Finite Group Databasebeta

← C139×#8521 #48003117

Subgroups — C139×#8521 #48003117

Order 35584.

690 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 142 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×#541×C139C211yesmaximal, characteristic
2#1822×C139C211yesmaximal, characteristic
3#1820×C139C211yesmaximal, characteristic
4#1511×C139C214yesmaximal
5#541×C139—28no—
6C2×C4⋊Q8×C139C411yescharacteristic, complemented
7C2×#126×C139—22no—
8C2×#125×C139—22no—
9C2×#125×C139C411yescharacteristic, complemented
10C2×C22⋊Q8×C139C2212yes—
11C2×C4×Q8×C139C412yescomplemented
12C2×#117×C139C2211yescharacteristic
13#407×C139C2212yes—
14#381×C139C2212yes—
15#343×C139—22no—
16#342×C139—22no—
17#328×C139—28no—
18C22×Q8×C139C2×C412yes—
19C23×C4×C139C2311yescharacteristic
20C2×M16×C139—22no—
21C4⋊Q8×C139—24no—
22#126×C139—216no—
23#125×C139—216no—
24#125×C139—24no—
25C22⋊Q8×C139—24no—
26C22⋊Q8×C139D418yes—
27C4×Q8×C139—24no—
28C4×Q8×C139—24no—
29#117×C139—24no—
30C2×C4⋊C4×C139—22no—
31C2×C4⋊C4×C139—22no—
32C2×C4⋊C4×C139—22no—
33C2×C4⋊C4×C139—22no—
34C2×C4⋊C4×C139C2×C412yes—
35C2×C4⋊C4×C139D412yes—
36C2×C22⋊C4×C139—22no—
37C2×C22⋊C4×C139—22no—
38C2×C22⋊C4×C139D412yes—
39C2×C42×C139—22no—
40C2×C42×C139C2×C411yescharacteristic
41C2×C42×C139C2×C411yescharacteristic
42C22⋊C8×C139—24no—
43#95×C139—24no—
44C24×C139C2×D411yescharacteristic
45C2×Q8×C139—22no—
46C2×Q8×C139—44no—
47C2×Q8×C139C22⋊C414yes—
48C22×C4×C139—22no—
49C22×C4×C139—22no—
50C22×C4×C139—42no—
51C22×C4×C139—42no—
52C22×C4×C139C22⋊C412yes—
53C22×C4×C139C22⋊C412yes—
54C22×C4×C139C22×C411yescharacteristic
55C22×C4×C139C2×D411yescharacteristic
56C22×C4×C139C2×D414yes—
57M16×C139—44no—
58C2×C8×C139—42no—
59C4⋊C4×C139—28no—
60C4⋊C4×C139—28no—
61C4⋊C4×C139—28no—
62C4⋊C4×C139—22no—
63C4⋊C4×C139—28no—
64C4⋊C4×C139—24no—
65C4⋊C4×C139C22⋊C414yes—
66C22⋊C4×C139—28no—
67C22⋊C4×C139—24no—
68C22⋊C4×C139—44no—
69C42×C139—28no—
70C42×C139—22no—
71C42×C139—22no—
72C23×C139—22no—
73C23×C139—42no—
74C23×C139C2×C22⋊C411yescharacteristic
75C23×C139#12012yes—
76Q8×C139—44no—
77Q8×C139—44no—
78C2×C4×C139—22no—
79C2×C4×C139—22no—
80C2×C4×C139—22no—
81C2×C4×C139—22no—
82C2×C4×C139—24no—
83C2×C4×C139—24no—
84C2×C4×C139—44no—
85C2×C4×C139—44no—
86C2×C4×C139—44no—
87C2×C4×C139—42no—
88C2×C4×C139—42no—
89C2×C4×C139—82no—
90C2×C4×C139—84no—
91C2×C4×C139C2×C22⋊C412yes—
92C2×C4×C139#12012yes—
93C8×C139—82no—
94C22×C139—22no—
95C22×C139—24no—
96C22×C139—22no—
97C22×C139—82no—
98C22×C139#37911yescharacteristic
99C22×C139#41012yes—
100C4×C139—22no—
101C4×C139—22no—
102C4×C139—42no—
103C4×C139—42no—
104C4×C139—44no—
105C4×C139—44no—
106C4×C139—162no—
107C2×C139—22no—
108C2×C139—42no—
109C2×C139#178211yescharacteristic
110C2×C139#179612yes—
111#8521C13911yesmaximal, characteristic, direct product factor, Sylow
112C139#852111yescharacteristic, direct product factor, Sylow
113C2×#541C2×C13911yescharacteristic
114#1822C2×C13911yescharacteristic
115#1820C2×C13911yescharacteristic
116#1511C2×C13914yes—
117#541—28no—
118C2×C4⋊Q8C4×C13911yescharacteristic, complemented
119C2×#126—22no—
120C2×#125—22no—
121C2×#125C4×C13911yescharacteristic, complemented
122C2×C22⋊Q8C22×C13912yes—
123C2×C4×Q8C4×C13912yescomplemented
124C2×#117C22×C13911yescharacteristic
125#407C22×C13912yes—
126#381C22×C13912yes—
127#343—22no—
128#342—22no—
129#328—28no—
130C22×Q8C2×C4×C13912yes—
131C23×C4C23×C13911yescharacteristic
132C2×M16—22no—
133C4⋊Q8—24no—
134#126—216no—
135#125—216no—
136#125—24no—
137C22⋊Q8—24no—
138C22⋊Q8D4×C13918yes—
139C4×Q8—24no—
140C4×Q8—24no—
141#117—24no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4C2×C4×C13912yes—
147C2×C4⋊C4D4×C13912yes—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4D4×C13912yes—
151C2×C42—22no—
152C2×C42C2×C4×C13911yescharacteristic
153C2×C42C2×C4×C13911yescharacteristic
154C22⋊C8—24no—
155#95—24no—
156C24C2×D4×C13911yescharacteristic
157C2×Q8—22no—
158C2×Q8—44no—
159C2×Q8C22⋊C4×C13914yes—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4C22⋊C4×C13912yes—
165C22×C4C22⋊C4×C13912yes—
166C22×C4C22×C4×C13911yescharacteristic
167C22×C4C2×D4×C13911yescharacteristic
168C22×C4C2×D4×C13914yes—
169M16—44no—
170C2×C8—42no—
171C4⋊C4—28no—
172C4⋊C4—28no—
173C4⋊C4—28no—
174C4⋊C4—22no—
175C4⋊C4—28no—
176C4⋊C4—24no—
177C4⋊C4C22⋊C4×C13914yes—
178C22⋊C4—28no—
179C22⋊C4—24no—
180C22⋊C4—44no—
181C42—28no—
182C42—22no—
183C42—22no—
184C23—22no—
185C23—42no—
186C23C2×C22⋊C4×C13911yescharacteristic
187C23#120×C13912yes—
188Q8—44no—
189Q8—44no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—44no—
197C2×C4—44no—
198C2×C4—44no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—82no—
202C2×C4—84no—
203C2×C4C2×C22⋊C4×C13912yes—
204C2×C4#120×C13912yes—
205C8—82no—
206C22—22no—
207C22—22no—
208C22—24no—
209C22—82no—
210C22#379×C13911yescharacteristic
211C22#410×C13912yes—
212C4—22no—
213C4—22no—
214C4—44no—
215C4—44no—
216C4—42no—
217C4—42no—
218C4—162no—
219C2—22no—
220C2—42no—
221C2#1782×C13911yescharacteristic
222C2#1796×C13912yes—
subgroupG/H
center, socleC22×C139#379
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊Q8×C139C4semidirect
9. C2×#125×C139C4semidirect
11. C2×C4×Q8×C139C4semidirect
111. #8521C139direct (N × H)
112. C139#8521direct (N × H)
118. C2×C4⋊Q8C4×C139semidirect
121. C2×#125C4×C139semidirect
123. C2×C4×Q8C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#541×C1392
#1822×C1392
#1820×C1392
#1511×C1392
#8521139