Finite Group Databasebeta

← #469438

Subgroups — #469438

Order 512.

1084 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2645C211yesmaximal, characteristic
2C2×#2057C211yesmaximal, characteristic
3C2×#2024C211yesmaximal, characteristic
4#14282C211yesmaximal, characteristic
5#11292C212yesmaximal
6#11219C212yesmaximal
7#11208C211yesmaximal, characteristic
8#11190C212yesmaximal
9#11124C212yesmaximal
10#11052C211yesmaximal, characteristic
11#10796C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×#107C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16#2645—24no—
17#2645—24no—
18C2×#401—21no—
19C2×#400—21no—
20C2×#400—21no—
21C2×#400—21no—
22C2×#391C2211yescharacteristic
23C2×#391C2211yescharacteristic
24C2×#391C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#382C2211yescharacteristic
29C2×#376C2211yescharacteristic
30#2057—24no—
31#2024—24no—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39C2×#336C2212yes—
40C2×#336C2212yes—
41#1446—21no—
42#1446—21no—
43#1445—21no—
44#1445—21no—
45C4⋊#95C2212yes—
46C4⋊#95C2212yes—
47C23×Q8—21no—
48C23×Q8C2311yescharacteristic
49C23×C8C2312yes—
50C23×C8C2312yes—
51C2×C4⋊Q8—24no—
52C2×C4⋊Q8—22no—
53C2×C4⋊Q8—22no—
54C2×C4⋊Q8—42no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C42C2311yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67C2×#107—24no—
68C2×#107—24no—
69C2×#107—42no—
70C2×#103—24no—
71C2×#103—24no—
72C2×#103—24no—
73C2×#103—42no—
74C2×#103—42no—
75C2×#103—42no—
76#401—28no—
77#400—28no—
78#400—28no—
79#400—28no—
80#391—22no—
81#391—22no—
82#391—22no—
83#391—22no—
84#391—22no—
85#391D414yes—
86#389—22no—
87#389—22no—
88#389—22no—
89#389—22no—
90#389—22no—
91#389D414yes—
92#382—42no—
93#376—22no—
94#376—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95D411yescharacteristic
111C2×#95D411yescharacteristic
112C2×#95D411yescharacteristic
113C2×#95D411yescharacteristic
114#340—24no—
115#340—24no—
116#340—24no—
117#340—42no—
118#340—42no—
119#336—24no—
120#336—22no—
121#336—22no—
122#336—42no—
123C22×Q8—24no—
124C22×Q8—21no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—21no—
131C22×Q8—22no—
132C22×Q8—21no—
133C22×Q8—42no—
134C22×Q8—42no—
135C22×Q8—82no—
136C22×Q8—82no—
137C22×Q8C2×D412yes—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—22no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2411yescharacteristic
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8#4114yes—
165C4⋊Q8—48no—
166C4⋊Q8—48no—
167C2×C4⋊C4—22no—
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—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—82no—
196C2×C4⋊C4—82no—
197C2×C4⋊C4—82no—
198C2×C4⋊C4C2×D412yes—
199C2×C4⋊C4C2×D412yes—
200C2×C4⋊C4C2×D412yes—
201C2×C4⋊C4#4114yes—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—21no—
208C2×C42—22no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—21no—
212C2×C42—21no—
213C2×C42—22no—
214C2×C42C2×D412yes—
215C2×C42C2×D412yes—
216#107—48no—
217#103—48no—
218#103—48no—
219#95—24no—
220#95—24no—
221#95—24no—
222#95—24no—
223#95—24no—
224#95—24no—
225#95—24no—
226#95—24no—
227#95—24no—
228#95—22no—
229#95—22no—
230#95—22no—
231#95—22no—
232#95—42no—
233#95—42no—
234#95—82no—
235#95—82no—
236#95—82no—
237#95—82no—
238C24C22×D411yescharacteristic
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—48no—
244C2×Q8—41no—
245C2×Q8—41no—
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—84no—
257C2×Q8—84no—
258C2×Q8—88no—
259C2×Q8—88no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—42no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4#12012yes—
325C22×C4#12012yes—
326C22×C4C22×D411yescharacteristic
327C22×C4C22×D411yescharacteristic
328C22×C4C2×#4112yes—
329C22×C4C2×#4112yes—
330C22×C4H(5,𝔽2)11yescharacteristic
331C22×C4H(5,𝔽2)12yes—
332C22×C42−1+411yescharacteristic
333C22×C42−1+411yescharacteristic
334C22×C42−1+411yescharacteristic
335C22×C42−1+412yes—
336C2×C8—24no—
337C2×C8—24no—
338C2×C8—24no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—42no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—48no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—84no—
368C4⋊C4—84no—
369C4⋊C4—84no—
370C42—24no—
371C42—24no—
372C42—41no—
373C42—41no—
374C42—41no—
375C42—41no—
376C42—42no—
377C42—42no—
378C23C2×#12011yescharacteristic
379C23#52511yescharacteristic
380C23#53211yescharacteristic
381C23#53511yescharacteristic
382C23#53611yescharacteristic
383C23#53611yescharacteristic
384C23#53711yescharacteristic
385C23#57612yes—
386C23#57712yes—
387C23#57812yes—
388C23#57812yes—
389Q8—44no—
390Q8—44no—
391Q8—816no—
392Q8—82no—
393Q8—82no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
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—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4#53611yescharacteristic
461C2×C4#53611yescharacteristic
462C2×C4#53711yescharacteristic
463C2×C4#53711yescharacteristic
464C2×C4#53812yes—
465C2×C4#54112yes—
466C2×C4#54212yes—
467C2×C4#54212yes—
468C2×C4#54612yes—
469C2×C4#54612yes—
470C2×C4#54712yes—
471C2×C4#54812yes—
472C2×C4#55212yes—
473C2×C4#55612yes—
474C2×C4#56312yes—
475C2×C4#56312yes—
476C8—44no—
477C8—82no—
478C22#240411yescharacteristic
479C22#243211yescharacteristic
480C22#260411yescharacteristic
481C22#261611yescharacteristic
482C22#263711yescharacteristic
483C22#266211yescharacteristic
484C22#282111yescharacteristic
485C22#300811yescharacteristic
486C22#301011yescharacteristic
487C22#301111yescharacteristic
488C22#301111yescharacteristic
489C22#311812yes—
490C22#312712yes—
491C22#317512yes—
492C22#317812yes—
493C22#322312yes—
494C22#322412yes—
495C22#324212yes—
496C22#324212yes—
497C22#324312yes—
498C22#324312yes—
499C22#325812yes—
500C22#326212yes—
501C4—42no—
502C4—42no—
503C4—81no—
504C4—82no—
505C4—81no—
506C4—82no—
507C4—81no—
508C4—82no—
509C4—81no—
510C4—82no—
511C4—84no—
512C4—162no—
513C4#269812yes—
514C4#270212yes—
515C4#271512yes—
516C4#271612yes—
517C2#1665611yescharacteristic
518C2#2394311yescharacteristic
519C2#2394511yescharacteristic
520C2#2568111yescharacteristic
521C2#2568611yescharacteristic
522C2#2952612yes—
523C2#2969611yescharacteristic
524C2#2969911yescharacteristic
525C2#3015912yes—
526C2#3035012yes—
527C2#3284612yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#26452
C2×#20572
C2×#20242
#142822
#112922
#112192
#112082
#111902
#111242
#110522
#107962