Finite Group Databasebeta

← #275985

Subgroups — #275985

Order 512.

585 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33198C211yesmaximal, characteristic
2#28717C211yesmaximal, characteristic
3#22825C211yesmaximal, characteristic
4C4×#475C211yesmaximal, characteristic
5#10482C212yesmaximal
6#10277C212yesmaximal
7#9745C212yesmaximal
8#9691C211yesmaximal, characteristic
9#9602C211yesmaximal, characteristic
10#9575C212yesmaximal
11#8586C211yesmaximal, characteristic
12C2×#487C2212yes—
13C2×#477C2212yes—
14C2×#475C2211yescharacteristic
15#2868C2211yescharacteristic
16C4×C4⋊Q8C2211yescharacteristic
17C42×Q8C2211yescharacteristic
18#2072—22no—
19#1990C2212yes—
20#1988C2211yescharacteristic
21#1987C2212yes—
22#1984C2212yes—
23#1948C2211yescharacteristic
24#1947—21no—
25#1947—21no—
26#1919—21no—
27#1917—22no—
28#1865—21no—
29#1842C2211yescharacteristic
30#1842C2211yescharacteristic
31#1831—21no—
32#1803—21no—
33#1803—21no—
34#1803—21no—
35#1803—21no—
36#1803C2211yescharacteristic
37C4×#106—21no—
38#1770C2212yes—
39#1767—21no—
40C4×C4⋊C8C2211yescharacteristic
41C4×C4⋊C8C2211yescharacteristic
42C4×#103—21no—
43C2×#334C2212yes—
44C2×#333C2212yes—
45C2×#333C2212yes—
46C2×#332C2212yes—
47#1296C2212yes—
48#1277C2212yes—
49C2×C4⋊Q8—21no—
50C2×C4⋊Q8—21no—
51C2×C4⋊Q8C2312yes—
52C2×C4⋊Q8C2311yescharacteristic
53C2×C4×Q8—21no—
54C2×C4×Q8D411yescharacteristic
55C2×C4×Q8D411yescharacteristic
56C2×C4×Q8C2311yescharacteristic
57#487—24no—
58#487—42no—
59#477—42no—
60#477—42no—
61#475—22no—
62#475—22no—
63C2×#107—22no—
64C2×#106—21no—
65C2×#106—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8D411yescharacteristic
71C2×C4⋊C8D411yescharacteristic
72C2×C4⋊C8C2312yes—
73C2×C4⋊C8C2312yes—
74C2×C4⋊C8C2311yescharacteristic
75C2×C4⋊C8C2311yescharacteristic
76C2×#103—21no—
77C2×#103—22no—
78C2×#103—21no—
79C2×#103—22no—
80C2×#103—22no—
81C2×#97—22no—
82C2×C4×C8—21no—
83C2×C4×C8C2312yes—
84#391—21no—
85#389—21no—
86#389—21no—
87#384—21no—
88#384—21no—
89#384—21no—
90#384—21no—
91#384C2311yescharacteristic
92C4×C4⋊C4—21no—
93C4×C4⋊C4—21no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4—21no—
97C4×C4⋊C4D411yescharacteristic
98C4×C4⋊C4D411yescharacteristic
99C4×C4⋊C4C2311yescharacteristic
100C43—21no—
101C43C2311yescharacteristic
102#340—22no—
103#340—22no—
104#340—22no—
105#340—22no—
106#340—21no—
107#340—21no—
108#340—21no—
109#340—21no—
110#336—22no—
111#336—22no—
112#336—22no—
113#336—21no—
114#336D412yes—
115#334—42no—
116#333—24no—
117#333—42no—
118#332—42no—
119C22×Q8—21no—
120C22×Q8—22no—
121C22×Q8C2×D411yescharacteristic
122C22×C8—21no—
123C22×C8—22no—
124C22×C8—21no—
125C22×C8—22no—
126C22×C8C2×D412yes—
127C22×C8C2×D412yes—
128C4⋊Q8—21no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—22no—
134C4⋊Q8—22no—
135C4⋊Q8—82no—
136C4⋊Q8—82no—
137C4⋊Q8#4112yes—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—21no—
142C4×Q8—21no—
143C4×Q8—21no—
144C4×Q8—21no—
145C4×Q8—41no—
146C4×Q8—42no—
147C4×Q8—42no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4C2×D411yescharacteristic
164C2×C4⋊C4C2×D411yescharacteristic
165C2×C4⋊C4C2×D411yescharacteristic
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—21no—
172C2×C42—41no—
173C2×C42C2×D411yescharacteristic
174C2×C42C2×D411yescharacteristic
175C2×C42C2×D411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42#4111yescharacteristic
178C2×C42#4111yescharacteristic
179C2×C42C2411yescharacteristic
180#107—44no—
181#106—24no—
182#106—42no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—21no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—22no—
192C4⋊C8—42no—
193C4⋊C8—42no—
194C4⋊C8—42no—
195C4⋊C8—81no—
196C4⋊C8#4112yes—
197#103—24no—
198#103—44no—
199#103—44no—
200#103—44no—
201#103—42no—
202#97—82no—
203C4×C8—22no—
204C4×C8—22no—
205C4×C8—42no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—41no—
210#95—41no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—22no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—41no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—82no—
225C2×Q8—82no—
226C2×Q8#13712yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4C22×D411yescharacteristic
239C22×C4C22×D411yescharacteristic
240C22×C4C2×#4111yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—42no—
251C2×C8—41no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C4⋊C4—82no—
283C4⋊C4—82no—
284C4⋊C4—82no—
285C4⋊C4—82no—
286C4⋊C4—82no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—22no—
292C42—41no—
293C42—42no—
294C42—41no—
295C42—41no—
296C42—41no—
297C42—41no—
298C42—42no—
299C42—42no—
300C42—81no—
301C42—82no—
302C42#13512yes—
303C42#13712yes—
304C42#13712yes—
305C42#13712yes—
306C42C2×#4111yescharacteristic
307C42C2×#4111yescharacteristic
308C42H(5,𝔽2)11yescharacteristic
309C42H(5,𝔽2)11yescharacteristic
310C23C2×#12111yescharacteristic
311Q8—22no—
312Q8—22no—
313Q8—41no—
314Q8—41no—
315Q8—42no—
316Q8—42no—
317Q8—81no—
318Q8—81no—
319Q8—162no—
320Q8—162no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—81no—
351C2×C4#46412yes—
352C2×C4#46412yes—
353C2×C4#47012yes—
354C2×C4#47012yes—
355C2×C4#47112yes—
356C2×C4#52511yescharacteristic
357C2×C4#53511yescharacteristic
358C2×C4#54611yescharacteristic
359C2×C4#55011yescharacteristic
360C2×C4#55311yescharacteristic
361C2×C4#55511yescharacteristic
362C2×C4C2×#13511yescharacteristic
363C2×C4C2×#13711yescharacteristic
364C2×C4C2×#13711yescharacteristic
365C2×C4C2×#13711yescharacteristic
366C2×C4C2×#13711yescharacteristic
367C2×C4#57511yescharacteristic
368C2×C4#57711yescharacteristic
369C2×C4#57811yescharacteristic
370C8—42no—
371C8—42no—
372C8—42no—
373C8—82no—
374C8—82no—
375C8—81no—
376C22#241411yescharacteristic
377C22C2×#46411yescharacteristic
378C22#304611yescharacteristic
379C22C2×#47011yescharacteristic
380C22#305611yescharacteristic
381C22C2×#47111yescharacteristic
382C22#306811yescharacteristic
383C4—21no—
384C4—21no—
385C4—22no—
386C4—22no—
387C4—41no—
388C4—42no—
389C4—81no—
390C4—82no—
391C4—81no—
392C4—81no—
393C4—162no—
394C4—161no—
395C4#170414yes—
396C4#311311yescharacteristic
397C4#311611yescharacteristic
398C4#321611yescharacteristic
399C4#321811yescharacteristic
400C4#330211yescharacteristic
401C4#333111yescharacteristic
402C4#339411yescharacteristic
403C4#339811yescharacteristic
404C2C2×#170411yescharacteristic
405C2#1917611yescharacteristic
406C2#1945311yescharacteristic
407C2#1950011yescharacteristic
408C2#2462911yescharacteristic
409C2#2466011yescharacteristic
410C2#2467311yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#121
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#331982
#287172
#228252
C4×#4752
#104822
#102772
#97452
#96912
#96022
#95752
#85862