Finite Group Databasebeta

← #34098659

Subgroups — #34098659

Order 20096.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#23757807C211yesmaximal, characteristic
2#23757330C211yesmaximal, characteristic, complemented
3#23757009C212yesmaximal, complemented
4#23757006C212yesmaximal
5C4×C4⋊C4×C157C211yesmaximal, characteristic, complemented
6#19097765—21no—
7#19097763C411yescharacteristic, complemented
8#19097759C411yescharacteristic, complemented
9#19097754—21no—
10#19097750C2211yescharacteristic
11#19097745C2211yescharacteristic
12C4×Dic314C411yescharacteristic, complemented
13C4×D628C411yescharacteristic, complemented
14C4×C22⋊D157—21no—
15#19097728—21no—
16C4⋊#11929434—21no—
17C22⋊#11929434C2212yes—
18#19097682—21no—
19C2×C4⋊C4×C157—21no—
20C2×C42×C157—21no—
21C2×C42×C157C2211yescharacteristic
22#95×C157C2212yes—
23C2×Dic314C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic
25C2×C22⋊D157—21no—
26C2×C4×D157—21no—
27C2×#11929434—22no—
28C4⋊Dic157C2×C411yescharacteristic
29C4⋊Dic157C2×C411yescharacteristic
30#14578933—21no—
31#14578933—21no—
32#14578933—21no—
33#14578933—21no—
34C22⋊Dic157—21no—
35#14578931—21no—
36#14578931—21no—
37#14578931—21no—
38#14578931—21no—
39C4×Dic157—21no—
40C22×C4×C157—22no—
41C22×C4×C157D411yescharacteristic
42C22×C4×C157D411yescharacteristic
43C22×C4×C157C2311yescharacteristic
44C4⋊C4×C157—24no—
45C42×C157—42no—
46C42×C157C2×C411yescharacteristic
47C42×C157C2×C411yescharacteristic
48C42×C157D411yescharacteristic
49C42×C157D411yescharacteristic
50C22×D157—21no—
51Dic314—41no—
52D628—41no—
53C22⋊D157—41no—
54C22⋊D157—41no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C4×D157—42no—
59#11929434—42no—
60C23×C157C2×D411yescharacteristic
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—22no—
64C2×C4×C157—24no—
65C2×C4×C157—41no—
66C2×C4×C157—42no—
67C2×C4×C157—42no—
68C2×C4×C157C22⋊C411yescharacteristic
69C2×C4×C157C22⋊C411yescharacteristic
70C2×C4×C157C22⋊C411yescharacteristic
71C2×C4×C157C22⋊C411yescharacteristic
72C2×C4×C157C22×C411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C22×C157—21no—
75C22×C157—21no—
76C22×C157C2×C22⋊C411yescharacteristic
77C22×C157AGL(1,ℤ/8)11yescharacteristic
78C22×C157#13711yescharacteristic
79C2×D157—41no—
80C2×D157—41no—
81C2×D157—41no—
82C4×C157—21no—
83C4×C157—21no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—21no—
87C4×C157—44no—
88C4×C157#10412yes—
89Dic157—41no—
90Dic157—41no—
91Dic157—41no—
92C2×C157—21no—
93C2×C157—21no—
94C2×C157#41011yescharacteristic
95C2×C157#41711yescharacteristic
96C2×C157C2×#10411yescharacteristic
97D157—81no—
98C157#150911yescharacteristic, complemented, Sylow
99#1509—1571nomaximal, Sylow
100#529—1571no—
101#432—1571no—
102C4×C4⋊C4D15711yescharacteristic, complemented
103#328—1572no—
104#327—1572no—
105#126—3141no—
106#125—1571no—
107#124—1571no—
108#123—3141no—
109C22⋊Q8—1571no—
110#121—1571no—
111C4×Q8—1571no—
112C4×D4—3141no—
113C4×D4—1571no—
114#117—3141no—
115C2×C4⋊C4—21no—
116C2×C42—21no—
117C2×C42C2×D15711yescharacteristic
118C4⋊C8—3141no—
119C22⋊C8—1572no—
120#97—3141no—
121#95C2×D15712yes—
122C2×Q8—1571no—
123C2×D4—3141no—
124C2×D4—1571no—
125C22×C4—22no—
126C22×C4—3141no—
127C22×C4C22⋊D15711yescharacteristic
128C22×C4C22⋊D15711yescharacteristic
129C22×C4C22×D15711yescharacteristic
130C2×C8—3142no—
131C4⋊C4—24no—
132C4⋊C4—3141no—
133C4⋊C4—3141no—
134C4⋊C4—3141no—
135C4⋊C4—3141no—
136C4⋊C4—1571no—
137C4⋊C4—1571no—
138C22⋊C4—3141no—
139C22⋊C4—3141no—
140C22⋊C4—3141no—
141C22⋊C4—3141no—
142C22⋊C4—3141no—
143C42—42no—
144C42—3141no—
145C42C4×D15711yescharacteristic
146C42C4×D15711yescharacteristic
147C42D62811yescharacteristic
148C42D62811yescharacteristic
149C23—3141no—
150C23C2×C22⋊D15711yescharacteristic
151Q8—6281no—
152D4—6281no—
153D4—6281no—
154D4—6281no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—3141no—
163C2×C4—3141no—
164C2×C4—3141no—
165C2×C4—6282no—
166C2×C4#1457893111yescharacteristic
167C2×C4#1457893111yescharacteristic
168C2×C4#1457893111yescharacteristic
169C2×C4#1457893111yescharacteristic
170C2×C4C2×C4×D15711yescharacteristic
171C2×C4C2×D62811yescharacteristic
172C8—6282no—
173C22—21no—
174C22—21no—
175C22—6281no—
176C22—6281no—
177C22—6281no—
178C22C2×#1457893111yescharacteristic
179C22#1909779711yescharacteristic
180C22#1909780211yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—44no—
187C4—6281no—
188C4—6281no—
189C4—6281no—
190C4#1909769912yes—
191C2—21no—
192C2—21no—
193C2—12561no—
194C2#2375724611yescharacteristic
195C2#2375727211yescharacteristic
196C2C2×#1909769911yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC4×C4⋊C4×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097745C22
cosocleC22×C4×C157C23
hypercenterC4×C4⋊C4D157
hypocenterC157#1509
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #23757330C2semidirect
3. #23757009C2semidirect
5. C4×C4⋊C4×C157C2semidirect
7. #19097763C4semidirect
8. #19097759C4semidirect
12. C4×Dic314C4semidirect
13. C4×D628C4semidirect
98. C157#1509semidirect
102. C4×C4⋊C4D157semidirect

Maximal subgroups

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

subgroupindex
#237578072
#237573302
#237570092
#237570062
C4×C4⋊C4×C1572
#1509157