Finite Group Databasebeta

← #472053

Subgroups — #472053

Order 512.

1204 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2095C212yesmaximal
2C2×#2083C211yesmaximal, characteristic
3C2×#2043C211yesmaximal, characteristic
4C2×#1956C211yesmaximal, characteristic
5C2×#1942C211yesmaximal, characteristic
6#15188C211yesmaximal, characteristic
7#15145C211yesmaximal, characteristic
8#11124C212yesmaximal
9#11124C212yesmaximal
10#11050C212yesmaximal
11#10797C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×#107C2212yes—
14C22×#107C2211yescharacteristic
15C22×#107C2211yescharacteristic
16C22×#103C2212yes—
17C22×#103C2212yes—
18C22×#103C2212yes—
19C22×#103C2212yes—
20C22×C4×C8C2211yescharacteristic
21C2×#398—22no—
22C2×#391C2212yes—
23C2×#391C2212yes—
24C2×#389C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#384C2211yescharacteristic
27C2×#384C2212yes—
28#2095—28no—
29#2083—24no—
30#2043—24no—
31#1956—24no—
32#1942—24no—
33C2×#340C2211yescharacteristic
34C2×#340C2212yes—
35C2×#340C2211yescharacteristic
36C2×#336C2212yes—
37C2×#336C2212yes—
38C2×#336C2211yescharacteristic
39#1444—22no—
40#1442—22no—
41#1441—22no—
42C4⋊#95C2212yes—
43C4×#95C2211yescharacteristic
44C23×Q8C2312yes—
45C23×C8C2311yescharacteristic
46C23×C8C2312yes—
47C23×C8C2311yescharacteristic
48C2×C4⋊Q8—24no—
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—22no—
51C2×C4⋊Q8—42no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2312yes—
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2311yescharacteristic
64C22×C42C2312yes—
65C22×C42C2311yescharacteristic
66C2×#107—22no—
67C2×#107—22no—
68C2×#107—24no—
69C2×#107—22no—
70C2×#107—24no—
71C2×#107—42no—
72C2×#107—42no—
73C2×#107D414yes—
74C2×#103—24no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—24no—
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—24no—
82C2×#103—42no—
83C2×#103—42no—
84C2×#103—42no—
85C2×#103—42no—
86C2×C4×C8—42no—
87C2×C4×C8D414yes—
88#398—48no—
89#391—24no—
90#391—24no—
91#391—42no—
92#391—42no—
93#389—22no—
94#389—22no—
95#389—22no—
96#389—22no—
97#384—24no—
98#384—22no—
99#384—22no—
100#384—42no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95D412yes—
107C2×#95D412yes—
108#340—24no—
109#340—22no—
110#340—22no—
111#336—24no—
112#336—42no—
113#336D414yes—
114C22×Q8—22no—
115C22×Q8—22no—
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#4114yes—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4—21no—
131C23×C4—22no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4C2×D414yes—
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2411yescharacteristic
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
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×C8C2×D414yes—
151C22×C8C2×D412yes—
152C22×C8C2×D412yes—
153C22×C8C2×D412yes—
154C22×C8#4112yes—
155C4⋊Q8—28no—
156C4⋊Q8—48no—
157C4⋊Q8—44no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—48no—
187C2×C4⋊C4—48no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—44no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—82no—
196C2×C4⋊C4—84no—
197C2×C4⋊C4C2×D412yes—
198C2×C4⋊C4C2×D412yes—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42C2×D412yes—
208C2×C42C2×D412yes—
209#107—28no—
210#107—48no—
211#107—44no—
212#103—48no—
213#103—48no—
214#103—48no—
215#103—48no—
216C4×C8—44no—
217#95—24no—
218#95—48no—
219#95—48no—
220#95—48no—
221#95—42no—
222#95—42no—
223#95Q1618yes—
224C24C22×D411yescharacteristic
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—24no—
229C2×Q8—24no—
230C2×Q8—24no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
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—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—44no—
289C22×C4—42no—
290C22×C4—44no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4#12712yes—
294C22×C4#12712yes—
295C22×C4C2×Q1618yes—
296C22×C4C2×Q1614yes—
297C22×C4AGL(1,ℤ/8)14yes—
298C22×C4C22×D411yescharacteristic
299C22×C4C22×D411yescharacteristic
300C22×C4C22×D411yescharacteristic
301C22×C4C2×#4111yescharacteristic
302C22×C4C2×#4112yes—
303C22×C4H(5,𝔽2)12yes—
304C22×C4H(5,𝔽2)11yescharacteristic
305C22×C4H(5,𝔽2)11yescharacteristic
306C22×C42−1+412yes—
307C22×C42−1+412yes—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—24no—
311C2×C8—24no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—24no—
316C2×C8—24no—
317C2×C8—24no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8#12114yes—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—48no—
330C4⋊C4—48no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—42no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—84no—
346C4⋊C4—816no—
347C4⋊C4—84no—
348C4⋊C4—84no—
349C4⋊C4—84no—
350C42—22no—
351C42—22no—
352C42—24no—
353C42—42no—
354C42—42no—
355C42—42no—
356C42—42no—
357C23C2×#12711yescharacteristic
358C23#53612yes—
359C23D4211yescharacteristic
360C23#54612yes—
361C23#55011yescharacteristic
362C23C22×Q1612yes—
363C23C2×AGL(1,ℤ/8)12yes—
364C23#57712yes—
365C23#57812yes—
366Q8—44no—
367Q8—44no—
368Q8—44no—
369Q8—44no—
370Q8—82no—
371Q8—82no—
372Q8—82no—
373Q8—82no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—28no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—28no—
380C2×C4—28no—
381C2×C4—28no—
382C2×C4—28no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—84no—
405C2×C4—82no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—82no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—84no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—84no—
415C2×C4—84no—
416C2×C4—82no—
417C2×C4#49414yes—
418C2×C4#49614yes—
419C2×C4C2×#12111yescharacteristic
420C2×C4#52511yescharacteristic
421C2×C4#53411yescharacteristic
422C2×C4#53511yescharacteristic
423C2×C4#53611yescharacteristic
424C2×C4#53611yescharacteristic
425C2×C4#53612yes—
426C2×C4#53712yes—
427C2×C4#53912yes—
428C2×C4#53912yes—
429C2×C4#53912yes—
430C2×C4D4211yescharacteristic
431C2×C4#54612yes—
432C2×C4#54812yes—
433C2×C4#55011yescharacteristic
434C2×C4#55212yes—
435C2×C4#56212yes—
436C2×C4#56212yes—
437C8—24no—
438C8—42no—
439C8—44no—
440C22#253911yescharacteristic
441C22#254111yescharacteristic
442C22#265811yescharacteristic
443C22#268112yes—
444C22#269412yes—
445C22C2×#49411yescharacteristic
446C22C2×#49611yescharacteristic
447C22#315411yescharacteristic
448C22#315611yescharacteristic
449C22#323014yes—
450C22#324214yes—
451C22#327212yes—
452C22D4×Q1612yes—
453C22#329914yes—
454C22#330814yes—
455C22#339512yes—
456C22#339712yes—
457C4—24no—
458C4—24no—
459C4—48no—
460C4—82no—
461C4—82no—
462C4—84no—
463C4—162no—
464C4—161no—
465C4—161no—
466C4#253611yescharacteristic
467C4#261811yescharacteristic
468C4#263311yescharacteristic
469C4#268112yes—
470C4#269412yes—
471C4#281611yescharacteristic
472C2#1681111yescharacteristic
473C2#2833311yescharacteristic
474C2#2834611yescharacteristic
475C2#2846211yescharacteristic
476C2#2847211yescharacteristic
477C2#3027911yescharacteristic
478C2#3028811yescharacteristic
479C2#3112214yes—
480C2#3157614yes—
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×#20952
C2×#20832
C2×#20432
C2×#19562
C2×#19422
#151882
#151452
#111242
#110502
#107972