Finite Group Databasebeta

← C2×#10375 #238253

Subgroups — C2×#10375 #238253

Order 512.

1254 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2549C211yesmaximal, characteristic
2C2×#1996C211yesmaximal, characteristic
3C2×#1520C211yesmaximal, characteristic
4C22×#328C211yesmaximal, characteristic
5#10375C218yesmaximal, direct product factor
6C2×#1294C211yesmaximal, characteristic
7C2×#1289C211yesmaximal, characteristic
8C2×#1282C211yesmaximal, characteristic
9C22×C22⋊Q8—21no—
10C22×C22⋊Q8C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12C22×C22⋊C8C2211yescharacteristic
13#2549—22no—
14#2549—22no—
15#2549—22no—
16#2549C2214yes—
17C2×#398—21no—
18C2×#395—21no—
19C2×#391—21no—
20C2×#389—21no—
21C2×#385—21no—
22C2×#380C2211yescharacteristic
23C2×#380C2211yescharacteristic
24C2×C4×C22⋊C4C2211yescharacteristic
25C22×#95C2211yescharacteristic
26#1996—22no—
27#1996C2214yes—
28C2×#342—21no—
29C2×#342—21no—
30#1520—22no—
31#1520C2214yes—
32C2×#328—21no—
33C2×#328—21no—
34C2×#328—22no—
35C2×#328—21no—
36C2×#328—21no—
37C2×#328C2214yes—
38#1294C2214yes—
39#1289C2214yes—
40#1282C2214yes—
41C23×Q8—21no—
42C23×Q8Q811yescharacteristic, complemented
43C24×C4—21no—
44C24×C4C2311yescharacteristic
45C23×C8—21no—
46C23×C8—21no—
47C2×C22⋊Q8—24no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8—24no—
51C2×C22⋊Q8—21no—
52C2×C22⋊Q8—21no—
53C2×C22⋊Q8—21no—
54C2×C22⋊Q8—21no—
55C2×C22⋊Q8—21no—
56C2×C22⋊Q8—21no—
57C2×C22⋊Q8—21no—
58C2×C22⋊Q8—21no—
59C2×C22⋊Q8—44no—
60C2×C22⋊Q8—44no—
61C2×C22⋊Q8Q812yescomplemented
62C2×C22⋊Q8C2312yes—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4Q811yescharacteristic, complemented
72C22×C22⋊C4—21no—
73C22×C22⋊C4—21no—
74C22×C22⋊C4—21no—
75C22×C22⋊C4D411yescharacteristic
76C22×C22⋊C4D411yescharacteristic
77C22×C42—21no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8—21no—
81C2×C22⋊C8—21no—
82C2×C22⋊C8—21no—
83C2×C22⋊C8—21no—
84C2×C22⋊C8—21no—
85C2×C22⋊C8—21no—
86C2×C22⋊C8—21no—
87C2×C22⋊C8—21no—
88C2×C22⋊C8C2312yes—
89C2×C22⋊C8C2312yes—
90#398—24no—
91#398—24no—
92#395—24no—
93#395—24no—
94#391—24no—
95#391—24no—
96#389—24no—
97#389—24no—
98#385—24no—
99#385—24no—
100#380—21no—
101#380—21no—
102#380—21no—
103#380—21no—
104#380—21no—
105#380D412yes—
106#380C2312yes—
107#380C2312yes—
108C4×C22⋊C4—21no—
109C4×C22⋊C4—21no—
110C4×C22⋊C4D412yes—
111C4×C22⋊C4C2312yes—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95D411yescharacteristic
120C2×#95D411yescharacteristic
121C2×#95D412yes—
122C2×#95D411yescharacteristic
123C2×#95D411yescharacteristic
124C2×#95C2312yes—
125#342—24no—
126#342—24no—
127#328—24no—
128#328—24no—
129#328—24no—
130#328—24no—
131C25C2×D411yescharacteristic
132C22×Q8—24no—
133C22×Q8—21no—
134C22×Q8—21no—
135C22×Q8—21no—
136C22×Q8—21no—
137C22×Q8—21no—
138C22×Q8—44no—
139C22×Q8—44no—
140C22×Q8—82no—
141C22×Q8—82no—
142C22×Q8C2×Q812yescomplemented
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—44no—
154C23×C4—42no—
155C23×C4—42no—
156C23×C4—41no—
157C23×C4—82no—
158C23×C4—82no—
159C23×C4C2×D411yescharacteristic
160C23×C4C2×D411yescharacteristic
161C23×C4C2×D411yescharacteristic
162C23×C4C2×D411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C23×C4C2×Q811yescharacteristic
165C23×C4C2×Q811yescharacteristic
166C23×C4#4111yescharacteristic
167C23×C4#4111yescharacteristic
168C23×C4#4111yescharacteristic
169C23×C4#4111yescharacteristic
170C23×C4#4111yescharacteristic
171C23×C4#4111yescharacteristic
172C23×C4C2411yescharacteristic
173C22×C8—22no—
174C22×C8—22no—
175C22×C8—41no—
176C22×C8—41no—
177C22×C8—41no—
178C22×C8—41no—
179C22×C8—82no—
180C22×C8—82no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C22⋊Q8—48no—
190C22⋊Q8—416no—
191C22⋊Q8—41no—
192C22⋊Q8—41no—
193C22⋊Q8—41no—
194C22⋊Q8—41no—
195C22⋊Q8—41no—
196C22⋊Q8—41no—
197C22⋊Q8—41no—
198C22⋊Q8—41no—
199C22⋊Q8—48no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—24no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—44no—
216C2×C4⋊C4—44no—
217C2×C4⋊C4—44no—
218C2×C4⋊C4—44no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—82no—
225C2×C4⋊C4—82no—
226C2×C4⋊C4—82no—
227C2×C4⋊C4C2×Q812yescomplemented
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—41no—
238C2×C22⋊C4—41no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—42no—
242C2×C22⋊C4—42no—
243C2×C22⋊C4—42no—
244C2×C22⋊C4—42no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4SD1614yes—
247C2×C22⋊C4Q1614yes—
248C2×C22⋊C4C2×D412yes—
249C2×C22⋊C4C2×D412yes—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—82no—
253C22⋊C8—22no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8—41no—
258C22⋊C8—41no—
259C22⋊C8—41no—
260C22⋊C8—41no—
261#95—24no—
262#95—24no—
263#95—22no—
264#95—21no—
265#95—21no—
266#95—22no—
267#95—21no—
268#95—21no—
269#95—22no—
270#95—22no—
271#95—22no—
272#95—41no—
273#95C2×D412yes—
274#95C2×D412yes—
275#95C2×D412yes—
276#95C2×D412yes—
277C24—42no—
278C24—42no—
279C24#12011yescharacteristic
280C24#12011yescharacteristic
281C24C22⋊Q811yescharacteristic
282C24C22⋊Q811yescharacteristic
283C24#12411yescharacteristic
284C24#12411yescharacteristic
285C24C2×SD1612yes—
286C24C2×Q1612yes—
287C24AGL(1,ℤ/8)12yes—
288C24#13712yes—
289C24C22×D411yescharacteristic
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—48no—
293C2×Q8—48no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—82no—
297C2×Q8—82no—
298C2×Q8—84no—
299C2×Q8—816no—
300C2×Q8—82no—
301C2×Q8—82no—
302C2×Q8—82no—
303C2×Q8—82no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—44no—
322C22×C4—44no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—44no—
345C22×C4—42no—
346C22×C4—81no—
347C22×C4—81no—
348C22×C4—81no—
349C22×C4—81no—
350C22×C4—81no—
351C22×C4—81no—
352C22×C4—81no—
353C22×C4—81no—
354C22×C4—82no—
355C22×C4—82no—
356C22×C4—88no—
357C22×C4—88no—
358C22×C4—82no—
359C22×C4—82no—
360C22×C4—82no—
361C22×C4—82no—
362C22×C4—82no—
363C22×C4#12011yescharacteristic
364C22×C4#12011yescharacteristic
365C22×C4C22⋊Q811yescharacteristic
366C22×C4C22⋊Q811yescharacteristic
367C22×C4C22⋊Q811yescharacteristic
368C22×C4C22⋊Q811yescharacteristic
369C22×C4C22⋊Q811yescharacteristic
370C22×C4C22⋊Q811yescharacteristic
371C22×C4C22⋊Q811yescharacteristic
372C22×C4C22⋊Q811yescharacteristic
373C22×C4C22⋊Q811yescharacteristic
374C22×C4C22⋊Q811yescharacteristic
375C22×C4#12411yescharacteristic
376C22×C4#12411yescharacteristic
377C22×C4#12411yescharacteristic
378C22×C4#12411yescharacteristic
379C22×C4#12411yescharacteristic
380C22×C4#12411yescharacteristic
381C22×C4#12411yescharacteristic
382C22×C4#12411yescharacteristic
383C22×C4#12411yescharacteristic
384C22×C4#12411yescharacteristic
385C22×C4C22×D411yescharacteristic
386C22×C4C22×D411yescharacteristic
387C22×C4C22×Q811yescharacteristic
388C22×C4C2×#4111yescharacteristic
389C22×C4C2×#4111yescharacteristic
390C22×C4C2×#4111yescharacteristic
391C2×C8—42no—
392C2×C8—42no—
393C2×C8—82no—
394C2×C8—82no—
395C2×C8—82no—
396C2×C8—82no—
397C2×C8—82no—
398C2×C8—82no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—48no—
402C4⋊C4—48no—
403C4⋊C4—48no—
404C4⋊C4—48no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—82no—
412C4⋊C4—82no—
413C4⋊C4—84no—
414C4⋊C4—82no—
415C4⋊C4—82no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C22⋊C4—44no—
427C22⋊C4—42no—
428C22⋊C4—42no—
429C22⋊C4—82no—
430C22⋊C4C2×SD1614yes—
431C22⋊C4C2×Q1614yes—
432C42—82no—
433C42—82no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—44no—
447C23—44no—
448C23—41no—
449C23—41no—
450C23—44no—
451C23—44no—
452C23#39311yescharacteristic
453C23#39311yescharacteristic
454C23#39311yescharacteristic
455C23#39311yescharacteristic
456C23#45012yes—
457C23#45012yes—
458C23#45112yes—
459C23#45112yes—
460C23#47512yes—
461C23#47512yes—
462C23#47712yes—
463C23#47712yes—
464C23#48712yes—
465C23#48712yes—
466C23#48912yes—
467C23#48912yes—
468C23C2×#12011yescharacteristic
469C23C2×C22⋊Q811yescharacteristic
470C23C2×#12411yescharacteristic
471C23C22×SD1611yescharacteristic
472C23C22×Q1611yescharacteristic
473C23C2×AGL(1,ℤ/8)11yescharacteristic
474C23C2×#13711yescharacteristic
475Q8—82no—
476Q8—82no—
477Q8—82no—
478Q8—82no—
479Q8—816no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—48no—
515C2×C4—48no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—48no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—84no—
532C2×C4—84no—
533C2×C4—88no—
534C2×C4—84no—
535C2×C4—84no—
536C2×C4—84no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—164no—
547C2×C4#39311yescharacteristic
548C2×C4#39311yescharacteristic
549C2×C4#39311yescharacteristic
550C2×C4#39311yescharacteristic
551C2×C4C2×C22⋊Q811yescharacteristic
552C2×C4C2×C22⋊Q811yescharacteristic
553C2×C4C2×#12411yescharacteristic
554C2×C4C2×#12411yescharacteristic
555C8—82no—
556C8—82no—
557C22—24no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22#202412yes—
586C22#202412yes—
587C22#202412yes—
588C22#202412yes—
589C22#203112yes—
590C22#203212yes—
591C22C2×#39311yescharacteristic
592C22C2×#45011yescharacteristic
593C22C2×#45111yescharacteristic
594C22C2×#47511yescharacteristic
595C22C2×#47711yescharacteristic
596C22C2×#48711yescharacteristic
597C22C2×#48911yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—44no—
607C4—44no—
608C4—44no—
609C4—82no—
610C4—82no—
611C4—82no—
612C4—82no—
613C4—82no—
614C4—162no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—22no—
622C2—22no—
623C2—22no—
624C2#1037514yesdirect product factor
625C2C2×#202411yescharacteristic
626C2C2×#203111yescharacteristic
627C2C2×#203211yescharacteristic
subgroupG/H
center, socleC23#393
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #10375C2direct (N × H)
42. C23×Q8Q8semidirect
61. C2×C22⋊Q8Q8semidirect
71. C22×C4⋊C4Q8semidirect
142. C22×Q8C2×Q8semidirect
227. C2×C4⋊C4C2×Q8semidirect
624. C2#10375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25492
C2×#19962
C2×#15202
C22×#3282
#103752
C2×#12942
C2×#12892
C2×#12822