Finite Group Databasebeta

← #467943

Subgroups — #467943

Order 512.

1078 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2043C212yesmaximal
2#15196C211yesmaximal, characteristic
3#14155C211yesmaximal, characteristic
4#11202C211yesmaximal, characteristic
5#11190C212yesmaximal
6#11190C212yesmaximal
7#11077C212yesmaximal
8#11050C212yesmaximal
9#10885C212yesmaximal
10C22×C4⋊Q8C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×#103C2212yes—
13C22×#103C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16C2×#391C2212yes—
17C2×#391C2212yes—
18C2×#389C2212yes—
19C2×#384C2211yescharacteristic
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22#2043—28no—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2212yes—
29C2×#336C2211yescharacteristic
30#1445—21no—
31#1445—21no—
32#1444—21no—
33#1444—21no—
34#1441—21no—
35#1441—21no—
36C4⋊#95—21no—
37C4⋊#95—21no—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40C23×Q8C2312yes—
41C23×C8C2312yes—
42C23×C8C2312yes—
43C2×C4⋊Q8—22no—
44C2×C4⋊Q8—41no—
45C2×C4⋊Q8—41no—
46C2×C4⋊Q8—41no—
47C2×C4⋊Q8—41no—
48C2×C4⋊Q8D414yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2312yes—
58C22×C4⋊C4C2312yes—
59C22×C42—21no—
60C22×C42C2311yescharacteristic
61C22×C42C2311yescharacteristic
62C22×C42C2311yescharacteristic
63C2×C4⋊C8—41no—
64C2×C4⋊C8—42no—
65C2×#103—24no—
66C2×#103—24no—
67C2×#103—24no—
68C2×#103—24no—
69C2×#103—24no—
70C2×#103—24no—
71C2×#103—42no—
72C2×#103—42no—
73C2×#103—42no—
74C2×#103—42no—
75C2×#103—42no—
76C2×#103—42no—
77#391—24no—
78#391—24no—
79#391—42no—
80#391—42no—
81#389—24no—
82#389—24no—
83#384—41no—
84#384—41no—
85C4×C4⋊C4—41no—
86C4×C4⋊C4—41no—
87C4×C4⋊C4—41no—
88C4×C4⋊C4—41no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—22no—
96C2×#95—21no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95D411yescharacteristic
100C2×#95D411yescharacteristic
101#340—24no—
102#340—24no—
103#340—42no—
104#340—42no—
105#336—24no—
106#336—41no—
107#336—42no—
108C22×Q8—22no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—22no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8C2×D414yes—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4C2411yescharacteristic
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×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C4⋊Q8—44no—
148C4⋊Q8—44no—
149C4⋊Q8—44no—
150C4⋊Q8—44no—
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—24no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
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—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—82no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4—82no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4Q1614yes—
186C2×C4⋊C4#4114yes—
187C2×C4⋊C4#4114yes—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—21no—
195C2×C42—22no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—22no—
200C2×C42—42no—
201C2×C42—42no—
202C2×C42—42no—
203C2×C42C2×D412yes—
204C2×C42#4112yes—
205C4⋊C8—44no—
206#103—48no—
207#103—48no—
208#103—48no—
209#103—48no—
210#95—41no—
211#95—41no—
212#95—44no—
213#95—44no—
214#95—44no—
215#95—44no—
216#95—42no—
217#95—42no—
218#95—44no—
219#95—42no—
220#95—82no—
221#95—82no—
222C24C22×D411yescharacteristic
223C2×Q8—24no—
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—24no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
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—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—24no—
272C22×C4—21no—
273C22×C4—24no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
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—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4#12112yes—
305C22×C4#12112yes—
306C22×C4C2×Q1612yes—
307C22×C4C2×Q1612yes—
308C22×C4C2×Q1612yes—
309C22×C4#13712yes—
310C22×C4#13712yes—
311C22×C4C22×D411yescharacteristic
312C22×C4C2×#4111yescharacteristic
313C22×C4C2×#4112yes—
314C22×C4C2×#4112yes—
315C22×C4H(5,𝔽2)11yescharacteristic
316C22×C4H(5,𝔽2)11yescharacteristic
317C22×C4H(5,𝔽2)11yescharacteristic
318C22×C4H(5,𝔽2)11yescharacteristic
319C22×C4H(5,𝔽2)12yes—
320C22×C42−1+412yes—
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—
333C2×C8—42no—
334C2×C8—42no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—44no—
340C4⋊C4—44no—
341C4⋊C4—48no—
342C4⋊C4—48no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—88no—
352C4⋊C4—84no—
353C4⋊C4—84no—
354C42—22no—
355C42—22no—
356C42—22no—
357C42—22no—
358C42—42no—
359C42—42no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42—41no—
364C42—84no—
365C23C2×#12111yescharacteristic
366C23#53411yescharacteristic
367C23#53511yescharacteristic
368C23#54612yes—
369C23#54812yes—
370C23C22×Q1611yescharacteristic
371C23C2×#13711yescharacteristic
372C23C2×#13711yescharacteristic
373C23#57511yescharacteristic
374C23#57712yes—
375C23#57712yes—
376Q8—44no—
377Q8—44no—
378Q8—44no—
379Q8—44no—
380Q8—82no—
381Q8—82no—
382Q8—82no—
383Q8—82no—
384C2×C4—22no—
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—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4#46214yes—
444C2×C4#52912yes—
445C2×C4#53411yescharacteristic
446C2×C4#53411yescharacteristic
447C2×C4#53811yescharacteristic
448C2×C4#53811yescharacteristic
449C2×C4#53912yes—
450C2×C4#54012yes—
451C2×C4#54012yes—
452C2×C4#54212yes—
453C2×C4#54212yes—
454C2×C4#54612yes—
455C2×C4#54712yes—
456C2×C4#55312yes—
457C2×C4#55511yescharacteristic
458C2×C4#55911yescharacteristic
459C2×C4#56011yescharacteristic
460C2×C4#56212yes—
461C2×C4#56311yescharacteristic
462C8—82no—
463C8—82no—
464C22#242712yes—
465C22#261711yescharacteristic
466C22#270911yescharacteristic
467C22#271112yes—
468C22#273111yescharacteristic
469C22C2×#46211yescharacteristic
470C22#303711yescharacteristic
471C22#304312yes—
472C22#318911yescharacteristic
473C22#319511yescharacteristic
474C22#320011yescharacteristic
475C22#320011yescharacteristic
476C22#320911yescharacteristic
477C22#321511yescharacteristic
478C22#322112yes—
479C22#329912yes—
480C22#330712yes—
481C22#332012yes—
482C22#333112yes—
483C22#336312yes—
484C22#336912yes—
485C22#337212yes—
486C22#337612yes—
487C4—24no—
488C4—42no—
489C4—42no—
490C4—42no—
491C4—42no—
492C4—81no—
493C4—84no—
494C4—84no—
495C4—84no—
496C4—162no—
497C4#259311yescharacteristic
498C4#265112yes—
499C4#269911yescharacteristic
500C4#270112yes—
501C4#272411yescharacteristic
502C4#283011yescharacteristic
503C2#1659611yescharacteristic
504C2#2532412yes—
505C2#2533112yes—
506C2#2971511yescharacteristic
507C2#2972211yescharacteristic
508C2#3202911yescharacteristic
509C2#3203711yescharacteristic
510C2#3208412yes—
511C2#3210512yes—
512C2#3263111yescharacteristic
513C2#3264511yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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×#20432
#151962
#141552
#112022
#111902
#110772
#110502
#108852