Finite Group Databasebeta

← #403187

Subgroups — #403187

Order 512.

1188 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2084C212yesmaximal
2C2×#2066C212yesmaximal
3C2×#1948C211yesmaximal, characteristic
4C2×#1927C211yesmaximal, characteristic
5#15199C211yesmaximal, characteristic
6#13821C211yesmaximal, characteristic
7#11357C211yesmaximal, characteristic
8#11322C211yesmaximal, characteristic
9#11077C211yesmaximal, characteristic
10#10932C212yesmaximal
11#10849C212yesmaximal
12C22×#106C2212yes—
13C22×#106C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×C4⋊C8C2212yes—
16C22×#103C2211yescharacteristic
17C22×#103C2212yes—
18C22×#103C2211yescharacteristic
19C2×#391C2212yes—
20C2×#391C2211yescharacteristic
21C2×#389C2212yes—
22C2×#384C2211yescharacteristic
23C2×#384C2212yes—
24C2×C4×C4⋊C4—21no—
25C2×C4×C4⋊C4C2212yes—
26C2×C4×C4⋊C4C2211yescharacteristic
27#2084—28no—
28#2066—28no—
29#1948—24no—
30#1927—24no—
31C2×#340C2212yes—
32C2×#340C2211yescharacteristic
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#336C2211yescharacteristic
37C2×#336C2212yes—
38#1444—21no—
39#1444—22no—
40#1444—21no—
41#1436—22no—
42C4⋊#95C2211yescharacteristic
43#1434—21no—
44C4×#95C2211yescharacteristic
45C23×Q8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C23×C8C2312yes—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4C2312yes—
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C42—21no—
60C22×C42—22no—
61C22×C42C2311yescharacteristic
62C22×C42C2312yes—
63C2×#106—24no—
64C2×#106—24no—
65C2×#106—24no—
66C2×#106—22no—
67C2×#106—24no—
68C2×C4⋊C8—24no—
69C2×C4⋊C8—22no—
70C2×C4⋊C8—24no—
71C2×C4⋊C8—24no—
72C2×C4⋊C8—42no—
73C2×#103—22no—
74C2×#103—22no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—22no—
79C2×#103—42no—
80C2×#103Q814yes—
81#391—24no—
82#391—22no—
83#391—22no—
84#391—24no—
85#389—24no—
86#389D418yes—
87#384—24no—
88#384—22no—
89#384—22no—
90#384—24no—
91C4×C4⋊C4—22no—
92C4×C4⋊C4—24no—
93C4×C4⋊C4—42no—
94C4×C4⋊C4—44no—
95C4×C4⋊C4D414yes—
96C2×#95—22no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—21no—
102C2×#95—22no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95D411yescharacteristic
106C2×#95D412yes—
107C2×#95D411yescharacteristic
108#340—24no—
109#340—24no—
110#340—24no—
111#340—22no—
112#340—24no—
113#336—24no—
114#336—22no—
115C22×Q8—21no—
116C22×Q8—21no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—21no—
120C22×Q8—21no—
121C22×Q8—22no—
122C22×Q8—21no—
123C22×Q8—22no—
124C22×Q8C2×Q812yes—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—22no—
131C23×C4C2×D412yes—
132C23×C4C2×D411yescharacteristic
133C23×C4C2×D412yes—
134C23×C4C2×D411yescharacteristic
135C23×C4C2411yescharacteristic
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—21no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—21no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—21no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—21no—
150C22×C8—21no—
151C22×C8C2×Q812yes—
152C22×C8#4114yes—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—28no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—82no—
181C2×C4⋊C4—82no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4—81no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—82no—
186C2×C4⋊C4—81no—
187C2×C4⋊C4C2×D414yes—
188C2×C4⋊C4C2×D412yes—
189C2×C4⋊C4C2×D412yes—
190C2×C4⋊C4C2×D414yes—
191C2×C4⋊C4C2×Q812yes—
192C2×C4⋊C4#4112yes—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—24no—
200C2×C42—42no—
201C2×C42—42no—
202C2×C42—44no—
203C2×C42—44no—
204C2×C42—82no—
205C2×C42C2×D412yes—
206C2×C42C2×D414yes—
207C2×C42#4112yes—
208C2×C42#4114yes—
209#106—48no—
210#106—44no—
211C4⋊C8—28no—
212C4⋊C8—48no—
213#103—28no—
214#103—48no—
215#103—44no—
216#95—24no—
217#95—28no—
218#95—22no—
219#95—24no—
220#95—44no—
221#95—44no—
222#95—42no—
223#95—42no—
224#95—44no—
225#95—42no—
226#95—81no—
227#95SD1614yes—
228C24C22×D411yescharacteristic
229C2×Q8—22no—
230C2×Q8—24no—
231C2×Q8—24no—
232C2×Q8—22no—
233C2×Q8—41no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—42no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—42no—
242C2×Q8—41no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4#12112yes—
300C22×C4#12114yes—
301C22×C4#12112yes—
302C22×C4#12114yes—
303C22×C4C2×SD1612yes—
304C22×C4C2×SD1614yes—
305C22×C4#13712yes—
306C22×C4#13714yes—
307C22×C4C22×D411yescharacteristic
308C22×C4C22×D412yes—
309C22×C4C22×Q811yescharacteristic
310C22×C4C2×#4111yescharacteristic
311C22×C4C2×#4112yes—
312C22×C4C2×#4112yes—
313C22×C4C2×#4111yescharacteristic
314C22×C4H(5,𝔽2)11yescharacteristic
315C22×C42−1+412yes—
316C22×C42−1+411yescharacteristic
317C2×C8—22no—
318C2×C8—24no—
319C2×C8—24no—
320C2×C8—24no—
321C2×C8—24no—
322C2×C8—42no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—42no—
333C2×C8—42no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—416no—
344C4⋊C4—42no—
345C4⋊C4—41no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—84no—
352C4⋊C4—88no—
353C4⋊C4—88no—
354C4⋊C4—84no—
355C4⋊C4C22⋊Q814yes—
356C4⋊C4#12714yes—
357C42—22no—
358C42—24no—
359C42—22no—
360C42—24no—
361C42—24no—
362C42—24no—
363C42—24no—
364C42—48no—
365C42—88no—
366C23C2×#12111yescharacteristic
367C23C2×#12112yes—
368C23#54611yescharacteristic
369C23#54712yes—
370C23D4×Q811yescharacteristic
371C23C22×SD1611yescharacteristic
372C23C2×#13711yescharacteristic
373C23C2×#13712yes—
374C23#57611yescharacteristic
375C23#57711yescharacteristic
376C23#57712yes—
377Q8—42no—
378Q8—42no—
379Q8—44no—
380Q8—81no—
381Q8—82no—
382Q8—81no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—81no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—81no—
440C2×C4—82no—
441C2×C4#46114yes—
442C2×C4#46118yes—
443C2×C4C2×C22⋊Q811yescharacteristic
444C2×C4#52511yescharacteristic
445C2×C4#52912yes—
446C2×C4C2×#12711yescharacteristic
447C2×C4#53211yescharacteristic
448C2×C4#53212yes—
449C2×C4#53312yes—
450C2×C4#53611yescharacteristic
451C2×C4#53711yescharacteristic
452C2×C4#53912yes—
453C2×C4#54112yes—
454C2×C4#54612yes—
455C2×C4#54712yes—
456C2×C4#54812yes—
457C2×C4D4×Q812yes—
458C2×C4#55211yescharacteristic
459C2×C4#55212yes—
460C2×C4#55411yescharacteristic
461C8—44no—
462C8—42no—
463C8—81no—
464C22#241311yescharacteristic
465C22#241711yescharacteristic
466C22#242512yes—
467C22#242912yes—
468C22#285611yescharacteristic
469C22C2×#46111yescharacteristic
470C22C2×#46112yes—
471C22#303911yescharacteristic
472C22#303912yes—
473C22#304311yescharacteristic
474C22#304312yes—
475C22#304511yescharacteristic
476C22#304512yes—
477C22#329511yescharacteristic
478C22#331612yes—
479C22#333111yescharacteristic
480C22#333512yes—
481C22#334412yes—
482C22#334612yes—
483C22#335612yes—
484C22Q8×SD1611yescharacteristic
485C22#338511yescharacteristic
486C22#338712yes—
487C4—24no—
488C4—28no—
489C4—42no—
490C4—44no—
491C4—44no—
492C4—44no—
493C4—82no—
494C4—84no—
495C4—162no—
496C4—161no—
497C4#239611yescharacteristic
498C4#251912yes—
499C4#254011yescharacteristic
500C4#254211yescharacteristic
501C4#255612yes—
502C4#266411yescharacteristic
503C2#1487011yescharacteristic
504C2#2458011yescharacteristic
505C2#2459611yescharacteristic
506C2#2481511yescharacteristic
507C2#2483111yescharacteristic
508C2#2520212yes—
509C2#2521912yes—
510C2#2545312yes—
511C2#2546712yes—
512C2#3316211yescharacteristic
513C2#3316711yescharacteristic
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×#20842
C2×#20662
C2×#19482
C2×#19272
#151992
#138212
#113572
#113222
#110772
#109322
#108492