Finite Group Databasebeta

← #445150

Subgroups — #445150

Order 512.

1070 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2099C211yesmaximal, characteristic
2C2×#2083C211yesmaximal, characteristic
3C2×#1918C211yesmaximal, characteristic
4C2×#1918C211yesmaximal, characteristic
5#15151C211yesmaximal, characteristic
6#13910C211yesmaximal, characteristic
7#11379C211yesmaximal, characteristic
8#11379C211yesmaximal, characteristic
9#11373C211yesmaximal, characteristic
10#11373C211yesmaximal, characteristic
11#11324C211yesmaximal, characteristic
12#11324C211yesmaximal, characteristic
13#10874C211yesmaximal, characteristic
14#10862C211yesmaximal, characteristic
15#10841C211yesmaximal, characteristic
16C22×#107C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21C2×#398—22no—
22C2×#389—22no—
23C2×#389C2211yescharacteristic
24C2×#389C2211yescharacteristic
25C2×#384C2211yescharacteristic
26C2×#384C2211yescharacteristic
27C2×#384C2211yescharacteristic
28C2×#384C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31#2099—24no—
32#2083—24no—
33#1918—24no—
34#1918—24no—
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1445—22no—
53#1444—22no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C23×C8C2311yescharacteristic
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4D412yes—
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C42—21no—
80C22×C42C2311yescharacteristic
81C22×C42C2311yescharacteristic
82C22×C42C2311yescharacteristic
83C2×#107—22no—
84C2×#107—22no—
85C2×#107—22no—
86C2×#107—22no—
87C2×#107—22no—
88C2×#107—22no—
89C2×#107—22no—
90C2×#107—22no—
91C2×#107—22no—
92C2×#107—41no—
93C2×#107—41no—
94C2×#107Q814yes—
95C2×C4×C8—22no—
96C2×C4×C8—22no—
97C2×C4×C8—41no—
98#398—48no—
99#389—22no—
100#389—22no—
101#389—22no—
102#389—22no—
103#389—48no—
104#384—22no—
105#384—22no—
106#384—22no—
107#384—22no—
108#384—22no—
109#384—22no—
110#384—41no—
111#384—41no—
112C4×C4⋊C4—22no—
113C4×C4⋊C4—22no—
114C4×C4⋊C4—22no—
115C4×C4⋊C4—22no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95—21no—
122C2×#95—21no—
123C2×#95—21no—
124C2×#95D412yes—
125#340—22no—
126#340—22no—
127#340—22no—
128#340—22no—
129#340—22no—
130#340—22no—
131#340—22no—
132#340—22no—
133#340—22no—
134#340—22no—
135#340—22no—
136#340—22no—
137#336—22no—
138#336—22no—
139#336—41no—
140#336D414yes—
141#336D414yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D412yes—
152C23×C4C2×D412yes—
153C23×C4C2×D411yescharacteristic
154C23×C4C2411yescharacteristic
155C22×C8—21no—
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—21no—
161C22×C8—21no—
162C22×C8—21no—
163C22×C8—21no—
164C22×C8—21no—
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—21no—
173C22×C8—21no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8C2×D412yes—
178C22×C8C2×D412yes—
179C22×C8C2×D412yes—
180C22×C8C2×D412yes—
181C22×C8C2×Q812yes—
182C22×C8#4112yes—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
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—44no—
230C2×C4⋊C4—44no—
231C2×C4⋊C4—44no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4—44no—
237C2×C4⋊C4—44no—
238C2×C4⋊C4—44no—
239C2×C4⋊C4—44no—
240C2×C4⋊C4—44no—
241C2×C4⋊C4—44no—
242C2×C4⋊C4—44no—
243C2×C4⋊C4—82no—
244C2×C4⋊C4—82no—
245C2×C4⋊C4—82no—
246C2×C4⋊C4D818yes—
247C2×C4⋊C4C2×Q812yes—
248C2×C4⋊C4C2×Q812yes—
249C2×C4⋊C4#4112yes—
250C2×C4⋊C4#4112yes—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42—42no—
266C2×C42—44no—
267C2×C42C2×D412yes—
268C2×C42C2×D412yes—
269C2×C42#4112yes—
270C2×C42#4112yes—
271#107—28no—
272#107—28no—
273#107—44no—
274#107—44no—
275C4×C8—44no—
276#95—24no—
277#95—42no—
278#95—42no—
279#95—42no—
280#95—44no—
281#95—44no—
282#95—44no—
283#95—44no—
284#95—44no—
285C24C22×D411yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4#12314yes—
344C22×C4#12712yes—
345C22×C4#12712yes—
346C22×C4C2×D814yes—
347C22×C4C2×D814yes—
348C22×C4C2×D814yes—
349C22×C4#13714yes—
350C22×C4C22×D411yescharacteristic
351C22×C4C22×D411yescharacteristic
352C22×C4C22×Q811yescharacteristic
353C22×C4C2×#4111yescharacteristic
354C22×C4C2×#4111yescharacteristic
355C22×C4C2×#4111yescharacteristic
356C22×C4C2×#4111yescharacteristic
357C22×C4C2×#4111yescharacteristic
358C22×C4H(5,𝔽2)11yescharacteristic
359C22×C42−1+411yescharacteristic
360C22×C42−1+411yescharacteristic
361C22×C42−1+411yescharacteristic
362C22×C42−1+411yescharacteristic
363C22×C42−1+411yescharacteristic
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—41no—
380C2×C8—41no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—41no—
390C2×C8—41no—
391C2×C8C22⋊Q814yes—
392C4⋊C4—216no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—88no—
426C4⋊C4—88no—
427C4⋊C4—84no—
428C4⋊C4—88no—
429C4⋊C4—84no—
430C4⋊C4—84no—
431C4⋊C4—84no—
432C42—22no—
433C42—22no—
434C42—22no—
435C42—22no—
436C42—22no—
437C42—22no—
438C42—22no—
439C42—22no—
440C42—41no—
441C42—41no—
442C42—41no—
443C42—41no—
444C42—84no—
445C23C2×#12311yescharacteristic
446C23C2×#12711yescharacteristic
447C23#53611yescharacteristic
448C23#54611yescharacteristic
449C23#54711yescharacteristic
450C23#54811yescharacteristic
451C23D4×Q811yescharacteristic
452C23C22×D812yes—
453C23C2×#13712yes—
454C23#57712yes—
455C23#57812yes—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4—82no—
515C2×C4—82no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4#48018yes—
519C2×C4#49314yes—
520C2×C4C2×C22⋊Q811yescharacteristic
521C2×C4#52511yescharacteristic
522C2×C4#52911yescharacteristic
523C2×C4#53311yescharacteristic
524C2×C4#53611yescharacteristic
525C2×C4#53711yescharacteristic
526C2×C4#53911yescharacteristic
527C2×C4#54111yescharacteristic
528C2×C4#54111yescharacteristic
529C2×C4#54111yescharacteristic
530C2×C4#54111yescharacteristic
531C2×C4#54411yescharacteristic
532C2×C4#54611yescharacteristic
533C2×C4#54711yescharacteristic
534C2×C4#54711yescharacteristic
535C2×C4#54711yescharacteristic
536C2×C4#54711yescharacteristic
537C2×C4#54711yescharacteristic
538C2×C4#54811yescharacteristic
539C2×C4D4×Q811yescharacteristic
540C2×C4#55111yescharacteristic
541C2×C4#55211yescharacteristic
542C2×C4#55211yescharacteristic
543C2×C4#55611yescharacteristic
544C2×C4#55711yescharacteristic
545C2×C4#55711yescharacteristic
546C2×C4#56311yescharacteristic
547C2×C4#56411yescharacteristic
548C8—24no—
549C8—42no—
550C8—42no—
551C8—42no—
552C22#241911yescharacteristic
553C22#244611yescharacteristic
554C22#250111yescharacteristic
555C22#254011yescharacteristic
556C22#254211yescharacteristic
557C22#271311yescharacteristic
558C22#271911yescharacteristic
559C22C2×#48012yes—
560C22#309712yes—
561C22C2×#49311yescharacteristic
562C22#315211yescharacteristic
563C22#315411yescharacteristic
564C22#315611yescharacteristic
565C22#322612yes—
566C22#324212yes—
567C22#329412yes—
568C22#331212yes—
569C22#333412yes—
570C22#334412yes—
571C22#335812yes—
572C22#337412yes—
573C22Q8×D812yes—
574C22#338712yes—
575C4—24no—
576C4—28no—
577C4—42no—
578C4—44no—
579C4—82no—
580C4—82no—
581C4—82no—
582C4—82no—
583C4—161no—
584C4—161no—
585C4—161no—
586C4—161no—
587C4#243811yescharacteristic
588C4#245311yescharacteristic
589C4#246211yescharacteristic
590C4#247811yescharacteristic
591C4#268911yescharacteristic
592C4#271911yescharacteristic
593C4#272211yescharacteristic
594C4#272611yescharacteristic
595C2#1580411yescharacteristic
596C2#2493312yes—
597C2#2627612yes—
598C2#2790911yescharacteristic
599C2#2792211yescharacteristic
600C2#2839711yescharacteristic
601C2#2842311yescharacteristic
602C2#2852711yescharacteristic
603C2#2855011yescharacteristic
604C2#3213012yes—
605C2#3231012yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ 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×#20992
C2×#20832
C2×#19182
#151512
#139102
#113792
#113732
#113242
#108742
#108622
#108412