Finite Group Databasebeta

← #410698

Subgroups — #410698

Order 512.

1038 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2099C211yesmaximal, characteristic
2C2×#2084C211yesmaximal, characteristic
3#14687C211yesmaximal, characteristic
4C4×#389C211yesmaximal, characteristic
5#11373C211yesmaximal, characteristic
6#11357C211yesmaximal, characteristic
7#11316C212yesmaximal
8#11220C212yesmaximal
9#10908C212yesmaximal
10#10807C212yesmaximal
11#10795C211yesmaximal, characteristic
12C22×#106C2212yes—
13C2×#389C2211yescharacteristic
14C2×#389C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×#384C2211yescharacteristic
17C2×#382—21no—
18C2×#382—21no—
19C2×C4×C4⋊C4—21no—
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×C43C2211yescharacteristic
23#2099—24no—
24#2084—24no—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#336C2212yes—
33C2×#336C2212yes—
34C2×#336C2211yescharacteristic
35C2×#336C2211yescharacteristic
36#1436—21no—
37#1436—21no—
38C4⋊#95—21no—
39C4⋊#95—21no—
40C4⋊#95C2211yescharacteristic
41C4⋊#95C2212yes—
42C4⋊#95C2212yes—
43C4⋊#95C2211yescharacteristic
44C4×#95—21no—
45C23×C8C2312yes—
46C23×C8C2312yes—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2312yes—
54C22×C4⋊C4C2312yes—
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C42—21no—
60C22×C42—21no—
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63C22×C42D411yescharacteristic
64C22×C42D411yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67C22×C42C2311yescharacteristic
68C2×#106—24no—
69C2×#106—24no—
70C2×#106—24no—
71#389—22no—
72#389—22no—
73#389—22no—
74#389D414yes—
75#384—22no—
76#384—22no—
77#384—22no—
78#384—22no—
79#382—44no—
80#382—44no—
81C4×C4⋊C4—22no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4—24no—
84C4×C4⋊C4—44no—
85C2×#95—21no—
86C2×#95—21no—
87C2×#95—21no—
88C2×#95—21no—
89C2×#95—21no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C43—24no—
98#340—24no—
99#340—24no—
100#340—24no—
101#340—24no—
102#340—24no—
103#340—24no—
104#340—24no—
105#336—24no—
106#336—22no—
107#336—22no—
108#336—24no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4C2×D411yescharacteristic
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C23×C4C2411yescharacteristic
122C22×C8—22no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8#4114yes—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4C2×D412yes—
179C2×C4⋊C4C2×D412yes—
180C2×C4⋊C4#4112yes—
181C2×C4⋊C4#4112yes—
182C2×C4⋊C4#4112yes—
183C2×C4⋊C4#4112yes—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—24no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—41no—
204C2×C42—41no—
205C2×C42—42no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42—42no—
209C2×C42—42no—
210C2×C42SD1614yes—
211C2×C42C2×D412yes—
212C2×C42#4112yes—
213C2×C42#4114yes—
214#106—48no—
215#95—24no—
216#95—24no—
217#95—24no—
218#95—42no—
219#95—42no—
220#95—44no—
221#95—44no—
222#95—42no—
223#95—44no—
224#95—44no—
225#95—42no—
226#95—42no—
227C24C22×D411yescharacteristic
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4#12112yes—
301C22×C4#12112yes—
302C22×C4#12312yes—
303C22×C4#12312yes—
304C22×C4C2×SD1612yes—
305C22×C4C2×SD1612yes—
306C22×C4C2×SD1612yes—
307C22×C4#13512yes—
308C22×C4AGL(1,ℤ/8)12yes—
309C22×C4AGL(1,ℤ/8)12yes—
310C22×C4#13712yes—
311C22×C4#13712yes—
312C22×C4C22×D411yescharacteristic
313C22×C4C2×#4111yescharacteristic
314C22×C4C2×#4111yescharacteristic
315C22×C4C2×#4111yescharacteristic
316C22×C4C2×#4112yes—
317C22×C4C2×#4112yes—
318C22×C4C2×#4111yescharacteristic
319C22×C4C2×#4111yescharacteristic
320C22×C42−1+412yes—
321C22×C42−1+412yes—
322C2×C8—24no—
323C2×C8—24no—
324C2×C8—24no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—48no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—48no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—84no—
356C4⋊C4—84no—
357C4⋊C4—84no—
358C4⋊C4—84no—
359C4⋊C4#12414yes—
360C42—28no—
361C42—24no—
362C42—24no—
363C42—24no—
364C42—24no—
365C42—28no—
366C42—44no—
367C42—44no—
368C42—48no—
369C42—42no—
370C42—42no—
371C42—84no—
372C23C2×#12111yescharacteristic
373C23C2×#12311yescharacteristic
374C23#52511yescharacteristic
375C23#52511yescharacteristic
376C23#53211yescharacteristic
377C23#53611yescharacteristic
378C23#53611yescharacteristic
379C23C22×SD1611yescharacteristic
380C23C2×#13511yescharacteristic
381C23C2×AGL(1,ℤ/8)11yescharacteristic
382C23C2×AGL(1,ℤ/8)11yescharacteristic
383C23C2×#13711yescharacteristic
384C23C2×#13711yescharacteristic
385C23#57511yescharacteristic
386C23#57511yescharacteristic
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4#46014yes—
469C2×C4#46314yes—
470C2×C4#48314yes—
471C2×C4C2×#12411yescharacteristic
472C2×C4#52912yes—
473C2×C4#52912yes—
474C2×C4#52911yescharacteristic
475C2×C4#52911yescharacteristic
476C2×C4#53211yescharacteristic
477C2×C4#54112yes—
478C2×C4#54112yes—
479C2×C4#54712yes—
480C2×C4#54812yes—
481C2×C4#55212yes—
482C2×C4#55212yes—
483C2×C4#55212yes—
484C2×C4#55212yes—
485C2×C4#55212yes—
486C2×C4#55612yes—
487C8—44no—
488C8—82no—
489C22#239511yescharacteristic
490C22#248411yescharacteristic
491C22#248611yescharacteristic
492C22#254511yescharacteristic
493C22#261111yescharacteristic
494C22#263411yescharacteristic
495C22#285011yescharacteristic
496C22C2×#46311yescharacteristic
497C22C2×#46011yescharacteristic
498C22#303911yescharacteristic
499C22#304011yescharacteristic
500C22C2×#48311yescharacteristic
501C22#309111yescharacteristic
502C22#309211yescharacteristic
503C22#309411yescharacteristic
504C22#310311yescharacteristic
505C22#310311yescharacteristic
506C22#310711yescharacteristic
507C22#310711yescharacteristic
508C22#311011yescharacteristic
509C22#311011yescharacteristic
510C22#311511yescharacteristic
511C22#311511yescharacteristic
512C22#316711yescharacteristic
513C22#317211yescharacteristic
514C22#318111yescharacteristic
515C22#318411yescharacteristic
516C22#322711yescharacteristic
517C22#322811yescharacteristic
518C22#322911yescharacteristic
519C22#323211yescharacteristic
520C22#323411yescharacteristic
521C22#323611yescharacteristic
522C22#323711yescharacteristic
523C22#323811yescharacteristic
524C4—24no—
525C4—24no—
526C4—24no—
527C4—44no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—82no—
532C4—82no—
533C4—82no—
534C4—162no—
535C4—162no—
536C4#248912yes—
537C4#251912yes—
538C4#252412yes—
539C4#252812yes—
540C2#1508511yescharacteristic
541C2#2375611yescharacteristic
542C2#2376111yescharacteristic
543C2#2761111yescharacteristic
544C2#2761511yescharacteristic
545C2#2764711yescharacteristic
546C2#2765111yescharacteristic
547C2#2865411yescharacteristic
548C2#2866011yescharacteristic
549C2#2957511yescharacteristic
550C2#2957811yescharacteristic
551C2#3009411yescharacteristic
552C2#3009911yescharacteristic
553C2#3302511yescharacteristic
554C2#3303211yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ 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×#20842
#146872
C4×#3892
#113732
#113572
#113162
#112202
#109082
#108072
#107952