Finite Group Databasebeta

← #504065

Subgroups — #504065

Order 512.

472 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28737C211yesmaximal, characteristic
2#22727C211yesmaximal, characteristic
3#13529C212yesmaximal
4#13483C212yesmaximal
5#13263C211yesmaximal, characteristic
6#13253C211yesmaximal, characteristic
7#13203C211yesmaximal, characteristic
8#13176C211yesmaximal, characteristic
9#13133C212yesmaximal
10#13132C212yesmaximal
11C4×#367C211yesmaximal, characteristic
12C2×#494C2211yescharacteristic
13C2×C8×Q8C2211yescharacteristic
14#2568—21no—
15#2355—21no—
16C2×#367C2211yescharacteristic
17C2×#367C2211yescharacteristic
18C2×#366C2212yes—
19C2×C4⋊C16C2211yescharacteristic
20C2×#358C2212yes—
21C2×#358C2212yes—
22C2×#358C2212yes—
23C2×#358C2212yes—
24C2×C4×C16C2211yescharacteristic
25#2056—22no—
26#1981—21no—
27#1969C2212yes—
28#1969C2212yes—
29#1949—22no—
30#1948—21no—
31#1846C2212yes—
32#1845C2211yescharacteristic
33C4×#107C2211yescharacteristic
34C4×#107C2212yes—
35C4×#107C2211yescharacteristic
36#1380C2212yes—
37#1380C2211yescharacteristic
38#1380C2211yescharacteristic
39#1374C2212yes—
40#1374C2212yes—
41C22×Q16—21no—
42C22×Q16C2312yes—
43C2×C4⋊Q8—21no—
44C2×C4×Q8D411yescharacteristic
45C22×C16C2311yescharacteristic
46C22×C16C2312yes—
47C22×C16C2311yescharacteristic
48#494—22no—
49#494—22no—
50C8×Q8—22no—
51C8×Q8—22no—
52C2×#107—21no—
53C2×#107C2312yes—
54C2×#107C2311yescharacteristic
55C2×#107C2311yescharacteristic
56C2×#107C2311yescharacteristic
57C2×#107C2311yescharacteristic
58C2×#106—22no—
59C2×C4⋊C8D412yes—
60C2×C4⋊C8D411yescharacteristic
61C2×#103—22no—
62C2×#103—22no—
63C2×C4×C8C2312yes—
64C2×C4×C8C2311yescharacteristic
65#400—42no—
66#391—22no—
67#391—22no—
68#391—41no—
69#391—41no—
70#387—42no—
71#384—21no—
72#382—22no—
73#382—41no—
74C4×C4⋊C4—21no—
75C4×C4⋊C4—21no—
76C4×C4⋊C4—22no—
77C4×C4⋊C4—41no—
78#367—22no—
79#367—22no—
80#366—42no—
81C4⋊C16—22no—
82#358—24no—
83#358—24no—
84#358—42no—
85#358—42no—
86C4×C16—22no—
87#340—21no—
88#340—22no—
89#340—21no—
90C22×Q8—22no—
91C22×Q8D811yescharacteristic
92C2×Q16—22no—
93C2×Q16—22no—
94C2×Q16—22no—
95C2×Q16—22no—
96C2×Q16—22no—
97C2×Q16—22no—
98C2×Q16—42no—
99C2×Q16—81no—
100C2×Q16—81no—
101C22×C8C2×D412yes—
102C22×C8C2×D411yescharacteristic
103C22×C8C2411yescharacteristic
104C4⋊Q8—42no—
105C4⋊Q8—42no—
106C4×Q8—22no—
107C4×Q8—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4D811yescharacteristic
118C2×C4⋊C4D812yes—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42—42no—
122C2×C42C2×D412yes—
123C2×C42C2×D411yescharacteristic
124C2×C16—21no—
125C2×C16—21no—
126C2×C16—21no—
127C2×C16—22no—
128C2×C16—22no—
129C2×C16—21no—
130C2×C16—22no—
131C2×C16—21no—
132C2×C16#4112yes—
133#107—21no—
134#107—22no—
135#107—21no—
136#107—21no—
137#107—21no—
138#107—21no—
139#107—22no—
140#107—21no—
141#107—21no—
142#107—81no—
143#107#4112yes—
144#106—82no—
145C4⋊C8—24no—
146C4⋊C8—22no—
147#103—82no—
148#103—82no—
149C4×C8—22no—
150C4×C8—22no—
151C4×C8#4112yes—
152C4×C8#4112yes—
153#95—41no—
154#95—42no—
155#95—41no—
156#95—42no—
157#95—42no—
158#95—42no—
159#95—42no—
160#95—42no—
161#95—42no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8—42no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4C2×D812yes—
178C22×C4C2×D812yes—
179C22×C4C2×D811yescharacteristic
180C22×C4C2×D811yescharacteristic
181C22×C4C22×D411yescharacteristic
182Q16—42no—
183Q16—42no—
184Q16—42no—
185Q16—42no—
186Q16—84no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8#12312yes—
193C2×C8C2×#4111yescharacteristic
194C2×C8C2×#4111yescharacteristic
195C2×C8C2×#4111yescharacteristic
196C2×C8C2×#4111yescharacteristic
197C2×C8H(5,𝔽2)11yescharacteristic
198C2×C82−1+411yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—24no—
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C4⋊C4—41no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C4⋊C4—82no—
214C4⋊C4—161no—
215C42—22no—
216C42—22no—
217C42—82no—
218C42—82no—
219C42—162no—
220C42#12312yes—
221C42#13712yes—
222C16—22no—
223C16—41no—
224C16—42no—
225C23C22×D811yescharacteristic
226Q8—44no—
227Q8—82no—
228Q8—82no—
229Q8—82no—
230Q8—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—82no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4—82no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4#48012yes—
258C2×C4#48012yes—
259C2×C4#50812yes—
260C2×C4#51012yes—
261C2×C4C2×#12311yescharacteristic
262C2×C4#54811yescharacteristic
263C2×C4#55011yescharacteristic
264C2×C4C2×#13711yescharacteristic
265C2×C4#57611yescharacteristic
266C2×C4#57711yescharacteristic
267C8—22no—
268C8—42no—
269C8#52911yescharacteristic
270C8#54211yescharacteristic
271C8#55611yescharacteristic
272C8#55911yescharacteristic
273C22C2×#48011yescharacteristic
274C22#335811yescharacteristic
275C22#339111yescharacteristic
276C22C2×#50811yescharacteristic
277C22C2×#51011yescharacteristic
278C22#341611yescharacteristic
279C22#341711yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—82no—
284C4—161no—
285C4—161no—
286C4—162no—
287C4—161no—
288C4—162no—
289C4#223714yes—
290C4#244811yescharacteristic
291C4#309611yescharacteristic
292C4#337511yescharacteristic
293C4#340011yescharacteristic
294C2#2631611yescharacteristic
295C2C2×#223711yescharacteristic
296C2#3365111yescharacteristic
297C2#3393111yescharacteristic
298C2#3393911yescharacteristic
299C2#3396111yescharacteristic
300C2#3396511yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D8
commutator, Frattini, cosocleC22×C8C24
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#287372
#227272
#135292
#134832
#132632
#132532
#132032
#131762
#131332
#131322
C4×#3672