Finite Group Databasebeta

← #34099120

Subgroups — #34099120

Order 20096.

280 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757831C211yesmaximal, characteristic
2#23757586C211yesmaximal, characteristic, complemented
3#23757199C211yesmaximal, characteristic, complemented
4#23757008C211yesmaximal, characteristic, complemented
5#23757007C211yesmaximal, characteristic, complemented
6#23756996C211yesmaximal, characteristic, complemented
7#480×C157C211yesmaximal, characteristic, complemented
8C2×D4×D157—21no—
9#19097756—21no—
10#19097753—21no—
11#19097745C2211yescharacteristic
12#19097743—21no—
13#19097741—21no—
14#19097739—21no—
15C2×#14578931—21no—
16C2×#14578931C2211yescharacteristic
17#19097704—21no—
18#19097691—21no—
19C22⋊#11929434C2211yescharacteristic, complemented
20#19097678—21no—
21#19097678C2211yescharacteristic, complemented
22#121×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic, complemented
24#107×C157—21no—
25#102×C157—21no—
26C22⋊C8×C157C2211yescharacteristic, complemented
27C23×D157—21no—
28C23×D157D411yescharacteristic
29C2×D628—21no—
30C2×D628D411yescharacteristic
31C2×C22⋊D157—21no—
32C2×C22⋊D157—21no—
33C2×C22⋊D157—21no—
34D4×D157—42no—
35D4×D157—42no—
36C22×Dic157—21no—
37C22×Dic157D411yescharacteristic
38C2×C4×D157—21no—
39C2×#11929434—21no—
40C4⋊Dic157D411yescharacteristic
41#14578933—21no—
42C22⋊Dic157—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47#14578931—42no—
48C2×D4×C157—21no—
49C2×D4×C157D411yescharacteristic
50C22×C4×C157—21no—
51C22×C4×C157C2311yescharacteristic
52C2×C8×C157—21no—
53C4⋊C4×C157—21no—
54C4⋊C4×C157—21no—
55C4⋊C4×C157D411yescharacteristic
56C22⋊C4×C157—21no—
57C22×D157—21no—
58C22×D157—21no—
59C22×D157—21no—
60C22×D157—42no—
61C22×D157—41no—
62C22×D157—41no—
63C22×D157—81no—
64C22×D157—81no—
65C22×D157D812yes—
66D628—41no—
67D628—42no—
68C22⋊D157—42no—
69C22⋊D157—41no—
70C22⋊D157—41no—
71C22⋊D157—81no—
72C2×Dic157—21no—
73C2×Dic157—21no—
74C2×Dic157—41no—
75C2×Dic157—41no—
76C2×Dic157—41no—
77C2×Dic157—41no—
78C4×D157—42no—
79#11929434—41no—
80C23×C157—21no—
81C23×C157C2×D411yescharacteristic
82D4×C157—41no—
83D4×C157—41no—
84D4×C157—41no—
85C2×C4×C157—21no—
86C2×C4×C157—41no—
87C2×C4×C157—41no—
88C2×C4×C157—41no—
89C2×C4×C157—41no—
90C2×C4×C157C2×D411yescharacteristic
91C2×C4×C157C2×D411yescharacteristic
92C8×C157—41no—
93C22×C157—21no—
94C22×C157—21no—
95C22×C157—41no—
96C22×C157—41no—
97C22×C157—41no—
98C22×C157#12011yescharacteristic
99C22×C157C2×D811yescharacteristic
100C22×C157AGL(1,ℤ/8)11yescharacteristic
101C2×D157—22no—
102C2×D157—41no—
103C2×D157—41no—
104C2×D157—42no—
105C2×D157—41no—
106C2×D157—41no—
107C2×D157—41no—
108C2×D157—81no—
109C2×D157—84no—
110C4×C157—21no—
111C4×C157—21no—
112C4×C157—41no—
113C4×C157—81no—
114Dic157—41no—
115Dic157—41no—
116Dic157—81no—
117C2×C157—21no—
118C2×C157—21no—
119C2×C157—81no—
120C2×C157#44711yescharacteristic
121C2×C157#45511yescharacteristic
122C2×C157#45811yescharacteristic
123D157—42no—
124D157—81no—
125C157#160711yescharacteristic, complemented, Sylow
126#1607—1571nomaximal, Sylow
127#534—1571no—
128#480—1571no—
129#480D15711yescharacteristic, complemented
130#397—1571no—
131#327—1571no—
132#327—1571no—
133#323—1571no—
134C22×D4—3141no—
135#123—3141no—
136#123—3141no—
137#121—3141no—
138#121—1571no—
139#121C2×D15711yescharacteristic
140#120—3141no—
141#120—3141no—
142C2×C4⋊C4C2×D15711yescharacteristic, complemented
143C2×C22⋊C4—3141no—
144C2×C22⋊C4—1571no—
145#107—21no—
146#107—3141no—
147#102—21no—
148#102—3141no—
149C22⋊C8—1571no—
150C22⋊C8C2×D15711yescharacteristic, complemented
151#95—3141no—
152#95—1571no—
153C24—3141no—
154C24—1571no—
155C2×D4—21no—
156C2×D4—3141no—
157C2×D4—3141no—
158C2×D4—3141no—
159C2×D4—3141no—
160C2×D4—6282no—
161C2×D4—6282no—
162C2×D4—1571no—
163C2×D4C22⋊D15711yescharacteristic
164C22×C4—21no—
165C22×C4—3141no—
166C22×C4—3141no—
167C22×C4—1571no—
168C22×C4C22×D15711yescharacteristic
169C2×C8—21no—
170C2×C8—3141no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—3141no—
174C4⋊C4—1571no—
175C4⋊C4C22⋊D15711yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—3141no—
178C22⋊C4—3141no—
179C22⋊C4—3141no—
180C22⋊C4—3141no—
181C22⋊C4—3141no—
182C22⋊C4—6282no—
183C23—21no—
184C23—3141no—
185C23—3141no—
186C23—3141no—
187C23—6281no—
188C23—6281no—
189C23—6282no—
190C23—1572no—
191C23—12561no—
192C23—12561no—
193C23D4×D15711yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—6281no—
198D4—6282no—
199D4—6282no—
200D4—6281no—
201D4—6281no—
202D4—12561no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—3141no—
209C2×C4—3141no—
210C2×C4—6282no—
211C2×C4—6281no—
212C2×C4—6281no—
213C2×C4—6281no—
214C2×C4—6281no—
215C2×C4D4×D15711yescharacteristic
216C2×C4C2×C22⋊D15711yescharacteristic
217C8—41no—
218C8—6281no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—3142no—
225C22—6282no—
226C22—6281no—
227C22—6281no—
228C22—6281no—
229C22—6281no—
230C22—6281no—
231C22—12561no—
232C22—12564no—
233C22#1909773911yescharacteristic
234C22D8×D15711yescharacteristic
235C22#1909779511yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—6281no—
241C4—6281no—
242C4—12561no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—6282no—
247C2—12561no—
248C2#2375740511yescharacteristic
249C2#2375744911yescharacteristic
250C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#480×C157C2
socleC22×C157#120
prime radical#23757831C2
hypercenter#480D157
hypocenterC157#1607
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23757586C2semidirect
3. #23757199C2semidirect
4. #23757008C2semidirect
5. #23757007C2semidirect
6. #23756996C2semidirect
7. #480×C157C2semidirect
19. C22⋊#11929434C22semidirect
21. #19097678C22semidirect
23. C2×C4⋊C4×C157C22semidirect
26. C22⋊C8×C157C22semidirect
125. C157#1607semidirect
129. #480D157semidirect
142. C2×C4⋊C4C2×D157semidirect
150. C22⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578312
#237575862
#237571992
#237570082
#237570072
#237569962
#480×C1572
#1607157