Finite Group Databasebeta

← #330772

Subgroups — #330772

Order 512.

506 conjugacy classes of subgroups.

The subgroup lattice has 337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2#33073C212yesmaximal
3#21339C211yesmaximal, characteristic
4#10658C212yesmaximal
5#10651C211yesmaximal, characteristic
6#10650C211yesmaximal, characteristic
7#10626C212yesmaximal
8#10618C211yesmaximal, characteristic
9#10617C211yesmaximal, characteristic
10#9901C212yesmaximal
11#8785C211yesmaximal, characteristic
12#2859C2212yes—
13C42×Q8C2211yescharacteristic
14#1984C2211yescharacteristic
15#1984C2211yescharacteristic
16#1948C2212yes—
17#1947C2212yes—
18#1942—21no—
19#1942—21no—
20#1942—21no—
21#1942—21no—
22#1939C2211yescharacteristic
23#1939C2211yescharacteristic
24#1920—22no—
25#1918—22no—
26#1916—21no—
27#1916—21no—
28#1865—22no—
29#1863—22no—
30#1845C2211yescharacteristic
31#1845C2211yescharacteristic
32#1834C2212yes—
33#1831C2212yes—
34#1803C2212yes—
35#1803C2212yes—
36C4×C4⋊C8—21no—
37C4×C4⋊C8C2211yescharacteristic
38#1744—21no—
39C42×C8C2211yescharacteristic
40#1296C2212yes—
41#1296C2212yes—
42#1296C2212yes—
43#1296C2212yes—
44#1277C2211yescharacteristic
45#1277C2211yescharacteristic
46#1277C2212yes—
47C2×#125—22no—
48C2×C4×Q8D411yescharacteristic
49C2×C4×Q8D411yescharacteristic
50C2×C4×Q8C2311yescharacteristic
51C2×#107—21no—
52C2×#107—21no—
53C2×#107—21no—
54C2×#107—21no—
55C2×#107—22no—
56C2×#106—22no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8C2312yes—
60C2×C4⋊C8C2312yes—
61C2×C4⋊C8C2311yescharacteristic
62C2×C4⋊C8C2311yescharacteristic
63C2×#103—22no—
64C2×#103—22no—
65C2×C4×C8—21no—
66C2×C4×C8D411yescharacteristic
67C2×C4×C8D411yescharacteristic
68C2×C4×C8D411yescharacteristic
69C2×C4×C8D411yescharacteristic
70C2×C4×C8C2311yescharacteristic
71C2×C4×C8C2311yescharacteristic
72#389—22no—
73#389—22no—
74#389—22no—
75#389—22no—
76#384C2312yes—
77#384C2312yes—
78#382—22no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—21no—
81C4×C4⋊C4—21no—
82C4×C4⋊C4D411yescharacteristic
83C4×C4⋊C4D411yescharacteristic
84C4×C4⋊C4C2311yescharacteristic
85C43—21no—
86C43C2311yescharacteristic
87#340—22no—
88#340—22no—
89#340—22no—
90#340—22no—
91#340—22no—
92#340—22no—
93#336—21no—
94#336—21no—
95#336—21no—
96#336—21no—
97#336—21no—
98#336—21no—
99#336—22no—
100#336—22no—
101#336—21no—
102C22×Q8C2×D411yescharacteristic
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8C2×D411yescharacteristic
108C22×C8C2×D411yescharacteristic
109C22×C8C2×D411yescharacteristic
110C22×C8C2×D411yescharacteristic
111#125—84no—
112C4×Q8—22no—
113C4×Q8—22no—
114C4×Q8—22no—
115C4×Q8—22no—
116C4×Q8—42no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
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—42no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4C2×D411yescharacteristic
129C2×C4⋊C4C2×D411yescharacteristic
130C2×C4⋊C4C2×D411yescharacteristic
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—21no—
136C2×C42—21no—
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42#4111yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42C2411yescharacteristic
144#107—44no—
145#107—42no—
146#107—42no—
147#107—42no—
148#107—42no—
149#106—44no—
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—42no—
157C4⋊C8—42no—
158#103—44no—
159#103—44no—
160C4×C8—22no—
161C4×C8—22no—
162C4×C8—22no—
163C4×C8—22no—
164C4×C8—41no—
165C4×C8—41no—
166C4×C8—42no—
167#95—21no—
168#95—21no—
169#95—21no—
170#95—42no—
171#95—42no—
172C2×Q8—21no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8#13512yes—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4#12111yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4#12111yescharacteristic
186C22×C4C22×D411yescharacteristic
187C22×C4C22×D411yescharacteristic
188C22×C4C2×#4111yescharacteristic
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—42no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8—41no—
205C2×C8—42no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—42no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8#13512yes—
212C2×C8#13712yes—
213C4⋊C4—24no—
214C4⋊C4—21no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—82no—
228C4⋊C4—82no—
229C4⋊C4—84no—
230C4⋊C4—84no—
231C4⋊C4#13512yes—
232C42—24no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—22no—
240C42—22no—
241C42—22no—
242C42—42no—
243C42—41no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—42no—
248C42—42no—
249C422−1+412yes—
250C422−1+412yes—
251C23C2×#12111yescharacteristic
252Q8—24no—
253Q8—42no—
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—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4#47212yes—
285C2×C4#47312yes—
286C2×C4#53611yescharacteristic
287C2×C4#53612yes—
288C2×C4#53611yescharacteristic
289C2×C4#54112yes—
290C2×C4C2×#13511yescharacteristic
291C2×C4C2×#13511yescharacteristic
292C2×C4C2×#13511yescharacteristic
293C2×C4C2×#13711yescharacteristic
294C2×C4#57512yes—
295C2×C4#57511yescharacteristic
296C2×C4#57511yescharacteristic
297C8—22no—
298C8—22no—
299C8—41no—
300C8—41no—
301C8—81no—
302C8—82no—
303C8—82no—
304C8—81no—
305C22#262111yescharacteristic
306C22#303511yescharacteristic
307C22#303711yescharacteristic
308C22#305011yescharacteristic
309C22#305411yescharacteristic
310C22C2×#47211yescharacteristic
311C22C2×#47311yescharacteristic
312C4—22no—
313C4—22no—
314C4—22no—
315C4—42no—
316C4—41no—
317C4—42no—
318C4—41no—
319C4—81no—
320C4—81no—
321C4—162no—
322C4—162no—
323C4#323111yescharacteristic
324C4#323211yescharacteristic
325C4#323212yes—
326C4#323312yes—
327C4#323611yescharacteristic
328C4#324011yescharacteristic
329C2#1912911yescharacteristic
330C2#1916011yescharacteristic
331C2#1926411yescharacteristic
332C2#1929011yescharacteristic
333C2#2987111yescharacteristic
334C2#2987911yescharacteristic
335C2#2988611yescharacteristic
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
#332582
#330732
#213392
#106582
#106512
#106502
#106262
#106182
#106172
#99012
#87852