Finite Group Databasebeta

← #34098840

Subgroups — #34098840

Order 20096.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#23757824C211yesmaximal, characteristic
2#23757329C211yesmaximal, characteristic, complemented
3#23757325C211yesmaximal, characteristic, complemented
4#23757019C211yesmaximal, characteristic, complemented
5#23757016C211yesmaximal, characteristic, complemented
6#23757016C211yesmaximal, characteristic, complemented
7#332×C157C211yesmaximal, characteristic, complemented
8C2×#14578955—21no—
9#19097768C2211yescharacteristic
10#19097760—21no—
11#19097746—21no—
12#19097746C412yes—
13#19097733—21no—
14#19097733C412yes—
15C42×D157C2211yescharacteristic
16C4⋊#11929434C2211yescharacteristic
17C4⋊#11929434C2211yescharacteristic
18#19097683—21no—
19#19097683—21no—
20#19097681—21no—
21C8×Dic157—21no—
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25#14578955—42no—
26#14578955—42no—
27C2×D628—22no—
28C2×D628—21no—
29C2×D628—21no—
30C2×D628C2×C412yes—
31C2×C4×D157—22no—
32C2×C4×D157C2×C411yescharacteristic
33C2×C4×D157D411yescharacteristic
34C2×C4×D157D411yescharacteristic
35C2×#11929434—21no—
36C2×#11929434—21no—
37#14578931—22no—
38#14578931—22no—
39C4×Dic157C2×C411yescharacteristic
40C4×Dic157D411yescharacteristic
41C4×Dic157D411yescharacteristic
42C2×Q8×C157—21no—
43C2×C8×C157—21no—
44C2×C8×C157—21no—
45C4⋊C4×C157—21no—
46C4⋊C4×C157C2×C412yes—
47C42×C157C2311yescharacteristic
48C22×D157—22no—
49C22×D157C22⋊C411yescharacteristic
50D628—42no—
51D628—44no—
52D628—41no—
53D628—41no—
54D628—41no—
55D628—41no—
56C2×Dic157C22⋊C411yescharacteristic
57C2×Dic157C22⋊C411yescharacteristic
58C2×Dic157C22⋊C411yescharacteristic
59C4×D157—21no—
60C4×D157—21no—
61C4×D157—21no—
62C4×D157—21no—
63C4×D157—41no—
64C4×D157—44no—
65#11929434—41no—
66#11929434—41no—
67Q8×C157—41no—
68Q8×C157—41no—
69C2×C4×C157—22no—
70C2×C4×C157C22×C411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C8×C157—41no—
74C8×C157—41no—
75C22×C157C2×C22⋊C411yescharacteristic
76C2×D157—21no—
77C2×D157—21no—
78C2×D157—21no—
79C2×D157—42no—
80C2×D157—42no—
81C2×D157—42no—
82C4×C157—21no—
83C4×C157—42no—
84C4×C157#13511yescharacteristic
85C4×C157#13511yescharacteristic
86C4×C157AGL(1,ℤ/8)11yescharacteristic
87C4×C157AGL(1,ℤ/8)11yescharacteristic
88Dic157—21no—
89Dic157—21no—
90Dic157—21no—
91C2×C157#41311yescharacteristic
92C2×C157#41611yescharacteristic
93C2×C157#41811yescharacteristic
94D157—41no—
95D157—82no—
96C157#155311yescharacteristic, complemented, Sylow
97#1553—1571nomaximal, Sylow
98#532—1571no—
99#432—1571no—
100#431—1571no—
101#332—1571no—
102#332D15711yescharacteristic, complemented
103#331—1571no—
104#331—1571no—
105C2×#41—3141no—
106C4⋊Q8C2×D15711yescharacteristic
107#127—1571no—
108#124—3141no—
109#121—3141no—
110#121—1572no—
111C4×D4—3141no—
112C4×D4—1572no—
113C2×C42—1571no—
114C4⋊C8—1571no—
115C4⋊C8—1571no—
116C4⋊C8C2×D15711yescharacteristic
117C4⋊C8C2×D15711yescharacteristic
118C22⋊C8—3141no—
119C22⋊C8—3141no—
120#97—3141no—
121C4×C8—3141no—
122#41—6282no—
123#41—6282no—
124C2×Q8—21no—
125C2×D4—3142no—
126C2×D4—3141no—
127C2×D4—3141no—
128C2×D4—1572no—
129C22×C4—3142no—
130C22×C4—1571no—
131C22×C4—1571no—
132C22×C4—1571no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—3141no—
136C2×C8—3141no—
137C4⋊C4—21no—
138C4⋊C4C4×D15712yes—
139C22⋊C4—3142no—
140C22⋊C4—3142no—
141C42—1571no—
142C42—1571no—
143C42—1571no—
144C42C22×D15711yescharacteristic
145C23—3142no—
146C23—1571no—
147Q8—41no—
148Q8—41no—
149D4—6282no—
150D4—6284no—
151D4—6281no—
152D4—6281no—
153D4—6281no—
154D4—6281no—
155C2×C4—22no—
156C2×C4—3141no—
157C2×C4—3141no—
158C2×C4—3141no—
159C2×C4—3141no—
160C2×C4—6281no—
161C2×C4—6284no—
162C2×C4—1571no—
163C2×C4—1571no—
164C2×C4—1571no—
165C2×C4C2×C4×D15711yescharacteristic
166C2×C4D4×D15711yescharacteristic
167C2×C4D4×D15711yescharacteristic
168C8—41no—
169C8—41no—
170C8—6281no—
171C8—6281no—
172C22—3141no—
173C22—3141no—
174C22—3141no—
175C22—6282no—
176C22—6282no—
177C22—6282no—
178C22C22⋊C4×D15711yescharacteristic
179C4—21no—
180C4—42no—
181C4—3141no—
182C4—3141no—
183C4—3141no—
184C4#1909779211yescharacteristic
185C4#1909779411yescharacteristic
186C4#1909779511yescharacteristic
187C4#1909779811yescharacteristic
188C2—6281no—
189C2—12562no—
190C2#2375725611yescharacteristic
191C2#2375726811yescharacteristic
192C2#2375727611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#332×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757824C2
cosocleC42×C157C23
hypercenter#332D157
hypocenterC157#1553
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #23757329C2semidirect
3. #23757325C2semidirect
4. #23757019C2semidirect
5. #23757016C2semidirect
6. #23757016C2semidirect
7. #332×C157C2semidirect
96. C157#1553semidirect
102. #332D157semidirect

Maximal subgroups

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

subgroupindex
#237578242
#237573292
#237573252
#237570192
#237570162
#332×C1572
#1553157