Finite Group Databasebeta

← #276418

Subgroups — #276418

Order 512.

579 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33198C211yesmaximal, characteristic
2#29206C211yesmaximal, characteristic
3#22821C211yesmaximal, characteristic
4C4×#477C211yesmaximal, characteristic
5#10620C212yesmaximal
6#10482C212yesmaximal
7#9898C211yesmaximal, characteristic
8#9611C212yesmaximal
9#9602C211yesmaximal, characteristic
10#9568C212yesmaximal
11#8587C211yesmaximal, characteristic
12C2×#477—21no—
13C2×#477C2211yescharacteristic
14#2868C2211yescharacteristic
15C4×C4⋊Q8C2211yescharacteristic
16C42×Q8C2211yescharacteristic
17#2058—22no—
18#1990C2212yes—
19#1987—21no—
20#1987C2211yescharacteristic
21#1984C2212yes—
22#1948—21no—
23#1948—21no—
24#1947—21no—
25#1947C2212yes—
26#1947C2211yescharacteristic
27#1921—21no—
28#1916—22no—
29#1863—21no—
30#1844C2212yes—
31#1842C2211yescharacteristic
32#1842C2211yescharacteristic
33#1831—21no—
34#1803—21no—
35#1803C2211yescharacteristic
36#1803C2212yes—
37C4×#107—21no—
38C8×C4⋊C4C2212yes—
39C4×C4⋊C8—21no—
40C4×C4⋊C8C2211yescharacteristic
41C4×C4⋊C8C2211yescharacteristic
42C4×#103—21no—
43C2×#334C2212yes—
44C2×#333C2212yes—
45#1296C2212yes—
46#1296C2212yes—
47#1296C2212yes—
48#1277C2212yes—
49C2×C4⋊Q8—21no—
50C2×C4⋊Q8—21no—
51C2×C4⋊Q8—21no—
52C2×C4⋊Q8C2311yescharacteristic
53C2×C4×Q8—21no—
54C2×C4×Q8D411yescharacteristic
55C2×C4×Q8D411yescharacteristic
56C2×C4×Q8C2311yescharacteristic
57#477—22no—
58#477—22no—
59#477—44no—
60C2×#107—21no—
61C2×#107—22no—
62C2×#107—21no—
63C2×#106—22no—
64C2×#106—22no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8D411yescharacteristic
70C2×C4⋊C8D411yescharacteristic
71C2×C4⋊C8C2312yes—
72C2×C4⋊C8C2312yes—
73C2×C4⋊C8C2311yescharacteristic
74C2×C4⋊C8C2311yescharacteristic
75C2×#103—21no—
76C2×#103—22no—
77C2×#103—21no—
78C2×C4×C8—21no—
79C2×C4×C8—22no—
80C2×C4×C8C2312yes—
81#391—21no—
82#389—21no—
83#389—21no—
84#384—21no—
85#384—21no—
86#384—21no—
87#384C2311yescharacteristic
88#384C2312yes—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C4×C4⋊C4—21no—
94C4×C4⋊C4D411yescharacteristic
95C4×C4⋊C4D411yescharacteristic
96C4×C4⋊C4C2311yescharacteristic
97C43—21no—
98C43C2311yescharacteristic
99#340—22no—
100#340—22no—
101#340—22no—
102#340—21no—
103#340—22no—
104#340—21no—
105#340—21no—
106#340—21no—
107#336—22no—
108#336—22no—
109#336—22no—
110#336—21no—
111#336D412yes—
112#334—24no—
113#333—24no—
114C22×Q8—21no—
115C22×Q8—41no—
116C22×Q8C2×D411yescharacteristic
117C22×C8—21no—
118C22×C8—22no—
119C22×C8—21no—
120C22×C8—22no—
121C22×C8C2×D412yes—
122C22×C8C2×D412yes—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—42no—
127C4⋊Q8—42no—
128C4⋊Q8—81no—
129C4⋊Q8—81no—
130C4⋊Q8—82no—
131C4⋊Q8#4112yes—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—21no—
135C4×Q8—21no—
136C4×Q8—21no—
137C4×Q8—21no—
138C4×Q8—41no—
139C4×Q8—82no—
140C4×Q8SD1614yes—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4C2×D411yescharacteristic
157C2×C4⋊C4C2×D411yescharacteristic
158C2×C4⋊C4C2×D411yescharacteristic
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—41no—
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42C2411yescharacteristic
173#107—24no—
174#107—44no—
175#107—42no—
176#106—82no—
177#106—82no—
178C4⋊C8—22no—
179C4⋊C8—21no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—21no—
184C4⋊C8—21no—
185C4⋊C8—22no—
186C4⋊C8—42no—
187C4⋊C8—42no—
188C4⋊C8—42no—
189C4⋊C8—81no—
190C4⋊C8Q1614yes—
191C4⋊C8#4112yes—
192#103—24no—
193#103—42no—
194#103—44no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—42no—
198C4×C8—82no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—41no—
203#95—41no—
204C2×Q8—21no—
205C2×Q8—21no—
206C2×Q8—21no—
207C2×Q8—22no—
208C2×Q8—21no—
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—82no—
212C2×Q8—82no—
213C2×Q8—81no—
214C2×Q8—81no—
215C2×Q8—82no—
216C2×Q8C2×SD1612yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22×D411yescharacteristic
229C22×C4C22×D411yescharacteristic
230C22×C4C2×#4111yescharacteristic
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—42no—
240C2×C8—41no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—41no—
244C2×C8—42no—
245C2×C8—41no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8C2×Q1614yes—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—24no—
252C4⋊C4—22no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—81no—
270C4⋊C4—82no—
271C4⋊C4—82no—
272C4⋊C4—82no—
273C4⋊C4—82no—
274C4⋊C4—82no—
275C4⋊C4C2×SD1612yes—
276C4⋊C4#13712yes—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—24no—
282C42—22no—
283C42—41no—
284C42—42no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C42—42no—
290C42—81no—
291C42—82no—
292C42C2×SD1612yes—
293C42C2×Q1612yes—
294C42#13512yes—
295C42#13712yes—
296C42C2×#4111yescharacteristic
297C42C2×#4111yescharacteristic
298C422−1+411yescharacteristic
299C422−1+411yescharacteristic
300C23C2×#12111yescharacteristic
301Q8—22no—
302Q8—22no—
303Q8—41no—
304Q8—41no—
305Q8—82no—
306Q8—82no—
307Q8—164no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—82no—
333C2×C4—81no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4#46212yes—
339C2×C4#46212yes—
340C2×C4#46512yes—
341C2×C4#46512yes—
342C2×C4#47112yes—
343C2×C4#52511yescharacteristic
344C2×C4#53611yescharacteristic
345C2×C4#54711yescharacteristic
346C2×C4#54811yescharacteristic
347C2×C4#55211yescharacteristic
348C2×C4#55611yescharacteristic
349C2×C4C22×SD1611yescharacteristic
350C2×C4C22×Q1611yescharacteristic
351C2×C4C2×#13511yescharacteristic
352C2×C4C2×#13711yescharacteristic
353C2×C4C2×#13711yescharacteristic
354C2×C4#57511yescharacteristic
355C2×C4#57611yescharacteristic
356C2×C4#57711yescharacteristic
357C8—24no—
358C8—42no—
359C8—42no—
360C8—82no—
361C8—82no—
362C8—81no—
363C22#241511yescharacteristic
364C22C2×#46211yescharacteristic
365C22#304511yescharacteristic
366C22C2×#46511yescharacteristic
367C22#305611yescharacteristic
368C22C2×#47111yescharacteristic
369C22#306811yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—22no—
374C4—41no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—81no—
379C4—82no—
380C4—161no—
381C4—162no—
382C4#167214yes—
383C4#310311yescharacteristic
384C4#310711yescharacteristic
385C4#322911yescharacteristic
386C4#323311yescharacteristic
387C4#333811yescharacteristic
388C4#335611yescharacteristic
389C4#336311yescharacteristic
390C4#337511yescharacteristic
391C2C2×#167211yescharacteristic
392C2#1917311yescharacteristic
393C2#1940911yescharacteristic
394C2#1948211yescharacteristic
395C2#2468211yescharacteristic
396C2#2470311yescharacteristic
397C2#2472111yescharacteristic
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
#292062
#228212
C4×#4772
#106202
#104822
#98982
#96112
#96022
#95682
#85872