Finite Group Databasebeta

← #331601

Subgroups — #331601

Order 512.

582 conjugacy classes of subgroups.

The subgroup lattice has 319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33290C211yesmaximal, characteristic
2#33289C211yesmaximal, characteristic
3#30305C211yesmaximal, characteristic
4#30304C211yesmaximal, characteristic
5#30205C211yesmaximal, characteristic
6#30205C211yesmaximal, characteristic
7#10684C212yesmaximal
8#10682C212yesmaximal
9#10682C212yesmaximal
10#10675C212yesmaximal
11#8133C211yesmaximal, characteristic
12#2868C2211yescharacteristic
13#2868C2211yescharacteristic
14#2862C2211yescharacteristic
15#2859C2211yescharacteristic
16#2084—22no—
17#2083—22no—
18#2072—22no—
19#2072—22no—
20#2058—22no—
21#2057—22no—
22#2024—22no—
23#2024—22no—
24#1991—22no—
25#1990—22no—
26#1990—22no—
27#1990C2211yescharacteristic
28#1990C2211yescharacteristic
29#1990C2211yescharacteristic
30#1990C2211yescharacteristic
31#1990C2212yes—
32#1990C2212yes—
33#1956C2212yes—
34#1956C2212yes—
35#1845C2212yes—
36#1844C2212yes—
37#1835—22no—
38#1834C2212yes—
39#1834C2212yes—
40#1834C2212yes—
41#1834C2212yes—
42#1744C2211yescharacteristic
43#1744C2211yescharacteristic
44C42×C8C2211yescharacteristic
45#1273C2212yes—
46#1273C2212yes—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8—21no—
49C2×C4⋊Q8—21no—
50C2×C4⋊Q8—21no—
51C2×C4⋊Q8—21no—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8C2311yescharacteristic
54C2×C4⋊Q8C2311yescharacteristic
55C2×#125—21no—
56C2×#107—24no—
57C2×#106—24no—
58C2×#103—24no—
59C2×#103—24no—
60C2×C4×C8D412yes—
61C2×C4×C8D412yes—
62C2×C4×C8C2311yescharacteristic
63C2×C4×C8C2311yescharacteristic
64C2×C4×C8C2312yes—
65C2×C4×C8C2312yes—
66#391—21no—
67#391—21no—
68#391—21no—
69#391—21no—
70#389—21no—
71#389—21no—
72#389—21no—
73#389—21no—
74#384—21no—
75#384—21no—
76#384—21no—
77#384—21no—
78#384—21no—
79#384—21no—
80#384C2311yescharacteristic
81#384C2312yes—
82#384C2312yes—
83#384C2311yescharacteristic
84#382—21no—
85#382—21no—
86#382—21no—
87C43C2311yescharacteristic
88#340—24no—
89#340—24no—
90#340—24no—
91#340—24no—
92#340—24no—
93#340—24no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#336D412yes—
99#336D412yes—
100#336D412yes—
101#336D412yes—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—41no—
105C22×Q8—41no—
106C22×C8C2×D414yes—
107C22×C8C2×D414yes—
108C22×C8C2×D412yes—
109C22×C8C2×D412yes—
110C4⋊Q8—22no—
111C4⋊Q8—22no—
112C4⋊Q8—22no—
113C4⋊Q8—22no—
114C4⋊Q8—44no—
115C4⋊Q8—44no—
116C4⋊Q8—82no—
117C4⋊Q8—82no—
118C4⋊Q8—82no—
119C4⋊Q8—82no—
120#125—44no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
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—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2411yescharacteristic
152#107—84no—
153#106—84no—
154#103—84no—
155#103—84no—
156C4×C8—24no—
157C4×C8—24no—
158C4×C8—22no—
159C4×C8—22no—
160C4×C8—22no—
161C4×C8—22no—
162C4×C8—22no—
163C4×C8—22no—
164#95—41no—
165#95—41no—
166#95—41no—
167#95—41no—
168#95—41no—
169#95—41no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—42no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—82no—
177C2×Q8—82no—
178C2×Q8—82no—
179C2×Q8—82no—
180C2×Q8—82no—
181C2×Q8—82no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4#12711yescharacteristic
189C22×C4#12711yescharacteristic
190C22×C4#12711yescharacteristic
191C22×C4#12711yescharacteristic
192C22×C4C22×D411yescharacteristic
193C22×C4C22×D411yescharacteristic
194C22×C4C22×D411yescharacteristic
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—24no—
198C2×C8—24no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—24no—
204C2×C8—24no—
205C2×C8—24no—
206C2×C8—24no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—44no—
216C4⋊C4—44no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C4⋊C4—44no—
220C4⋊C4—44no—
221C4⋊C4—42no—
222C4⋊C4—44no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—82no—
226C4⋊C4—82no—
227C4⋊C4—82no—
228C4⋊C4—82no—
229C4⋊C4—82no—
230C4⋊C4—82no—
231C4⋊C4—82no—
232C4⋊C4—82no—
233C42—22no—
234C42—22no—
235C42—22no—
236C42—22no—
237C42#13514yes—
238C42#13714yes—
239C422−1+412yes—
240C422−1+412yes—
241C23C2×#12711yescharacteristic
242Q8—84no—
243Q8—84no—
244Q8—164no—
245Q8—164no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4#49512yes—
273C2×C4#49512yes—
274C2×C4#49712yes—
275C2×C4#49712yes—
276C2×C4#53611yescharacteristic
277C2×C4#53611yescharacteristic
278C2×C4#53612yes—
279C2×C4#53612yes—
280C2×C4C2×#13512yes—
281C2×C4C2×#13712yes—
282C2×C4#57612yes—
283C2×C4#57712yes—
284C2×C4#57712yes—
285C2×C4#57812yes—
286C8—42no—
287C8—42no—
288C8—44no—
289C8—44no—
290C22#265811yescharacteristic
291C22C2×#49511yescharacteristic
292C22C2×#49711yescharacteristic
293C22#315411yescharacteristic
294C22#315411yescharacteristic
295C22#315511yescharacteristic
296C22#315611yescharacteristic
297C4—22no—
298C4—22no—
299C4—22no—
300C4—22no—
301C4—161no—
302C4—161no—
303C4—161no—
304C4—162no—
305C4—161no—
306C4—162no—
307C4#323112yes—
308C4#323112yes—
309C4#324314yes—
310C4#324414yes—
311C2#1965811yescharacteristic
312C2#1965911yescharacteristic
313C2#1970511yescharacteristic
314C2#1970611yescharacteristic
315C2#3028111yescharacteristic
316C2#3028911yescharacteristic
317C2#3029011yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#127
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
#332902
#332892
#303052
#303042
#302052
#106842
#106822
#106752
#81332