Finite Group Databasebeta

← #501945

Subgroups — #501945

Order 512.

452 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28265C211yesmaximal, characteristic
2#22727C211yesmaximal, characteristic
3#13539C212yesmaximal
4#13483C212yesmaximal
5#13263C211yesmaximal, characteristic
6#13177C211yesmaximal, characteristic
7#13132C212yesmaximal
8#13110C212yesmaximal
9#12888C211yesmaximal, characteristic
10#12812C211yesmaximal, characteristic
11C4×#358C211yesmaximal, characteristic
12C2×C8×Q8C2211yescharacteristic
13C2×C4×Q16C2211yescharacteristic
14#2582—21no—
15#2355—21no—
16C2×#367C2212yes—
17C2×C4⋊C16C2211yescharacteristic
18C2×#358C2212yes—
19C2×#358C2211yescharacteristic
20C2×#358C2211yescharacteristic
21C2×C4×C16C2211yescharacteristic
22#2068—22no—
23#1969C2212yes—
24#1949—22no—
25#1948—21no—
26#1942C2212yes—
27#1846C2212yes—
28#1845C2211yescharacteristic
29#1845C2211yescharacteristic
30#1803—21no—
31C4×#107C2212yes—
32C4×#107C2211yescharacteristic
33#1380C2212yes—
34#1380C2211yescharacteristic
35#1380C2212yes—
36#1380C2212yes—
37#1380C2211yescharacteristic
38#1380C2212yes—
39#1374C2212yes—
40#1374C2212yes—
41C22×Q16C2311yescharacteristic
42C2×C4×Q8—21no—
43C2×C4×Q8D411yescharacteristic
44C22×C16C2311yescharacteristic
45C22×C16C2311yescharacteristic
46C22×C16C2312yes—
47C8×Q8—22no—
48C8×Q8—22no—
49C4×Q16—22no—
50C4×Q16—22no—
51C2×#107—21no—
52C2×#107—21no—
53C2×#107C2312yes—
54C2×#107C2312yes—
55C2×#107C2311yescharacteristic
56C2×#107C2311yescharacteristic
57C2×#107C2311yescharacteristic
58C2×#106—22no—
59C2×C4⋊C8D411yescharacteristic
60C2×C4⋊C8D412yes—
61C2×#103—21no—
62C2×#103—22no—
63C2×C4×C8C2312yes—
64C2×C4×C8C2311yescharacteristic
65#398—42no—
66#391—22no—
67#391—41no—
68#391—41no—
69#389—22no—
70#389—41no—
71#387—42no—
72#384—21no—
73#384—21no—
74#382—22no—
75C4×C4⋊C4—21no—
76C4×C4⋊C4—22no—
77C4×C4⋊C4—41no—
78#367—24no—
79C4⋊C16—22no—
80#358—24no—
81#358—22no—
82#358—22no—
83C4×C16—22no—
84#340—22no—
85#340—22no—
86#340—21no—
87C22×Q8—21no—
88C22×Q8D811yescharacteristic
89C2×Q16—21no—
90C2×Q16—21no—
91C2×Q16—21no—
92C2×Q16—21no—
93C2×Q16—21no—
94C2×Q16#4112yes—
95C22×C8C2×D412yes—
96C22×C8C2×D411yescharacteristic
97C22×C8C2411yescharacteristic
98C4×Q8—22no—
99C4×Q8—22no—
100C4×Q8—42no—
101C4×Q8—42no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4D811yescharacteristic
114C2×C4⋊C4D812yes—
115C2×C42—41no—
116C2×C42—41no—
117C2×C42—42no—
118C2×C42C2×D412yes—
119C2×C42C2×D411yescharacteristic
120C2×C16—21no—
121C2×C16—21no—
122C2×C16—22no—
123C2×C16—21no—
124C2×C16—21no—
125C2×C16—22no—
126C2×C16—22no—
127C2×C16—21no—
128C2×C16—21no—
129#107—21no—
130#107—22no—
131#107—21no—
132#107—22no—
133#107—21no—
134#107—21no—
135#107—22no—
136#107—22no—
137#107—21no—
138#107—81no—
139#107—81no—
140#107#4112yes—
141#106—82no—
142C4⋊C8—24no—
143C4⋊C8—22no—
144#103—42no—
145#103—82no—
146C4×C8—22no—
147C4×C8—22no—
148C4×C8#4112yes—
149C4×C8#4112yes—
150#95—41no—
151#95—42no—
152#95—42no—
153#95—42no—
154#95—42no—
155#95—42no—
156#95—42no—
157C2×Q8—22no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—41no—
172C22×C4C2×D812yes—
173C22×C4C2×D812yes—
174C22×C4C2×D811yescharacteristic
175C22×C4C2×D811yescharacteristic
176C22×C4C22×D411yescharacteristic
177Q16—22no—
178Q16—22no—
179Q16—41no—
180Q16—41no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8#12312yes—
187C2×C8C2×#4111yescharacteristic
188C2×C8C2×#4111yescharacteristic
189C2×C8C2×#4111yescharacteristic
190C2×C8C2×#4111yescharacteristic
191C2×C82−1+411yescharacteristic
192C2×C82−1+411yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—82no—
206C4⋊C4—82no—
207C4⋊C4—82no—
208C4⋊C4—161no—
209C4⋊C4—161no—
210C4⋊C4—162no—
211C42—22no—
212C42—22no—
213C42—82no—
214C42—82no—
215C42—162no—
216C42#12312yes—
217C42#13712yes—
218C16—42no—
219C16—41no—
220C16—41no—
221C23C22×D811yescharacteristic
222Q8—44no—
223Q8—42no—
224Q8—42no—
225Q8—81no—
226Q8—81no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—81no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4—81no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4#48012yes—
254C2×C4#48012yes—
255C2×C4#50812yes—
256C2×C4#51012yes—
257C2×C4C2×#12311yescharacteristic
258C2×C4#54811yescharacteristic
259C2×C4#54811yescharacteristic
260C2×C4C2×#13711yescharacteristic
261C2×C4#57711yescharacteristic
262C2×C4#57711yescharacteristic
263C8—22no—
264C8—42no—
265C8#52911yescharacteristic
266C8#54111yescharacteristic
267C8#55211yescharacteristic
268C8#55611yescharacteristic
269C22C2×#48011yescharacteristic
270C22#335811yescharacteristic
271C22#335811yescharacteristic
272C22C2×#50811yescharacteristic
273C22C2×#51011yescharacteristic
274C22#341611yescharacteristic
275C22#341611yescharacteristic
276C4—22no—
277C4—42no—
278C4—42no—
279C4—82no—
280C4—82no—
281C4—161no—
282C4—162no—
283C4—162no—
284C4—161no—
285C4#223714yes—
286C4#242111yescharacteristic
287C4#309911yescharacteristic
288C4#336911yescharacteristic
289C4#337211yescharacteristic
290C2#2499011yescharacteristic
291C2C2×#223711yescharacteristic
292C2#3365311yescharacteristic
293C2#3393211yescharacteristic
294C2#3393211yescharacteristic
295C2#3393611yescharacteristic
296C2#3393911yescharacteristic
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
#282652
#227272
#135392
#134832
#132632
#131772
#131322
#131102
#128882
#128122
C4×#3582