Finite Group Databasebeta

← #366908

Subgroups — #366908

Order 512.

1244 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic
2C2×#1998C211yesmaximal, characteristic
3C2×#1998C211yesmaximal, characteristic
4#21146C211yesmaximal, characteristic
5C2×#1801C211yesmaximal, characteristic
6C4⋊C4×M16C211yesmaximal, characteristic
7C2×C4×#101C211yesmaximal, characteristic
8#11355C211yesmaximal, characteristic
9#11354C211yesmaximal, characteristic
10#11045C211yesmaximal, characteristic
11#11045C211yesmaximal, characteristic
12#10963C211yesmaximal, characteristic
13#10963C211yesmaximal, characteristic
14#10858C211yesmaximal, characteristic
15#10857C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C2×#423C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C2×#423C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C22×#101C2211yescharacteristic
23C22×#101C2211yescharacteristic
24C22×#101C2211yescharacteristic
25C22×#101C2211yescharacteristic
26C2×C4×M16C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28C2×C4×M16C2211yescharacteristic
29C2×C4×M16C2211yescharacteristic
30#2565—22no—
31#2565—22no—
32#2565—21no—
33#2565—21no—
34#2565—21no—
35#2565—21no—
36C2×#398C414yes—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#387C414yes—
40C2×#384C2211yescharacteristic
41C2×#382C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1998—24no—
44#1998—24no—
45#1940—22no—
46#1939—22no—
47#1801—24no—
48#1771—21no—
49#1771—21no—
50#1770—21no—
51C8×C4⋊C4—21no—
52C4×#101—24no—
53C2×#343C2211yescharacteristic
54C2×#343C2211yescharacteristic
55C2×#343C2211yescharacteristic
56C2×#343C2211yescharacteristic
57C2×#343C2211yescharacteristic
58C2×#343C2211yescharacteristic
59C2×#343C2211yescharacteristic
60C2×#343C2211yescharacteristic
61C2×#343C2211yescharacteristic
62C2×#343C2211yescharacteristic
63C2×#343C2211yescharacteristic
64C2×#343C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1728C2211yescharacteristic
68#1728C2211yescharacteristic
69C23×Q8C2311yescharacteristic
70C22×M16C2311yescharacteristic
71C22×M16C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C22×M16C2311yescharacteristic
77C22×M16C2311yescharacteristic
78C2×#125—21no—
79C2×#125—21no—
80C2×#125—21no—
81C2×#125—21no—
82C2×#125—22no—
83C2×#125—22no—
84C2×#125—22no—
85C2×#125—22no—
86C2×C4×Q8—21no—
87C2×C4×Q8—21no—
88C2×C4×Q8—21no—
89C2×C4×Q8—21no—
90C2×C4×Q8—22no—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—22no—
94C22×C4⋊C4C2×C412yes—
95C22×C4⋊C4C2×C412yes—
96C22×C4⋊C4C2×C412yes—
97C22×C4⋊C4C2×C414yes—
98C22×C4⋊C4C2×C412yes—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C42C2×C412yes—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106#423—22no—
107#423—22no—
108#423—22no—
109#423—22no—
110#423—22no—
111#423—41no—
112#423—41no—
113#423D414yes—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—21no—
120C2×#101—22no—
121C2×#101—22no—
122C2×#101—22no—
123C2×#101—22no—
124C2×#101—22no—
125C2×#101—22no—
126C2×#101—22no—
127C2×#101—22no—
128C2×#101—22no—
129C2×#101—41no—
130C2×#101—41no—
131C2×#101Q814yes—
132C4×M16—22no—
133C4×M16—22no—
134C4×M16—22no—
135C4×M16—22no—
136C4×M16—22no—
137C4×M16—41no—
138C4×M16—41no—
139C4×M16D414yes—
140C2×#97—21no—
141C2×#97—21no—
142C2×#97—21no—
143C2×#97—21no—
144C2×C4×C8—21no—
145C2×C4×C8—21no—
146C2×C4×C8—21no—
147C2×C4×C8—21no—
148#398—24no—
149#398—24no—
150#398—24no—
151#398—24no—
152#391—21no—
153#391—21no—
154#391—22no—
155#391—21no—
156#391—21no—
157#391—22no—
158#387—24no—
159#387—24no—
160#387—24no—
161#387—24no—
162#384—21no—
163#384—21no—
164#384—22no—
165#382—21no—
166#382—21no—
167#382—22no—
168C4×C4⋊C4D412yes—
169C4×C4⋊C4D412yes—
170C4×C4⋊C4D411yescharacteristic
171C4×C4⋊C4D411yescharacteristic
172C4×C4⋊C4D411yescharacteristic
173C4×C4⋊C4D411yescharacteristic
174C2×#95C2×C414yes—
175C2×#95C2×C414yes—
176C2×#95C2×C414yes—
177C2×#95C2×C412yes—
178#343—22no—
179#343—22no—
180#343—22no—
181#343—22no—
182#343—22no—
183#343—22no—
184#343—22no—
185#343—22no—
186#343—22no—
187#343—22no—
188#343—22no—
189#343—22no—
190#336—22no—
191#336—22no—
192#336—21no—
193#336—21no—
194#336—21no—
195#336—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8C2×Q812yes—
209C22×Q8#4112yes—
210C23×C4C22×C412yes—
211C23×C4C22×C412yes—
212C23×C4C22×C412yes—
213C23×C4C22×C412yes—
214C23×C4C22×C412yes—
215C23×C4C22×C412yes—
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C2411yescharacteristic
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16C2×D412yes—
260C2×M16C2×D412yes—
261C2×M16C2×D412yes—
262C2×M16C2×D412yes—
263C2×M16C2×Q812yes—
264C2×M16C2×Q812yes—
265C2×M16#4112yes—
266C2×M16#4112yes—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275#125—42no—
276#125—42no—
277#125—42no—
278#125—42no—
279#125—42no—
280#125—42no—
281#125—42no—
282#125—42no—
283C4×Q8—42no—
284C4×Q8—42no—
285C4×Q8—42no—
286C4×Q8—42no—
287C4×Q8—42no—
288C4×Q8—42no—
289C4×Q8—42no—
290C4×Q8—42no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—48no—
325C2×C4⋊C4C22⋊C412yes—
326C2×C4⋊C4C22⋊C412yes—
327C2×C4⋊C4C22⋊C412yes—
328C2×C4⋊C4C22⋊C412yes—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D412yes—
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D412yes—
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D412yes—
350C2×C42C2×D412yes—
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42#4112yes—
354C2×C42#4112yes—
355C4⋊C8—24no—
356C4⋊C8—24no—
357C4⋊C8—44no—
358C4⋊C8—44no—
359C4⋊C8—42no—
360C4⋊C8—42no—
361#101—28no—
362#101—28no—
363#101—44no—
364#101—44no—
365#97—24no—
366#97—42no—
367#97—42no—
368#97—42no—
369C4×C8—24no—
370C4×C8—42no—
371C4×C8—42no—
372C4×C8—42no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95C22⋊C412yes—
380#95C22⋊C412yes—
381#95C22⋊C412yes—
382#95C22⋊C412yes—
383C24C23×C411yescharacteristic
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
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—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4C2×C22⋊C412yes—
441C22×C4C2×C22⋊C412yes—
442C22×C4C2×C22⋊C412yes—
443C22×C4C2×C22⋊C411yescharacteristic
444C22×C4C2×C22⋊C411yescharacteristic
445C22×C4C2×C22⋊C411yescharacteristic
446C22×C4C2×C22⋊C411yescharacteristic
447C22×C4C2×C22⋊C412yes—
448C22×C4C4×D412yes—
449C22×C4C4×D412yes—
450C22×C4C4×D412yes—
451C22×C4C4×D412yes—
452C22×C4C4×Q814yes—
453C22×C4C22×D411yescharacteristic
454C22×C4C22×D411yescharacteristic
455C22×C4C22×D411yescharacteristic
456C22×C4C22×D411yescharacteristic
457C22×C4C22×Q811yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4C2×#4111yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4C2×#4111yescharacteristic
462C22×C4C2×#4111yescharacteristic
463C22×C4H(5,𝔽2)11yescharacteristic
464C22×C42−1+411yescharacteristic
465C22×C42−1+411yescharacteristic
466C22×C42−1+411yescharacteristic
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16—41no—
488M16—41no—
489M16—41no—
490M16—41no—
491M16—41no—
492M16—41no—
493M16—41no—
494M16—41no—
495M16—41no—
496M16—41no—
497M16—41no—
498M16C22⋊Q814yes—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—48no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—48no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—22no—
552C42—22no—
553C42—21no—
554C42—22no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—22no—
559C42—44no—
560C42—44no—
561C42#12112yes—
562C42#12112yes—
563C42#12112yes—
564C42#12112yes—
565C42#12412yes—
566C42#12412yes—
567C42#12712yes—
568C42#12712yes—
569C23—22no—
570C23—22no—
571C23C22×C22⋊C411yescharacteristic
572C23C2×C4×D411yescharacteristic
573C23C2×C4×D411yescharacteristic
574C23C2×C4×Q811yescharacteristic
575C23C4×#4111yescharacteristic
576C23#51911yescharacteristic
577C23#52011yescharacteristic
578Q8—42no—
579Q8—42no—
580Q8—42no—
581Q8—42no—
582Q8—42no—
583Q8—42no—
584Q8—42no—
585Q8—42no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4—82no—
627C2×C4—82no—
628C2×C4#39012yes—
629C2×C4#39012yes—
630C2×C4#39012yes—
631C2×C4#39012yes—
632C2×C4#41314yes—
633C2×C4C2×#12111yescharacteristic
634C2×C4C2×#12111yescharacteristic
635C2×C4C2×C22⋊Q811yescharacteristic
636C2×C4#52511yescharacteristic
637C2×C4C2×#12411yescharacteristic
638C2×C4#52911yescharacteristic
639C2×C4C2×#12711yescharacteristic
640C2×C4#53311yescharacteristic
641C2×C4#53611yescharacteristic
642C2×C4#53711yescharacteristic
643C2×C4#54111yescharacteristic
644C2×C4#54211yescharacteristic
645C2×C4#54611yescharacteristic
646C2×C4#54611yescharacteristic
647C2×C4#54611yescharacteristic
648C2×C4#54711yescharacteristic
649C2×C4#54711yescharacteristic
650C2×C4#54711yescharacteristic
651C2×C4#54811yescharacteristic
652C2×C4#54811yescharacteristic
653C2×C4#54811yescharacteristic
654C2×C4D4×Q811yescharacteristic
655C2×C4D4×Q811yescharacteristic
656C2×C4D4×Q811yescharacteristic
657C2×C4#55211yescharacteristic
658C2×C4#55211yescharacteristic
659C2×C4#55411yescharacteristic
660C2×C4#55611yescharacteristic
661C8—24no—
662C8—42no—
663C8—42no—
664C8—42no—
665C8—42no—
666C8—42no—
667C8—81no—
668C8—81no—
669C22—22no—
670C22—22no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—22no—
676C22—22no—
677C22C2×#39011yescharacteristic
678C22C4×C22⋊Q811yescharacteristic
679C22#232311yescharacteristic
680C22#233911yescharacteristic
681C22Q8×C22⋊C411yescharacteristic
682C22#236011yescharacteristic
683C22#236211yescharacteristic
684C22C2×#41312yes—
685C22#288912yes—
686C4—24no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—44no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—82no—
696C4—82no—
697C4—82no—
698C4#241511yescharacteristic
699C4#241711yescharacteristic
700C4#242711yescharacteristic
701C4#242911yescharacteristic
702C4#248911yescharacteristic
703C4#249211yescharacteristic
704C4#254011yescharacteristic
705C4#254211yescharacteristic
706C2—21no—
707C2—21no—
708C2—21no—
709C2—21no—
710C2#1399711yescharacteristic
711C2#2121811yescharacteristic
712C2#2122011yescharacteristic
713C2#2248012yes—
714C2#2251712yes—
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#19982
#211462
C2×#18012
C4⋊C4×M162
C2×C4×#1012
#113552
#113542
#110452
#109632
#108582
#108572