Finite Group Databasebeta

← #34101362

Subgroups — #34101362

Order 20096.

290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19097698C212yesmaximal, complemented
2#23757274C212yesmaximal, complemented
3#23757138C211yesmaximal, characteristic, complemented
4#23757042C211yesmaximal, characteristic, complemented
5#537×C157C211yesmaximal, characteristic
6C2×#14578938C2212yes—
7C2×C4⋊Dic157C2211yescharacteristic
8C2×C4×Dic157C2211yescharacteristic
9#19097698—24no—
10#19097695—22no—
11#19097692—22no—
12#19097678—22no—
13C2×#41×C157C2212yes—
14C22⋊Q8×C157—22no—
15#121×C157—22no—
16#121×C157—22no—
17C2×C4⋊C4×C157C2211yescharacteristic
18C22×Dic157—21no—
19C22×Dic157—21no—
20#14578938—22no—
21#14578938—22no—
22C2×#11929434—22no—
23C4⋊Dic157—22no—
24C4×Dic157—21no—
25C4×Dic157D412yescomplemented
26#41×C157—22no—
27#41×C157—22no—
28#41×C157—22no—
29#41×C157—22no—
30C2×Q8×C157D412yes—
31C2×D4×C157—22no—
32C2×D4×C157—22no—
33C2×D4×C157D412yes—
34C22×C4×C157—22no—
35C22×C4×C157D412yes—
36C22×C4×C157C2311yescharacteristic
37C4⋊C4×C157—22no—
38C4⋊C4×C157—22no—
39C22⋊C4×C157—24no—
40C2×Dic157—22no—
41C2×Dic157—41no—
42C2×Dic157—41no—
43C2×Dic157—42no—
44C2×Dic157—41no—
45#11929434—42no—
46C23×C157—22no—
47C23×C157C2×D411yescharacteristic
48Q8×C157—22no—
49Q8×C157—22no—
50D4×C157—22no—
51D4×C157—22no—
52D4×C157—42no—
53D4×C157—42no—
54D4×C157—82no—
55C2×C4×C157—22no—
56C2×C4×C157—22no—
57C2×C4×C157—42no—
58C2×C4×C157—42no—
59C2×C4×C157—42no—
60C2×C4×C157C2×D411yescharacteristic
61C2×C4×C157C2×D412yes—
62C2×C4×C157#4112yes—
63C2×C4×C157#4111yescharacteristic
64C22×C157—21no—
65C22×C157—21no—
66C22×C157—42no—
67C22×C157—42no—
68C22×C157—42no—
69C22×C157#12011yescharacteristic
70C22×C157#12111yescharacteristic
71C22×C157#12411yescharacteristic
72C4×C157—42no—
73C4×C157—42no—
74C4×C157#12112yes—
75C4×C157#12312yes—
76Dic157—42no—
77Dic157—81no—
78C2×C157—21no—
79C2×C157—21no—
80C2×C157—82no—
81C2×C157#39411yescharacteristic
82C2×C157#45411yescharacteristic
83C2×C157#45511yescharacteristic
84C157#204011yescharacteristic, complemented, Sylow
85#2040—1571nomaximal, Sylow
86#537D15711yescharacteristic
87C2×#104—1572no—
88#417—1572no—
89#382—1571no—
90#343—1571no—
91C2×#41C2×D15712yes—
92C2×M16—1572no—
93C22⋊Q8—22no—
94#121—22no—
95#121—22no—
96C2×C4⋊C4—1571no—
97C2×C4⋊C4C2×D15711yescharacteristic
98C2×C42—1571no—
99#104—3144no—
100#103—3142no—
101#102—3142no—
102#95—3142no—
103#41—22no—
104#41—22no—
105#41—22no—
106#41—22no—
107C2×Q8C22⋊D15712yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4C22⋊D15712yes—
111C22×C4—22no—
112C22×C4—3141no—
113C22×C4—3141no—
114C22×C4C22⋊D15712yes—
115C22×C4C22×D15711yescharacteristic
116M16—3142no—
117M16—3142no—
118C2×C8—3142no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—3142no—
122C22⋊C4—24no—
123C42—3141no—
124C42—1572no—
125C23—22no—
126C23C2×C22⋊D15711yescharacteristic
127Q8—22no—
128Q8—22no—
129D4—22no—
130D4—22no—
131D4—42no—
132D4—42no—
133D4—82no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—3142no—
140C2×C4—6281no—
141C2×C4—6281no—
142C2×C4—6282no—
143C2×C4—6281no—
144C2×C4D4×D15711yescharacteristic
145C2×C4C2×C22⋊D15712yes—
146C2×C4#1457895312yes—
147C2×C4#1457895311yescharacteristic
148C8—6282no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22#1909774011yescharacteristic
155C22#1909774211yescharacteristic
156C22#1909775811yescharacteristic
157C4—42no—
158C4—42no—
159C4—6282no—
160C4—12561no—
161C4#1909774312yes—
162C4#1909775212yes—
163C2—21no—
164C2—21no—
165C2—82no—
166C2#2375718711yescharacteristic
167C2#2375744611yescharacteristic
168C2#2375745111yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting, prime radical#537×C157C2
socleC22×C157#120
hypercenter#537D157
hypocenterC157#2040
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#19097698C2semidirect
2. #23757274C2semidirect
3. #23757138C2semidirect
4. #23757042C2semidirect
25. C4×Dic157D4semidirect
84. C157#2040semidirect

Maximal subgroups

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

subgroupindex
C2×#190976982
#237572742
#237571382
#237570422
#537×C1572
#2040157