Finite Group Databasebeta

← #34099180

Subgroups — #34099180

Order 20096.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757904C211yesmaximal, characteristic
2#23757609C212yesmaximal
3#23757212C211yesmaximal, characteristic
4#23757011C212yesmaximal
5#324×C157C211yesmaximal, characteristic
6#19097770—22no—
7#19097762—22no—
8#19097750—21no—
9#19097750C2212yes—
10#19097730—21no—
11C2×C4⋊Dic157C2211yescharacteristic
12#19097705—22no—
13#19097696—22no—
14#19097678—21no—
15#19097678—21no—
16#19097678C2211yescharacteristic
17C2×C4⋊C4×C157C2211yescharacteristic
18C22⋊C8×C157C2212yes—
19C2×Dic314—21no—
20C2×Dic314D412yes—
21C22×Dic157—21no—
22C22×Dic157—21no—
23C4⋊Dic157—21no—
24C4⋊Dic157—21no—
25C4⋊Dic157—21no—
26C4⋊Dic157—22no—
27C4⋊Dic157D412yes—
28#14578933—22no—
29#14578933—22no—
30C22⋊Dic157—22no—
31C4×Dic157—22no—
32C22×C4×C157D411yescharacteristic
33C22×C4×C157D411yescharacteristic
34C22×C4×C157C2311yescharacteristic
35C2×C8×C157—22no—
36C4⋊C4×C157—22no—
37Dic314—42no—
38Dic314—81no—
39C2×Dic157—22no—
40C2×Dic157—22no—
41C2×Dic157—41no—
42C2×Dic157—41no—
43C2×Dic157—42no—
44C2×Dic157—41no—
45C2×Dic157—41no—
46C23×C157C2×D411yescharacteristic
47C2×C4×C157—21no—
48C2×C4×C157—21no—
49C2×C4×C157—21no—
50C2×C4×C157—41no—
51C2×C4×C157—41no—
52C2×C4×C157Q1612yes—
53C2×C4×C157C2×D412yes—
54C8×C157—42no—
55C22×C157—21no—
56C22×C157—21no—
57C22×C157#12011yescharacteristic
58C22×C157C2×Q1611yescharacteristic
59C22×C157#13711yescharacteristic
60C4×C157—22no—
61C4×C157—22no—
62C4×C157—41no—
63Dic157—42no—
64Dic157—42no—
65Dic157—81no—
66Dic157—81no—
67C2×C157—21no—
68C2×C157—21no—
69C2×C157#45111yescharacteristic
70C2×C157#45411yescharacteristic
71C2×C157#45811yescharacteristic
72C157#161711yescharacteristic, complemented, Sylow
73#1617—1571nomaximal, Sylow
74#544—1571no—
75#484—1572no—
76#400—1571no—
77#328—1572no—
78#324D15711yescharacteristic
79C4⋊Q8—3142no—
80#125—3142no—
81C22⋊Q8—3141no—
82C22⋊Q8—1572no—
83#117—3141no—
84C2×C4⋊C4—1571no—
85C2×C4⋊C4C2×D15711yescharacteristic
86#107—3142no—
87#103—3142no—
88C22⋊C8C2×D15712yes—
89#95—3141no—
90#95—3141no—
91#95—1571no—
92C2×Q8—3141no—
93C2×Q8—1572no—
94C22×C4—3141no—
95C22×C4—3141no—
96C22×C4D62811yescharacteristic
97C22×C4D62811yescharacteristic
98C22×C4C22×D15711yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—3141no—
102C4⋊C4—3141no—
103C4⋊C4—3141no—
104C4⋊C4—3142no—
105C4⋊C4—3142no—
106C4⋊C4—3142no—
107C4⋊C4—1572no—
108C22⋊C4—3142no—
109C42—3142no—
110C23C2×D62811yescharacteristic
111Q8—6282no—
112Q8—12561no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—3142no—
119C2×C4—3142no—
120C2×C4—6281no—
121C2×C4—6281no—
122C2×C4—6282no—
123C2×C4—6281no—
124C2×C4—6281no—
125C2×C4Dic62812yes—
126C2×C4D4×D15712yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1909774111yescharacteristic
131C22C2×Dic62811yescharacteristic
132C22#1909780411yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—6282no—
137C4—6282no—
138C4—12561no—
139C4—12561no—
140C2—21no—
141C2—21no—
142C2#2375743111yescharacteristic
143C2#2375744811yescharacteristic
144C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#324×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#324D157
hypocenterC157#1617
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
72. C157#1617semidirect

Maximal subgroups

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

subgroupindex
#237579042
#237576092
#237572122
#237570112
#324×C1572
#1617157