Finite Group Databasebeta

← #400834

Subgroups — #400834

Order 512.

1068 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1947C211yesmaximal, characteristic
2C2×#1928C211yesmaximal, characteristic
3C2×#1928C212yesmaximal
4#15185C211yesmaximal, characteristic
5#13818C211yesmaximal, characteristic
6#11371C211yesmaximal, characteristic
7#11255C211yesmaximal, characteristic
8#11219C212yesmaximal
9#11077C211yesmaximal, characteristic
10#11067C212yesmaximal
11#10907C212yesmaximal
12C22×#107C2212yes—
13C22×#107C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2211yescharacteristic
16C22×#103C2212yes—
17C22×#103C2211yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#391C2212yes—
20C2×#389C2212yes—
21C2×#384C2211yescharacteristic
22C2×C4×C4⋊C4C2212yes—
23C2×C4×C4⋊C4C2211yescharacteristic
24#1947—24no—
25#1928—28no—
26#1928—24no—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2211yescharacteristic
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#336C2212yes—
33C2×#336C2211yescharacteristic
34C2×#336C2212yes—
35#1445—22no—
36#1442—21no—
37#1442—21no—
38#1436—22no—
39C4⋊#95—21no—
40C4⋊#95C2211yescharacteristic
41C4⋊#95C2212yes—
42C4×#95—21no—
43C4×#95C2211yescharacteristic
44C23×Q8C2311yescharacteristic
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2312yes—
48C22×C4⋊C4—22no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2311yescharacteristic
52C22×C4⋊C4C2312yes—
53C22×C4⋊C4C2312yes—
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C42—21no—
57C22×C42—22no—
58C22×C42C2312yes—
59C22×C42C2311yescharacteristic
60C2×#107—24no—
61C2×#107—22no—
62C2×#107—24no—
63C2×#107—24no—
64C2×#107—24no—
65C2×C4⋊C8—24no—
66C2×C4⋊C8—22no—
67C2×#103—24no—
68C2×#103—24no—
69C2×#103—22no—
70C2×#103—24no—
71C2×#103—22no—
72C2×#103—22no—
73C2×#103—24no—
74C2×#103D414yes—
75#391—24no—
76#391—22no—
77#391—22no—
78#391—42no—
79#389—24no—
80#389—24no—
81#384—22no—
82#384—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4—24no—
85C4×C4⋊C4—42no—
86C4×C4⋊C4D414yes—
87C2×#95—22no—
88C2×#95—21no—
89C2×#95—21no—
90C2×#95—22no—
91C2×#95—21no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95D411yescharacteristic
99C2×#95D412yes—
100C2×#95D411yescharacteristic
101#340—24no—
102#340—22no—
103#340—24no—
104#340—24no—
105#340—42no—
106#336—24no—
107#336—24no—
108#336—22no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—21no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—21no—
116C22×Q8—22no—
117C22×Q8—21no—
118C22×Q8C2×D412yes—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—21no—
125C23×C4C2×D412yes—
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D412yes—
128C23×C4C2×D411yescharacteristic
129C23×C4C2411yescharacteristic
130C22×C8—21no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—21no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—21no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—21no—
144C22×C8—21no—
145C22×C8C2×D412yes—
146C22×C8#4114yes—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
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—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—28no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—82no—
172C2×C4⋊C4—82no—
173C2×C4⋊C4—82no—
174C2×C4⋊C4C2×D412yes—
175C2×C4⋊C4C2×D412yes—
176C2×C4⋊C4C2×D412yes—
177C2×C4⋊C4#4114yes—
178C2×C4⋊C4#4112yes—
179C2×C4⋊C4#4114yes—
180C2×C42—22no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—24no—
189C2×C42—44no—
190C2×C42—44no—
191C2×C42—82no—
192C2×C42—82no—
193C2×C42C2×D412yes—
194C2×C42#4112yes—
195#107—48no—
196#107—44no—
197C4⋊C8—28no—
198#103—216no—
199#103—28no—
200#103—44no—
201#95—28no—
202#95—24no—
203#95—22no—
204#95—42no—
205#95—44no—
206#95—44no—
207#95—44no—
208#95—42no—
209#95—42no—
210#95—42no—
211#95—82no—
212#95—81no—
213#95—82no—
214#95Q1614yes—
215C24C22×D411yescharacteristic
216C2×Q8—22no—
217C2×Q8—24no—
218C2×Q8—22no—
219C2×Q8—24no—
220C2×Q8—41no—
221C2×Q8—42no—
222C2×Q8—41no—
223C2×Q8—42no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
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—21no—
249C22×C4—22no—
250C22×C4—21no—
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—22no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—41no—
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—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4#12112yes—
288C22×C4#12112yes—
289C22×C4C2×Q1614yes—
290C22×C4C2×Q1612yes—
291C22×C4#13712yes—
292C22×C4C22×D411yescharacteristic
293C22×C4C22×D411yescharacteristic
294C22×C4C2×#4111yescharacteristic
295C22×C4C2×#4112yes—
296C22×C4C2×#4112yes—
297C22×C4C2×#4112yes—
298C22×C4C2×#4111yescharacteristic
299C22×C4H(5,𝔽2)11yescharacteristic
300C22×C42−1+412yes—
301C22×C42−1+411yescharacteristic
302C2×C8—22no—
303C2×C8—24no—
304C2×C8—24no—
305C2×C8—24no—
306C2×C8—24no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—41no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—42no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—42no—
318C2×C8—42no—
319C4⋊C4—24no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—42no—
331C4⋊C4—41no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—84no—
336C4⋊C4—84no—
337C4⋊C4—88no—
338C4⋊C4#12114yes—
339C4⋊C4#12414yes—
340C42—22no—
341C42—22no—
342C42—24no—
343C42—42no—
344C42—42no—
345C42—42no—
346C42—42no—
347C42—84no—
348C42—88no—
349C23C2×#12111yescharacteristic
350C23#52512yes—
351C23D4211yescharacteristic
352C23#54712yes—
353C23#54811yescharacteristic
354C23C22×Q1611yescharacteristic
355C23C2×#13711yescharacteristic
356C23#57512yes—
357C23#57612yes—
358C23#57711yescharacteristic
359C23#57811yescharacteristic
360Q8—42no—
361Q8—44no—
362Q8—42no—
363Q8—81no—
364Q8—82no—
365Q8—81no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
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—82no—
420C2×C4—82no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4#46214yes—
424C2×C4C2×#12111yescharacteristic
425C2×C4#52511yescharacteristic
426C2×C4#52512yes—
427C2×C4C2×#12411yescharacteristic
428C2×C4#52912yes—
429C2×C4#52912yes—
430C2×C4#53211yescharacteristic
431C2×C4#53611yescharacteristic
432C2×C4#53711yescharacteristic
433C2×C4#53912yes—
434C2×C4#54112yes—
435C2×C4#54711yescharacteristic
436C2×C4#54712yes—
437C2×C4#55212yes—
438C2×C4#55311yescharacteristic
439C2×C4#55612yes—
440C2×C4#55612yes—
441C2×C4#55912yes—
442C8—44no—
443C8—42no—
444C8—81no—
445C22#241311yescharacteristic
446C22#241611yescharacteristic
447C22#245512yes—
448C22#246912yes—
449C22#285011yescharacteristic
450C22C2×#46211yescharacteristic
451C22#304011yescharacteristic
452C22#304111yescharacteristic
453C22#304611yescharacteristic
454C22#310412yes—
455C22#311612yes—
456C22#311812yes—
457C22#312412yes—
458C22#326812yes—
459C22#327811yescharacteristic
460C22D4×Q1611yescharacteristic
461C22#333812yes—
462C22#334612yes—
463C22#334812yes—
464C22#335212yes—
465C22#336311yescharacteristic
466C22#337012yes—
467C22#337411yescharacteristic
468C4—24no—
469C4—44no—
470C4—42no—
471C4—44no—
472C4—44no—
473C4—82no—
474C4—84no—
475C4—82no—
476C4—161no—
477C4—162no—
478C4#239211yescharacteristic
479C4#247812yes—
480C4#254711yescharacteristic
481C4#259211yescharacteristic
482C4#259612yes—
483C4#266411yescharacteristic
484C2#1480811yescharacteristic
485C2#2458211yescharacteristic
486C2#2459511yescharacteristic
487C2#2473211yescharacteristic
488C2#2474911yescharacteristic
489C2#2655912yes—
490C2#2657212yes—
491C2#2713212yes—
492C2#2715212yes—
493C2#3302711yescharacteristic
494C2#3303611yescharacteristic
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×#19472
C2×#19282
#151852
#138182
#113712
#112552
#112192
#110772
#110672
#109072