Finite Group Databasebeta

← #23758222

Subgroups — #23758222

Order 10048.

154 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×C4⋊#10597845C211yesmaximal, characteristic
2C2×C4×#10597845C211yesmaximal, characteristic
3(C2×#10597845)⋊C4C211yesmaximal, characteristic
4(C2×#10597845)⋊C4C211yesmaximal, characteristic
5(C2×#10597845)⋊C4C211yesmaximal, characteristic
6(C2×#10597845)⋊C4C211yesmaximal, characteristic
7C4⋊C4×D157C211yesmaximal, characteristic
8C22×#10597845C2211yescharacteristic
9C22×#10597845C2211yescharacteristic
10C22×#10597845C2211yescharacteristic
11C22×#10597845C2211yescharacteristic
12C4⋊#10597845—22no—
13C4×#10597845—22no—
14C2×C4×D157C2211yescharacteristic
15C2×C4×D157C2211yescharacteristic
16C2×C4×D157C2211yescharacteristic
17C4⋊Dic157C411yescharacteristic, complemented
18#14578933C411yescharacteristic, complemented
19#14578933C411yescharacteristic, complemented
20C4⋊C4×C157C411yescharacteristic, complemented
21C2×#10597845—21no—
22C2×#10597845—21no—
23C2×#10597845—21no—
24C2×#10597845—21no—
25C2×#10597845—21no—
26C2×#10597845—21no—
27C2×#10597845—21no—
28C2×#10597845—21no—
29C2×#10597845—21no—
30C2×#10597845—21no—
31C2×#10597845D412yes—
32C2×#10597845Q812yes—
33C22×D157C2311yescharacteristic
34C2×Dic157C2×C411yescharacteristic
35C2×Dic157C2×C411yescharacteristic
36C2×Dic157C2×C411yescharacteristic
37C4×D157—21no—
38C4×D157—21no—
39C4×D157—21no—
40C4×D157—21no—
41C4×D157—21no—
42C4×D157—21no—
43C2×C4×C157C2×C411yescharacteristic
44C2×C4×C157C2×C411yescharacteristic
45C2×C4×C157C2×C411yescharacteristic
46C22×C157C22×C411yescharacteristic
47C2×D157C2×D411yescharacteristic
48C2×D157C2×Q811yescharacteristic
49C2×D157#4111yescharacteristic
50C2×D157#4111yescharacteristic
51C2×D157#4111yescharacteristic
52C2×D157#4111yescharacteristic
53#10597845—22no—
54#10597845—22no—
55#10597845—41no—
56#10597845—41no—
57C4×C157—21no—
58C4×C157—21no—
59C4×C157—21no—
60Dic157—21no—
61Dic157—21no—
62Dic157—21no—
63C2×C157#11711yescharacteristic
64C2×C157C4×D411yescharacteristic
65C2×C157C4×Q811yescharacteristic
66D157C22⋊Q811yescharacteristic
67D157#12311yescharacteristic
68D157#12511yescharacteristic
69D157#12611yescharacteristic
70C157#38711yescharacteristic, complemented, Sylow
71#387—1571nomaximal, Sylow
72C2×C4⋊C4—1571no—
73C2×C4⋊C4—1571no—
74C2×C42—1571no—
75#95—1571no—
76#95—1571no—
77#95—1571no—
78#95—1571no—
79C22×C4—1571no—
80C22×C4—1571no—
81C22×C4—1571no—
82C22×C4—1571no—
83C22×C4—1571no—
84C22×C4—1571no—
85C22×C4—1571no—
86C4⋊C4—3142no—
87C4⋊C4—1571no—
88C4⋊C4—1571no—
89C4⋊C4—1571no—
90C4⋊C4#1059784511yescharacteristic, complemented
91C42—3142no—
92C23—1571no—
93C2×C4—3141no—
94C2×C4—3141no—
95C2×C4—3141no—
96C2×C4—3141no—
97C2×C4—3141no—
98C2×C4—3141no—
99C2×C4—3141no—
100C2×C4—3141no—
101C2×C4—3141no—
102C2×C4—3141no—
103C2×C4—3141no—
104C2×C4—3141no—
105C2×C4—3141no—
106C2×C4—3141no—
107C2×C4—3141no—
108C2×C4—3141no—
109C2×C4—1572no—
110C2×C4—1572no—
111C2×C4—1571no—
112C2×C4—1571no—
113C2×C4—1571no—
114C2×C4C2×#1059784511yescharacteristic
115C2×C4C2×#1059784511yescharacteristic
116C2×C4C2×#1059784511yescharacteristic
117C22—1571no—
118C22—1571no—
119C22—1571no—
120C22—1571no—
121C22—1571no—
122C22—1571no—
123C22C22×#1059784511yescharacteristic
124C4—21no—
125C4—21no—
126C4—21no—
127C4—3142no—
128C4—3142no—
129C4—3141no—
130C4—3141no—
131C4—3141no—
132C4—6281no—
133C4—6281no—
134C2—1571no—
135C2—1571no—
136C2—1571no—
137C2—1571no—
138C2#1909785011yescharacteristic
139C2D4×#1059784511yescharacteristic
140C2Q8×#1059784511yescharacteristic
subgroupG/H
center, FrattiniC22C22×#10597845
commutator, socleC22×C157C22×C4
FittingC4⋊C4×C157C4
prime radical, cosocleC22×D157C23
hypercenterC4⋊C4#10597845
hypocenterC157#387
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
17. C4⋊Dic157C4semidirect
18. #14578933C4semidirect
19. #14578933C4semidirect
20. C4⋊C4×C157C4semidirect
70. C157#387semidirect
90. C4⋊C4#10597845semidirect