Finite Group Databasebeta

← #34098828

Subgroups — #34098828

Order 20096.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#23757821C211yesmaximal, characteristic
2#23757329C211yesmaximal, characteristic, complemented
3C4⋊C8×D157C211yesmaximal, characteristic, complemented
4#23757021C211yesmaximal, characteristic, complemented
5#23757021C211yesmaximal, characteristic, complemented
6#23757017C211yesmaximal, characteristic, complemented
7#331×C157C211yesmaximal, characteristic, complemented
8C2×#14578953C412yes—
9C2×C8×D157—21no—
10#19097771C2211yescharacteristic
11#19097758C412yes—
12#19097742—21no—
13#19097742—21no—
14D4×Dic157—21no—
15D4×Dic157—21no—
16C42×D157C2211yescharacteristic
17C4⋊#11929434C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19#19097700—21no—
20#19097683—21no—
21#19097681—21no—
22#127×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25#14578953—44no—
26C2×Dic314C2×C412yes—
27C2×C22⋊D157—22no—
28C22×Dic157—22no—
29C2×C4×D157C2×C411yescharacteristic
30C2×C4×D157D411yescharacteristic
31C2×C4×D157D411yescharacteristic
32C2×#11929434—21no—
33C2×#11929434—21no—
34C8×D157—42no—
35C4⋊Dic157—21no—
36C4⋊Dic157—21no—
37C22⋊Dic157—22no—
38C22⋊Dic157—22no—
39C4×Dic157C2×C411yescharacteristic
40C4×Dic157D411yescharacteristic
41C4×Dic157D411yescharacteristic
42C2×D4×C157—21no—
43C2×D4×C157—21no—
44C2×D4×C157C2×C412yes—
45C2×C8×C157—21no—
46C2×C8×C157—21no—
47C42×C157C2311yescharacteristic
48C22×D157C22⋊C411yescharacteristic
49Dic314—42no—
50C22⋊D157—44no—
51C2×Dic157—22no—
52C2×Dic157—44no—
53C2×Dic157C22⋊C411yescharacteristic
54C2×Dic157C22⋊C411yescharacteristic
55C2×Dic157C22⋊C411yescharacteristic
56C4×D157—22no—
57C4×D157—21no—
58C4×D157—21no—
59C4×D157—21no—
60C4×D157—21no—
61#11929434—41no—
62#11929434—41no—
63C23×C157—22no—
64D4×C157—42no—
65D4×C157—41no—
66D4×C157—41no—
67D4×C157—41no—
68D4×C157—41no—
69C2×C4×C157C22×C411yescharacteristic
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C8×C157—41no—
73C8×C157—41no—
74C22×C157—42no—
75C22×C157—42no—
76C22×C157—42no—
77C22×C157C2×C22⋊C411yescharacteristic
78C2×D157—21no—
79C2×D157—21no—
80C2×D157#10012yes—
81C4×C157—21no—
82C4×C157#13511yescharacteristic
83C4×C157#13511yescharacteristic
84C4×C157AGL(1,ℤ/8)11yescharacteristic
85C4×C157#13711yescharacteristic
86Dic157—21no—
87Dic157—21no—
88Dic157—21no—
89Dic157—42no—
90C2×C157—82no—
91C2×C157C2×#10011yescharacteristic
92C2×C157#41611yescharacteristic
93C2×C157#41711yescharacteristic
94D157—22no—
95C157#155111yescharacteristic, complemented, Sylow
96#1551—1571nomaximal, Sylow
97#532—1571no—
98#432—1571no—
99C2×C4⋊C8—1571no—
100#333—1571no—
101#333—1571no—
102#331—1571no—
103#331D15711yescharacteristic, complemented
104C2×#41—1572no—
105C22×C8—3141no—
106C4⋊Q8—1571no—
107#127C2×D15711yescharacteristic
108#124—1572no—
109#121—3141no—
110#121—3141no—
111C4×D4—3141no—
112C4×D4—3141no—
113C2×C42—1571no—
114C4⋊C8—3141no—
115C4⋊C8—1571no—
116C4⋊C8—1571no—
117C4⋊C8C2×D15711yescharacteristic
118C4⋊C8C2×D15711yescharacteristic
119C22⋊C8—3141no—
120#97—3141no—
121#41—6284no—
122C2×Q8—1572no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—3142no—
126C2×D4C4×D15712yes—
127C22×C4—3142no—
128C22×C4—1571no—
129C22×C4—1571no—
130C22×C4—1571no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—3141no—
134C2×C8—3141no—
135C2×C8—6282no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C22⋊C4—3142no—
139C22⋊C4—3142no—
140C42—1571no—
141C42—1571no—
142C42—1571no—
143C42C22×D15711yescharacteristic
144C23—22no—
145C23—1571no—
146Q8—6282no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—6284no—
153C2×C4—3142no—
154C2×C4—3141no—
155C2×C4—3141no—
156C2×C4—3141no—
157C2×C4—3141no—
158C2×C4—3142no—
159C2×C4—6284no—
160C2×C4—1571no—
161C2×C4—1571no—
162C2×C4—1571no—
163C2×C4C2×C4×D15711yescharacteristic
164C2×C4D4×D15711yescharacteristic
165C2×C4D4×D15711yescharacteristic
166C8—41no—
167C8—41no—
168C8—6281no—
169C8—6281no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—3141no—
174C22—3141no—
175C22—1572no—
176C22C22⋊C4×D15711yescharacteristic
177C4—21no—
178C4—3141no—
179C4—3141no—
180C4—3141no—
181C4—6282no—
182C4#1909779011yescharacteristic
183C4#1909779211yescharacteristic
184C4#1909779511yescharacteristic
185C4#1909780011yescharacteristic
186C2—82no—
187C2—3142no—
188C2#100×D15711yescharacteristic
189C2#2375726611yescharacteristic
190C2#2375727111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#331×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757821C2
cosocleC42×C157C23
hypercenter#331D157
hypocenterC157#1551
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #23757329C2semidirect
3. C4⋊C8×D157C2semidirect
4. #23757021C2semidirect
5. #23757021C2semidirect
6. #23757017C2semidirect
7. #331×C157C2semidirect
95. C157#1551semidirect
103. #331D157semidirect

Maximal subgroups

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

subgroupindex
#237578212
#237573292
C4⋊C8×D1572
#237570212
#237570172
#331×C1572
#1551157