Finite Group Databasebeta

← #105000

Subgroups — #105000

Order 512.

356 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29290C211yesmaximal, characteristic
2#9870C211yesmaximal, characteristic
3#9870C211yesmaximal, characteristic
4#8784C211yesmaximal, characteristic
5#8587C211yesmaximal, characteristic
6#8587C211yesmaximal, characteristic
7#7050C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2087—22no—
11#1987—21no—
12#1987—21no—
13#1947—21no—
14#1947—21no—
15#1842C2211yescharacteristic
16#1842C2211yescharacteristic
17#1842C2211yescharacteristic
18#1842C2211yescharacteristic
19C42×C8C2211yescharacteristic
20C2×#333—21no—
21C2×#333—21no—
22#1296—21no—
23#1296—21no—
24#1279—21no—
25#1279—21no—
26#1279—21no—
27#1279—21no—
28#1277—22no—
29C2×C4⋊Q8D411yescharacteristic
30C2×C4⋊Q8D411yescharacteristic
31C2×C4×Q8—21no—
32C2×C4×Q8—21no—
33C2×#107—22no—
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⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D412yes—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8D411yescharacteristic
49C2×C4×C8D411yescharacteristic
50#391—21no—
51#391—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#384D411yescharacteristic
57#384D411yescharacteristic
58C4×C4⋊C4—21no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C43C2311yescharacteristic
63#340—22no—
64#340—22no—
65#340—22no—
66#333—42no—
67#333—42no—
68C22×Q8—21no—
69C22×Q8—21no—
70C22×C8—21no—
71C22×C8—21no—
72C22×C8—22no—
73C22×C8—41no—
74C22×C8—41no—
75C22×C8—41no—
76C4⋊Q8—21no—
77C4⋊Q8—21no—
78C4⋊Q8—21no—
79C4⋊Q8—21no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8SD1612yes—
83C4⋊Q8Q1612yes—
84C4×Q8—81no—
85C4×Q8—81no—
86C4×Q8—81no—
87C4×Q8—81no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C42—41no—
101C2×C42—41no—
102C2×C42C2×D411yescharacteristic
103C2×C42C2×D411yescharacteristic
104C2×C42C2×D411yescharacteristic
105C2×C42C2×D411yescharacteristic
106C2×C42#4111yescharacteristic
107C2×C42#4111yescharacteristic
108C2×C42#4111yescharacteristic
109#107—82no—
110C4⋊C8—42no—
111C4⋊C8—42no—
112C4⋊C8—41no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
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⋊C8—81no—
130C4×C8—21no—
131C4×C8—21no—
132C4×C8—21no—
133C4×C8—41no—
134C4×C8—41no—
135C4×C8—42no—
136C4×C8Q1612yes—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—81no—
146C2×Q8—81no—
147C2×Q8—81no—
148C2×Q8—81no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4#12011yescharacteristic
154C22×C4#12111yescharacteristic
155C22×C4#12111yescharacteristic
156C22×C4#12111yescharacteristic
157C22×C4#12311yescharacteristic
158C22×C4#12311yescharacteristic
159C22×C4#12411yescharacteristic
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—81no—
170C2×C8—81no—
171C2×C8—81no—
172C2×C8—81no—
173C2×C8—81no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—41no—
205C42—81no—
206C42—81no—
207C42—81no—
208C42—81no—
209C42C2×SD1611yescharacteristic
210C42C2×Q1611yescharacteristic
211C42C2×Q1611yescharacteristic
212C42#13511yescharacteristic
213C42#13511yescharacteristic
214C42#13511yescharacteristic
215C42AGL(1,ℤ/8)11yescharacteristic
216C42#13711yescharacteristic
217C42#13711yescharacteristic
218C42#13711yescharacteristic
219C42#13711yescharacteristic
220C42#13711yescharacteristic
221C23#39411yescharacteristic
222Q8—82no—
223Q8—82no—
224Q8—82no—
225Q8—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4#44811yescharacteristic
248C2×C4#44911yescharacteristic
249C2×C4#45111yescharacteristic
250C2×C4#45211yescharacteristic
251C2×C4#45411yescharacteristic
252C2×C4#45511yescharacteristic
253C2×C4#46211yescharacteristic
254C2×C4#46211yescharacteristic
255C2×C4#46411yescharacteristic
256C2×C4#46411yescharacteristic
257C2×C4#46511yescharacteristic
258C2×C4#46711yescharacteristic
259C2×C4#46711yescharacteristic
260C2×C4#46811yescharacteristic
261C2×C4#47011yescharacteristic
262C2×C4#47011yescharacteristic
263C2×C4#47111yescharacteristic
264C2×C4#47111yescharacteristic
265C2×C4#47211yescharacteristic
266C2×C4#47211yescharacteristic
267C2×C4#48311yescharacteristic
268C2×C4#48411yescharacteristic
269C2×C4#48511yescharacteristic
270C2×C4#48511yescharacteristic
271C8—42no—
272C8—42no—
273C8—82no—
274C8—161no—
275C8—161no—
276C8—161no—
277C22#203511yescharacteristic
278C22#203611yescharacteristic
279C22#204011yescharacteristic
280C22#205011yescharacteristic
281C22#205111yescharacteristic
282C22#205111yescharacteristic
283C22#205611yescharacteristic
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4—161no—
294C4—161no—
295C4#162611yescharacteristic
296C4#163611yescharacteristic
297C4#164011yescharacteristic
298C4#164511yescharacteristic
299C4#167211yescharacteristic
300C4#167611yescharacteristic
301C4#167811yescharacteristic
302C4#168411yescharacteristic
303C4#169211yescharacteristic
304C4#169611yescharacteristic
305C4#169811yescharacteristic
306C4#170411yescharacteristic
307C2#1043811yescharacteristic
308C2#1046011yescharacteristic
309C2#1046111yescharacteristic
310C2#1048211yescharacteristic
311C2#1048311yescharacteristic
312C2#1052311yescharacteristic
313C2#1053111yescharacteristic
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
#292902
#98702
#87842
#85872
#70502