Finite Group Databasebeta

← #34101158

Subgroups — #34101158

Order 20096.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#19097797C211yesmaximal, characteristic
2#23757847C211yesmaximal, characteristic, complemented
3C2×#19097699C211yesmaximal, characteristic, complemented
4#23757278C211yesmaximal, characteristic, complemented
5C2×#19097690C211yesmaximal, characteristic, complemented
6#23757033C211yesmaximal, characteristic, complemented
7C2×#124×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9#19097797—22no—
10#19097797—22no—
11C2×#14578942—21no—
12C2×#14578939—21no—
13C2×#14578938C2211yescharacteristic
14C2×#14578938C2211yescharacteristic
15#19097769—21no—
16#19097760—21no—
17#19097754—22no—
18#19097747—22no—
19#19097730C2211yescharacteristic
20#19097699—22no—
21#19097692—22no—
22#19097690—22no—
23C22×Q8×C157C2211yescharacteristic
24C22×D4×C157C2211yescharacteristic
25#124×C157—22no—
26#124×C157—22no—
27C2×C22⋊C4×C157—22no—
28C2×C42×C157C2211yescharacteristic
29#14578954—21no—
30#14578954—21no—
31#14578954—21no—
32#14578954—21no—
33C2×Dic314D411yescharacteristic
34C2×D628D411yescharacteristic
35C2×C22⋊D157—21no—
36C2×C4×D157—21no—
37#14578942—24no—
38#14578939—24no—
39#14578938—21no—
40#14578938—21no—
41#14578938—21no—
42#14578938D412yes—
43C2×#11929434—21no—
44C2×#11929434—21no—
45C4⋊Dic157D412yes—
46#14578933—24no—
47C22⋊Dic157—21no—
48#14578931—24no—
49C4×Dic157—21no—
50C24×C157—21no—
51C2×Q8×C157—21no—
52C2×Q8×C157—21no—
53C2×Q8×C157—21no—
54C2×Q8×C157—21no—
55C2×Q8×C157—21no—
56C2×Q8×C157—21no—
57C2×D4×C157—21no—
58C2×D4×C157—21no—
59C2×D4×C157—21no—
60C2×D4×C157—21no—
61C2×D4×C157—21no—
62C2×D4×C157D412yes—
63C22×C4×C157—21no—
64C22×C4×C157D412yes—
65C22×C4×C157C2311yescharacteristic
66C22⋊C4×C157—28no—
67C42×C157—21no—
68C42×C157D412yes—
69C22×D157—21no—
70Dic314—21no—
71Dic314—21no—
72D628—21no—
73D628—21no—
74C22⋊D157—41no—
75C22⋊D157—41no—
76C2×Dic157—21no—
77C2×Dic157—22no—
78C4×D157—41no—
79C4×D157—41no—
80#11929434—22no—
81#11929434—41no—
82C23×C157—22no—
83C23×C157—44no—
84C23×C157—41no—
85C23×C157—41no—
86C23×C157C2×D411yescharacteristic
87Q8×C157—41no—
88Q8×C157—41no—
89Q8×C157—41no—
90Q8×C157—41no—
91D4×C157—22no—
92D4×C157—22no—
93D4×C157—41no—
94D4×C157—41no—
95C2×C4×C157—22no—
96C2×C4×C157—22no—
97C2×C4×C157—22no—
98C2×C4×C157—22no—
99C2×C4×C157—42no—
100C2×C4×C157C2×D411yescharacteristic
101C2×C4×C157C2×D411yescharacteristic
102C2×C4×C157C2×D411yescharacteristic
103C2×C4×C157C2×D411yescharacteristic
104C2×C4×C157C2×D411yescharacteristic
105C2×C4×C157#4111yescharacteristic
106C22×C157—22no—
107C22×C157—44no—
108C22×C157—42no—
109C22×C157—82no—
110C22×C157—82no—
111C22×C157#12011yescharacteristic
112C22×C157#12011yescharacteristic
113C22×C157#12111yescharacteristic
114C2×D157—41no—
115C2×D157—42no—
116C4×C157—42no—
117C4×C157—42no—
118C4×C157#12011yescharacteristic
119C4×C157#12111yescharacteristic
120C4×C157#12111yescharacteristic
121C4×C157#12711yescharacteristic
122Dic157—41no—
123Dic157—42no—
124C2×C157—21no—
125C2×C157—21no—
126C2×C157—82no—
127C2×C157#39211yescharacteristic
128C2×C157#45412yes—
129D157—81no—
130C157#200311yescharacteristic, complemented, Sylow
131#2003—1571nomaximal, Sylow
132C2×AGL(1,ℤ/8)—1571no—
133#536—1571no—
134C2×#124D15711yescharacteristic, complemented
135C2×#104—1571no—
136#418—1571no—
137C2×#101—1571no—
138#339—1571no—
139C2×#41—1571no—
140C22×Q8C2×D15711yescharacteristic
141C22×D4C2×D15711yescharacteristic
142AGL(1,ℤ/8)—3142no—
143AGL(1,ℤ/8)—3142no—
144C2×SD16—3141no—
145C2×D8—3141no—
146C2×M16—1571no—
147C2×M16—1571no—
148C4⋊Q8—3141no—
149#124—22no—
150#124—22no—
151#124—3141no—
152#123—3142no—
153C22⋊Q8—3142no—
154#117—1571no—
155C2×C22⋊C4—22no—
156C2×C42C2×D15711yescharacteristic
157#104—3142no—
158#102—3142no—
159#101—3142no—
160C24—21no—
161#41—3141no—
162#41—3141no—
163#41—3141no—
164#41—3141no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—1571no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—3141no—
178C2×D4—1571no—
179C2×D4C22⋊D15712yes—
180C22×C4—21no—
181C22×C4—3141no—
182C22×C4C22⋊D15712yes—
183C22×C4C22×D15711yescharacteristic
184SD16—3144no—
185D8—3144no—
186M16—3141no—
187M16—3141no—
188M16—3141no—
189M16—1572no—
190C2×C8—3141no—
191C2×C8—3141no—
192C4⋊C4—3144no—
193C4⋊C4—1572no—
194C22⋊C4—28no—
195C22⋊C4—3144no—
196C22⋊C4—3141no—
197C42—21no—
198C42—3141no—
199C42C22⋊D15712yes—
200C23—22no—
201C23—44no—
202C23—41no—
203C23—41no—
204C23—3141no—
205C23C2×C22⋊D15711yescharacteristic
206Q8—41no—
207Q8—41no—
208Q8—41no—
209Q8—41no—
210Q8—3141no—
211Q8—3141no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—3141no—
217D4—3141no—
218D4—6281no—
219D4—6281no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—3142no—
226C2×C4—3141no—
227C2×C4—6281no—
228C2×C4—6281no—
229C2×C4D4×D15711yescharacteristic
230C2×C4D4×D15711yescharacteristic
231C2×C4D4×D15711yescharacteristic
232C2×C4C2×C22⋊D15711yescharacteristic
233C2×C4C2×C22⋊D15711yescharacteristic
234C2×C4#1457895311yescharacteristic
235C8—3142no—
236C8—6281no—
237C22—22no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—82no—
242C22—6281no—
243C22—6282no—
244C22#1909773911yescharacteristic
245C22#1909774011yescharacteristic
246C22#1909774311yescharacteristic
247C4—42no—
248C4—42no—
249C4—6281no—
250C4—6282no—
251C4#1909773911yescharacteristic
252C4#1909774211yescharacteristic
253C4#1909774311yescharacteristic
254C4#1909776711yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—12561no—
259C2#2375718111yescharacteristic
260C2#2375744512yes—
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#124×C157C2
socleC22×C157#120
prime radicalC2×#19097797C2
hypercenterC2×#124D157
hypocenterC157#2003
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #23757847C2semidirect
3. C2×#19097699C2semidirect
4. #23757278C2semidirect
5. C2×#19097690C2semidirect
6. #23757033C2semidirect
7. C2×#124×C157C2semidirect
130. C157#2003semidirect
134. C2×#124D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977972
#237578472
C2×#190976992
#237572782
C2×#190976902
#237570332
C2×#124×C1572
#2003157