Finite Group Databasebeta

← #402398

Subgroups — #402398

Order 512.

1058 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1865C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3#15197C211yesmaximal, characteristic
4#13817C211yesmaximal, characteristic
5#11357C211yesmaximal, characteristic
6#11255C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11190C212yesmaximal
9#11190C212yesmaximal
10#10908C212yesmaximal
11#10806C212yesmaximal
12C22×C4×Q8C2211yescharacteristic
13C22×#106C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2211yescharacteristic
16C22×#103C2212yes—
17C22×#103C2211yescharacteristic
18C2×#391C2212yes—
19C2×#389C2211yescharacteristic
20C2×#384C2211yescharacteristic
21C2×C4×C4⋊C4C2212yes—
22#1865—24no—
23#1803—24no—
24C2×#340C2211yescharacteristic
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#336C2211yescharacteristic
31C2×#336C2212yes—
32C2×#336C2212yes—
33#1442—22no—
34#1441—21no—
35#1441—21no—
36#1436—22no—
37C4⋊#95C2212yes—
38C4⋊#95C2211yescharacteristic
39C4⋊#95C2212yes—
40#1434—21no—
41C4×#95—21no—
42C4×#95C2211yescharacteristic
43C23×Q8C2311yescharacteristic
44C23×C8C2312yes—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C2×C4×Q8—22no—
48C2×C4×Q8—24no—
49C2×C4×Q8—42no—
50C2×C4×Q8D414yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C42—21no—
61C22×C42—22no—
62C22×C42C2312yes—
63C22×C42C2311yescharacteristic
64C2×#106—22no—
65C2×#106—24no—
66C2×C4⋊C8—22no—
67C2×C4⋊C8—42no—
68C2×#103—22no—
69C2×#103—22no—
70C2×#103—22no—
71C2×#103—24no—
72C2×#103—22no—
73C2×#103—24no—
74C2×#103—24no—
75C2×#103—42no—
76#391—24no—
77#391—24no—
78#389—22no—
79#389—22no—
80#384—22no—
81#384—22no—
82C4×C4⋊C4—24no—
83C4×C4⋊C4—42no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95—21no—
87C2×#95—22no—
88C2×#95—21no—
89C2×#95—21no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95D411yescharacteristic
95C2×#95D411yescharacteristic
96C2×#95D412yes—
97#340—24no—
98#340—22no—
99#340—24no—
100#340—24no—
101#340—24no—
102#340—42no—
103#336—24no—
104#336—22no—
105#336—42no—
106C22×Q8—21no—
107C22×Q8—22no—
108C22×Q8—22no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—22no—
112C22×Q8—21no—
113C22×Q8—21no—
114C22×Q8C2×D412yes—
115C22×Q8#4114yes—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—21no—
122C23×C4C2×D412yes—
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D412yes—
125C23×C4C2×D411yescharacteristic
126C23×C4C2411yescharacteristic
127C22×C8—21no—
128C22×C8—22no—
129C22×C8—21no—
130C22×C8—22no—
131C22×C8—21no—
132C22×C8—22no—
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—21no—
142C22×C8—21no—
143C22×C8#4112yes—
144C4×Q8—28no—
145C4×Q8—44no—
146C4×Q8—48no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—44no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—82no—
177C2×C4⋊C4—81no—
178C2×C4⋊C4—81no—
179C2×C4⋊C4C2×D412yes—
180C2×C4⋊C4#4114yes—
181C2×C4⋊C4#4112yes—
182C2×C4⋊C4#4114yes—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—24no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—44no—
193C2×C42—44no—
194C2×C42—44no—
195C2×C42—82no—
196C2×C42C2×D412yes—
197C2×C42#4112yes—
198#106—44no—
199C4⋊C8—44no—
200#103—28no—
201#103—44no—
202#103—48no—
203#95—28no—
204#95—28no—
205#95—22no—
206#95—22no—
207#95—24no—
208#95—44no—
209#95—42no—
210#95—42no—
211#95—82no—
212#95—81no—
213#95—82no—
214#95—82no—
215#95—82no—
216C24C22×D411yescharacteristic
217C2×Q8—24no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—24no—
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8#12414yes—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4#12112yes—
291C22×C4#12112yes—
292C22×C4#13512yes—
293C22×C4#13714yes—
294C22×C4#13712yes—
295C22×C4C22×D411yescharacteristic
296C22×C4C2×#4112yes—
297C22×C4C2×#4111yescharacteristic
298C22×C4C2×#4111yescharacteristic
299C22×C4C2×#4112yes—
300C22×C4C2×#4112yes—
301C22×C4C2×#4111yescharacteristic
302C22×C4H(5,𝔽2)12yes—
303C22×C42−1+411yescharacteristic
304C22×C42−1+411yescharacteristic
305C2×C8—22no—
306C2×C8—24no—
307C2×C8—41no—
308C2×C8—42no—
309C2×C8—41no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—42no—
315C2×C8—41no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C4⋊C4—22no—
323C4⋊C4—24no—
324C4⋊C4—22no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—48no—
329C4⋊C4—41no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—42no—
340C4⋊C4—84no—
341C4⋊C4—84no—
342C4⋊C4—84no—
343C4⋊C4#12314yes—
344C42—22no—
345C42—22no—
346C42—24no—
347C42—48no—
348C42—42no—
349C42—42no—
350C42—42no—
351C42—42no—
352C42—88no—
353C23C2×#12111yescharacteristic
354C23#52512yes—
355C23#54612yes—
356C23#54711yescharacteristic
357C23#54811yescharacteristic
358C23C2×#13511yescharacteristic
359C23C2×#13712yes—
360C23C2×#13711yescharacteristic
361C23#57611yescharacteristic
362C23#57711yescharacteristic
363C23#57712yes—
364Q8—24no—
365Q8—24no—
366Q8—44no—
367Q8—42no—
368Q8—42no—
369Q8—44no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4—81no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4#46414yes—
430C2×C4C2×#12311yescharacteristic
431C2×C4#52511yescharacteristic
432C2×C4C2×#12411yescharacteristic
433C2×C4#52912yes—
434C2×C4#52912yes—
435C2×C4#52912yes—
436C2×C4#53211yescharacteristic
437C2×C4#53411yescharacteristic
438C2×C4#53611yescharacteristic
439C2×C4#53912yes—
440C2×C4#54212yes—
441C2×C4#55112yes—
442C2×C4#55212yes—
443C2×C4#55212yes—
444C2×C4#55211yescharacteristic
445C2×C4#55312yes—
446C2×C4#55312yes—
447C2×C4#55611yescharacteristic
448C8—42no—
449C8—82no—
450C8—81no—
451C22#241211yescharacteristic
452C22#241511yescharacteristic
453C22#246012yes—
454C22#246812yes—
455C22#285011yescharacteristic
456C22C2×#46411yescharacteristic
457C22#303911yescharacteristic
458C22#304311yescharacteristic
459C22#304511yescharacteristic
460C22#310712yes—
461C22#311312yes—
462C22#311912yes—
463C22#312612yes—
464C22#330112yes—
465C22#331412yes—
466C22#332012yes—
467C22#333112yes—
468C22#334011yescharacteristic
469C22#334412yes—
470C22#335711yescharacteristic
471C22#336111yescharacteristic
472C22#336912yes—
473C22#337211yescharacteristic
474C4—24no—
475C4—42no—
476C4—44no—
477C4—44no—
478C4—44no—
479C4—82no—
480C4—84no—
481C4—82no—
482C4—162no—
483C4—161no—
484C4#239511yescharacteristic
485C4#250311yescharacteristic
486C4#253012yes—
487C4#257712yes—
488C4#259111yescharacteristic
489C4#266311yescharacteristic
490C2#1484111yescharacteristic
491C2#2453311yescharacteristic
492C2#2454811yescharacteristic
493C2#2467911yescharacteristic
494C2#2469811yescharacteristic
495C2#2676312yes—
496C2#2677512yes—
497C2#2710512yes—
498C2#2711712yes—
499C2#3303311yescharacteristic
500C2#3303911yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ 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×#18652
C2×#18032
#151972
#138172
#113572
#112552
#112272
#111902
#109082
#108062