Finite Group Databasebeta

← #34098682

Subgroups — #34098682

Order 20096.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#23757823C211yesmaximal, characteristic
2#23757330C211yesmaximal, characteristic, complemented
3#23757006C214yesmaximal, complemented
4#383×C157C211yesmaximal, characteristic, complemented
5C2×#14578954—21no—
6#19097771C411yescharacteristic, complemented
7#19097768C411yescharacteristic, complemented
8#19097759—21no—
9#19097745—21no—
10#19097745C2212yes—
11C4×D628—21no—
12C4×D628C412yescomplemented
13C4⋊#11929434—21no—
14C22⋊#11929434C2212yes—
15#19097682—21no—
16C2×C42×C157C2211yescharacteristic
17#95×C157—21no—
18#95×C157—21no—
19#95×C157C2212yes—
20#14578954—44no—
21C2×Dic314—21no—
22C2×D628—21no—
23C2×D628—21no—
24C2×D628C2×C412yes—
25C2×C22⋊D157—22no—
26C2×C4×D157—22no—
27C2×#11929434—22no—
28C4⋊Dic157—21no—
29C4⋊Dic157C2×C412yes—
30#14578931—22no—
31#14578931—22no—
32C22×C4×C157—22no—
33C22×C4×C157D411yescharacteristic
34C22×C4×C157D411yescharacteristic
35C22×C4×C157C2311yescharacteristic
36C42×C157C2×C411yescharacteristic
37C42×C157C2×C411yescharacteristic
38C42×C157D411yescharacteristic
39C42×C157D411yescharacteristic
40C22×D157—22no—
41Dic314—42no—
42D628—42no—
43D628—42no—
44D628—42no—
45C22⋊D157—44no—
46C2×Dic157—22no—
47C4×D157—44no—
48#11929434—42no—
49C23×C157C2×D411yescharacteristic
50C2×C4×C157—22no—
51C2×C4×C157—41no—
52C2×C4×C157—41no—
53C2×C4×C157—42no—
54C2×C4×C157—42no—
55C2×C4×C157—42no—
56C2×C4×C157C22⋊C411yescharacteristic
57C2×C4×C157C22⋊C411yescharacteristic
58C2×C4×C157C22⋊C411yescharacteristic
59C2×C4×C157C22⋊C411yescharacteristic
60C2×C4×C157C22×C411yescharacteristic
61C2×C4×C157C2×D411yescharacteristic
62C22×C157—21no—
63C22×C157—21no—
64C22×C157C2×C22⋊C411yescharacteristic
65C22×C157AGL(1,ℤ/8)12yes—
66C2×D157—42no—
67C2×D157—42no—
68C2×D157—42no—
69C4×C157—21no—
70C4×C157—21no—
71C4×C157—21no—
72C4×C157—21no—
73C4×C157—21no—
74C4×C157—21no—
75C4×C157—82no—
76Dic157—42no—
77C2×C157—22no—
78C2×C157#41011yescharacteristic
79C2×C157#41811yescharacteristic
80C2×C157#42111yescharacteristic
81D157—82no—
82C157#151411yescharacteristic, complemented, Sylow
83#1514—1571nomaximal, Sylow
84#532—1571no—
85#432—1571no—
86#383D15711yescharacteristic, complemented
87#327—1574no—
88C2×#41—3141no—
89C4⋊Q8—1571no—
90#127—1571no—
91#124—3141no—
92#121—3141no—
93#121—1572no—
94C4×D4—3141no—
95C4×D4—1572no—
96C2×C42C2×D15711yescharacteristic
97C4⋊C8—3141no—
98C22⋊C8—1572no—
99#97—3141no—
100#95—21no—
101#95—21no—
102#95C2×D15712yes—
103#41—6284no—
104C2×Q8—3141no—
105C2×D4—3142no—
106C2×D4—3141no—
107C2×D4—3141no—
108C2×D4—1572no—
109C22×C4—22no—
110C22×C4—3142no—
111C22×C4C22⋊D15711yescharacteristic
112C22×C4C22⋊D15711yescharacteristic
113C22×C4C22×D15711yescharacteristic
114C2×C8—3142no—
115C4⋊C4—3141no—
116C4⋊C4—1572no—
117C22⋊C4—3142no—
118C22⋊C4—3142no—
119C42C4×D15711yescharacteristic
120C42C4×D15711yescharacteristic
121C42D62811yescharacteristic
122C42D62811yescharacteristic
123C23—3142no—
124C23C2×C22⋊D15711yescharacteristic
125Q8—6282no—
126D4—6282no—
127D4—6282no—
128D4—6282no—
129D4—6284no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—42no—
136C2×C4—3142no—
137C2×C4—6284no—
138C2×C4#1457893111yescharacteristic
139C2×C4#1457893111yescharacteristic
140C2×C4#1457893111yescharacteristic
141C2×C4#1457893111yescharacteristic
142C2×C4C2×C4×D15711yescharacteristic
143C2×C4C2×D62811yescharacteristic
144C8—6282no—
145C22—21no—
146C22—21no—
147C22—6282no—
148C22—6282no—
149C22—6282no—
150C22C2×#1457893111yescharacteristic
151C22#1909779612yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—82no—
159C4—6282no—
160C2—22no—
161C2—12562no—
162C2#2375724611yescharacteristic
163C2#2375727711yescharacteristic
164C2#2375729111yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#383×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757823C2
cosocleC22×C4×C157C23
hypercenter#383D157
hypocenterC157#1514
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #23757330C2semidirect
3. #23757006C2semidirect
4. #383×C157C2semidirect
6. #19097771C4semidirect
7. #19097768C4semidirect
12. C4×D628C4semidirect
82. C157#1514semidirect
86. #383D157semidirect

Maximal subgroups

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

subgroupindex
#237578232
#237573302
#237570062
#383×C1572
#1514157