Finite Group Databasebeta

← C139×#9438 #48004034

Subgroups — C139×#9438 #48004034

Order 35584.

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

normal subgroups only

This group has 452 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#3138×C139C211yesmaximal, characteristic
2#2986×C139C211yesmaximal, characteristic, complemented
3#1561×C139C211yesmaximal, characteristic, complemented
4#1545×C139C212yesmaximal
5#1299×C139C212yesmaximal, complemented
6#533×C139C2211yescharacteristic
7C2×#127×C139C2211yescharacteristic
8#490×C139C414yes—
9#486×C139—22no—
10#446×C139—22no—
11C8×Q8×C139—22no—
12#433×C139—22no—
13#431×C139C2212yes—
14#423×C139C2212yes—
15#418×C139—22no—
16C4×M16×C139C2211yescharacteristic
17#332×C139—22no—
18#331×C139—22no—
19#331×C139—22no—
20C22×D4×C139—21no—
21C22×D4×C139—22no—
22C2×M16×C139—21no—
23C2×M16×C139—22no—
24C4⋊Q8×C139D412yes—
25#127×C139—21no—
26#127×C139—22no—
27#127×C139C2×C412yes—
28#125×C139C2×C412yes—
29C22⋊Q8×C139—22no—
30C4×Q8×C139—22no—
31#117×C139D412yes—
32C2×C42×C139C2311yescharacteristic
33C4⋊C8×C139—24no—
34C4⋊C8×C139—22no—
35C4⋊C8×C139—22no—
36C4⋊C8×C139D412yes—
37C4⋊C8×C139D412yes—
38#102×C139—28no—
39C22⋊C8×C139—22no—
40#97×C139—22no—
41#97×C139C2×C412yes—
42C4×C8×C139—22no—
43C4×C8×C139—21no—
44C4×C8×C139—22no—
45C24×C139—41no—
46C2×Q8×C139—22no—
47C2×D4×C139—22no—
48C2×D4×C139—24no—
49C2×D4×C139—44no—
50C2×D4×C139—41no—
51C2×D4×C139—42no—
52C2×D4×C139—82no—
53C2×D4×C139—82no—
54C22×C4×C139C2×D411yescharacteristic
55C22×C4×C139#4112yes—
56M16×C139—42no—
57M16×C139—82no—
58C2×C8×C139—22no—
59C2×C8×C139—22no—
60C2×C8×C139—22no—
61C2×C8×C139—42no—
62C4⋊C4×C139—24no—
63C4⋊C4×C139—22no—
64C4⋊C4×C139C22⋊C414yes—
65C22⋊C4×C139—22no—
66C42×C139—22no—
67C42×C139C22×C411yescharacteristic
68C42×C139C2×D411yescharacteristic
69C42×C139C2×D412yes—
70C23×C139—42no—
71C23×C139—82no—
72C23×C139—84no—
73C23×C139#12311yescharacteristic
74Q8×C139—42no—
75Q8×C139—42no—
76D4×C139—44no—
77D4×C139—84no—
78D4×C139—82no—
79D4×C139—82no—
80D4×C139—82no—
81C2×C4×C139—22no—
82C2×C4×C139—22no—
83C2×C4×C139—22no—
84C2×C4×C139—24no—
85C2×C4×C139C2×C22⋊C411yescharacteristic
86C2×C4×C139C4×D412yes—
87C2×C4×C139#12011yescharacteristic
88C2×C4×C139#12112yes—
89C8×C139—42no—
90C8×C139—42no—
91C8×C139—42no—
92C8×C139—82no—
93C22×C139—21no—
94C22×C139—22no—
95C22×C139—82no—
96C22×C139—84no—
97C22×C139—164no—
98C22×C139#38611yescharacteristic
99C4×C139—21no—
100C4×C139—22no—
101C4×C139—44no—
102C4×C139#45412yes—
103C4×C139#47112yes—
104C4×C139#47212yes—
105C2×C139—41no—
106C2×C139—162no—
107C2×C139#188811yescharacteristic
108C2×C139#190712yes—
109#9438C13911yesmaximal, characteristic, direct product factor, Sylow
110C139#943811yescharacteristic, direct product factor, Sylow
111#3138C2×C13911yescharacteristic
112#2986C2×C13911yescharacteristic, complemented
113#1561C2×C13911yescharacteristic, complemented
114#1545C2×C13912yes—
115#1299C2×C13912yescomplemented
116#533C22×C13911yescharacteristic
117C2×#127C22×C13911yescharacteristic
118#490C4×C13914yes—
119#486—22no—
120#446—22no—
121C8×Q8—22no—
122#433—22no—
123#431C22×C13912yes—
124#423C22×C13912yes—
125#418—22no—
126C4×M16C22×C13911yescharacteristic
127#332—22no—
128#331—22no—
129#331—22no—
130C22×D4—21no—
131C22×D4—22no—
132C2×M16—21no—
133C2×M16—22no—
134C4⋊Q8D4×C13912yes—
135#127—22no—
136#127—21no—
137#127C2×C4×C13912yes—
138#125C2×C4×C13912yes—
139C22⋊Q8—22no—
140C4×Q8—22no—
141#117D4×C13912yes—
142C2×C42C23×C13911yescharacteristic
143C4⋊C8—24no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8D4×C13912yes—
147C4⋊C8D4×C13912yes—
148#102—28no—
149C22⋊C8—22no—
150#97—22no—
151#97C2×C4×C13912yes—
152C4×C8—22no—
153C4×C8—21no—
154C4×C8—22no—
155C24—41no—
156C2×Q8—22no—
157C2×D4—22no—
158C2×D4—24no—
159C2×D4—44no—
160C2×D4—41no—
161C2×D4—42no—
162C2×D4—82no—
163C2×D4—82no—
164C22×C4C2×D4×C13911yescharacteristic
165C22×C4#41×C13912yes—
166M16—42no—
167M16—82no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—42no—
172C4⋊C4—24no—
173C4⋊C4—22no—
174C4⋊C4C22⋊C4×C13914yes—
175C22⋊C4—22no—
176C42—22no—
177C42C22×C4×C13911yescharacteristic
178C42C2×D4×C13911yescharacteristic
179C42C2×D4×C13912yes—
180C23—42no—
181C23—82no—
182C23—84no—
183C23#123×C13911yescharacteristic
184Q8—42no—
185Q8—42no—
186D4—44no—
187D4—84no—
188D4—82no—
189D4—82no—
190D4—82no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4C2×C22⋊C4×C13911yescharacteristic
196C2×C4C4×D4×C13912yes—
197C2×C4#120×C13911yescharacteristic
198C2×C4#121×C13912yes—
199C8—42no—
200C8—42no—
201C8—42no—
202C8—82no—
203C22—21no—
204C22—22no—
205C22—82no—
206C22—84no—
207C22—164no—
208C22#386×C13911yescharacteristic
209C4—21no—
210C4—22no—
211C4—44no—
212C4#454×C13912yes—
213C4#471×C13912yes—
214C4#472×C13912yes—
215C2—41no—
216C2—162no—
217C2#1888×C13911yescharacteristic
218C2#1907×C13912yes—
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC2×#127×C139C22
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
2. #2986×C139C2semidirect
3. #1561×C139C2semidirect
5. #1299×C139C2semidirect
109. #9438C139direct (N × H)
110. C139#9438direct (N × H)
112. #2986C2×C139semidirect
113. #1561C2×C139semidirect
115. #1299C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3138×C1392
#2986×C1392
#1561×C1392
#1545×C1392
#1299×C1392
#9438139