Finite Group Databasebeta

← C139×#9426 #48004022

Subgroups — C139×#9426 #48004022

Order 35584.

422 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 118 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#3139×C139C211yesmaximal, characteristic
2#2381×C139C211yesmaximal, characteristic
3#1558×C139C211yesmaximal, characteristic
4#1515×C139C212yesmaximal
5#1288×C139C212yesmaximal
6#533×C139C2211yescharacteristic
7C2×C4⋊Q8×C139C2211yescharacteristic
8#491×C139—22no—
9#487×C139C414yescomplemented
10#432×C139C2212yes—
11#419×C139—22no—
12C4×M16×C139C2211yescharacteristic
13#391×C139—22no—
14#387×C139—24no—
15#383×C139C2212yes—
16#333×C139—22no—
17#328×C139—24no—
18C22×Q8×C139D412yes—
19C2×M16×C139—21no—
20C4⋊Q8×C139—22no—
21C4⋊Q8×C139C2×C412yes—
22C4⋊Q8×C139C2×C412yes—
23C4⋊Q8×C139D412yes—
24#125×C139—21no—
25C22⋊Q8×C139—22no—
26C4×Q8×C139—22no—
27#117×C139—21no—
28C2×C4⋊C4×C139—22no—
29C2×C4⋊C4×C139—22no—
30C2×C42×C139—22no—
31C2×C42×C139C2311yescharacteristic
32C4⋊C8×C139—22no—
33#103×C139—28no—
34C22⋊C8×C139—22no—
35#97×C139—21no—
36#97×C139—22no—
37C4×C8×C139C2×C412yes—
38#95×C139—24no—
39#95×C139—22no—
40#95×C139—22no—
41#95×C139D414yes—
42C2×Q8×C139—22no—
43C2×Q8×C139—22no—
44C2×Q8×C139—42no—
45C2×Q8×C139—42no—
46C2×Q8×C139C22⋊C414yes—
47C22×C4×C139—22no—
48C22×C4×C139—24no—
49C22×C4×C139C2×D411yescharacteristic
50C22×C4×C139C2×D412yes—
51M16×C139—42no—
52C2×C8×C139—22no—
53C2×C8×C139—42no—
54C4⋊C4×C139—24no—
55C4⋊C4×C139—24no—
56C4⋊C4×C139—22no—
57C4⋊C4×C139—22no—
58C4⋊C4×C139—42no—
59C4⋊C4×C139—82no—
60C22⋊C4×C139—41no—
61C42×C139—41no—
62C42×C139—82no—
63C42×C139C22×C411yescharacteristic
64C42×C139C2×D411yescharacteristic
65C42×C139#4112yes—
66C23×C139#12011yescharacteristic
67Q8×C139—44no—
68Q8×C139—82no—
69Q8×C139—82no—
70C2×C4×C139—22no—
71C2×C4×C139—24no—
72C2×C4×C139—42no—
73C2×C4×C139—42no—
74C2×C4×C139—42no—
75C2×C4×C139—48no—
76C2×C4×C139—42no—
77C2×C4×C139—44no—
78C2×C4×C139C2×C22⋊C411yescharacteristic
79C2×C4×C139C4×D412yes—
80C2×C4×C139#12112yes—
81C2×C4×C139#12311yescharacteristic
82C8×C139—42no—
83C8×C139—82no—
84C22×C139—22no—
85C22×C139#38611yescharacteristic
86C22×C139#45512yes—
87C4×C139—21no—
88C4×C139—21no—
89C4×C139—22no—
90C4×C139—22no—
91C4×C139—44no—
92C4×C139—84no—
93C4×C139—82no—
94C2×C139—22no—
95C2×C139#188511yescharacteristic
96C2×C139#190512yes—
97#9426C13911yesmaximal, characteristic, direct product factor, Sylow
98C139#942611yescharacteristic, direct product factor, Sylow
99#3139C2×C13911yescharacteristic
100#2381C2×C13911yescharacteristic
101#1558C2×C13911yescharacteristic
102#1515C2×C13912yes—
103#1288C2×C13912yes—
104#533C22×C13911yescharacteristic
105C2×C4⋊Q8C22×C13911yescharacteristic
106#491—22no—
107#487C4×C13914yescomplemented
108#432C22×C13912yes—
109#419—22no—
110C4×M16C22×C13911yescharacteristic
111#391—22no—
112#387—24no—
113#383C22×C13912yes—
114#333—22no—
115#328—24no—
116C22×Q8D4×C13912yes—
117C2×M16—21no—
118C4⋊Q8—22no—
119C4⋊Q8C2×C4×C13912yes—
120C4⋊Q8C2×C4×C13912yes—
121C4⋊Q8D4×C13912yes—
122#125—21no—
123C22⋊Q8—22no—
124C4×Q8—22no—
125#117—21no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C42—22no—
129C2×C42C23×C13911yescharacteristic
130C4⋊C8—22no—
131#103—28no—
132C22⋊C8—22no—
133#97—21no—
134#97—22no—
135C4×C8C2×C4×C13912yes—
136#95—24no—
137#95—22no—
138#95—22no—
139#95D4×C13914yes—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8C22⋊C4×C13914yes—
145C22×C4—22no—
146C22×C4—24no—
147C22×C4C2×D4×C13911yescharacteristic
148C22×C4C2×D4×C13912yes—
149M16—42no—
150C2×C8—22no—
151C2×C8—42no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—42no—
157C4⋊C4—82no—
158C22⋊C4—41no—
159C42—41no—
160C42—82no—
161C42C22×C4×C13911yescharacteristic
162C42C2×D4×C13911yescharacteristic
163C42#41×C13912yes—
164C23#120×C13911yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—82no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—48no—
174C2×C4—44no—
175C2×C4—42no—
176C2×C4C2×C22⋊C4×C13911yescharacteristic
177C2×C4C4×D4×C13912yes—
178C2×C4#121×C13912yes—
179C2×C4#123×C13911yescharacteristic
180C8—42no—
181C8—82no—
182C22—22no—
183C22#386×C13911yescharacteristic
184C22#455×C13912yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—84no—
191C4—82no—
192C2—22no—
193C2#1885×C13911yescharacteristic
194C2#1905×C13912yes—
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC23×C139#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
9. #487×C139C4semidirect
97. #9426C139direct (N × H)
98. C139#9426direct (N × H)
107. #487C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3139×C1392
#2381×C1392
#1558×C1392
#1515×C1392
#1288×C1392
#9426139