Finite Group Databasebeta

← #416963

Subgroups — #416963

Order 512.

1050 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1988C211yesmaximal, characteristic
2C2×#1987C211yesmaximal, characteristic
3C2×#1949C211yesmaximal, characteristic
4C2×#1832C211yesmaximal, characteristic
5#14282C211yesmaximal, characteristic
6#13783C211yesmaximal, characteristic
7#11316C212yesmaximal
8#11315C212yesmaximal
9#11220C212yesmaximal
10#11219C212yesmaximal
11#10850C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×#107C2211yescharacteristic
14C22×#106C2211yescharacteristic
15C22×C4⋊C8C2211yescharacteristic
16C22×C4⋊C8C2211yescharacteristic
17C2×#389C2212yes—
18C2×#382C2211yescharacteristic
19C2×C4×C4⋊C4C2211yescharacteristic
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×#376C2211yescharacteristic
22#1988—24no—
23#1987—24no—
24#1949—24no—
25#1832—24no—
26C2×#340C2211yescharacteristic
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2211yescharacteristic
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2212yes—
35C2×#336C2212yes—
36#1446—22no—
37#1445—21no—
38#1445—21no—
39#1436—22no—
40C4⋊#95—21no—
41C4⋊#95C2212yes—
42C4⋊#95C2212yes—
43C4⋊#95C2212yes—
44#1434—21no—
45C23×Q8—21no—
46C23×C8C2312yes—
47C23×C8C2311yescharacteristic
48C23×C8C2311yescharacteristic
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—22no—
51C2×C4⋊Q8—22no—
52C2×C4⋊Q8—22no—
53C2×C4⋊Q8—22no—
54C2×C4⋊Q8Q814yes—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2312yes—
61C22×C4⋊C4C2312yes—
62C22×C4⋊C4C2311yescharacteristic
63C22×C42—21no—
64C22×C42—21no—
65C22×C42C2312yes—
66C22×C42C2311yescharacteristic
67C2×#107—22no—
68C2×#107—24no—
69C2×#106—22no—
70C2×#106—24no—
71C2×C4⋊C8—22no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—22no—
74C2×C4⋊C8—22no—
75C2×C4⋊C8—22no—
76C2×C4⋊C8D414yes—
77#389—24no—
78#389—24no—
79#382—22no—
80#382—22no—
81C4×C4⋊C4—22no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4D414yes—
85#376—22no—
86#376—22no—
87C2×#95—22no—
88C2×#95—21no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95D411yescharacteristic
99C2×#95D411yescharacteristic
100C2×#95D412yes—
101#340—24no—
102#340—24no—
103#340—22no—
104#340—22no—
105#340—24no—
106#340—24no—
107#340—24no—
108#340—24no—
109#336—24no—
110#336—24no—
111C22×Q8—24no—
112C22×Q8—42no—
113C22×Q8—42no—
114C22×Q8—81no—
115C22×Q8—81no—
116C22×Q8—81no—
117C22×Q8—81no—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4C2×D412yes—
125C23×C4C2×D412yes—
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C23×C4C2411yescharacteristic
129C22×C8—21no—
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×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8C2×D412yes—
145C22×C8C2×D412yes—
146C4⋊Q8—28no—
147C4⋊Q8—28no—
148C4⋊Q8—44no—
149C4⋊Q8—44no—
150C2×C4⋊C4—21no—
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—24no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—28no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4—82no—
179C2×C4⋊C4C2×D412yes—
180C2×C4⋊C4C2×D412yes—
181C2×C4⋊C4C2×Q814yes—
182C2×C4⋊C4#4114yes—
183C2×C4⋊C4#4114yes—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—24no—
191C2×C42—42no—
192C2×C42—82no—
193C2×C42—81no—
194C2×C42—81no—
195C2×C42C2×D412yes—
196C2×C42C2×D412yes—
197C2×C42C2×Q812yes—
198C2×C42#4112yes—
199C2×C42#4112yes—
200C2×C42#4112yes—
201#107—44no—
202#106—44no—
203C4⋊C8—28no—
204C4⋊C8—44no—
205#95—28no—
206#95—24no—
207#95—22no—
208#95—22no—
209#95—24no—
210#95—42no—
211#95—42no—
212#95—42no—
213#95—82no—
214#95—82no—
215#95—82no—
216#95—82no—
217#95—82no—
218#95—82no—
219C24C22×D411yescharacteristic
220C2×Q8—48no—
221C2×Q8—84no—
222C2×Q8—84no—
223C2×Q8—84no—
224C2×Q8—84no—
225C2×Q8—84no—
226C2×Q8—84no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4—41no—
255C22×C4—42no—
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—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4#12112yes—
282C22×C4#12112yes—
283C22×C4#12112yes—
284C22×C4#12112yes—
285C22×C4C22⋊Q812yes—
286C22×C4C22⋊Q812yes—
287C22×C4C22×D411yescharacteristic
288C22×C4C22×D411yescharacteristic
289C22×C4C22×Q811yescharacteristic
290C22×C4C2×#4111yescharacteristic
291C22×C4C2×#4111yescharacteristic
292C22×C4C2×#4111yescharacteristic
293C22×C4C2×#4112yes—
294C22×C4C2×#4112yes—
295C22×C42−1+412yes—
296C22×C42−1+412yes—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—24no—
300C2×C8—24no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—24no—
321C4⋊C4—24no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—48no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—88no—
335C4⋊C4#12414yes—
336C42—42no—
337C42—42no—
338C42—42no—
339C42—42no—
340C42—84no—
341C42—84no—
342C42#12114yes—
343C42C22⋊Q814yes—
344C42C22⋊Q814yes—
345C42#12614yes—
346C23C2×#12111yescharacteristic
347C23C2×#12111yescharacteristic
348C23C2×C22⋊Q811yescharacteristic
349C23#52512yes—
350C23#53612yes—
351C23#57611yescharacteristic
352C23#57611yescharacteristic
353C23#57711yescharacteristic
354C23#57711yescharacteristic
355C23#57712yes—
356C23#57812yes—
357Q8—816no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4#39614yes—
417C2×C4#39614yes—
418C2×C4C2×#12111yescharacteristic
419C2×C4C2×C22⋊Q811yescharacteristic
420C2×C4C2×C22⋊Q811yescharacteristic
421C2×C4C2×#12411yescharacteristic
422C2×C4C2×#12611yescharacteristic
423C2×C4#52912yes—
424C2×C4#53211yescharacteristic
425C2×C4#53611yescharacteristic
426C2×C4#53611yescharacteristic
427C2×C4#54112yes—
428C2×C4#54712yes—
429C2×C4#54812yes—
430C2×C4#55212yes—
431C2×C4#55612yes—
432C2×C4#55612yes—
433C2×C4#55612yes—
434C2×C4#55712yes—
435C2×C4#55712yes—
436C8—42no—
437C8—42no—
438C8—82no—
439C22C2×#39611yescharacteristic
440C22#241512yes—
441C22#258112yes—
442C22#262111yescharacteristic
443C22#285011yescharacteristic
444C22#304211yescharacteristic
445C22#304411yescharacteristic
446C22#304511yescharacteristic
447C22#304511yescharacteristic
448C22#305711yescharacteristic
449C22#305811yescharacteristic
450C22#306312yes—
451C22#308111yescharacteristic
452C22#308111yescharacteristic
453C22#308212yes—
454C22#311812yes—
455C22#312112yes—
456C22#312412yes—
457C22#312512yes—
458C22#324112yes—
459C22#324212yes—
460C22#324312yes—
461C22#324412yes—
462C4—24no—
463C4—24no—
464C4—44no—
465C4—84no—
466C4—82no—
467C4—84no—
468C4—82no—
469C4—82no—
470C4—161no—
471C4—161no—
472C4#245312yes—
473C4#251412yes—
474C4#254511yescharacteristic
475C4#254711yescharacteristic
476C4#256511yescharacteristic
477C4#256811yescharacteristic
478C2#1523711yescharacteristic
479C2#2361211yescharacteristic
480C2#2361511yescharacteristic
481C2#2471212yes—
482C2#2471812yes—
483C2#2928112yes—
484C2#2928212yes—
485C2#2987411yescharacteristic
486C2#2987511yescharacteristic
487C2#3303411yescharacteristic
488C2#3303511yescharacteristic
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×#19882
C2×#19872
C2×#19492
C2×#18322
#142822
#137832
#113162
#113152
#112202
#112192
#108502