Finite Group Databasebeta

← #411187

Subgroups — #411187

Order 512.

1032 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14712C211yesmaximal, characteristic
2C4×#389C211yesmaximal, characteristic
3#11316C212yesmaximal
4#11293C212yesmaximal
5#11267C211yesmaximal, characteristic
6#11267C211yesmaximal, characteristic
7#11207C211yesmaximal, characteristic
8#11207C211yesmaximal, characteristic
9#10885C212yesmaximal
10#10885C212yesmaximal
11#10795C211yesmaximal, characteristic
12C2×#389—21no—
13C2×#389—21no—
14C2×#389C2211yescharacteristic
15C2×#389C2212yes—
16C2×#389C2211yescharacteristic
17C2×#384C2211yescharacteristic
18C2×#384C2211yescharacteristic
19C2×C4×C4⋊C4—21no—
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×C43C2211yescharacteristic
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#336C2211yescharacteristic
32C2×#336C2211yescharacteristic
33C2×#336C2212yes—
34C2×#336C2212yes—
35#1436—21no—
36#1436—21no—
37C4⋊#95—21no—
38C4⋊#95—21no—
39C4⋊#95C2211yescharacteristic
40C4⋊#95C2212yes—
41C4⋊#95C2211yescharacteristic
42C4×#95—21no—
43C23×C8C2312yes—
44C23×C8C2312yes—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4C2312yes—
53C22×C4⋊C4C2311yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C42—21no—
59C22×C42—21no—
60C22×C42D411yescharacteristic
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63C22×C42D411yescharacteristic
64C22×C42C2311yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67#389—22no—
68#389—22no—
69#389—22no—
70#389—24no—
71#389—24no—
72#389—44no—
73#389—44no—
74#389Q814yes—
75#384—24no—
76#384—42no—
77C4×C4⋊C4—22no—
78C4×C4⋊C4—22no—
79C4×C4⋊C4—42no—
80C4×C4⋊C4—44no—
81C2×#95—21no—
82C2×#95—21no—
83C2×#95—21no—
84C2×#95—21no—
85C2×#95—21no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—21no—
92C43—42no—
93#340—24no—
94#340—24no—
95#340—24no—
96#340—24no—
97#340—24no—
98#340—24no—
99#340—42no—
100#340—42no—
101#336—22no—
102#336—22no—
103#336—24no—
104#336—42no—
105C23×C4—21no—
106C23×C4—22no—
107C23×C4—21no—
108C23×C4—21no—
109C23×C4—21no—
110C23×C4—22no—
111C23×C4C2×D411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C23×C4C2×D411yescharacteristic
114C23×C4C2×D411yescharacteristic
115C23×C4C2×D411yescharacteristic
116C23×C4C2×D411yescharacteristic
117C23×C4C2411yescharacteristic
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
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—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
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—24no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
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—42no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
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—44no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4C2×Q812yes—
177C2×C4⋊C4C2×Q812yes—
178C2×C4⋊C4#4112yes—
179C2×C4⋊C4#4114yes—
180C2×C4⋊C4#4112yes—
181C2×C4⋊C4#4112yes—
182C2×C4⋊C4#4112yes—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—24no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—41no—
196C2×C42—41no—
197C2×C42—41no—
198C2×C42—41no—
199C2×C42—41no—
200C2×C42—41no—
201C2×C42—41no—
202C2×C42—41no—
203C2×C42—42no—
204C2×C42—42no—
205C2×C42—42no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42SD1614yes—
209C2×C42Q1614yes—
210C2×C42C2×Q812yes—
211C2×C42#4112yes—
212C2×C42#4114yes—
213#95—24no—
214#95—24no—
215#95—24no—
216#95—42no—
217#95—42no—
218#95—44no—
219#95—44no—
220#95—44no—
221#95—42no—
222#95—42no—
223#95—42no—
224C24C22×D411yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
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—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
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—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
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×C4C22⋊Q812yes—
298C22×C4C22⋊Q812yes—
299C22×C4#12412yes—
300C22×C4#12412yes—
301C22×C4C2×SD1612yes—
302C22×C4C2×SD1612yes—
303C22×C4C2×SD1612yes—
304C22×C4C2×Q1612yes—
305C22×C4C2×Q1612yes—
306C22×C4C2×Q1612yes—
307C22×C4AGL(1,ℤ/8)12yes—
308C22×C4AGL(1,ℤ/8)12yes—
309C22×C4C22×Q811yescharacteristic
310C22×C4C2×#4111yescharacteristic
311C22×C4C2×#4111yescharacteristic
312C22×C4C2×#4111yescharacteristic
313C22×C4C2×#4112yes—
314C22×C4C2×#4111yescharacteristic
315C22×C4C2×#4112yes—
316C22×C4C2×#4111yescharacteristic
317C22×C4H(5,𝔽2)12yes—
318C22×C42−1+412yes—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—48no—
342C4⋊C4—48no—
343C4⋊C4—48no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—48no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—84no—
355C4⋊C4—84no—
356C4⋊C4—88no—
357C4⋊C4#12514yes—
358C42—24no—
359C42—24no—
360C42—24no—
361C42—24no—
362C42—44no—
363C42—44no—
364C42—48no—
365C42—44no—
366C42—44no—
367C42—42no—
368C42—42no—
369C42—84no—
370C23C2×C22⋊Q811yescharacteristic
371C23#52511yescharacteristic
372C23#52511yescharacteristic
373C23#52511yescharacteristic
374C23C2×#12411yescharacteristic
375C23#53411yescharacteristic
376C23#53611yescharacteristic
377C23C22×SD1611yescharacteristic
378C23C22×Q1611yescharacteristic
379C23C2×AGL(1,ℤ/8)11yescharacteristic
380C23C2×AGL(1,ℤ/8)11yescharacteristic
381C23#57511yescharacteristic
382C23#57511yescharacteristic
383C23#57511yescharacteristic
384C23#57511yescharacteristic
385C2×C4—22no—
386C2×C4—22no—
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—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4#47614yes—
467C2×C4#47714yes—
468C2×C4#48714yes—
469C2×C4C2×#12511yescharacteristic
470C2×C4#52912yes—
471C2×C4#52911yescharacteristic
472C2×C4#52912yes—
473C2×C4#52911yescharacteristic
474C2×C4#53311yescharacteristic
475C2×C4#53912yes—
476C2×C4#54212yes—
477C2×C4#55212yes—
478C2×C4#55312yes—
479C2×C4#55312yes—
480C2×C4#55312yes—
481C2×C4#55412yes—
482C2×C4#55612yes—
483C2×C4#55612yes—
484C2×C4#55712yes—
485C8—82no—
486C8—82no—
487C22#239811yescharacteristic
488C22#256811yescharacteristic
489C22#257911yescharacteristic
490C22#259111yescharacteristic
491C22#259911yescharacteristic
492C22#263811yescharacteristic
493C22#285111yescharacteristic
494C22C2×#47611yescharacteristic
495C22C2×#47711yescharacteristic
496C22#308011yescharacteristic
497C22#308011yescharacteristic
498C22#310111yescharacteristic
499C22#310111yescharacteristic
500C22#310311yescharacteristic
501C22#310411yescharacteristic
502C22#310411yescharacteristic
503C22#310411yescharacteristic
504C22#311411yescharacteristic
505C22#311411yescharacteristic
506C22#311511yescharacteristic
507C22#311511yescharacteristic
508C22#311511yescharacteristic
509C22#311511yescharacteristic
510C22C2×#48711yescharacteristic
511C22#313511yescharacteristic
512C22#313811yescharacteristic
513C22#314211yescharacteristic
514C22#318711yescharacteristic
515C22#318911yescharacteristic
516C22#319411yescharacteristic
517C22#319411yescharacteristic
518C22#322711yescharacteristic
519C22#323011yescharacteristic
520C22#324011yescharacteristic
521C22#324011yescharacteristic
522C4—24no—
523C4—24no—
524C4—24no—
525C4—44no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—84no—
530C4—82no—
531C4—82no—
532C4—82no—
533C4—162no—
534C4#250912yes—
535C4#252512yes—
536C4#258512yes—
537C4#259412yes—
538C2#1510811yescharacteristic
539C2#2381611yescharacteristic
540C2#2382411yescharacteristic
541C2#2921811yescharacteristic
542C2#2922711yescharacteristic
543C2#2923511yescharacteristic
544C2#2924111yescharacteristic
545C2#2932911yescharacteristic
546C2#2933711yescharacteristic
547C2#2939211yescharacteristic
548C2#2939411yescharacteristic
549C2#3016611yescharacteristic
550C2#3016911yescharacteristic
551C2#3306811yescharacteristic
552C2#3306911yescharacteristic
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
#147122
C4×#3892
#113162
#112932
#112672
#112072
#108852
#107952