Finite Group Databasebeta

← #410768

Subgroups — #410768

Order 512.

940 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14709C211yesmaximal, characteristic
2C4×#382C211yesmaximal, characteristic
3#11385C211yesmaximal, characteristic
4#11385C211yesmaximal, characteristic
5#11372C212yesmaximal
6#11268C212yesmaximal
7#11268C211yesmaximal, characteristic
8#11268C211yesmaximal, characteristic
9#10807C212yesmaximal
10#10806C212yesmaximal
11#10795C211yesmaximal, characteristic
12C22×#125C2211yescharacteristic
13C2×#382C2211yescharacteristic
14C2×#382C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×C43C2211yescharacteristic
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2211yescharacteristic
29C2×#336C2211yescharacteristic
30C2×#336C2212yes—
31#1436—22no—
32#1436—22no—
33C4⋊#95C2212yes—
34C4⋊#95C2211yescharacteristic
35C4⋊#95C2211yescharacteristic
36C4⋊#95C2212yes—
37#1434—22no—
38C4×#95—22no—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C2×#125—24no—
42C2×#125—22no—
43C2×#125—22no—
44C2×#125—42no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2311yescharacteristic
48C22×C4⋊C4C2311yescharacteristic
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2311yescharacteristic
51C22×C4⋊C4C2311yescharacteristic
52C22×C42—21no—
53C22×C42—21no—
54C22×C42D412yes—
55C22×C42D412yes—
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58C22×C42C2311yescharacteristic
59#382—22no—
60#382—22no—
61#382—22no—
62#382—42no—
63#382Q814yes—
64C4×C4⋊C4—24no—
65C4×C4⋊C4—24no—
66C2×#95—22no—
67C2×#95—22no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—22no—
77C43—22no—
78C43—22no—
79#340—24no—
80#340—24no—
81#340—24no—
82#340—24no—
83#340—42no—
84#340—42no—
85#340—42no—
86#340—42no—
87#336—24no—
88#336—22no—
89#336—22no—
90#336—24no—
91C23×C4—22no—
92C23×C4—21no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—22no—
97C23×C4C2×D412yes—
98C23×C4C2×D412yes—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2411yescharacteristic
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116#125—48no—
117#125—48no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
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—28no—
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—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—44no—
143C2×C4⋊C4—44no—
144C2×C4⋊C4C2×Q812yes—
145C2×C4⋊C4C2×Q812yes—
146C2×C4⋊C4#4114yes—
147C2×C4⋊C4#4112yes—
148C2×C4⋊C4#4112yes—
149C2×C42—22no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—22no—
157C2×C42—22no—
158C2×C42—24no—
159C2×C42—24no—
160C2×C42—24no—
161C2×C42—42no—
162C2×C42—42no—
163C2×C42—42no—
164C2×C42—44no—
165C2×C42—42no—
166C2×C42—42no—
167C2×C42—44no—
168C2×C42C2×Q812yes—
169C2×C42#4112yes—
170C2×C42#4112yes—
171C2×C42#4112yes—
172C2×C42#4114yes—
173#95—28no—
174#95—28no—
175#95—44no—
176#95—44no—
177#95—44no—
178#95—44no—
179#95—44no—
180#95—44no—
181#95—42no—
182#95—42no—
183#95—44no—
184C24C22×D411yescharacteristic
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
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—24no—
209C22×C4—42no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
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—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4C22⋊Q814yes—
239C22×C4#12314yes—
240C22×C4#12412yes—
241C22×C4#12412yes—
242C22×C4#13514yes—
243C22×C4C22×Q811yescharacteristic
244C22×C4C2×#4111yescharacteristic
245C22×C4C2×#4111yescharacteristic
246C22×C4C2×#4112yes—
247C22×C4C2×#4112yes—
248C22×C4C2×#4111yescharacteristic
249C22×C4C2×#4111yescharacteristic
250C22×C4C2×#4111yescharacteristic
251C22×C4H(5,𝔽2)12yes—
252C22×C42−1+412yes—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—416no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C42—22no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—24no—
289C42—24no—
290C42—24no—
291C42—24no—
292C42—48no—
293C42—48no—
294C42—84no—
295C42—84no—
296C23C2×C22⋊Q811yescharacteristic
297C23C2×#12311yescharacteristic
298C23#52511yescharacteristic
299C23#52511yescharacteristic
300C23C2×#12411yescharacteristic
301C23#53511yescharacteristic
302C23#53611yescharacteristic
303C23C2×#13512yes—
304C23#57512yes—
305C23#57512yes—
306C23#57512yes—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4#48814yes—
365C2×C4#52912yes—
366C2×C4#52912yes—
367C2×C4#52911yescharacteristic
368C2×C4#52911yescharacteristic
369C2×C4#53311yescharacteristic
370C2×C4#53311yescharacteristic
371C2×C4#54212yes—
372C2×C4#54212yes—
373C2×C4#55112yes—
374C2×C4#55112yes—
375C2×C4#55212yes—
376C2×C4#55212yes—
377C2×C4#55412yes—
378C2×C4#55512yes—
379C2×C4#55612yes—
380C2×C4#55712yes—
381C8—82no—
382C8—82no—
383C22#239811yescharacteristic
384C22#248211yescharacteristic
385C22#250311yescharacteristic
386C22#256311yescharacteristic
387C22#258111yescharacteristic
388C22#263211yescharacteristic
389C22#285511yescharacteristic
390C22#307612yes—
391C22#308012yes—
392C22#309112yes—
393C22#309312yes—
394C22#310212yes—
395C22#310212yes—
396C22#311112yes—
397C22#311112yes—
398C22C2×#48811yescharacteristic
399C22#313511yescharacteristic
400C22#314011yescharacteristic
401C22#314211yescharacteristic
402C22#321212yes—
403C22#321912yes—
404C22#323212yes—
405C22#324012yes—
406C4—24no—
407C4—42no—
408C4—44no—
409C4—44no—
410C4—82no—
411C4—82no—
412C4—84no—
413C4—82no—
414C4—82no—
415C4—162no—
416C4#252012yes—
417C4#252012yes—
418C4#253212yes—
419C4#253212yes—
420C2#1508911yescharacteristic
421C2#2381811yescharacteristic
422C2#2382611yescharacteristic
423C2#2759012yes—
424C2#2796411yescharacteristic
425C2#2796711yescharacteristic
426C2#2914011yescharacteristic
427C2#2914611yescharacteristic
428C2#2927912yes—
429C2#3006512yes—
430C2#3315212yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ 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
#147092
C4×#3822
#113852
#113722
#112682
#108072
#108062
#107952