Finite Group Databasebeta

← C139×#7310 #48001906

Subgroups — C139×#7310 #48001906

Order 35584.

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

normal subgroups only

This group has 650 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#1781×C139C211yesmaximal, characteristic
2#1781×C139C212yesmaximal
3C23×D4×C139C2211yescharacteristic
4C2×#99×C139—22no—
5C2×#99×C139—22no—
6C2×#99×C139C414yescomplemented
7#379×C139—22no—
8#379×C139C412yescomplemented
9C25×C139C2×C411yescharacteristic
10C25×C139D411yescharacteristic
11C22×D4×C139—44no—
12C22×D4×C139—42no—
13C22×D4×C139C2×C412yes—
14C22×D4×C139D412yes—
15C23×C4×C139Q811yescharacteristic
16C2×C22⋊C4×C139—22no—
17C2×C22⋊C4×C139—24no—
18C2×C22⋊C4×C139—44no—
19C2×C22⋊C4×C139—42no—
20#99×C139—44no—
21#99×C139—44no—
22#99×C139—44no—
23C24×C139—22no—
24C24×C139—24no—
25C24×C139—42no—
26C24×C139—41no—
27C24×C139—82no—
28C24×C139—82no—
29C24×C139C4211yescharacteristic
30C24×C139C22⋊C412yes—
31C24×C139C22⋊C411yescharacteristic
32C24×C139C4⋊C411yescharacteristic
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—42no—
41C22×C4×C139—41no—
42C22×C4×C139—44no—
43C22×C4×C139—42no—
44C22×C4×C139C4⋊C412yes—
45C22⋊C4×C139—44no—
46C22⋊C4×C139—44no—
47C22⋊C4×C139—44no—
48C22⋊C4×C139—88no—
49C22⋊C4×C139—84no—
50C23×C139—22no—
51C23×C139—21no—
52C23×C139—22no—
53C23×C139—22no—
54C23×C139—22no—
55C23×C139—21no—
56C23×C139—22no—
57C23×C139—42no—
58C23×C139—44no—
59C23×C139—44no—
60C23×C139—48no—
61C23×C139—44no—
62C23×C139—82no—
63C23×C139—84no—
64C23×C139—82no—
65C23×C139—81no—
66C23×C139—81no—
67C23×C139—82no—
68C23×C139—84no—
69C23×C139—82no—
70C23×C139—84no—
71C23×C139#9511yescharacteristic
72C23×C139#9914yes—
73C23×C139#9912yes—
74D4×C139—48no—
75D4×C139—48no—
76C2×C4×C139—22no—
77C2×C4×C139—22no—
78C2×C4×C139—22no—
79C2×C4×C139—44no—
80C2×C4×C139—82no—
81C2×C4×C139—84no—
82C2×C4×C139—84no—
83C2×C4×C139—88no—
84C22×C139—22no—
85C22×C139—24no—
86C22×C139—24no—
87C22×C139—22no—
88C22×C139—41no—
89C22×C139—42no—
90C22×C139—44no—
91C22×C139—44no—
92C22×C139—41no—
93C22×C139—42no—
94C22×C139—42no—
95C22×C139—41no—
96C22×C139—41no—
97C22×C139—82no—
98C22×C139—82no—
99C22×C139—82no—
100C22×C139—88no—
101C22×C139—88no—
102C22×C139#34212yes—
103C22×C139#34211yescharacteristic
104C4×C139—42no—
105C4×C139—164no—
106C4×C139—162no—
107C2×C139—21no—
108C2×C139—22no—
109C2×C139—44no—
110C2×C139—42no—
111C2×C139—42no—
112C2×C139—81no—
113C2×C139#130411yescharacteristic
114#7310C13911yesmaximal, characteristic, direct product factor, Sylow
115C139#731011yescharacteristic, direct product factor, Sylow
116#1781C2×C13912yes—
117#1781C2×C13911yescharacteristic
118C23×D4C22×C13911yescharacteristic
119C2×#99—22no—
120C2×#99—22no—
121C2×#99C4×C13914yescomplemented
122#379—22no—
123#379C4×C13912yescomplemented
124C25C2×C4×C13911yescharacteristic
125C25D4×C13911yescharacteristic
126C22×D4—44no—
127C22×D4—42no—
128C22×D4C2×C4×C13912yes—
129C22×D4D4×C13912yes—
130C23×C4Q8×C13911yescharacteristic
131C2×C22⋊C4—24no—
132C2×C22⋊C4—22no—
133C2×C22⋊C4—44no—
134C2×C22⋊C4—42no—
135#99—44no—
136#99—44no—
137#99—44no—
138C24—22no—
139C24—24no—
140C24—42no—
141C24—41no—
142C24—82no—
143C24—82no—
144C24C42×C13911yescharacteristic
145C24C22⋊C4×C13912yes—
146C24C22⋊C4×C13911yescharacteristic
147C24C4⋊C4×C13911yescharacteristic
148C2×D4—24no—
149C2×D4—24no—
150C2×D4—24no—
151C2×D4—42no—
152C2×D4—42no—
153C2×D4—42no—
154C2×D4—416no—
155C22×C4—42no—
156C22×C4—41no—
157C22×C4—44no—
158C22×C4—42no—
159C22×C4C4⋊C4×C13912yes—
160C22⋊C4—44no—
161C22⋊C4—44no—
162C22⋊C4—44no—
163C22⋊C4—88no—
164C22⋊C4—84no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23—22no—
172C23—42no—
173C23—44no—
174C23—44no—
175C23—48no—
176C23—44no—
177C23—82no—
178C23—84no—
179C23—82no—
180C23—81no—
181C23—81no—
182C23—82no—
183C23—84no—
184C23—82no—
185C23—84no—
186C23#95×C13911yescharacteristic
187C23#99×C13914yes—
188C23#99×C13912yes—
189D4—48no—
190D4—48no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—82no—
196C2×C4—84no—
197C2×C4—84no—
198C2×C4—88no—
199C22—22no—
200C22—24no—
201C22—24no—
202C22—22no—
203C22—41no—
204C22—42no—
205C22—44no—
206C22—44no—
207C22—41no—
208C22—42no—
209C22—42no—
210C22—41no—
211C22—41no—
212C22—82no—
213C22—82no—
214C22—82no—
215C22—88no—
216C22—88no—
217C22#342×C13912yes—
218C22#342×C13911yescharacteristic
219C4—42no—
220C4—164no—
221C4—162no—
222C2—21no—
223C2—22no—
224C2—44no—
225C2—42no—
226C2—42no—
227C2—81no—
228C2#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
6. C2×#99×C139C4semidirect
8. #379×C139C4semidirect
114. #7310C139direct (N × H)
115. C139#7310direct (N × H)
121. C2×#99C4×C139semidirect
123. #379C4×C139semidirect

Maximal subgroups

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

subgroupindex
#1781×C1392
#7310139