Finite Group Databasebeta

← C139×#8733 #48003329

Subgroups — C139×#8733 #48003329

Order 35584.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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#2298×C139C211yesmaximal, characteristic
2#1458×C139C212yesmaximal
3#1276×C139C212yesmaximal, complemented
4#1274×C139C212yesmaximal, complemented
5C2×#117×C139C2211yescharacteristic
6#431×C139C2214yes—
7#388×C139—22no—
8#387×C139—22no—
9C4×C4⋊C4×C139C412yes—
10C4×C22⋊C4×C139C412yes—
11#376×C139C2211yescharacteristic
12C43×C139C2211yescharacteristic
13#324×C139—22no—
14#323×C139—22no—
15C23×C4×C139C2×C411yescharacteristic
16#117×C139—22no—
17#117×C139—22no—
18C2×C4⋊C4×C139—22no—
19C2×C4⋊C4×C139D412yes—
20C2×C22⋊C4×C139—22no—
21C2×C22⋊C4×C139D412yes—
22C2×C42×C139—22no—
23C2×C42×C139C2×C412yes—
24C2×C42×C139C2×C412yes—
25C2×C42×C139C2×C411yescharacteristic
26C2×C42×C139C2311yescharacteristic
27C4⋊C8×C139—24no—
28C22⋊C8×C139—24no—
29C4×C8×C139—24no—
30#95×C139—22no—
31#95×C139—22no—
32#95×C139—22no—
33C24×C139C22⋊C411yescharacteristic
34C22×C4×C139—22no—
35C22×C4×C139—21no—
36C22×C4×C139—21no—
37C22×C4×C139—24no—
38C22×C4×C139—22no—
39C22×C4×C139C22⋊C411yescharacteristic
40C22×C4×C139C22⋊C412yes—
41C22×C4×C139C22×C411yescharacteristic
42C22×C4×C139C2×D412yes—
43C2×C8×C139—44no—
44C4⋊C4×C139—24no—
45C4⋊C4×C139—44no—
46C22⋊C4×C139—24no—
47C22⋊C4×C139—44no—
48C42×C139—21no—
49C42×C139—21no—
50C42×C139—24no—
51C42×C139—24no—
52C42×C139—44no—
53C42×C139#4112yes—
54C42×C139#4112yes—
55C23×C139—21no—
56C23×C139—22no—
57C23×C139—42no—
58C23×C139C2×C22⋊C411yescharacteristic
59C2×C4×C139—24no—
60C2×C4×C139—22no—
61C2×C4×C139—21no—
62C2×C4×C139—22no—
63C2×C4×C139—42no—
64C2×C4×C139—42no—
65C2×C4×C139—42no—
66C2×C4×C139—42no—
67C2×C4×C139—42no—
68C2×C4×C139—42no—
69C2×C4×C139—42no—
70C2×C4×C139—42no—
71C2×C4×C139—42no—
72C2×C4×C139#11711yescharacteristic
73C2×C4×C139#11711yescharacteristic
74C2×C4×C139#12314yes—
75C2×C4×C139#13114yes—
76C8×C139—84no—
77C22×C139—22no—
78C22×C139—41no—
79C22×C139—42no—
80C22×C139—82no—
81C22×C139#38111yescharacteristic
82C22×C139#40812yes—
83C4×C139—24no—
84C4×C139—44no—
85C4×C139—41no—
86C4×C139—42no—
87C4×C139—82no—
88C4×C139#43312yes—
89C4×C139#43312yes—
90C2×C139—22no—
91C2×C139—81no—
92C2×C139#181811yescharacteristic
93C2×C139#182712yes—
94#8733C13911yesmaximal, characteristic, direct product factor, Sylow
95C139#873311yescharacteristic, direct product factor, Sylow
96#2298C2×C13911yescharacteristic
97#1458C2×C13912yes—
98#1276C2×C13912yescomplemented
99#1274C2×C13912yescomplemented
100C2×#117C22×C13911yescharacteristic
101#431C22×C13914yes—
102#388—22no—
103#387—22no—
104C4×C4⋊C4C4×C13912yes—
105C4×C22⋊C4C4×C13912yes—
106#376C22×C13911yescharacteristic
107C43C22×C13911yescharacteristic
108#324—22no—
109#323—22no—
110C23×C4C2×C4×C13911yescharacteristic
111#117—22no—
112#117—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4D4×C13912yes—
115C2×C22⋊C4—22no—
116C2×C22⋊C4D4×C13912yes—
117C2×C42—22no—
118C2×C42C2×C4×C13912yes—
119C2×C42C2×C4×C13912yes—
120C2×C42C2×C4×C13911yescharacteristic
121C2×C42C23×C13911yescharacteristic
122C4⋊C8—24no—
123C22⋊C8—24no—
124C4×C8—24no—
125#95—22no—
126#95—22no—
127#95—22no—
128C24C22⋊C4×C13911yescharacteristic
129C22×C4—22no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4C22⋊C4×C13911yescharacteristic
135C22×C4C22⋊C4×C13912yes—
136C22×C4C22×C4×C13911yescharacteristic
137C22×C4C2×D4×C13912yes—
138C2×C8—44no—
139C4⋊C4—24no—
140C4⋊C4—44no—
141C22⋊C4—24no—
142C22⋊C4—44no—
143C42—21no—
144C42—21no—
145C42—24no—
146C42—24no—
147C42—44no—
148C42#41×C13912yes—
149C42#41×C13912yes—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×C22⋊C4×C13911yescharacteristic
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4#117×C13911yescharacteristic
168C2×C4#117×C13911yescharacteristic
169C2×C4#123×C13914yes—
170C2×C4#131×C13914yes—
171C8—84no—
172C22—22no—
173C22—41no—
174C22—42no—
175C22—82no—
176C22#381×C13911yescharacteristic
177C22#408×C13912yes—
178C4—24no—
179C4—44no—
180C4—41no—
181C4—42no—
182C4—82no—
183C4#433×C13912yes—
184C4#433×C13912yes—
185C2—22no—
186C2—81no—
187C2#1818×C13911yescharacteristic
188C2#1827×C13912yes—
subgroupG/H
centerC2×C4×C139#117
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
socleC22×C139#381
prime radicalC24×C139C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ #376×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1276×C139C2semidirect
4. #1274×C139C2semidirect
94. #8733C139direct (N × H)
95. C139#8733direct (N × H)
98. #1276C2×C139semidirect
99. #1274C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2298×C1392
#1458×C1392
#1276×C1392
#1274×C1392
#8733139