Finite Group Databasebeta

← #468892

Subgroups — #468892

Order 512.

968 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2647C211yesmaximal, characteristic
2C2×#2100C211yesmaximal, characteristic
3C2×#2099C211yesmaximal, characteristic
4#14277C211yesmaximal, characteristic
5#11293C212yesmaximal
6#11292C212yesmaximal
7#11208C211yesmaximal, characteristic
8#11208C211yesmaximal, characteristic
9#11208C212yesmaximal
10#11207C212yesmaximal
11#10796C211yesmaximal, characteristic
12#2647—24no—
13#2647—24no—
14C2×#400—21no—
15C2×#400—21no—
16C2×#398—21no—
17C2×#398—21no—
18C2×#389C2211yescharacteristic
19C2×#389C2211yescharacteristic
20C2×#389C2212yes—
21C2×#389C2211yescharacteristic
22C2×#389C2211yescharacteristic
23C2×#384C2211yescharacteristic
24C2×#384C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C2×#382C2211yescharacteristic
27C2×#376C2211yescharacteristic
28#2100—24no—
29#2099—24no—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40C2×#336C2212yes—
41C2×#336C2212yes—
42#1444—21no—
43#1444—21no—
44#1442—21no—
45#1442—21no—
46C4⋊#95C2212yes—
47C23×C8C2312yes—
48C23×C8C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C42C2311yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67#400—28no—
68#400—28no—
69#398—28no—
70#398—28no—
71#389—22no—
72#389—22no—
73#389—22no—
74#389—22no—
75#389—22no—
76#389—22no—
77#389—24no—
78#389—24no—
79#389D414yes—
80#389D414yes—
81#384—22no—
82#384—22no—
83#384—22no—
84#384—22no—
85#382—22no—
86#382—22no—
87#382—24no—
88#376—22no—
89#376—22no—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95D411yescharacteristic
102C2×#95D411yescharacteristic
103C2×#95D411yescharacteristic
104C2×#95D411yescharacteristic
105#340—24no—
106#340—24no—
107#340—24no—
108#340—24no—
109#340—24no—
110#340—24no—
111#340—42no—
112#340—42no—
113#336—22no—
114#336—22no—
115#336—24no—
116#336—42no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C23×C4C2×D411yescharacteristic
129C23×C4C2411yescharacteristic
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
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—82no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—82no—
186C2×C4⋊C4—82no—
187C2×C4⋊C4—82no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4—82no—
190C2×C4⋊C4C2×D412yes—
191C2×C4⋊C4C2×D412yes—
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4C2×D412yes—
194C2×C4⋊C4#4114yes—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42C2×D412yes—
207C2×C42C2×D412yes—
208C2×C42#4114yes—
209#95—24no—
210#95—24no—
211#95—24no—
212#95—24no—
213#95—24no—
214#95—24no—
215#95—24no—
216#95—24no—
217#95—22no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95—44no—
222#95—82no—
223#95—82no—
224C24C22×D411yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—24no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4#12012yes—
286C22×C4#12012yes—
287C22×C4#12412yes—
288C22×C4#12412yes—
289C22×C4C22×D411yescharacteristic
290C22×C4C22×D411yescharacteristic
291C22×C4C2×#4112yes—
292C22×C4C2×#4112yes—
293C22×C4H(5,𝔽2)11yescharacteristic
294C22×C42−1+411yescharacteristic
295C22×C42−1+411yescharacteristic
296C22×C42−1+411yescharacteristic
297C22×C42−1+412yes—
298C22×C42−1+412yes—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—42no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—84no—
334C4⋊C4—84no—
335C4⋊C4—88no—
336C4⋊C4—84no—
337C4⋊C4—84no—
338C4⋊C4—84no—
339C4⋊C4—84no—
340C4⋊C4—84no—
341C4⋊C4—84no—
342C42—24no—
343C42—24no—
344C42—24no—
345C42—24no—
346C42—41no—
347C42—41no—
348C42—41no—
349C42—41no—
350C23C2×#12011yescharacteristic
351C23#52511yescharacteristic
352C23C2×#12411yescharacteristic
353C23#53611yescharacteristic
354C23#53611yescharacteristic
355C23#53611yescharacteristic
356C23#53711yescharacteristic
357C23#57612yes—
358C23#57712yes—
359C23#57712yes—
360C23#57812yes—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4#53611yescharacteristic
426C2×C4#53611yescharacteristic
427C2×C4#53711yescharacteristic
428C2×C4#53711yescharacteristic
429C2×C4#54112yes—
430C2×C4#54112yes—
431C2×C4#54112yes—
432C2×C4#54112yes—
433C2×C4#54712yes—
434C2×C4#54712yes—
435C2×C4#54812yes—
436C2×C4#54812yes—
437C2×C4#55212yes—
438C2×C4#55312yes—
439C2×C4#56312yes—
440C2×C4#56412yes—
441C8—82no—
442C8—82no—
443C22#240611yescharacteristic
444C22#243611yescharacteristic
445C22#256211yescharacteristic
446C22#261611yescharacteristic
447C22#263411yescharacteristic
448C22#264211yescharacteristic
449C22#282211yescharacteristic
450C22#300811yescharacteristic
451C22#300911yescharacteristic
452C22#301011yescharacteristic
453C22#301111yescharacteristic
454C22#312412yes—
455C22#312512yes—
456C22#313612yes—
457C22#313712yes—
458C22#324112yes—
459C22#324112yes—
460C22#324212yes—
461C22#324212yes—
462C22#324312yes—
463C22#324412yes—
464C22#325712yes—
465C22#325812yes—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—81no—
471C4—82no—
472C4—82no—
473C4—81no—
474C4—82no—
475C4—82no—
476C4—84no—
477C4—162no—
478C4#271912yes—
479C4#271912yes—
480C4#272512yes—
481C4#272512yes—
482C2#1663411yescharacteristic
483C2#2407311yescharacteristic
484C2#2407411yescharacteristic
485C2#2591411yescharacteristic
486C2#2591511yescharacteristic
487C2#2913712yes—
488C2#2969811yescharacteristic
489C2#2969911yescharacteristic
490C2#3010412yes—
491C2#3023212yes—
492C2#3285412yes—
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×#26472
C2×#21002
C2×#20992
#142772
#112932
#112922
#112082
#112072
#107962