Finite Group Databasebeta

← #34101439

Subgroups — #34101439

Order 20096.

264 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 67 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#23757301C211yesmaximal, characteristic, complemented
2#23757269C212yesmaximal, complemented
3#23757247C212yesmaximal, complemented
4#23757030C211yesmaximal, characteristic, complemented
5#575×C157C211yesmaximal, characteristic
6C22×#11929434C2211yescharacteristic
7#19097730C2212yes—
8#19097730C2211yescharacteristic
9#19097700—22no—
10#19097695—22no—
11#19097692—22no—
12#19097686—24no—
13C2×#41×C157C2212yes—
14#137×C157—22no—
15AGL(1,ℤ/8)×C157—22no—
16#135×C157—22no—
17C2×M16×C157C2211yescharacteristic
18C2×#11929434—22no—
19C2×#11929434—21no—
20C4⋊Dic157—22no—
21C4⋊Dic157—21no—
22C22⋊Dic157—22no—
23C22⋊Dic157D412yes—
24C4×Dic157—21no—
25C4×Dic157—22no—
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×C157D412yes—
33C22×C4×C157—22no—
34C22×C4×C157C2311yescharacteristic
35Q16×C157—22no—
36SD16×C157—24no—
37D8×C157—22no—
38M16×C157—22no—
39C2×C8×C157D412yes—
40C2×Dic157—22no—
41C2×Dic157—42no—
42#11929434—41no—
43C23×C157—22no—
44C23×C157C2×D411yescharacteristic
45Q8×C157—22no—
46Q8×C157—22no—
47D4×C157—22no—
48D4×C157—22no—
49D4×C157—42no—
50D4×C157—42no—
51C2×C4×C157—22no—
52C2×C4×C157—42no—
53C2×C4×C157—42no—
54C2×C4×C157C2×D412yes—
55C2×C4×C157C2×D411yescharacteristic
56C2×C4×C157#4111yescharacteristic
57C2×C4×C157#4112yes—
58C8×C157—22no—
59C22×C157—41no—
60C22×C157—42no—
61C22×C157—82no—
62C22×C157#12111yescharacteristic
63C22×C157#12112yes—
64C4×C157—42no—
65C4×C157#12011yescharacteristic
66C4×C157#12312yes—
67C4×C157#12411yescharacteristic
68Dic157—42no—
69Dic157—82no—
70C2×C157—21no—
71C2×C157—22no—
72C2×C157—82no—
73C2×C157#39411yescharacteristic
74C157#205311yescharacteristic, complemented, Sylow
75#2053—1571nomaximal, Sylow
76#575D15711yescharacteristic
77#424—1571no—
78#416—1572no—
79#410—1572no—
80H(3,ℤ/4)—1571no—
81C2×#41C2×D15712yes—
82#137—22no—
83AGL(1,ℤ/8)—22no—
84#135—22no—
85C2×M16C2×D15711yescharacteristic
86C22×C8—1571no—
87#117—1572no—
88#117—1571no—
89C4⋊C8—3142no—
90#103—3142no—
91#102—3142no—
92#99—3144no—
93#41—22no—
94#41—22no—
95#41—22no—
96#41—22no—
97C2×Q8C22⋊D15712yes—
98C2×D4—22no—
99C2×D4C22⋊D15712yes—
100C22×C4—22no—
101C22×C4C22×D15711yescharacteristic
102Q16—22no—
103SD16—24no—
104D8—22no—
105M16—22no—
106C2×C8—3142no—
107C2×C8—3141no—
108C2×C8C22⋊D15712yes—
109C4⋊C4—3141no—
110C4⋊C4—3142no—
111C22⋊C4—3142no—
112C22⋊C4—1572no—
113C42—3141no—
114C42—3142no—
115C23—22no—
116C23D4×D15711yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—3142no—
127C2×C4—6282no—
128C2×C4C2×C22⋊D15712yes—
129C2×C4C2×C22⋊D15711yescharacteristic
130C2×C4#1457895311yescharacteristic
131C2×C4#1457895312yes—
132C8—22no—
133C8—6281no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#1909774211yescharacteristic
138C22#1909774312yes—
139C4—42no—
140C4—6282no—
141C4—12562no—
142C4#1909774011yescharacteristic
143C4#1909775212yes—
144C4#1909775811yescharacteristic
145C2—21no—
146C2—22no—
147C2—82no—
148C2#2375718711yescharacteristic
subgroupG/H
centerC4#19097758
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting, prime radical#575×C157C2
socleC2×C157#394
hypercenter#575D157
hypocenterC157#2053
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23757301C2semidirect
2. #23757269C2semidirect
3. #23757247C2semidirect
4. #23757030C2semidirect
74. C157#2053semidirect

Maximal subgroups

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

subgroupindex
#237573012
#237572692
#237572472
#237570302
#575×C1572
#2053157