Finite Group Databasebeta

← #34101779

Subgroups — #34101779

Order 20096.

280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757833C211yesmaximal, characteristic
2#100×D157C211yesmaximal, characteristic, complemented
3#99×D157C211yesmaximal, characteristic, complemented
4#23757064C211yesmaximal, characteristic, complemented
5#23757062C211yesmaximal, characteristic, complemented
6#23757060C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C157C211yesmaximal, characteristic, complemented
8C22×C22⋊D157C411yescharacteristic, complemented
9C2×D4×D157C2211yescharacteristic
10M16×D157—21no—
11#19097755C411yescharacteristic, complemented
12#19097753—21no—
13#19097752C2211yescharacteristic
14#19097744—21no—
15#19097742—21no—
16#19097740C411yescharacteristic, complemented
17#19097739—21no—
18C22⋊C4×D157—21no—
19C22⋊C4×D157C411yescharacteristic, complemented
20#19097688C2211yescharacteristic
21#19097687—21no—
22#19097686C2211yescharacteristic
23#19097685—21no—
24#120×C157C2211yescharacteristic
25#100×C157C2211yescharacteristic
26#99×C157C2211yescharacteristic
27C23×D157C2×C411yescharacteristic
28C23×D157D411yescharacteristic
29C2×D628D411yescharacteristic
30C2×C22⋊D157—21no—
31C2×C22⋊D157—21no—
32C2×C22⋊D157—21no—
33C2×C22⋊D157—41no—
34C2×C22⋊D157—41no—
35C2×C22⋊D157C2×C411yescharacteristic
36C2×C22⋊D157D411yescharacteristic
37D4×D157—41no—
38D4×D157—41no—
39C22×Dic157C2×C411yescharacteristic, complemented
40C2×C4×D157—21no—
41C2×C4×D157—41no—
42C2×C4×D157D411yescharacteristic
43#14578938—21no—
44#14578937—41no—
45C8×D157—41no—
46C4⋊Dic157—21no—
47#14578933—21no—
48C22⋊Dic157—21no—
49C22⋊Dic157—21no—
50C22⋊Dic157—21no—
51C22⋊Dic157C2×C411yescharacteristic, complemented
52#14578931—21no—
53#14578931—21no—
54#14578931—41no—
55C24×C157C2×C411yescharacteristic, complemented
56C2×D4×C157—21no—
57C2×D4×C157C2311yescharacteristic
58M16×C157—21no—
59C22⋊C4×C157—21no—
60C22⋊C4×C157—21no—
61C22⋊C4×C157C2×C411yescharacteristic, complemented
62C22×D157—21no—
63C22×D157—21no—
64C22×D157—21no—
65C22×D157—21no—
66C22×D157—81no—
67C22×D157—81no—
68C22×D157C22⋊C411yescharacteristic
69C22×D157C22⋊C411yescharacteristic
70C22×D157C22⋊C411yescharacteristic
71D628—41no—
72C22⋊D157—41no—
73C22⋊D157—41no—
74C22⋊D157—42no—
75C22⋊D157—41no—
76C22⋊D157—41no—
77C22⋊D157—81no—
78C2×Dic157—21no—
79C2×Dic157—21no—
80C2×Dic157—41no—
81C2×Dic157—41no—
82C2×Dic157C22⋊C411yescharacteristic
83C4×D157—21no—
84C4×D157—21no—
85C4×D157—81no—
86C4×D157—82no—
87#11929434—41no—
88C23×C157—21no—
89C23×C157—41no—
90C23×C157—81no—
91C23×C157C22×C411yescharacteristic
92C23×C157C2×D411yescharacteristic
93D4×C157—41no—
94D4×C157—81no—
95C2×C4×C157—21no—
96C2×C4×C157—41no—
97C2×C4×C157C2×D411yescharacteristic
98C8×C157—41no—
99C22×C157—21no—
100C22×C157—21no—
101C22×C157—41no—
102C22×C157—41no—
103C22×C157—41no—
104C22×C157—41no—
105C22×C157—41no—
106C22×C157—82no—
107C22×C157C2×C22⋊C411yescharacteristic
108C2×D157—21no—
109C2×D157—21no—
110C2×D157—41no—
111C2×D157—42no—
112C2×D157—41no—
113C2×D157—41no—
114C2×D157—81no—
115C2×D157—81no—
116C2×D157—81no—
117C2×D157#9911yescharacteristic
118C2×D157#9911yescharacteristic
119C4×C157—21no—
120C4×C157—41no—
121C4×C157—81no—
122Dic157—21no—
123Dic157—41no—
124Dic157—41no—
125Dic157—81no—
126C2×C157—21no—
127C2×C157—41no—
128C2×C157—41no—
129C2×C157—81no—
130C2×C157C2×#9911yescharacteristic
131D157—21no—
132D157—21no—
133D157—41no—
134D157—41no—
135C157#212111yescharacteristic, complemented, Sylow
136#2121—1571nomaximal, Sylow
137#534—1571no—
138C2×#100—1571no—
139C2×#99—1571no—
140#352—1571no—
141#352—1571no—
142AΣL(1,𝔽16)—1571no—
143AΣL(1,𝔽16)D15711yescharacteristic, complemented
144C22×D4—1571no—
145C22×D4—1571no—
146C2×M16—3141no—
147#123—3141no—
148#123—1571no—
149#123—1571no—
150#121—3141no—
151#121—3141no—
152#120—3141no—
153#120—1571no—
154#120C2×D15711yescharacteristic
155C2×C22⋊C4—3141no—
156C2×C22⋊C4—1571no—
157#100—3141no—
158#100—1571no—
159#100C2×D15711yescharacteristic
160#99—3141no—
161#99—1571no—
162#99C2×D15711yescharacteristic
163C24—1571no—
164C24—1571no—
165C24C4×D15711yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—3141no—
168C2×D4—3141no—
169C2×D4—3141no—
170C2×D4—6281no—
171C2×D4—6281no—
172C2×D4—6281no—
173C2×D4—6281no—
174C2×D4—1571no—
175C2×D4—1571no—
176C2×D4—1571no—
177C2×D4C22×D15711yescharacteristic
178C22×C4—3141no—
179C22×C4—6281no—
180C22×C4—1571no—
181C22×C4—1571no—
182M16—21no—
183M16—3141no—
184M16—6281no—
185C2×C8—6281no—
186C4⋊C4—3141no—
187C4⋊C4—3141no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—3141no—
191C22⋊C4—3141no—
192C22⋊C4—3141no—
193C22⋊C4—3141no—
194C22⋊C4—3141no—
195C22⋊C4—6281no—
196C22⋊C4—1571no—
197C22⋊C4C4×D15711yescharacteristic, complemented
198C23—21no—
199C23—41no—
200C23—81no—
201C23—3141no—
202C23—3141no—
203C23—3141no—
204C23—3141no—
205C23—1571no—
206C23—1571no—
207C23—1571no—
208C23—12561no—
209C23—12561no—
210C23C2×C4×D15711yescharacteristic
211C23D4×D15711yescharacteristic
212D4—41no—
213D4—81no—
214D4—6281no—
215D4—6281no—
216D4—6281no—
217D4—6282no—
218D4—6281no—
219D4—6281no—
220D4—12561no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—3141no—
224C2×C4—3141no—
225C2×C4—3141no—
226C2×C4—3141no—
227C2×C4—6281no—
228C2×C4—6281no—
229C2×C4—1571no—
230C2×C4—12561no—
231C2×C4—12562no—
232C2×C4D4×D15711yescharacteristic
233C8—41no—
234C8—6281no—
235C22—21no—
236C22—21no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—82no—
243C22—3141no—
244C22—3141no—
245C22—6281no—
246C22—6281no—
247C22—6281no—
248C22—6282no—
249C22—1571no—
250C22—1571no—
251C22—12561no—
252C22—12561no—
253C22—12561no—
254C22C22⋊C4×D15711yescharacteristic
255C4—21no—
256C4—41no—
257C4—81no—
258C4—3141no—
259C4—6281no—
260C4—6281no—
261C4—12561no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2—81no—
266C2—3141no—
267C2—3141no—
268C2—6281no—
269C2—6281no—
270C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC23×C157C22×C4
FrattiniC2×D4C22×D157
FittingAΣL(1,𝔽16)×C157C2
socleC2×C157C2×#99
prime radical#23757833C2
cosocleC2×D4×C157C23
hypercenterAΣL(1,𝔽16)D157
hypocenterC157#2121
LCSG ▷ C23×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #100×D157C2semidirect
3. #99×D157C2semidirect
4. #23757064C2semidirect
5. #23757062C2semidirect
6. #23757060C2semidirect
7. AΣL(1,𝔽16)×C157C2semidirect
8. C22×C22⋊D157C4semidirect
11. #19097755C4semidirect
16. #19097740C4semidirect
19. C22⋊C4×D157C4semidirect
39. C22×Dic157C2×C4semidirect
51. C22⋊Dic157C2×C4semidirect
55. C24×C157C2×C4semidirect
61. C22⋊C4×C157C2×C4semidirect
135. C157#2121semidirect
143. AΣL(1,𝔽16)D157semidirect
165. C24C4×D157semidirect
197. C22⋊C4C4×D157semidirect

Maximal subgroups

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

subgroupindex
#237578332
#100×D1572
#99×D1572
#237570642
#237570622
#237570602
AΣL(1,𝔽16)×C1572
#2121157