Finite Group Databasebeta

← #413660

Subgroups — #413660

Order 512.

1064 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2085C212yesmaximal
2C2×#2083C212yesmaximal
3C2×#1949C211yesmaximal, characteristic
4C2×#1947C211yesmaximal, characteristic
5#14354C211yesmaximal, characteristic
6#13783C211yesmaximal, characteristic
7#11358C212yesmaximal
8#11357C212yesmaximal
9#10850C211yesmaximal, characteristic
10#10849C211yesmaximal, characteristic
11#10833C211yesmaximal, characteristic
12C22×#107C2211yescharacteristic
13C22×#107C2212yes—
14C22×#106C2211yescharacteristic
15C22×C4⋊C8C2211yescharacteristic
16C22×C4⋊C8C2211yescharacteristic
17C2×#389C2212yes—
18C2×#384C2212yes—
19C2×#384C2211yescharacteristic
20C2×#382C2212yes—
21C2×#382C2211yescharacteristic
22C2×C4×C4⋊C4C2211yescharacteristic
23C2×C4×C4⋊C4C2211yescharacteristic
24C2×#376C2211yescharacteristic
25#2085—28no—
26#2083—28no—
27#1949—24no—
28#1947—24no—
29C2×#340C2211yescharacteristic
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2211yescharacteristic
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#336C2212yes—
37C2×#336C2212yes—
38#1444—21no—
39#1444—21no—
40#1444—22no—
41#1436—22no—
42C4⋊#95—21no—
43C4⋊#95C2212yes—
44#1434—21no—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2312yes—
48C22×C4⋊C4—22no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2311yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2312yes—
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2312yes—
58C22×C4⋊C4C2311yescharacteristic
59C22×C42—21no—
60C22×C42—21no—
61C22×C42C2312yes—
62C22×C42C2311yescharacteristic
63C2×#107—24no—
64C2×#107—24no—
65C2×#107—24no—
66C2×#107—24no—
67C2×#107—22no—
68C2×#106—24no—
69C2×#106—22no—
70C2×C4⋊C8—22no—
71C2×C4⋊C8—22no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—22no—
74C2×C4⋊C8Q814yes—
75C2×C4⋊C8Q814yes—
76#389—24no—
77#389D418yes—
78#384—24no—
79#384—22no—
80#384—24no—
81#384—22no—
82#382—24no—
83#382—22no—
84#382—24no—
85#382—22no—
86C4×C4⋊C4—22no—
87C4×C4⋊C4—22no—
88C4×C4⋊C4—22no—
89C4×C4⋊C4D414yes—
90#376—22no—
91#376—22no—
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95D411yescharacteristic
102C2×#95D411yescharacteristic
103C2×#95D412yes—
104#340—24no—
105#340—24no—
106#340—24no—
107#340—24no—
108#340—24no—
109#340—22no—
110#340—22no—
111#336—24no—
112#336—24no—
113C23×C4—21no—
114C23×C4—22no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—22no—
118C23×C4—21no—
119C23×C4C2×D412yes—
120C23×C4C2×D412yes—
121C23×C4C2×D411yescharacteristic
122C23×C4C2×D411yescharacteristic
123C23×C4C2411yescharacteristic
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—21no—
129C22×C8—22no—
130C22×C8—21no—
131C22×C8—21no—
132C22×C8—21no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8C2×Q812yes—
139C22×C8C2×Q812yes—
140C22×C8C2×Q814yes—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—28no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—82no—
171C2×C4⋊C4—82no—
172C2×C4⋊C4—82no—
173C2×C4⋊C4—81no—
174C2×C4⋊C4—81no—
175C2×C4⋊C4—82no—
176C2×C4⋊C4—82no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4—82no—
179C2×C4⋊C4C2×D412yes—
180C2×C4⋊C4C2×D414yes—
181C2×C4⋊C4C2×D412yes—
182C2×C4⋊C4C2×D414yes—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—24no—
188C2×C42—42no—
189C2×C42—82no—
190C2×C42—81no—
191C2×C42—81no—
192C2×C42C2×D414yes—
193C2×C42C2×D412yes—
194C2×C42C2×Q812yes—
195C2×C42C2×Q812yes—
196C2×C42#4114yes—
197C2×C42#4112yes—
198C2×C42#4112yes—
199C2×C42#4112yes—
200#107—44no—
201#107—48no—
202#106—44no—
203C4⋊C8—28no—
204C4⋊C8—28no—
205#95—24no—
206#95—28no—
207#95—22no—
208#95—22no—
209#95—24no—
210#95—44no—
211#95—44no—
212#95—42no—
213#95—42no—
214#95—42no—
215#95—82no—
216#95—82no—
217C24C22×D411yescharacteristic
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—42no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—41no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4#12114yes—
271C22×C4#12114yes—
272C22×C4#12112yes—
273C22×C4#12112yes—
274C22×C4#12312yes—
275C22×C4#12312yes—
276C22×C4C4⋊Q812yes—
277C22×C4C4⋊Q812yes—
278C22×C4C22×D411yescharacteristic
279C22×C4C22×D412yes—
280C22×C4C22×Q811yescharacteristic
281C22×C4C22×Q811yescharacteristic
282C22×C4C2×#4111yescharacteristic
283C22×C4C2×#4111yescharacteristic
284C22×C4C2×#4111yescharacteristic
285C22×C4C2×#4112yes—
286C22×C42−1+412yes—
287C22×C42−1+412yes—
288C2×C8—22no—
289C2×C8—24no—
290C2×C8—22no—
291C2×C8—24no—
292C2×C8—24no—
293C2×C8—24no—
294C2×C8—24no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—42no—
298C2×C8—41no—
299C2×C8—42no—
300C2×C8—41no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C4⋊C4—22no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—88no—
325C4⋊C4—84no—
326C4⋊C4—84no—
327C4⋊C4—88no—
328C4⋊C4—88no—
329C4⋊C4#12714yes—
330C42—24no—
331C42—24no—
332C42—24no—
333C42—24no—
334C42—84no—
335C42—84no—
336C42C22⋊Q814yes—
337C42C22⋊Q814yes—
338C42#12514yes—
339C42#12514yes—
340C23C2×#12111yescharacteristic
341C23C2×#12112yes—
342C23C2×#12311yescharacteristic
343C23C2×C4⋊Q811yescharacteristic
344C23#53612yes—
345C23#57611yescharacteristic
346C23#57612yes—
347C23#57711yescharacteristic
348C23#57711yescharacteristic
349C23#57811yescharacteristic
350C23#57812yes—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—81no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—81no—
400C2×C4—82no—
401C2×C4—81no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—81no—
407C2×C4—82no—
408C2×C4—81no—
409C2×C4#39814yes—
410C2×C4#39814yes—
411C2×C4C2×C22⋊Q811yescharacteristic
412C2×C4C2×C22⋊Q811yescharacteristic
413C2×C4C2×#12511yescharacteristic
414C2×C4C2×#12511yescharacteristic
415C2×C4C2×#12711yescharacteristic
416C2×C4#53211yescharacteristic
417C2×C4#53212yes—
418C2×C4#53611yescharacteristic
419C2×C4#53611yescharacteristic
420C2×C4#54112yes—
421C2×C4#54712yes—
422C2×C4#54712yes—
423C2×C4D4×Q812yes—
424C2×C4D4×Q812yes—
425C2×C4#55212yes—
426C2×C4#55212yes—
427C2×C4#55712yes—
428C2×C4#55712yes—
429C8—42no—
430C8—42no—
431C8—44no—
432C22C2×#39811yescharacteristic
433C22#248612yes—
434C22#254612yes—
435C22#262111yescharacteristic
436C22#285611yescharacteristic
437C22#304112yes—
438C22#304111yescharacteristic
439C22#304412yes—
440C22#304411yescharacteristic
441C22#304512yes—
442C22#304511yescharacteristic
443C22#304612yes—
444C22#304611yescharacteristic
445C22#309611yescharacteristic
446C22#309711yescharacteristic
447C22#309812yes—
448C22#316311yescharacteristic
449C22#316411yescharacteristic
450C22#316412yes—
451C22#324112yes—
452C22#324212yes—
453C22#324312yes—
454C22#324312yes—
455C4—24no—
456C4—24no—
457C4—44no—
458C4—44no—
459C4—44no—
460C4—84no—
461C4—82no—
462C4—161no—
463C4—162no—
464C4—161no—
465C4#250612yes—
466C4#250612yes—
467C4#254211yescharacteristic
468C4#254211yescharacteristic
469C4#256511yescharacteristic
470C4#256511yescharacteristic
471C2#1515111yescharacteristic
472C2#2366011yescharacteristic
473C2#2366211yescharacteristic
474C2#2765512yes—
475C2#2765612yes—
476C2#2869712yes—
477C2#2869812yes—
478C2#2987211yescharacteristic
479C2#2987511yescharacteristic
480C2#3316611yescharacteristic
481C2#3316911yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#20852
C2×#20832
C2×#19492
C2×#19472
#143542
#137832
#113582
#113572
#108502
#108492
#108332