Finite Group Databasebeta

← #317639

Subgroups — #317639

Order 512.

512 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29277C211yesmaximal, characteristic
2#29273C211yesmaximal, characteristic
3#22307C211yesmaximal, characteristic
4#22248C211yesmaximal, characteristic
5#10655C212yesmaximal
6#10543C212yesmaximal
7#9568C212yesmaximal
8#9567C212yesmaximal
9#8788C211yesmaximal, characteristic
10#8594C211yesmaximal, characteristic
11#8594C211yesmaximal, characteristic
12C2×#500C2211yescharacteristic
13C4×C4⋊Q8C2211yescharacteristic
14C4×C4⋊Q8C2211yescharacteristic
15C4×C4⋊Q8C2211yescharacteristic
16#2100—21no—
17#2099—21no—
18#2058—21no—
19#2057—21no—
20#1990C2211yescharacteristic
21#1990C2211yescharacteristic
22#1987C2212yes—
23#1987C2212yes—
24#1984—22no—
25#1948C2212yes—
26#1947C2212yes—
27#1939C2212yes—
28#1921—22no—
29#1921—22no—
30#1921—22no—
31#1919—22no—
32#1916—22no—
33#1834C2211yescharacteristic
34#1831C2211yescharacteristic
35#1831C2211yescharacteristic
36#1831C2211yescharacteristic
37C8×C4⋊C4C2212yes—
38#1744C2211yescharacteristic
39C2×#333C2212yes—
40C2×#333C2212yes—
41#1296C2212yes—
42#1296C2212yes—
43#1277C2212yes—
44#1277C2212yes—
45C2×C4⋊Q8D411yescharacteristic
46C2×C4⋊Q8C2311yescharacteristic
47C2×C4⋊Q8C2311yescharacteristic
48C2×C4×Q8—21no—
49C2×C4×Q8—21no—
50C2×C4×Q8—21no—
51#500—22no—
52#500—22no—
53C2×#107—22no—
54C2×#107—22no—
55C2×#106—22no—
56C2×C4⋊C8—22no—
57C2×C4⋊C8C2312yes—
58C2×C4⋊C8C2312yes—
59C2×C4⋊C8C2312yes—
60C2×C4×C8—22no—
61C2×C4×C8C2311yescharacteristic
62C2×C4×C8C2311yescharacteristic
63#391—21no—
64#391—21no—
65#391—21no—
66#389—21no—
67#389—21no—
68#389—21no—
69#389—21no—
70#389—21no—
71#389D412yes—
72#384D411yescharacteristic
73#384C2311yescharacteristic
74#384C2311yescharacteristic
75C4×C4⋊C4—21no—
76C4×C4⋊C4—21no—
77C4×C4⋊C4—21no—
78C4×C4⋊C4—21no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4C2312yes—
81C43C2311yescharacteristic
82#340—22no—
83#340—22no—
84#340—22no—
85#340—22no—
86#340—22no—
87#340—22no—
88#340—22no—
89#340—22no—
90#340—22no—
91#336—22no—
92#336—22no—
93#336—21no—
94#336—21no—
95#336—21no—
96#336—21no—
97#336—21no—
98#336—21no—
99#336D412yes—
100#336D412yes—
101#333—24no—
102#333—24no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—21no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8C2×D412yes—
110C22×C8C2×D412yes—
111C4⋊Q8—24no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—21no—
115C4⋊Q8—21no—
116C4⋊Q8—21no—
117C4⋊Q8—21no—
118C4⋊Q8#4112yes—
119C4⋊Q8#4112yes—
120C4×Q8—82no—
121C4×Q8—82no—
122C4×Q8—82no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4C2×D412yes—
140C2×C4⋊C4C2×D412yes—
141C2×C42—22no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150C2×C42C2411yescharacteristic
151#107—28no—
152#107—44no—
153#106—44no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—82no—
161C4×C8—21no—
162C4×C8—21no—
163C4×C8—21no—
164C4×C8—21no—
165C4×C8—82no—
166#95—22no—
167#95—22no—
168#95—41no—
169#95—41no—
170#95—41no—
171#95—41no—
172C2×Q8—24no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—81no—
178C2×Q8—81no—
179C2×Q8—81no—
180C2×Q8—81no—
181C2×Q8—81no—
182C2×Q8—81no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4#12111yescharacteristic
190C22×C4#12111yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4#12111yescharacteristic
193C22×C4C22×D411yescharacteristic
194C22×C4C22×D411yescharacteristic
195C22×C4C2×#4111yescharacteristic
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—81no—
227C4⋊C4—82no—
228C4⋊C4—81no—
229C4⋊C4—81no—
230C4⋊C4—81no—
231C4⋊C4—82no—
232C4⋊C4—82no—
233C4⋊C4#13514yes—
234C42—22no—
235C42—22no—
236C42—22no—
237C42—22no—
238C42—41no—
239C42—41no—
240C42—42no—
241C42—42no—
242C42—82no—
243C42—82no—
244C42C2×#4111yescharacteristic
245C42C2×#4111yescharacteristic
246C422−1+411yescharacteristic
247C422−1+411yescharacteristic
248C23C2×#12111yescharacteristic
249Q8—82no—
250Q8—82no—
251Q8—82no—
252Q8—82no—
253Q8—84no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—24no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4#52511yescharacteristic
287C2×C4#53611yescharacteristic
288C2×C4#54811yescharacteristic
289C2×C4#54811yescharacteristic
290C2×C4#55211yescharacteristic
291C2×C4#55211yescharacteristic
292C2×C4C2×#13512yes—
293C2×C4#57712yes—
294C2×C4#57812yes—
295C2×C4#57812yes—
296C8—42no—
297C8—42no—
298C8—82no—
299C8—82no—
300C8—82no—
301C22#253611yescharacteristic
302C22#304211yescharacteristic
303C22#304411yescharacteristic
304C22#305011yescharacteristic
305C22#305911yescharacteristic
306C22#306811yescharacteristic
307C22#306811yescharacteristic
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—44no—
314C4—41no—
315C4—82no—
316C4—82no—
317C4—82no—
318C4—161no—
319C4—161no—
320C4#312112yes—
321C4#324212yes—
322C4#336412yes—
323C4#336412yes—
324C2#1939411yescharacteristic
325C2#1940611yescharacteristic
326C2#1951511yescharacteristic
327C2#1953111yescharacteristic
328C2#2819011yescharacteristic
329C2#2821311yescharacteristic
330C2#2822011yescharacteristic
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
#292772
#292732
#223072
#222482
#106552
#105432
#95682
#95672
#87882
#85942