Finite Group Databasebeta

← #34101304

Subgroups — #34101304

Order 20096.

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

normal subgroups only

This group has 290 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#23757899C211yesmaximal, characteristic
2#23757134C212yesmaximal
3#23757134C211yesmaximal, characteristic
4#23757039C212yesmaximal
5#342×C157C211yesmaximal, characteristic
6C23×Dic157C2211yescharacteristic
7#19097750—22no—
8#19097748—24no—
9C2×C22⋊Dic157C2211yescharacteristic
10C2×C22⋊Dic157C2212yes—
11#19097678—22no—
12#19097678—24no—
13C2×C22⋊C4×C157C2212yes—
14C2×C22⋊C4×C157C2211yescharacteristic
15C2×Dic314—22no—
16C22×Dic157—22no—
17C22×Dic157—21no—
18C22×Dic157—21no—
19C22×Dic157—21no—
20C22×Dic157—22no—
21C22×Dic157D414yes—
22C22×Dic157Q812yescomplemented
23C4⋊Dic157—22no—
24#14578933—24no—
25C22⋊Dic157—22no—
26C22⋊Dic157—22no—
27C22⋊Dic157—22no—
28C24×C157C2311yescharacteristic
29C22×C4×C157—22no—
30C22×C4×C157D412yes—
31C22⋊C4×C157—22no—
32C22⋊C4×C157—22no—
33C22⋊C4×C157—22no—
34Dic314—82no—
35C2×Dic157—24no—
36C2×Dic157—24no—
37C2×Dic157—22no—
38C2×Dic157—41no—
39C2×Dic157—42no—
40C2×Dic157—41no—
41C2×Dic157—44no—
42C2×Dic157—42no—
43C2×Dic157—41no—
44C23×C157—42no—
45C23×C157C2×D412yes—
46C23×C157C2×D411yescharacteristic
47C23×C157C2×Q811yescharacteristic
48C23×C157#4111yescharacteristic
49C23×C157#4112yes—
50C2×C4×C157—22no—
51C2×C4×C157—42no—
52C2×C4×C157—44no—
53C2×C4×C157—42no—
54C22×C157—24no—
55C22×C157—22no—
56C22×C157—41no—
57C22×C157—41no—
58C22×C157—42no—
59C22×C157#12011yescharacteristic
60C22×C157C22⋊Q812yes—
61C22×C157C22⋊Q811yescharacteristic
62C22×C157#12412yes—
63C22×C157#12411yescharacteristic
64C4×C157—42no—
65C4×C157—82no—
66Dic157—42no—
67Dic157—44no—
68Dic157—81no—
69C2×C157—21no—
70C2×C157—22no—
71C2×C157—22no—
72C2×C157—21no—
73C2×C157#39311yescharacteristic
74C2×C157#45812yes—
75C157#203011yescharacteristic, complemented, Sylow
76#2030—1571nomaximal, Sylow
77#543—1571no—
78#381—1572no—
79#381—1571no—
80#342—1572no—
81#342D15711yescharacteristic
82C23×C4—1571no—
83C22⋊Q8—3144no—
84C22⋊Q8—3142no—
85C2×C22⋊C4—1571no—
86C2×C22⋊C4—1572no—
87C2×C22⋊C4C2×D15712yes—
88C2×C22⋊C4C2×D15711yescharacteristic
89#95—3144no—
90#95—3142no—
91C24C22×D15711yescharacteristic
92C2×Q8—3142no—
93C22×C4—22no—
94C22×C4—3142no—
95C22×C4—3141no—
96C22×C4—3141no—
97C22×C4—3142no—
98C22×C4—3141no—
99C22×C4—1572no—
100C22×C4—1574no—
101C22×C4D62812yes—
102C4⋊C4—3144no—
103C4⋊C4—3142no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—3142no—
108C22⋊C4—3142no—
109C22⋊C4—3142no—
110C23—42no—
111C23D4×D15712yes—
112C23C2×D62811yescharacteristic
113C23Q8×D15711yescharacteristic
114C23#1457895311yescharacteristic
115C23#1457895412yes—
116Q8—12562no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—3144no—
122C2×C4—3144no—
123C2×C4—3142no—
124C2×C4—6281no—
125C2×C4—6282no—
126C2×C4—6281no—
127C2×C4—6284no—
128C2×C4—6282no—
129C2×C4—6281no—
130C22—24no—
131C22—22no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1909774111yescharacteristic
136C22#1909774912yes—
137C22#1909775111yescharacteristic
138C22#1909775712yes—
139C22#1909775911yescharacteristic
140C4—42no—
141C4—82no—
142C4—6282no—
143C4—6284no—
144C4—12561no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#2375718611yescharacteristic
150C2#2375746412yes—
subgroupG/H
centerC22#19097741
commutator, prime radical, cosocleC24×C157C23
FrattiniC24C22×D157
Fitting#342×C157C2
socleC22×C157#120
hypercenter#342D157
hypocenterC157#2030
LCSG ▷ C24×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
22. C22×Dic157Q8semidirect
75. C157#2030semidirect

Maximal subgroups

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

subgroupindex
#237578992
#237571342
#237570392
#342×C1572
#2030157