Finite Group Databasebeta

← #444842

Subgroups — #444842

Order 512.

942 conjugacy classes of subgroups.

The subgroup lattice has 401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15151C211yesmaximal, characteristic
2#13954C211yesmaximal, characteristic
3#11293C212yesmaximal
4#11292C212yesmaximal
5#11208C212yesmaximal
6#11207C212yesmaximal
7#10885C212yesmaximal
8#10880C212yesmaximal
9#10874C211yesmaximal, characteristic
10C22×C4×C8C2211yescharacteristic
11C2×#398—22no—
12C2×#389C2212yes—
13C2×#389C2212yes—
14C2×#389C2212yes—
15C2×#384C2211yescharacteristic
16C2×#382C2211yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×C4×C4⋊C4C2211yescharacteristic
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2211yescharacteristic
29C2×#336C2212yes—
30#1445—22no—
31#1444—22no—
32C4⋊#95—22no—
33C4⋊#95C2212yes—
34C4⋊#95C2211yescharacteristic
35C23×C8C2312yes—
36C23×C8C2312yes—
37C22×C4⋊C4—22no—
38C22×C4⋊C4—22no—
39C22×C4⋊C4—22no—
40C22×C4⋊C4—22no—
41C22×C4⋊C4D412yes—
42C22×C4⋊C4C2312yes—
43C22×C4⋊C4C2312yes—
44C22×C4⋊C4C2312yes—
45C22×C4⋊C4C2312yes—
46C22×C42—21no—
47C22×C42C2311yescharacteristic
48C22×C42C2311yescharacteristic
49C22×C42C2311yescharacteristic
50C2×C4×C8—41no—
51C2×C4×C8—42no—
52#398—48no—
53#389—24no—
54#389—24no—
55#389—24no—
56#389—24no—
57#389—42no—
58#389—42no—
59#384—41no—
60#384—41no—
61#382—41no—
62#382—41no—
63C4×C4⋊C4—24no—
64C4×C4⋊C4—41no—
65C4×C4⋊C4—41no—
66C2×#95—21no—
67C2×#95—22no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—21no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95—21no—
74C2×#95—22no—
75C2×#95D412yes—
76#340—24no—
77#340—24no—
78#340—24no—
79#340—42no—
80#340—42no—
81#340—42no—
82#340—42no—
83#340Q818yes—
84#336—24no—
85#336—41no—
86#336—42no—
87C23×C4—22no—
88C23×C4—22no—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D412yes—
94C23×C4C2×D412yes—
95C23×C4C2411yescharacteristic
96C22×C8—22no—
97C22×C8—22no—
98C22×C8—22no—
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8C2×Q814yes—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—24no—
118C2×C4⋊C4—24no—
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—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4—44no—
134C2×C4⋊C4—44no—
135C2×C4⋊C4—44no—
136C2×C4⋊C4—44no—
137C2×C4⋊C4—44no—
138C2×C4⋊C4—44no—
139C2×C4⋊C4—44no—
140C2×C4⋊C4—44no—
141C2×C4⋊C4—44no—
142C2×C4⋊C4—44no—
143C2×C4⋊C4—82no—
144C2×C4⋊C4—82no—
145C2×C4⋊C4C2×Q814yes—
146C2×C4⋊C4C2×Q814yes—
147C2×C4⋊C4#4114yes—
148C2×C4⋊C4#4114yes—
149C2×C42—22no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42—22no—
153C2×C42—22no—
154C2×C42—21no—
155C2×C42—22no—
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—22no—
160C2×C42—24no—
161C2×C42—82no—
162C2×C42#4114yes—
163C4×C8—44no—
164#95—24no—
165#95—42no—
166#95—44no—
167#95—44no—
168#95—42no—
169#95—42no—
170#95—44no—
171#95—44no—
172#95—44no—
173#95—44no—
174C24C22×D411yescharacteristic
175C22×C4—21no—
176C22×C4—24no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—24no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—24no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—24no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4#12412yes—
224C22×C4#12412yes—
225C22×C4#13514yes—
226C22×C4AGL(1,ℤ/8)14yes—
227C22×C4C22×Q812yes—
228C22×C4C2×#4112yes—
229C22×C4C2×#4112yes—
230C22×C4C2×#4112yes—
231C22×C4H(5,𝔽2)12yes—
232C22×C4H(5,𝔽2)11yescharacteristic
233C22×C4H(5,𝔽2)11yescharacteristic
234C22×C42−1+412yes—
235C2×C8—24no—
236C2×C8—24no—
237C2×C8—24no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—48no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—88no—
266C4⋊C4—88no—
267C4⋊C4—88no—
268C4⋊C4—88no—
269C4⋊C4#12518yes—
270C42—24no—
271C42—24no—
272C42—42no—
273C42—42no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42—84no—
279C23#52511yescharacteristic
280C23C2×#12411yescharacteristic
281C23#53411yescharacteristic
282C23#54612yes—
283C23D4×Q812yes—
284C23C2×#13512yes—
285C23C2×AGL(1,ℤ/8)12yes—
286C23#57712yes—
287C23#57812yes—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—28no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—41no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4C2×#12512yes—
341C2×C4#53312yes—
342C2×C4#53912yes—
343C2×C4#54012yes—
344C2×C4#54212yes—
345C2×C4#54412yes—
346C2×C4#55212yes—
347C2×C4#55312yes—
348C2×C4#55312yes—
349C2×C4#55412yes—
350C2×C4#55412yes—
351C2×C4#55612yes—
352C2×C4Q8211yescharacteristic
353C2×C4#55911yescharacteristic
354C2×C4#56011yescharacteristic
355C2×C4#56311yescharacteristic
356C8—44no—
357C8—82no—
358C22#247312yes—
359C22#249212yes—
360C22#259111yescharacteristic
361C22#270911yescharacteristic
362C22#273411yescharacteristic
363C22#310612yes—
364C22#312311yescharacteristic
365C22#312711yescharacteristic
366C22#313111yescharacteristic
367C22#313712yes—
368C22#313811yescharacteristic
369C22#318812yes—
370C22#320112yes—
371C22#329612yes—
372C22#330012yes—
373C22#330612yes—
374C22#330812yes—
375C22#338112yes—
376C22#338312yes—
377C22#338412yes—
378C22#338612yes—
379C4—44no—
380C4—44no—
381C4—42no—
382C4—42no—
383C4—48no—
384C4—84no—
385C4—162no—
386C4—162no—
387C4#250712yes—
388C4#257012yes—
389C4#279012yes—
390C4#279312yes—
391C2#1579011yescharacteristic
392C2#2730312yes—
393C2#2730712yes—
394C2#2781812yes—
395C2#2783012yes—
396C2#2933111yescharacteristic
397C2#2934111yescharacteristic
398C2#3203212yes—
399C2#3268812yes—
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
#151512
#139542
#112932
#112922
#112082
#112072
#108852
#108802
#108742