Finite Group Databasebeta

← #34099154

Subgroups — #34099154

Order 20096.

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

normal subgroups only

This group has 288 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#23757591C211yesmaximal, characteristic, complemented
3#23757208C211yesmaximal, characteristic, complemented
4#23757008C211yesmaximal, characteristic, complemented
5#23757007C211yesmaximal, characteristic, complemented
6#23756996C211yesmaximal, characteristic, complemented
7#481×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×#14578933—21no—
16C2×#14578931—21no—
17C2×#14578931C2211yescharacteristic
18#19097702—21no—
19#19097691—21no—
20C22⋊#11929434C2211yescharacteristic, complemented
21#19097678C2211yescharacteristic, complemented
22#121×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic, complemented
24#106×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—
42#14578933—42no—
43C22⋊Dic157—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47#14578931—21no—
48#14578931—42no—
49C2×D4×C157—21no—
50C2×D4×C157D411yescharacteristic
51C22×C4×C157—21no—
52C22×C4×C157C2311yescharacteristic
53C2×C8×C157—21no—
54C4⋊C4×C157—21no—
55C4⋊C4×C157—21no—
56C4⋊C4×C157D411yescharacteristic
57C22⋊C4×C157—21no—
58C22×D157—21no—
59C22×D157—21no—
60C22×D157—21no—
61C22×D157—42no—
62C22×D157—41no—
63C22×D157—41no—
64C22×D157—81no—
65C22×D157—81no—
66C22×D157SD1612yes—
67D628—41no—
68D628—42no—
69C22⋊D157—42no—
70C22⋊D157—41no—
71C22⋊D157—41no—
72C22⋊D157—81no—
73C2×Dic157—22no—
74C2×Dic157—21no—
75C2×Dic157—21no—
76C2×Dic157—41no—
77C2×Dic157—41no—
78C2×Dic157—41no—
79C4×D157—42no—
80#11929434—41no—
81C23×C157—21no—
82C23×C157C2×D411yescharacteristic
83D4×C157—41no—
84D4×C157—41no—
85D4×C157—41no—
86C2×C4×C157—21no—
87C2×C4×C157—41no—
88C2×C4×C157—41no—
89C2×C4×C157—41no—
90C2×C4×C157—41no—
91C2×C4×C157C2×D411yescharacteristic
92C2×C4×C157C2×D411yescharacteristic
93C8×C157—41no—
94C22×C157—21no—
95C22×C157—21no—
96C22×C157—41no—
97C22×C157—41no—
98C22×C157—41no—
99C22×C157#12011yescharacteristic
100C22×C157C2×SD1611yescharacteristic
101C22×C157AGL(1,ℤ/8)11yescharacteristic
102C2×D157—22no—
103C2×D157—41no—
104C2×D157—41no—
105C2×D157—42no—
106C2×D157—41no—
107C2×D157—41no—
108C2×D157—41no—
109C2×D157—81no—
110C2×D157—84no—
111C4×C157—21no—
112C4×C157—21no—
113C4×C157—41no—
114C4×C157—81no—
115Dic157—42no—
116Dic157—41no—
117Dic157—41no—
118C2×C157—21no—
119C2×C157—21no—
120C2×C157—81no—
121C2×C157#45011yescharacteristic
122C2×C157#45311yescharacteristic
123C2×C157#45811yescharacteristic
124D157—42no—
125D157—81no—
126C157#161311yescharacteristic, complemented, Sylow
127#1613—1571nomaximal, Sylow
128#534—1571no—
129#481—1571no—
130#481D15711yescharacteristic, complemented
131#399—1571no—
132#327—1571no—
133#327—1571no—
134#323—1571no—
135C22×D4—3141no—
136#123—3141no—
137#123—3141no—
138#121—3141no—
139#121—1571no—
140#121C2×D15711yescharacteristic
141#120—3141no—
142#120—3141no—
143C2×C4⋊C4—3141no—
144C2×C4⋊C4C2×D15711yescharacteristic, complemented
145C2×C22⋊C4—3141no—
146C2×C22⋊C4—1571no—
147#106—21no—
148#106—3141no—
149#102—21no—
150#102—3141no—
151C22⋊C8—1571no—
152C22⋊C8C2×D15711yescharacteristic, complemented
153#95—1571no—
154C24—3141no—
155C24—1571no—
156C2×D4—21no—
157C2×D4—3141no—
158C2×D4—3141no—
159C2×D4—3141no—
160C2×D4—3141no—
161C2×D4—6282no—
162C2×D4—6282no—
163C2×D4—1571no—
164C2×D4C22⋊D15711yescharacteristic
165C22×C4—21no—
166C22×C4—3141no—
167C22×C4—3141no—
168C22×C4—1571no—
169C22×C4C22×D15711yescharacteristic
170C2×C8—21no—
171C2×C8—3141no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—3141no—
175C4⋊C4—6282no—
176C4⋊C4—1571no—
177C4⋊C4C22⋊D15711yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—3141no—
180C22⋊C4—3141no—
181C22⋊C4—3141no—
182C22⋊C4—3141no—
183C22⋊C4—3141no—
184C22⋊C4—6282no—
185C23—21no—
186C23—3141no—
187C23—3141no—
188C23—3141no—
189C23—6281no—
190C23—6281no—
191C23—6282no—
192C23—1572no—
193C23—12561no—
194C23—12561no—
195C23D4×D15711yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—6281no—
200D4—6282no—
201D4—6282no—
202D4—6281no—
203D4—6281no—
204D4—12561no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—3142no—
211C2×C4—3141no—
212C2×C4—3141no—
213C2×C4—6282no—
214C2×C4—6281no—
215C2×C4—6281no—
216C2×C4—6281no—
217C2×C4D4×D15711yescharacteristic
218C2×C4C2×C22⋊D15711yescharacteristic
219C8—41no—
220C8—6281no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—3142no—
227C22—6282no—
228C22—6281no—
229C22—6281no—
230C22—6281no—
231C22—6281no—
232C22—6281no—
233C22—12561no—
234C22—12564no—
235C22#1909773911yescharacteristic
236C22SD16×D15711yescharacteristic
237C22#1909779811yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—6282no—
243C4—6281no—
244C4—6281no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—6282no—
249C2—12561no—
250C2#2375742211yescharacteristic
251C2#2375743911yescharacteristic
252C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#481×C157C2
socleC22×C157#120
prime radical#23757831C2
hypercenter#481D157
hypocenterC157#1613
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #23757591C2semidirect
3. #23757208C2semidirect
4. #23757008C2semidirect
5. #23757007C2semidirect
6. #23756996C2semidirect
7. #481×C157C2semidirect
20. C22⋊#11929434C22semidirect
21. #19097678C22semidirect
23. C2×C4⋊C4×C157C22semidirect
26. C22⋊C8×C157C22semidirect
126. C157#1613semidirect
130. #481D157semidirect
144. C2×C4⋊C4C2×D157semidirect
152. C22⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578312
#237575912
#237572082
#237570082
#237570072
#237569962
#481×C1572
#1613157