Finite Group Databasebeta

← #34102354

Subgroups — #34102354

Order 20096.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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#23757528C211yesmaximal, characteristic
2#23757320C211yesmaximal, characteristic
3#23757097C211yesmaximal, characteristic, complemented
4#23757096C211yesmaximal, characteristic, complemented
5#23757089C211yesmaximal, characteristic, complemented
6#23757054C211yesmaximal, characteristic
7#362×C157C211yesmaximal, characteristic, complemented
8C2×#14578937C2211yescharacteristic
9M16×D157—21no—
10#19097747—21no—
11#19097711C2211yescharacteristic
12#19097707C2211yescharacteristic
13#19097706—21no—
14#19097703C2211yescharacteristic
15#19097695—21no—
16C2×Q16×C157C2211yescharacteristic
17M32×C157C2211yescharacteristic
18#108×C157C2211yescharacteristic
19C2×C4×D157D411yescharacteristic
20#14578938—21no—
21#14578937—21no—
22#14578937—21no—
23#14578937—41no—
24C2×#11929434D411yescharacteristic
25C8×D157—41no—
26C4⋊Dic157—21no—
27#14578933—41no—
28#14578931—41no—
29#14578929—21no—
30C2×Q8×C157—21no—
31Q16×C157—21no—
32Q16×C157—21no—
33M16×C157—21no—
34C2×C8×C157C2311yescharacteristic
35C16×C157—21no—
36C22×D157SD1611yescharacteristic
37C2×Dic157—41no—
38C2×Dic157SD1611yescharacteristic
39C4×D157—21no—
40C4×D157—21no—
41#11929434—21no—
42#11929434—41no—
43Q8×C157—41no—
44Q8×C157—41no—
45C2×C4×C157—41no—
46C2×C4×C157C2×D411yescharacteristic
47C8×C157—41no—
48C8×C157#4111yescharacteristic
49C8×C157#4111yescharacteristic
50C22×C157C2×SD1611yescharacteristic
51C2×D157—21no—
52C2×D157—41no—
53C4×C157—81no—
54C4×C157#12311yescharacteristic
55C4×C157AGL(1,ℤ/8)11yescharacteristic
56Dic157—21no—
57Dic157—81no—
58C2×C157—21no—
59C2×C157#48111yescharacteristic
60D157—41no—
61C157#223911yescharacteristic, complemented, Sylow
62#2239—1571nomaximal, Sylow
63#470—1571no—
64#430—1571no—
65#365—1571no—
66#365—1571no—
67#362—1571no—
68#362D15711yescharacteristic, complemented
69#349—1571no—
70C2×Q16C2×D15711yescharacteristic
71C2×M16—3141no—
72C2×M16—1571no—
73C22⋊Q8—3141no—
74M32—1571no—
75M32C2×D15711yescharacteristic
76#108—3141no—
77#108—1571no—
78#108C2×D15711yescharacteristic
79#106—1571no—
80#103—3141no—
81C2×Q8—21no—
82C22×C4—1571no—
83Q16—21no—
84Q16—21no—
85M16—21no—
86M16—3141no—
87M16—3141no—
88M16—3141no—
89M16—6281no—
90C2×C8—6281no—
91C2×C8—1571no—
92C2×C8C22×D15711yescharacteristic
93C4⋊C4—3141no—
94C4⋊C4—6281no—
95C22⋊C4—6281no—
96C16—21no—
97C16—3141no—
98C23—1571no—
99Q8—41no—
100Q8—41no—
101C2×C4—41no—
102C2×C4—3141no—
103C2×C4—3141no—
104C2×C4—6281no—
105C2×C4—1571no—
106C2×C4D4×D15711yescharacteristic
107C8—41no—
108C8—3141no—
109C8—6281no—
110C8#1457895311yescharacteristic
111C8#1457895411yescharacteristic
112C22—3141no—
113C22—6281no—
114C22SD16×D15711yescharacteristic
115C4—81no—
116C4—3141no—
117C4—12561no—
118C4#1909775311yescharacteristic
119C4#1909779511yescharacteristic
120C2—21no—
121C2—6281no—
122C2#2375759011yescharacteristic
subgroupG/H
centerC2#23757590
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#362×C157C2
socleC2×C157#481
prime radicalC22×D157SD16
hypercenter#362D157
hypocenterC157#2239
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
3. #23757097C2semidirect
4. #23757096C2semidirect
5. #23757089C2semidirect
7. #362×C157C2semidirect
61. C157#2239semidirect
68. #362D157semidirect

Maximal subgroups

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

subgroupindex
#237575282
#237573202
#237570972
#237570962
#237570892
#237570542
#362×C1572
#2239157