Finite Group Databasebeta

← #402396

Subgroups — #402396

Order 512.

1058 conjugacy classes of subgroups.

The subgroup lattice has 497 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1863C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3#15197C211yesmaximal, characteristic
4#13817C211yesmaximal, characteristic
5#11357C211yesmaximal, characteristic
6#11255C211yesmaximal, characteristic
7#11228C211yesmaximal, characteristic
8#11190C212yesmaximal
9#11190C212yesmaximal
10#10907C212yesmaximal
11#10807C212yesmaximal
12C22×C4×Q8C2211yescharacteristic
13C22×#107C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2211yescharacteristic
16C22×#103C2212yes—
17C22×#103C2211yescharacteristic
18C2×#391C2212yes—
19C2×#389C2211yescharacteristic
20C2×#384C2211yescharacteristic
21C2×C4×C4⋊C4C2212yes—
22#1863—24no—
23#1803—24no—
24C2×#340C2211yescharacteristic
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#336C2211yescharacteristic
31C2×#336C2212yes—
32C2×#336C2212yes—
33#1442—21no—
34#1442—21no—
35#1441—22no—
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×#107—22no—
65C2×#107—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×#95D412yes—
96C2×#95D411yescharacteristic
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—44no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—82no—
176C2×C4⋊C4—81no—
177C2×C4⋊C4—81no—
178C2×C4⋊C4C2×D412yes—
179C2×C4⋊C4#4114yes—
180C2×C4⋊C4#4112yes—
181C2×C4⋊C4#4114yes—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—24no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—44no—
192C2×C42—44no—
193C2×C42—44no—
194C2×C42—82no—
195C2×C42C2×D412yes—
196C2×C42#4112yes—
197#107—44no—
198C4⋊C8—44no—
199#103—28no—
200#103—44no—
201#103—48no—
202#95—28no—
203#95—28no—
204#95—22no—
205#95—42no—
206#95—44no—
207#95—42no—
208#95—42no—
209#95—82no—
210#95—81no—
211#95—82no—
212#95—82no—
213#95—82no—
214#95Q1614yes—
215C24C22×D411yescharacteristic
216C2×Q8—24no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—24no—
223C2×Q8—24no—
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8#12414yes—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4#12112yes—
288C22×C4#12112yes—
289C22×C4C2×Q1614yes—
290C22×C4C2×Q1612yes—
291C22×C4#13712yes—
292C22×C4C22×D411yescharacteristic
293C22×C4C2×#4112yes—
294C22×C4C2×#4111yescharacteristic
295C22×C4C2×#4111yescharacteristic
296C22×C4C2×#4112yes—
297C22×C4C2×#4112yes—
298C22×C4C2×#4111yescharacteristic
299C22×C4H(5,𝔽2)12yes—
300C22×C42−1+411yescharacteristic
301C22×C42−1+411yescharacteristic
302C2×C8—22no—
303C2×C8—24no—
304C2×C8—41no—
305C2×C8—42no—
306C2×C8—41no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C4⋊C4—22no—
320C4⋊C4—24no—
321C4⋊C4—22no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—22no—
325C4⋊C4—48no—
326C4⋊C4—41no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—84no—
338C4⋊C4—84no—
339C4⋊C4—84no—
340C4⋊C4#12314yes—
341C42—22no—
342C42—22no—
343C42—24no—
344C42—48no—
345C42—42no—
346C42—42no—
347C42—42no—
348C42—42no—
349C42—88no—
350C23C2×#12111yescharacteristic
351C23#52512yes—
352C23#54612yes—
353C23#54711yescharacteristic
354C23#54811yescharacteristic
355C23C22×Q1611yescharacteristic
356C23C2×#13711yescharacteristic
357C23#57512yes—
358C23#57611yescharacteristic
359C23#57712yes—
360C23#57711yescharacteristic
361Q8—24no—
362Q8—24no—
363Q8—44no—
364Q8—42no—
365Q8—42no—
366Q8—44no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—81no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4#46214yes—
425C2×C4C2×#12311yescharacteristic
426C2×C4#52511yescharacteristic
427C2×C4C2×#12411yescharacteristic
428C2×C4#52912yes—
429C2×C4#52912yes—
430C2×C4#52912yes—
431C2×C4#53211yescharacteristic
432C2×C4#53411yescharacteristic
433C2×C4#53611yescharacteristic
434C2×C4#53912yes—
435C2×C4#54212yes—
436C2×C4#55112yes—
437C2×C4#55212yes—
438C2×C4#55212yes—
439C2×C4#55211yescharacteristic
440C2×C4#55312yes—
441C2×C4#55312yes—
442C2×C4#55611yescharacteristic
443C8—42no—
444C8—82no—
445C8—81no—
446C22#241211yescharacteristic
447C22#241511yescharacteristic
448C22#246012yes—
449C22#246812yes—
450C22#285011yescharacteristic
451C22C2×#46211yescharacteristic
452C22#304011yescharacteristic
453C22#304311yescharacteristic
454C22#304511yescharacteristic
455C22#310412yes—
456C22#311612yes—
457C22#311912yes—
458C22#312612yes—
459C22#329912yes—
460C22#330712yes—
461C22#331612yes—
462C22#332212yes—
463C22#333811yescharacteristic
464C22#334812yes—
465C22#335611yescharacteristic
466C22#336311yescharacteristic
467C22#337511yescharacteristic
468C22#337612yes—
469C4—24no—
470C4—44no—
471C4—42no—
472C4—44no—
473C4—44no—
474C4—82no—
475C4—84no—
476C4—82no—
477C4—162no—
478C4—161no—
479C4#239511yescharacteristic
480C4#250311yescharacteristic
481C4#253012yes—
482C4#257712yes—
483C4#259111yescharacteristic
484C4#266311yescharacteristic
485C2#1484111yescharacteristic
486C2#2453211yescharacteristic
487C2#2454911yescharacteristic
488C2#2468211yescharacteristic
489C2#2469511yescharacteristic
490C2#2675812yes—
491C2#2677812yes—
492C2#2710012yes—
493C2#2712012yes—
494C2#3302711yescharacteristic
495C2#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×#18632
C2×#18032
#151972
#138172
#113572
#112552
#112282
#111902
#109072
#108072