Finite Group Databasebeta

← C139×#21828 #48016424

Subgroups — C139×#21828 #48016424

Order 35584.

990 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 366 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
1C2×#544×C139C211yesmaximal, characteristic
2#2313×C139C212yesmaximal
3#1996×C139C218yesmaximal
4#1820×C139C214yesmaximal
5#544×C139—28no—
6C2×C4⋊Q8×C139C414yescomplemented
7C2×#125×C139C414yescomplemented
8C2×C22⋊Q8×C139C2214yes—
9C2×#117×C139C2212yes—
10C22×C4⋊C4×C139C2211yescharacteristic
11#387×C139—28no—
12#381×C139C2214yes—
13#380×C139C2214yes—
14C4×C22⋊C4×C139C2214yes—
15#342×C139C22116yes—
16C22×Q8×C139C2×C414yes—
17C23×C4×C139C2311yescharacteristic
18C23×C4×C139C2312yes—
19C4⋊Q8×C139—216no—
20#125×C139—216no—
21C22⋊Q8×C139—28no—
22C22⋊Q8×C139—28no—
23#117×C139—28no—
24C2×C4⋊C4×C139—24no—
25C2×C4⋊C4×C139C2×C412yes—
26C2×C4⋊C4×C139C2×C412yes—
27C2×C4⋊C4×C139C2×C414yes—
28C2×C4⋊C4×C139C2×C418yes—
29C2×C4⋊C4×C139C2×C414yes—
30C2×C4⋊C4×C139D418yes—
31C2×C22⋊C4×C139C2318yes—
32C2×C22⋊C4×C139C2314yes—
33C2×C42×C139—24no—
34C2×C42×C139C2×C414yes—
35#95×C139—24no—
36#95×C139—24no—
37#95×C139—28no—
38C24×C139C2411yescharacteristic
39C2×Q8×C139—28no—
40C2×Q8×C139—84no—
41C22×C4×C139—24no—
42C22×C4×C139—28no—
43C22×C4×C139—82no—
44C22×C4×C139C22×C412yes—
45C22×C4×C139C22×C414yes—
46C22×C4×C139C22×C414yes—
47C22×C4×C139C22×C414yes—
48C22×C4×C139C2×D414yes—
49C22×C4×C139C2×D414yes—
50C22×C4×C139C2×D414yes—
51C4⋊C4×C139—24no—
52C4⋊C4×C139—24no—
53C4⋊C4×C139—28no—
54C4⋊C4×C139—216no—
55C4⋊C4×C139—84no—
56C4⋊C4×C139C22⋊C4116yes—
57C22⋊C4×C139—28no—
58C22⋊C4×C139—216no—
59C42×C139—28no—
60C42×C139—84no—
61C23×C139—41no—
62C23×C139—41no—
63C23×C139C23×C411yescharacteristic
64C23×C139C22×D412yes—
65C23×C1392−1+414yes—
66Q8×C139—88no—
67C2×C4×C139—24no—
68C2×C4×C139—28no—
69C2×C4×C139—24no—
70C2×C4×C139—24no—
71C2×C4×C139—44no—
72C2×C4×C139—44no—
73C2×C4×C139—44no—
74C2×C4×C139—44no—
75C2×C4×C139—44no—
76C2×C4×C139—48no—
77C2×C4×C139—48no—
78C2×C4×C139—48no—
79C2×C4×C139C2×C22⋊C414yes—
80C2×C4×C139C2×C22⋊C418yes—
81C22×C139—21no—
82C22×C139—22no—
83C22×C139—21no—
84C22×C139—22no—
85C22×C139—44no—
86C22×C139C22×C22⋊C411yescharacteristic
87C22×C139#51912yes—
88C22×C139#53614yes—
89C4×C139—24no—
90C4×C139—28no—
91C4×C139—44no—
92C4×C139—44no—
93C4×C139—88no—
94C2×C139—24no—
95C2×C139—22no—
96C2×C139#231011yescharacteristic
97C2×C139#288311yescharacteristic
98C2×C139#288411yescharacteristic
99#21828C13911yesmaximal, characteristic, direct product factor, Sylow
100C139#2182811yescharacteristic, direct product factor, Sylow
101C2×#544C2×C13911yescharacteristic
102#2313C2×C13912yes—
103#1996C2×C13918yes—
104#1820C2×C13914yes—
105#544—28no—
106C2×C4⋊Q8C4×C13914yescomplemented
107C2×#125C4×C13914yescomplemented
108C2×C22⋊Q8C22×C13914yes—
109C2×#117C22×C13912yes—
110C22×C4⋊C4C22×C13911yescharacteristic
111#387—28no—
112#381C22×C13914yes—
113#380C22×C13914yes—
114C4×C22⋊C4C22×C13914yes—
115#342C22×C139116yes—
116C22×Q8C2×C4×C13914yes—
117C23×C4C23×C13911yescharacteristic
118C23×C4C23×C13912yes—
119C4⋊Q8—216no—
120#125—216no—
121C22⋊Q8—28no—
122C22⋊Q8—28no—
123#117—28no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4C2×C4×C13912yes—
126C2×C4⋊C4C2×C4×C13912yes—
127C2×C4⋊C4C2×C4×C13914yes—
128C2×C4⋊C4C2×C4×C13918yes—
129C2×C4⋊C4C2×C4×C13914yes—
130C2×C4⋊C4D4×C13918yes—
131C2×C22⋊C4C23×C13918yes—
132C2×C22⋊C4C23×C13914yes—
133C2×C42—24no—
134C2×C42C2×C4×C13914yes—
135#95—24no—
136#95—24no—
137#95—28no—
138C24C24×C13911yescharacteristic
139C2×Q8—28no—
140C2×Q8—84no—
141C22×C4—24no—
142C22×C4—28no—
143C22×C4—82no—
144C22×C4C22×C4×C13912yes—
145C22×C4C22×C4×C13914yes—
146C22×C4C22×C4×C13914yes—
147C22×C4C22×C4×C13914yes—
148C22×C4C2×D4×C13914yes—
149C22×C4C2×D4×C13914yes—
150C22×C4C2×D4×C13914yes—
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—28no—
154C4⋊C4—216no—
155C4⋊C4—84no—
156C4⋊C4C22⋊C4×C139116yes—
157C22⋊C4—28no—
158C22⋊C4—216no—
159C42—28no—
160C42—84no—
161C23—41no—
162C23—41no—
163C23C23×C4×C13911yescharacteristic
164C23C22×D4×C13912yes—
165C232−1+4×C13914yes—
166Q8—88no—
167C2×C4—24no—
168C2×C4—28no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—48no—
178C2×C4—48no—
179C2×C4C2×C22⋊C4×C13914yes—
180C2×C4C2×C22⋊C4×C13918yes—
181C22—21no—
182C22—22no—
183C22—21no—
184C22—22no—
185C22—44no—
186C22C22×C22⋊C4×C13911yescharacteristic
187C22#519×C13912yes—
188C22#536×C13914yes—
189C4—24no—
190C4—28no—
191C4—44no—
192C4—44no—
193C4—88no—
194C2—24no—
195C2—22no—
196C2#2310×C13911yescharacteristic
197C2#2883×C13911yescharacteristic
198C2#2884×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×C22⋊C4
commutatorC23C23×C4×C139
Frattini, cosocleC24C24×C139
prime radicalC24×C139C24
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C22×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊Q8×C139C4semidirect
7. C2×#125×C139C4semidirect
99. #21828C139direct (N × H)
100. C139#21828direct (N × H)
106. C2×C4⋊Q8C4×C139semidirect
107. C2×#125C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1392
#2313×C1392
#1996×C1392
#1820×C1392
#21828139