Finite Group Databasebeta

← #470381

Subgroups — #470381

Order 512.

1188 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2552C211yesmaximal, characteristic
2C2×#2072C211yesmaximal, characteristic
3C2×#1928C211yesmaximal, characteristic
4#15193C211yesmaximal, characteristic
5#11371C211yesmaximal, characteristic
6#11346C211yesmaximal, characteristic
7#11328C212yesmaximal
8#11207C212yesmaximal
9#11067C212yesmaximal
10#11050C212yesmaximal
11#10807C211yesmaximal, characteristic
12C22×#125—21no—
13C22×#107C2211yescharacteristic
14C22×#103C2211yescharacteristic
15C22×#103C2212yes—
16C22×#103C2211yescharacteristic
17#2552—24no—
18#2552—24no—
19C2×#398—22no—
20C2×#391C2211yescharacteristic
21C2×#391C2212yes—
22C2×#389—21no—
23C2×#389C2212yes—
24C2×#389C2212yes—
25C2×#384C2212yes—
26C2×#384C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29#2072—24no—
30#1928—24no—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2211yescharacteristic
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39C2×#336C2212yes—
40C2×#336C2212yes—
41#1445—22no—
42#1445—21no—
43#1444—21no—
44C4⋊#95C2211yescharacteristic
45C23×Q8C2311yescharacteristic
46C23×C8C2312yes—
47C23×C8C2311yescharacteristic
48C23×C8C2311yescharacteristic
49C2×#125—28no—
50C2×#125—48no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4D411yescharacteristic
58C22×C4⋊C4D411yescharacteristic
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2312yes—
63C22×C4⋊C4C2312yes—
64C22×C42—21no—
65C22×C42C2312yes—
66C22×C42C2311yescharacteristic
67C2×#107—22no—
68C2×#107—42no—
69C2×#103—22no—
70C2×#103—22no—
71C2×#103—22no—
72C2×#103—24no—
73C2×#103—24no—
74C2×#103—22no—
75C2×#103—42no—
76C2×#103—42no—
77#398—216no—
78#391—24no—
79#391—22no—
80#391—22no—
81#391—42no—
82#389—28no—
83#389—24no—
84#389—24no—
85#389—24no—
86#389—42no—
87#384—24no—
88#384—24no—
89#384—22no—
90#384D414yes—
91C4×C4⋊C4—22no—
92C4×C4⋊C4—22no—
93C4×C4⋊C4—22no—
94C4×C4⋊C4D414yes—
95C2×#95—21no—
96C2×#95—22no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95—21no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95D412yes—
105#340—24no—
106#340—24no—
107#340—22no—
108#340—24no—
109#340—42no—
110#340—42no—
111#336—22no—
112#336—22no—
113#336—42no—
114#336—42no—
115C22×Q8—21no—
116C22×Q8—21no—
117C22×Q8—21no—
118C22×Q8—22no—
119C22×Q8—21no—
120C22×Q8—22no—
121C22×Q8—21no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8#4112yes—
125C23×C4—22no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4C2×D411yescharacteristic
132C23×C4C2×D412yes—
133C23×C4C2×D412yes—
134C23×C4C2×D411yescharacteristic
135C23×C4C2411yescharacteristic
136C22×C8—21no—
137C22×C8—21no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—21no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—21no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—21no—
152C22×C8#4112yes—
153#125—432no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—28no—
173C2×C4⋊C4—28no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—28no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4—44no—
192C2×C4⋊C4—82no—
193C2×C4⋊C4—82no—
194C2×C4⋊C4—82no—
195C2×C4⋊C4—82no—
196C2×C4⋊C4Q1614yes—
197C2×C4⋊C4C2×D412yes—
198C2×C4⋊C4C2×D414yes—
199C2×C4⋊C4C2×D412yes—
200C2×C4⋊C4#4114yes—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—24no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—44no—
211C2×C42C2×D412yes—
212C2×C42C2×D412yes—
213#107—44no—
214#103—28no—
215#103—48no—
216#103—44no—
217#95—28no—
218#95—24no—
219#95—24no—
220#95—44no—
221#95—44no—
222#95—44no—
223#95—42no—
224#95—42no—
225#95—42no—
226#95—81no—
227C24C22×D411yescharacteristic
228C2×Q8—22no—
229C2×Q8—24no—
230C2×Q8—22no—
231C2×Q8—24no—
232C2×Q8—41no—
233C2×Q8—42no—
234C2×Q8—41no—
235C2×Q8—42no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C22×C4—22no—
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—22no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4#12012yes—
299C22×C4#12012yes—
300C22×C4C2×Q1614yes—
301C22×C4C2×Q1612yes—
302C22×C4AGL(1,ℤ/8)14yes—
303C22×C4#13712yes—
304C22×C4C22×D411yescharacteristic
305C22×C4C22×D411yescharacteristic
306C22×C4C2×#4111yescharacteristic
307C22×C4C2×#4111yescharacteristic
308C22×C4C2×#4112yes—
309C22×C4H(5,𝔽2)12yes—
310C22×C4H(5,𝔽2)11yescharacteristic
311C22×C42−1+412yes—
312C22×C42−1+412yes—
313C22×C42−1+411yescharacteristic
314C2×C8—22no—
315C2×C8—24no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—42no—
322C2×C8—41no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C4⋊C4—28no—
332C4⋊C4—28no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—48no—
342C4⋊C4—416no—
343C4⋊C4—416no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—42no—
354C4⋊C4—84no—
355C4⋊C4—88no—
356C4⋊C4—88no—
357C42—22no—
358C42—22no—
359C42—24no—
360C42—48no—
361C42—42no—
362C42—42no—
363C42—42no—
364C42—42no—
365C23C2×#12011yescharacteristic
366C23#53612yes—
367C23#54612yes—
368C23#54811yescharacteristic
369C23#55011yescharacteristic
370C23C22×Q1611yescharacteristic
371C23C2×AGL(1,ℤ/8)12yes—
372C23C2×#13711yescharacteristic
373C23#57712yes—
374C23#57711yescharacteristic
375C23#57811yescharacteristic
376Q8—42no—
377Q8—42no—
378Q8—44no—
379Q8—81no—
380Q8—81no—
381Q8—82no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—81no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4#45114yes—
440C2×C4#52511yescharacteristic
441C2×C4#53211yescharacteristic
442C2×C4#53511yescharacteristic
443C2×C4#53611yescharacteristic
444C2×C4#53611yescharacteristic
445C2×C4#53612yes—
446C2×C4#53711yescharacteristic
447C2×C4#53912yes—
448C2×C4#53912yes—
449C2×C4#53912yes—
450C2×C4#54112yes—
451C2×C4#54611yescharacteristic
452C2×C4#54711yescharacteristic
453C2×C4#55012yes—
454C2×C4#55212yes—
455C2×C4#55212yes—
456C2×C4#56212yes—
457C2×C4#56312yes—
458C8—42no—
459C8—81no—
460C8—82no—
461C22#240711yescharacteristic
462C22#243111yescharacteristic
463C22#261411yescharacteristic
464C22#269012yes—
465C22#269412yes—
466C22C2×#45111yescharacteristic
467C22#300311yescharacteristic
468C22#300911yescharacteristic
469C22#301311yescharacteristic
470C22#323012yes—
471C22#323912yes—
472C22#324212yes—
473C22#324412yes—
474C22#329912yes—
475C22#330612yes—
476C22#330812yes—
477C22#333112yes—
478C22#336311yescharacteristic
479C22#336812yes—
480C22#337411yescharacteristic
481C22#339511yescharacteristic
482C22#339712yes—
483C22#340011yescharacteristic
484C4—24no—
485C4—42no—
486C4—44no—
487C4—44no—
488C4—82no—
489C4—84no—
490C4—82no—
491C4—84no—
492C4—82no—
493C4—161no—
494C4#261111yescharacteristic
495C4#263311yescharacteristic
496C4#266411yescharacteristic
497C4#269412yes—
498C4#272112yes—
499C4#282011yescharacteristic
500C2#1668211yescharacteristic
501C2#2419111yescharacteristic
502C2#2420011yescharacteristic
503C2#2557311yescharacteristic
504C2#2557711yescharacteristic
505C2#2964211yescharacteristic
506C2#2964811yescharacteristic
507C2#3146012yes—
508C2#3147612yes—
509C2#3157612yes—
510C2#3159012yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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×#25522
C2×#20722
C2×#19282
#151932
#113712
#113462
#113282
#112072
#110672
#110502
#108072