋊C4—82no—
207C2×C4⋊C4—82no—
208C2×C4⋊C4—82no—
209C2×C4⋊C4C2×D412yes—
210C2×C4⋊C4C2×D412yes—
211C2×C4⋊C4C2×D412yes—
212C2×C4⋊C4C2×D412yes—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—42no—
218C2×C22⋊C4—42no—
219C2×C22⋊C4—42no—
220C2×C22⋊C4—42no—
221#107—48no—
222#106—48no—
223C22⋊C8—24no—
224C22⋊C8—24no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8C2×Q814yes—
228C22⋊C8C2×Q814yes—
229#95—24no—
230#95—24no—
231#95—24no—
232#95—24no—
233#95—22no—
234#95—22no—
235#95—22no—
236#95—22no—
237#95—24no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95—22no—
242#95—22no—
243#95—48no—
244#95C2×Q814yes—
245C24—22no—
246C24—22no—
247C24—22no—
248C24—22no—
249C24#12011yescharacteristic
250C24#12011yescharacteristic
251C24C22⋊Q812yes—
252C24C4⋊Q812yes—
253C24#13512yes—
254C24#13512yes—
255C24AGL(1,ℤ/8)12yes—
256C24#13712yes—
257C24C22×D411yescharacteristic
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—216no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—44no—
285C22×C4—44no—
286C22×C4—44no—
287C22×C4—44no—
288C22×C4—41no—
289C22×C4—48no—
290C22×C4—42no—
291C22×C4—48no—
292C22×C4—48no—
293C22×C4—48no—
294C22×C4—48no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—48no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—48no—
305C22×C4—48no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—44no—
309C22×C4—48no—
310C22×C4—48no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—44no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—81no—
336C22×C4—81no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—84no—
340C22×C4—84no—
341C22×C4—82no—
342C22×C4—82no—
343C22×C4—82no—
344C22×C4—82no—
345C22×C4—84no—
346C22×C4—84no—
347C22×C4#12011yescharacteristic
348C22×C4#12011yescharacteristic
349C22×C4C22⋊Q812yes—
350C22×C4C22⋊Q812yes—
351C22×C4C22⋊Q812yes—
352C22×C4C22⋊Q812yes—
353C22×C4C22⋊Q812yes—
354C22×C4C4⋊Q812yes—
355C22×C4C4⋊Q812yes—
356C22×C4C4⋊Q812yes—
357C22×C4C4⋊Q812yes—
358C22×C4C4⋊Q812yes—
359C22×C4C22×D411yescharacteristic
360C22×C4C22×D411yescharacteristic
361C22×C4C22×Q811yescharacteristic
362C22×C4C22×Q811yescharacteristic
363C22×C4C22×Q811yescharacteristic
364C22×C4C2×#4111yescharacteristic
365C2×C8—24no—
366C2×C8—24no—
367C2×C8—42no—
368C2×C8—42no—
369C2×C8—48no—
370C2×C8—48no—
371C2×C8—42no—
372C2×C8—42no—
373C4⋊C4—24no—
374C4⋊C4—24no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C4⋊C4—44no—
382C4⋊C4—44no—
383C4⋊C4—432no—
384C4⋊C4—81no—
385C4⋊C4—81no—
386C4⋊C4—81no—
387C4⋊C4—81no—
388C4⋊C4—84no—
389C4⋊C4—84no—
390C4⋊C4—84no—
391C4⋊C4—84no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—44no—
397C22⋊C4—44no—
398C23—24no—
399C23—24no—
400C23—24no—
401C23—24no—
402C23—24no—
403C23—24no—
404C23—24no—
405C23—24no—
406C23—24no—
407C23—24no—
408C23—24no—
409C23—24no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23#39512yes—
419C23#39512yes—
420C23#44912yes—
421C23#44912yes—
422C23#45212yes—
423C23#45212yes—
424C23#45312yes—
425C23#45612yes—
426C23B(4,𝔽2)12yes—
427C23#45812yes—
428C23#47814yes—
429C23#47914yes—
430C23#49914yes—
431C23#50114yes—
432C23C2×#12011yescharacteristic
433C23C2×C22⋊Q811yescharacteristic
434C23C2×C4⋊Q811yescharacteristic
435C23C2×#13511yescharacteristic
436C23C2×#13511yescharacteristic
437C23C2×AGL(1,ℤ/8)11yescharacteristic
438C23C2×#13711yescharacteristic
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—28no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—432no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—44no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—84no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4—88no—
496C2×C4—84no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4—88no—
500C2×C4—84no—
501C2×C4—84no—
502C2×C4—84no—
503C2×C4—84no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4#39512yes—
509C2×C4#39512yes—
510C2×C4C2×C22⋊Q811yescharacteristic
511C2×C4C2×C22⋊Q811yescharacteristic
512C2×C4C2×C4⋊Q811yescharacteristic
513C2×C4C2×C4⋊Q811yescharacteristic
514C8—44no—
515C8—44no—
516C22—21no—
517C22—21no—
518C22—22no—
519C22—21no—
520C22—21no—
521C22—22no—
522C22—28no—
523C22—28no—
524C22—28no—
525C22—28no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—21no—
536C22—21no—
537C22—22no—
538C22#160014yes—
539C22#160314yes—
540C22#160914yes—
541C22#161814yes—
542C22#205914yes—
543C22#205914yes—
544C22#206014yes—
545C22#206214yes—
546C22C2×#39511yescharacteristic
547C22C2×#44911yescharacteristic
548C22C2×#45211yescharacteristic
549C22C2×#45311yescharacteristic
550C22C2×#45611yescharacteristic
551C22C2×B(4,𝔽2)11yescharacteristic
552C22C2×#45811yescharacteristic
553C22C2×#47811yescharacteristic
554C22C2×#47911yescharacteristic
555C22C2×#49911yescharacteristic
556C22C2×#50111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—22no—
562C4—22no—
563C4—48no—
564C4—82no—
565C4—82no—
566C4—82no—
567C4—82no—
568C4—84no—
569C4—82no—
570C4—82no—
571C2—21no—
572C2—21no—
573C2—24no—
574C2—21no—
575C2—21no—
576C2#1057218yesdirect product factor
577C2C2×#160311yescharacteristic
578C2C2×#160911yescharacteristic
579C2C2×#160011yescharacteristic
580C2C2×#161811yescharacteristic
581C2C2×#205911yescharacteristic
582C2C2×#206011yescharacteristic
583C2C2×#206211yescharacteristic
subgroupG/H
center, socleC24#120
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #10572C2direct (N × H)
576. C2#10572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26462
C2×#18532
C2×#18522
C2×#14442
#105722
C2×#12942
C2×#12802