Finite Group Databasebeta

← #401482

Subgroups — #401482

Order 512.

1122 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1947C211yesmaximal, characteristic
2C2×#1947C212yesmaximal
3C2×#1918C211yesmaximal, characteristic
4#15145C211yesmaximal, characteristic
5#13821C211yesmaximal, characteristic
6#11373C211yesmaximal, characteristic
7#11322C211yesmaximal, characteristic
8#11227C212yesmaximal
9#11227C211yesmaximal, characteristic
10#11207C212yesmaximal
11#10907C212yesmaximal
12C22×#107C2212yes—
13C22×#107C2211yescharacteristic
14C22×C4⋊C8C2212yes—
15C22×C4⋊C8C2211yescharacteristic
16C2×#398—21no—
17C2×#398—21no—
18C2×#389C2211yescharacteristic
19C2×#389C2212yes—
20C2×#384C2211yescharacteristic
21C2×#384C2212yes—
22C2×C4×C4⋊C4—21no—
23C2×C4×C4⋊C4C2212yes—
24C2×C4×C4⋊C4C2211yescharacteristic
25#1947—28no—
26#1947—24no—
27#1918—24no—
28C2×#340C2211yescharacteristic
29C2×#340C2211yescharacteristic
30C2×#340C2211yescharacteristic
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#336C2211yescharacteristic
37C2×#336C2212yes—
38#1444—22no—
39#1436—22no—
40C4⋊#95C2212yes—
41C4⋊#95C2211yescharacteristic
42#1434—21no—
43C4×#95C2211yescharacteristic
44C23×C8C2311yescharacteristic
45C23×C8C2311yescharacteristic
46C23×C8C2312yes—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2312yes—
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C42—21no—
60C22×C42—22no—
61C22×C42C2311yescharacteristic
62C22×C42C2312yes—
63C2×#107—22no—
64C2×#107—22no—
65C2×#107—24no—
66C2×#107—24no—
67C2×#107—24no—
68C2×#107D414yes—
69C2×C4⋊C8—24no—
70C2×C4⋊C8—24no—
71C2×C4⋊C8—24no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—24no—
74#398—44no—
75#398—44no—
76#389—24no—
77#389—22no—
78#389—22no—
79#389Q818yes—
80#384—24no—
81#384—22no—
82#384—22no—
83#384—42no—
84C4×C4⋊C4—22no—
85C4×C4⋊C4—24no—
86C4×C4⋊C4—42no—
87C4×C4⋊C4—44no—
88C4×C4⋊C4D414yes—
89C2×#95—22no—
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95D411yescharacteristic
98C2×#95D412yes—
99C2×#95D411yescharacteristic
100#340—24no—
101#340—24no—
102#340—22no—
103#340—22no—
104#340—22no—
105#340—24no—
106#340—24no—
107#340—42no—
108#336—22no—
109#336—24no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—21no—
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D412yes—
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D412yes—
120C23×C4C2411yescharacteristic
121C22×C8—21no—
122C22×C8—22no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—21no—
130C22×C8—22no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—21no—
134C22×C8—22no—
135C22×C8—21no—
136C22×C8C2×D412yes—
137C22×C8#4114yes—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—28no—
152C2×C4⋊C4—22no—
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—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4—81no—
179C2×C4⋊C4—81no—
180C2×C4⋊C4—82no—
181C2×C4⋊C4C2×D412yes—
182C2×C4⋊C4C2×D412yes—
183C2×C4⋊C4C2×D412yes—
184C2×C4⋊C4C2×D412yes—
185C2×C4⋊C4C2×Q814yes—
186C2×C4⋊C4C2×Q814yes—
187C2×C4⋊C4#4112yes—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—24no—
195C2×C42—42no—
196C2×C42—42no—
197C2×C42—44no—
198C2×C42—44no—
199C2×C42—82no—
200C2×C42C2×D412yes—
201C2×C42C2×Q814yes—
202C2×C42#4112yes—
203C2×C42#4114yes—
204#107—28no—
205#107—48no—
206C4⋊C8—28no—
207C4⋊C8—216no—
208#95—24no—
209#95—28no—
210#95—22no—
211#95—24no—
212#95—44no—
213#95—44no—
214#95—42no—
215#95—42no—
216#95—44no—
217#95—81no—
218#95D814yes—
219C24C22×D411yescharacteristic
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—41no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4#12112yes—
275C22×C4#12112yes—
276C22×C4C22⋊Q814yes—
277C22×C4C22⋊Q814yes—
278C22×C4C2×D812yes—
279C22×C4C2×D814yes—
280C22×C4AGL(1,ℤ/8)12yes—
281C22×C4#13714yes—
282C22×C4C22×D411yescharacteristic
283C22×C4C22×D411yescharacteristic
284C22×C4C22×Q812yes—
285C22×C4C2×#4111yescharacteristic
286C22×C4C2×#4112yes—
287C22×C4C2×#4112yes—
288C22×C4C2×#4111yescharacteristic
289C22×C4H(5,𝔽2)11yescharacteristic
290C22×C42−1+412yes—
291C22×C42−1+411yescharacteristic
292C2×C8—22no—
293C2×C8—24no—
294C2×C8—24no—
295C2×C8—24no—
296C2×C8—24no—
297C2×C8—42no—
298C2×C8—41no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—41no—
303C2×C8—42no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—42no—
308C2×C8—42no—
309C4⋊C4—22no—
310C4⋊C4—24no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—416no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—88no—
331C4⋊C4—84no—
332C4⋊C4—88no—
333C4⋊C4—84no—
334C4⋊C4—84no—
335C4⋊C4#12114yes—
336C4⋊C4C4⋊Q814yes—
337C42—22no—
338C42—24no—
339C42—22no—
340C42—24no—
341C42—24no—
342C42—24no—
343C42—24no—
344C42—48no—
345C42—88no—
346C23C2×#12111yescharacteristic
347C23C2×C22⋊Q812yes—
348C23D4211yescharacteristic
349C23#54712yes—
350C23#54811yescharacteristic
351C23C22×D811yescharacteristic
352C23C2×AGL(1,ℤ/8)11yescharacteristic
353C23C2×#13712yes—
354C23#57611yescharacteristic
355C23#57711yescharacteristic
356C23#57812yes—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—81no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—81no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4—82no—
417C2×C4#45914yes—
418C2×C4#47418yes—
419C2×C4C2×#12111yescharacteristic
420C2×C4#52511yescharacteristic
421C2×C4#52512yes—
422C2×C4#52912yes—
423C2×C4C2×C4⋊Q811yescharacteristic
424C2×C4#53211yescharacteristic
425C2×C4#53312yes—
426C2×C4#53611yescharacteristic
427C2×C4#53711yescharacteristic
428C2×C4#53912yes—
429C2×C4#54112yes—
430C2×C4#54711yescharacteristic
431C2×C4D4×Q812yes—
432C2×C4#55212yes—
433C2×C4#55311yescharacteristic
434C2×C4#55412yes—
435C2×C4#55712yes—
436C2×C4#55712yes—
437C8—42no—
438C8—44no—
439C8—81no—
440C22#241311yescharacteristic
441C22#241611yescharacteristic
442C22#244912yes—
443C22#245312yes—
444C22#285711yescharacteristic
445C22C2×#45911yescharacteristic
446C22#303911yescharacteristic
447C22#304411yescharacteristic
448C22#304511yescharacteristic
449C22C2×#47412yes—
450C22#307912yes—
451C22#308212yes—
452C22#308312yes—
453C22#327012yes—
454C22#327211yescharacteristic
455C22D4×D811yescharacteristic
456C22#333412yes—
457C22#334312yes—
458C22#334612yes—
459C22#335612yes—
460C22#335811yescharacteristic
461C22#336611yescharacteristic
462C22#337412yes—
463C4—24no—
464C4—28no—
465C4—42no—
466C4—44no—
467C4—44no—
468C4—44no—
469C4—82no—
470C4—84no—
471C4—161no—
472C4—162no—
473C4#239211yescharacteristic
474C4#246212yes—
475C4#254611yescharacteristic
476C4#258411yescharacteristic
477C4#258512yes—
478C4#266411yescharacteristic
479C2#1481811yescharacteristic
480C2#2457611yescharacteristic
481C2#2459611yescharacteristic
482C2#2472611yescharacteristic
483C2#2474611yescharacteristic
484C2#2633612yes—
485C2#2635512yes—
486C2#2650612yes—
487C2#2652412yes—
488C2#3319511yescharacteristic
489C2#3320611yescharacteristic
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×#19182
#151452
#138212
#113732
#113222
#112272
#112072
#109072