Finite Group Databasebeta

← #120246

Subgroups — #120246

Order 512.

502 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21351C211yesmaximal, characteristic
2C2×#1568C211yesmaximal, characteristic
3C4×#341C211yesmaximal, characteristic
4#8035C212yesmaximal
5C2×#1291C212yesmaximal
6C2×#432C2212yes—
7C2×#432C2211yescharacteristic
8C2×C4×M16C2212yes—
9C22×C4×C8C2211yescharacteristic
10#2283C2211yescharacteristic
11#1939C411yescharacteristic
12#1939C411yescharacteristic
13#1939C411yescharacteristic
14#1939C411yescharacteristic
15#1850—21no—
16#1850—21no—
17#1768—21no—
18#1768—21no—
19C2×#341—21no—
20C2×#341—21no—
21#1568—24no—
22C2×#335—21no—
23C2×#334—21no—
24#1295—22no—
25#1295—22no—
26#1291—24no—
27C22×M16—22no—
28C23×C8D411yescharacteristic
29C23×C8D411yescharacteristic
30C22×C42C2311yescharacteristic
31#432—22no—
32#432—22no—
33#432—22no—
34#432—22no—
35#432—22no—
36#432D414yes—
37C2×C4⋊C8—22no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8C2×C411yescharacteristic
43C2×C4⋊C8C2×C411yescharacteristic
44C2×C22⋊C8—22no—
45C2×C22⋊C8—21no—
46C4×M16—22no—
47C4×M16—22no—
48C4×M16—22no—
49C4×M16Q814yes—
50C2×#97—22no—
51C2×#97—22no—
52C2×#97—21no—
53C2×C4×C8—22no—
54C2×C4×C8—22no—
55C2×C4×C8—22no—
56C2×C4×C8C2×C411yescharacteristic
57C2×C4×C8C2×C411yescharacteristic
58C2×C4×C8D411yescharacteristic
59C2×C4×C8D411yescharacteristic
60#383—21no—
61#382D411yescharacteristic
62#382D411yescharacteristic
63#381—21no—
64#380Q811yescharacteristic
65#380Q811yescharacteristic
66C4×C4⋊C4C2×C411yescharacteristic
67C4×C4⋊C4C2×C411yescharacteristic
68C4×C22⋊C4—21no—
69#376—21no—
70#341—24no—
71#341—24no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#335—24no—
77#334—24no—
78C23×C4C2×D411yescharacteristic
79C23×C4C2×Q811yescharacteristic
80C23×C4#4111yescharacteristic
81C2×M16—24no—
82C2×M16—24no—
83C2×M16—24no—
84C2×M16—42no—
85C2×M16—42no—
86C2×M16—42no—
87C22×C8—22no—
88C22×C8—22no—
89C22×C8—22no—
90C22×C8—22no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—41no—
94C22×C8—41no—
95C22×C8—42no—
96C22×C8—42no—
97C22×C8C22⋊C411yescharacteristic
98C22×C8C22⋊C411yescharacteristic
99C22×C8C22⋊C411yescharacteristic
100C22×C8C22⋊C411yescharacteristic
101C2×C4⋊C4C4⋊C411yescharacteristic
102C2×C4⋊C4C4⋊C411yescharacteristic
103C2×C4⋊C4C4⋊C411yescharacteristic
104C2×C4⋊C4C4⋊C411yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107C2×C42—21no—
108C2×C42—21no—
109C2×C42C22×C411yescharacteristic
110C2×C42C2×D412yes—
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×Q812yes—
114C2×C42#4112yes—
115C2×C42#4112yes—
116C2×C42#4111yescharacteristic
117C4⋊C8—22no—
118C4⋊C8—22no—
119C4⋊C8—24no—
120C4⋊C8—42no—
121C4⋊C8—42no—
122C4⋊C8—42no—
123C4⋊C8—42no—
124C4⋊C8—42no—
125C22⋊C8—24no—
126C22⋊C8—42no—
127C22⋊C8—42no—
128#97—24no—
129#97—24no—
130#97—41no—
131#97—42no—
132#97—42no—
133#97—41no—
134C4×C8—22no—
135C4×C8—22no—
136C4×C8—21no—
137C4×C8—21no—
138C4×C8—24no—
139C4×C8—21no—
140C4×C8—21no—
141C4×C8—42no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—21no—
150C24C22⋊Q811yescharacteristic
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4C2×C22⋊C411yescharacteristic
164C22×C4C2×C4⋊C411yescharacteristic
165C22×C4#11711yescharacteristic
166C22×C4#12112yes—
167C22×C4#12111yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4C22⋊Q812yes—
170C22×C4C22⋊Q811yescharacteristic
171C22×C4#12312yes—
172C22×C4#12512yes—
173C22×C4#12512yes—
174C22×C4C4⋊Q812yes—
175M16—28no—
176M16—44no—
177M16—44no—
178M16—44no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—44no—
190C2×C8—44no—
191C2×C8—44no—
192C2×C8—44no—
193C2×C8—44no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—44no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—82no—
202C2×C8—82no—
203C2×C8#10412yes—
204C2×C8#10412yes—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C42—41no—
212C42—41no—
213C42—41no—
214C42—41no—
215C42C4×D412yes—
216C42C4×Q812yes—
217C42#12011yescharacteristic
218C42#12112yes—
219C42C22⋊Q812yes—
220C42C22⋊Q812yes—
221C42#12311yescharacteristic
222C42#12411yescharacteristic
223C42#12612yes—
224C42C4⋊Q811yescharacteristic
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23—21no—
231C23#38011yescharacteristic
232C23#39812yes—
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—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4#38611yescharacteristic
264C2×C4#38712yes—
265C2×C4#38912yes—
266C2×C4#39111yescharacteristic
267C2×C4#39411yescharacteristic
268C2×C4#39511yescharacteristic
269C2×C4#39612yes—
270C2×C4#39811yescharacteristic
271C2×C4#40011yescharacteristic
272C2×C4C2×#10411yescharacteristic
273C2×C4C2×#10411yescharacteristic
274C2×C4#42111yescharacteristic
275C2×C4#42111yescharacteristic
276C8—22no—
277C8—22no—
278C8—48no—
279C8—41no—
280C8—41no—
281C8—84no—
282C8—81no—
283C8—81no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22#144111yescharacteristic
292C22#180611yescharacteristic
293C22#180611yescharacteristic
294C22#181311yescharacteristic
295C22#181311yescharacteristic
296C22#181411yescharacteristic
297C22#181411yescharacteristic
298C4—22no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—22no—
304C4—21no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—81no—
309C4#187111yescharacteristic
310C4#187111yescharacteristic
311C4#199411yescharacteristic
312C4#199511yescharacteristic
313C2—42no—
314C2#869011yescharacteristic
315C2#869111yescharacteristic
316C2#869211yescharacteristic
317C2#869311yescharacteristic
318C2#1120911yescharacteristic
319C2#1123011yescharacteristic
320C2#1124111yescharacteristic
subgroupG/H
center, socleC23#380
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#213512
C2×#15682
C4×#3412
#80352
C2×#12912