Finite Group Databasebeta

← #384995

Subgroups — #384995

Order 512.

1000 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1927C211yesmaximal, characteristic
2#14000C211yesmaximal, characteristic
3#13921C211yesmaximal, characteristic
4#11323C211yesmaximal, characteristic
5#11316C211yesmaximal, characteristic
6#11190C211yesmaximal, characteristic
7#11122C211yesmaximal, characteristic
8#11122C211yesmaximal, characteristic
9#11077C211yesmaximal, characteristic
10#10926C211yesmaximal, characteristic
11#10908C211yesmaximal, characteristic
12#10908C211yesmaximal, characteristic
13#10876C211yesmaximal, characteristic
14#10861C211yesmaximal, characteristic
15#10849C211yesmaximal, characteristic
16C22×#106C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C2×#391C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#384C2211yescharacteristic
29C2×#383—21no—
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32#1927C418yescomplemented
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46#1443—21no—
47#1443—21no—
48#1442—21no—
49#1442—21no—
50#1436—21no—
51#1436—21no—
52C4⋊#95C2211yescharacteristic
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58#1434—21no—
59C4×#95C2211yescharacteristic
60C23×Q8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C22×C4⋊C4—21no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4C2311yescharacteristic
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C42—21no—
75C22×C42—21no—
76C22×C42C2311yescharacteristic
77C22×C42C2311yescharacteristic
78C22×C42C2311yescharacteristic
79C2×#106—22no—
80C2×#106—22no—
81C2×#106—41no—
82C2×#106—41no—
83C2×#106—41no—
84C2×#106—41no—
85C2×#106—41no—
86C2×#106—41no—
87C2×#106C2×C414yes—
88C2×C4⋊C8—22no—
89C2×C4⋊C8—22no—
90C2×C4⋊C8—41no—
91C2×#103—22no—
92C2×#103—22no—
93C2×#103—22no—
94C2×#103—41no—
95C2×#103—41no—
96C2×#103—41no—
97C2×#103—41no—
98C2×#103—41no—
99C2×#103—41no—
100C2×#103—41no—
101C2×#103C2×C414yes—
102C2×#103C2×C414yes—
103C2×C4×C8—22no—
104C2×C4×C8—41no—
105C2×C4×C8—41no—
106#391—22no—
107#391—22no—
108#391—41no—
109#391—41no—
110#391—41no—
111#391C2×C414yes—
112#384—22no—
113#384—41no—
114#383—44no—
115C4×C4⋊C4—22no—
116C4×C4⋊C4—41no—
117C4×C4⋊C4—41no—
118C4×C4⋊C4C2×C414yes—
119C2×#95—21no—
120C2×#95—21no—
121C2×#95—21no—
122C2×#95—21no—
123C2×#95—21no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95D411yescharacteristic
140C2×#95D411yescharacteristic
141C2×#95D411yescharacteristic
142C2×#95D411yescharacteristic
143#340—22no—
144#340—41no—
145#340—41no—
146#340—41no—
147#340—41no—
148#340—41no—
149#340—41no—
150#340—41no—
151#340C2×C414yes—
152#336—22no—
153#336—22no—
154#336—41no—
155#336C2×C414yes—
156C22×Q8—21no—
157C22×Q8—21no—
158C22×Q8—21no—
159C22×Q8—21no—
160C22×Q8—21no—
161C22×Q8—21no—
162C22×Q8—21no—
163C22×Q8—21no—
164C22×Q8—21no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8C22×C412yes—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2411yescharacteristic
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8C22×C412yes—
209C22×C8C22×C412yes—
210C22×C8#4112yes—
211C22×C8#4112yes—
212C22×C8#4112yes—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—81no—
256C2×C4⋊C4—81no—
257C2×C4⋊C4C22×C412yes—
258C2×C4⋊C4C22×C412yes—
259C2×C4⋊C4C22×C412yes—
260C2×C4⋊C4#4112yes—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42—24no—
266C2×C42—21no—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—42no—
279C2×C42—42no—
280C2×C42—42no—
281C2×C42—81no—
282C2×C42—81no—
283C2×C42C22×C412yes—
284C2×C42#4112yes—
285#106—44no—
286#106—44no—
287#106—44no—
288C4⋊C8—44no—
289#103—28no—
290#103—44no—
291#103—44no—
292#103—44no—
293C4×C8—44no—
294#95—24no—
295#95—24no—
296#95—24no—
297#95—22no—
298#95—22no—
299#95—41no—
300#95—42no—
301#95—42no—
302#95—42no—
303#95—42no—
304#95—42no—
305#95—42no—
306#95—42no—
307#95—42no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95—42no—
312#95—81no—
313#95—81no—
314#95—81no—
315#95—81no—
316#95—81no—
317#95SD1614yes—
318C24C22×D411yescharacteristic
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—41no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4C4×D412yes—
439C22×C4C4×D412yes—
440C22×C4C2×SD1612yes—
441C22×C4C2×SD1612yes—
442C22×C4C2×SD1612yes—
443C22×C4#13512yes—
444C22×C4#13712yes—
445C22×C4C23×C411yescharacteristic
446C22×C4C2×#4111yescharacteristic
447C22×C4C2×#4111yescharacteristic
448C22×C4C2×#4111yescharacteristic
449C22×C4C2×#4111yescharacteristic
450C22×C4C2×#4111yescharacteristic
451C22×C4H(5,𝔽2)11yescharacteristic
452C22×C4H(5,𝔽2)11yescharacteristic
453C22×C4H(5,𝔽2)11yescharacteristic
454C22×C4H(5,𝔽2)11yescharacteristic
455C22×C4H(5,𝔽2)11yescharacteristic
456C22×C42−1+411yescharacteristic
457C22×C42−1+411yescharacteristic
458C22×C42−1+411yescharacteristic
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8#11714yes—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—84no—
516C4⋊C4—84no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—41no—
522C42—41no—
523C42—41no—
524C42—41no—
525C42—41no—
526C42—41no—
527C42—41no—
528C42—41no—
529C42—48no—
530C42—84no—
531C23C2×C4×D411yescharacteristic
532C23#53511yescharacteristic
533C23#53711yescharacteristic
534C23#54611yescharacteristic
535C23#54711yescharacteristic
536C23#54711yescharacteristic
537C23#55011yescharacteristic
538C23C22×SD1611yescharacteristic
539C23C2×#13511yescharacteristic
540C23C2×#13711yescharacteristic
541C23#57511yescharacteristic
542C23#57711yescharacteristic
543C23#57711yescharacteristic
544C23#57711yescharacteristic
545C23#57811yescharacteristic
546Q8—42no—
547Q8—42no—
548Q8—42no—
549Q8—42no—
550Q8—81no—
551Q8—81no—
552Q8—81no—
553Q8—81no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4C4×SD1614yes—
652C2×C4C2×#11711yescharacteristic
653C2×C4C4×#4111yescharacteristic
654C2×C4#51811yescharacteristic
655C2×C4#52011yescharacteristic
656C2×C4#52011yescharacteristic
657C2×C4#52011yescharacteristic
658C2×C4#53811yescharacteristic
659C2×C4#53811yescharacteristic
660C2×C4#53811yescharacteristic
661C2×C4#53811yescharacteristic
662C2×C4#53911yescharacteristic
663C2×C4#53911yescharacteristic
664C2×C4#54011yescharacteristic
665C2×C4#54211yescharacteristic
666C2×C4#54211yescharacteristic
667C2×C4#54211yescharacteristic
668C2×C4#55111yescharacteristic
669C2×C4#55211yescharacteristic
670C2×C4#55311yescharacteristic
671C2×C4#55311yescharacteristic
672C2×C4#55511yescharacteristic
673C2×C4#55611yescharacteristic
674C2×C4#55611yescharacteristic
675C2×C4#55611yescharacteristic
676C2×C4#56011yescharacteristic
677C2×C4#56311yescharacteristic
678C2×C4#56311yescharacteristic
679C2×C4#56311yescharacteristic
680C8—24no—
681C8—42no—
682C8—42no—
683C8—81no—
684C22#232411yescharacteristic
685C22#235411yescharacteristic
686C22#235911yescharacteristic
687C22#271411yescharacteristic
688C22#271511yescharacteristic
689C22#271811yescharacteristic
690C22#272711yescharacteristic
691C22C2×C4×SD1611yescharacteristic
692C22C4×#13711yescharacteristic
693C22#294711yescharacteristic
694C22#295211yescharacteristic
695C22#320611yescharacteristic
696C22#321211yescharacteristic
697C22#322211yescharacteristic
698C22#322511yescharacteristic
699C22#324611yescharacteristic
700C22#324811yescharacteristic
701C22#325811yescharacteristic
702C22#326311yescharacteristic
703C22#329611yescharacteristic
704C22#329811yescharacteristic
705C22#331111yescharacteristic
706C22#332011yescharacteristic
707C22#333511yescharacteristic
708C22#333511yescharacteristic
709C22#333611yescharacteristic
710C22#334011yescharacteristic
711C22#334411yescharacteristic
712C22#334911yescharacteristic
713C22#335111yescharacteristic
714C22#335611yescharacteristic
715C22#339211yescharacteristic
716C22#339411yescharacteristic
717C22#339811yescharacteristic
718C22#340111yescharacteristic
719C4—24no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—82no—
725C4—81no—
726C4—82no—
727C4—82no—
728C4—82no—
729C4—82no—
730C4—161no—
731C4—161no—
732C4—161no—
733C4#231811yescharacteristic
734C4#233711yescharacteristic
735C4#234711yescharacteristic
736C4#238311yescharacteristic
737C4#275611yescharacteristic
738C4#275911yescharacteristic
739C4#277511yescharacteristic
740C4#277711yescharacteristic
741C2#1439611yescharacteristic
742C2#2214611yescharacteristic
743C2#2215911yescharacteristic
744C2#2280511yescharacteristic
745C2#2281811yescharacteristic
746C2#2292011yescharacteristic
747C2#2293011yescharacteristic
748C2#3216611yescharacteristic
749C2#3217011yescharacteristic
750C2#3219811yescharacteristic
751C2#3220211yescharacteristic
752C2#3228011yescharacteristic
753C2#3228711yescharacteristic
754C2#3252511yescharacteristic
755C2#3253011yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
32. #1927C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19272
#140002
#139212
#113232
#113162
#111902
#111222
#110772
#109262
#109082
#108762
#108612
#108492