Finite Group Databasebeta

← #362978

Subgroups — #362978

Order 512.

1542 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×Q8C211yesmaximal, characteristic
2C2×#1916C212yesmaximal
3#11380C212yesmaximal
4#11202C212yesmaximal
5#10874C212yesmaximal
6#10832C211yesmaximal, characteristic
7#10795C211yesmaximal, characteristic
8#10795C211yesmaximal, characteristic
9#10795C211yesmaximal, characteristic
10#10795C211yesmaximal, characteristic
11C4×#336C211yesmaximal, characteristic
12C22×C4×Q8C411yescharacteristic
13C22×C4×Q8C411yescharacteristic
14C22×C4×Q8C2211yescharacteristic
15C22×C4⋊C8C2212yes—
16C22×C4×C8C2212yes—
17C42×Q8—28no—
18C2×C4×C4⋊C4C411yescharacteristic
19C2×C4×C4⋊C4C411yescharacteristic
20C2×C4×C4⋊C4C411yescharacteristic
21C2×C4×C4⋊C4C411yescharacteristic
22C2×C4×C4⋊C4C411yescharacteristic
23C2×C4×C4⋊C4C411yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×C43C2211yescharacteristic
28C2×C43C2211yescharacteristic
29C2×C43C2211yescharacteristic
30#1916—28no—
31C2×#336C2212yes—
32C2×#336C2212yes—
33C2×#336C2212yes—
34C2×#336C2212yes—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38C2×#336C2212yes—
39C2×#336C2212yes—
40C2×#336C2212yes—
41C2×#336C2212yes—
42C2×#336C2212yes—
43C2×#336C2212yes—
44C2×#336C2211yescharacteristic
45C23×Q8C2×C411yescharacteristic
46C23×C8C2312yes—
47C23×C8C2312yes—
48C23×C8C2312yes—
49C23×C8C2312yes—
50C2×C4×Q8—24no—
51C2×C4×Q8—24no—
52C2×C4×Q8—24no—
53C2×C4×Q8—24no—
54C2×C4×Q8—24no—
55C2×C4×Q8—24no—
56C2×C4×Q8—24no—
57C2×C4×Q8—22no—
58C2×C4×Q8—22no—
59C2×C4×Q8C818yescomplemented
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C4⋊C4C2×C411yescharacteristic
64C22×C4⋊C4C2×C411yescharacteristic
65C22×C4⋊C4C2×C411yescharacteristic
66C22×C4⋊C4C2×C411yescharacteristic
67C22×C4⋊C4C2×C411yescharacteristic
68C22×C4⋊C4C2×C411yescharacteristic
69C22×C42C2×C411yescharacteristic
70C22×C42C2×C411yescharacteristic
71C22×C42C2×C411yescharacteristic
72C22×C42C2×C411yescharacteristic
73C22×C42C2×C411yescharacteristic
74C22×C42C2×C411yescharacteristic
75C22×C42C2×C411yescharacteristic
76C22×C42C2×C411yescharacteristic
77C22×C42C2×C411yescharacteristic
78C22×C42C2×C411yescharacteristic
79C22×C42C2×C411yescharacteristic
80C22×C42C2×C411yescharacteristic
81C22×C42C2311yescharacteristic
82C22×C42C2311yescharacteristic
83C22×C42C2311yescharacteristic
84C22×C42C2311yescharacteristic
85C22×C42C2311yescharacteristic
86C22×C42C2311yescharacteristic
87C22×C42C2311yescharacteristic
88C2×C4⋊C8—24no—
89C2×C4⋊C8—24no—
90C2×C4⋊C8—42no—
91C2×C4×C8—24no—
92C2×C4×C8—24no—
93C2×C4×C8—42no—
94C4×C4⋊C4—24no—
95C4×C4⋊C4—24no—
96C4×C4⋊C4—24no—
97C4×C4⋊C4—24no—
98C4×C4⋊C4—24no—
99C4×C4⋊C4—24no—
100C4×C4⋊C4—24no—
101C4×C4⋊C4—24no—
102C4×C4⋊C4D418yes—
103C2×#95C2×C411yescharacteristic
104C2×#95C2×C411yescharacteristic
105C2×#95C2×C411yescharacteristic
106C2×#95C2×C411yescharacteristic
107C2×#95C2×C411yescharacteristic
108C2×#95C2×C411yescharacteristic
109C43—24no—
110C43—24no—
111C43—24no—
112#336—24no—
113#336—24no—
114#336—24no—
115#336—24no—
116#336—24no—
117#336—24no—
118#336—24no—
119#336—24no—
120#336—24no—
121#336—22no—
122#336—22no—
123#336—22no—
124#336—42no—
125#336Q814yescomplemented
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8C2×C814yes—
133C23×C4C22×C411yescharacteristic
134C23×C4C22×C411yescharacteristic
135C23×C4C22×C411yescharacteristic
136C23×C4C22×C411yescharacteristic
137C23×C4C22×C411yescharacteristic
138C23×C4C22×C411yescharacteristic
139C23×C4C22×C411yescharacteristic
140C23×C4C22×C411yescharacteristic
141C23×C4C22×C411yescharacteristic
142C23×C4C22×C411yescharacteristic
143C23×C4C22×C411yescharacteristic
144C23×C4C22×C411yescharacteristic
145C23×C4C22×C411yescharacteristic
146C23×C4C22×C411yescharacteristic
147C23×C4C2411yescharacteristic
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8—22no—
165C22×C8—22no—
166C22×C8—22no—
167C22×C8—22no—
168C22×C8—22no—
169C22×C8—22no—
170C22×C8—22no—
171C22×C8—22no—
172C22×C8—22no—
173C22×C8—22no—
174C22×C8C2×Q814yes—
175C22×C8#4114yes—
176C4×Q8—232no—
177C4×Q8—216no—
178C4×Q8—216no—
179C4×Q8—232no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4C22⋊C414yes—
201C2×C4⋊C4C22⋊C414yes—
202C2×C4⋊C4C2×C814yes—
203C2×C4⋊C4C2×C814yes—
204C2×C4⋊C4C2×C814yes—
205C2×C4⋊C4M1614yes—
206C2×C4⋊C4M1614yes—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—21no—
226C2×C42—21no—
227C2×C42—22no—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42—22no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—41no—
254C2×C42—41no—
255C2×C42—41no—
256C2×C42—41no—
257C2×C42—41no—
258C2×C42—41no—
259C2×C42C2×C814yes—
260C2×C42C2×C814yes—
261C2×C42C2×C814yes—
262C2×C42M1614yes—
263C2×C42C2×D414yes—
264C2×C42C2×D414yes—
265C2×C42C2×D414yes—
266C2×C42C2×Q812yes—
267C2×C42#4114yes—
268C2×C42#4112yes—
269C2×C42#4112yes—
270C2×C42#4112yes—
271C4⋊C8—48no—
272C4×C8—48no—
273#95—22no—
274#95—22no—
275#95—22no—
276#95—22no—
277#95C22⋊C414yes—
278#95C22⋊C414yes—
279C24C23×C411yescharacteristic
280C2×Q8—28no—
281C2×Q8—28no—
282C2×Q8—28no—
283C2×Q8—28no—
284C2×Q8—28no—
285C2×Q8—28no—
286C2×Q8—28no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
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×C4C2×C22⋊C412yes—
356C22×C4C2×C22⋊C412yes—
357C22×C4C2×C22⋊C412yes—
358C22×C4C2×C22⋊C412yes—
359C22×C4C2×C22⋊C412yes—
360C22×C4C2×C22⋊C412yes—
361C22×C4#11712yes—
362C22×C4#11712yes—
363C22×C4#11712yes—
364C22×C4#11712yes—
365C22×C4C4×Q812yes—
366C22×C4C4×Q812yes—
367C22×C4C22×C812yes—
368C22×C4C22×C812yes—
369C22×C4C22×C812yes—
370C22×C4C22×C812yes—
371C22×C4C22×C812yes—
372C22×C4C22×C812yes—
373C22×C4C22×C812yes—
374C22×C4C2×M1612yes—
375C22×C4C2×M1612yes—
376C22×C4C2×M1612yes—
377C22×C4C2×M1612yes—
378C22×C4C2×M1612yes—
379C22×C4C2×M1612yes—
380C22×C4C2×M1612yes—
381C22×C4C2×M1612yes—
382C22×C4C2×M1612yes—
383C22×C4#13112yes—
384C22×C4#13112yes—
385C22×C4C22×D412yes—
386C22×C4C22×Q811yescharacteristic
387C22×C4C2×#4112yes—
388C22×C4C2×#4111yescharacteristic
389C22×C4C2×#4111yescharacteristic
390C22×C4C2×#4111yescharacteristic
391C22×C4C2×#4112yes—
392C22×C4H(5,𝔽2)11yescharacteristic
393C22×C42−1+411yescharacteristic
394C22×C42−1+412yes—
395C2×C8—24no—
396C2×C8—24no—
397C2×C8—24no—
398C2×C8—24no—
399C2×C8—24no—
400C2×C8—24no—
401C2×C8—42no—
402C2×C8—42no—
403C2×C8—42no—
404C2×C8—42no—
405C2×C8—42no—
406C2×C8—42no—
407C2×C8—42no—
408C2×C8—42no—
409C2×C8—42no—
410C2×C8—42no—
411C2×C8—42no—
412C2×C8—42no—
413C2×C8—42no—
414C2×C8—42no—
415C2×C8—42no—
416C2×C8—42no—
417C2×C8—42no—
418C2×C8—42no—
419C2×C8—42no—
420C2×C8—42no—
421C2×C8—42no—
422C2×C8—42no—
423C4⋊C4—28no—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—28no—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—28no—
431C4⋊C4C22⋊C8116yes—
432C42—28no—
433C42—28no—
434C42—24no—
435C42—24no—
436C42—24no—
437C42—24no—
438C42—24no—
439C42—24no—
440C42—24no—
441C42—24no—
442C42—24no—
443C42—24no—
444C42—24no—
445C42—24no—
446C42—28no—
447C42—28no—
448C42—28no—
449C42—28no—
450C42—44no—
451C42—44no—
452C42—44no—
453C42—44no—
454C42—44no—
455C42—44no—
456C42—42no—
457C42—42no—
458C23C22×C22⋊C411yescharacteristic
459C23C2×#11711yescharacteristic
460C23C2×#11711yescharacteristic
461C23C2×C4×Q811yescharacteristic
462C23C4×#4111yescharacteristic
463C23#51911yescharacteristic
464C23#52011yescharacteristic
465C23C23×C811yescharacteristic
466C23C22×M1611yescharacteristic
467C23C22×M1611yescharacteristic
468C23C22×M1611yescharacteristic
469C23C2×#13111yescharacteristic
470C23C2×#13111yescharacteristic
471C23#56811yescharacteristic
472C23#56811yescharacteristic
473Q8—232no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4C2×C22⋊C814yes—
565C2×C4C2×C22⋊C814yes—
566C2×C4C2×C22⋊C814yes—
567C2×C4#40714yes—
568C2×C4#43114yes—
569C2×C4#43114yes—
570C2×C4C8×Q814yes—
571C2×C4#44614yes—
572C2×C4#52512yes—
573C2×C4#52512yes—
574C2×C4#52912yes—
575C2×C4#53312yes—
576C2×C4#54112yes—
577C2×C4#54212yes—
578C2×C4#54612yes—
579C2×C4#54712yes—
580C2×C4#54812yes—
581C2×C4D4×Q812yes—
582C2×C4#55212yes—
583C2×C4#55411yescharacteristic
584C2×C4#55612yes—
585C2×C4#55611yescharacteristic
586C2×C4#55711yescharacteristic
587C2×C4#55911yescharacteristic
588C8—44no—
589C8—44no—
590C8—82no—
591C8—82no—
592C22#228011yescharacteristic
593C22#229511yescharacteristic
594C22#232011yescharacteristic
595C22#233911yescharacteristic
596C22Q8×C22⋊C411yescharacteristic
597C22#235511yescharacteristic
598C22#235611yescharacteristic
599C22C22×C22⋊C811yescharacteristic
600C22C2×#40711yescharacteristic
601C22#288011yescharacteristic
602C22#288011yescharacteristic
603C22C2×#43111yescharacteristic
604C22C2×#43111yescharacteristic
605C22#292011yescharacteristic
606C22#292011yescharacteristic
607C22#292211yescharacteristic
608C22#292311yescharacteristic
609C22#292511yescharacteristic
610C22#292511yescharacteristic
611C22C2×C8×Q811yescharacteristic
612C22C2×#44611yescharacteristic
613C22Q8×M1611yescharacteristic
614C22Q8×M1611yescharacteristic
615C22C8×#4111yescharacteristic
616C22#296511yescharacteristic
617C22#297011yescharacteristic
618C22#297011yescharacteristic
619C22#298211yescharacteristic
620C22#298311yescharacteristic
621C22#298411yescharacteristic
622C22#298411yescharacteristic
623C22#298811yescharacteristic
624C22#298911yescharacteristic
625C22#299011yescharacteristic
626C22#299011yescharacteristic
627C4—24no—
628C4—24no—
629C4—24no—
630C4—24no—
631C4—24no—
632C4—24no—
633C4—24no—
634C4—24no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4#245812yes—
642C4#246212yes—
643C4#246512yes—
644C4#246912yes—
645C2#1392711yescharacteristic
646C2#2071411yescharacteristic
647C2#2072011yescharacteristic
648C2#2133911yescharacteristic
649C2#2134611yescharacteristic
650C2#2201811yescharacteristic
651C2#2202011yescharacteristic
652C2#2246911yescharacteristic
653C2#2247111yescharacteristic
654C2Q8×C22⋊C811yescharacteristic
655C2#2251011yescharacteristic
656C2#2282111yescharacteristic
657C2#2282311yescharacteristic
658C2#2282811yescharacteristic
659C2#2283011yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socle, prime radicalC24C23×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
59. C2×C4×Q8C8semidirect
125. #336Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C42×Q82
C2×#19162
#113802
#112022
#108742
#108322
#107952
C4×#3362