Finite Group Databasebeta

← #99489

Subgroups — #99489

Order 512.

337 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22723C211yesmaximal, characteristic
2#9604C211yesmaximal, characteristic
3#8787C211yesmaximal, characteristic
4#8568C211yesmaximal, characteristic
5#7562C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#446—21no—
9#2295C2211yescharacteristic
10#1940—21no—
11#1940—21no—
12#1939—21no—
13#1843—21no—
14#1842C2211yescharacteristic
15#1842C2211yescharacteristic
16#1768—21no—
17#1767C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20#1744C2211yescharacteristic
21C2×#335—21no—
22C2×Q8⋊C8—21no—
23#1279—21no—
24#1277—21no—
25#1277—21no—
26#1277—21no—
27#1272C411yescharacteristic
28#1272C411yescharacteristic
29#1271C411yescharacteristic
30#1271C411yescharacteristic
31C2×C4×Q8D411yescharacteristic
32#446—42no—
33#446—42no—
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⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×#97—21no—
50C2×#97—21no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55#391C2×C411yescharacteristic
56#391Q811yescharacteristic
57#389C2×C411yescharacteristic
58#389Q811yescharacteristic
59#387—21no—
60#387—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4D411yescharacteristic
63#376—21no—
64C43C2311yescharacteristic
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336C2×C411yescharacteristic
71#336C2×C411yescharacteristic
72#336C2×C411yescharacteristic
73#336C2×C411yescharacteristic
74#335—42no—
75Q8⋊C8—42no—
76C22×Q8C4⋊C411yescharacteristic
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—41no—
86C22×C8—41no—
87C4×Q8—21no—
88C4×Q8—21no—
89C4×Q8D812yes—
90C4×Q8Q1612yes—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4C4⋊C411yescharacteristic
95C2×C4⋊C4C4⋊C411yescharacteristic
96C2×C4⋊C4C4⋊C411yescharacteristic
97C2×C42—21no—
98C2×C42—21no—
99C2×C42C22×C411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42C2×D411yescharacteristic
103C2×C42C2×Q811yescharacteristic
104C2×C42#4111yescharacteristic
105C2×C42#4111yescharacteristic
106C4⋊C8—22no—
107C4⋊C8—21no—
108C4⋊C8—21no—
109C4⋊C8—21no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113C4⋊C8—42no—
114C4⋊C8—42no—
115C4⋊C8—42no—
116C4⋊C8—42no—
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—81no—
126C4⋊C8—81no—
127C4⋊C8SD1612yes—
128#97—42no—
129#97—41no—
130#97—41no—
131C4×C8—41no—
132C4×C8—41no—
133C4×C8—42no—
134C4×C8—41no—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8—41no—
138#95—21no—
139#95—21no—
140#95—21no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145C2×Q8—21no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8#10712yes—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4C2×C4⋊C411yescharacteristic
154C22×C4C4×D411yescharacteristic
155C22×C4C4×D411yescharacteristic
156C22×C4#12011yescharacteristic
157C22×C4C22⋊Q811yescharacteristic
158C22×C4C22⋊Q811yescharacteristic
159C22×C4#12311yescharacteristic
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
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—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C4⋊C4—21no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—81no—
198C4⋊C4#10712yes—
199C42—21no—
200C42—21no—
201C42—22no—
202C42—22no—
203C42—21no—
204C42—21no—
205C42—41no—
206C42—41no—
207C42—41no—
208C42—41no—
209C42—41no—
210C42C2×D811yescharacteristic
211C42C2×SD1611yescharacteristic
212C42C2×Q1611yescharacteristic
213C42#13511yescharacteristic
214C42AGL(1,ℤ/8)11yescharacteristic
215C42#13711yescharacteristic
216C42#13711yescharacteristic
217C42#13711yescharacteristic
218C23#38511yescharacteristic
219Q8—42no—
220Q8—81no—
221C2×C4—21no—
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—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4C2×#10711yescharacteristic
247C2×C4#42811yescharacteristic
248C2×C4C4×SD1611yescharacteristic
249C2×C4#44111yescharacteristic
250C2×C4#44311yescharacteristic
251C2×C4#44411yescharacteristic
252C2×C4#44711yescharacteristic
253C2×C4#44811yescharacteristic
254C2×C4#45111yescharacteristic
255C2×C4#45211yescharacteristic
256C2×C4#45411yescharacteristic
257C2×C4#45511yescharacteristic
258C2×C4#47511yescharacteristic
259C2×C4#47911yescharacteristic
260C2×C4#48011yescharacteristic
261C2×C4#48411yescharacteristic
262C8—42no—
263C8—42no—
264C8—81no—
265C8—81no—
266C8—81no—
267C8—82no—
268C8—81no—
269C8—81no—
270C8—81no—
271C8—161no—
272C22#185211yescharacteristic
273C22#185811yescharacteristic
274C22#186011yescharacteristic
275C22#186111yescharacteristic
276C22#186511yescharacteristic
277C22#186611yescharacteristic
278C22#186811yescharacteristic
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—41no—
292C4—81no—
293C4—81no—
294C4#162711yescharacteristic
295C4#163611yescharacteristic
296C4#164111yescharacteristic
297C4#164511yescharacteristic
298C2#886111yescharacteristic
299C2#887711yescharacteristic
300C2#888111yescharacteristic
301C2#889211yescharacteristic
302C2#890211yescharacteristic
303C2#891711yescharacteristic
304C2#893111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#385
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
#227232
#96042
#87872
#85682
#75622
#70312
#70272