Finite Group Databasebeta

← #475958

Subgroups — #475958

Order 512.

884 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2100C211yesmaximal, characteristic
2C2×#2099C211yesmaximal, characteristic
3#14277C211yesmaximal, characteristic
4#14276C211yesmaximal, characteristic
5#11358C212yesmaximal
6#11267C212yesmaximal
7#11228C212yesmaximal
8#11227C212yesmaximal
9#11208C211yesmaximal, characteristic
10#11208C211yesmaximal, characteristic
11#10833C211yesmaximal, characteristic
12C22×C4⋊C8C2212yes—
13C2×#389C2211yescharacteristic
14C2×#389C2211yescharacteristic
15C2×#389C2212yes—
16C2×#384C2211yescharacteristic
17C2×#384C2211yescharacteristic
18C2×#382C2211yescharacteristic
19C2×#382C2211yescharacteristic
20C2×#376C2211yescharacteristic
21#2100—24no—
22#2099—24no—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#336C2212yes—
32C2×#336C2211yescharacteristic
33C2×#336C2211yescharacteristic
34#1444—22no—
35#1442—22no—
36#1441—22no—
37#1441—22no—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40C4⋊#95C2211yescharacteristic
41C23×C8C2312yes—
42C23×C8C2312yes—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2311yescharacteristic
51C22×C4⋊C4C2311yescharacteristic
52C22×C4⋊C4C2312yes—
53C22×C4⋊C4C2311yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58C2×C4⋊C8—24no—
59C2×C4⋊C8—42no—
60C2×C4⋊C8—42no—
61#389—22no—
62#389—22no—
63#389—22no—
64#389—22no—
65#389—24no—
66#389—24no—
67#384—22no—
68#384—42no—
69#384D414yes—
70#382—22no—
71#382—42no—
72#382Q814yes—
73#376—42no—
74C2×#95—22no—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—22no—
78C2×#95—21no—
79C2×#95—21no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95D412yes—
85C2×#95D412yes—
86#340—24no—
87#340—24no—
88#340—24no—
89#340—24no—
90#340—42no—
91#340—42no—
92#340—42no—
93#340—42no—
94#336—22no—
95#336—22no—
96#336—24no—
97C23×C4—22no—
98C23×C4—21no—
99C23×C4—21no—
100C23×C4—21no—
101C23×C4—21no—
102C23×C4—22no—
103C23×C4C2×D411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C23×C4C2×D412yes—
106C23×C4C2×D412yes—
107C23×C4C2411yescharacteristic
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—44no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—82no—
158C2×C4⋊C4—82no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4—82no—
161C2×C4⋊C4—82no—
162C2×C4⋊C4—82no—
163C2×C4⋊C4—82no—
164C2×C4⋊C4—82no—
165C2×C4⋊C4C2×D414yes—
166C2×C4⋊C4C2×Q812yes—
167C2×C4⋊C4C2×Q812yes—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—22no—
171C2×C42—21no—
172C2×C42—22no—
173C2×C42—21no—
174C2×C42—22no—
175C2×C42C2×D412yes—
176C2×C42C2×Q812yes—
177C2×C42#4112yes—
178C2×C42#4112yes—
179C2×C42#4114yes—
180C4⋊C8—48no—
181#95—28no—
182#95—42no—
183#95—42no—
184#95—42no—
185#95—42no—
186#95—42no—
187#95—42no—
188#95—44no—
189#95—82no—
190#95—82no—
191#95—82no—
192#95—82no—
193C24C22×D411yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4#12112yes—
249C22×C4#12112yes—
250C22×C4C22⋊Q814yes—
251C22×C4#12414yes—
252C22×C4C22×D411yescharacteristic
253C22×C4C22×Q811yescharacteristic
254C22×C4C2×#4112yes—
255C22×C4C2×#4111yescharacteristic
256C22×C4C2×#4111yescharacteristic
257C22×C4H(5,𝔽2)12yes—
258C22×C4H(5,𝔽2)11yescharacteristic
259C22×C42−1+412yes—
260C22×C42−1+411yescharacteristic
261C22×C42−1+412yes—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—84no—
297C4⋊C4—84no—
298C4⋊C4—88no—
299C4⋊C4—84no—
300C4⋊C4—84no—
301C4⋊C4—88no—
302C42—24no—
303C42—24no—
304C42—24no—
305C42—24no—
306C42—24no—
307C42—24no—
308C23C2×#12111yescharacteristic
309C23C2×C22⋊Q811yescharacteristic
310C23C2×#12411yescharacteristic
311C23#53411yescharacteristic
312C23#53611yescharacteristic
313C23#53611yescharacteristic
314C23#53711yescharacteristic
315C23#57612yes—
316C23#57712yes—
317C23#57712yes—
318C23#57812yes—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4#53712yes—
378C2×C4#53812yes—
379C2×C4#53912yes—
380C2×C4#53912yes—
381C2×C4#53912yes—
382C2×C4#54412yes—
383C2×C4#54712yes—
384C2×C4D4×Q811yescharacteristic
385C2×C4#55011yescharacteristic
386C2×C4#55411yescharacteristic
387C2×C4#55612yes—
388C2×C4#55612yes—
389C2×C4#55611yescharacteristic
390C2×C4#55712yes—
391C2×C4#56312yes—
392C2×C4#56412yes—
393C8—82no—
394C8—82no—
395C22#253811yescharacteristic
396C22#254711yescharacteristic
397C22#256811yescharacteristic
398C22#261811yescharacteristic
399C22#262711yescharacteristic
400C22#263911yescharacteristic
401C22#282211yescharacteristic
402C22#304111yescharacteristic
403C22#304211yescharacteristic
404C22#304311yescharacteristic
405C22#304411yescharacteristic
406C22#308312yes—
407C22#308412yes—
408C22#313612yes—
409C22#313712yes—
410C22#319812yes—
411C22#320112yes—
412C22#324112yes—
413C22#324112yes—
414C22#324212yes—
415C22#324212yes—
416C22#326212yes—
417C22#326312yes—
418C4—44no—
419C4—42no—
420C4—42no—
421C4—44no—
422C4—84no—
423C4—82no—
424C4—82no—
425C4—161no—
426C4—161no—
427C4—162no—
428C4#272612yes—
429C4#272712yes—
430C4#280512yes—
431C4#281012yes—
432C2#1707411yescharacteristic
433C2#2828811yescharacteristic
434C2#2828911yescharacteristic
435C2#2872811yescharacteristic
436C2#2872911yescharacteristic
437C2#2922812yes—
438C2#2976311yescharacteristic
439C2#2976411yescharacteristic
440C2#2997912yes—
441C2#3019512yes—
442C2#3285512yes—
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×#21002
C2×#20992
#142772
#142762
#113582
#112672
#112282
#112272
#112082
#108332