Finite Group Databasebeta

← #522262

Subgroups — #522262

Order 512.

2130 conjugacy classes of subgroups.

The subgroup lattice has 673 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2859C211yesmaximal, characteristic
2#14460C214yesmaximal
3#14459C214yesmaximal
4#14266C212yesmaximal
5#14151C211yesmaximal, characteristic
6#14151C211yesmaximal, characteristic
7#14054C212yesmaximal
8#14054C212yesmaximal
9#14051C212yesmaximal
10#14050C212yesmaximal
11#14006C212yesmaximal
12#13982C212yesmaximal
13C4⋊C42C211yesmaximal, characteristic
14C4⋊C42C211yesmaximal, characteristic
15#13783C212yesmaximal
16C4×#382C211yesmaximal, characteristic
17#13755C211yesmaximal, characteristic
18C22×#125C2212yes—
19#2859C4116yescomplemented
20C2×#389C2212yes—
21C2×#389C2212yes—
22C2×#389C2212yes—
23C2×#389C2212yes—
24C2×#389C2212yes—
25C2×#389C2212yes—
26C2×#389C2212yes—
27C2×#389C2212yes—
28C2×#384C2211yescharacteristic
29C2×#384C2211yescharacteristic
30C2×#382C2211yescharacteristic
31C2×#382C2211yescharacteristic
32C2×#382C2212yes—
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2212yes—
37C2×C4×C4⋊C4C2212yes—
38C2×C4×C4⋊C4C2212yes—
39C2×C4×C4⋊C4C2212yes—
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×#376C2212yes—
42C2×C43C2211yescharacteristic
43#1445C2214yes—
44#1445C2214yes—
45#1443C2214yes—
46#1443C2214yes—
47#1442C2214yes—
48#1442C2214yes—
49#1441C2214yes—
50#1441C2214yes—
51#1441C2214yes—
52#1441C2214yes—
53#1436C2214yes—
54#1436C2214yes—
55#1436C2214yes—
56#1436C2214yes—
57#1436C2214yes—
58#1436C2214yes—
59C4⋊#95C2212yes—
60C4⋊#95C2212yes—
61C4⋊#95C2212yes—
62C4⋊#95C2212yes—
63C4⋊#95C2214yes—
64C4⋊#95C2214yes—
65C4⋊#95C2212yes—
66C4⋊#95C2212yes—
67C4⋊#95C2211yescharacteristic
68C4⋊#95C2211yescharacteristic
69C4⋊#95C2211yescharacteristic
70C4⋊#95C2211yescharacteristic
71C4⋊#95C2211yescharacteristic
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75#1434C2212yes—
76#1434C2212yes—
77#1434C2214yes—
78#1434C2212yes—
79#1434C2212yes—
80#1434C2214yes—
81C4×#95C2212yes—
82C4×#95C2212yes—
83C4×#95C2212yes—
84C2×#125—44no—
85C2×#125—44no—
86C2×#125C2×C4116yes—
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2312yes—
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2314yes—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C42C2312yes—
106C22×C42C2312yes—
107C22×C42C2312yes—
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2312yes—
113C22×C42C2314yes—
114C22×C42C2314yes—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118#389—28no—
119#389—44no—
120#389—44no—
121#389—44no—
122#389C2×C4116yes—
123#389C2×C4116yes—
124#389C2×C4116yes—
125#389C2×C4116yes—
126#384C2×C418yes—
127#384C2×C418yes—
128#382—24no—
129#382—24no—
130#382C2×C4116yes—
131C4×C4⋊C4—28no—
132C4×C4⋊C4—24no—
133C4×C4⋊C4—24no—
134C4×C4⋊C4—24no—
135C4×C4⋊C4—44no—
136C4×C4⋊C4—44no—
137C4×C4⋊C4—44no—
138C4×C4⋊C4Q818yes—
139#376—44no—
140C2×#95C2312yes—
141C2×#95C2312yes—
142C2×#95C2312yes—
143C2×#95C2312yes—
144C2×#95C2312yes—
145C2×#95C2312yes—
146C2×#95C2312yes—
147C2×#95C2314yes—
148C2×#95C2314yes—
149C2×#95C2312yes—
150C2×#95C2312yes—
151C2×#95C2312yes—
152C2×#95C2312yes—
153C2×#95C2312yes—
154C2×#95C2312yes—
155C2×#95C2312yes—
156C2×#95C2312yes—
157C2×#95C2312yes—
158C2×#95C2314yes—
159C2×#95C2312yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2312yes—
164C2×#95C2312yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C43C2×C418yes—
175C23×C4C2412yes—
176C23×C4C2412yes—
177C23×C4C2412yes—
178C23×C4C2412yes—
179C23×C4C2414yes—
180C23×C4C2414yes—
181C23×C4C2411yescharacteristic
182C23×C4C2411yescharacteristic
183C23×C4C2411yescharacteristic
184C23×C4C2411yescharacteristic
185C23×C4C2412yes—
186C23×C4C2412yes—
187C23×C4C2412yes—
188C23×C4C2412yes—
189C23×C4C2411yescharacteristic
190C23×C4C2411yescharacteristic
191C23×C4C2411yescharacteristic
192#125—432no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—44no—
227C2×C4⋊C4—44no—
228C2×C4⋊C4—44no—
229C2×C4⋊C4—44no—
230C2×C4⋊C4—44no—
231C2×C4⋊C4—44no—
232C2×C4⋊C4—44no—
233C2×C4⋊C4—44no—
234C2×C4⋊C4—44no—
235C2×C4⋊C4C22×C418yes—
236C2×C4⋊C4C22×C418yes—
237C2×C4⋊C4C22×C418yes—
238C2×C4⋊C4C22×C418yes—
239C2×C4⋊C4C22×C4116yes—
240C2×C4⋊C4C22×C4116yes—
241C2×C4⋊C4C22×C418yes—
242C2×C4⋊C4C22×C418yes—
243C2×C4⋊C4C2×Q814yes—
244C2×C4⋊C4C2×Q814yes—
245C2×C4⋊C4#4114yes—
246C2×C4⋊C4#4114yes—
247C2×C42—24no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—24no—
254C2×C42—22no—
255C2×C42—22no—
256C2×C42—22no—
257C2×C42—24no—
258C2×C42—24no—
259C2×C42—24no—
260C2×C42—24no—
261C2×C42—24no—
262C2×C42—24no—
263C2×C42—24no—
264C2×C42—24no—
265C2×C42—24no—
266C2×C42—28no—
267C2×C42—41no—
268C2×C42—41no—
269C2×C42—41no—
270C2×C42—41no—
271C2×C42—44no—
272C2×C42—44no—
273C2×C42—44no—
274C2×C42—44no—
275C2×C42—44no—
276C2×C42C22×C414yes—
277C2×C42C22×C414yes—
278C2×C42C22×C414yes—
279C2×C42C22×C414yes—
280C2×C42C22×C414yes—
281C2×C42C22×C414yes—
282C2×C42C22×C414yes—
283C2×C42C2×Q818yes—
284C2×C42C2×Q814yes—
285C2×C42#4114yes—
286#95—28no—
287#95—24no—
288#95—24no—
289#95—24no—
290#95—24no—
291#95—24no—
292#95—24no—
293#95—24no—
294#95—28no—
295#95—42no—
296#95—42no—
297#95—42no—
298#95—44no—
299#95—44no—
300#95—44no—
301#95—42no—
302#95—42no—
303#95—42no—
304#95—42no—
305#95—42no—
306#95—44no—
307#95—42no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95—44no—
312#95—44no—
313#95—44no—
314#95—44no—
315#95—44no—
316#95—44no—
317#95C22×C4116yes—
318#95C22×C4116yes—
319#95C2×Q818yes—
320C24C2511yescharacteristic
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—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
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—22no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
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—22no—
413C22×C4C23×C412yes—
414C22×C4C23×C412yes—
415C22×C4C23×C418yes—
416C22×C4C23×C418yes—
417C22×C4C23×C412yes—
418C22×C4C23×C412yes—
419C22×C4C23×C412yes—
420C22×C4C23×C412yes—
421C22×C4C23×C412yes—
422C22×C4C22×Q814yes—
423C22×C4C22×Q814yes—
424C22×C4C22×Q812yes—
425C22×C4C22×Q812yes—
426C22×C4C22×Q812yes—
427C22×C4C2×#4114yes—
428C22×C4C2×#4114yes—
429C22×C4C2×#4112yes—
430C22×C4C2×#4112yes—
431C22×C4C2×#4112yes—
432C22×C4C2×#4112yes—
433C22×C4C2×#4112yes—
434C22×C4H(5,𝔽2)12yes—
435C22×C4H(5,𝔽2)12yes—
436C22×C4H(5,𝔽2)12yes—
437C22×C42−1+412yes—
438C22×C42−1+412yes—
439C22×C42−1+412yes—
440C4⋊C4—216no—
441C4⋊C4—216no—
442C4⋊C4—216no—
443C4⋊C4—216no—
444C4⋊C4—28no—
445C4⋊C4—28no—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—48no—
449C4⋊C4—48no—
450C4⋊C4—416no—
451C4⋊C4—416no—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4—44no—
455C4⋊C4—44no—
456C4⋊C4—88no—
457C4⋊C4—88no—
458C42—28no—
459C42—28no—
460C42—28no—
461C42—28no—
462C42—216no—
463C42—44no—
464C42—44no—
465C42—48no—
466C42—48no—
467C42—48no—
468C42—88no—
469C42—88no—
470C42C4×Q8116yes—
471C23C24×C411yescharacteristic
472C23C23×Q811yescharacteristic
473C23C22×#4111yescharacteristic
474C23C22×#4111yescharacteristic
475C23C22×#4111yescharacteristic
476C23C2×H(5,𝔽2)11yescharacteristic
477C23C2×H(5,𝔽2)11yescharacteristic
478C23C2×H(5,𝔽2)11yescharacteristic
479C23C2×2−1+411yescharacteristic
480C23C2×2−1+411yescharacteristic
481C23C2×2−1+411yescharacteristic
482C23#58511yescharacteristic
483C23#58511yescharacteristic
484C23#58511yescharacteristic
485C23#58511yescharacteristic
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—28no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—28no—
498C2×C4—28no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—28no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—28no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—44no—
537C2×C4—41no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—41no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4C2×C4×Q814yes—
591C2×C4C2×C4×Q814yes—
592C2×C4C2×C4×Q814yes—
593C2×C4C4×#4114yes—
594C2×C4#51814yes—
595C2×C4#51914yes—
596C2×C4#52014yes—
597C2×C4#54214yes—
598C2×C4#54214yes—
599C2×C4#54414yes—
600C2×C4#54414yes—
601C2×C4#55214yes—
602C2×C4#55314yes—
603C2×C4#55414yes—
604C2×C4#55714yes—
605C22C22×C4×Q811yescharacteristic
606C22C2×C4×#4111yescharacteristic
607C22C2×#51811yescharacteristic
608C22C2×#51911yescharacteristic
609C22C2×#52011yescharacteristic
610C22#342811yescharacteristic
611C22#342811yescharacteristic
612C22C2×#54211yescharacteristic
613C22C2×#54211yescharacteristic
614C22C2×#54411yescharacteristic
615C22C2×#54411yescharacteristic
616C22C2×#55211yescharacteristic
617C22C2×#55311yescharacteristic
618C22C2×#55411yescharacteristic
619C22C2×#55711yescharacteristic
620C22#350411yescharacteristic
621C22#350411yescharacteristic
622C22#351211yescharacteristic
623C22#351211yescharacteristic
624C22#351411yescharacteristic
625C22#351411yescharacteristic
626C22#351511yescharacteristic
627C22#351511yescharacteristic
628C22#351711yescharacteristic
629C22#351711yescharacteristic
630C22#351811yescharacteristic
631C22#351811yescharacteristic
632C22#354611yescharacteristic
633C22#354611yescharacteristic
634C22#354711yescharacteristic
635C22#354711yescharacteristic
636C22#355411yescharacteristic
637C22#355411yescharacteristic
638C22#355511yescharacteristic
639C22#355511yescharacteristic
640C4—24no—
641C4—44no—
642C4—44no—
643C4—44no—
644C4—44no—
645C4—42no—
646C4—48no—
647C4—42no—
648C4—42no—
649C4—42no—
650C4—48no—
651C4—82no—
652C4—82no—
653C4—82no—
654C4—82no—
655C4#233118yes—
656C4#237018yes—
657C2C2×#233111yescharacteristic
658C2C2×#237011yescharacteristic
659C2#3421711yescharacteristic
660C2#3423111yescharacteristic
661C2#3423211yescharacteristic
662C2#3439311yescharacteristic
663C2#3439411yescharacteristic
664C2#3896611yescharacteristic
665C2#3896711yescharacteristic
666C2#3897711yescharacteristic
667C2#3897811yescharacteristic
668C2#3918211yescharacteristic
669C2#3918311yescharacteristic
670C2#3919311yescharacteristic
671C2#3919411yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC24C25
commutatorC23C24×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
19. #2859C4semidirect

Maximal subgroups

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

subgroupindex
C2×#28592
#144602
#144592
#142662
#141512
#140542
#140512
#140502
#140062
#139822
C4⋊C422
#137832
C4×#3822
#137552