Finite Group Databasebeta

← C139×#8758 #48003354

Subgroups — C139×#8758 #48003354

Order 35584.

394 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 110 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#2313×C139C211yesmaximal, characteristic
2#1463×C139C212yesmaximal
3#1305×C139C214yesmaximal
4C22×C4⋊C4×C139C2211yescharacteristic
5#407×C139C2214yes—
6#387×C139—24no—
7#381×C139C412yes—
8#380×C139C2212yes—
9C4×C22⋊C4×C139C412yes—
10#324×C139—24no—
11C23×C4×C139C2×C411yescharacteristic
12C23×C4×C139C2×C411yescharacteristic
13C23×C4×C139C2311yescharacteristic
14C2×M16×C139—24no—
15C2×C4⋊C4×C139—24no—
16C2×C4⋊C4×C139—22no—
17C2×C4⋊C4×C139D414yes—
18C2×C22⋊C4×C139C2×C414yes—
19C2×C42×C139—22no—
20C22⋊C8×C139—24no—
21C22⋊C8×C139—24no—
22#95×C139—22no—
23#95×C139—24no—
24#95×C139—22no—
25C24×C139C22×C411yescharacteristic
26C22×C4×C139—22no—
27C22×C4×C139—22no—
28C22×C4×C139—24no—
29C22×C4×C139—42no—
30C22×C4×C139—81no—
31C22×C4×C139—81no—
32C22×C4×C139C22⋊C412yes—
33C22×C4×C139C22⋊C412yes—
34C22×C4×C139C2×D412yes—
35C22×C4×C139#4114yes—
36M16×C139—84no—
37C2×C8×C139—44no—
38C4⋊C4×C139—28no—
39C4⋊C4×C139—82no—
40C22⋊C4×C139—44no—
41C42×C139—82no—
42C23×C139—22no—
43C23×C139—41no—
44C23×C139—41no—
45C23×C139C2×C22⋊C411yescharacteristic
46C23×C139#11712yes—
47C2×C4×C139—22no—
48C2×C4×C139—22no—
49C2×C4×C139—24no—
50C2×C4×C139—42no—
51C2×C4×C139—44no—
52C2×C4×C139—44no—
53C2×C4×C139—42no—
54C2×C4×C139—44no—
55C2×C4×C139—44no—
56C2×C4×C139—44no—
57C2×C4×C139—82no—
58C2×C4×C139#12314yes—
59C8×C139—84no—
60C22×C139—21no—
61C22×C139—21no—
62C22×C139—22no—
63C22×C139—22no—
64C22×C139—22no—
65C22×C139—44no—
66C22×C139#38111yescharacteristic
67C22×C139#41312yes—
68C4×C139—24no—
69C4×C139—42no—
70C4×C139—42no—
71C4×C139—84no—
72C2×C139—22no—
73C2×C139—42no—
74C2×C139#182211yescharacteristic
75C2×C139#182811yescharacteristic
76C2×C139#183011yescharacteristic
77#8758C13911yesmaximal, characteristic, direct product factor, Sylow
78C139#875811yescharacteristic, direct product factor, Sylow
79#2313C2×C13911yescharacteristic
80#1463C2×C13912yes—
81#1305C2×C13914yes—
82C22×C4⋊C4C22×C13911yescharacteristic
83#407C22×C13914yes—
84#387—24no—
85#381C4×C13912yes—
86#380C22×C13912yes—
87C4×C22⋊C4C4×C13912yes—
88#324—24no—
89C23×C4C2×C4×C13911yescharacteristic
90C23×C4C2×C4×C13911yescharacteristic
91C23×C4C23×C13911yescharacteristic
92C2×M16—24no—
93C2×C4⋊C4—24no—
94C2×C4⋊C4—22no—
95C2×C4⋊C4D4×C13914yes—
96C2×C22⋊C4C2×C4×C13914yes—
97C2×C42—22no—
98C22⋊C8—24no—
99C22⋊C8—24no—
100#95—22no—
101#95—24no—
102#95—22no—
103C24C22×C4×C13911yescharacteristic
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—24no—
107C22×C4—42no—
108C22×C4—81no—
109C22×C4—81no—
110C22×C4C22⋊C4×C13912yes—
111C22×C4C22⋊C4×C13912yes—
112C22×C4C2×D4×C13912yes—
113C22×C4#41×C13914yes—
114M16—84no—
115C2×C8—44no—
116C4⋊C4—28no—
117C4⋊C4—82no—
118C22⋊C4—44no—
119C42—82no—
120C23—22no—
121C23—41no—
122C23—41no—
123C23C2×C22⋊C4×C13911yescharacteristic
124C23#117×C13912yes—
125C2×C4—24no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—42no—
129C2×C4—44no—
130C2×C4—44no—
131C2×C4—42no—
132C2×C4—44no—
133C2×C4—44no—
134C2×C4—44no—
135C2×C4—82no—
136C2×C4#123×C13914yes—
137C8—84no—
138C22—21no—
139C22—21no—
140C22—22no—
141C22—22no—
142C22—22no—
143C22—44no—
144C22#381×C13911yescharacteristic
145C22#413×C13912yes—
146C4—24no—
147C4—42no—
148C4—42no—
149C4—84no—
150C2—22no—
151C2—42no—
152C2#1822×C13911yescharacteristic
153C2#1828×C13911yescharacteristic
154C2#1830×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#381
commutatorC24C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC24×C139C22×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
77. #8758C139direct (N × H)
78. C139#8758direct (N × H)

Maximal subgroups

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

subgroupindex
#2313×C1392
#1463×C1392
#1305×C1392
#8758139