Finite Group Databasebeta

← #34098812

Subgroups — #34098812

Order 20096.

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

normal subgroups only

This group has 260 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#23757824C211yesmaximal, characteristic
2#23757295C211yesmaximal, characteristic, complemented
3C4⋊C8×D157C211yesmaximal, characteristic, complemented
4#23757019C211yesmaximal, characteristic, complemented
5#23757016C211yesmaximal, characteristic, complemented
6#23757016C211yesmaximal, characteristic, complemented
7#332×C157C211yesmaximal, characteristic, complemented
8C2×#14578955—21no—
9C2×#14578937—21no—
10C2×C8×D157—21no—
11#19097768C2211yescharacteristic
12#19097760—21no—
13#19097746—21no—
14#19097746C412yes—
15#19097733—21no—
16#19097733C412yes—
17C42×D157C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19C4⋊#11929434C2211yescharacteristic
20#19097700—21no—
21#19097700—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
35#14578937—42no—
36C2×#11929434—21no—
37C2×#11929434—21no—
38C8×D157—42no—
39#14578931—22no—
40#14578931—22no—
41C4×Dic157C2×C411yescharacteristic
42C4×Dic157D411yescharacteristic
43C4×Dic157D411yescharacteristic
44C2×Q8×C157—21no—
45C2×C8×C157—21no—
46C2×C8×C157—21no—
47C4⋊C4×C157—21no—
48C4⋊C4×C157C2×C412yes—
49C42×C157C2311yescharacteristic
50C22×D157—22no—
51C22×D157C22⋊C411yescharacteristic
52D628—42no—
53D628—44no—
54D628—41no—
55D628—41no—
56D628—41no—
57D628—41no—
58C2×Dic157C22⋊C411yescharacteristic
59C2×Dic157C22⋊C411yescharacteristic
60C2×Dic157C22⋊C411yescharacteristic
61C4×D157—21no—
62C4×D157—21no—
63C4×D157—41no—
64C4×D157—44no—
65C4×D157D812yes—
66C4×D157SD1612yes—
67#11929434—41no—
68#11929434—41no—
69Q8×C157—41no—
70Q8×C157—41no—
71C2×C4×C157—22no—
72C2×C4×C157C22×C411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C8×C157—41no—
76C8×C157—41no—
77C22×C157C2×C22⋊C411yescharacteristic
78C2×D157—21no—
79C2×D157—21no—
80C2×D157—42no—
81C2×D157—42no—
82C2×D157—42no—
83C2×D157#10212yes—
84C4×C157—21no—
85C4×C157—42no—
86C4×C157C2×D811yescharacteristic
87C4×C157C2×SD1611yescharacteristic
88C4×C157AGL(1,ℤ/8)11yescharacteristic
89C4×C157#13711yescharacteristic
90Dic157—21no—
91Dic157—21no—
92Dic157#10212yes—
93C2×C157#41311yescharacteristic
94C2×C157C2×#10211yescharacteristic
95C2×C157#41711yescharacteristic
96D157—22no—
97D157—82no—
98C157#154711yescharacteristic, complemented, Sylow
99#1547—1571nomaximal, Sylow
100#532—1571no—
101#423—1571no—
102C2×C4⋊C8—1571no—
103#332—1571no—
104#332D15711yescharacteristic, complemented
105#331—1571no—
106#331—1571no—
107C2×#41—3141no—
108C2×M16—3141no—
109C22×C8—3141no—
110C4⋊Q8C2×D15711yescharacteristic
111#127—1571no—
112#124—3141no—
113#121—3141no—
114#121—1572no—
115C4×D4—3141no—
116C4×D4—1572no—
117C2×C42—1571no—
118C4⋊C8—3141no—
119C4⋊C8—3141no—
120C4⋊C8—1571no—
121C4⋊C8—1571no—
122C4⋊C8C2×D15711yescharacteristic
123C4⋊C8C2×D15711yescharacteristic
124#41—6282no—
125#41—6282no—
126C2×Q8—21no—
127C2×D4—3142no—
128C2×D4—3141no—
129C2×D4—3141no—
130C2×D4—1572no—
131C22×C4—3142no—
132C22×C4—1571no—
133C22×C4—1571no—
134C22×C4—1571no—
135M16—6282no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—3141no—
139C2×C8—3141no—
140C2×C8—6282no—
141C4⋊C4—21no—
142C4⋊C4C4×D15712yes—
143C22⋊C4—3142no—
144C22⋊C4—3142no—
145C42—1571no—
146C42—1571no—
147C42—1571no—
148C42C22×D15711yescharacteristic
149C23—3142no—
150C23—1571no—
151Q8—41no—
152Q8—41no—
153D4—6282no—
154D4—6284no—
155D4—6281no—
156D4—6281no—
157D4—6281no—
158D4—6281no—
159C2×C4—22no—
160C2×C4—3141no—
161C2×C4—3141no—
162C2×C4—6281no—
163C2×C4—6284no—
164C2×C4—1571no—
165C2×C4—1571no—
166C2×C4—1571no—
167C2×C4—1572no—
168C2×C4—1572no—
169C2×C4C2×C4×D15711yescharacteristic
170C2×C4D4×D15711yescharacteristic
171C2×C4D4×D15711yescharacteristic
172C8—41no—
173C8—41no—
174C8—6281no—
175C8—6281no—
176C22—3141no—
177C22—3141no—
178C22—6282no—
179C22—6282no—
180C22—6282no—
181C22—1572no—
182C22C22⋊C4×D15711yescharacteristic
183C4—21no—
184C4—42no—
185C4—3141no—
186C4—3141no—
187C4—1572no—
188C4D8×D15711yescharacteristic
189C4SD16×D15711yescharacteristic
190C4#1909779811yescharacteristic
191C4#1909780311yescharacteristic
192C2—3142no—
193C2—12562no—
194C2#2375725611yescharacteristic
195C2#102×D15711yescharacteristic
196C2#2375727311yescharacteristic
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#1547
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. #23757295C2semidirect
3. C4⋊C8×D157C2semidirect
4. #23757019C2semidirect
5. #23757016C2semidirect
6. #23757016C2semidirect
7. #332×C157C2semidirect
98. C157#1547semidirect
104. #332D157semidirect

Maximal subgroups

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

subgroupindex
#237578242
#237572952
C4⋊C8×D1572
#237570192
#237570162
#332×C1572
#1547157