Finite Group Databasebeta

← #664770

Subgroups — #664770

Order 512.

2314 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2514C211yesmaximal, characteristic
2C2×#2365C211yesmaximal, characteristic
3#15819C214yesmaximal
4#15604C214yesmaximal
5#15240C211yesmaximal, characteristic
6#15190C211yesmaximal, characteristic
7#15188C211yesmaximal, characteristic
8#15180C211yesmaximal, characteristic
9#14944C214yesmaximal
10#14714C211yesmaximal, characteristic
11#14056C214yesmaximal
12#14049C211yesmaximal, characteristic
13#14024C211yesmaximal, characteristic
14#14024C211yesmaximal, characteristic
15#14003C211yesmaximal, characteristic
16#14003C211yesmaximal, characteristic
17#13942C211yesmaximal, characteristic
18C4×#391C211yesmaximal, characteristic
19C4×#387C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25#2514—28no—
26C2×#401C2212yes—
27C2×#400C2212yes—
28#2365—28no—
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2212yes—
44C2×#387C2212yes—
45C2×#387C2212yes—
46C2×#387C2212yes—
47C2×#387C2214yes—
48C2×#387C2212yes—
49C2×#384C2211yescharacteristic
50C2×#383C2212yes—
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C43C2211yescharacteristic
59#1445C2214yes—
60#1445C2214yes—
61#1445C2214yes—
62#1444C2214yes—
63#1444C2214yes—
64#1443C2214yes—
65#1443C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1436C2212yes—
74#1436C2214yes—
75#1436C2212yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2214yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2214yes—
83C4⋊#95C2211yescharacteristic
84#1434C2214yes—
85#1434C2214yes—
86#1434C2214yes—
87#1434C2212yes—
88C4×#95C2211yescharacteristic
89C4×#95C2211yescharacteristic
90C4×#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2311yescharacteristic
95C23×Q8C2311yescharacteristic
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—42no—
103C2×C4⋊Q8—42no—
104C2×C4⋊Q8—42no—
105C2×C4×Q8—24no—
106C2×C4×Q8—24no—
107C2×C4×Q8—24no—
108C2×C4×Q8—24no—
109C2×C4×Q8—42no—
110C2×C4×Q8—42no—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C22×C42C2312yes—
130C22×C42C2311yescharacteristic
131C22×C42C2312yes—
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2312yes—
135C22×C42C2312yes—
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140#401—28no—
141#400—28no—
142#391—24no—
143#391—24no—
144#391—24no—
145#391—24no—
146#391—24no—
147#391—24no—
148#391—24no—
149#391—24no—
150#391—24no—
151#391—42no—
152#391—42no—
153#391—42no—
154#391—42no—
155#389—28no—
156#389—24no—
157#387—28no—
158#387—28no—
159#387—28no—
160#387—28no—
161#387—216no—
162#384—24no—
163#383—28no—
164#382—24no—
165#382—42no—
166C4×C4⋊C4—28no—
167C4×C4⋊C4—24no—
168C4×C4⋊C4—24no—
169C4×C4⋊C4—42no—
170C4×C4⋊C4D418yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2312yes—
210C43—42no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8#4114yes—
231C22×Q8#4114yes—
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2412yes—
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C23×C4C2411yescharacteristic
241C23×C4C2411yescharacteristic
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2411yescharacteristic
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C4⋊Q8—232no—
252C4⋊Q8—416no—
253C4⋊Q8—416no—
254C4×Q8—416no—
255C4×Q8—416no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×D414yes—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4#4114yes—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—24no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—24no—
313C2×C42—24no—
314C2×C42—24no—
315C2×C42—22no—
316C2×C42—24no—
317C2×C42—28no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—24no—
327C2×C42—24no—
328C2×C42—24no—
329C2×C42—28no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42C2×D414yes—
335C2×C42C2×D414yes—
336C2×C42C2×D414yes—
337C2×C42#4114yes—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—28no—
354#95—28no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—24no—
364#95—28no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—42no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95C2×D414yes—
375#95C2×D414yes—
376#95#4118yes—
377C24C2511yescharacteristic
378C2×Q8—28no—
379C2×Q8—28no—
380C2×Q8—28no—
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—28no—
384C2×Q8—44no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8—44no—
388C2×Q8—44no—
389C2×Q8—44no—
390C2×Q8—44no—
391C2×Q8—44no—
392C2×Q8—44no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8—44no—
396C2×Q8—44no—
397C2×Q8—44no—
398C2×Q8—44no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4C22×D412yes—
488C22×C4C22×D412yes—
489C22×C4C22×D412yes—
490C22×C4C22×D412yes—
491C22×C4C22×D412yes—
492C22×C4C22×D412yes—
493C22×C4C22×D412yes—
494C22×C4C2×#4114yes—
495C22×C4C2×#4114yes—
496C22×C4C2×#4114yes—
497C22×C4C2×#4114yes—
498C22×C4C2×#4114yes—
499C22×C4C2×#4114yes—
500C22×C4C2×#4114yes—
501C22×C4C2×#4112yes—
502C22×C4C2×#4112yes—
503C22×C4C2×#4112yes—
504C22×C4C2×#4112yes—
505C22×C4H(5,𝔽2)12yes—
506C22×C4H(5,𝔽2)12yes—
507C22×C42−1+414yes—
508C22×C42−1+414yes—
509C22×C42−1+414yes—
510C4⋊C4—216no—
511C4⋊C4—216no—
512C4⋊C4—28no—
513C4⋊C4—28no—
514C4⋊C4—28no—
515C4⋊C4—48no—
516C4⋊C4—48no—
517C4⋊C4—48no—
518C4⋊C4—416no—
519C4⋊C4—416no—
520C4⋊C4—44no—
521C4⋊C4—48no—
522C4⋊C4—44no—
523C4⋊C4—44no—
524C4⋊C4—44no—
525C4⋊C4—416no—
526C42—28no—
527C42—28no—
528C42—28no—
529C42—28no—
530C42—48no—
531C42—48no—
532C42—48no—
533C42—48no—
534C42—48no—
535C42—48no—
536C42—44no—
537C42—44no—
538C42—44no—
539C23C23×D411yescharacteristic
540C23C22×#4111yescharacteristic
541C23C22×#4111yescharacteristic
542C23C22×#4111yescharacteristic
543C23C22×#4111yescharacteristic
544C23C22×#4112yes—
545C23C2×H(5,𝔽2)11yescharacteristic
546C23C2×H(5,𝔽2)11yescharacteristic
547C23C2×2−1+412yes—
548C23C2×2−1+412yes—
549C23C2×2−1+412yes—
550Q8—416no—
551Q8—416no—
552Q8—88no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—28no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—42no—
594C2×C4—42no—
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—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—44no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—44no—
647C2×C4—42no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—44no—
654C2×C4#52514yes—
655C2×C4#52914yes—
656C2×C4#53214yes—
657C2×C4#53614yes—
658C2×C4#53814yes—
659C2×C4#54614yes—
660C2×C4#55014yes—
661C2×C4#55114yes—
662C2×C4#55314yes—
663C2×C4#55618yes—
664C22C2×#52511yescharacteristic
665C22C2×#52911yescharacteristic
666C22C2×#53211yescharacteristic
667C22C2×#53611yescharacteristic
668C22C2×#53811yescharacteristic
669C22C2×#54611yescharacteristic
670C22C2×#55011yescharacteristic
671C22C2×#55111yescharacteristic
672C22C2×#55311yescharacteristic
673C22C2×#55612yes—
674C22#348212yes—
675C22#348212yes—
676C22#348212yes—
677C22#349911yescharacteristic
678C22#349911yescharacteristic
679C22#350912yes—
680C22#351112yes—
681C22#352012yes—
682C22#352312yes—
683C22#352312yes—
684C22#352312yes—
685C22#353812yes—
686C22#355212yes—
687C4—28no—
688C4—24no—
689C4—24no—
690C4—42no—
691C4—42no—
692C4—44no—
693C4—42no—
694C4—44no—
695C4—44no—
696C4—44no—
697C4—44no—
698C4—42no—
699C4—82no—
700C4—82no—
701C4—82no—
702C4—82no—
703C4—82no—
704C4—82no—
705C4#246718yes—
706C2C2×#246711yescharacteristic
707C2#3497211yescharacteristic
708C2#3567011yescharacteristic
709C2#3631312yes—
710C2#3640611yescharacteristic
711C2#3659411yescharacteristic
712C2#3808111yescharacteristic
713C2#3974411yescharacteristic
714C2#4010012yes—
715C2#5942512yes—
716C2#5969512yes—
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25142
C2×#23652
#158192
#156042
#152402
#151902
#151882
#151802
#149442
#147142
#140562
#140492
#140242
#140032
#139422
C4×#3912
C4×#3872