Finite Group Databasebeta

← C139×#7443 #48002039

Subgroups — C139×#7443 #48002039

Order 35584.

198 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 46 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#2060×C139C211yesmaximal, characteristic
2#1325×C139C211yesmaximal, characteristic
3#1296×C139C211yesmaximal, characteristic
4#544×C139C411yescharacteristic
5#428×C139—21no—
6C2×C4⋊C8×C139—21no—
7#384×C139C2211yescharacteristic
8#343×C139C411yescharacteristic
9#339×C139—21no—
10#324×C139—21no—
11C2×M16×C139—21no—
12C22×C8×C139—41no—
13C4⋊Q8×C139—41no—
14#125×C139—41no—
15C22⋊Q8×C139—41no—
16#117×C139—21no—
17C2×C4⋊C4×C139—41no—
18C2×C4⋊C4×C139C2×C411yescharacteristic
19C2×C4⋊C4×C139D411yescharacteristic
20C2×C42×C139D411yescharacteristic
21#107×C139—41no—
22#106×C139—41no—
23C4⋊C8×C139—22no—
24C4⋊C8×C139—41no—
25C22⋊C8×C139—41no—
26C2×Q8×C139—41no—
27C22×C4×C139—21no—
28C22×C4×C139—21no—
29C22×C4×C139—21no—
30C22×C4×C139C22⋊C411yescharacteristic
31M16×C139—22no—
32M16×C139—41no—
33C2×C8×C139—41no—
34C2×C8×C139—42no—
35C2×C8×C139—81no—
36C2×C8×C139—81no—
37C2×C8×C139—81no—
38C4⋊C4×C139—21no—
39C4⋊C4×C139—21no—
40C4⋊C4×C139—41no—
41C4⋊C4×C139—41no—
42C4⋊C4×C139—41no—
43C4⋊C4×C139—42no—
44C4⋊C4×C139—81no—
45C4⋊C4×C139—81no—
46C22⋊C4×C139—41no—
47C42×C139—21no—
48C42×C139—41no—
49C42×C139SD1611yescharacteristic
50C42×C139Q1611yescharacteristic
51C23×C139#9911yescharacteristic
52Q8×C139—161no—
53C2×C4×C139—21no—
54C2×C4×C139—21no—
55C2×C4×C139—21no—
56C2×C4×C139—21no—
57C2×C4×C139—21no—
58C2×C4×C139—21no—
59C2×C4×C139—21no—
60C2×C4×C139—21no—
61C2×C4×C139—41no—
62C2×C4×C139—41no—
63C2×C4×C139—41no—
64C2×C4×C139—41no—
65C2×C4×C139—81no—
66C2×C4×C139—81no—
67C2×C4×C139#10311yescharacteristic
68C2×C4×C139#10411yescharacteristic
69C8×C139—42no—
70C8×C139—82no—
71C8×C139—161no—
72C22×C139—21no—
73C22×C139—21no—
74C22×C139#32811yescharacteristic
75C22×C139AΣL(1,𝔽16)11yescharacteristic
76C22×C139#35611yescharacteristic
77C4×C139—21no—
78C4×C139—21no—
79C4×C139—21no—
80C4×C139—21no—
81C4×C139—21no—
82C4×C139—21no—
83C4×C139—81no—
84C4×C139—81no—
85C4×C139—81no—
86C4×C139—81no—
87C2×C139—21no—
88C2×C139—21no—
89C2×C139#135411yescharacteristic
90C2×C139#140211yescharacteristic
91C2×C139#140511yescharacteristic
92#7443C13911yesmaximal, characteristic, direct product factor, Sylow
93C139#744311yescharacteristic, direct product factor, Sylow
94#2060C2×C13911yescharacteristic
95#1325C2×C13911yescharacteristic
96#1296C2×C13911yescharacteristic
97#544C4×C13911yescharacteristic
98#428—21no—
99C2×C4⋊C8—21no—
100#384C22×C13911yescharacteristic
101#343C4×C13911yescharacteristic
102#339—21no—
103#324—21no—
104C2×M16—21no—
105C22×C8—41no—
106C4⋊Q8—41no—
107#125—41no—
108C22⋊Q8—41no—
109#117—21no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4C2×C4×C13911yescharacteristic
112C2×C4⋊C4D4×C13911yescharacteristic
113C2×C42D4×C13911yescharacteristic
114#107—41no—
115#106—41no—
116C4⋊C8—22no—
117C4⋊C8—41no—
118C22⋊C8—41no—
119C2×Q8—41no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4C22⋊C4×C13911yescharacteristic
124M16—22no—
125M16—41no—
126C2×C8—41no—
127C2×C8—42no—
128C2×C8—81no—
129C2×C8—81no—
130C2×C8—81no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—42no—
137C4⋊C4—81no—
138C4⋊C4—81no—
139C22⋊C4—41no—
140C42—21no—
141C42—41no—
142C42SD16×C13911yescharacteristic
143C42Q16×C13911yescharacteristic
144C23#99×C13911yescharacteristic
145Q8—161no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4#103×C13911yescharacteristic
161C2×C4#104×C13911yescharacteristic
162C8—42no—
163C8—82no—
164C8—161no—
165C22—21no—
166C22—21no—
167C22#328×C13911yescharacteristic
168C22AΣL(1,𝔽16)×C13911yescharacteristic
169C22#356×C13911yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—81no—
179C4—81no—
180C2—21no—
181C2—21no—
182C2#1354×C13911yescharacteristic
183C2#1402×C13911yescharacteristic
184C2#1405×C13911yescharacteristic
subgroupG/H
center, socleC22×C139AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C139
Frattini, cosocle#384C22×C139
prime radicalC23×C139#99
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C22×C4×C139 ◁ #384×C139 ◁ G

Complements

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

NH ≅ G/Ntype
92. #7443C139direct (N × H)
93. C139#7443direct (N × H)

Maximal subgroups

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

subgroupindex
#2060×C1392
#1325×C1392
#1296×C1392
#7443139