Finite Group Databasebeta

← #331562

Subgroups — #331562

Order 512.

626 conjugacy classes of subgroups.

The subgroup lattice has 325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33316C211yesmaximal, characteristic
2#33293C211yesmaximal, characteristic
3#33289C211yesmaximal, characteristic
4#33278C211yesmaximal, characteristic
5#30305C211yesmaximal, characteristic
6#30205C211yesmaximal, characteristic
7#10681C212yesmaximal
8#10681C212yesmaximal
9#10680C212yesmaximal
10#10675C212yesmaximal
11#8132C211yesmaximal, characteristic
12C2×#501—22no—
13#2868C2211yescharacteristic
14#2868C2211yescharacteristic
15#2862C2211yescharacteristic
16#2859C2211yescharacteristic
17#2084—22no—
18#2072—22no—
19#2058—22no—
20#2024—22no—
21#1993—22no—
22#1990—22no—
23#1990—22no—
24#1990C2212yes—
25#1990C2212yes—
26#1990C2211yescharacteristic
27#1990C2212yes—
28#1990C2211yescharacteristic
29#1956C2212yes—
30#1956C2211yescharacteristic
31#1956C2211yescharacteristic
32#1933—22no—
33#1933—22no—
34#1847—22no—
35#1845C2212yes—
36#1844C2212yes—
37#1844C2212yes—
38#1836—22no—
39#1834C2212yes—
40#1834C2212yes—
41#1834C2212yes—
42#1744C2211yescharacteristic
43C4×#97C2211yescharacteristic
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—
56#501—48no—
57C2×#107—24no—
58C2×#106—24no—
59C2×#106—24no—
60C2×#103—22no—
61C2×#103—22no—
62C2×#103—24no—
63C2×#97D412yes—
64C2×#97D412yes—
65C2×C4×C8D412yes—
66C2×C4×C8D412yes—
67C2×C4×C8C2311yescharacteristic
68C2×C4×C8C2311yescharacteristic
69C2×C4×C8C2312yes—
70C2×C4×C8C2312yes—
71#391—21no—
72#391—21no—
73#391—21no—
74#391—21no—
75#389—21no—
76#389—21no—
77#389—21no—
78#389—21no—
79#384—21no—
80#384—21no—
81#384—21no—
82#384—21no—
83#384—21no—
84#384—21no—
85#384C2312yes—
86#384C2311yescharacteristic
87#384C2312yes—
88#384C2311yescharacteristic
89#382—21no—
90#382—21no—
91#382—21no—
92C43C2311yescharacteristic
93#340—24no—
94#340—24no—
95#340—24no—
96#340—24no—
97#340—24no—
98#340—24no—
99#340—22no—
100#340—22no—
101#336D412yes—
102#336D412yes—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—41no—
106C22×Q8—41no—
107C22×C8C2×D414yes—
108C22×C8C2×D412yes—
109C22×C8C2×D412yes—
110C22×C8C2×D414yes—
111C4⋊Q8—22no—
112C4⋊Q8—22no—
113C4⋊Q8—22no—
114C4⋊Q8—22no—
115C4⋊Q8—44no—
116C4⋊Q8—44no—
117C4⋊Q8—44no—
118C4⋊Q8—44no—
119C4⋊Q8—82no—
120C4⋊Q8—82no—
121#125—44no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
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—21no—
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×C4⋊C4—41no—
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2411yescharacteristic
153#107—48no—
154#106—48no—
155#106—84no—
156#103—44no—
157#103—44no—
158#103—84no—
159#97—24no—
160#97SD1618yes—
161C4×C8—22no—
162C4×C8—22no—
163C4×C8—22no—
164C4×C8—22no—
165C4×C8—22no—
166C4×C8—22no—
167C4×C8—42no—
168C4×C8—42no—
169#95—41no—
170#95—41no—
171#95—41no—
172#95—41no—
173#95—41no—
174#95—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—82no—
183C2×Q8—82no—
184C2×Q8—82no—
185C2×Q8—82no—
186C2×Q8—82no—
187C2×Q8—82no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4#12711yescharacteristic
195C22×C4#12711yescharacteristic
196C22×C4#12711yescharacteristic
197C22×C4#12711yescharacteristic
198C22×C4C22×D411yescharacteristic
199C22×C4C22×D411yescharacteristic
200C22×C4C22×D411yescharacteristic
201C2×C8—24no—
202C2×C8—24no—
203C2×C8—22no—
204C2×C8—22no—
205C2×C8—24no—
206C2×C8—22no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—22no—
210C2×C8—24no—
211C2×C8—24no—
212C2×C8C2×SD1618yes—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—44no—
220C4⋊C4—42no—
221C4⋊C4—44no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—44no—
225C4⋊C4—44no—
226C4⋊C4—44no—
227C4⋊C4—42no—
228C4⋊C4—44no—
229C4⋊C4—42no—
230C4⋊C4—82no—
231C4⋊C4—82no—
232C4⋊C4—82no—
233C4⋊C4—82no—
234C4⋊C4—82no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C4⋊C4—82no—
238C42—22no—
239C42—22no—
240C42—22no—
241C42—22no—
242C42C2×SD1614yes—
243C42#13714yes—
244C422−1+412yes—
245C422−1+412yes—
246C23C2×#12711yescharacteristic
247Q8—82no—
248Q8—82no—
249Q8—84no—
250Q8—164no—
251Q8—164no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4#49212yes—
279C2×C4#49212yes—
280C2×C4#49712yes—
281C2×C4#49712yes—
282C2×C4#53612yes—
283C2×C4#53611yescharacteristic
284C2×C4#53611yescharacteristic
285C2×C4#53612yes—
286C2×C4C22×SD1612yes—
287C2×C4C2×#13712yes—
288C2×C4#57512yes—
289C2×C4#57512yes—
290C2×C4#57612yes—
291C2×C4#57812yes—
292C8—28no—
293C8—42no—
294C8—42no—
295C8—44no—
296C22#265811yescharacteristic
297C22C2×#49211yescharacteristic
298C22C2×#49711yescharacteristic
299C22#315311yescharacteristic
300C22#315311yescharacteristic
301C22#315511yescharacteristic
302C22#315611yescharacteristic
303C4—22no—
304C4—22no—
305C4—22no—
306C4—22no—
307C4—161no—
308C4—161no—
309C4—161no—
310C4—162no—
311C4—161no—
312C4—162no—
313C4#322914yes—
314C4#324012yes—
315C4#324012yes—
316C4#324314yes—
317C2#1962311yescharacteristic
318C2#1962411yescharacteristic
319C2#1968111yescharacteristic
320C2#1968211yescharacteristic
321C2#3028011yescharacteristic
322C2#3028611yescharacteristic
323C2#3028911yescharacteristic
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
#333162
#332932
#332892
#332782
#303052
#302052
#106812
#106802
#106752
#81322