Finite Group Databasebeta

← C139×#7501 #48002097

Subgroups — C139×#7501 #48002097

Order 35584.

286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 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#2132×C139C212yesmaximal
2#1962×C139C211yesmaximal, characteristic
3#532×C139C2211yescharacteristic
4#423×C139C411yescharacteristic
5C2×#104×C139—22no—
6#413×C139—22no—
7C43×C139C411yescharacteristic
8#356×C139—22no—
9#355×C139C414yescomplemented
10C2×#41×C139D412yes—
11C2×M16×C139—21no—
12C2×M16×C139—42no—
13C4⋊Q8×C139D411yescharacteristic
14#127×C139Q811yescharacteristic
15#124×C139C2×C412yes—
16#121×C139—41no—
17C4×D4×C139—41no—
18C2×C42×C139—21no—
19C2×C42×C139—41no—
20C2×C42×C139C2×C411yescharacteristic
21C4⋊C8×C139—41no—
22#104×C139—44no—
23#101×C139—24no—
24#100×C139—42no—
25#41×C139—42no—
26#41×C139—42no—
27C2×Q8×C139C22⋊C412yes—
28C2×D4×C139—22no—
29C2×D4×C139—41no—
30C2×D4×C139C4⋊C412yes—
31C22×C4×C139—21no—
32C22×C4×C139—22no—
33C22×C4×C139—41no—
34C22×C4×C139C22⋊C411yescharacteristic
35M16×C139—44no—
36M16×C139—42no—
37M16×C139—82no—
38C2×C8×C139—41no—
39C2×C8×C139—82no—
40C4⋊C4×C139—41no—
41C22⋊C4×C139—42no—
42C42×C139—21no—
43C42×C139—22no—
44C42×C139—41no—
45C42×C139—44no—
46C42×C139C4211yescharacteristic
47C42×C139C4⋊C411yescharacteristic
48C23×C139—22no—
49C23×C139#9911yescharacteristic
50Q8×C139—42no—
51D4×C139—42no—
52D4×C139—82no—
53D4×C139—82no—
54C2×C4×C139—21no—
55C2×C4×C139—21no—
56C2×C4×C139—21no—
57C2×C4×C139—21no—
58C2×C4×C139—22no—
59C2×C4×C139—42no—
60C2×C4×C139—42no—
61C2×C4×C139—44no—
62C2×C4×C139—42no—
63C2×C4×C139—42no—
64C2×C4×C139#9511yescharacteristic
65C2×C4×C139#9911yescharacteristic
66C8×C139—84no—
67C8×C139—81no—
68C22×C139—21no—
69C22×C139—41no—
70C22×C139—42no—
71C22×C139—82no—
72C22×C139#34211yescharacteristic
73C4×C139—22no—
74C4×C139—21no—
75C4×C139—41no—
76C4×C139—44no—
77C4×C139—42no—
78C4×C139#35311yescharacteristic
79C4×C139#35411yescharacteristic
80C2×C139—21no—
81C2×C139—41no—
82C2×C139—82no—
83C2×C139#139311yescharacteristic
84#7501C13911yesmaximal, characteristic, direct product factor, Sylow
85C139#750111yescharacteristic, direct product factor, Sylow
86#2132C2×C13912yes—
87#1962C2×C13911yescharacteristic
88#532C22×C13911yescharacteristic
89#423C4×C13911yescharacteristic
90C2×#104—22no—
91#413—22no—
92C43C4×C13911yescharacteristic
93#356—22no—
94#355C4×C13914yescomplemented
95C2×#41D4×C13912yes—
96C2×M16—21no—
97C2×M16—42no—
98C4⋊Q8D4×C13911yescharacteristic
99#127Q8×C13911yescharacteristic
100#124C2×C4×C13912yes—
101#121—41no—
102C4×D4—41no—
103C2×C42—21no—
104C2×C42—41no—
105C2×C42C2×C4×C13911yescharacteristic
106C4⋊C8—41no—
107#104—44no—
108#101—24no—
109#100—42no—
110#41—42no—
111#41—42no—
112C2×Q8C22⋊C4×C13912yes—
113C2×D4—22no—
114C2×D4—41no—
115C2×D4C4⋊C4×C13912yes—
116C22×C4—21no—
117C22×C4—22no—
118C22×C4—41no—
119C22×C4C22⋊C4×C13911yescharacteristic
120M16—44no—
121M16—42no—
122M16—82no—
123C2×C8—41no—
124C2×C8—82no—
125C4⋊C4—41no—
126C22⋊C4—42no—
127C42—21no—
128C42—22no—
129C42—41no—
130C42—44no—
131C42C42×C13911yescharacteristic
132C42C4⋊C4×C13911yescharacteristic
133C23—22no—
134C23#99×C13911yescharacteristic
135Q8—42no—
136D4—42no—
137D4—82no—
138D4—82no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4#95×C13911yescharacteristic
150C2×C4#99×C13911yescharacteristic
151C8—84no—
152C8—81no—
153C22—21no—
154C22—41no—
155C22—42no—
156C22—82no—
157C22#342×C13911yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—44no—
162C4—42no—
163C4#353×C13911yescharacteristic
164C4#354×C13911yescharacteristic
165C2—21no—
166C2—41no—
167C2—82no—
168C2#1393×C13911yescharacteristic
subgroupG/H
centerC4×C139#354
commutatorC42C42×C139
Frattini, cosocle#532C22×C139
socleC2×C139#1393
prime radical#532×C139C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C139 ◁ C2×C4×C139 ◁ C22×C4×C139 ◁ #532×C139 ◁ G

Complements

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

NH ≅ G/Ntype
9. #355×C139C4semidirect
84. #7501C139direct (N × H)
85. C139#7501direct (N × H)
94. #355C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2132×C1392
#1962×C1392
#7501139