Finite Group Databasebeta

← #401152

Subgroups — #401152

Order 512.

1202 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1981C211yesmaximal, characteristic
2C2×#1928C212yesmaximal
3C2×#1918C211yesmaximal, characteristic
4#15188C211yesmaximal, characteristic
5#13821C211yesmaximal, characteristic
6#11255C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11067C212yesmaximal
9#11067C212yesmaximal
10#11010C211yesmaximal, characteristic
11#10932C212yesmaximal
12C22×C4⋊Q8C2211yescharacteristic
13C22×#107C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2212yes—
16C22×#103C2212yes—
17C22×#103C2212yes—
18C22×#103C2212yes—
19C2×#391C2212yes—
20C2×#391C2212yes—
21C2×#389C2211yescharacteristic
22C2×#389C2212yes—
23C2×C4×C4⋊C4—21no—
24C2×C4×C4⋊C4C2212yes—
25C2×C4×C4⋊C4C2211yescharacteristic
26#1981—24no—
27#1928—28no—
28#1918—24no—
29C2×#340C2211yescharacteristic
30C2×#340C2211yescharacteristic
31C2×#340C2211yescharacteristic
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2211yescharacteristic
35C2×#336C2212yes—
36C2×#336C2212yes—
37#1442—22no—
38#1441—21no—
39#1441—21no—
40#1436—22no—
41C4⋊#95C2211yescharacteristic
42#1434—21no—
43C4×#95C2211yescharacteristic
44C23×Q8C2312yes—
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C2×C4⋊Q8—24no—
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—22no—
51C2×C4⋊Q8—42no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C42—21no—
62C22×C42—22no—
63C22×C42C2312yes—
64C22×C42C2311yescharacteristic
65C2×#107—22no—
66C2×#107—22no—
67C2×#107D414yes—
68C2×C4⋊C8—22no—
69C2×C4⋊C8—42no—
70C2×#103—24no—
71C2×#103—24no—
72C2×#103—24no—
73C2×#103—24no—
74C2×#103—24no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—24no—
79C2×#103—24no—
80C2×#103—42no—
81C2×#103—42no—
82#391—24no—
83#391—24no—
84#391—42no—
85#391—42no—
86#389—24no—
87#389—24no—
88#389—22no—
89#389—22no—
90C4×C4⋊C4—22no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4—44no—
93C4×C4⋊C4—42no—
94C4×C4⋊C4D414yes—
95C2×#95—22no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95D411yescharacteristic
106C2×#95D412yes—
107C2×#95D411yescharacteristic
108#340—22no—
109#340—22no—
110#340—22no—
111#340—24no—
112#340—42no—
113#336—24no—
114#336—22no—
115#336—42no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8#4114yes—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—22no—
133C23×C4—21no—
134C23×C4—22no—
135C23×C4—21no—
136C23×C4C2×D412yes—
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D412yes—
139C23×C4C2×D411yescharacteristic
140C23×C4C2411yescharacteristic
141C22×C8—21no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—21no—
145C22×C8—21no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—21no—
156C22×C8—21no—
157C22×C8C2×D412yes—
158C4⋊Q8—28no—
159C4⋊Q8—48no—
160C4⋊Q8—44no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—28no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4C2×D412yes—
191C2×C4⋊C4C2×D412yes—
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4C2×D412yes—
194C2×C4⋊C4#4114yes—
195C2×C4⋊C4#4112yes—
196C2×C4⋊C4#4114yes—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—24no—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42—44no—
209C2×C42—44no—
210C2×C42—82no—
211C2×C42C2×D412yes—
212C2×C42#4112yes—
213#107—28no—
214C4⋊C8—44no—
215#103—216no—
216#103—48no—
217#103—48no—
218#103—48no—
219#95—28no—
220#95—24no—
221#95—22no—
222#95—22no—
223#95—24no—
224#95—44no—
225#95—44no—
226#95—44no—
227#95—44no—
228#95—44no—
229#95—42no—
230#95—42no—
231#95—81no—
232C24C22×D411yescharacteristic
233C2×Q8—24no—
234C2×Q8—24no—
235C2×Q8—24no—
236C2×Q8—24no—
237C2×Q8—24no—
238C2×Q8—24no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8—42no—
260C2×Q8—42no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—42no—
318C22×C4#12112yes—
319C22×C4#12112yes—
320C22×C4#13512yes—
321C22×C4AGL(1,ℤ/8)12yes—
322C22×C4#13714yes—
323C22×C4C22×D411yescharacteristic
324C22×C4C22×D411yescharacteristic
325C22×C4C2×#4111yescharacteristic
326C22×C4C2×#4112yes—
327C22×C4C2×#4112yes—
328C22×C4C2×#4112yes—
329C22×C4C2×#4111yescharacteristic
330C22×C4H(5,𝔽2)12yes—
331C22×C4H(5,𝔽2)11yescharacteristic
332C22×C42−1+411yescharacteristic
333C2×C8—22no—
334C2×C8—24no—
335C2×C8—41no—
336C2×C8—42no—
337C2×C8—41no—
338C2×C8—42no—
339C2×C8—42no—
340C2×C8—41no—
341C2×C8—42no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—42no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—416no—
360C4⋊C4—48no—
361C4⋊C4—48no—
362C4⋊C4—41no—
363C4⋊C4—42no—
364C4⋊C4—41no—
365C4⋊C4—42no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—42no—
369C4⋊C4—84no—
370C4⋊C4#12114yes—
371C4⋊C4#12414yes—
372C42—22no—
373C42—22no—
374C42—24no—
375C42—42no—
376C42—42no—
377C42—42no—
378C42—42no—
379C42—48no—
380C42—88no—
381C23C2×#12111yescharacteristic
382C23#52512yes—
383C23D4211yescharacteristic
384C23#54612yes—
385C23#54811yescharacteristic
386C23C2×#13511yescharacteristic
387C23C2×AGL(1,ℤ/8)11yescharacteristic
388C23C2×#13712yes—
389C23#57711yescharacteristic
390C23#57811yescharacteristic
391C23#57812yes—
392Q8—44no—
393Q8—44no—
394Q8—44no—
395Q8—44no—
396Q8—82no—
397Q8—82no—
398Q8—82no—
399Q8—82no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—81no—
445C2×C4—82no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4#46314yes—
462C2×C4C2×#12111yescharacteristic
463C2×C4#52511yescharacteristic
464C2×C4#52512yes—
465C2×C4C2×#12411yescharacteristic
466C2×C4#52912yes—
467C2×C4#52912yes—
468C2×C4#53211yescharacteristic
469C2×C4#53511yescharacteristic
470C2×C4#53711yescharacteristic
471C2×C4#53812yes—
472C2×C4#54212yes—
473C2×C4#54711yescharacteristic
474C2×C4#55012yes—
475C2×C4#55112yes—
476C2×C4#55212yes—
477C2×C4#55312yes—
478C2×C4#55311yescharacteristic
479C2×C4#55912yes—
480C8—42no—
481C8—81no—
482C8—82no—
483C22#241111yescharacteristic
484C22#241611yescharacteristic
485C22#245612yes—
486C22#245812yes—
487C22#285011yescharacteristic
488C22C2×#46311yescharacteristic
489C22#303911yescharacteristic
490C22#304411yescharacteristic
491C22#304611yescharacteristic
492C22#310712yes—
493C22#311012yes—
494C22#312012yes—
495C22#312712yes—
496C22#327012yes—
497C22#327211yescharacteristic
498C22#328311yescharacteristic
499C22#330012yes—
500C22#330812yes—
501C22#332012yes—
502C22#332812yes—
503C22#336011yescharacteristic
504C22#336711yescharacteristic
505C22#337412yes—
506C4—24no—
507C4—44no—
508C4—44no—
509C4—44no—
510C4—42no—
511C4—84no—
512C4—82no—
513C4—84no—
514C4—82no—
515C4—161no—
516C4#239211yescharacteristic
517C4#247912yes—
518C4#254811yescharacteristic
519C4#256211yescharacteristic
520C4#259712yes—
521C4#266211yescharacteristic
522C2#1481311yescharacteristic
523C2#2448111yescharacteristic
524C2#2449611yescharacteristic
525C2#2472711yescharacteristic
526C2#2474611yescharacteristic
527C2#2662212yes—
528C2#2664112yes—
529C2#2670312yes—
530C2#2670712yes—
531C2#3303211yescharacteristic
532C2#3304111yescharacteristic
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×#19812
C2×#19282
C2×#19182
#151882
#138212
#112552
#112272
#110672
#110102
#109322