Finite Group Databasebeta

← #416961

Subgroups — #416961

Order 512.

1018 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1989C211yesmaximal, characteristic
2C2×#1989C211yesmaximal, characteristic
3C2×#1947C211yesmaximal, characteristic
4C2×#1832C211yesmaximal, characteristic
5#14283C211yesmaximal, characteristic
6#13783C211yesmaximal, characteristic
7#11316C212yesmaximal
8#11315C212yesmaximal
9#11219C212yesmaximal
10#11219C212yesmaximal
11#10849C211yesmaximal, characteristic
12C22×#125C2211yescharacteristic
13C22×#107C2212yes—
14C22×C4⋊C8C2211yescharacteristic
15C22×C4⋊C8C2211yescharacteristic
16C2×#389C2212yes—
17C2×#384C2211yescharacteristic
18C2×C4×C4⋊C4C2211yescharacteristic
19C2×C4×C4⋊C4C2211yescharacteristic
20C2×#376C2211yescharacteristic
21#1989—24no—
22#1989—24no—
23#1947—24no—
24#1832—24no—
25C2×#340C2211yescharacteristic
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2211yescharacteristic
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#336C2212yes—
35C2×#336C2212yes—
36#1441—21no—
37#1441—21no—
38#1441—22no—
39#1436—22no—
40C4⋊#95—21no—
41C4⋊#95C2212yes—
42C4⋊#95C2212yes—
43C4⋊#95C2212yes—
44#1434—21no—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2312yes—
48C2×#125—22no—
49C2×#125—22no—
50C2×#125—22no—
51C2×#125—22no—
52C2×#125—22no—
53C2×#125Q814yes—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2311yescharacteristic
65C22×C42—21no—
66C22×C42—21no—
67C22×C42C2312yes—
68C22×C42C2311yescharacteristic
69C2×#107—24no—
70C2×#107—24no—
71C2×#107—24no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—22no—
74C2×C4⋊C8—22no—
75C2×C4⋊C8—22no—
76C2×C4⋊C8—22no—
77C2×C4⋊C8D414yes—
78#389—24no—
79#389—24no—
80#384—22no—
81#384—22no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4—22no—
85C4×C4⋊C4D414yes—
86#376—22no—
87#376—22no—
88C2×#95—22no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95D411yescharacteristic
98C2×#95D411yescharacteristic
99C2×#95D412yes—
100#340—24no—
101#340—24no—
102#340—24no—
103#340—22no—
104#340—22no—
105#340—22no—
106#340—22no—
107#340—24no—
108#340—24no—
109#336—24no—
110#336—24no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—22no—
115C23×C4—21no—
116C23×C4—22no—
117C23×C4C2×D412yes—
118C23×C4C2×D412yes—
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—21no—
129C22×C8—21no—
130C22×C8—21no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—21no—
135C22×C8—21no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8C2×D414yes—
139#125—28no—
140#125—28no—
141#125—44no—
142#125—44no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—28no—
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⋊C4—82no—
179C2×C4⋊C4—81no—
180C2×C4⋊C4—81no—
181C2×C4⋊C4—82no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4C2×D412yes—
184C2×C4⋊C4C2×D412yes—
185C2×C4⋊C4C2×Q812yes—
186C2×C4⋊C4C2×Q812yes—
187C2×C4⋊C4#4114yes—
188C2×C4⋊C4#4114yes—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—24no—
196C2×C42—42no—
197C2×C42—82no—
198C2×C42—81no—
199C2×C42—81no—
200C2×C42C2×D412yes—
201C2×C42C2×D412yes—
202C2×C42C2×Q812yes—
203C2×C42#4112yes—
204C2×C42#4112yes—
205C2×C42#4112yes—
206#107—48no—
207C4⋊C8—28no—
208C4⋊C8—44no—
209#95—28no—
210#95—24no—
211#95—22no—
212#95—22no—
213#95—24no—
214#95—42no—
215#95—82no—
216#95—82no—
217#95—82no—
218#95—82no—
219#95—82no—
220#95—82no—
221C24C22×D411yescharacteristic
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—42no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4#12112yes—
279C22×C4#12112yes—
280C22×C4#12112yes—
281C22×C4#12112yes—
282C22×C4C22⋊Q812yes—
283C22×C4C22⋊Q812yes—
284C22×C4C22×D411yescharacteristic
285C22×C4C22×D411yescharacteristic
286C22×C4C22×Q811yescharacteristic
287C22×C4C2×#4111yescharacteristic
288C22×C4C2×#4111yescharacteristic
289C22×C4C2×#4111yescharacteristic
290C22×C4C2×#4112yes—
291C22×C4C2×#4112yes—
292C22×C42−1+412yes—
293C22×C42−1+412yes—
294C2×C8—24no—
295C2×C8—24no—
296C2×C8—24no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—42no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—48no—
329C4⋊C4—48no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—84no—
335C4⋊C4—84no—
336C4⋊C4—88no—
337C4⋊C4#12414yes—
338C42—42no—
339C42—42no—
340C42—42no—
341C42—42no—
342C42—84no—
343C42—84no—
344C42#12114yes—
345C42C22⋊Q814yes—
346C42C22⋊Q814yes—
347C42#12614yes—
348C23C2×#12111yescharacteristic
349C23C2×#12111yescharacteristic
350C23C2×C22⋊Q811yescharacteristic
351C23#52512yes—
352C23#53612yes—
353C23#57612yes—
354C23#57611yescharacteristic
355C23#57711yescharacteristic
356C23#57711yescharacteristic
357C23#57812yes—
358C23#57811yescharacteristic
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4#39614yes—
420C2×C4#39614yes—
421C2×C4C2×#12111yescharacteristic
422C2×C4C2×C22⋊Q811yescharacteristic
423C2×C4C2×C22⋊Q811yescharacteristic
424C2×C4C2×#12411yescharacteristic
425C2×C4C2×#12611yescharacteristic
426C2×C4#52912yes—
427C2×C4#53211yescharacteristic
428C2×C4#53611yescharacteristic
429C2×C4#53611yescharacteristic
430C2×C4#54112yes—
431C2×C4#54712yes—
432C2×C4#54812yes—
433C2×C4#55212yes—
434C2×C4#55612yes—
435C2×C4#55612yes—
436C2×C4#55612yes—
437C2×C4#55712yes—
438C2×C4#55712yes—
439C8—44no—
440C8—81no—
441C8—81no—
442C22C2×#39611yescharacteristic
443C22#241512yes—
444C22#258112yes—
445C22#262111yescharacteristic
446C22#285011yescharacteristic
447C22#304111yescharacteristic
448C22#304411yescharacteristic
449C22#304511yescharacteristic
450C22#304611yescharacteristic
451C22#306112yes—
452C22#306211yescharacteristic
453C22#306311yescharacteristic
454C22#308312yes—
455C22#308311yescharacteristic
456C22#308411yescharacteristic
457C22#311912yes—
458C22#312012yes—
459C22#312212yes—
460C22#312712yes—
461C22#324112yes—
462C22#324212yes—
463C22#324312yes—
464C22#324312yes—
465C4—24no—
466C4—24no—
467C4—44no—
468C4—82no—
469C4—82no—
470C4—82no—
471C4—84no—
472C4—82no—
473C4—82no—
474C4—162no—
475C4#245312yes—
476C4#251412yes—
477C4#254511yescharacteristic
478C4#254711yescharacteristic
479C4#256511yescharacteristic
480C4#256811yescharacteristic
481C2#1523711yescharacteristic
482C2#2361111yescharacteristic
483C2#2361611yescharacteristic
484C2#2471312yes—
485C2#2471512yes—
486C2#2928312yes—
487C2#2928512yes—
488C2#2987211yescharacteristic
489C2#2987511yescharacteristic
490C2#3303811yescharacteristic
491C2#3304111yescharacteristic
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×#19892
C2×#19472
C2×#18322
#142832
#137832
#113162
#113152
#112192
#108492