Finite Group Databasebeta

← C139×#32800 #48027396

Subgroups — C139×#32800 #48027396

Order 35584.

816 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 238 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#2868×C139C211yesmaximal, characteristic, complemented
2#2860×C139C211yesmaximal, characteristic
3#2043×C139C216yesmaximal, complemented
4#2013×C139C216yesmaximal
5#1839×C139C211yesmaximal, characteristic, complemented
6C22×SD16×C139C2214yes—
7C2×C4⋊Q8×C139C2216yes—
8C2×#126×C139—21no—
9C2×#103×C139C22112yes—
10#390×C139C2213yes—
11#389×C139C2213yes—
12#388×C139—23no—
13#384×C139—23no—
14#384×C139—21no—
15C43×C139C2211yescharacteristic
16#336×C139C2216yes—
17C22×Q8×C139C2314yes—
18C22×D4×C139C2311yescharacteristic
19C2×SD16×C139—412no—
20C22×C8×C139C2314yes—
21C4⋊Q8×C139—412no—
22#126×C139—44no—
23C2×C4⋊C4×C139—23no—
24C2×C4⋊C4×C139—26no—
25C2×C4⋊C4×C139—26no—
26C2×C4⋊C4×C139C2313yes—
27C2×C22⋊C4×C139—23no—
28C2×C22⋊C4×C139—23no—
29C2×C42×C139D413yes—
30C2×C42×C139D411yescharacteristic
31C2×C42×C139C2313yes—
32#103×C139—412no—
33#95×C139—23no—
34C24×C139—21no—
35C2×Q8×C139—212no—
36C2×Q8×C139—212no—
37C2×D4×C139—26no—
38C22×C4×C139—23no—
39C22×C4×C139—24no—
40C22×C4×C139C2×D413yes—
41C22×C4×C139C2×D413yes—
42C22×C4×C139C2411yescharacteristic
43SD16×C139—416no—
44C2×C8×C139—212no—
45C4⋊C4×C139—26no—
46C4⋊C4×C139—412no—
47C4⋊C4×C139—412no—
48C4⋊C4×C139—46no—
49C22⋊C4×C139—46no—
50C22⋊C4×C139—46no—
51C42×C139—26no—
52C42×C139—26no—
53C42×C139SD1614yescomplemented
54C23×C139—43no—
55C23×C139—41no—
56C23×C139—43no—
57C23×C139C22×D411yescharacteristic
58Q8×C139—44no—
59Q8×C139—412no—
60D4×C139—44no—
61C2×C4×C139—23no—
62C2×C4×C139—23no—
63C2×C4×C139—23no—
64C2×C4×C139—23no—
65C2×C4×C139—43no—
66C2×C4×C139—412no—
67C2×C4×C139—43no—
68C2×C4×C139—43no—
69C2×C4×C139C2×SD1616yes—
70C2×C4×C139#13716yes—
71C2×C4×C139H(5,𝔽2)16yes—
72C8×C139—44no—
73C22×C139—81no—
74C22×C139—83no—
75C22×C139—83no—
76C22×C139#53513yes—
77C22×C139C22×SD1611yescharacteristic
78C22×C139C2×#13713yes—
79C4×C139—26no—
80C4×C139—26no—
81C4×C139—84no—
82C4×C139—83no—
83C4×C139#56014yes—
84C2×C139—161no—
85C2×C139#281811yescharacteristic
86C2×C139#320613yes—
87C2×C139#321813yes—
88#32800C13911yesmaximal, characteristic, direct product factor, Sylow
89C139#3280011yescharacteristic, direct product factor, Sylow
90#2868C2×C13911yescharacteristic, complemented
91#2860C2×C13911yescharacteristic
92#2043C2×C13916yescomplemented
93#2013C2×C13916yes—
94#1839C2×C13911yescharacteristic, complemented
95C22×SD16C22×C13914yes—
96C2×C4⋊Q8C22×C13916yes—
97C2×#126—21no—
98C2×#103C22×C139112yes—
99#390C22×C13913yes—
100#389C22×C13913yes—
101#388—23no—
102#384—23no—
103#384—21no—
104C43C22×C13911yescharacteristic
105#336C22×C13916yes—
106C22×Q8C23×C13914yes—
107C22×D4C23×C13911yescharacteristic
108C2×SD16—412no—
109C22×C8C23×C13914yes—
110C4⋊Q8—412no—
111#126—44no—
112C2×C4⋊C4—23no—
113C2×C4⋊C4—26no—
114C2×C4⋊C4—26no—
115C2×C4⋊C4C23×C13913yes—
116C2×C22⋊C4—23no—
117C2×C22⋊C4—23no—
118C2×C42D4×C13913yes—
119C2×C42D4×C13911yescharacteristic
120C2×C42C23×C13913yes—
121#103—412no—
122#95—23no—
123C24—21no—
124C2×Q8—212no—
125C2×Q8—212no—
126C2×D4—26no—
127C22×C4—23no—
128C22×C4—24no—
129C22×C4C2×D4×C13913yes—
130C22×C4C2×D4×C13913yes—
131C22×C4C24×C13911yescharacteristic
132SD16—416no—
133C2×C8—212no—
134C4⋊C4—26no—
135C4⋊C4—412no—
136C4⋊C4—412no—
137C4⋊C4—46no—
138C22⋊C4—46no—
139C22⋊C4—46no—
140C42—26no—
141C42—26no—
142C42SD16×C13914yescomplemented
143C23—43no—
144C23—41no—
145C23—43no—
146C23C22×D4×C13911yescharacteristic
147Q8—44no—
148Q8—412no—
149D4—44no—
150C2×C4—23no—
151C2×C4—23no—
152C2×C4—23no—
153C2×C4—23no—
154C2×C4—43no—
155C2×C4—412no—
156C2×C4—43no—
157C2×C4—43no—
158C2×C4C2×SD16×C13916yes—
159C2×C4#137×C13916yes—
160C2×C4H(5,𝔽2)×C13916yes—
161C8—44no—
162C22—81no—
163C22—83no—
164C22—83no—
165C22#535×C13913yes—
166C22C22×SD16×C13911yescharacteristic
167C22C2×#137×C13913yes—
168C4—26no—
169C4—26no—
170C4—84no—
171C4—83no—
172C4#560×C13914yes—
173C2—161no—
174C2#2818×C13911yescharacteristic
175C2#3206×C13913yes—
176C2#3218×C13913yes—
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D4×C139C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C43×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2868×C139C2semidirect
3. #2043×C139C2semidirect
5. #1839×C139C2semidirect
53. C42×C139SD16semidirect
88. #32800C139direct (N × H)
89. C139#32800direct (N × H)
90. #2868C2×C139semidirect
92. #2043C2×C139semidirect
94. #1839C2×C139semidirect
142. C42SD16×C139semidirect

Maximal subgroups

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

subgroupindex
#2868×C1392
#2860×C1392
#2043×C1392
#2013×C1392
#1839×C1392
#32800139