Finite Group Databasebeta

← C139×#7311 #48001907

Subgroups — C139×#7311 #48001907

Order 35584.

590 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 74 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#1783×C139C212yesmaximal
2#1781×C139C211yesmaximal, characteristic
3C23×D4×C139C2211yescharacteristic
4C2×#100×C139—22no—
5C2×#100×C139C414yescomplemented
6C2×#99×C139—22no—
7#407×C139—22no—
8#379×C139C412yes—
9C25×C139C2×C411yescharacteristic
10C25×C139Q811yescharacteristic
11C22×D4×C139—44no—
12C22×D4×C139—42no—
13C22×D4×C139C2×C412yes—
14C22×D4×C139D412yes—
15C23×C4×C139D411yescharacteristic
16C2×M16×C139—24no—
17C2×C22⋊C4×C139—22no—
18C2×C22⋊C4×C139—42no—
19#100×C139—44no—
20#100×C139—44no—
21#99×C139—44no—
22C22⋊C8×C139—44no—
23C24×C139—22no—
24C24×C139—42no—
25C24×C139—42no—
26C24×C139—41no—
27C24×C139—82no—
28C24×C139—82no—
29C24×C139C4211yescharacteristic
30C24×C139C22⋊C411yescharacteristic
31C24×C139C4⋊C411yescharacteristic
32C24×C139C4⋊C412yes—
33C2×D4×C139—24no—
34C2×D4×C139—24no—
35C2×D4×C139—24no—
36C2×D4×C139—42no—
37C2×D4×C139—42no—
38C2×D4×C139—42no—
39C2×D4×C139—416no—
40C22×C4×C139—24no—
41C22×C4×C139—41no—
42C22×C4×C139—42no—
43C22×C4×C139C22⋊C412yes—
44M16×C139—44no—
45M16×C139—44no—
46C2×C8×C139—44no—
47C22⋊C4×C139—44no—
48C22⋊C4×C139—84no—
49C23×C139—22no—
50C23×C139—21no—
51C23×C139—22no—
52C23×C139—21no—
53C23×C139—22no—
54C23×C139—22no—
55C23×C139—22no—
56C23×C139—22no—
57C23×C139—42no—
58C23×C139—44no—
59C23×C139—44no—
60C23×C139—44no—
61C23×C139—82no—
62C23×C139—84no—
63C23×C139—84no—
64C23×C139—81no—
65C23×C139—81no—
66C23×C139—82no—
67C23×C139—82no—
68C23×C139—84no—
69C23×C139—82no—
70C23×C139—84no—
71C23×C139#9511yescharacteristic
72C23×C139#9912yes—
73D4×C139—48no—
74D4×C139—48no—
75C2×C4×C139—22no—
76C2×C4×C139—22no—
77C2×C4×C139—44no—
78C2×C4×C139—82no—
79C2×C4×C139—84no—
80C2×C4×C139#9914yes—
81C8×C139—84no—
82C22×C139—22no—
83C22×C139—24no—
84C22×C139—22no—
85C22×C139—41no—
86C22×C139—42no—
87C22×C139—41no—
88C22×C139—42no—
89C22×C139—42no—
90C22×C139—41no—
91C22×C139—41no—
92C22×C139—42no—
93C22×C139—82no—
94C22×C139—82no—
95C22×C139—82no—
96C22×C139—82no—
97C22×C139—82no—
98C22×C139—88no—
99C22×C139—88no—
100C22×C139#34211yescharacteristic
101C22×C139#34212yes—
102C4×C139—24no—
103C4×C139—162no—
104C2×C139—21no—
105C2×C139—22no—
106C2×C139—42no—
107C2×C139—42no—
108C2×C139—81no—
109C2×C139—82no—
110C2×C139#130411yescharacteristic
111#7311C13911yesmaximal, characteristic, direct product factor, Sylow
112C139#731111yescharacteristic, direct product factor, Sylow
113#1783C2×C13912yes—
114#1781C2×C13911yescharacteristic
115C23×D4C22×C13911yescharacteristic
116C2×#100—22no—
117C2×#100C4×C13914yescomplemented
118C2×#99—22no—
119#407—22no—
120#379C4×C13912yes—
121C25C2×C4×C13911yescharacteristic
122C25Q8×C13911yescharacteristic
123C22×D4—44no—
124C22×D4—42no—
125C22×D4C2×C4×C13912yes—
126C22×D4D4×C13912yes—
127C23×C4D4×C13911yescharacteristic
128C2×M16—24no—
129C2×C22⋊C4—22no—
130C2×C22⋊C4—42no—
131#100—44no—
132#100—44no—
133#99—44no—
134C22⋊C8—44no—
135C24—22no—
136C24—42no—
137C24—42no—
138C24—41no—
139C24—82no—
140C24—82no—
141C24C42×C13911yescharacteristic
142C24C22⋊C4×C13911yescharacteristic
143C24C4⋊C4×C13911yescharacteristic
144C24C4⋊C4×C13912yes—
145C2×D4—24no—
146C2×D4—24no—
147C2×D4—24no—
148C2×D4—42no—
149C2×D4—42no—
150C2×D4—42no—
151C2×D4—416no—
152C22×C4—24no—
153C22×C4—41no—
154C22×C4—42no—
155C22×C4C22⋊C4×C13912yes—
156M16—44no—
157M16—44no—
158C2×C8—44no—
159C22⋊C4—44no—
160C22⋊C4—84no—
161C23—22no—
162C23—21no—
163C23—22no—
164C23—21no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23—22no—
169C23—42no—
170C23—44no—
171C23—44no—
172C23—44no—
173C23—82no—
174C23—84no—
175C23—84no—
176C23—81no—
177C23—81no—
178C23—82no—
179C23—82no—
180C23—84no—
181C23—82no—
182C23—84no—
183C23#95×C13911yescharacteristic
184C23#99×C13912yes—
185D4—48no—
186D4—48no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—82no—
191C2×C4—84no—
192C2×C4#99×C13914yes—
193C8—84no—
194C22—22no—
195C22—24no—
196C22—22no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22—42no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—82no—
209C22—82no—
210C22—88no—
211C22—88no—
212C22#342×C13911yescharacteristic
213C22#342×C13912yes—
214C4—24no—
215C4—162no—
216C2—21no—
217C2—22no—
218C2—42no—
219C2—42no—
220C2—81no—
221C2—82no—
222C2#1304×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#1304
commutatorC24C42×C139
Frattini, cosocleC23×D4C22×C139
prime radicalC23×D4×C139C22
LCSG ▷ C24 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C23×C139 ◁ C23×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×#100×C139C4semidirect
111. #7311C139direct (N × H)
112. C139#7311direct (N × H)
117. C2×#100C4×C139semidirect

Maximal subgroups

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

subgroupindex
#1783×C1392
#1781×C1392
#7311139