Finite Group Databasebeta

← #34101131

Subgroups — #34101131

Order 20096.

496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19097742C212yesmaximal, complemented
2C2×#19097692C212yesmaximal, complemented
3C2×#19097683C211yesmaximal, characteristic, complemented
4#23757036C211yesmaximal, characteristic, complemented
5C22×D8×C157C211yesmaximal, characteristic, complemented
6C22×C22⋊D157—22no—
7C22×C4×D157C2211yescharacteristic
8C22×#11929434C2211yescharacteristic
9#19097742—24no—
10#19097742—24no—
11C2×C4⋊Dic157C2212yes—
12C2×C22⋊Dic157—22no—
13#19097692—24no—
14#19097683—22no—
15C22×D4×C157C2212yes—
16C2×D8×C157—24no—
17C2×D8×C157—22no—
18C22×C8×C157C2211yescharacteristic
19C23×D157D411yescharacteristic
20C2×C22⋊D157—28no—
21C2×C22⋊D157—44no—
22C2×C22⋊D157—44no—
23C22×Dic157—22no—
24C22×Dic157D411yescharacteristic
25C2×C4×D157—21no—
26C2×C4×D157—22no—
27C2×C4×D157—22no—
28C2×C4×D157—21no—
29C2×#11929434—21no—
30C2×#11929434—22no—
31C4⋊Dic157—22no—
32C4⋊Dic157D414yescomplemented
33C22⋊Dic157—28no—
34C24×C157—22no—
35C2×D4×C157—22no—
36C2×D4×C157—22no—
37C2×D4×C157—22no—
38C2×D4×C157—22no—
39C2×D4×C157—22no—
40C2×D4×C157D414yescomplemented
41C22×C4×C157C2311yescharacteristic
42D8×C157—28no—
43C2×C8×C157—22no—
44C2×C8×C157D412yescomplemented
45C22×D157—22no—
46C22×D157—21no—
47C22×D157—21no—
48C22×D157—22no—
49C22×D157D812yescomplemented
50C22⋊D157—416no—
51C2×Dic157—22no—
52C2×Dic157—24no—
53C2×Dic157—21no—
54C2×Dic157—42no—
55C2×Dic157—42no—
56C4×D157—41no—
57C4×D157—42no—
58C4×D157—41no—
59#11929434—41no—
60C23×C157—24no—
61C23×C157—42no—
62C23×C157—42no—
63C23×C157—42no—
64C23×C157—42no—
65C23×C157—42no—
66C23×C157—42no—
67C23×C157C2×D411yescharacteristic
68D4×C157—24no—
69D4×C157—24no—
70D4×C157—42no—
71D4×C157—42no—
72C2×C4×C157C2×D412yes—
73C2×C4×C157C2×D412yes—
74C2×C4×C157C2×D411yescharacteristic
75C2×C4×C157#4111yescharacteristic
76C8×C157—22no—
77C22×C157—44no—
78C22×C157—44no—
79C22×C157—44no—
80C22×C157—82no—
81C22×C157—82no—
82C22×C157—82no—
83C22×C157—82no—
84C22×C157#12012yes—
85C22×C157#12111yescharacteristic
86C22×C157C2×D811yescharacteristic
87C22×C157#13511yescharacteristic
88C22×C157AGL(1,ℤ/8)12yes—
89C2×D157—24no—
90C2×D157—22no—
91C2×D157—41no—
92C2×D157—42no—
93C2×D157—41no—
94C4×C157#12011yescharacteristic
95C4×C157#12112yes—
96C4×C157#12711yescharacteristic
97Dic157—41no—
98Dic157—44no—
99C2×C157—84no—
100C2×C157#39211yescharacteristic
101C2×C157#44712yes—
102C2×C157#44912yes—
103C2×C157#46611yescharacteristic
104C2×C157#46911yescharacteristic
105D157—42no—
106C157#199911yescharacteristic, complemented, Sylow
107#1999—1571nomaximal, Sylow
108C22×D8D15711yescharacteristic, complemented
109C2×#121—1572no—
110C2×#102—1572no—
111C2×C22⋊C8—1571no—
112#340—1571no—
113C22×D4—3142no—
114C22×D4C2×D15712yes—
115C23×C4—1571no—
116C2×D8—24no—
117C2×D8—22no—
118C22×C8—1571no—
119C22×C8C2×D15711yescharacteristic
120#121—3144no—
121#121—3144no—
122C2×C4⋊C4—1572no—
123C2×C22⋊C4—3142no—
124#102—3144no—
125C22⋊C8—3142no—
126C24—22no—
127C24—1571no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—22no—
132C2×D4—22no—
133C2×D4—3148no—
134C2×D4—6284no—
135C2×D4—6284no—
136C2×D4C22⋊D15714yescomplemented
137C22×C4—3142no—
138C22×C4—3142no—
139C22×C4—3141no—
140C22×C4—3142no—
141C22×C4—3141no—
142C22×C4—1571no—
143C22×C4C22×D15711yescharacteristic
144D8—28no—
145C2×C8—22no—
146C2×C8—3142no—
147C2×C8—3141no—
148C2×C8C22⋊D15712yescomplemented
149C4⋊C4—3142no—
150C4⋊C4—1574no—
151C22⋊C4—3148no—
152C23—24no—
153C23—42no—
154C23—42no—
155C23—42no—
156C23—42no—
157C23—42no—
158C23—42no—
159C23—3142no—
160C23—3141no—
161C23—3141no—
162C23—3142no—
163C23—1572no—
164C23D4×D15711yescharacteristic
165D4—24no—
166D4—24no—
167D4—42no—
168D4—42no—
169D4—62816no—
170C2×C4—3142no—
171C2×C4—3144no—
172C2×C4—3141no—
173C2×C4—6282no—
174C2×C4—6282no—
175C2×C4—6281no—
176C2×C4—6282no—
177C2×C4—6281no—
178C2×C4D4×D15712yes—
179C2×C4C2×C22⋊D15712yes—
180C2×C4C2×C22⋊D15711yescharacteristic
181C2×C4#1457895311yescharacteristic
182C8—22no—
183C8—6281no—
184C22—44no—
185C22—44no—
186C22—44no—
187C22—82no—
188C22—82no—
189C22—82no—
190C22—82no—
191C22—3144no—
192C22—3142no—
193C22—6282no—
194C22—6281no—
195C22—6281no—
196C22#1909773912yes—
197C22#1909774211yescharacteristic
198C22D8×D15711yescharacteristic
199C22#1909779011yescharacteristic
200C22#1909779512yes—
201C4—6284no—
202C4—6281no—
203C4#1909774011yescharacteristic
204C4#1909774312yes—
205C4#1909776711yescharacteristic
206C2—84no—
207C2—6282no—
208C2#2375718111yescharacteristic
209C2#2375740512yes—
210C2#2375741512yes—
211C2#2375750611yescharacteristic
212C2#2375752311yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC22×D8×C157C2
socleC23×C157C2×D4
hypercenterC22×D8D157
hypocenterC157#1999
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#19097742C2semidirect
2. C2×#19097692C2semidirect
3. C2×#19097683C2semidirect
4. #23757036C2semidirect
5. C22×D8×C157C2semidirect
32. C4⋊Dic157D4semidirect
40. C2×D4×C157D4semidirect
44. C2×C8×C157D4semidirect
49. C22×D157D8semidirect
106. C157#1999semidirect
108. C22×D8D157semidirect
136. C2×D4C22⋊D157semidirect
148. C2×C8C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977422
C2×#190976922
C2×#190976832
#237570362
C22×D8×C1572
#1999157