Finite Group Databasebeta

← #34098838

Subgroups — #34098838

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#23757821C211yesmaximal, characteristic
2#23757329C211yesmaximal, characteristic, complemented
3#23757325C211yesmaximal, characteristic, complemented
4#23757020C211yesmaximal, characteristic, complemented
5#23757018C211yesmaximal, characteristic, complemented
6#23757017C211yesmaximal, characteristic, complemented
7#331×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9#19097771C2211yescharacteristic
10#19097758—21no—
11#19097742—21no—
12#19097742C412yes—
13D4×Dic157—21no—
14D4×Dic157C412yes—
15C42×D157C2211yescharacteristic
16C4⋊#11929434C2211yescharacteristic
17C4⋊#11929434C2211yescharacteristic
18#19097683—21no—
19#19097683—21no—
20#19097681—21no—
21C8×Dic157—21no—
22#127×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25#14578953—42no—
26#14578953—42no—
27C2×Dic314—21no—
28C2×C22⋊D157—22no—
29C22×Dic157—22no—
30C2×C4×D157C2×C411yescharacteristic
31C2×C4×D157D411yescharacteristic
32C2×C4×D157D411yescharacteristic
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157C2×C412yes—
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—41no—
50Dic314—41no—
51C22⋊D157—44no—
52C2×Dic157—22no—
53C2×Dic157—44no—
54C2×Dic157C22⋊C411yescharacteristic
55C2×Dic157C22⋊C411yescharacteristic
56C2×Dic157C22⋊C411yescharacteristic
57C4×D157—21no—
58C4×D157—21no—
59C4×D157—21no—
60C4×D157—21no—
61C4×D157—41no—
62#11929434—41no—
63#11929434—41no—
64C23×C157—22no—
65D4×C157—42no—
66D4×C157—41no—
67D4×C157—41no—
68D4×C157—41no—
69D4×C157—41no—
70C2×C4×C157C22×C411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C8×C157—41no—
74C8×C157—41no—
75C22×C157—42no—
76C22×C157—42no—
77C22×C157—42no—
78C22×C157C2×C22⋊C411yescharacteristic
79C2×D157—21no—
80C2×D157—21no—
81C2×D157—21no—
82C4×C157—21no—
83C4×C157#13511yescharacteristic
84C4×C157#13511yescharacteristic
85C4×C157AGL(1,ℤ/8)11yescharacteristic
86C4×C157AGL(1,ℤ/8)11yescharacteristic
87Dic157—21no—
88Dic157—21no—
89Dic157—21no—
90Dic157—42no—
91C2×C157—82no—
92C2×C157#41311yescharacteristic
93C2×C157#41611yescharacteristic
94C2×C157#41811yescharacteristic
95D157—41no—
96C157#155311yescharacteristic, complemented, Sylow
97#1553—1571nomaximal, Sylow
98#532—1571no—
99#432—1571no—
100#431—1571no—
101#332—1571no—
102#332—1571no—
103#331—1571no—
104#331D15711yescharacteristic, complemented
105C2×#41—3141no—
106C4⋊Q8—1571no—
107#127C2×D15711yescharacteristic
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—3141no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—3142no—
128C2×D4C4×D15712yes—
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—3141no—
138C4⋊C4—1572no—
139C22⋊C4—3142no—
140C22⋊C4—3142no—
141C42—1571no—
142C42—1571no—
143C42—1571no—
144C42C22×D15711yescharacteristic
145C23—22no—
146C23—1571no—
147Q8—6281no—
148Q8—6281no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—6284no—
155C2×C4—3141no—
156C2×C4—3141no—
157C2×C4—3141no—
158C2×C4—3141no—
159C2×C4—3142no—
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—42no—
173C22—42no—
174C22—42no—
175C22—3141no—
176C22—3141no—
177C22—3141no—
178C22C22⋊C4×D15711yescharacteristic
179C4—21no—
180C4—3141no—
181C4—3141no—
182C4—3141no—
183C4—6282no—
184C4#1909779011yescharacteristic
185C4#1909779211yescharacteristic
186C4#1909779511yescharacteristic
187C4#1909779811yescharacteristic
188C2—82no—
189C2—6281no—
190C2#2375725411yescharacteristic
191C2#2375726611yescharacteristic
192C2#2375727611yescharacteristic
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#1553
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. #23757325C2semidirect
4. #23757020C2semidirect
5. #23757018C2semidirect
6. #23757017C2semidirect
7. #331×C157C2semidirect
96. C157#1553semidirect
104. #331D157semidirect

Maximal subgroups

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

subgroupindex
#237578212
#237573292
#237573252
#237570202
#237570182
#237570172
#331×C1572
#1553157