Finite Group Databasebeta

← #105107

Subgroups — #105107

Order 512.

369 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#28717C211yesmaximal, characteristic
2#9896C211yesmaximal, characteristic
3#9896C211yesmaximal, characteristic
4#9865C211yesmaximal, characteristic
5#9601C211yesmaximal, characteristic
6#8586C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#487—21no—
9#2868C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2072—22no—
12#1990—21no—
13#1842C2211yescharacteristic
14#1842C2211yescharacteristic
15#1803—21no—
16#1803—21no—
17C4×C4⋊C8C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C2×#335—21no—
21C2×#332—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—
34#487—42no—
35#487—42no—
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⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×#103—22no—
48C2×#103—22no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384D411yescharacteristic
59#384D412yes—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C43C2311yescharacteristic
63#340—22no—
64#340—22no—
65#336—21no—
66#336—21no—
67#336—21no—
68#335—42no—
69#332—42no—
70C22×Q8—21no—
71C22×Q8—41no—
72C22×C8—21no—
73C22×C8—21no—
74C22×C8—21no—
75C22×C8—21no—
76C22×C8—41no—
77C22×C8—41no—
78C22×C8—41no—
79C4⋊Q8—21no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—41no—
83C4⋊Q8—41no—
84C4⋊Q8—41no—
85C4⋊Q8—41no—
86C4⋊Q8—81no—
87C4⋊Q8—81no—
88C4⋊Q8—82no—
89C4⋊Q8D812yes—
90C4×Q8—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—41no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C42—41no—
107C2×C42C2×D411yescharacteristic
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113C2×C42#4111yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—21no—
116C4⋊C8—21no—
117C4⋊C8—21no—
118C4⋊C8—21no—
119C4⋊C8—21no—
120C4⋊C8—21no—
121C4⋊C8—21no—
122C4⋊C8—41no—
123C4⋊C8—42no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—81no—
133C4⋊C8Q1612yes—
134#103—44no—
135#103—44no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8—41no—
141C4×C8—41no—
142#95—41no—
143#95—41no—
144C2×Q8—22no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—82no—
151C2×Q8—82no—
152C2×Q8—81no—
153C2×Q8—81no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4#12011yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12311yescharacteristic
162C22×C4#12311yescharacteristic
163C22×C4#12411yescharacteristic
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—42no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—81no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—41no—
212C42—81no—
213C42—81no—
214C42C2×D811yescharacteristic
215C42C2×Q1611yescharacteristic
216C42#13511yescharacteristic
217C42#13511yescharacteristic
218C42#13511yescharacteristic
219C42#13511yescharacteristic
220C42AGL(1,ℤ/8)11yescharacteristic
221C42AGL(1,ℤ/8)11yescharacteristic
222C42#13711yescharacteristic
223C42#13711yescharacteristic
224C42#13711yescharacteristic
225C42#13711yescharacteristic
226C23#39411yescharacteristic
227Q8—42no—
228Q8—42no—
229Q8—81no—
230Q8—81no—
231Q8—162no—
232Q8—162no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—82no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4—81no—
250C2×C4—82no—
251C2×C4#44711yescharacteristic
252C2×C4#44911yescharacteristic
253C2×C4#45211yescharacteristic
254C2×C4#45211yescharacteristic
255C2×C4#45411yescharacteristic
256C2×C4#45611yescharacteristic
257C2×C4#46211yescharacteristic
258C2×C4#46211yescharacteristic
259C2×C4#46311yescharacteristic
260C2×C4#46411yescharacteristic
261C2×C4#46411yescharacteristic
262C2×C4#46411yescharacteristic
263C2×C4#46611yescharacteristic
264C2×C4#46711yescharacteristic
265C2×C4#46811yescharacteristic
266C2×C4#47011yescharacteristic
267C2×C4#47111yescharacteristic
268C2×C4#47111yescharacteristic
269C2×C4#47111yescharacteristic
270C2×C4#47311yescharacteristic
271C2×C4#48011yescharacteristic
272C2×C4#48211yescharacteristic
273C2×C4#48811yescharacteristic
274C2×C4#48911yescharacteristic
275C8—42no—
276C8—82no—
277C8—81no—
278C8—81no—
279C8—81no—
280C8—161no—
281C8—161no—
282C22#203311yescharacteristic
283C22#203811yescharacteristic
284C22#204211yescharacteristic
285C22#204611yescharacteristic
286C22#204811yescharacteristic
287C22#205211yescharacteristic
288C22#205611yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—41no—
296C4—82no—
297C4—161no—
298C4—162no—
299C4#162511yescharacteristic
300C4#163811yescharacteristic
301C4#164711yescharacteristic
302C4#165211yescharacteristic
303C4#167411yescharacteristic
304C4#168211yescharacteristic
305C4#168311yescharacteristic
306C4#168411yescharacteristic
307C4#169211yescharacteristic
308C4#170011yescharacteristic
309C4#170311yescharacteristic
310C4#170411yescharacteristic
311C2#1041611yescharacteristic
312C2#1044211yescharacteristic
313C2#1047811yescharacteristic
314C2#1049411yescharacteristic
315C2#1050611yescharacteristic
316C2#1054111yescharacteristic
317C2#1055111yescharacteristic
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
#287172
#98962
#98652
#96012
#85862
#70312