Finite Group Databasebeta

← #470528

Subgroups — #470528

Order 512.

934 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1918C212yesmaximal
2#15151C211yesmaximal, characteristic
3#13911C211yesmaximal, characteristic
4#11315C212yesmaximal
5#11267C212yesmaximal
6#11256C212yesmaximal
7#11232C212yesmaximal
8#11207C212yesmaximal
9#11202C211yesmaximal, characteristic
10C22×#107C2212yes—
11C22×C4⋊C8C2211yescharacteristic
12C2×#398—21no—
13C2×#398—21no—
14C2×#389C2212yes—
15C2×#384C2211yescharacteristic
16C2×#384C2211yescharacteristic
17C2×#382—21no—
18C2×C4×C4⋊C4C2211yescharacteristic
19C2×C4×C4⋊C4C2211yescharacteristic
20#1918—28no—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#336C2212yes—
29C2×#336C2212yes—
30C2×#336C2211yescharacteristic
31#1445—21no—
32#1445—21no—
33#1442—21no—
34#1442—21no—
35C4⋊#95—21no—
36C4⋊#95C2212yes—
37C4⋊#95C2212yes—
38C4⋊#95C2211yescharacteristic
39C4⋊#95C2212yes—
40C23×C8C2312yes—
41C23×C8C2312yes—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4D411yescharacteristic
48C22×C4⋊C4D411yescharacteristic
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C4⋊C4C2312yes—
53C22×C42—21no—
54C22×C42C2311yescharacteristic
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C2×#107—24no—
58C2×#107—24no—
59C2×#107—24no—
60C2×C4⋊C8—24no—
61C2×C4⋊C8—41no—
62#398—44no—
63#398—44no—
64#389—24no—
65#389—24no—
66#384—41no—
67#384—41no—
68#384—41no—
69#384—41no—
70#382—44no—
71C4×C4⋊C4—22no—
72C4×C4⋊C4—41no—
73C4×C4⋊C4—41no—
74C4×C4⋊C4D414yes—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—22no—
78C2×#95—21no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95D411yescharacteristic
86C2×#95D411yescharacteristic
87#340—24no—
88#340—24no—
89#340—24no—
90#340—24no—
91#340—24no—
92#340—42no—
93#340—42no—
94#336—24no—
95#336—24no—
96#336—41no—
97C23×C4—22no—
98C23×C4—22no—
99C23×C4—22no—
100C23×C4—22no—
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C23×C4C2×D411yescharacteristic
106C23×C4C2×D411yescharacteristic
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#4114yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—82no—
163C2×C4⋊C4D814yes—
164C2×C4⋊C4C2×D414yes—
165C2×C4⋊C4#4114yes—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—24no—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—21no—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—42no—
180C2×C42—42no—
181C2×C42C2×D412yes—
182C2×C42#4112yes—
183#107—216no—
184C4⋊C8—44no—
185#95—24no—
186#95—41no—
187#95—41no—
188#95—42no—
189#95—44no—
190#95—44no—
191#95—44no—
192#95—44no—
193#95—42no—
194#95—44no—
195#95—82no—
196#95—82no—
197C24C22×D411yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—24no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
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—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4#12112yes—
252C22×C4#12112yes—
253C22×C4C2×D812yes—
254C22×C4C2×D812yes—
255C22×C4C2×D812yes—
256C22×C4AGL(1,ℤ/8)12yes—
257C22×C4#13712yes—
258C22×C4C22×D411yescharacteristic
259C22×C4C2×#4112yes—
260C22×C4C2×#4112yes—
261C22×C4C2×#4111yescharacteristic
262C22×C4H(5,𝔽2)11yescharacteristic
263C22×C4H(5,𝔽2)11yescharacteristic
264C22×C42−1+412yes—
265C22×C42−1+412yes—
266C22×C42−1+411yescharacteristic
267C22×C42−1+411yescharacteristic
268C2×C8—24no—
269C2×C8—24no—
270C2×C8—24no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—44no—
287C4⋊C4—44no—
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—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—84no—
301C4⋊C4—84no—
302C4⋊C4—84no—
303C4⋊C4—84no—
304C4⋊C4—88no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—22no—
309C42—42no—
310C42—42no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—48no—
316C23C2×#12111yescharacteristic
317C23#53411yescharacteristic
318C23#53611yescharacteristic
319C23#54712yes—
320C23#54812yes—
321C23C22×D811yescharacteristic
322C23C2×AGL(1,ℤ/8)11yescharacteristic
323C23C2×#13711yescharacteristic
324C23#57511yescharacteristic
325C23#57712yes—
326C23#57812yes—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—44no—
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—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4#45914yes—
387C2×C4#52512yes—
388C2×C4#53612yes—
389C2×C4#53711yescharacteristic
390C2×C4#53711yescharacteristic
391C2×C4#53911yescharacteristic
392C2×C4#53911yescharacteristic
393C2×C4#54112yes—
394C2×C4#54112yes—
395C2×C4#54212yes—
396C2×C4#54212yes—
397C2×C4#55111yescharacteristic
398C2×C4#55212yes—
399C2×C4#55212yes—
400C2×C4#55511yescharacteristic
401C2×C4#55612yes—
402C2×C4#56311yescharacteristic
403C2×C4#56311yescharacteristic
404C2×C4#56412yes—
405C8—44no—
406C8—82no—
407C22#241512yes—
408C22#261811yescharacteristic
409C22#271711yescharacteristic
410C22#271912yes—
411C22#273111yescharacteristic
412C22C2×#45911yescharacteristic
413C22#303711yescharacteristic
414C22#304612yes—
415C22#318611yescharacteristic
416C22#319311yescharacteristic
417C22#320011yescharacteristic
418C22#320211yescharacteristic
419C22#322611yescharacteristic
420C22#323411yescharacteristic
421C22#324212yes—
422C22#333412yes—
423C22#334412yes—
424C22#334912yes—
425C22#335412yes—
426C22#335812yes—
427C22#336712yes—
428C22#337112yes—
429C22#337412yes—
430C4—24no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—81no—
436C4—84no—
437C4—84no—
438C4—162no—
439C4—162no—
440C4#260911yescharacteristic
441C4#263712yes—
442C4#276712yes—
443C4#276911yescharacteristic
444C4#278911yescharacteristic
445C4#282211yescharacteristic
446C2#1668811yescharacteristic
447C2#2467612yes—
448C2#2469112yes—
449C2#2975411yescharacteristic
450C2#2976611yescharacteristic
451C2#3225811yescharacteristic
452C2#3227011yescharacteristic
453C2#3231012yes—
454C2#3233512yes—
455C2#3262811yescharacteristic
456C2#3264411yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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×#19182
#151512
#139112
#113152
#112672
#112562
#112322
#112072
#112022