Finite Group Databasebeta

← #34108459

Subgroups — #34108459

Order 20096.

582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19097754C211yesmaximal, characteristic
2C22×C4×Dic157C211yesmaximal, characteristic, complemented
3#23757165C214yesmaximal, complemented
4#23757158C214yesmaximal, complemented
5#23757150C212yesmaximal
6#23757148C212yesmaximal, complemented
7#381×C157C211yesmaximal, characteristic, complemented
8C22×C22⋊D157C2211yescharacteristic
9C23×Dic157C2212yes—
10#19097754—24no—
11C2×C4⋊Dic157C2214yes—
12C2×#14578933C2212yes—
13C2×C22⋊Dic157C2211yescharacteristic
14C2×#14578931C2214yes—
15C2×#14578931C2212yes—
16C2×C4×Dic157—24no—
17C2×C4×Dic157C2214yes—
18#19097678C2214yes—
19#19097678C2214yes—
20C23×C4×C157C2211yescharacteristic
21C2×C22⋊C4×C157C2212yes—
22#95×C157C2214yes—
23C23×D157C2311yescharacteristic
24C2×C22⋊D157—22no—
25C2×C22⋊D157—24no—
26C22×Dic157—28no—
27C22×Dic157—24no—
28C22×Dic157C2311yescharacteristic
29C22×Dic157C2312yes—
30C22×Dic157C2314yes—
31C4⋊Dic157—28no—
32#14578933—24no—
33C22⋊Dic157—22no—
34#14578931—28no—
35#14578931—24no—
36C4×Dic157—28no—
37C24×C157C2311yescharacteristic
38C22×C4×C157—24no—
39C22×C4×C157D414yes—
40C22×C4×C157C2314yes—
41C22×C4×C157C2312yes—
42C22⋊C4×C157—24no—
43C22×D157—21no—
44C22×D157—22no—
45C22×D157—24no—
46C22⋊D157—44no—
47C2×Dic157—216no—
48C2×Dic157—24no—
49C2×Dic157—24no—
50C2×Dic157—21no—
51C2×Dic157—22no—
52C2×Dic157—22no—
53C2×Dic157—24no—
54C2×Dic157#4118yes—
55C23×C157—24no—
56C23×C157C2×D412yes—
57C23×C157#4114yes—
58C23×C157C2411yescharacteristic
59C2×C4×C157—28no—
60C2×C4×C157—24no—
61C2×C4×C157—24no—
62C2×C4×C157—24no—
63C2×C4×C157—24no—
64C2×C4×C157C2×D414yes—
65C22×C157—24no—
66C22×C157—28no—
67C22×C157#12314yes—
68C22×C157C22×D411yescharacteristic
69C22×C157C2×#4114yes—
70C22×C157C2×#4112yes—
71C2×D157—41no—
72C2×D157—42no—
73C2×D157—44no—
74C4×C157—24no—
75C4×C157—44no—
76Dic157—28no—
77Dic157—41no—
78Dic157—42no—
79C2×C157—24no—
80C2×C157C2×#12311yescharacteristic
81C2×C157#52512yes—
82C2×C157#52914yes—
83D157—81no—
84C157#285311yescharacteristic, complemented, Sylow
85#2853—1571nomaximal, Sylow
86C2×#123—1571no—
87C22×C42—1571no—
88#388—1574no—
89#387—1574no—
90#386—1572no—
91#385—1572no—
92#381D15711yescharacteristic, complemented
93C22×D4—1571no—
94C23×C4—1572no—
95C23×C4C2×D15711yescharacteristic
96#123—3144no—
97C2×C4⋊C4—1572no—
98C2×C4⋊C4—1574no—
99C2×C22⋊C4—1571no—
100C2×C22⋊C4—1572no—
101C2×C22⋊C4—1574no—
102C2×C22⋊C4C2×D15712yes—
103C2×C42—3144no—
104C2×C42—1574no—
105#95—1574no—
106#95—1574no—
107#95C2×D15714yes—
108C24—1571no—
109C24C22×D15711yescharacteristic
110C2×D4—3142no—
111C2×D4—3144no—
112C22×C4—24no—
113C22×C4—3144no—
114C22×C4—3148no—
115C22×C4—1571no—
116C22×C4—1572no—
117C22×C4—1574no—
118C22×C4D62814yes—
119C22×C4C22×D15714yes—
120C22×C4C22×D15712yes—
121C4⋊C4—3148no—
122C4⋊C4—3144no—
123C22⋊C4—24no—
124C22⋊C4—3148no—
125C22⋊C4—3142no—
126C22⋊C4—3144no—
127C42—3148no—
128C23—24no—
129C23—3141no—
130C23—3144no—
131C23—3142no—
132C23C2×D62812yes—
133C23#1457895314yes—
134C23C23×D15711yescharacteristic
135D4—6284no—
136C2×C4—28no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—31416no—
142C2×C4—3144no—
143C2×C4—3144no—
144C2×C4—3142no—
145C2×C4—3141no—
146C2×C4—3144no—
147C2×C4—3142no—
148C2×C4—1578no—
149C2×C4C2×D62814yes—
150C22—24no—
151C22—28no—
152C22—6281no—
153C22—6282no—
154C22—6284no—
155C22#1909775514yes—
156C22C22×D62811yescharacteristic
157C22#41×D15714yes—
158C22C2×#1457895312yes—
159C4—24no—
160C4—44no—
161C4—3148no—
162C4—6281no—
163C4—6282no—
164C2—24no—
165C2—12561no—
166C2C2×#1909775511yescharacteristic
167C2#2375778512yes—
168C2#2375780014yes—
subgroupG/H
center, FrattiniC23C23×D157
commutator, socle, cosocleC23×C157C24
Fitting#381×C157C2
prime radicalC22×C22⋊D157C22
hypercenter#381D157
hypocenterC157#2853
LCSG ▷ C23×C157 ▷ C157
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic157C2semidirect
3. #23757165C2semidirect
4. #23757158C2semidirect
6. #23757148C2semidirect
7. #381×C157C2semidirect
84. C157#2853semidirect
92. #381D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977542
C22×C4×Dic1572
#237571652
#237571582
#237571502
#237571482
#381×C1572
#2853157