Finite Group Databasebeta

← #105133

Subgroups — #105133

Order 512.

351 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29218C211yesmaximal, characteristic
2#9898C211yesmaximal, characteristic
3#9896C211yesmaximal, characteristic
4#9864C211yesmaximal, characteristic
5#9601C211yesmaximal, characteristic
6#8587C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2100—22no—
11#1990—21no—
12#1987—21no—
13#1987—21no—
14#1842C2211yescharacteristic
15#1842C2211yescharacteristic
16#1834—21no—
17C4×C4⋊C8C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C2×#335—21no—
21C2×#333—21no—
22#1296—21no—
23#1296—21no—
24#1296—21no—
25#1296—22no—
26#1279—21no—
27#1279—21no—
28#1277—21no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8D411yescharacteristic
33C2×C4×Q8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8D411yescharacteristic
42C2×C4⋊C8D411yescharacteristic
43C2×C4⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×C4×C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48#391—21no—
49#389—21no—
50#389—21no—
51#384—21no—
52#384—21no—
53#384—21no—
54#384D411yescharacteristic
55#384D412yes—
56C4×C4⋊C4—21no—
57C4×C4⋊C4—21no—
58C43C2311yescharacteristic
59#340—22no—
60#340—22no—
61#340—22no—
62#340—22no—
63#336—21no—
64#336—21no—
65#336—21no—
66#335—42no—
67#333—42no—
68C22×Q8—21no—
69C22×Q8—41no—
70C22×C8—21no—
71C22×C8—21no—
72C22×C8—21no—
73C22×C8—21no—
74C22×C8—41no—
75C22×C8—41no—
76C22×C8—41no—
77C4⋊Q8—21no—
78C4⋊Q8—21no—
79C4⋊Q8—21no—
80C4⋊Q8—41no—
81C4⋊Q8—41no—
82C4⋊Q8—41no—
83C4⋊Q8—41no—
84C4⋊Q8—81no—
85C4⋊Q8—81no—
86C4⋊Q8—82no—
87C4⋊Q8Q1612yes—
88C4×Q8—81no—
89C4×Q8—81no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C42—41no—
103C2×C42C2×D411yescharacteristic
104C2×C42C2×D411yescharacteristic
105C2×C42C2×D411yescharacteristic
106C2×C42C2×D411yescharacteristic
107C2×C42#4111yescharacteristic
108C2×C42#4111yescharacteristic
109C2×C42#4111yescharacteristic
110C4⋊C8—22no—
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8—21no—
114C4⋊C8—21no—
115C4⋊C8—21no—
116C4⋊C8—21no—
117C4⋊C8—21no—
118C4⋊C8—41no—
119C4⋊C8—42no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—81no—
129C4⋊C8Q1612yes—
130C4×C8—41no—
131C4×C8—41no—
132C4×C8—41no—
133C4×C8—41no—
134C4×C8—41no—
135C4×C8—41no—
136#95—41no—
137#95—41no—
138C2×Q8—22no—
139C2×Q8—41no—
140C2×Q8—82no—
141C2×Q8—82no—
142C2×Q8—81no—
143C2×Q8—81no—
144C2×Q8—81no—
145C2×Q8—81no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—42no—
149C22×C4#12011yescharacteristic
150C22×C4#12111yescharacteristic
151C22×C4#12111yescharacteristic
152C22×C4#12111yescharacteristic
153C22×C4#12311yescharacteristic
154C22×C4#12311yescharacteristic
155C22×C4#12411yescharacteristic
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—42no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—81no—
170C2×C8—81no—
171C2×C8—81no—
172C2×C8—81no—
173C2×C8—81no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—81no—
188C4⋊C4—82no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—82no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—41no—
203C42—81no—
204C42—81no—
205C42C2×Q1611yescharacteristic
206C42C2×Q1611yescharacteristic
207C42#13511yescharacteristic
208C42#13511yescharacteristic
209C42#13511yescharacteristic
210C42#13511yescharacteristic
211C42AGL(1,ℤ/8)11yescharacteristic
212C42AGL(1,ℤ/8)11yescharacteristic
213C42#13711yescharacteristic
214C42#13711yescharacteristic
215C42#13711yescharacteristic
216C42#13711yescharacteristic
217C23#39411yescharacteristic
218Q8—82no—
219Q8—82no—
220Q8—162no—
221Q8—162no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—82no—
235C2×C4—81no—
236C2×C4—82no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4#44911yescharacteristic
241C2×C4#44911yescharacteristic
242C2×C4#45111yescharacteristic
243C2×C4#45211yescharacteristic
244C2×C4#45411yescharacteristic
245C2×C4#45611yescharacteristic
246C2×C4#46211yescharacteristic
247C2×C4#46211yescharacteristic
248C2×C4#46311yescharacteristic
249C2×C4#46411yescharacteristic
250C2×C4#46411yescharacteristic
251C2×C4#46411yescharacteristic
252C2×C4#46711yescharacteristic
253C2×C4#46711yescharacteristic
254C2×C4#46811yescharacteristic
255C2×C4#47011yescharacteristic
256C2×C4#47111yescharacteristic
257C2×C4#47111yescharacteristic
258C2×C4#47111yescharacteristic
259C2×C4#47211yescharacteristic
260C2×C4#48411yescharacteristic
261C2×C4#48511yescharacteristic
262C2×C4#48811yescharacteristic
263C2×C4#48911yescharacteristic
264C8—42no—
265C8—82no—
266C8—81no—
267C8—81no—
268C8—81no—
269C8—161no—
270C8—161no—
271C22#203611yescharacteristic
272C22#203811yescharacteristic
273C22#204211yescharacteristic
274C22#204611yescharacteristic
275C22#204811yescharacteristic
276C22#205111yescharacteristic
277C22#205611yescharacteristic
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—41no—
285C4—82no—
286C4—162no—
287C4—161no—
288C4#162811yescharacteristic
289C4#163611yescharacteristic
290C4#164811yescharacteristic
291C4#165211yescharacteristic
292C4#167611yescharacteristic
293C4#168311yescharacteristic
294C4#168411yescharacteristic
295C4#168411yescharacteristic
296C4#169211yescharacteristic
297C4#169811yescharacteristic
298C4#170311yescharacteristic
299C4#170411yescharacteristic
300C2#1042211yescharacteristic
301C2#1045311yescharacteristic
302C2#1048311yescharacteristic
303C2#1049111yescharacteristic
304C2#1050611yescharacteristic
305C2#1054111yescharacteristic
306C2#1055311yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#292182
#98982
#98962
#98642
#96012
#85872
#70312