Finite Group Databasebeta

← #475086

Subgroups — #475086

Order 512.

1018 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1984C211yesmaximal, characteristic
2C2×#1933C211yesmaximal, characteristic
3#15202C211yesmaximal, characteristic
4#15201C211yesmaximal, characteristic
5#11316C212yesmaximal
6#11293C212yesmaximal
7#11228C211yesmaximal, characteristic
8#11190C212yesmaximal
9#11077C211yesmaximal, characteristic
10#11067C212yesmaximal
11#10820C211yesmaximal, characteristic
12C22×C4×Q8C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×#103C2211yescharacteristic
15C22×#103C2212yes—
16C22×#103C2211yescharacteristic
17C22×C4×C8C2211yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#391C2212yes—
20C2×#389C2211yescharacteristic
21C2×#389C2212yes—
22#1984—24no—
23#1933—24no—
24C2×#340C2211yescharacteristic
25C2×#340C2212yes—
26C2×#340C2211yescharacteristic
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#336C2212yes—
32C2×#336C2212yes—
33#1446—21no—
34#1446—21no—
35#1444—21no—
36#1444—22no—
37#1442—21no—
38#1442—22no—
39C4⋊#95C2212yes—
40C4⋊#95C2212yes—
41C4⋊#95C2211yescharacteristic
42C4⋊#95C2211yescharacteristic
43C23×Q8D411yescharacteristic
44C23×Q8C2311yescharacteristic
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C2×C4×Q8—22no—
49C2×C4×Q8—22no—
50C2×C4×Q8—42no—
51C2×C4×Q8—42no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4D412yes—
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2312yes—
61C22×C42C2312yes—
62C22×C42C2311yescharacteristic
63C2×C4⋊C8—22no—
64C2×C4⋊C8—42no—
65C2×#103—22no—
66C2×#103—22no—
67C2×#103—22no—
68C2×#103—24no—
69C2×#103—22no—
70C2×#103—24no—
71C2×#103—42no—
72C2×#103—42no—
73C2×C4×C8—42no—
74C2×C4×C8D414yes—
75#391—22no—
76#391—22no—
77#391—42no—
78#391—42no—
79#389—22no—
80#389—22no—
81#389—42no—
82#389—42no—
83C2×#95—22no—
84C2×#95—21no—
85C2×#95—22no—
86C2×#95—21no—
87C2×#95—22no—
88C2×#95—21no—
89C2×#95—22no—
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—21no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95—22no—
96C2×#95—21no—
97#340—22no—
98#340—22no—
99#340—24no—
100#340—24no—
101#340—24no—
102#340—42no—
103#340—42no—
104#336—24no—
105#336—24no—
106C22×Q8—22no—
107C22×Q8—22no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—21no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8—21no—
117C22×Q8—42no—
118C22×Q8—42no—
119C22×Q8Q1614yes—
120C22×Q8#4112yes—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4C2×D412yes—
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D412yes—
130C23×C4C2×D411yescharacteristic
131C23×C4C2411yescharacteristic
132C22×C8—22no—
133C22×C8—21no—
134C22×C8—21no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—21no—
138C22×C8—22no—
139C22×C8—21no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8C2×D412yes—
148C22×C8C2×D412yes—
149C4×Q8—44no—
150C4×Q8—44no—
151C4×Q8—48no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—82no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—82no—
186C2×C4⋊C4#4112yes—
187C2×C4⋊C4#4114yes—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42C2×D412yes—
197C2×C42#4112yes—
198C4⋊C8—44no—
199#103—28no—
200#103—48no—
201#103—44no—
202C4×C8—44no—
203#95—44no—
204#95—44no—
205#95—44no—
206#95—44no—
207#95—44no—
208#95—42no—
209#95—42no—
210#95—42no—
211#95—42no—
212#95—42no—
213#95—81no—
214#95—81no—
215#95—82no—
216#95—82no—
217C24C22×D411yescharacteristic
218C2×Q8—28no—
219C2×Q8—22no—
220C2×Q8—24no—
221C2×Q8—24no—
222C2×Q8—22no—
223C2×Q8—48no—
224C2×Q8—44no—
225C2×Q8—48no—
226C2×Q8—44no—
227C2×Q8—41no—
228C2×Q8—42no—
229C2×Q8—41no—
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
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—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—42no—
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—41no—
278C22×C4—41no—
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—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4#12112yes—
295C22×C4#12112yes—
296C22×C4C2×Q1614yes—
297C22×C4C2×Q1612yes—
298C22×C4#13512yes—
299C22×C4C22×D411yescharacteristic
300C22×C4C2×#4111yescharacteristic
301C22×C4C2×#4111yescharacteristic
302C22×C4C2×#4112yes—
303C22×C4C2×#4111yescharacteristic
304C22×C4H(5,𝔽2)12yes—
305C22×C4H(5,𝔽2)12yes—
306C22×C42−1+411yescharacteristic
307C22×C42−1+412yes—
308C22×C42−1+411yescharacteristic
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—44no—
331C4⋊C4—48no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—42no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—84no—
347C4⋊C4—88no—
348C42—22no—
349C42—22no—
350C42—24no—
351C42—42no—
352C42—42no—
353C42—42no—
354C42—42no—
355C23C2×#12111yescharacteristic
356C23#53412yes—
357C23#54812yes—
358C23#54811yescharacteristic
359C23#54811yescharacteristic
360C23C22×Q1611yescharacteristic
361C23C2×#13511yescharacteristic
362C23#57512yes—
363C23#57712yes—
364C23#57711yescharacteristic
365C23#57711yescharacteristic
366Q8—416no—
367Q8—42no—
368Q8—42no—
369Q8—44no—
370Q8—81no—
371Q8—81no—
372Q8—82no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—81no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—81no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4#46714yes—
431C2×C4#52511yescharacteristic
432C2×C4#53211yescharacteristic
433C2×C4#53411yescharacteristic
434C2×C4#53511yescharacteristic
435C2×C4#53611yescharacteristic
436C2×C4#53611yescharacteristic
437C2×C4#53812yes—
438C2×C4#53912yes—
439C2×C4#53912yes—
440C2×C4#54212yes—
441C2×C4#54212yes—
442C2×C4#55112yes—
443C2×C4#55211yescharacteristic
444C2×C4#55211yescharacteristic
445C2×C4#55512yes—
446C2×C4#55612yes—
447C2×C4#56312yes—
448C2×C4#56312yes—
449C8—42no—
450C8—42no—
451C8—82no—
452C22#253611yescharacteristic
453C22#254511yescharacteristic
454C22#261711yescharacteristic
455C22#272812yes—
456C22#273112yes—
457C22C2×#46711yescharacteristic
458C22#305411yescharacteristic
459C22#305711yescharacteristic
460C22#306011yescharacteristic
461C22#318912yes—
462C22#319112yes—
463C22#320012yes—
464C22#320412yes—
465C22#336012yes—
466C22#336311yescharacteristic
467C22#336311yescharacteristic
468C22#336312yes—
469C22#336511yescharacteristic
470C22#336511yescharacteristic
471C22#337112yes—
472C22#337112yes—
473C22#337612yes—
474C22#337612yes—
475C4—24no—
476C4—44no—
477C4—42no—
478C4—82no—
479C4—84no—
480C4—82no—
481C4—82no—
482C4—161no—
483C4—162no—
484C4—161no—
485C4#261011yescharacteristic
486C4#263811yescharacteristic
487C4#266311yescharacteristic
488C4#274512yes—
489C4#277512yes—
490C4#282111yescharacteristic
491C2#1702311yescharacteristic
492C2#2818711yescharacteristic
493C2#2819211yescharacteristic
494C2#2863811yescharacteristic
495C2#2864411yescharacteristic
496C2#2973111yescharacteristic
497C2#2974111yescharacteristic
498C2#3254712yes—
499C2#3254812yes—
500C2#3263112yes—
501C2#3263312yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ 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×#19842
C2×#19332
#152022
#152012
#113162
#112932
#112282
#111902
#110772
#110672
#108202